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The 99% confidence interval for the population mean based on the given sample is (61.86, 69.94). This means that we are 99% confident that the true population mean falls within this interval.

To find the 99% confidence interval for a sample with a sample size of 68, a sample mean of 65.9, and a standard deviation of 16.5, we can use the formula for calculating the confidence interval for a population mean when the population standard deviation is known.

The formula is given by:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / sqrt(sample size))

First, we need to find the critical value corresponding to a 99% confidence level. Since the sample size is large (n = 68), we can use the Z-table or a Z-table calculator to find the critical value. For a 99% confidence level, the critical value is approximately 2.576.

Next, we can substitute the given values into the formula to calculate the confidence interval:

Confidence Interval = 65.9 ± 2.576 * (16.5 / sqrt(68))

Using a calculator or mathematical software, we can calculate the standard error of the mean:

Standard Error = standard deviation / sqrt(sample size) = 16.5 / sqrt(68) ≈ 1.997

Substituting the standard error into the formula, we have:

Confidence Interval = 65.9 ± 2.576 * 1.997

Calculating the values inside the interval, we get:

Confidence Interval = (65.9 - 2.576 * 1.997, 65.9 + 2.576 * 1.997)

Simplifying further, we have:

Confidence Interval = (61.86, 69.94)

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Answer:

The front-end ratio is calculated by dividing an individual's anticipated monthly mortgage payment by his/her monthly gross income. The mortgage payment generally consists of principal, interest, taxes, and mortgage insurance (PITI). Lenders use the front-end ratio in conjunction with the back-end ratio to determine how much to lend.

Step-by-step explanation:

Answer:

6c for the total

Answer:

8.1

Step-by-step explanation:

Subtract 2.9 to get Y alone.

11 - 2.9 = 8.1

Answer:

B.

3^4 = 81

3^2 = 9

81/9 = 9

Step-by-step explanation:

Answer: B. 9

Step-by-step explanation:

3^4-2=3²

3²=9

Answer:

C

Step-by-step explanation:

Y= MX (The Slope which is Rise/Run) minus 2 (The Y-Intercept).

Step-by-step explanation:

Factor −6 out of −6x

-6(x)+12

Factor −6 out of 12.

−6(x)−6(−2)

Factor −6 out of −6 (x)−6(−2).

-6(x-2)

Upon solving the given system of equations:

[tex]x(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * cos(2t) + (1/2) * (c_1 + e^{-t}) * sin(2t),\\y(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * sin(2t) - (1/4) * (c_1 + e^{-t}) * cos(2t)[/tex]

To solve the system of equations:

x' = 2x - 3y + 2sin(2t)

y' = x - 2y - 2cos(2t)

We can use the method of undetermined coefficients to find the particular solution. Assuming the particular solution takes the form:

[tex]x_p(t) = A sin(2t) + B cos(2t)\\y_p(t) = C sin(2t) + D cos(2t)[/tex]

Substituting these expressions into the original equations, we get:

2(A sin(2t) + B cos(2t)) - 3(C sin(2t) + D cos(2t)) + 2sin(2t) = 2sin(2t)

(A sin(2t) + B cos(2t)) - 2(C sin(2t) + D cos(2t)) - 2cos(2t) = cos(2t)

(2A - 3C + 2)sin(2t) + (2B - 3D)cos(2t) = 2sin(2t)

(A - 2C)sin(2t) + (B - 2D - 2)cos(2t) = cos(2t)

By comparing the coefficients of sine and cosine on both sides, we can equate them separately:

2A - 3C + 2 = 2

2B - 3D = 0

A - 2C = 0

B - 2D - 2 = 1

Solving these equations, we find:

A = 1

B = 3/2

C = 1/2

D = -1/4

So the particular solution is:

[tex]x_p(t)[/tex] = sin(2t) + (3/2)cos(2t)

[tex]y_p(t)[/tex] = (1/2)sin(2t) - (1/4)cos(2t)

To find the complementary solution, we solve the homogeneous system:

x' = 2x - 3y

y' = x - 2y

We can rewrite this system as a matrix equation:

X' = AX

where [tex]X = [x, y]^T[/tex] and

[tex]A = \left[\begin{array}{ccc}2&-3\\1&-2\end{array}\right][/tex]

The characteristic equation is:

det(A - λI) = 0, where I is the identity matrix. Solving this equation, we find the eigenvalues:

[tex]\lambda_1 = -1\\\lambda_2 = -1[/tex]

For each eigenvalue, we solve the corresponding eigenvector equation:

(A - λI)V = 0

For [tex]\lambda_1 = -1[/tex], we have:

[tex]\left[\begin{array}{ccc}3&-3\\1&-1\end{array}\right] * V_1 = 0[/tex]

Solving this system, we find the eigenvector:

[tex]V_1 = [1\ \ 1][/tex]

For [tex]\lambda_2 = -1[/tex], we have:

[tex]\left[\begin{array}{ccc}3&-3\\1&-1\end{array}\right] * V_2= 0[/tex]

Solving this system, we find the eigenvector:

[tex]V_2 = [3\ \ 1][/tex]

So the complementary solution is:

[tex]x_c(t) = c_1 * e^{-t} * [1\ \ 1]^T + c_2 * e^{-t} * [3\ \ 1]^T\\y_c(t) = c_1 * e^{-t} * [1\ \1]^T + c_2 * e^{-t} * [3\ \ 1]^T[/tex]

where

[tex]c_1\ and\ c_2[/tex] are arbitrary constants.

The general solution is the sum of the particular and complementary solutions:

[tex]x(t) = x_p(t) + x_c(t)\\y(t) = y_p(t) + y_c(t)[/tex]

Simplifying and combining terms, we get:

[tex]x(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * cos(2t) + (1/2) * (c_1 + e^{-t}) * sin(2t)\\y(t) = (c_1 + e^{-t}) + (3/2) * (c_2 + e^{-t}) * sin(2t) - (1/4) * (c_1 + e^{-t}) * cos(2t)[/tex]

where [tex]c_1\ and\ c_2[/tex] are arbitrary constants.

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Answer:

D. 50

Step-by-step explanation:

50-54 is 30

55-59 is 20

The surface area of the figure is 204 sq.unit.

The surface area of a three dimensional figure is the sum of area of all its faces.

Here a three dimensional figure is given and surface area has to be calculated.

The base is a cuboid

Surface Area of a cuboid = SA= 2lw+2lh+2hw

SA = 2 * 6 * 6 +2 * 6 * 3 + 2 * 6 * 3

SA = 144 sq.units

The Surface Area of the 4 triangle surface = 4 * (1/2) * base * height

SA = 2 * 6 * 5 = 60 sq.units

The total surface area = 144 +60 = 204 sq.units

Therefore the surface area of the figure is 204 sq.unit.

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Complete question :

A chef at a restaurant uses 12 pounds of butter each day. About how many grams of butter does the chef use each day? use the conversion factors 16 oz/1 lb and 28.35 grams/1oz

Answer:

5,424 grams

Step-by-step explanation:

To convert using the conversion factor :

Number of pounds of butter * (16 oz/1) * (28.35) /1

Hence,

12 * 16oz/ 1 * 28.35/1

(12 * 16 * 28)

= 5,424 grams

The estimated proportion of college students who drive stick shift cars is calculated with 90% confidence using sample data.

To estimate the proportion of college students who drive stick shift cars, we can use the sample data of 121 cars, out of which 22 have stick shifts. We will construct a confidence interval to estimate the true proportion. Using a graphing calculator, we can perform a proportion confidence interval calculation.

The calculator will take into account the sample size, the number of successes (cars with stick shifts), and the desired confidence level (90% in this case).

The resulting confidence interval will provide an estimate of the proportion of college students who drive stick shift cars. The answer should be rounded to at least three decimal places for accuracy.

This interval will represent a range within which we can be 90% confident that the true proportion of college students who drive stick shift cars lies.

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Answer:

132.5 degrees. Check to see if there is missing information in the question or any mistakes.

Step-by-step explanation:

Supplementary angles = 180 degrees

180 - 47.5 = 132.5

The 2-point backward difference formula for approximating the derivative of a function at a point x0 is graphically represented by the slope of the line connecting the points (x0 - h, f(x0 - h)) and (x0, f(x0)), where h is a positive value.

The 2-point backward difference formula is a numerical method used to approximate the derivative of a function at a specific point. To understand its graphical interpretation, consider a function f and a point x0 on its graph. The formula involves calculating the slope of a line that connects two points on the graph. The first point is (x0 - h, f(x0 - h)), which corresponds to a slightly shifted x-value from x0, denoted as x0 - h, and its corresponding y-value is f(x0 - h). The second point is (x0, f(x0)), representing the original point on the graph. The value of h is chosen to be positive, indicating that the first point is to the left of the second point. By calculating the slope of the line connecting these two points using the familiar slope formula, rise over run, we obtain an approximation of the derivative of the function at x0 using the 2-point backward difference formula.

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Answer:

I think there are about 16-20 ducks with red marks on them.

Answer:

Around 10 ducks have a red mark

Answer:

x = 26

Step-by-step explanation:

Answer:

It depends on the size of the fish tank, so this question cannot be properly answered.

Answer:It depends I can give a ratio

Step-by-step explanation:

If one tank needs 45 gallons of water and another needs 30 you will need 75 gallons of water. If your using pints or quarts you can find converter calculators

Answer:

7/24 i think i hope this helps and im right

Answer:

Independent events

Step-by-step explanation:

Given

[tex]P(A) = 0.50[/tex]

[tex]P(B)= 0.70[/tex]

[tex]P(A\ u\ B) = 0.85[/tex]

Required

Determine the relationship between the events

To do this, we simply calculate P(A n B) using:

[tex]P(A\ n\ B) = P(A) * P(B)[/tex]

and

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

So, we have:

[tex]P(A\ n\ B) = P(A) * P(B)[/tex]

[tex]P(A\ n\ B) = 0.50 * 0.70[/tex]

[tex]P(A\ n\ B) = 0.35[/tex]

and

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

[tex]P(A\ n\ B) = 0.50 + 0.70 - 0.85[/tex]

[tex]P(A\ n\ B) = 0.35[/tex]

Since: [tex]P(A\ n\ B) = P(A) * P(B)[/tex] [tex]= 0.35[/tex]

Then: the events are independent

Answer:

-4m

Step-by-step explanation:

=11m-7m-(2m+6m)

=11m-7m-8m

=-4m

plz mark me as brainliest

Answer:

-4m

Step-by-step explanation:

Hey!

==================================================================

First, We should remove the Parentheses.

To remove them, we distribute the negative over (2m + 6m).

⇒ 11m - 7m - (2m + 6m)

⇒ 11m - 7m - 2m - 6m

Work the Problem from Left to Right.

⇒ 4m - 2m - 6m

⇒ 2m - 6m

⇒ -4m

==================================================================

Hope I Helped, Feel free to ask any questions to clarify :)

Have a great day!

More Love, More Peace, Less Hate.

       -Aadi x

The statement "a - c|ab + cd if and only if a - cl ad + bc" is false. It does not hold for all values of a, b, c, and d in the set of integers.

The given statement is not true in general. To prove its falseness, we can provide a counterexample. Consider a = 2, b = 3, c = 1, and d = 4. Using these values, we have a - c = 2 - 1 = 1.

However, ab + cd = (2)(3) + (1)(4) = 10, which is not divisible by 1. On the other hand, a - cl ad + bc = 2 - (1)(2)(4) + (1)(3) = -2 + 3 = 1. Here, a - cl ad + bc equals a - c, but ab + cd does not satisfy the divisibility condition. Hence, the given statement is false.

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Answer:

ok so i can have i insteaof f too

Step-by-step explanation:

(a) The cardinality of A is 37.

The set A is defined as {2, 3, 4, 5, ..., 38}, which is a set of consecutive integers. To find the cardinality of A, we count the number of elements in the set. We can do this by subtracting the smallest element from the largest element and then adding 1:

|A| = 38 - 2 + 1 = 37

Therefore, the cardinality of A is 37.

(b) The cardinality of A is 16.

The set A is defined as the set of all complex numbers of the form a + bi, where a and b are integers such that -1 ≤ a ≤ 2 and -2 ≤ b ≤ 1. To find the cardinality of A, we count the number of elements in the set.

The set of possible values for a is {-1, 0, 1, 2}, and the set of possible values for b is {-2, -1, 0, 1}. Therefore, the set A has 4 × 4 = 16 elements.

Alternatively, we can write out all the elements in the set:

A = {-1 - 2i, -1 - i, -1, -1 + i, 0 - 2i, 0 - i, 0, 0 + i, 1 - 2i, 1 - i, 1, 1 + i, 2 - 2i, 2 - i, 2, 2 + i}

Therefore, the cardinality of A is 16.

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Answer:

3 seconds

Step-by-step explanation:

Complete question:

An object is dropped from a bridge and allowed to freefall to the ground. The height of the object over time can be modeled using h(t)=144-16t2. How many seconds will it take the object to reach the ground? 2 seconds 3 seconds 9 seconds 16 seconds

Given the height of an object modelled by the expression;

h(t)=144-16t²

The object will reach the ground when h(t) = 0

Substitute into the formula

0 = 144 - 16t²

-144 = -16t²

144 = 16t²

Swap

16t² = 144

t² = 144/16

t² = 9

Square root both sides

√t² = ±√9

t = ±3secs

Since the time cannot be negative, hence the object will reach the ground 3 seconds after

Answer:

4.997

Step-by-step explanation:

Answer:

[tex]w = \frac{93}{40} [/tex]

Answer:

87.75

Step-by-step explanation:

You are correct

Answer:

15.3125

Step-by-step explanation:

i gotchu

Answer:

no it does not show a fucntion