Question 4 (10 marks) Respondents to a Pew survey in 2013 who owned mobile phones were asked whether they had, in the past 30 days, looked up the price of a product while they were in a store to see if they could find a better price somewhere else. Below is a table of their responses by income level (now split into two categories only). a) The above table is an example of secondary data. If interest were simply in the use of mobiles to look up prices (without involving income levels), what is the proportion of people in the survey who did? [1 mark] b) Using Excel, provide a clustered bar chart involving the variables LookUp and Income. Without quoting any percentages, what does this chart suggest? [2 marks] c) Use Excel to conduct the appropriate formal hypothesis test, at the 5% significance level, of whether Income is related to LookUp. Apply the ste that were outlined in the notes to obtain the p-value. [7 marks]

To find the volumes of the solids generated by revolving the region between the curves y = √(4x) and y = x^2/8 about the x-axis and y-axis, we can use the disk or washer method.

a) Volume about the x-axis:

The curves intersect at x = 0 and x = 16. We can set up the integral to find the volume as follows:

V = π∫[0,16] [(r(x))^2 - (R(x))^2] dx

where r(x) is the radius of the inner curve y = √(4x) and R(x) is the radius of the outer curve y = x^2/8.

r(x) = √(4x) and R(x) = x^2/8, so we have:

V = π∫[0,16] [(√(4x))^2 - (x^2/8)^2] dx

= π∫[0,16] [4x - (x^4/64)] dx

= π[2x^2 - (x^5/80)]|[0,16]

≈ 1853.7 cubic units (rounded to one decimal place)

b) Volume about the y-axis:

The curves intersect at x = 0 and x = 16. We can set up the integral to find the volume as follows:

V = π∫[0,4] [(r(y))^2 - (R(y))^2] dy

where r(y) is the radius of the inner curve x = √(y/4) and R(y) is the radius of the outer curve x = 2√y.

r(y) = √(y/4) and R(y) = 2√y, so we have:

V = π∫[0,4] [(√(y/4))^2 - (2√y)^2] dy

= π∫[0,4] [y/4 - 4y] dy

= π[-(15/4)y^2]|[0,4]

= 15π cubic units

Therefore, the volume of the solid generated by revolving the region between y = √(4x) and y = x^2/8 about the x-axis is approximately 1853.7 cubic units (rounded to one decimal place), and the volume of the solid generated by revolving the region about the y-axis is 15π cubic units.

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The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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A) Required exponential function, constant ratio and y intercept of [tex]-2×3^{(x-1)}[/tex] are [tex]y = -2(3)^x[/tex], 3 and (-2) respectively.

B) Required exponential function, constant ratio and y intercept of [tex]45×2^{(x-1)}[/tex] are [tex]y = 45(2)^x[/tex], 2 and 45 respectively.

C) Required exponential function, constant ratio and y intercept of [tex]1234 × 0.1^{(x-1)}[/tex] are [tex]y = 1234(0.1)^x[/tex], 0.1 and 1234 respectively.

D) Required exponential function, constant ratio and y intercept of [tex]-5. ( \frac{1}{2} ) ^{(x-1)}[/tex]

are [tex]y = -5( \frac{1}{2} )^x[/tex]

, (1/2) and (-5) respectively.

What is the general form of exponential function?

An exponential function has the form

[tex]y = a(b)^x[/tex], where 'a' is the y-intercept and 'b' is the constant ratio.

A) Given explicit formula is [tex]-2×3^{(x-1)}[/tex].

We need to rewrite this as y = a(b)^x for find the exponential function.

Here we notice that 3 is the base of the exponent, so we can write it as 3 = 3¹.

Then, we can use the rules of exponents to rewrite the expression as [tex]-2×3^{(x-1)} = -2(3^1)^{(x-1)} = -2(3^{(x-1)})[/tex]

This gives us a = -2 and b = 3.

Therefore, the exponential function is [tex]y = -2(3)^x[/tex], and the constant ratio is 3, while the y-intercept is -2.

B) The explicit formula is [tex]45×2^{(x-1)}[/tex]

We can rewrite this as [tex]45×2^{(x-1)} = 45(2^1)^{(x-1)} = 45(2^{(x-1)})[/tex]

This gives us a = 45 and b = 2. Therefore, the exponential function is [tex]y = 45(2)^x[/tex], and the constant ratio is 2, while the y-intercept is 45.

C) The explicit formula is [tex]1234 × 0.1^{(x-1)}[/tex]

We can rewrite this as [tex]1234 × 0.1^{(x-1)} = 1234(0.1^1)^{(x-1)} = 1234(0.1^{(x-1)})[/tex]

This gives us a = 1234 and b = 0.1.

Therefore, the exponential function is [tex]y = 1234(0.1)^x[/tex], and the constant ratio is 0.1, while the y-intercept is 1234.

D) The explicit formula is [tex]-5. ( \frac{1}{2} ) ^{(x-1)}[/tex].

We can rewrite this as [tex]-5. ( \frac{1}{2} ) ^{(x-1)} = -5( (\frac{1}{2}) ^1)^{(x-1)} = -5(( \frac{1}{2}) ^{(x-1)})[/tex]

This gives us a = -5 and b = 1/2.

Therefore, the exponential function is

[tex]y = -5( \frac{1}{2} )^x[/tex], and the constant ratio is 1/2, while the y-intercept is -5.

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We can conclude that for x < -7/5, f(x) is increasing, and for x > -7/5,

f(x) is decreasing.

First, we need to find the critical value of the function f(x), which is where

its derivative equals zero or does not exist.

To find the derivative of f(x), we can use the power rule and the chain

rule:

f'(x) = 3(7 + 5x)2 × 5 = 15(7 + 5x)2

Setting this equal to zero and solving for x, we get:

15(7 + 5x)2 = 0

7 + 5x = 0

x = -7/5

So the critical value of f(x) is x = -7/5.

To determine the behavior of f(x) around this critical value, we can use

the first derivative test.

For x < -7/5, f'(x) < 0, which means that f(x) is decreasing.

For x > -7/5, f'(x) > 0, which means that f(x) is increasing.

Therefore, the critical value at x = -7/5 is a local minimum.

For x < -7/5, f(x) is decreasing from positive values to the local minimum

at (-7/5, f(-7/5)).

For x > -7/5, f(x) is increasing from the local minimum at (-7/5, f(-7/5)) to

positive values.

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The correction factor for the adjacent side of a right triangle is the cosine of the given angle (θ)

To find the correction factor for the adjacent side of a right triangle, you need to use the concept of trigonometric ratios. In a right triangle, the correction factor for the adjacent side can be found using the cosine ratio.

Step 1: Identify the given angle (θ) and the hypotenuse length (H).
Step 2: Use the cosine ratio formula: Cos(θ) = Adjacent Side / Hypotenuse (H)
Step 3: Solve for the adjacent side: Adjacent Side = Cos(θ) * Hypotenuse (H)

The correction factor for the adjacent side of a right triangle is the cosine of the given angle (θ). By multiplying the cosine of the angle with the hypotenuse length, you can find the length of the adjacent side.

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lim (5/n) - 3n gives us a limit of negative infinity. lim n tan A-100 - 00 evaluates to negative infinity.

(a) To find the limit of lim (5/n) - 3n as t approaches 400, we can first simplify the expression by combining the two terms using a common denominator:

lim [(5 - 3n^2) / (n)] as n approaches 400

Now we can apply L'Hopital's rule by taking the derivative of the numerator and denominator with respect to n:

lim [-6n / 1] as n approaches 400

This gives us a limit of -2400.

For the limit of lim (2/n) - 4n as n approaches infinity, we can once again combine the terms and simplify:

lim [(2 - 4n^2) / n] as n approaches infinity

Applying L'Hopital's rule again:

lim [-8n / 1] as n approaches infinity

This gives us a limit of negative infinity.

(b) To find the limit of lim 24/*, we need to know what the denominator approaches. If the denominator approaches 0, then the limit will be infinity or negative infinity depending on the sign of the numerator. If the denominator approaches a finite number, then the limit will be 0. Without more information, we cannot determine the value of this limit.

(c) To find the limit of lim n tan(A-100) as A approaches 0, we can use the fact that tan(x) approaches 0 as x approaches 0:

lim n tan(A-100) = lim n (tan(A) - tan(100)) as A approaches 0

Using the tangent subtraction formula, we can simplify this expression:

lim n [(tan(A) - tan(100)) / (1 + tan(A) tan(100))] as A approaches 0

Now we can use the fact that tan(x) approaches 0 faster than any power of x:

lim n [(tan(A) - tan(100)) / (tan(A) tan(100))] as A approaches 0

Simplifying further:

lim [-n / tan(100)] as A approaches 0

Since tan(100) is a constant, the limit evaluates to negative infinity.

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The sum of the number of operations needed to LU-decompose a general n x n matrix, including multiplications, divisions, additions, and subtractions, is given by:

(C) [tex]\frac{2}{3 }n^3 + \frac{n^2}{2 }- \frac{7}{6n}[/tex]

Lower-upper (LU) decomposition, sometimes referred to as matrix factorization or lower-upper decomposition, is a technique used in linear algebra to break down a square method into the product of a lower and an upper triangular matrix. Numerous techniques, including Gaussian elimination, Crout's algorithm, Doolittle's algorithm, and Cholesky's decomposition, can be used to perform LU decomposition. It is used to solve the system of equations.

The sum of the number of operations needed to LU-decompose a general n x n matrix, including multiplications, divisions, additions, and subtractions, is given by:
(C) [tex]\frac{2}{3 }n^3 + \frac{n^2}{2 }- \frac{7}{6n}[/tex]

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We can use an F-test to determine if there is evidence of a difference in variation between the two populations. The null hypothesis is that the variances of the two populations are equal, and the alternative hypothesis is that they are not equal. We can calculate the F-test statistic as:

F = s1^2 / s2^2

where s1^2 and s2^2 are the sample variances for the two groups. We can then compare this to the F-distribution with (n1-1) and (n2-1) degrees of freedom.

Using the data given, we have:

n1 = 6

n2 = 8

s1^2 = 6.505

s2^2 = 5.811

So, our F-test statistic is:

F = s1^2 / s2^2 = 1.119

Using an F-table or calculator with (5,7) degrees of freedom, we find the critical value of F for a 0.10 significance level to be 3.11.

Since our calculated F-value (1.119) is less than the critical value (3.11), we fail to reject the null hypothesis. There is not enough evidence to suggest a difference in the variation of the cracking torsion moments between the two types of T-beams. (1.119) is less than the critical value (3.11), we fail to reject the null hypothesis. There is not enough evidence to suggest a difference in the variation of the cracking torsion moments between the two types of T-beams.

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The arc length of the partial circle is 2.5π or approximately 7.85 units.

An arc is a part of a curved line that is a continuous portion of the curve. In geometry, an arc is often used to describe a section of a circle's circumference. It is defined as a portion of a circle's circumference, or any other curved line, that is a continuous part of the curve.

The arc length of a partial circle with radius 5 and angle 90 degrees can be found using the formula:

Arc length = (angle/360) x 2πr

where r is the radius of the circle.

Substituting the given values, we get:

Arc length = (90/360) x 2π(5)

Arc length = (1/4) x 2π(5)

Arc length = (1/2)π(5)

Arc length = 2.5π

Therefore, the arc length of the partial circle is 2.5π or approximately 7.85 units.

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Answer:

you would take 10 and divide that by 16 to get .63, so you take .63 and minus that from 100 and you get 37. so the officer had a 37% decrease.

Step-by-step explanation:

The derivative of the function is h'(z) = -e^(-z)

Given data ,

Let the function be represented as h ( z )

Now , the value of h ( z ) is

h(z) = e^(-2z/2)

To find the derivative of h(z) with respect to z, we can use the chain rule. The derivative of e^u, where u is a function of z, is given by e^u * du/dz.

In this case, u = -2z/2, so du/dz = -2/2 = -1. Therefore, we have:

h'(z) = e^(-2z/2) * (-1).

On further simplification , we get

h'(z) = -e^(-z)

Hence , the derivative of the function is h'(z) = -e^(-z)

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Supposing that W and are random variables, The correct answer is D. 72‾‾‾√.

We know that V(W) = 8, which means that the variance of the random variable W is 8. We also know that X = -3W + 2, which means that X is a linear combination of W.

To find the variance of X, we can use the following property:

Var(aW + b) = a^2 Var(W)

where a and b are constants.

Using this property, we can find the variance of X as follows:

Var(X) = Var(-3W + 2)

= 9 Var(W) (since a = -3)

= 9 * 8 (since Var(W) = 8)

= 72

So we have found that Var(X) = 72.

The standard deviation of X, denoted by (), is the square root of the variance of X. Therefore, we have:

() = sqrt(Var(X))

= [tex]\sqrt{72}[/tex]

= [tex]\sqrt{36 * 2}[/tex]

= [tex]\sqrt{36} *\sqrt{2}[/tex]

= [tex]6 * \sqrt{2}[/tex]

= 4.24 (rounded to two decimal places)

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The test statistic, z, for the hypothesis test H0: p = 0.17 versus Ha: p > 0.17 is approximately 2.76.

1. Calculate the sample proportion (p-hat) by dividing the number of over-filled bags by the total number of bags: p-hat = 26/91 ≈ 0.286.
2. Calculate the standard error (SE) using the formula SE = sqrt[(p(1-p))/n], where p is the assumed proportion (0.17) and n is the sample size (91): SE ≈ sqrt[(0.17(1-0.17))/91] ≈ 0.0367.
3. Calculate the test statistic (z) using the formula z = (p-hat - p)/SE: z = (0.286 - 0.17)/0.0367 ≈ 2.76.

The test statistic z is approximately 2.76, indicating that the observed proportion of over-filled bags is 2.76 standard errors above the assumed proportion of 0.17.

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To construct the 90% confidence interval, we need to first find the sample mean and standard deviation of the increase in customers using the program for the 10 stores. Let's assume that the increase in customers is normally distributed.

Next, we can use a t-distribution to calculate the confidence interval since the sample size is small (n = 10). We use a t-distribution with 9 degrees of freedom since we are estimating the population mean from a sample.

The formula for the confidence interval is:

sample mean ± t-value x (sample standard deviation / square root of sample size)

Since we want a 90% confidence interval, we need to find the t-value with a 5% tail on each end of the distribution. From a t-distribution table or calculator with 9 degrees of freedom, the t-value for a 5% tail is approximately 1.833.

Let's say the sample mean increase in customers using the program for the 10 stores is 50, and the sample standard deviation is 10.

Plugging in the values, we get:

50 ± 1.833 x (10 / √10)

Simplifying the expression, we get:

50 ± 6.05

Therefore, the 90% confidence interval is (43.95, 56.05). This means we can be 90% confident that the true mean increase in customers using the program for all stores falls between 43.95 and 56.05.

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1. Instantaneous velocity: The derivative of the height function s(t) with respect to time t gives the instantaneous velocity v(t) = ds/dt = -9.8t.

2. Average velocity: Calculate the average velocity by dividing the change in height by the change in time.
Average velocity = (s(9) - s(0)) / (9 - 0) = (178.2 - 300) / 9 = -13.53 m/s

3. Find the time t when instantaneous velocity equals average velocity:
t = 13.53 / 9.8 ≈ 1.38 seconds
Thus, the instantaneous velocity equals the average velocity at approximately 1.38 seconds during the first 9 seconds of the fall.

To find the time during the first 9 seconds of fall at which the instantaneous velocity equals the average velocity, we need to first find the average velocity.

The average velocity of the object during the first 9 seconds can be found by calculating the displacement (change in height) divided by the time taken:

Average velocity = (s(9) - s(0)) / 9
                = (-4.912(9)^2 + 300 - (-4.912(0)^2 + 300)) / 9
                = (-393.768 + 300) / 9
                = -11.9747 m/s (rounded to 4 decimal places)

Now we need to find the time during the first 9 seconds at which the instantaneous velocity equals -11.9747 m/s.

The instantaneous velocity of the object at any time t can be found by taking the derivative of s(t):

v(t) = s'(t) = -9.824t

We want to find the time t during the first 9 seconds at which v(t) = -11.9747 m/s.

-9.824t = -11.9747
t = 1.2195 seconds (rounded to 4 decimal places)

Therefore, the time during the first 9 seconds of fall at which the instantaneous velocity equals the average velocity is 1.2195 seconds.

Answer: 1.2195 seconds.

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Answer:

|n - 1| + 1 = 0

|n - 1| = -1

no solution

The sum of the finite power series is [tex]\frac{x^7-x^{11}}{1-x}[/tex]

Given is a finite series with 4 terms,

5x⁷ + 5x⁸ + 5x⁹ + 5x¹⁰

The sum of the finite power series is = qᵃ - qᵇ⁺¹ / 1-q

Here, q = x, a = 7, b = 10

So, the sum = x⁷ - x¹⁰⁺¹ / 1-x =  [tex]\frac{x^7-x^{11}}{1-x}[/tex]

Hence, the sum of the finite power series is [tex]\frac{x^7-x^{11}}{1-x}[/tex]

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Rounded to the nearest tenth of a meter, the height of the 14th bounce is 0.1 m.

Bounce is a marketing term that refers to a user's interaction with a website, email, or advertisement. It is commonly used to describe when a user leaves a page without taking any action. This could be due to not finding what they were looking for, being distracted, or not being interested in the content or product. Bounce rate is the percentage of visitors who leave a website without taking any action. It is typically used to measure the effectiveness of a website's design, content, and overall user experience.

The heights of the first three bounces are 600 m, 150 m, and 37.5 m, respectively. This means that the height of the 13th bounce is:
37.5 m x (1/4)¹¹ = 0.00244 m
Therefore, the height of the 14th bounce is:
0.00244 m x (1/4) = 0.00061 m
Rounded to the nearest tenth of a meter, the height of the 14th bounce is 0.1 m.

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The average production level over the region R is approximately 1519.31 units.

To find the average production level, we need to calculate the total

production level over the region R and divide it by the area of R.

The region R is defined by x ranging from 10 to 50 and y ranging from 20

to 40. So, we have:

R = {10 ≤ x ≤ 50, 20 ≤ y ≤ 40}

The total production level over R is given by:

Pavg = 1/A ∬R P(x,y) dA

where dA = dx dy is the area element and A is the area of the region R.

We can evaluate the integral by integrating first with respect to x and then with respect to y:

Pavg = [tex]1/A \int 20^{40} \int 10^{50} P(x,y) dx dy[/tex]

Pavg =[tex]1/A \int 20^{40} \int 10^50 500x^0.2y^0.8 dx dy[/tex]

Pavg =[tex]1/A (500/0.3) \int 20^{40} [x^0.3y^0.8]10^{50} dy[/tex]

Pavg =[tex](500/0.3A) \int 20^{40} [(50^0.3 - 10^0.3)y^0.8] dy[/tex]

Pavg =[tex](500/0.3A) [(50^0.3 - 10^0.3)/0.9] ∫20^{40} y^0.8 dy[/tex]

Pavg =[tex](500/0.3A) [(50^{0.3} - 10^{0.3})/0.9] [(40^{1.8 }- 20^{1.8})/1.8][/tex]

Pavg ≈ 1519.31

Therefore, the average production level over the region R is

approximately 1519.31 units.

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The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of descriptive statistics.

This is an example of descriptive statistics. Descriptive statistics involves the collection, organization, and summarization of data to describe the characteristics of a population or sample. In this case, the data collected pertains to the employees of a particular firm. On the other hand, inferential statistics involves making inferences and drawing conclusions about a larger population based on data collected from a sample.

Descriptive statistics is the branch of statistics that deals with the collection, analysis, interpretation, and presentation of data.

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To solve the system of equations 15 - 3x + y = -15 and 3 (which I assume is the value of the second equation), we can start by simplifying the first equation:

15 - 3x + y = -15
y - 3x = -30

Now we can substitute the value of 3 for the second equation into the simplified first equation:

y - 3x = -30
y - 9 = -30
y = -21

So we have solved for y, and now we can substitute this value back into either of the original equations to solve for x:

15 - 3x + y = -15
15 - 3x - 21 = -15
-3x = 21
x = -7

Therefore, the solution to the system is (x, y) = (-7, -21).

Since there is only one solution, we do not have infinitely many solutions, and we do not need to write a general form of the solution.

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The nurse needs a sample size of 12 infants to be 95% confident that the true mean is within 4 ounces of the sample mean, given a standard deviation of 7 ounces.

To estimate the required sample size for the nurse's study, we can use the following formula for a known standard deviation:

n = (Z × σ / E)²

Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (1.96 for 95% confidence)
σ = standard deviation (7 ounces)
E = margin of error (4 ounces)

Plugging in the values:

n = (1.96 × 7 / 4)²
n ≈ (3.43)²
n ≈ 11.77

Since we cannot have a fraction of a sample, we round up to the nearest whole number.

Therefore, the nurse needs a sample size of 12 infants to be 95% confident that the true mean is within 4 ounces of the sample mean, given a standard deviation of 7 ounces.

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The statements with the properties of the parallelogram are

Given that

ABCD is a parallelogram

As a general rule of parallelogram, opposite sides are equal

So, we have

AB = CD and AC = BC

Also, opposite angles are congruent

So, we have

∠A ≅ ∠C and ∠B ≅ ∠D

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At the 5% level of significance, we cannot conclude that there is a significant difference in mean household debt between Regina and Saskatoon households. The z-score of 1.51 is below the critical value of 1.96, which means we fail to reject the null hypothesis.

Based on the calculated z-score of 1.51 and a significance level of 5%, we can conclude that there is not enough evidence to reject the null hypothesis. In other words, we cannot conclude that there is a significant difference in mean household debt between Regina and Saskatoon households.
At the 5% level of significance, we cannot conclude that there is a significant difference in mean household debt between Regina and Saskatoon households. The z-score of 1.51 is below the critical value of 1.96, which means we fail to reject the null hypothesis.

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dt/dw = (t^2 + 2) / 8t

(a) Using the Chain Rule, we have:

dw/dt = dw/dx * dx/dt + dw/dy * dy/dt

Since w = ln(x^2 + y), we have:

dw/dx = 2x / (x^2 + y)

dw/dy = 1 / (x^2 + y)

And since x = 2t and y = 4, we have:

dx/dt = 2

dy/dt = 0

Substituting these into the formula, we get:

dw/dt = [2x / (x^2 + y)] * 2 + [1 / (x^2 + y)] * 0

= 4x / (x^2 + y)

= 4(2t) / [(2t)^2 + 4]

= 8t / (t^2 + 2)

So dw/dt = 8t / (t^2 + 2).

(b) We have w = ln(x^2 + y), so we can substitute x = 2t and y = 4 to get:

w = ln((2t)^2 + 4)

= ln(4t^2 + 4)

Now we can differentiate with respect to t using the Chain Rule for logarithmic functions:

dw/dt = d/dt [ln(4t^2 + 4)]

= 1 / (4t^2 + 4) * d/dt [4t^2 + 4]

= 1 / (4t^2 + 4) * (8t)

= 8t / (4t^2 + 4)

Simplifying, we get:

dw/dt = 2t / (t^2 + 1)

To find dt/dw, we can solve for dt/dw in terms of dw/dt:

dt/dw = 1 / (dw/dt)

= (t^2 + 2) / 8t

So dt/dw = (t^2 + 2) / 8t

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The probability of event A given that event B has occurred is equal to the probability of event A, which is 0.7.

If A and B are independent events, then the occurrence of event B does not affect the probability of event A. Therefore, we can use the formula for conditional probability, P(A|B) = P(A ∩ B) / P(B), to calculate the probability of event A given that event B has occurred.

However, since A and B are independent, we know that P(A ∩ B) = P(A) x P(B), which gives us:

P(A | B) = P(A ∩ B) / P(B) = (P(A) x P(B)) / P(B) = P(A) = 0.7

This makes sense because the independence of A and B implies that knowing the outcome of event B does not provide any additional information about the probability of event A.

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Using hypothesis tests the 90% confidence interval is the true mean number of minutes that Minnesotans watch a sporting event on TV each week falls within the range of 152.342 to 157.658 minutes.

We're given a random sample of 300 Minnesotans, where X = 155 minutes and s = 28 minutes. We want to find a 90% confidence interval for the true mean number of minutes that Minnesotans watch a sporting event on TV each week.

First, we need to calculate the standard error (SE) using the formula: SE = s / √(n), where n is the sample size. Plugging in our values, we get SE = 28 / √(300) = 1.617.

Next, we need to find the critical value for a 90% confidence level using a t-distribution table with degrees of freedom (df) = n - 1 = 299. For a 90% confidence level and 299 df, the critical value is approximately 1.645.

Now we can calculate the margin of error (ME) using the formula: ME = critical value × SE. Plugging in our values, we get ME = 1.645 × 1.617 = 2.658.

Finally, we can construct the confidence interval using the formula: CI = X ± ME. Plugging in our values, we get CI = 155 ± 2.658, which simplifies to (152.342, 157.658).

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Answer:

Step-by-step explanation:

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We get: y = (-1/3)x + 4

To find the equation of the tangent line to the curve xyz - x^2y = -6 at the point (3,1), we need to first find the derivative of the curve. Using the product rule and chain rule, we get:

dy/dx = (xz - 2xy) / (xz - x^2)

To find the slope of the tangent line at (3,1), we substitute x=3 and y=1 into the derivative:

dy/dx = (3z - 2) / (3z - 9)

At (3,1), we have xyz - x^2y = -6, so substituting x=3 and y=1 gives us:

3z - 9 = -6

Solving for z, we get z = 1. From the derivative, we get:

dy/dx = (3 - 2) / (3 - 9) = -1/3

So the slope of the tangent line at (3,1) is -1/3. To find the equation of the tangent line, we use the point-slope form:

y - y1 = m(x - x1)

Plugging in (3,1) and -1/3 for m, we get:

y - 1 = (-1/3)(x - 3)

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