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To prove the statement, we need to show that the limit of the integral tends to zero as n approaches infinity:

[tex]Lim(n→∞) ∫[0,1] [f(x)]^n dx = 0[/tex]

Given that f(x) is a strictly increasing continuous function on the interval [0,1], we can make use of the properties of such functions to prove the statement.

Additionally, [f(x)]^n  increases positive integer and is continuous on the interval [0,1] because it is a composition of continuous functions (f(x) and the power function).

[tex]∫[0,1] [f(x)]^n dx[/tex]

Integrating this inequality over the interval [0,1], we have:

[tex]0 ≤ ∫[0,1] [f(x)]^n dx ≤ ∫[0,1] 1 dx0 ≤ ∫[0,1] [f(x)]^n dx ≤ 1[/tex]

0 and 1 are for the positive integer n

Now, as n approaches infinity, we can apply the squeeze theorem. Since the integral is bounded between 0 and 1, and both 0 and 1 approach zero as n tends to infinity, the limit of the integral must also be zero:

[tex]Lim(n→∞) ∫[0,1] [f(x)]^n dx = 0[/tex]

Therefore, we have proven that the limit of the integral as n approaches infinity is zero:

[tex]1 lim(n→∞) ∫[0,1] [f(x)]^n dx = 0[/tex]

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The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

y = 3x + 4 ---(2)

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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Correct Question is:

A car company charges x dollars to rent a car plus extra options as shown in table.

Car seat = 50 $

Insurance = 75 $

Car Wash = 15 $

Three people each rented a car with insurance and one more person rented a car with a car wash. What is the expression for the total cost?

Step-by-step explanation:

3 people rented with insurance = (x + 75) * 3) = 3x +225

one person rented with car wash = (15+x)

Total car rental will be adding both equations = 3x +225 + 15 + x = 4x + 240

Answer:

4x plus 20y

Step-by-step explanation:

4 times x  plus 20xy

4x plus 20y

Answer:

Step-by-step explanation:

X-intercept means y-coordinate of 0:

4x +7×0 = 28

 4x = 28

   x = 7         ← x-coordinate

Y-intercept means x-coordinate of 0:

4×0 +7y = 28

 7y = 28

   y = 4         ← y-coordinate

Each seat on the ferris wheel is at an angle of 24 degrees.

To determine the angle of each seat on a ferris wheel with 15 seats, we can use the concept of angles in a circle.

A circle has a total of 360 degrees. Since the ferris wheel has 15 seats evenly spaced around the circumference, we can divide 360 degrees by 15 to find the angle of each seat.

The calculation is as follows:

360 degrees ÷ 15 seats = 24 degrees per seat.

To visualize this, imagine drawing a circle and dividing it into 15 equal parts. Each part would represent a seat on the ferris wheel, and the angle between each part would be 24 degrees.

Note: The assumption here is that the seats are evenly spaced around the circumference of the ferris wheel. In practice, some ferris wheels may have seats arranged differently, so the angle per seat may vary.

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Answer:

x = 13y + 0.625

Step-by-step explanation:

4(2x - 3y) = y + 5

8x - 12y = y + 5

8x = y + 5 + 12y

8x = 5 + 13y

8x ÷ 8 = 5 + 13y ÷ 8

x = 5 + 13y ÷ 8

x= 13y + 5 ÷8

x = 13y + 0.625

A:  The alternative hypothesis is that the population mean is not equal to the specified value

B: p-value for a two-tailed test with a t-value of 0.9945 is 0.3739.

C: 95% confidence that the true population mean falls within the range of 6.0172 to 11.6970

A. The null hypothesis is that the population mean is equal to a specified value (μ = specified value), and the alternative hypothesis is that the population mean is not equal to the specified value (μ ≠ specified value).

B. To perform the hypothesis test,

we first need to calculate the sample mean and standard deviation.

Since we have,

Sample size (n) = 7

Sample mean (X) = (13+9+10+5+10+7+9) / 7 = 8.8571

Sample standard deviation (s) = 2.1561

Using the formula for the one-sample t-test, we get,

⇒ t = (X- μ) / (s / √(n))

Assuming the specified value is 8, then we have,

⇒ t = (8.8571 - 8) / (2.1561 / √(7))

⇒ t = 0.9945

Using a t-distribution table with 6 degrees of freedom (df = n - 1),

we find that the p-value for a two-tailed test with a t-value of 0.9945 is 0.3739.

C. Based on this test, we cannot reject the null hypothesis that the true population mean is equal to 8 at a 5% level of significance since the p-value (0.3739) is greater than the significance level (0.05).

Therefore, we do not have enough evidence to conclude that the population mean is different from 8. In other words, we can state with 95% confidence that the true population mean falls within the range of 6.0172 to 11.6970.

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Answer:

C

Step-by-step explanation:

CHOOSE C

Answer:

The answer of the function is y=x-5

Step-by-step explanation:

Area of Rectangle = Length x Width

Area of Top Rectangle =

[tex]22 \times (31 - 18) \\ = 22 \times 13 \\ = 286 {ft}^{2} [/tex]

Area of bottom Rectangle =

[tex]18 \times 9 \\ = 162 {ft}^{2} [/tex]

Area of Composite figure = Area of top Rectangle + Area of bottom rectangle

[tex] = 286 + 162 \\ = 448 {ft}^{2} [/tex]

Answer:

x = 7.98ft or x = 8ft

Step-by-step explanation:

Hope that helps :)

Assume all of the statistics used have a normal sampling distribution. Use 3 decimal places. Below are the steps of calculation:(a) For a 98% confidence interval for a population mean based on n = 11 observations with known: We know that margin of error formula = Zα/2 σ/√n, Where Zα/2 is the quantile of the normal distribution at α/2, σ is the population standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and Zα/2 = 2.326. The sample size is small, and therefore we assume a normal distribution. Using the formula above, we obtain: margin of error = Zα/2 σ/√n = 2.326 σ/√11(b) For a 98% confidence interval for a population mean based on n = 11 observations with unknown. We know that margin of error formula = tα/2 s/√n. Where tα/2 is the quantile of the t-distribution at α/2, s is the sample standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and tα/2 = 2.718. The sample size is small, and therefore we assume a normal distribution.

Using the formula above, we obtain: margin of error = tα/2 s/√n = 2.718 s/√11(c) For a 90% confidence interval for a population proportion, p, based on n = 11 observations. We know that margin of error formula = Zα/2 √((p(1-p))/n)Where Zα/2 is the quantile of the normal distribution at α/2, n is the sample size, and p is the sample proportion. In this case, α = 0.1, n = 11 and Zα/2 = 1.645.Using the formula above, we obtain: margin of error = Zα/2 √((p(1-p))/n) = 1.645 √((p(1-p))/11)(d) For a 92% confidence interval based on n = 14 observations for the slope parameter. We know that margin of error formula = tα/2 * SE. Where tα/2 is the quantile of the t-distribution at α/2, and SE is the standard error of the estimate. In this case, α = 0.08, n = 14 and tα/2 = 1.771.

Using the formula above, we obtain: margin of error = tα/2 * SE = 1.771 * SE. Therefore, the correct quantile for the margin of error of each confidence interval is as follows:(a) 2.670(b) 2.570(c) 0.512(d) 1.564.

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Answer: Your Answer would be A

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

Percent increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

Increase = $27 - $15 = $12 , then

percent increase = [tex]\frac{12}{15}[/tex] × 100% = 0.8 × 100% = 80%

Step-by-step explanation:

Percentage Increase = Amount of Increase/ Orginal Amount x 100%

27-15= 12

$12= Amount of Increase

Percentage Increase= 12/15 x 100

                                  = 80% increase in stock price

Hope this Helps

The 95% confidence interval to estimate the average beer consumption per cruise is from 79,440 bottles to 83,662 bottles.

The only assumption needed is that the population follows the Student's t-distribution; option B.

a. Construct a 95% confidence interval:

The formula for a confidence interval, CI, for the population mean (μ) is:

CI = sample mean ± (critical value * standard error)

Given:

Sample mean (x) = 81,551 bottles

Sample standard deviation (s) = 4,572 bottles

Sample size (n) = 15

Confidence level = 95%

With a confidence level of 95% and 15 degrees of freedom (n - 1), the critical value from the t-distribution is approximately 2.131.

Standard error (SE) = s / √n

SE = 4572 / √15

Lower limit of the confidence interval = x - (critical value * SE)

Upper limit of the confidence interval = x + (critical value * SE)

The confidence interval:

Lower limit = 81551 - (2.131 * (4572 / √15))

Upper limit = 81551 + (2.131 * (4572 / √15))

Lower limit ≈ 79440 bottles

Upper limit ≈ 83662 bottles

b. Assumptions about the population:

The only assumption needed is that the population follows the Student's t-distribution. This assumption is required when the population standard deviation is unknown, and we use the sample standard deviation as an estimate.

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Answer:

The answer is 5x - 13

Step-by-step explanation:

All we do is add the x's and the other numbers.

2 + 3 = 5 and 10 + 3 = 13

So, the equation is 5x - 13

Hope this helps! :)

Answer:

24cm

Step-by-step explanation:

Assuming sides AC and BC are equivalent:

AC = 3cm + 9cm = 12cm

BC = AC = 12cm

AB = 3cm + 3cm = 6cm

AB + BC + AC = 12cm + 12cm + 6cm = 24cm

Answer:

30

Step-by-step explanation:

30

Answer: `h² + 18h + 108`

We have to evaluate the difference quotient of the formula `f(x) when `f(6+ h)?

f(6)` and the expression will be simplified by dividing it by 'h.'

Difference quotient:

The difference quotient is a formula used to find the average rate of change of a function over a specific interval. The difference quotient is defined as:```f(x + h) - f(x) / h```

To find the difference quotient for f(x) = x³, we need to substitute the values as shown below:

f(x + h) = (6 + h)³f(x) = 6³f(x + h) - f(x) = (6 + h)³ - 6³

Now we can substitute these values in the formula of the difference quotient :

'f (6+ h). f(6)`h = (6 + h)³ - 6³ - h/ h

By simplifying the difference quotient we get;`

(6 + h)³ - 6³ - h/ h = (6³ + 3 * 6²h + 3 * 6h² + h³ - 6³) / h`

After simplifying the expression above, the terms 6³ and -6³ cancel out.

We can then combine the like terms (3 * 6²h and 3 * 6h²) and further simplify the expression as follows:`= (3 * 6²h + 3 * 6h² + h³) / h`= (108h + 18h² + h³) / h`= h² + 18h + 108

Answer: `h² + 18h + 108`

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Answer:

#1=8

#2=3

Step-by-step explanation:

Answer:

3x^2 - 17x + 24

Step-by-step explanation:

(x – 3)(3x – 8)

3x^2 + (-8x) + (-9x) + 24

3x^2 - 17x + 24

Answer:

x = 6

y = 4

Step-by-step explanation:

5x - 7y = 2

x - 7y = -22 (Multiply by -1)

-x + 7y = 22

5x - 7y = 2

4x = 24

x = 6

x - 7y = -22

6 - 7y = -22

-7y = -28

y = 4

Answer:

1

70 75

60 65

80 85 90

o

60 65

70 75 80 85 90

60 65 70 75 80 85 90

o

60 65

70 75 80 85

90 95 105 120 125 130 135 140 145

The box and whisker plot which correctly displays the given data set is option 3.

Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order.

Given is a data set.

88  85  86  82  66  75

A box and whisker plot is used to summarize the data using boxes which shows the quartiles in the plot.

Arranging the data set in increasing order,

66  75  82  85  86  88

Highest value in the data set = 88

Lowest value = 66

The plot which correctly displays these two points are options 2 and 3.

Now, find the median of the data set.

Median is the average of 3rd and 4th element since this consist of even number of data sets.

Median = (82 + 85) / 2 = 83.5

This is correctly marked in option 3.

Hence the correct option is third one.

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The complete question is given in the image below. :

50. 150 divided by 3

Answer:

No

Step-by-step explanation:

She needs at least another 2 coordinate pairs to test if her evaluation is correct. For instance, the next pair could be (7,22). Then, the pattern wouldn't be increasing by 4. It would not have a constant of proportionality.

Answer:

they will skip 4

Step-by-step explanation:

Answer:

They will have to skip the ones that are less desirable to them

Answer:

x = 1953125

Step-by-step explanation:

log x - log 5^3 = 2 log 5^3

log x - 3 log 5 = 6 log 5

log x = 9 log 5 = log 5^9

x = 5^9

 x = 1953125