HELPPPPP

Sparrowtown Street and Seaside Avenue intersect. If the diagonal distance across the
intersection is 8 meters and Sparrowtown Street is 5 meters wide, how wide is Seaside
Avenue? If necessary, round to the nearest tenth.
Submit
meters

Step-by-step explanation:

(8 x 10,000=80,000)

 (5 x 1,000=5,000) 

(3 x 100=300)

(8 x 1=8)

80,000+5,000+300+8

Answer:

85308

Step-by-step explanation:

[tex]8*10000=80000[/tex]

[tex]5*1000=5000[/tex]

[tex]3*100=300[/tex]

[tex]8*1=8[/tex]

[tex]80000+5000+300+8=85308[/tex]

Hope this helps :)

Pls brainliest...

Answer:

recess makes up 1/28 of the school day.

Step-by-step explanation:

Using the compound interest formula A = P[tex](1 + r/n)^{(nt)}[/tex] it is deduced that t will take approximately 16.8 years for your account to catch up to your friend's account.

We can use the formula for compound interest to solve this problem:

A = P[tex](1 + r/n)^{(nt)}[/tex]

where:

A = the amount of money at the end of the investment period

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

For your account:

P = 1000

r = 0.08/12 = 0.00666667 (monthly interest rate)

n = 12 (compounded monthly)

A = P[tex](1 + r/n)^{(nt)}[/tex] = 1000[tex](1 + 0.00666667/12)^{(12t)}[/tex]

For your friend's account:

P = 2000

r = 0.05/12 = 0.00416667 (monthly interest rate)

n = 12 (compounded monthly)

A = P[tex](1 + r/n)^{(nt)}[/tex] = 2000[tex](1 + 0.00416667/12)^{(12t)}[/tex]

We want to find the time t when the two accounts have the same value:

1000[tex](1 + 0.00666667/12)^{(12t)}[/tex] = 2000[tex](1 + 0.00416667/12)^{(12t)}[/tex]

Dividing both sides by 1000 and simplifying, we get:

[tex](1 + 0.00666667/12)^{(12t)}[/tex] = 2[tex](1 + 0.00416667/12)^{(12t)}[/tex]

[tex](1.00055556)^{(12t)}[/tex] = 2[tex](1.00034722)^{(12t)}[/tex]

Taking the natural logarithm of both sides:

12t × ln(1.00055556) = ln(2) + 12t × ln(1.00034722)

12t = ln(2)/(ln(1.00034722) - ln(1.00055556))

t = 16.8 years (rounded to the nearest tenth of a year)

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The addition is one of the four fundamental mathematical operations. The length of the missing side length is 6ft.

Since,

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

In the given diagram, the line AB, CD, and EF are parallel to each other, therefore, we can write the length of AB as,

Length of AB = Length of EF - Length of CD

                     = 13ft - 7ft

                     = 6ft

Hence, the length of the missing side length is 6ft.

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The coordinate of the triangle after the dilation is (3, 3), (6, 3), (3, 6)

From the question, we have the following parameters that can be used in our computation:

(5, 5), (10,5), (5, 10)

Scale factor = 3/5

The coordinate of the triangle after the dilation is calculated as

Image' = triangle * Scale factor

Substitute the known values in the above equation, so, we have the following representation

(5, 5), (10,5), (5, 10) * 3/5

Evaluate

(3, 3), (6, 3), (3, 6)

Hence, the image is (3, 3), (6, 3), (3, 6) and it is attached

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The volume of the triangular prism will be 25.92 cubic cm.

Given that:

Base, b = 2.4 cm

Height, h = 3.6 cm

Length, L = 6 cm

The volume of the triangular prism is given as,

V = 1/2 x b x h x L

The volume of the triangular prism is calculated as,

V = 1/2 x 2.4 x 3.6 x 6

V = 2.4 x 3.6 x 3

V = 25.92 cubic cm

The volume of the triangular prism will be 25.92 cubic cm.

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Answer:

Step-by-step explanation:

yes, he jumped more then 100 inches

Answer:

The winner did jump more than 100in

Step-by-step explanation:

[tex]8.5ft( \frac{12in}{1ft} ) = 102 \: in[/tex]

Answer:

Firstly, it is essential to remain calm and composed. Reacting with anger or frustration can escalate the situation and make it worse. Instead, try to approach the person and speak to them calmly and respectfully. Explain how their behavior is affecting others and the overall atmosphere of the game or event.

If the person continues to display poor sportsmanship despite your attempts to communicate with them, it may be necessary to involve a coach, referee, or authority figure who can address the situation more effectively. It's important to remember that poor sportsmanship not only ruins the game for others but also reflects poorly on the individual displaying it.

In some cases, it may be best to simply ignore the behavior and focus on the game or event. As difficult as it may be, sometimes the best course of action is to rise above the negativity and continue playing with good sportsmanship. This can set a positive example for others and show that poor sportsmanship will not be tolerated.

Overall, it's important to handle poor sportsmanship with maturity, respect, and a focus on creating a positive and enjoyable experience for everyone involved.

The measures that are appropriate to accurately summarize the data are the mean and the median

From the question, we have the following parameters that can be used in our computation:

1, 8, 2, 2, 5, 6, and 4

When sorted we have

1, 2, 2, 4, 5, 6, 8

The mean is calculated as

Mean = (1 + 2 + 2 + 4 + 5 + 6 + 8)/7

Mean = 4

The median is the middle value

So, we have

Median = 4

The mode is the data with the highest frequency

So, we have

Mode = 2

Lasltly, the measures that are appropriate to accurately summarize the data are the mean and the median

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The horizontal distance from the observation station to the fire is approximately 290.4 feet.

In this problem, we are given the angle of depression (θ) and the vertical distance (FS) from an observation station to a fire. We need to find the horizontal distance (x) from the station to the fire.

To solve the problem, we can use the trigonometric function tangent, which relates the opposite side to the adjacent side of a right triangle. In this case, the opposite side is the vertical distance FS, and the adjacent side is the horizontal distance x.

We can set up the following equation:

tan(θ) = FS / x

We know that θ = 15 degrees and FS = 87 feet, so we can plug these values into the equation:

tan(15) = 87 / x

Next, we can solve for x by multiplying both sides of the equation by x and dividing both sides by tan(15):

x = 87 / tan(15)

Using a calculator, we can evaluate the expression and get:

x ≈ 290.4 feet

We round our answer to the nearest tenth of a foot, which is why we keep one decimal place.

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Answer: 1327.3 feet cubed[tex]V=\pi\cdot r^2\cdot h\\V=\pi\cdot(6.5)^2\cdot10\\V=\pi\cdot 42.25\cdot10\\V=422.5\pi ft^3\\or\\V\approx 1327.3 ft^3[/tex]

Step-by-step explanation:

Volume of a cylinder:

The probability of receiving exactly 7 calls in the next three hours is approximately 0.104, which corresponds to answer (b).

To solve this problem, we need to use the Poisson probability formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the number of calls, k is the desired number of calls (7 in this case), λ is the average rate of calls per time period (5 calls per hour), and e is the base of the natural logarithm (approximately 2.71828).

Since we want to know the probability of receiving 7 calls in 3 hours, we need to adjust our λ value accordingly. Since the rate is 5 calls per hour, the average rate for 3 hours would be 5 * 3 = 15 calls.

Now, we can plug these values into the formula:

[tex]P(X = 7) = (e^(-15) * 15^7) / 7![/tex]

P(X = 7) ≈ 0.104

So, the probability of receiving exactly 7 calls in the next three hours is approximately 0.104, which corresponds to answer (b).

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The vertex and axis of symmetry of each function are as follows:

15. (2, -4)

16. -½x + ½

17. (-4, 3)

18. (-5, 2)

19. (-5, -3)

20. (-2, -1)

15. f(x) = -3 (x - 2)² - 4

Rewrite the function

f(x)=-3x²+12x-16 Identify the coefficients

a=-3, b=12

Substitute the coefficients into the expression

X = — ¹²/2 x (-3) Solve the equation

X = 2

Evaluate the function for x = 2

f(x) = -3 (x-2)² - 4, x=2

Calculate the function value

f(2) = -4

The vertex is at (2, -4)

16. f(x) = - ¼x (x - 1)² + 4

Take the derivative

f'(x) = ᵈ/dx (-¼x x (x-1)² + 4)

Calculate

f'(x) = ᵈ/dx (— (x-1)²/4 + 4)

Use differentiation rules

f'(x) = ᵈ/dx ( (x-1)²/4) + ᵈ/dx (4)

Differentiate

f¹(x) = - ¼ x 2 (x - 1) + 0

Simplify

f'(x) = -½x + ½

17. f ( x ) = ¼ × (x + 4)² +3

Rewrite the function

f(x) = ¼x² + ⁸/₄x + ¹⁶/₄ + 3

Identify the coefficients

a= ¼, b = ⁸/₄

Substitute the coefficients into the expression

X = — (⁸/₄)/2 x ¼

Solve the equation

X= -4

Evaluate the function for x = -4

f ( x ) = ¼ × (x + 4)² +3, x = -4

f(-4) = 3

The vertex is at (-4, 3)

18. f (x) = ¼ × (x + 5)² + 2

Rewrite the function

f(x) = ¼x² + ¹⁰/₄x + ³¾

Identify the coefficients

a = ¼, b = ¹⁰/₄

Substitute the coefficients into the expression

x = (¹⁰/₄)/2 x ¼

Solve the equation

X= -5

Evaluate the function for x = -5

f (x) = ¼ × (x + 5)² + 2, x = -5

Calculate the function

f(-5) = 2

The vertex is at (-5, 2)

19. f(x) = -2(x+5)² - 3

Rewrite the function

f(x) = -2x² - 20x - 53

Identify the coefficients

a = -2, b = -20

Substitute the coefficients into the expression

X = — ²⁰/2 x (-2)

Solve the equation

X= -5

Evaluate the function for x = -5

f(x) = -2(x+5)² - 3, x = -5

Calculate

f (-5) = -3

The vertex is at (-5, -3)

20. f(x) = (x + 2)² - 1

Rewrite the function

f(x)= x² +;4x + 3

Identify the coefficients

a = 1, b = 4

Substitute the coefficients into the expression

x = — ⁴/2 x 1

Solve the equation

X = - 2

Evaluate the function for x= -2

f(x) = (x+2)² - 1, x = -2

Calculate the function value

f(-2) = -1

The vertex is at (-2, -1)

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this is a answer, thanks

The variance for this data set of ages is 18.0 (rounded to one decimal place). The variance for this data set can be found using the formula: Variance = (Σ(x - μ)²) / n

Where Σ represents the sum of, x represents the individual ages in the data set, μ represents the mean of the data set, and n represents the total number of ages.

To find the mean (μ), we first need to add up all the ages and divide by the total number of ages:

(6 + 3 + 14 + 11 + 14 + 6) / 6 = 54 / 6 = 9

So the mean age of the grandchildren is 9.

Next, we need to calculate the sum of each age minus the mean, squared:

(6 - 9)² + (3 - 9)² + (14 - 9)² + (11 - 9)² + (14 - 9)² + (6 - 9)² = 9 + 36 + 25 + 4 + 25 + 9 = 108

Finally, we divide this sum by the total number of ages (6) to get the variance:

Variance = 108 / 6 = 18

Rounding to one decimal place, the variance for this data set is 18.0.

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The savings account paid a simple interest rate of 25.96%.

We can use the simple interest formula:

I = Prt

where I is the interest earned, P is the principal (initial amount deposited), r is the interest rate (in decimal form), and t is the time (in years).

The interest earned in 2 years is:

I = 759.60 - 500 = 259.60

Substituting the values into the formula, we get:

259.60 = 500 × r × 2

Simplifying and solving for r, we get:

r = 0.2596 or 25.96%

Therefore, the savings account paid a simple interest rate of 25.96%.

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mario has $759.60 in the bank after 2 years. assuming he made no additional deposits or withdrawls, what simple interest rate did the savings account pay? The initial amount deposited is $500

Dirichlet's theorem on arithmetic progressions states that for any two coprime positive integers a and d, there are infinitely many prime numbers of the form a + nd, where n is a non-negative integer. We can use this theorem to prove that there exist prime numbers with arbitrarily many 0's in its digits.

Let's consider the arithmetic progression 10^k, 10^k + 1, 10^k + 2, ..., 10^k + 9. This progression consists of all the positive integers with k+1 digits that end in a non-zero digit. Note that 10^k and 10^k + 1 are coprime, as are 10^k and 10^k + 2, and so on, up to 10^k and 10^k + 9. By Dirichlet's theorem, there are infinitely many primes of the form 10^k + nd, where n is a non-negative integer and d is any one of the 10 numbers 1, 2, ..., 9. Since 10^k has k+1 digits, we can choose k to be any positive integer, and thus there exist prime numbers with arbitrarily many 0's in its digits. For example, if we choose k = 1000, then there exist infinitely many prime numbers with at least 1000 zeros in its digits, since there are infinitely many primes of the form 10^1000 + nd, where d is any one of the 10 digits 1, 2, ..., 9.

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The correct equation which represents the graph is,

⇒ y = 1/3x - 2

We know that;

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (3, -1) and (0, -2).

Now,

Since, The equation of line passes through the points (3, -1) and (0, -2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 2 - (-1)) / (0 - 3)

m = - 1 / -3

m = 1/3

Thus, The equation of line with slope 1/3 is,

⇒ y - (-1)= 1/3 (x - 3)

⇒ y + 1 = 1/3x - 1

⇒ y = 1/3x - 2

Therefore, The equation of line passes through the points ((3, -1) and

(0, -2).will be;

⇒ y = 1/3x - 2

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Answer:

Its B!

Step-by-step explanation:

:)

In this case, we want to predict the total amount of Lexapro in the bloodstream (continuous outcome) based on the time in days (continuous predictor). The output will give us the equation for the model:
[tex]P(t) = \frac{11.834}{e^{-0.621(4-2.94)} }[/tex]

To fill in the table, we use the given information that the medication is eliminated from the body at a rate of approximately 2.3% per hour. This means that after one hour, 97.7% of the medication remains in the body. We can use this information to calculate the amount remaining from the previous dose and the total amount in the bloodstream for each day.

Time (days) | Amount Remaining from Previous Doses (mg) | New Dose Added (mg) | Total Amount in Blood Stream (mg)
0          | NA                                      | 10                  | 10
1          | 5.76                                    | 10                  | 15.76
2          | 9.07                                    | 10                  | 19.07
3          | 10.99                                   | 10                  | 20.99
4          | 12.08                                   | 10                  | 22.08
5          | 12.72                                   | 10                  | 22.72
6          | 13.08                                   | 10                  | 23.08
7          | 13.30                                   | 10                  | 23.30
8          | 13.42                                   | 10                  | 23.42
9          | 13.49                                   | 10                  | 23.49
10         | 13.53                                   | 10                  | 23.53

For example, on day 1, the amount remaining from the previous dose is 10 x 0.977 = 9.77 mg, and the total amount in the bloodstream is

9.77 + 10 = 19.77 mg.

On day 2, the amount remaining from the previous dose is

19.77 x 0.977 = 19.30 mg, and the total amount in the bloodstream is 19.30 + 10 = 29.30 mg.

We continue this process each day to fill in the table.

To find a model for the total amount of Lexapro in the bloodstream as a function of time in days, we can use logistic regression. Logistic regression is a statistical method used to analyze data with a binary outcome (i.e. 0 or 1), but it can also be used for continuous outcomes by transforming the data.

In this case, we want to predict the total amount of Lexapro in the bloodstream (continuous outcome) based on the time in days (continuous predictor). We can use a logistic regression calculator to find the model. The output will give us the equation for the model:
[tex]P(t) = \frac{11.834}{e^{-0.621(4-2.94)} }[/tex]

where P(t) is the predicted total amount of Lexapro in the bloodstream at time t in days. This model suggests that the total amount of Lexapro in the bloodstream increases over time but at a decreasing rate. The model can be used to make predictions about the total amount of Lexapro in the bloodstream at different time points.

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The five-number summary is (7, 9, 13, 21.5, 24).

A five-number summary is a set of statistics that describes a data set. It consists of the minimum, first quartile, median, third quartile, and maximum of the data12. A box plot is a graphical display of the five-number summary using a number line and a rectangular box13.

To find the five-number summary and make a box plot for your data set, you need to follow these steps:

Arrange the data in ascending order: 7, 8, 10, 10, 13, 16, 19, 23, 24

Find the minimum and maximum values: Minimum = 7, Maximum = 24

Find the median (the middle value) of the data: Median = 13

Find the first quartile (the median of the lower half of the data): First quartile = 9

Find the third quartile (the median of the upper half of the data): Third quartile = 21.5

Therefore, by the number line the answer will be (7, 9, 13, 21.5, 24).

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The probability that the dealership will make a profit if 4 customers enter on Friday is approximately 24.01%.

a. You can estimate the Hypergeometric Distribution with the Binomial Distribution under the following conditions:
1. The sample size (n) is relatively small compared to the population size (N).
2. The probabilities of success (p) and failure (q) remain approximately constant throughout the sampling process.

In this case, since we're assuming sampling with replacement, identical cars, and independent trials with constant probability, it's appropriate to use the Binomial Distribution.

b. To calculate the probability that the dealership will make a profit if 4 customers enter on Friday, we can use the Binomial Distribution formula:

P(X = k) = (nCk) * (p^k) * (q^(n-k))

Where:
- P(X = k) is the probability of exactly k successes (cars sold)
- nCk is the number of combinations of n items taken k at a time
- p is the probability of success (car sold)
- q is the probability of failure (car not sold)
- n is the number of trials (customers)
- k is the number of successes (cars sold)

Here, n = 4, p = 0.70, and q = 1 - p = 0.30. We need to find the probability of selling at least 4 cars (k ≥ 4) to make a profit:

P(X ≥ 4) = P(X = 4)
P(X = 4) = (4C4) * (0.70^4) * (0.30^0)
P(X = 4) = 1 * (0.2401) * (1)
P(X = 4) = 0.2401

Therefore, the probability that the dealership will make a profit if 4 customers enter on Friday is approximately 24.01%.

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The value of the given expression is -2.

The given expression is -14-(-12).

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Here, -14+12 (Because -×- = +)

= -2

Therefore, the value of the given expression is -2.

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Absolute convergence refers to the convergence of a series regardless of the order in which its terms are added, while conditional convergence refers to convergence only when the terms are added in a specific order. In this case, we have shown that the series converges, but we cannot determine whether it converges absolutely or conditionally without further analysis.

To test the series for convergence or divergence, we will use the Divergence Test and the Alternating Series Test. We will break it down into steps.

Given series: ∑((-1)^n * n^110) / (n^21 + 2)^(1/2)

Part 1: Divergence Test
The given question is about testing a series for convergence or divergence using different methods. In part 1, we are asked to use the Divergence Test to determine whether the series converges or diverges. To apply this test, we need to identify the corresponding positive terms, which in this case are given as bn = n110/(n^21+2)^(1/2). Then, we need to evaluate the limit of this sequence as n approaches infinity, which is lim bn = 0 as the denominator grows faster than the numerator. Since the limit is equal to 0, the Divergence Test does not provide any conclusive results.

In part 2, we are asked to use the Alternating Series Test to test for convergence. For this, we need to compute the derivative of the given sequence, which is given as bn = (200119-n-30)/2(n^21+. The derivative is eventually always less than zero, indicating that the sequence is eventually monotone. Therefore, the Alternating Series Test tells us that the series converges.

Step 1: Identify the corresponding positive terms:
bn = n^110 / (n^21 + 2)^(1/2)

Step 2: Evaluate the limit:
lim (n→∞) bn = lim (n→∞) (n^110 / (n^21 + 2)^(1/2))

The limit is equal to 0, so the Divergence Test does not provide any information on the convergence or divergence of the series.

Part 2: Alternating Series Test

Step 3: Test for Convergence
Since the series is an alternating series with positive terms bn, we need to check if the sequence of positive terms is decreasing and if its limit is 0.

Step 4: Check if the sequence is decreasing
Since the derivative of bn with respect to n is negative for all n > 4, the sequence is eventually monotone (decreasing).

Step 5: Check if the limit of the sequence is 0
We already found the limit of the sequence in Step 2, which is 0.

Since both conditions of the Alternating Series Test are satisfied, the series converges.
Finally, we can distinguish between absolute and conditional convergence. Absolute convergence refers to the convergence of a series regardless of the order in which its terms are added, while conditional convergence refers to convergence only when the terms are added in a specific order. In this case, we have shown that the series converges, but we cannot determine whether it converges absolutely or conditionally without further analysis.
In conclusion, the given series converges conditionally according to the Alternating Series Test.

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The Falcons had the best overall record for the season because they have a larger median value of 24 points.

The data is given as:

Eagles: 3, 7, 10, 10, 13, 14, 17, 21, 24, 24, 27, 27, 37, 40, 55

Falcons: 6, 7, 10, 14, 16, 17, 21, 24, 24, 24, 28, 28, 30, 30, 35

The mean and median values for both data sets:

Eagles: mean = 22, median = 21

Falcons: mean = 21, median = 24

Based on the mean and median values, we can see that the Eagles have a larger mean value of about 22 points while Falcons have a larger median value of 24 points.

Since the mean is affected by outliers and the Falcons have one game where they scored significantly higher than their other games (55 points), the median is a better measure of center to use for this comparison.

Therefore, we can conclude that the Falcons had the best overall record for the season.

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Therefore, the value of the test statistic is 2.02 (rounded to two decimal places).

To test the claim that the actual percentage of computer chips that do not fail in the first 1000 hours of their use is different from the stated percentage of 44%, we can use a hypothesis test with the following null and alternative hypotheses:

Null hypothesis: The proportion of computer chips that do not fail in the first 1000 hours of their use is equal to 44%.

Alternative hypothesis: The proportion of computer chips that do not fail in the first 1000 hours of their use is not equal to 44%.

We can use a normal approximation to the binomial distribution to calculate the test statistic:

z = (p - P) / √(P(1-P)/n)

where:

p = sample proportion = 0.46

P = hypothesized proportion = 0.44

n = sample size = 900

Plugging in the values, we get:

z = (0.46 - 0.44) / √(0.44*0.56/900)

z = 2.02

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The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.

To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.

Step 1:

Convert the percentage to a decimal.
65.3 / 100 = 0.653

Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

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The limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

To use the ratio test, we take the limit of the absolute value of the ratio of the (k+1)th term to the kth term:

lim as k approaches infinity of |(6(k+1)^4)/(6k^4)|

Simplifying this expression, we get:

lim as k approaches infinity of |(k+1)^4/k^4|

Using L'Hopital's rule, we can evaluate this limit:

lim as k approaches infinity of |4(k+1)^3/4k^3|

lim as k approaches infinity of |(k+1)/k|^3

Since the limit is less than 1, by the ratio test, the series converges absolutely.

Alternatively, we can use the root test, which involves taking the kth root of the absolute value of the kth term:

lim as k approaches infinity of |(6k^4 k)^(1/k)|

Simplifying this expression, we get:

lim as k approaches infinity of |6^(1/k) * k^(4+1/k)|

The exponent 4+1/k approaches 4 as k approaches infinity, so we can ignore the 1/k term. Taking the limit of just the k^(4) term, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k)

Using the fact that lim as k approaches infinity of 6^(1/k) = 1 and lim as k approaches infinity of k^(4/k) = 1, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k) = 1

Since the limit is less than 1, by the root test, the series converges absolutely.
To determine if the given series converges absolutely or diverges, we can use the Ratio Test. The series is given as:

Σ(6k^4 * k) for k = 1 to ∞

First, let's simplify the series:

Σ(6k^5) for k = 1 to ∞

For the Ratio Test, we need to compute the limit as k goes to infinity of the ratio of consecutive terms:

lim (k → ∞) (|a_(k+1)| / |a_k|)

For our series, a_k = 6(k+1)^5 and a_(k+1) = 6k^5. So we have:

lim (k → ∞) (|6(k+1)^5| / |6k^5|)

We can simplify by canceling the common factor of 6:

lim (k → ∞) ((k+1)^5 / k^5)

Now, let's take the limit:

lim (k → ∞) (1 + 1/k)^5 / 1 = 1^5 / 1 = 1

For the Ratio Test, if the limit is less than 1, the series converges absolutely; if it is equal to 1, the test is inconclusive; if it is greater than 1, the series diverges.

In this case, the limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

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Answer:

The only value of n that makes the inequality true is 5.

Explanation:

To solve the inequality, we need to isolate n on one side of the inequality symbol. First, we can multiply both sides by 7/3 to get:

n > (4/3) × 27/7

Simplifying, we get:

n > 4

So any value of n greater than 4 would make the inequality true. Among the given choices, only 5 is greater than 4, so it is the only value that satisfies the inequality.

The solution that equals a in this equation is [tex]a = 3 / 8[/tex]. The Option B.

An expression means collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that:

The expression is 1 over 4a = 2 over 3.

We can then simplify as:

1 / 4a = 2 / 3

Make a cross multiplacation, we get:

3 = 2 x 4a

3 = 8a

a = 3 / 8

Therefore, the solution of the expression is a = 3 / 8

Full question "1 over 4a = 2 over 3. Which of the following equals a in this equation? 1/6, 3/8 11/12, 2 and 2/3"

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