What is the value of c?

If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.

However, the frog slips back 1 foot while resting for an hour, so the frog would only have covered 5 feet of the well after each hour of climbing. The frog would need to climb for a total of

40/5 = 8 hours

to reach the top of the well. Additionally, the frog would need to take 8 hours of rest to make up for the slipping back.

So the total time it would take the frog to get out of the well would be 8 hours + 8 hours = 16 hours.

If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.

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The minimum required sample size is 47 as it is very important for safety, the 99% confidence interval needs to have a margin smaller than 0.06.

To estimate the mean tensile strength for roof hangers with a 99% confidence interval margin of 0.06, we can use the formula:

Margin of error = z* (standard deviation / sqrt(sample size))

where z is the z-score for the desired confidence level, which for a 99% confidence interval is 2.576.

Plugging in the given values, we get:

0.06 = 2.576 * (0.25 / sqrt(sample size))

Solving for the sample size, we get:

sample size = (2.576 * 0.25 / 0.06)^2

sample size = 89.59

Rounding up to the nearest whole number, the minimum required sample size is 90.

Therefore, we need to take a sample of at least 90 roof hangers to estimate the mean tensile strength with a 99% confidence interval margin of 0.06.

To estimate the mean tensile strength for roof hangers with a 99% confidence interval and a margin of error smaller than 0.06, you'll need to determine the minimum required sample size.

For a 99% confidence level, the Z-score (critical value) is approximately 2.576.

The known standard deviation is 0.25. The desired margin of error is less than 0.06. Use the formula:

Margin of Error = Z-score * (Standard Deviation / sqrt(Sample Size))

Rearrange the formula to find the sample size:

Sample Size = (Z-score * Standard Deviation / Margin of Error)^2

Sample Size = (2.576 * 0.25 / 0.06)^2

Sample Size ≈ 46.24

Since you cannot have a fraction of a sample, round up to the nearest whole number. The minimum required sample size is 47.

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Answer:

Step-by-step explanation: yes

This is NOT a function.

For a relation to be a function, each x-value needs to have only 1 y-value. This is not the case for the data points given here. The x-value 160 has 7 different y-values. If these points were graphed, it would form a straight line and a straight line is not a function (it does not pass the vertical line test!).

Hope this helps!

The expression will become cos²(7x) = \(\frac{1}{2}\)(1 + cos14x).

Power reduction formulas like double angle and half angle formula are used to simplify the calculations requires to solve a given expression.

Power reduction formulas allow us to reduce the power on one of the trigonometric functions when the power is an even integer.

The trigonometric power reduction identities allow us to rewrite expressions involving trigonometric terms with trigonometric terms of smaller powers.

The power reduction formula is

cos²θ = \(\frac{1}{2}\)(1 + cos2θ)

sin²θ =\(\frac{1}{2}\)(1 - cos2θ)

For the given equation we will use cosine formula.

Therefore

cos²(7x) = \(\frac{1}{2}\)(1 + cos2(7x))

cos²(7x) = \(\frac{1}{2}\)(1 + cos14x).

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Answer:

20 kilograms

Step-by-step explanation:

Answer:

About 19.95 kilograms

Step-by-step explanation:

Hope this helped! :)

Answer: (0, -6)

Step-by-step explanation:

The center is the midpoint of the diameter, meaning that the coordinates of Y must be (0, -6).

Answer:

ji aap ka answer (24) hai

Answer:

parallel

Step-by-step explanation:

Parallel lines have equal slopes.

Calculate the slopes m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (2, 3)

m = \(\frac{3-2}{2+1}\) = \(\frac{1}{3}\)

Repeat with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (3, 1)

m = \(\frac{1-0}{3-0}\) = \(\frac{1}{3}\)

Since slopes are equal then parallel

To find the probability that the dispensers dispense less than 9.95 gallons, we can use the Central Limit Theorem and approximate the distribution of the sample mean as a normal distribution.

Given that the average of the 80 samples is 9.8 gallons and the standard deviation of each sample is 0.1 gallons, we can consider the sample mean as an estimate of the population mean. The Central Limit Theorem states that as the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Since the sample size is large (80 samples), we can approximate the distribution of the sample mean as a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the population standard deviation is 0.1 gallons, and the square root of the sample size is √80.

To calculate the probability that the dispensers dispense less than 9.95 gallons, we can standardize the value using the z-score formula:

z = (x - μ) / (σ / √n)

Where x is the value we are interested in (9.95 gallons), μ is the population mean (9.8 gallons), σ is the population standard deviation (0.1 gallons), and n is the sample size (80).

Substituting the values into the formula:

z = (9.95 - 9.8) / (0.1 / √80)

Calculate the z-value and find the corresponding probability from the standard normal distribution table or using statistical software.

By finding the probability associated with the z-value, you can determine the probability that the dispensers dispense less than 9.95 gallons.

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Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

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In order for the system of equations to be a consistent system, the value of k must be equal to -4.

To determine the value of k that makes the system of equations consistent, we can use the method of elimination or substitution. Let's use the method of elimination.

First, we can multiply the first equation by 5, the second equation by -1, and the third equation by 2 to make the coefficients of x in the three equations cancel each other out when added together.

The modified system of equations becomes:

5x - 10y + 20z = 20

5x - 9y + 22z = 16

-4x + 6y - 20z = 2k

Now, let's subtract the first equation from the second equation:

(5x - 9y + 22z) - (5x - 10y + 20z) = 16 - 20

y + 2z = -4

Next, let's add this equation to the third equation:

(-4x + 6y - 20z) + (y + 2z) = 2k - 4

-4x + 7y - 18z = 2k - 4

For the system of equations to be consistent, there must be no contradictions or inconsistencies. This means that the equations must be linearly dependent, and the last equation must be a multiple of the second equation.

Comparing the last equation (-4x + 7y - 18z = 2k - 4) with the second equation (y + 2z = -4), we can see that the two equations will be dependent and consistent if 2k - 4 is equal to 0.

2k - 4 = 0

2k = 4

k = 2

Therefore, in order for the system of equations to be a consistent system, the value of k must be equal to -4.

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Answer:

22

Step-by-step explanation:

6 divided 6 equals 1 and 1 times 22 equals 22

Brainliest ?

Answer: D

Step-by-step explanation:

Answer:

24 centimetre

hope it is helpful

ANSWER

44 cm

EXPLANATION

The perimeter of a polygon is the sum of the side lengths. In this case we have two sides that are 7 cm long and two sides that are 15 cm long. The perimeter is:

Option 1 (not paying 100k) has a higher expected value of 108k, while Option 2 (paying 100k) has an expected value of 8k. Therefore, it would be more financially beneficial not to pay the 100k.

Your question is about a painting and whether it is an original or not. If it is an original, it is worth 500k, and if it is not, it is worth 10k. The probability that it is an original is 0.2. You have the option to pay 100k.

Based on the information provided, let's calculate the expected value of each option:

1. Option 1: Do not pay 100k:
  - Probability of it being an original: 0.2
  - Value if it's an original: 500k
  - Value if it's not an original: 10k
  - Expected value: (0.2 * 500k) + (0.8 * 10k) = 100k + 8k = 108k

2. Option 2: Pay 100k:
  - Probability of it being an original: 0.2
  - Value if it's an original: 500k - 100k (paid) = 400k
  - Value if it's not an original: 10k - 100k (paid) = -90k (negative value)
  - Expected value: (0.2 * 400k) + (0.8 * -90k) = 80k - 72k = 8k

Comparing the expected values, Option 1 (not paying 100k) has a higher expected value of 108k, while Option 2 (paying 100k) has an expected value of 8k. Therefore, it would be more financially beneficial not to pay the 100k.

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Answer:

  127/924 ≈ 0.1374

Step-by-step explanation:

Given a box with 2 pennies, 4 nickels, 6 dimes, you want the probability that 6 randomly chosen coins will have a value of 50 cents or more.

The ways 50 cents (or more) can be made from those coins are ...

There is 6C6 = 1 way to choose 6 dimes.

There are (6C5)(4C1) = 6·4 = 24 ways to choose 5 dimes and 1 nickel

There are (6C5)(2C1) = 6·2 = 12 ways to choose 5 dimes and 1 penny

There are (6C4)(4C2) = 15·6 = 90 ways to choose 4 dimes and 2 nickels

The total number of ways to get 50¢ or more is ...

  1 +24 +12 +90 = 127

The total number of ways to choose 6 coins from the 12 is ...

  12C6 = 924

The probability of choosing 6 coins that total 50¢ or more is ...

  127/924 ≈ 0.1374

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Answer:

2 2/4

Step-by-step explanation:

because I guess they want you too add so I added them

Monthly payment before deferral: $345.09. Balance after deferral: $67,901.53. Monthly payment after deferral: $380.57. Monthly payment to pay off debt within 25 years from graduation: $421.63.

To calculate the monthly payment for a student loan, we can use the loan amortization formula.

Monthly payment calculation:

We can use the formula for calculating the monthly payment on an amortizing loan:

PMT = (P * r) / (1 - (1 + r)^(-n))

where PMT is the monthly payment, P is the loan amount, r is the monthly interest rate, and n is the total number of payments.

Given:

P = $62,100 (loan amount)

r = 4.6% per year / 12 months = 0.046/12 (monthly interest rate)

n = 25 years * 12 months = 300 (total number of payments)

Substituting these values into the formula, we can calculate the monthly payment:

PMT = (62,100 * (0.046/12)) / (1 - (1 + (0.046/12))^(-300))

Balance after deferral period:

To calculate the balance after the deferral period of 2 years, we need to calculate the interest accrued during that period and add it to the original loan amount:

Interest accrued during deferral = P * r * deferral period (in years)

New balance = P + Interest accrued during deferral

New monthly payment after deferral period:

To calculate the new monthly payment after the deferral period, we can use the same formula as before, but with the new balance and the remaining number of payments:

New PMT = (New balance * r) / (1 - (1 + r)^(-n))

Monthly payment to pay off the debt within 25 years from graduation:

To calculate the monthly payment to pay off the debt within 25 years from graduation, we need to adjust the remaining number of payments:

Remaining number of payments = 25 years * 12 months - deferral period

Then we can use the same formula as before to calculate the monthly payment.

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The paired t-test statistic is infinity, which indicates a significant difference in the means of math scores and science scores.

Let's consider an example of a paired t-test and a two-sample t-test on a dataset of 5 students' scores in two different exams: math and science. Let's assume that the students took both exams, and their scores are paired. We want to test whether there is a significant difference in the means of math scores and science scores.

We calculate the difference between each student's math score and science score and compute the mean difference and standard deviation of the differences:

Student Math Score Science Score Difference

1                      80      75                        5

2                      90      85                        5

3                      85      80                        5

4                       95      90                        5

5                    75              70                        5

Mean difference = 5

Standard deviation of differences = 0

We can calculate the paired t-test statistic as:

t = (mean difference - hypothesized difference) / (standard deviation of differences / square root of sample size)

Let's assume the hypothesized difference is 0 (i.e., there is no difference between the means). Then the t-test statistic is:

t = (5 - 0) / (0 / √(10)) = infinity

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You would expect approximately 136 numbers in the data set to be between 56 and 74.

To determine the number of numbers you would expect to be between 56 and 74 in a normally distributed data set with a mean of 65 and a standard deviation of 9, we can utilize the properties of the standard normal distribution.

First, we need to standardize the values of 56 and 74 by converting them to z-scores. The z-score formula is:

z = (x - μ) / σ

where z is the z-score, x is the data value, μ is the mean, and σ is the standard deviation.

For 56:

z = (56 - 65) / 9

z = -1

For 74:

z = (74 - 65) / 9

z = 1

Next, we need to find the area under the standard normal curve between the z-scores -1 and 1. We can use a standard normal distribution table or a calculator to find this probability.

Using a standard normal distribution table, the area between -1 and 1 is approximately 0.6826. This represents the proportion of the data that falls within one standard deviation of the mean.

To find the number of numbers expected to be between 56 and 74, we multiply the proportion by the total number of data points:

Expected number = Proportion * Total number of data points

Expected number = 0.6826 * 200

Expected number ≈ 136.52

As a result, you would anticipate that roughly 136 of the data set's numbers would fall between 56 and 74.

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Answer:

1,044

Step-by-step explanation:

14 x 46 = 644

16 x 25 = 400

644 + 400 = 1,044

Answer:

0.1 ounce

Step-by-step explanation:

5  cookies = 0.5 ounces

1 cookie = 0.5 / 5 = 0.1 ounce

Answer:

Number of Activity books = 8

Number of Storybooks = 5

Explanation:

Let x represent the number of activity books.

Let y represent the number of storybooks.

Let's go ahead and set up our equations as follows;

From equation 1, we can see that x = 13 - y

Let's go ahead and substitute the value of x into equation 2 and solve for y;

Since y = 5, let's substitute the value of y into equation 1 and solve for x;

The answer is D. No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is normal.

In order to perform inference with a confidence interval for the difference in population means, certain conditions need to be met. One of the conditions is that the sample sizes should be sufficiently large.

For the distribution of the difference in sample means to be approximately normal, both sample sizes should ideally be large, typically with a guideline of at least 30 observations. In this case, the sample sizes are 35 for manager A and 40 for manager B, which are relatively small compared to the guideline.

Therefore, (D) the condition of having large enough sample sizes to assume a normal distribution for the difference in sample means is not met. As a result, the conditions for inference with a confidence interval for the difference in population means have not been met.

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This question is incomplete

Complete Question

Nico and Lorena used different methods to determine the product of three fractions.

Nico’s Method =

(one-sixth) (Negative four-fifths)(2) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) = StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction = Negative StartFraction 8 over 30 EndFraction

Lorena’s Method

= Negative StartFraction 4 over 15 EndFraction (2) (one-sixth) (Negative four-fifths) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) = StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction = Negative StartFraction 8 over Negative 30 EndFraction = StartFraction 4 over 15 EndFraction

Whose solution is correct and why?

a) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over negative 5 EndFraction.

b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.

c) Lorena is correct because she knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction

d) Lorena is correct because she knew that Negative four-fifths = StartFraction negative 4 over negative 5 EndFraction

Answer:

b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.

Step-by-step explanation:

In the above question

We start from Nico's method

Nico’s Method =

Step 1 : (one-sixth) (Negative four-fifths)(2)=

(1/6)(-4/5)(2)

Step 2 : (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) =

= (2/1)(1/6)(-4/5)

Step 3: StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction

= (2)(1)(-4)/(1)(6)(5)

Step 4: Negative StartFraction 8 over 30 EndFraction

= (-8/30)

Step 5 : Negative StartFraction 4 over 15

EndFraction

= -4/15

Nico is correct

For Lorena’s Method

Step 1: Negative StartFraction 4 over 5 EndFraction (2) (one-sixth)

= -4/5(2)(1/6)

Step 2: (Negative four-fifths) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) =

(2/1)(1/6)(-4/-5)

Step 3: StartFraction (2) (1) (negative 4) over (1) (6) (negative 5) EndFraction

(2)(-1)(-4)/(1)(6)(-5)

Step 4: Negative StartFraction 8 over Negative 30 EndFraction =

-8/-30

Step 5: StartFraction 4 over 15

EndFraction

= 4/15

Lorena is wrong because

that Negative four-fifths ≠StartFraction negative 4 over negative 5 EndFraction

Mathematically

-4/5 ≠ -4/-5

Therefore,option b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.

                   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\(\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\)

        What are the coefficients in the polynomial 4x²+3x-3?

\(\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to solve:-}}}}\diamond\)

Coefficient:-  A number before a variable

Coefficients in this polynomial:-

4 (the number before x²) and 3 (the number before x)

So we conclude that the right option is:-

\(\bigcirc\!\!\!\!\!\large\checkmark\) 4, 3 (Option B)

            - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

We have that, the first quartile of the given sample of twenty numbers is 59.

To find the first quartile of the given sample of twenty numbers

52, 54, 58, 59, 59, 60, 60, 63, 65, 66, 67, 68, 69, 73, 74, 77, 78, 79, 79, 98

use the following formula: Formula to calculate the first quartile:

\($$\mathrm{Q_1} = \mathrm{\frac{n+1}{4}}$$\)

So, plugging the values into the formula,

\($$\mathrm{Q_1} = \frac{20+1}{4}$$$$\mathrm{Q_1} = \frac{21}{4}$$$$\mathrm{Q_1} = $5.25 $\)

Then round 5.25 to the nearest whole number. To do this, compare 0.25 to 0.5, if it is greater than or equal to 0.5, then round up. If it is less than 0.5, round down. Since 0.25 is less than 0.5, round 5.25 to the nearest whole number. Therefore, the first quartile of the given sample of twenty numbers is 59.

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