So overall, you can expect to make a profit of $166.67 if you play the game 100 times.
What is probability ?
Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.
To determine how much you expect to win or lose if you play the game 100 times, we need to calculate the expected value of each round and then multiply it by the number of rounds.
Let X be the random variable that represents the amount you win in one round of the game. The possible outcomes of X are winning $14, winning $12, or losing $10. We can calculate the expected value of X using the following formula:
E(X) = P(win $14) × $14 + P(win $12) × $12 + P(lose $10) × (-$10)
To calculate the probabilities, we can use the fact that there are 5 red balls, 3 green balls, and 4 yellow balls in the bag. The probability of drawing a red ball is therefore 5/12, the probability of drawing a green ball is 3/12, and the probability of drawing a yellow ball is 4/12.
So we have:
E(X) = (5/12) × $14 + (4/12) × $12 + (3/12) × (-$10)
E(X) = $5/3
This means that on average, you expect to win $5/3 per round. Over 100 rounds, you can expect to win:
100 × $5/3 = $166.67
However, it's important to note that this is just an average - in reality, you may win more or less than this amount depending on the luck of the draw.
Therefore, overall, you can expect to make a profit of $166.67 if you play the game 100 times.
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grogg draws the following figure. it so happens that $\angle sap$ is $174^\circ$ less than 4 times $\angle sop$. find the degree measure of $\angle sap.$
The degree measure of [tex]$\angle sap$ is $726^\circ - 4 \times \angle sop$.[/tex]
What is angle?Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.
We can use the following formula to calculate the degree measure of $\angle sap$:
[tex]$\angle sap = 4 \times \angle sop - 174^\circ$[/tex]
Therefore, [tex]$\angle sap = 4 \times \angle sop - 174^\circ = 4 \times (180^\circ - \angle sop) - 174^\circ = 726^\circ - 4 \times \angle sop$[/tex]
Therefore, the degree measure of [tex]$\angle sap$ is $726^\circ - 4 \times \angle sop$.[/tex]
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my son is having trouble with this problem he (6) can you tell him the answer 9+10
Answer:
19
Step-by-step explanation:
111111111
+
1111111111
count how many 1ns are there.
ans is 19
What is the total number of pencils that Mr. Moretti gives to his students if he puts 3 mechanical pencils in each bag?
Answer:
it depends on how many students?
Step-by-step explanation:
b-3. which of the following statements is most accurate with respect to outliers in this example? multiple choice 3 the boxplot and z-scores provide consistent results. the boxplot is more reliable because the distribution is not symmetric. the z-scores are more reliable because the distribution is not symmetric. the z-scores are more reliable because the distribution is symmetric.
The correct statements are -
the boxplot and z-scores provide consistent resultsthe z-scores are more reliable because the distribution is symmetric.What are outliers?In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set.
Given is to identify which of the following statements is most accurate with respect to outliers in this example.
The correct statements are -
the boxplot and z-scores provide consistent resultsthe z-scores are more reliable because the distribution is symmetric.Therefore, the correct statements are -
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ricky took out a $258,000, 20-year mortgage at an APR of 3.84%.
what is the monthly payment?
what will be his total interest charges after 20 years?
The total monthly payment of Ricky with an APR of 3.84 % is given by the equation M = $ 1,208.0523
What is Annual Percentage Yield?The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. An APR is a number that represents the total yearly cost of borrowing money, expressed as a percentage of the principal loan amount.
The monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]
where
M = Total monthly payment
P = The total amount of your loan
I = Your interest rate, as a monthly percentage
N = number of months for paying off your mortgage
Given data ,
Let the monthly payment be represented as M
Now , the number of years n = 20 years
The annual interest rate i = 3.84 %
The total loan amount P = $ 258,000
Now , the monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]
On simplifying , we get
[tex]M = 258,000 [ ( \frac{ 0.0384}{12} ) ( 1 + \frac{ 0.0384}{12} )^{12*30} ] / [ ( 1 + \frac{ 0.0384}{12} )^{12*30} - 1 ][/tex]
[tex]M = 258,000 [ (0.0032 ) ( 1.0032 )^{360} ] / [ ( 1.0032 )^{360} - 1 ][/tex]
On further simplification , we get
M = 258,000 [ 0.0101078417 ] / [ 2.158700543922579 ]
M = 258,000 ( 0.00468237327729 )
M = $ 1,208.0523
Hence , the monthly payment of Ricky is $ 1,208.0523
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x=-2/3t find the value of t .if x=-1/6
Answer:t= 1/4
Step-by-step explanation:
Divide both sides by -2/3, and simplify which would leave u with 1/4.
is 74.721 repeating rational or irrational
Answer:
Step-by-step explanation:
rational
PLEASE I NEED HELP, in the first colom it says spring,then summer, then fall and winter, the vertical line is in milions
The number of hamburgers sold in the winter is 57 million.
What is percentage ?
Percentage is a way of expressing a fraction or ratio as a portion of 100. It is denoted by the symbol "%".
For example, if there are 10 green balls in a bag of 20 balls, we can say that the percentage of green balls is:
(10/20) x 100% = 50%
This means that 50% of the balls in the bag are green.
Percentages are often used to represent proportions or amounts in many contexts, such as finance, statistics, and everyday life. They can be used to express changes, comparisons, and relationships between different quantities.
In addition, percentages are commonly used in calculations involving tax, interest rates, discounts, and other types of financial transactions. It is important to have a good understanding of percentages in order to manage personal finances, make informed business decisions, and interpret data accurately.
Let's suppose that the total number of hamburgers sold by the fast food chain in a year is represented by the height of the bars in the bar graph. We know that 25% of the hamburgers are sold in the fall, which means that the bar representing the fall sales must be 25% of the total height of the bars.
Since there are four seasons in a year, each season must represent 25% / 4 = 6.25% of the total height of the bars. Therefore, the height of each bar is 6.25% of the total number of hamburgers sold.
Let's denote the number of hamburgers sold in the winter by x. Then, the height of the winter bar is also x/100 of the total height of the bars.
We know that the winter bar is covered by a smudge, but we can still use the information we have to set up an equation. Since the heights of the bars must add up to the total height, we can write:
25% + 6.25% + 6.25% + 6.25% + x/100 = 100%
Simplifying the left-hand side, we get:
43% + x/100 = 100%
Subtracting 43% from both sides, we get:
x/100 = 57%
Multiplying both sides by 100, we get:
x = 57 million hamburgers.
Therefore, the number of hamburgers sold in the winter is 57 million.
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PLSS ANSWER THE QUESTION QUICKLY
Answer:
C
The value of the variables in answer C satisfies both of the equations
Find the perimeter of the triangle whose vertices are (−1,−14)
, (7,1)
, and (−1,7)
. Write the exact answer. Do not round.
To find the perimeter of the triangle, we need to calculate the length of each of its sides and then add them up.
Let's start by finding the length of the side between (-1, -14) and (7, 1). We can use the distance formula for this:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((7 - (-1))^2 + (1 - (-14))^2)
= sqrt(8^2 + 15^2)
= sqrt(289)
= 17
So the length of the first side is 17.
Now let's find the length of the side between (-1, -14) and (-1, 7):
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((-1 - (-1))^2 + (7 - (-14))^2)
= sqrt(0^2 + 21^2)
= 21
So the length of the second side is 21.
Finally, let's find the length of the side between (7, 1) and (-1, 7):
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((-1 - 7)^2 + (7 - 1)^2)
= sqrt((-8)^2 + 6^2)
= sqrt(100)
= 10
So the length of the third side is 10.
Now we can add up the lengths of all three sides to get the perimeter:
perimeter = 17 + 21 + 10
= 48
Therefore, the perimeter of the triangle is 48.
find the volume of a sphere vd(r) of radius r in d dimensions. in order to accomplish this task, first find the surface area ad of a sphere of unit radius in d dimensions by considering the integral
The formula for the volume of a d-dimensional sphere of radius r is:
V_d(r) = (π^(d/2) / Γ(d/2 + 1)) * r^d
How to explain the volumeIt should be noted that in the formula, Γ is the gamma function.
Let's break down the formula:
π^(d/2) is pi raised to the power of d/2.
Γ(d/2 + 1) is the gamma function evaluated at d/2 + 1.
r^d is the radius raised to the power of d.
Putting it all together, we get the formula above.
For a 2-dimensional sphere (a circle) of radius r, we have d=2, so:
V_2(r) = (π^(2/2) / Γ(2/2 + 1)) * r^2
= (π / Γ(3/2)) * r^2
= (π / (1/2) * √π) * r^2
= 2πr^2
For a 3-dimensional sphere of radius r, we have d=3, so:
V_3(r) = (π^(3/2) / Γ(3/2 + 1)) * r^3
= (4/3) * π * r^3
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Using the digits 0-9 once, create accurate number line
The digits are arranged in increasing order from left to right, and that each digit is used exactly once.
What is a number line?
A number line is a visual representation of numbers arranged in a straight line from left to right or from right to left. It is a tool commonly used in mathematics to help visualize numerical relationships, such as addition, subtraction, multiplication, and division.
A typical number line starts at zero in the middle and extends infinitely in both directions, with positive numbers increasing to the right and negative numbers decreasing to the left. The distance between any two points on the number line represents the absolute difference between the corresponding numbers.
Here's a number line using the digits 0-9 exactly once:
-9 --- -8 --- -7 --- -6 --- -5 --- -4 --- -3 --- -2 --- -1 --- 0 --- 1 --- 2 --- 3 --- 4 --- 5 --- 6 --- 7 --- 8 --- 9
Note that the digits are arranged in increasing order from left to right, and that each digit is used exactly once.
Therefore, the digits are arranged in increasing order from left to right, and that each digit is used exactly once.
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A student concludes that the solution to the equation x+3=2x-4, in one variable, is the x-coordinate of the solution to the graph of this linear system.
x-y=-3
2x-y=4
Which statement justifies this conclusion based on the student's work?
A Each side of the equation, in one variable, can be found by isolating the x-variable of each equation
in the system. The solution is the y-coordinate, where the x-coordinates of both graphs are the
same.
B Each side of the equation, in one variable, can be found by isolating the y-variable of each equation
in the system. The solution is the x-coordinate, where the x- coordinates of both graphs are the
same.
C. A solution to both equations in the system is (7, 10). Since that point is where the equations
intersect, it must be the solution to the system.
D. The solution to the equation, in one variable, is x = 7. Since both equations in the system have
y-values when x = 7, it must be the solution to the system.
Answer:based on the student's work?A Each side of the equation, in one variable, can be found by isolating the x-variable of each equationin the s
Step-by-step explanation:
Chart that arranges all of the known elements in a particular order.
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
Rearrange unknown terms to the left side of the equation: [tex]x-2x = -4 - 3[/tex]
Combine like terms: [tex]-x = -4-3[/tex]
Calculate the sum or difference: [tex]-x = -7[/tex]
Divide both sides of the equation by the coefficient of variable: [tex]x = 7[/tex]
find the exact value using formulas from geometry. ∫ (1+3x) with upper bound as 3 and lower bound as 1.
The value of the integral ∫(1+3x) dx is equal to 14.
What is integration?Integration is a process of adding up small elemental volumes to find the larger volume.
Given is to find the integral -
∫(1+3x)
We can find the equivalent values as -
∫(1+3x) dx = ∫1 dx + ∫3x dx
∫(1+3x) dx = x + 3x²/2
For the limit x = 1 to x = 3, we can write -
∫(1+3x) dx = (3 + 27/2) - (1 + 3/2)
∫(1+3x) dx = 33/2 - 5/2 = 14
Therefore, the value of the integral ∫(1+3x) dx is equal to 14.
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If a rock is thrown upward on an exoplanet of a nearby star with initial velocity of 20 m/s , its height in meters t seconds later is given by y = 20t - 1.87t².
The rock has an instantaneous velocity of 16 meters per second.
How to determine the average velocity and instantaneous velocity of a rock thrown upward
In this problem we need to determine the average velocity of the rock, represented by a secant line, and estimate its instantaneous velocity, represented by a tangent line. The average speed is defined by the following expression:
u = [y(t + Δt) - y(t)] / Δt
Where:
y(t) - Initial position, in meters. y(t + Δt) - Final position, in meters. Δt - Time interval, in seconds. u - Average speed, in meters per second.The instantaneous speed is the average speed when Δt ⇒ 0.
Part A
Case I
y(1) = 20 · 1 - 1.87 · 1²
y(1) = 20 - 1.87
y(1) = 18.13 m
y(2) = 20 · 2 - 1.87 · 2²
y(2) = 40 - 7.48
y(2) = 32.52 m
u = (32.52 m - 18.13 m) / 1 s
u = 14.39 m / s
Case II
y(1.1) = 20 · 1.1 - 1.87 · 1.1²
y(1.1) = 19.737 m
u = (19.737 m - 18.13 m) / 0.1 s
u = 16.07 m / s
Case III
y(1.01) = 20 · 1.01 - 1.87 · 1.01²
y(1.01) = 18.292 m
u = (18.292 m - 18.13 m) / 0.01 s
u = 16.2 m / s
Case IV
y(1.001) = 20 · 1.001 - 1.87 · 1.001²
y(1.001) = 18.146 m
u = (18.146 m - 18.13 m) / 0.001 s
u = 16 m / s
And the instantaneous velocity of the rock is approximately 16 meters per second.
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Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place. PLEASE EXPLAIN WELL THANK YOU
Answer:
68.1 square units
Step-by-step explanation:
l = Length of rectangle
= 9 units
w = Width of rectangle
= 6 units
The dashed lines represent the diameter of the circle. Semi-circle is exact half of a circle. This diameter is parallel to the width of the rectangle and is equal in measurement:
r = Radius of semi-circle
= [tex]\frac{Diameter}{2}[/tex]
= [tex]\frac{6}{2}[/tex] units
= 3 units
∴Area of composite solid = Area of rectangle + Area of semi-circle
= [(l × w) + [tex]\frac{1}{2}(\pi r^{2})[/tex]] [tex]units^{2}[/tex]
= {[9 × 6] + [tex]\frac{1}{2}[\pi (3)^{2}][/tex]} [tex]units^{2}[/tex]
= [54 + [tex]\frac{9}{2}\pi[/tex]] [tex]units^{2}[/tex]
= 68.137 [tex]units^{2}[/tex]
= 68.1 square units (Rounded to the nearest tenths place)
The stem and leaf plot shows the number of laps around a track
that several teams walked as part of a fund-raiser for the library.
The teams that walked more than 50 laps raised an extra $100 for
the library.
What fraction of the teams raised this extra money?
The fraction of the teams which walked as part of the fundraiser for the library, that raised extra money, is D. 1 / 3.
What fraction of the teams raised extra funds ?You must count the number of teams that were able to walk more than 50 laps in order to determine the percentage of teams that raised the additional funds. The distance walked by teams more than 50 laps were :
5363 6365 miles.There are 12 teams overall, which is equal to the number of leaves.
The fraction of teams that raised additional funds is:
= 4 teams / 12 total teams
= ( 4 ÷ 4 ) / ( 12 ÷ 4 )
= 1 / 3
In conclusion, the fraction of teams which raised extra money was 1 / 3.
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Explain a right triangle to a group of 6th graders. What do
they need to know? Is there one kind- or more? What makes
them unique? Are there any special kind of right triangles?
Use vocabulary from Geometry and Pre-Cal/Trig. Use
complete sentences trying your best to make things clear to
the younger student.
Answer:
A right triangle is a type of triangle that has one angle measuring 90 degrees and two acute angles. It has a hypotenuse and two legs, and it is the only type of triangle that the Pythagorean theorem can be applied to. There are different types of right triangles, including isosceles right triangles, 45-45-90 triangles, and 30-60-90 triangles, each with its own unique properties.
Step-by-step explanation:
A right triangle is a type of triangle that has one angle which measures exactly 90 degrees, which we call the right angle. The other two angles are called acute angles and they are always less than 90 degrees.
A right triangle has a special property: the side opposite the right angle is called the hypotenuse. This is the longest side of the triangle and it is always opposite to the right angle. The other two sides are called legs.
One important thing to note is that the Pythagorean theorem only works for right triangles. This theorem tells us that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This formula is often written as a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse.
There are actually several different types of right triangles. For example, if the two legs have the same length, we call it an isosceles right triangle. If one of the acute angles measures exactly 45 degrees, we call it a 45-45-90 triangle, and if one of the acute angles measures exactly 30 degrees and the other measures 60 degrees, we call it a 30-60-90 triangle. These triangles have special properties that make them useful in many different areas of math and science.
In summary, a right triangle is a type of triangle that has one angle measuring 90 degrees and two acute angles. It has a hypotenuse and two legs, and it is the only type of triangle that the Pythagorean theorem can be applied to. There are different types of right triangles, including isosceles right triangles, 45-45-90 triangles, and 30-60-90 triangles, each with its own unique properties.
Which of the following is the best linear approximation for f(x) = cos(x) near x equals pi divided by 2 ?
y equals x minus pi over 2
y equals negative x plus pi over 2
y equals negative x plus pi over 2 plus 1
y equals x minus pi over 2 plus 1
Answer:
Please Mark Brainlaiest Answer
Step-by-step explanation:
The best linear approximation for f(x) = cos(x) near x = pi/2 is given by the equation:
y = -(x - pi/2) + 1
This is because the linear approximation should have the same value and slope as the original function at x = pi/2.
At x = pi/2, the value of f(x) = cos(pi/2) = 0. The value of the linear approximation at x = pi/2 is:
y = -(pi/2 - pi/2) + 1 = 1
So, the value of the linear approximation matches the value of the original function at x = pi/2.
The slope of the original function at x = pi/2 is -sin(pi/2) = -1. The slope of the linear approximation is:
y' = -1
So, the slope of the linear approximation also matches the slope of the original function at x = pi/2.
Therefore, the best linear approximation for f(x) = cos(x) near x = pi/2 is:
y = -(x - pi/2) + 1
Hence, the correct option is "y equals negative x plus pi over 2 plus 1".
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Verified Answer ✅
Susan Marciano invested part of her $19000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered a %4 loss. Find the amount of each investment if her overall net profit was $520
Answer:
The investment in the fund was $19000 x 0.12 = $2280
The investment in the stock was $19000 - $2280 = $16720
The net profit was $520, so the amount of the profit from the fund was $520 x (2280/16720) = $136
The amount of the loss from the stock was $520 - $136 = $384
Need help solving problem
The equations that determine the cost of each hamburger and each fries is 4x + 5y = 20 and 10x + 7y = 41.20
What is an equation?
An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
Let x represent the cost of each hamburger and y represent the cost of each fries.
She purchased 4 hamburgers and 5 fries for $20.00, hence:
4x + 5y = 20 (1)
She purchased 10 hamburgers and 7 fries for $41.20, hence:
10x + 7y = 41.20 (2)
From both equations, solving simultaneously:
x = 3; y = 1.6
The cost of each hamburger is $3 while the cost of each fries is $1.6
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Sylvia buys a snack pack of nuts as an after lunch treat.she notices that there are twice as many cashews as almonds,so she eats ten cashews and seed there a still five more cashews than almonds.how many almonds were in the snack pack?
45. 30. 15. 5.
Answer:
there were 15 almonds in the snack pack.
Step-by-step explanation:
Let's use variables to represent the unknown quantities. Let's call the number of almonds in the snack pack "a", and the number of cashews in the snack pack "c".
we can use the following equations to represent the problem:
c = 2a (the number of cashews is twice the number of almonds)
c - 10 = a + 5 (there are 5 more cashews than almonds after Sylvia eats 10 cashews)
Substituting the first equation into the second equation, we get:
2a - 10 = a + 5
Solving for "a", we get:
a = 15
So there were 15 almonds in the snack pack.
Classify the triangle by its angles , x, 102, x a right,acute or obtuse triangle
The solution is, x = 39. Since we have a 102 degree angle it is a obtuse triangle.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
given that,
its angles , x, 102, x
now, we know,
The sum of the angles in a triangle add to 180
i.e.
x+ 102+x = 180
Combine like terms
so, we get,
102 + 2x = 180
Subtract 102 from each side
2x = 78
divide by 2, both sides,
x =39
Since we have a 102 degree angle it is a obtuse triangle.
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find the coordinates of all points where the lines x + y = 8, y = 5, and x = 1 intersect
Intersection points for the lines are,
⇒ (3, 5) (1, 7) and (1, 5)
What is Line segment?Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.
Given that;
The equation of lines are,
x + y = 8 .. (i)
y = 5 .. (ii)
x = 1 .. (iii)
Now, Intersect point for equation (i) and (ii);
x + y = 8 .. (i)
y = 5 .. (ii)
⇒ x + 5 = 8
⇒ x = 3
Hence, The intersection point = (3, 5)
And, Intersect point for equation (i) and (iii);
x + y = 8 .. (i)
x = 1 .. (iii)
⇒ x + y = 8
⇒ y = 8 - 1
⇒ y = 7
Hence, The intersection point = (1, 7)
And, Intersect point for equation (ii) and (iii);
⇒ (1, 5)
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graph translation of (x,y) (x, y-2)
Answer:
can you explain a bit better what the problem is?
Please help me answer this question ASAP!!
The solution to the equation 17(4 + 15) is 323
What is an equation?
An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
Given the equation:
17(4 + 15)
= 17(19)
= 323
OR
17(4 + 15)
= 17(4) + 17(15)
= 68 + 255
= 323
The solution to 17(4 + 15) can be gotten by determining the product of 17 and 19; or adding the product of 17 and 4 to the product of 17 and 15
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Olivia planted bean seeds. After they started to grow, she measured their heights and recorded the heights in the line plot below. image a97cc9c5036040c58918973d56401d70 How many plants were less than 3 cm tall? A. 1 B. 18 C. 14 D. 3 answers
The height of the balloon is 1.3 miles above the ground.
What is height?Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).
The answer to this question can be found by using the trigonometric formula of Tangent. To calculate the height of the balloon, we must find the length of the hypotenuse in the triangle formed by the two towns and the balloonist.
Using the formula for tangent, we can calculate the length of the hypotenuse. The formula is:
tan (angle) = opposite side/adjacent side
In this case, the opposite sides are the two towns, and the adjacent side is the height of the balloon.
For the first town, the formula is:
tan 36° = 1.6/x
Solving for x, we can calculate the length of the hypotenuse for the first town to be 2.8 miles.
For the second town, the formula is:
tan 32° = 1.6/x
Solving for x, we can calculate the length of the hypotenuse for the second town to be 2.9 miles.
Since the hypotenuse is the total distance between the two towns and the balloonist, the height of the balloon can be calculated by subtracting the total length of the two towns (1.6 miles) from the hypotenuse of the second town (2.9 miles).
The height of the balloon is 1.3 miles above the ground.
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Answer:
What is height?
Height:
When a rectangle is drawn with horizontal and vertical sides, the word height makes it clear which dimension is meant; height labels how high (how tall) the rectangle is. That makes it easy to indicate the other dimension—how wide the rectangle is from side to side—by using the word width. And if the side-to-side measurement is greater than the height, calling it the length of the rectangle is also acceptable, as it creates no confusion.
The answer to this question can be found by using the trigonometric formula of Tangent. To calculate the height of the balloon, we must find the length of the hypotenuse in the triangle formed by the two towns and the balloonist.
Using the formula for tangent, we can calculate the length of the hypotenuse. The formula is:
tan (angle) = opposite side/adjacent side
In this case, the opposite sides are the two towns, and the adjacent side is the height of the balloon.
For the first town, the formula is:
tan 36° = 1.6/x
Solving for x, we can calculate the length of the hypotenuse for the first town to be 2.8 miles.
For the second town, the formula is:
tan 32° = 1.6/x
Solving for x, we can calculate the length of the hypotenuse for the second town to be 2.9 miles.
Since the hypotenuse is the total distance between the two towns and the balloonist, the height of the balloon can be calculated by subtracting the total length of the two towns (1.6 miles) from the hypotenuse of the second town (2.9 miles).
The height of the balloon is 1.3 miles above the ground.
Solve the system of equations. Write the solution as an ordered pair. 4x + 3y = 36 and y = -1/3x + 6
Substitute the expression for y in the second equation into the first equation and solve for x:
4x + 3(-1/3x + 6) = 36
4x - x + 18 = 36
3x = 18
x = 6
Now substitute x = 6 into the second equation to solve for y:
y = (-1/3)(6) + 6
y = 4
Therefore, the solution to the system of equations is the ordered pair (6, 4).
The figure shows the graph of the function.
f(x)=
The domain are the possible input while the range are the possible output of a function.
(a) The domain = [-√2, √2], the range = [0, 2]
(b) The domain = [-1, 1], the range = [0, 1]
(c) The domain = [-1, 1], the range = [0, -1]
(d) The domain = [0, 2], the range = [0, 1]
(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]
Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
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3 three sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 5?
The probability that the sum of numbers we will get will be 6 is 7/27.
What is probability?Probability is simply the possibility that something will happen.
Since we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.
The study of events that fit into a probability distribution is known as statistics.
Probability, or the likelihood that an event will occur, is calculated by dividing the number of favorable outcomes by the total number of potential possibilities.
A coin toss serves as the most simple illustration.
When you flip a coin, there are only two possible outcomes: heads or tails.
So, the probability formula:
P(E) = Favourable events/Total events
We need to get the probability of getting the sum of 6.
Then, calculate as follows:
P(E) = Favourable events/Total events
P(E) = 7/27
Therefore, the probability that the sum of numbers we will get will be 6 is 7/27.
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Correct question:
3 three-sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 6?
