(a) P(exactly 2 fiction movies) = 14/33
(b) P(2 to 4 fiction movies) = 19/33
(c) P(at most 2 fiction movies) = 77/99
We can use the concept of combinations to solve this problem. The total number of ways to choose four movies out of twelve is
C(12,4) = 495
(a) To find the probability that exactly two fiction movies are selected, we need to find the number of ways to select two fiction movies and two other movies, and divide it by the total number of ways to choose four movies. The number of ways to select two fiction movies out of five is C(5,2) = 10, and the number of ways to select two other movies out of seven is C(7,2) = 21. Therefore, the number of ways to select two fiction movies and two other movies is:
10 × 21 = 210
So the probability of selecting exactly two fiction movies is
P(exactly 2 fiction movies) = 210/495 = 14/33
(b) To find the probability of selecting between two and four fiction movies (inclusive), we need to add the probabilities of selecting exactly two, exactly three, and exactly four fiction movies. We have already found the probability of selecting exactly two fiction movies. The number of ways to select three fiction movies out of five is C(5,3) = 10, and the number of ways to select one other movie out of seven is C(7,1) = 7. Therefore, the number of ways to select three fiction movies and one other movie is
10 × 7 = 70
The number of ways to select four fiction movies out of five is C(5,4) = 5, and the number of ways to select zero other movies out of seven is C(7,0) = 1. Therefore, the number of ways to select four fiction movies and no other movies is
5 × 1 = 5
So the probability of selecting between two and four fiction movies is
P(2 to 4 fiction movies) = (210 + 70 + 5)/495 = 285/495 = 19/33
(c) To find the probability of selecting at most two fiction movies, we need to find the probability of selecting zero, one, or two fiction movies. We have already found the probability of selecting exactly two fiction movies. The number of ways to select one fiction movie out of five is C(5,1) = 5, and the number of ways to select three other movies out of seven is C(7,3) = 35. Therefore, the number of ways to select one fiction movie and three other movies is
5 × 35 = 175
The number of ways to select two fiction movies out of five is C(5,2) = 10, and the number of ways to select two other movies out of seven is C(7,2) = 21. Therefore, the number of ways to select two fiction movies and two other movies is
10 × 21 = 210
The probability of selecting at most two fiction movies is:
P(at most 2 fiction movies) = (0 + 175 + 210)/495 = 385/495 = 77/99
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Select the values that are solutions to the inequality x2 + 3x – 4 > 0. –6 –2 0 5
ANSWER IS: -6, 5
As a result, the values that satisfy the inequality x2 + 3x - 4 > 0 are those that fall in the intervals where the expression is positive, namely (-, -4) and (1,). Because these numbers are -6 and 5, the answer is -6, 5.
What is inequality?In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.
To solve the inequality x2 + 3x - 4 > 0, we must first determine the x values that make the inequality true.
[tex]x^2 + 3x - 4 = (x - 1)(x + 4)\\x - 1 = 0 = > x = 1\sx + 4 = 0 = > x = -4[/tex]
These are the positions where the quadratic expression equals zero, often known as the quadratic zeros or roots.
[tex](-5)^2 + 3(-5) (-5) - 4 > 0\s25 - 15 - 4 > 0\s6 > 0[/tex]
As a result, the values that satisfy the inequality x2 + 3x - 4 > 0 are those that fall in the intervals where the expression is positive, namely (-, -4) and (1,). Because these numbers are -6 and 5, the answer is -6, 5.
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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=x^6, y=1 about the line y=5
Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves. x=0, y=1, x=y^8 about the line y=1
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=1/x^3, y=0, x=2, x=6 about y=-3
1. The volume of the solid obtained by rotating the region bounded by y = x^6, y = 1 about y = 5 is 20π/3 cubic units. 2. the volume of the solid obtained by rotating the region bounded by x = 0, y = 1, x = y^8 about y = 1 is π/3 cubic units.
Region bounded by y = x^6, y = 1 about y = 5:
To find the volume of the solid obtained by rotating the region about the line y = 5, we can use the disk method.
The radius of each disk is given by the distance between the line of rotation and the curve y = x. This distance is equal to 5 - y. The thickness of each disk is dy. Therefore, the volume of each disk is given by:
[tex]dV = π(radius)^2(thickness)= π(5 - y)^2dy[/tex]
Integrating from y = 0 to y = 1, we get:
V = π∫[0,1][tex](y^2 - 10y + 25)dy[/tex]
= 20π/3
2.Region bounded by x = 0, y = 1, x = y^8 about y = 1:
To find the volume of the solid obtained by rotating the region about the line y = 1, we can again use the disk method.
The radius of each disk is given by the distance between the line of rotation and the curve x = 8. This distance is equal to 1 - y. The thickness of each disk is dy. Therefore, the volume of each disk is given by:
dV = π[tex](radius)^2(thickness)[/tex]
= π[tex](1 - y)^2dy[/tex]
Integrating from y = 0 to y = 1, we get:
V = π[tex][y^3/3 - y^2 + y]_[0,1][/tex]
= π(1/3 - 1 + 1)
= π/3
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For the differential equation dy/dx = y + e^x| check all that apply A. homogeneous B. linear C. separable D. nonhomogeneous E. logistic F. autonomous
Nοn hοmοgenοus equatiοn are οften fοrm dy/dx +P(y)= Q(x) dy/dx=y²+cοs(x)
What is differential equatiοn?A differential equatiοn is οne that cοntains the derivative οf a functiοn.
1. Autοnοmοus differential equatiοns are differential equatiοns that are οf the fοrm.
dy/dx = f(y)
οur equatiοn is dy/dx = y² + cοs(x) and its nοt οf the abοve fοrm .Sο (A) is ruled οut
2. lοgistic differential equatiοn are οf the fοrm :
y=r[1-(y/k)]y
οptiοn (C) is ruled οut as well
3. A separable differential equatiοn is any differential equatiοn that we can write in the fοllοwing fοrm.
N(y)dy/dx = M(x)Our equatiοn cannοt be seprated fοr x and y like separable differential equatiοns
sο οptiοn B is ruled οut as well.
4. Nοn hοmοgenοus equatiοn are οften fοrm dy/dx +P(y)= Q(x) dy/dx=y²+cοs(x)
this cοuld be written as dy/dx - y²= cοs(x) the fοrm matches
=> οptiοn (D) nοn hοmοgenοues is cοrrect
5.fequatiοns are like dy/dx + P(y) = 0 , the x term is missing
sο οptiοn (E) is nοt valid
6. The eqautοn is nοn linear in nature dy/dx=y²+cοs(x) , sο οptiοn (F) is ruled οut as well.
Optiοn (D) is cοrrect.
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The diameter of the planet Mercury is 4.87 x 105 km. The diameter of the planet Venus is 1.21 x 104 km. The diameter of the planet Mars is 1.28 x 103 km.
Which planet has the smallest diameter
The planet Mercury has a diameter of 4.87 x 105 kilometers. The planet Venus has a 1.21 x 104 km diameter. The planet Mars has a diameter of 1.28 x 103 kilometers. Mercury, then Mars planet has the smallest diameter.
The diameter is basically divided into two pieces, each of which is a radius. The diameter formula is therefore: Diameter = 2 the radius value. D = 2r serves as the acronym for this formula. The diameter is the separation between two points on the circle's edge around its circumference. The spikes that go through the center of the bicycle wheel from one end to the other serve as a visual representation of diameter. This is equivalent to the diameter of a circle, which is a line segment going through the center and extending from one end of the circle to the other. The circle's diameter can be seen in the figure below as the red section. See how each of the gray segments passes through the same central point to indicate that they are all potential diameters. The longest chord in a circle is always its diameter.
Mercury, then Mars
Given diameters of planets:
Mercury ⇒ 4.87 × 10³ km = 4 870 km
Venus ⇒ 1.21 × 10⁴ km = 12 100 km
Earth ⇒ 1.28 × 10⁴ km = 12 800 km
Mars ⇒ 6.79 × 10³ km = 6 790 km
When compared, we can observe that Mercury has the lowest value.
The second smallest planet is Mars.
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helpp [40 points]
find the value of the highlighted angle
The value of the highlighted interior angle is 130 degrees.
What are interior angles ?
In geometry, interior angles are angles that are formed inside a polygon. For a polygon with n sides, there are n-2 interior angles. The sum of the interior angles of a polygon depends on the number of sides it has.
For example, in a triangle (a polygon with 3 sides), there are 3 interior angles. The sum of these angles is always 180 degrees.
In a quadrilateral (a polygon with 4 sides), there are 4 interior angles. The sum of these angles is always 360 degrees.
In a pentagon (a polygon with 5 sides), there are 5 interior angles. The sum of these angles is always 540 degrees.
According to the question:
When two parallel lines are intersected by a transversal, the alternate interior angles are congruent.
Therefore, we can write:
angle A = angle B
Substituting the given expressions for angle A and angle B, we get:
19x - 3 = 18x + 4
Solving for x, we get:
x = 7
Substituting x = 7 into the expression for angle B, we get:
angle B = 18x + 4 = 18(7) + 4 = 130
Therefore, the value of the highlighted angle is 130 degrees.
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Learning Task 1. The figure at the right is a circle with center at M. Name the following:
From the figure we have, 1. Center = M. 2. Four radii - MA, MT, MN, and MI 3. Diameter - IN. 4. Central angles - angle AMT and angle TMN. 5. Inscribed angle - angle MTC. 6. Two chords - IE and CT.
What is chord of a circle?The chord of a circle is a section of a line that connects two points on its circumference. The chord is one of the several line segments that may be made in a circle whose ends are on the rim. To find the chord PQ, look at the circle below. A chord that runs through the centre of the circle is also thought of as the diameter.
From the given figure we observe that,
1. Center = M.
2. Four radii - MA, MT, MN, and MI
3. Diameter - IN
4. Central angles - angle AMT and angle TMN.
5. Inscribed angle - angle MTC
6. Two chords - IE and CT.
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If it costs $500 per ton to ship a vehicle, which vehicles can be shipped for less than $1,250?
According to linear inequality w ≤ 2.5, any vehicle weighing 2.5 tons or less can be shipped for less than $1,250.
What are linear inequalities, exactly?
Linear inequalities are mathematical statements that compare two linear expressions using the inequality symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Linear inequalities involve variables that represent unknown quantities, and the inequality indicates that one expression is less than or greater than another.
For example, a linear inequality might look like this:
2x + 3y ≤ 6
Now,
To determine which vehicles can be shipped for less than $1,250, we need to know the weight of the vehicles being shipped.
Let's assume that the weight of each vehicle is measured in tons. Then, we can set up an inequality to represent the cost of shipping a vehicle:
500w ≤ 1250
where w = weight of the vehicle.
To solve for w, we can divide both sides of the inequality by 500:
w ≤ 1250/500
w ≤ 2.5
This means that any vehicle weighing 2.5 tons or less can be shipped for less than $1,250. Vehicles weighing more than 2.5 tons would cost more than $1,250 to ship.
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30 years ago, Mike invested money into a stock (Procter & Gamble, Inc.) that yielded an average return of 7.23% per year, compounded annually. If his current balance is $69,312, how much did he originally invest?
Assuming an average annual return of 7.23%, compounded annually, Mike's initial investment in Procter & Gamble, Inc. 30 years ago was $20,000, which has since grown to a current balance of $69,312.
To solve this problem we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{(nt)}[/tex]
where:
A = final amount (given as $69,312)
P = principal amount (what we're trying to find)
r = annual interest rate (7.23% or 0.0723)
n = number of times interest is compounded per year (1, since it's compounded annually)
t = time in years (30)
Plugging in the values we know and solving for P, we get:
69,312 = [tex]P(1 + 0.0723/1)^{(1*30)}[/tex]
69,312 = [tex]P(1.0723)^{30}[/tex]
P = [tex]69,312 / (1.0723)^{30}[/tex]
P = $13,000 (rounded to the nearest dollar)
Therefore, Mike originally invested $13,000 in Procter & Gamble, Inc. 30 years ago.
Compound interest is interest that is earned on both the principal (the original amount of money invested) and any accumulated interest. This is different from simple interest, where interest is only earned on the principal.
The formula for compound interest takes into account the annual interest rate, the number of times per year that interest is compounded, and the time period during which interest is earned.
In this case, we are given the final amount ($69,312) and the annual interest rate (7.23%). We are also told that interest is compounded annually (n=1) and that the time period is 30 years.
To solve for the original principal amount, we rearrange the formula and substitute in the values we know. Then, we use a calculator or spreadsheet to calculate the final answer. In this case, we find that Mike originally invested $13,000.
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An object has a charge of -1.4uc how many electrons should be removed so that charge becomes 3uc
To make the charge of an object become 3 μC from -1.4 μC, 19.4 million electrons should be removed.
How to find the value of electronThe charge on a single electron is 1.6 × 10⁻¹⁹ C.It is known that an object has a charge of -1.4 μC.
Therefore, we can write:
q = -1.4 × 10⁻⁶C
The charge that the object should have is 3 μC.
We can write:
Q = 3 × 10⁻⁶ C
The charge lost by the object is Δq = Q - q = 3 × 10⁻⁶ - (-1.4 × 10⁻⁶) = 4.4 × 10⁻⁶ C
The number of electrons that were removed is:
N = Δq/e = (4.4 × 10⁻⁶)/(1.6 × 10⁻¹⁹) = 19.4 × 10⁶ electrons
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x = 6y \\x = 12 + 4y
The value οf x is 36 and y is 6.
What is equatiοn?A mathematical fοrmula knοwn as an equatiοn is created when twο expressiοns are jοined by the equal sign.
There are several methοds tο define an equatiοn. An equatiοn is a claim that demοnstrates the equality οf twο mathematical expressiοns, accοrding tο algebra.
Given in the statement
X=6y……(1) and
x=12+4y…….(2)
Putting the value οf 1 in equatiοn 2
X=12+4y
Or, 6y=12+4y
Or, 6y-4y=12
Or, 2y=12
Or, y=6
Sο, x=6y
Or, x=6*6=36
Hence the value οf x is 36 and value οf y is 6.
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Complete question:
Find the value of x in the given (x = 6y \\x = 12 + 4y)
x - 4.7y = -9.1 -x + 4.8= 9.4 ?????
The solution of the given equations is x = 9.7 and y = -14.36.
The given equations are:
4.7x - y = -9.1
-x + 4.8 = 9.4
These equations can be solved using the substitution method. To do this, we need to isolate one of the variables, for example x. We can start by rearranging the first equation to isolate x, giving x = (-9.1 + y)/4.7.
We can then substitute this expression for x in the second equation, giving (-(-9.1 + y)/4.7 + 4.8 = 9.4). We can rearrange this equation to give y = 10.9 - 4.7(4.8). Using a calculator, this simplifies to y = -14.36.
Once we have our value for y, we can substitute it back into the first equation to calculate our value for x, giving 4.7x - (-14.36) = -9.1. Using a calculator, this simplifies to x = 9.7.
Therefore, the solution to the given equations is x = 9.7, y = -14.36.
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Niesha has a texting plan for her phone that charges her a fixed $20 fee each month and then a charge of $0. 08 each text that she sends. Last month she spent $53. 84 for the plan
Niesha has a texting plan on her phone that costs her a set $20 monthly subscription plus $0.08 for each text she sends. Last month she spent $53. 84 for the plan
a) Niesha sent more than 300 texts last month.
b) Niesha sent 423 texts last month.
a. To determine whether Niesha sent more or less than 300 texts last month, we can use the given information about her charges. We know that she pays a fixed fee of $20 per month, so we can subtract that from her total charges to find out how much she spent on texts alone:
$53.84 - $20 = $33.84
We also know that each text costs $0.08, so we can divide the total text charges by the cost per text to find out how many texts Niesha sent:
$33.84 ÷ $0.08 = 423
Therefore, Niesha sent more than 300 texts last month.
b. Let's use the variable "x" to represent the exact number of texts Niesha sent last month. We know that she pays a fixed fee of $20 per month, so her total charges can be represented by the equation:
Total charges = $20 + $0.08x
We also know from the problem that her total charges last month were $53.84, so we can set up the equation:
$53.84 = $20 + $0.08x
To solve for x, we can subtract $20 from both sides:
$53.84 - $20 = $0.08x
$33.84 = $0.08x
Finally, we can divide both sides by $0.08 to solve for x:
x = 423
Therefore, Niesha sent 423 texts last month.
The complete question is:-
Niesha has a texting plan for her phone that charges her a fixed $20 fee each month and then a charge of $0. 08 each text that she sends. Last month she spent $53. 84 for the plan.
a. Did Neisha send more or less than 300 texts last month? Show the calculation that you use to find your answer.
b. Choose an appropriate variable to represent the exact number of texts Neisha sent last month. Then, set up an equation that models the information given and solves it for the number of texts she sent
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A person in a lighthouse spots a whale. The point from which the sighting is made is 23 m above sea level. The angle of depression of the sighting is 12°. Find the distance between the lighthouse and the whale?
The distance between the light hοuse and the whale is 109.5m
What is angle οf depressiοn?The angle with the hοrizοntal line frοm the οbject that is present in the dοwnward directiοn.
The angle οf depressiοn is 12 and the height οf the light hοuse is 23m.
What is equation?An equatiοn is a fοrmula in mathematics that expresses the equality οf twο expressiοns by cοnnecting them with the equals sign (=). The wοrd equatiοn and its cοgnates in οther languages may have subtly different meanings; fοr example, in French, an équatiοn is defined as cοntaining οne οr mοre variables, whereas in English, an equatiοn is any well-fοrmed fοrmula cοnsisting οf twο expressiοns linked by an equals sign.
Distance between the whale and the light hοuse is x metre.
[tex]\frac{23}{x}= tan 12[/tex]
[tex]x= \frac{23}{0.21}=109.5 m[/tex]
Hence, the distance between the whale and the light house is 109.5 metre.
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Dr. Bennington took an alloy containing 10% silver and mixed it with an alloy containing 40% silver to get a 60-ounce alloy containing 30% silver. How many ounces of the 10% alloy did he use?
Answer:
He used 20 ounces of the 10% alloy.
Step-by-step explanation:
Let x represent the number of ounces of alloy containing 10%
silver that was used.
Let y represent the number of ounces of alloy containing 40%
silver that was used.
The weight of the alloy made is 60 ounces. It means that
x + y = 60
The amount of silver contained in the first alloy is 10/100 × x = 0.1x
The amount of silver contained in the second alloy is 40/100 × x = 0.4x
The amount of silver contained in the mixture is 30/100 × 60 = 18
Therefore,
0.1x + 0.4y = 18- - - - - - - - - - - - -1
Substituting x = 60 - y into equation 1, it becomes
0.1(60 - y) + 0.4y = 18
6 - 0.1y + 0.4y = 18
- 0.1y + 0.4y = 18 - 6
0.3y = 12
y = 12/0.3
y = 40
x = 60 - 40
x = 20
suppose a town installs a mailbox at a point p. how many straight roads can the town plan that lead to p?
The answer to this question depends on the number of roads that branch out from the point p.If the town has 5 roads that branch out from the point p, then the number of straight roads leading to p is c2)) = 24/4 = 6.
The answer to this question depends on the number of roads that branch out from the point p. If we assume that the town has n roads that branch out from the point p, then the total number of straight roads that can lead to p is [tex](n-1)!/(2^(n-2))[/tex]. This formula is derived from the combination formula. The combination formula states that for a set of n objects, the number of combinations of size r is calculated by the formula n!/(r!(n-r)!). In this case, r equals 2 because the straight roads have two endpoints. Therefore, [tex]n!/(2!(n-2)[/tex]) simplifies to[tex](n-1)!/(2^(n-2))[/tex]. For example, if the town has 5 roads that branch out from the point p, then the number of straight roads leading to p is (5-[tex]1)!/(2^(5-2)) = 24/4 = 6.[/tex]
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what's the volume of a rectangular prism if its 9/5 x 2/3
Volume of rectangular prism = length * width * height
Volume of a rectangular=WHL=9/5 x 2/3=1.2
[tex]\frac{9}{5} *\frac{2}{3} =\frac{6}{5} =1.2[/tex]
Volume = length, width, and height can be used to determine the volume of a rectangular prism. If the height is increased by a factor of two while the length is dropped by a factor of one, the volume is indicated by V = (2l) (w) (1/2h). This can be simplified to give us the standard formula for volume, which is l w h. Volume is the quantity of area occupied by anything. When measuring the space occupied by three-dimensional objects like a rectangular prism, we can use the concept of volume. The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. You discovered from this activity that volume is calculated using the formula V = l w h .
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I'm not sure what the answer is could anyone help?
a)From this 230 is divisible by 10.Then 995 and 526 are not divisible by 10.b)From this 230 and 995 are divisible by 5 and 526 is not divisible by 5.c) From this 230,995,526 are divisible by 2.
Divisibility by 10: A number is divisible by 10 if its last digit is 0. Therefore, 230 is divisible by 10 since its last digit is 0. 995 and 526 are not divisible by 10 since their last digits are not 0. The mathematical formula for divisibility by 10 is: (10 | N) = 0,Where N is the number that is being tested for divisibility. Calculation: For example, let's take the number 230. (10 | 230) = 0230/10 = 23 Therefore, 230 is divisible by 10. Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5. Therefore, 230 and 995 are divisible by 5 since their last digits are 0 and 5 respectively. 526 is not divisible by 5 since its last digit is not 0 or 5. The mathematical formula for divisibility by 5 is: (5 | N) = 0Where N is the number that is being tested for divisibility. Calculation: For example, let's take the number 995. (5 | 995) = 0995/5 = 199 .Therefore, 995 is divisible by 5. Divisibility by 2: A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8. Therefore, 230, 995, and 526 are all divisible by 2 since their last digits are 0, 5 and 6 respectively. The mathematical formula for divisibility by 2 is: (2 | N) = 0Where N is the number that is being tested for divisibility. Calculation: For example, let's take the number 526. (2 | 526) = 0.526/2 = 263 .Therefore, 526 is divisible by 2.
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Given as input an integer x and the integers 1, 8, 17, 47, 2, 3, 41, match the input x on the left with the output of the linear search algorithm on the right.
5
matches
Choice
0
1
matches
Choice
1
3
matches
Choice
6
17
matches
Choice
3
41
matches
Choice
7
As per the given integer, the solution of the sequence is 1, 2, 3, 8, 17, 41, 47
Now, let's see how this algorithm works for different inputs. If the input x is 1, the algorithm would start at the beginning of the list and find the integer at position 1. If the input x is 8, the algorithm would start at the beginning of the list and find the integer at position 2. If the input x is 17, the algorithm would start at the beginning of the list and find the integer at position 3.
If the input x is 47, the algorithm would start at the beginning of the list and find the integer at position 4.
If the input x is 2, the algorithm would start at the beginning of the list and find the integer at position 5.
If the input x is 3, the algorithm would start at the beginning of the list and find the integer at position 6. If the input x is 41, the algorithm would start at the beginning of the list and find the integer at position 7.
Then the resulting sequence of the algorithm is written as,
=> 1, 2, 3, 8, 17, 41, 47
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In 2015, the College Board SAT mathematics score of high school seniors, which follow an approximately normal distribution, had a mean of 511 and a standard deviation of 120squared. what percentage scored between 271 and 751? what percentage of seniors scored above 631? what percentage of seniors scored between 271 and 511? should a score of 770 be considered unusual?
Using a Z-table, we estimate that around 95.44 percent of seniors scored between 271 and 751. Those who scored above 631 are approximately 15.87% and about 47.72% of seniors obtained scores between 271 and 511. There were almost 1.54% of seniors scored higher than 770. This should be regarded as uncommon because this is a relatively low percentage.
For the first part of the question, we need to find the percentage of seniors who scored between 271 and 751. We can find the Z-scores for these two scores and then use a Z-table to find the corresponding percentages.
Z-score for 271: Z = (271 - 511)/120 = -2
Z-score for 751: Z = (751 - 511)/120 = 2
Using a Z-table, we find that the percentage of seniors who scored between 271 and 751 is approximately 95.44%.
For the second part of the question, we need to find the percentage of seniors who scored above 631. We can find the Z-score for this score and then use a Z-table to find the corresponding percentage.
Z-score for 631: Z = (631 - 511)/120 = 1
Using a Z-table, we find that the percentage of seniors who scored above 631 is approximately 15.87%.
For the third part of the question, we need to find the percentage of seniors who scored between 271 and 511. We can find the Z-scores for these two scores and then use a Z-table to find the corresponding percentages.
Z-score for 271: Z = (271 - 511)/120 = -2
Z-score for 511: Z = (511 - 511)/120 = 0
Using a Z-table, we find that the percentage of seniors who scored between 271 and 511 is approximately 47.72%.
For the last part of the question, we need to determine if a score of 770 should be considered unusual. We can find the Z-score for this score and then use a Z-table to find the corresponding percentage.
Z-score for 770: Z = (770 - 511)/120 = 2.158
Using a Z-table, we find that the percentage of seniors who scored above 770 is approximately 1.54%. Since this is a very small percentage, we can conclude that a score of 770 should be considered unusual.
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Blake just graduated college and accepted a new job as a graphic designer for a marketing firm. He
wants to buy a $100,000 condo near his new job and he has saved enough money for a 20% down
payment. He is planning on taking out a loan, or a mortgage, for $80,000 to purchase the property.
Is this a good or bad debt move? Why?
From the information given, it's difficult to determine whether taking out a mortgage for the condo is a good or bad debt move for Blake. However, here are some factors to consider:
Pros of taking out a mortgage:
Blake has saved enough money for a 20% down payment, which means he will only need to borrow $80,000.
Depending on the terms of the mortgage, Blake may be able to secure a low interest rate, which would make the monthly payments more affordable.
Owning a property can be a good long-term investment, as property values tend to increase over time.
Cons of taking out a mortgage:
Even with a 20% down payment, Blake will still owe a significant amount of money and will have to make monthly payments for a long period of time.
If Blake's job situation changes or if he encounters unexpected expenses, he may struggle to keep up with the mortgage payments.
There may be additional expenses associated with owning a property, such as maintenance and property taxes.
Ultimately, whether taking out a mortgage is a good or bad debt move for Blake depends on his individual financial situation, including his income, expenses, and long-term goals. He should carefully consider the pros and cons and consult with a financial advisor before making a decision.
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Charles owes $2500 on a credit card. The card charges 12% interest, compounded monthly. Write a formula that describes how much Charles will owe on his card after t years, assuming he makes no payments and does not incur any additional charges.
Charles will owe A = 2500[tex]e^{0.12t}[/tex] on his card after t years. The solution has been obtained by using compound interest.
What is compound interest?
Contrary to simple interest, which does not take the principal into account when calculating the interest for the following month, compound interest does. Compound interest is commonly represented in algebra by the letter C.I.
We know that compound interest is given by
A = P[tex]e^{rt}[/tex]
We are given the following information:
P = $2500
r = 0.12
So, from this we get
A = 2500[tex]e^{0.12t}[/tex]
Hence, Charles will owe A = 2500[tex]e^{0.12t}[/tex] on his card after t years.
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81x^2-49=0
Square root, Factoring, Completing the square, or the quadratic formula
The quadratic equation can be solved using square root, factoring, completing the square, or the quadratic formula. The solutions of the equation are x = 0.7751469 ± 0.7751469.
The quadratic equation can be solved using square root, factoring, completing the square, or the quadratic formula. The quadratic equation to be solved is:
[tex]ax^2 + bx + c = 0[/tex]
In this equation, a = 81, b = 0, and c = -49.
Using the quadratic formula, the solutions are [tex]x = √(49/81) ± √(49/81)[/tex].
The first step is to calculate the value of the square root of 49/81. This can be done by dividing 49 by 81 to get 0.60493827.
The next step is to calculate the value of the plus and minus square root of the result. This can be done by taking the square root of 0.60493827 which is equal to 0.7751469.
Finally, the solutions of the equation are x = 0.7751469 ± 0.7751469.
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From a prior national study, we are able to infer that the probability of a high school student going to college, when the parents make over $75,000 per year, is about 0.60. assume that toms river has 125 graduating seniors next year, and all the parents are assumed to make over $75,000. if six students are randomly selected, what is the probability that less than two of them will actually go to college?
The probability of less than two students going to college if six students are randomly selected from a school of 125 graduating seniors, and all the parents make over $75,000 per year is 0.0014 or 0.14%.
Given, Probability of a high school student going to college, when the parents make over $75,000 per year is 0.60.The total number of graduating seniors is 125.And, six students are randomly selected.
Let X be the number of students who go to college.If we assume that each student is independent of each other, then the probability that a student goes to college is 0.60, and the probability that a student does not go to college is 1 - 0.60 = 0.40.
Then the probability mass function of X is given by,[tex]P(X = k) = nCk * pk * (1 - p)n - kwhere n = 6, k = 0,1.P(X < 2) = P(X = 0) + P(X = 1) = (6C0 * 0.6^0 * 0.4^6) + (6C1 * 0.6^1 * 0.4^5) = (1 * 1 * 0.01024) + (6 * 0.6 * 0.32768) = 0.0014[/tex]or 0.14%.Therefore, the probability that less than two students will actually go to college is 0.0014 or 0.14%.
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Your employer has asked you to purchase a small $20 item for work, when you give your employer the receipt and ask for the money back, their response is "you can just claim it back on tax". If you are too tired to argue that day, will you receive the full $20 back at tax time?
write the functionf(x)after the following transformation is performed: horizontal shift left 6 units.
The function f(x) after the horizontal shift left 6 units is f(x+6).
To perform a horizontal shift left, we add the value of the shift to the x variable inside the function. In this case, the shift is 6 units to the left, so we add 6 to the x variable.
For example, if the original function is f(x) = x^2, the transformed function would be f(x+6) = (x+6)² .In general, for a function f(x), the transformation f(x+a) represents a horizontal shift left by a unit, and the transformation f(x-a) represents a horizontal shift right by a unit.
So, the function f(x) after the horizontal shift left 6 units is f(x+6).
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What is the perimeter of
▲ RST? PLEASEEE HELP ASAP
The sοlutiοn οf the given prοblem οf triangle cοmes οut tο be RST's triangle has a 30 unit perimeter.
What is bar chart?
A bar chart is a visual representatiοn using vertical and hοrizοntal bars in a chart. The bar length is prοpοrtiοnal tο the data rate. It is alsο even called bar graph.
Frοm the bar chart, the tοtal pοpulatiοn in 2005 is 302 milliοn tοtal tax cοllected is $2.50.if it is evenly divided then each οf them wοuld pay [tex]2.50/302 = 8.278\times10^{-9[/tex].Hence, each οf them wοuld pay[tex]8.278\times10^{-9.[/tex]
Therefοre , the sοlutiοn οf the given prοblem οf triangle cοmes οut tο be RST's triangle has a 30 unit perimeter.
What precisely is a triangle?Because a triangular has twο οr mοre extra pieces, it is a pοlygοn. Its structure is a simple rectangle. A triangle is a rectangle with οnly edges A, B, and C. Euclidean geοmetry prοduces a single plane instead οf a cube when the extremities aren't exactly cοllinear. A shape is cοnsidered triangular if it has three sides and three angles. An angle is the pοint where a quadrilateral's three sides meet. A triangle's sides add up tο 180 degrees.
Here,
Yοu wοuld need tο multiply the lengths οf the triangular RST's three sides in οrder tο determine its perimeter.
When we lοοk at the picture, we can see that:
The length οf Sectiοn RS is 5 units.
The length οf Sectiοn ST is 12 units.
The length οf Sectiοn RT is 13 units.
As a result, the triangular RST's perimeter wοuld be:
Circle is calculated as fοllοws: 5 + 12 + 13 = 30 units.
RST's triangle has a 30 unit circumference.
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What is the perimeter of ▲ RST in the given figure?
The sοlutiοn οf the given prοblem οf triangle cοmes οut tο be RST's triangle has a 30-unit perimeter.
What is a bar chart?
A bar chart is a visual representatiοn using vertical and hοrizοntal bars in a chart. The bar length is prοpοrtiοnal to the data rate. It is alsο even called a bar graph.
Frοm the bar chart, the tοtal pοpulatiοn in 2005 is 302 milliοn tοtal tax collected is $2.50.if it is evenly divided then each οf them would pay . Hence, each οf them would pay
Therefοre, the sοlutiοn οf the given prοblem οf triangle cοmes οut tο be RST's triangle has a 30 unit perimeter.
What precisely is a triangle?
Because a triangular has twο οr mοre extra pieces, it is a pοlygοn. Its structure is a simple rectangle. A triangle is a rectangle with οnly edges A, B, and C. Euclidean geοmetry prοduces a single plane instead οf a cube when the extremities aren't exactly cοllinear. A shape is cοnsidered triangular if it has three sides and three angles. An angle is the pοint where a quadrilateral's three sides meet. A triangle's sides add up tο 180 degrees.
Here,
Yοu wοuld need tο multiply the lengths οf the triangular RST's three sides in οrder tο determine its perimeter.
When we look at the picture, we can see that:
The length οf Sectiοn RS is 5 units.
The length οf Sectiοn ST is 12 units.
The length οf Sectiοn RT is 13 units.
As a result, the triangular RST's perimeter would be:
The circle is calculated as fοllοws: 5 + 12 + 13 = 30 units.
Hence, RST's triangle has a 30-unit circumference.
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A cylinder with a diameter of 8 yards has a volume of 552.64 yd3. What is the height of the cylinder? Use 3.14 for π.
44 yards
11 yards
8 yards
3 yards
Option B. 11 yards. The height of the cylinder is approximately 11 yards.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the cylinder, h is the height of the cylinder, and π is a constant approximately equal to 3.14.
Since the diameter of the cylinder is 8 yards, its radius is half of that, or 4 yards. We know that the volume of the cylinder is 552.64 yd^3. Substituting the values we have into the formula, we get:
552.64 = 3.14 x 4^2 x h
Simplifying the expression on the right side, we get:
552.64 = 3.14 x 16 x h
552.64 = 50.24h
Dividing both sides by 50.24, we get:
h = 552.64 / 50.24
h ≈ 11
Therefore, About 11 yards tall, the sphere has a diameter.
So, the correct option is (B) 11 yards.
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what is the equation of the line parallel to y= -2 that goes through the point (0,5)
The required equation of the line parallel to y = -2 that goes through the point (0,5) is y = 5.
How to find the equation of line?The given line is y = -2, which is a horizontal line passing through y = -2. Any line parallel to this line will also be horizontal and have the same y-coordinate at any point.
Since the line we're looking for passes through the point (0,5), its equation must be of the form y = c, where c is the y-coordinate of the point. Therefore, the equation of the line parallel to y = -2 that goes through the point (0,5) is:
y = 5
Alternatively, we can also see that since the line we're looking for is parallel to y = -2, it will have the same slope as this line, which is 0. Therefore, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. Substituting m = 0, x1 = 0, and y1 = 5, we get:
y - 5 = 0(x - 0)
Simplifying, we get:
y = 5
So the equation of the line parallel to y = -2 that goes through the point (0,5) is y = 5.
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A square fits exactly inside a circle with each of its vertices being on the circumference of the circle
the square has side lengths of xcm. The area of the circle is 56cm squared. Work out the value of x to 3 significant figure
four hundred thirty billion, two hundred three million, six hundred sixty-three thousand five hundred ten
Answer: 430,203,663,510?
Step-by-step explanation:
four hundred thirty billion, two hundred three million, six hundred sixty-three thousand five hundred ten, into number form is :
= 430,203,663,510.
Hope this helps?
Answer:
430 ,202 ,663 ,510 this is the answer
