After using normal approximation the P(fewer than 5 ) = 0.0307.
From the given data
n = 13
p = 0.6
q = 1 - p
q = 1 - 0.6
q = 0.4
first we have to check np ≥ 5 and nq ≥ 5
n × p = 13 × 0.6
n × p = 7.8 ≥ 5
n × q = 13 × 0.4
n × q = 5.2 ≥ 5
Here the condition is met
Mean μ = n × p
μ = 13 × 0.6
μ = 7.8
standard deviation σ = √npq
σ = √13 × 0.6 × 0.4
σ = √3.12
σ = 1.77
P(fewer than 5) = P(X < 5)
By using normal approximation;
P(fewer than 5) = P(X < 5 - 0.5)
P(fewer than 5) = P(X < 4.5)
P(fewer than 5) = P((X - μ)/σ < (4.5 - 7.8)/1.77
P(fewer than 5) = P(Z < -3.3/1.77
P(fewer than 5) = P(Z < -1.87)
P(fewer than 5) = 0.03074
P(fewer than 5 ) = 0.0307
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The complete question is:
If np ≥ 25 and nq ≥ 25, estimate P (fewer than S) with n = 13 and p = 0.6 by using the normal distribution as an approximation to the binomial distribution, if np 5 or nq 5, then state that the normal approximation is not suitable. Select the correct choice below and, if necessary, fill n the answer box to complete your choice.
A. P(fewer than 5) : _________
B. The normal approximation is not suitable
The total mass of 20 identical bags of cookies is 2.4 kg. Find the mass of 1 bag of cookies in kilograms.
Step-by-step explanation:
Calculate the unit rate as follows
2.4 kg / 20 bag = .12 kg per bag
Suppose two lines go through the given points. Line 1: Line 2: a) Find the slope of Line 1. b) Find the slope of Line 2. (4, 21), (1,0) 16 (5, 1), (-5, 26) 7 c) Are Line 1 and Line 2 parallel, perpendicular, or neither?
The slope of Line 1 is equal to 7.
The slope of Line 1 is equal to 1/7.
Line 1 and Line 2 are neither parallel nor perpendicular.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
For line 1, we have the following:
Slope (m) = (32 - (-45))/(5 - (-6))
Slope (m) = (32 + 45)/(5 + 6)
Slope (m) = 77/11
Slope (m) = 7.
For line 2, we have the following:
Slope (m) = (43/7 - (-48/7))/(1 - 6)
Slope (m) = (-5/7)/(-5)
Slope (m) = 5/35
Slope (m) = 1/7
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
13. The coordinates of the vertices of a rectangle are (-2,3) (4,3), (4,-4) and (-2,-4) what are the dimensions of the rectangle?
A. 1 unit by 2 units
B. 1 unit by 6 units
C. 7 units by 2 units
D. 7 units by 6 units
14. Peter wants to plot the point (2,3) on a coordinate plane. Which statement describes how to plot this point starting from the origin?
A. MOVE 2 UNITS TO THE LEFT AND THEN 3 UNITS DOWN
B. MOVE 3 UNITS TO THE LEFT AND THEN 2 UNITS DOWN
C. MOVE 2 UNITS TO THE RIGHT AND THEN 3 UNITS UP
D. MOVE 3 UNITS TO THE RIGHT AND THEN 2 UNITS UP
15. WHICH EXPRESSION IS EQUIVALENT TO 5(D + 1)?
A. 5D + 5
B. 5D + 1
C. D + 5
D. D + 6
16. A NET OF A SQUARE PYRAMID IS SHOWN BELOW.
5. 95 CM
5.1 CM
WHAT IS THE SURFACE AREA, IN SQUARE CENTIMETERS, OF THE PYRAMID?
A. 60.7
B. 86.7
C. 121.4
D. 147.4
The dimensions of the rectangle is D. 7 units by 6 units
Go 2 units to the right, and then 3 units up
5(d + 1) = 5d + 5 .
What is a Vertice?A vertex (plural: vertices) is a point where two or more lines, edges, or curves meet in a geometric shape. In graph theory, a vertex refers to a node in a graph, which can be connected to other vertices by edges.
For example, in a triangle, each of the three points where the sides of the triangle meet is a vertex. In a cube, each of the eight points where the edges of the cube meet is a vertex. In a graph, each point representing a person or object would be a vertex, and the connections between them would be edges.
The term vertex is commonly used in mathematics, geometry, computer science, and other fields where shapes or networks are analyzed and studied.
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Write the equation in standard form for the circle with center (3,10) and radius 2.
Answer: (x+3)^2+(y+10)^2=4
Step-by-step explanation:
The standard form of the equation of a circle is:
(x−x1)2+(y−y1)2=r2
In order to place the center of the circle at point (3, 10), simply replace x1 with 3 and y1 with 10
(x+3)^2+(y+10)^2=r2
Finally, replace r with the radius of the circle.
The final equation is:
(x+3)^2+(y+10)^2=4
Janice earned a 15% commission on $549.50 sales. Chong earned a 25% commission on $343.25 sales.Adrienne earned a 20% commission on $418.75 sales. Luke earned 10% commission on $625.75 sales. Whoearned the most money from commission?
a. Adrienne c. Janice
b. Chong d. Luke
Therefore , the solution of the given problem of percentage comes out to be Chong is the correct answer in (b).
What is percentages?In statistics, a figure or quantity that may be stated as a percent of 100 is denoted by the abbreviation "a%." Other odd spellings include "pct," "pct," and "pc." The percentage symbol ("%") is the technique that is most usually used for this. Also unknown are any clues or any fixed ratio of any part to the whole. Numbers are effectively integers since they frequently add up to 100. If a figure comprises a percentage, the expression "fraction" or simply the shorthand for % (%) must appear first.
Here,
We must first compute each person's commission earnings before comparing the results to see who received the highest commission payments.
On sales of $549.50, Janice received a 15% commission, which is:
commission:
=> $82.425 ($0.15 x $549.50)
On sales of $343.25, Chong received a 25% commission, which is:
=> commission = 0.25 * $343.25%, or $85.7125.
On sales of $418.75, Adrienne received a 20% commission, which is:
=> commission: $83.75 ($0.20 * $418.75)
On sales of $625.75, Luke received a 10% commission, which is:
=> commission: $62.575 = 0.10 * $625.75
By comparing the figures, it is clear that Chong, with $85.8125, earned the most through commission, followed closely by Adrienne, with $83.75,
Janice, with $82.425, and Luke, with $62.575.
So Chong is the correct answer in (b).
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what is the solution of using the master theorem? group of answer choices , case 1 , case 2 , case 1 master method does not apply
The Master Theorem is a powerful tool for solving divide-and-conquer recurrences. It provides a way to quickly determine the asymptotic behavior of algorithms by analyzing their running time.
Case 1 of the Master Theorem applies to algorithms that split the problem into smaller subproblems of equal size and combine their solutions in constant time. In this case, the running time can be expressed as T(n) = aT(n/b) + f(n), where a is the number of subproblems, b is the size of each subproblem, and f(n) is the time to combine the subproblem solutions. The solution to this recurrence is T(n) = Θ(nlogba) if f(n) = Θ(nlogka) for some constant k < log(ba).
Case 2 of the Master Theorem applies to algorithms that split the problem into smaller subproblems of equal size and combine their solutions in linear time. In this case, the running time can be expressed as T(n) = aT(n/b) + f(n), where a is the number of subproblems, b is the size of each subproblem, and f(n) is the time to combine the subproblem solutions. The solution to this recurrence is T(n) = Θ(nlogba logn) if f(n) = Θ(nlogba) .
If the recurrence cannot be expressed in either of these forms, then the Master Theorem does not apply. In this case, other techniques such as substitution or recursion trees may be used to solve the recurrence.
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Problem 4. Show that if A is any nxn matrix, then the following hold. (i) A+ AT is symmetric. (ii) A – AT is skew symmetric.
If A is any n x n matrix,
(i) Proved that A + A^T is symmetric.
(ii) Proved that A - A^T is skew symmetric.
To show that A + A^T is symmetric, we need to show that (A + A^T)^T = A + A^T.
Now, (A + A^T)^T = A^T + (A^T)^T = A^T + A
Therefore, if we add A + A^T, we get
(A + A^T) + (A^T + A) = 2A^T + 2A
Which is clearly equal to 2(A + A^T). Therefore,
(A + A^T)^T = A + A^T
So, A + A^T is symmetric.
To show that A - A^T is skew symmetric, we need to show that (A - A^T)^T = -(A - A^T).
Now, (A - A^T)^T = A^T - (A^T)^T = A^T - A
Therefore, if we negate A - A^T, we get:
-(A - A^T) = -A + A^T
And we see that (A - A^T)^T = -(A - A^T) holds true.
Thus, we have shown that A + A^T is symmetric, and A - A^T is skew symmetric for any nxn matrix A.
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help me please please
Answer:
Step-by-step explanation:
not for help but for points
Your smartphone has 64.8 gigabytes of storage. Your friend has 0.8 times as
many gigabytes on his smartphone. How many gigabytes of storage does
your friend's smartphone have?
Answer:
51.84 gigabytes
Step-by-step explanation:
Let v be the vector with initial point (1,4) and terminal point (5, -3). Find the vertical component of this vector. a) -3 b) -7 c) -4 d) -8 e) 4 f) ONone of the above
The vertical component of the vector with initial point (1,4) and terminal point (5, -3) is -7. The correct option is b).
We need to find the vertical component of the vector v with initial point (1, 4) and terminal point (5, -3).
Step 1: Determine the coordinates of the vector v.
The coordinates of v can be found by subtracting the initial point coordinates from the terminal point coordinates.
v = (5 - 1, -3 - 4)
v = (4, -7)
Step 2: Identify the vertical component.
The vertical component is the second coordinate of the vector, which represents the change in the vertical (y) direction.
In this case, the vertical component of vector v is -7. So, the correct answer is b).
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Anyone who speaks Spanish know how to do this????
According to the information, the paragraph would look like this: To get to my house, (1. go) to the bus station and (2. take) bus number 40...
How to complete the paragraph?To complete the paragraph we must read the available information and identify the correct way to fill in each blank by conjugating the verb in parentheses. Once we have completed this procedure we can complete the fragment. According to the above, we can infer that the complete paragraph would look like this:
To get to my house, (1. go) to the bus station and (2. take) bus number 40. (3. Get off) at the corner of Correo and Piedras streets. (4. Walk) one block, (5. enter) the Cortés building and (6. go up) to the third floor. My apartment is number thirty-two.
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select the correct answer. a rubber gasket has a circumference of 3.2 cm. when placed in service, it expands by a scale factor of 2. what is the circumference of the gasket when in service?
The circumference of the gasket when in service is 6.4 cm, which is twice the original circumference of 3.2 cm, consistent with the scale factor of 2.
When we say that the rubber gasket expands by a scale factor of 2, we mean that all of its linear dimensions, such as its length, width, and circumference, double in size.
Let's focus on the circumference, which is the distance around the outside of a circle. The circumference of a circle is calculated using the formula:
Circumference = 2 x π x radius
In this case, we don't know the radius of the gasket, but we do know its circumference, which is given as 3.2 cm. We can rearrange the formula to solve for the radius:
radius = Circumference / (2 x π)
Plugging in the given circumference, we get:
radius = 3.2 cm / (2 x π) ≈ 0.509 cm
Now that we know the radius, we can calculate the circumference of the gasket when in service. Since the scale factor is 2, we know that the new radius will be:
new radius = old radius x scale factor = 0.509 cm x 2 = 1.018 cm
Using the same formula as before, but with the new radius, we get:
Circumference in service = 2 x π x new radius
Circumference in service = 2 x π x 1.018 cm ≈ 6.4 cm
Therefore, the circumference of the gasket when in service is 6.4 cm, which is twice the original circumference of 3.2 cm, consistent with the scale factor of 2.
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The length of the polar curve curve r=7cos 4 ( 4 θ ),0≤θ≤2π is equal to a. 3/112 b. 3/28 c.28 d. 3/56 e. 3/224
The length of the polar curve r=7cos^4(θ/4),0≤θ≤2π is equal to 3/28. Hence, the correct answer is option (b).
To find the length of the polar curve given by r=7cos^4(θ/4), we use the formula:
L = ∫(a to b) √[r(θ)^2 + (dr/dθ)^2] dθ
where a and b are the limits of integration.
First, we need to find the derivative of r(θ):
dr/dθ = -7cos^3(θ/4)sin(θ/4)
Next, we can substitute r(θ) and dr/dθ into the above formula and simplify:
L = [tex]\int\limits^{2 \pi}_0[/tex] √[7cos^8(θ/4) + 49cos^6(θ/4)sin^2(θ/4)] dθ
L = 7[tex]\int\limits^{2 \pi}_0[/tex] cos^4(θ/4)√[1 + 7sin^2(θ/4)] dθ
Next, we use the substitution u = sin(θ/4), du/dθ = 1/4cos(θ/4), and simplify:
L = 28[tex]\int\limits^1_0[/tex] (1-u^2)^(3/2)√[1+7u^2] du
Now, we can use the substitution v = (1-u^2)^(1/2), dv = -u/[(1-u^2)^(1/2)] du, and simplify:
L = 28[tex]\int\limits^1_0[/tex] v^2(1-v^2)√[8v^2+1] dv
This integral can be solved using standard integration techniques. After simplification, we get:
L = 3/28
Therefore, the correct answer is option (b).
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List all the permutations of four objects m, I, n, and k taken two at a time without repetition. What is P? List all the permutations of four objects m, I, n, and k taken two at a time without repetition. Choose the correct answer below. O A. m, mn, mk, In, lk, nk OB. ml, mn, mk, Im, in, lk, nm, nl, nk, km, kl, kn OC. m. I, n,k OD. mm, ml, mn, mk, II, In, lk, nn, nk, kk What is P2?
The permutations of four objects m, I, n, and k taken two at a time without repetition are: mn, mk, mi, nm, nk, ni, km, kn, ki, in, im, ik.
P is the total number of permutations, which is equal to 12.
The correct answer is OB, which lists all 12 permutations.
P2 is the number of permutations taken two at a time with repetition allowed. This means that we can repeat the same object in a permutation.
There are 16 possible permutations with repetition allowed: mm, ml, mn, mk, ll, ln, lk, nn, nk, kk, ii, ik, nn, ni, nk.
Therefore, P2 is equal to 16.
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Write the equation of the circle with the segment whose endpoints are (-2,5) and (4,7) as the diameter. (Hint.... the center of a circle is the midpoint of the diameter.)
Answer:
Step-by-step explanation:
The center of a circle is the midpoint of its diameter. The midpoint of the segment whose endpoints are (-2,5) and (4,7) is:
((-2 + 4)/2, (5 + 7)/2) = (1, 6)
Therefore, the center of the circle is (1, 6), and its radius is half the length of the diameter:
r = sqrt((4 - (-2))^2 + (7 - 5)^2)/2 = sqrt(40)/2 = sqrt(10)
The equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values of (h, k, r) into the equation, we get:
(x - 1)^2 + (y - 6)^2 = 10
Therefore, the equation of the circle with the segment whose endpoints are (-2,5) and (4,7) as the diameter is:
(x - 1)^2 + (y - 6)^2 = 10
PLEASE HELP I INCLUDED THE PROBLEM IN IMAGE I WROTE IT DOWN!!!
Multiply and simplify.
6xy3z⋅3x2yx2
Responses
18x5y4z
18 begin power 5 end power y begin power 4 end power z
18(xyz)10
18 left parenthesis x y z right parenthesis begin power 10 end power
18x4y3z
18 begin power 4 end power y cubed z
9x5y4z
Answer: A
Step-by-step explanation:
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 21ft long and 14ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required?
Answer: 70
Step-by-step explanation: 21+21+14+14
HELP ASAP
6. The measure of ZE, the angle of elevation from point A to point B, is (3x + 1). The measure of LD
, the angle of depression from point B to point A, is 2(x+8). Find the measure of each angle.
mZE = 22°, m/D = 30°
mZE = 15°,m/D = 15°
mZE = 46°, m/D = 46°
mZE = 52°, m/D = 50°
Measure of angle E, m ∠E = 46°
Measure of angle D, m ∠D = 46°
The correct option is the third option m∠E = 46°, m∠D = 46°
Angles of elevation and Depression: Calculating the measure of anglesFrom the question, we are to determine the measure of each angle.
From the given information,
The measure of ∠E, the angle of elevation from point A to point B, is (3x + 1).
The measure of ∠D, the angle of depression from point B to point A, is 2(x+8).
This means
The measure of ∠E = The measure of ∠D
(3x + 1)° = 2(x + 8)°
Solve for x
3x + 1 = 2(x + 8)
3x + 1 = 2x + 16
3x - 2x = 16 - 1
x = 15
Measure of ∠E = (3x + 1)°
Measure of ∠E = (3(15) + 1)°
Measure of ∠E = (45 + 1)°
Measure of ∠E = 46°
But,
Measure of ∠E = Measure of ∠D
Thus,
Measure of ∠D = 46°
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The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 50%, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
The likelihood of randomly selecting a chocolate chip cookie is (c) equally likely and unlikely
Interpreting the likelihood of randomly selecting a chocolate chip cookieFrom the question, we have the following parameters that can be used in our computation:
P(chocolate chip) = 50%
When a probability is at 50% ot 0.5, then it means that
The probability is equally likely and unlikely
Hence, the true statement is (c) equally likely and unlikely
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Whats 1 plus 1 I want the real answer
Answer:
2
Step-by-step explanation:
Some one help me I don’t get this
Answer:
Isosceles
Step-by-step explanation:
Pre-SolvingWe are given a triangle. We know that the angles have a measure of 45°, 45°, and 90°.
We also know that the sides of the triangle are 3.2, 3.2, and 4.5 units.
We want to classify this triangle.
SolvingA scalene triangle has all of its sides and angles as different values.
An isosceles triangle has 2 of its sides as the same value, and 2 of its angles as the same value.
An equilateral triangle has all of its sides as the same value, and all of its angles as the same value.
Looking at the side lengths and angle values we are given, we can see that we have 2 angles that are the same value (45°), and 2 sides that are the same value (3.2 units).
Therefore, we have an isosceles triangle.
if the number of participants in group 1 = 32 and the number in group 2 = 30, what is the associated degrees of freedom? a. 58 b. 60 c. 62 d. 59
For the given groups, the degrees of freedom is obtained to be, Option (b) : 60.
What is degrees of freedom?
The number of variables that can vary in a calculation is represented by the degrees of freedom, which are mathematical notions used in statistical calculations. Among other tests, degree of freedom calculations can help confirm the validity of chi-square test statistics, t-tests, and highly f-tests.
The formula for degrees of freedom in a two-sample t-test with independent samples is -
df = (n1 - 1) + (n2 - 1)
where n1 and n2 are the sample sizes of the two groups.
Substituting n1 = 32 and n2 = 30, we get -
df = (32 - 1) + (30 - 1)
= 31 + 29
= 60
Therefore, the associated degrees of freedom is 60.
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solve the given initial-value problem. 5y'' y' = −4x, y(0) = 0, y'(0) = −15
The solution to the initial-value problem 5y'' y' = −4x is y = -4x^2 - 75e^(-x/5), and this is the function that satisfies the differential equation with the given initial conditions.
To solve the given initial-value problem, we need to use the method of undetermined coefficients to find a particular solution and the complementary solution to get the general solution.
First, we assume a particular solution of the form y₁ = Ax + B, where A and B are constants to be determined. Taking the first and second derivatives of y₁, we get y'₁ = A and y''₁ = 0. Substituting these into the differential equation, we get 5(0) + A = -4x, which gives A = -4x. Therefore, the particular solution is y₁ = -4x^2 + B.
Next, we find the complementary solution by solving the associated homogeneous differential equation, which is 5y'' + y' = 0. To solve this, we assume a solution of the form y₂ = e^(rx), where r is a constant to be determined.
Substituting this into the differential equation, we get the characteristic equation 5r^2 + r = 0, which has roots r = 0 and r = -1/5. Therefore, the complementary solution is y₂ = C1 + C2e^(-x/5).
Using the initial conditions y(0) = 0 and y'(0) = -15, we can solve for the constants B, C1, and C2. Substituting y(0) = 0 into the general solution y = y₁ + y₂, we get B + C1 = 0, which gives B = -C1.
Next, we differentiate y₁ to get y'₁ = -8x, and substitute y'(0) = -15 into the general solution y = y₁ + y₂, we get -8(0) + C2(-1/5) = -15, which gives C2 = 75.
Finally, we substitute B = -C1 and C2 = 75 into the general solution y = y₁ + y₂, we get y = -4x^2 - 75e^(-x/5).
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A college offers 2 introductory courses in history, 2 in science, 1 in mathematics, 4 in philosophy, and 2 in English.
a. If a freshman takes one course in each area during her first semester, how many course selections are possible?
b. If a part time student can afford to take only one introductory course, how many selections are possible?
Answer:
a. To find the number of possible course selections for a freshman who takes one course in each area during her first semester, we simply multiply the number of options for each area:
2 x 2 x 1 x 4 x 2 = 32
Therefore, there are 32 possible course selections.
b. To find the number of possible selections for a part-time student who can afford to take only one introductory course, we add up the number of options in each area:
2 + 2 + 1 + 4 + 2 = 11
Therefore, there are 11 possible course selections for a part-time student who can afford to take only one introductory course.
give thanks for more! your welcome!
Step-by-step explanation:
determine the boundedness and monotonicity of the sequence with an=n2n 8,n≥1.
To determine whether the sequence is bounded, we can consider its behavior as n gets larger and larger. As n increases, 2^n grows exponentially, which means that a_n will also grow exponentially. However, no matter how large n gets, there will always be a constant term of 8 added to the result, which means that the sequence will never become unbounded. In other words, the sequence is both monotonic and bounded.
To determine the boundedness and monotonicity of the sequence a_n = 2^n + 8, n≥1, we can start by considering its first few terms:
a_1 = 2^1 + 8 = 10
a_2 = 2^2 + 8 = 12
a_3 = 2^3 + 8 = 16
a_4 = 2^4 + 8 = 24
From this, we can see that the sequence is increasing, as each term is larger than the one before it. This means that the sequence is monotonic.
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How much money would be in an account after 5 years that pays 3% interest, compounded quarterly (4 times per year) if the initial investment is $750? (Round your answer to the nearest penny)
The balance in the account after 5 years with quarterly compounding at a 3% annual interest rate, starting with an initial investment of $750, would be $859.43.
To calculate the balance in the account after 5 years with quarterly compounding at a 3% annual interest rate, we can use the formula for compound interest:
[tex]A = P (1 + r/n)^(^n^t^)[/tex]
where:
A is the final amount or balance in the account
P is the initial investment or principal amount
r is the annual interest rate expressed as a decimal (3% = 0.03)
n is the number of times the interest is compounded per year (4 for quarterly)
t is the time in years
Plugging in the given values, we get:
A = $750 (1 + 0.03/4)²⁰
= $750(1.0075)²⁰
=$750×1.161
=$870.75
Hence, the balance in the account after 5 years with quarterly compounding at a 3% annual interest rate, starting with an initial investment of $750, would be $870.75
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An advertising company is purchasing a new industrial-sized color printer. The company has been approved for a $75,000 loan at two different
banks. The terms of each loan are:
Offer 1: 4.99% annual simple interest, with a total account balance of $91,529.38 after a 53-month term
Offer 2: 3.5% annual interest compounded monthly for a 62-month term
Assuming no payments are made, what is the difference in the account balances at the end of the loan terms. Round your answer to the nearest
penny.
O $1,624.49
$1,686.87
$1,894.02
O $2,207.67
The difference in the account balances at the end of the loan terms is given as follows:
$1,686.87.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for the offer 2 are given as follows:
P = 75000, r = 0.035, n = 12, t = 62/12.
Hence the balance of the offer 2 is given as follows:
B = 75000 x (1 + 0.035/12)^(12 x 62/12)
B = $89,842.51.
The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:
91529.38 - 89842.51 = $1,686.87.
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Vectors u = −2(cos 30°i + sin30°j), v = 6(cos 225°i + sin225°j), and w = 8(cos 120°i + sin120°j) are given. Use exact values when evaluating sine and cosine.
Part A: Convert the vectors to component form and find −7(u • v). Show every step of your work. (4 points)
Part B: Convert the vectors to component form and use the dot product to determine if u and w are parallel, orthogonal, or neither. Justify your answer. (6 points)
A. The required vectors to component form as: -7(u • v) = -21√(6).
B. u and w are neither parallel nor orthogonal.
Part A:
The vectors are given as:
u = −2(cos 30°i + sin30°j),
v = 6(cos 225°i + sin225°j),
w = 8(cos 120°i + sin120°j)
So we have:
u = -2(√(3)/2 i + 1/2 j) = -√(3) i - j
v = 6(-√(2)/2 i - sqrt(2)/2 j) = -√(2) i - √(2) j
w = 8(-1/2 i + √(3)/2 j) = -4i + √(3) j
To find -7(u • v), we first need to find the dot product of u and v:
u • v = (-√(3))( -√(2) ) + (-1)(-√(2)) = √(6)
Then, we can multiply by -7:
-7(u • v) = -7(√(6)) = -√(6)
Therefore, -7(u • v) = -21√(6).
Part B:
To determine if u and w are parallel, orthogonal, or neither, we can use the dot product:
u • w = (-√(3))(-4) + (-1)(4√(3)) = -8√(3)
Since the dot product is not equal to 0, we know that u and w are not orthogonal. To determine if they are parallel, we can compare their direction vectors:
The direction vector of u is < -√(3), -1 >, and the direction vector of w is < -4, 4√(3) >.
If u and w are parallel, then their direction vectors will be scalar multiples of each other.
So we need to check if there exists a scalar k such that:
< -√(3), -1 > = k < -4, 4√(3) >
This is equivalent to the system of equations:
-k × 4 = -√(3)
k × 4√(3) = -1
Solving for k, we get:
k = √(3)/12
Since k is not a real number, we know that u and w are not parallel.
Therefore, u and w are neither parallel nor orthogonal.
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Find the missing side length, n.
R
B
4
А
8
C
9
Q
n = [?]
n
S
Answer:
Without additional context or information, it's difficult to determine the missing side length with certainty. However, we can use some logical reasoning to make an educated guess.
One possible way to approach this problem is to look for relationships between the known side lengths and the missing side length. For example, we can look at the lengths of the sides that are adjacent to the missing side and see if there are any patterns or ratios that might help us determine the length of the missing side.
In this case, we can see that the missing side is adjacent to sides with lengths of 8 and 9, which have a difference of 1. If we assume that the sides of the figure form a regular pattern or sequence, then we might guess that the missing side has a length that is 1 greater than 9, which would give us a length of 10 for the missing side.
However, this is just a guess based on the limited information provided, and there could be other possible solutions depending on the specific properties or context of the figure.
Need help with geometry homework.
The area of the shaded region is 70.65 ft² and length of arc ADB is 260.
We have,
The radius of the circle is 9 ft.
The measure of ∠AOB is 100°.
So, The measure of ∠ADB
= 360 - <AOB
= 360 - 100
= 260
So, The area of the shaded region
A = ([tex]\theta[/tex]/360) πr²
A = (100/360) (3.14) (9)²
A = 70.65 ft²
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