A unicorn whose mass is 65 kg is moving at a speed of 4 m/s. What is the unicorn's kinetic energy?

Answer:

0.264

Step-by-step explanation:

Answer:

3 11/14 is your fraction answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

f ( x ) = 17 ( 3 + x )

f ( -2 ) = 17 ( 3 + -2 )

f ( -2 ) = 51 + -34

f ( -2 ) = 17

= 17

Answer:

\(\displaystyle 385\)

Step-by-step explanation:

The rate of change [slope] of the graph is 35, and for every two blocks you horisontally move represents seventy blocks vertical-wise, therefore an ELEVENTH block would require you to split 70 in half, giving you 35, then add this to 350 to get 385.

I am joyous to assist you at any time.

Answer:

The answer is Option B.) 385

Step-by-step explanation:

The pace of progress of the chart is 35, and for each two squares you horizontally move addresses seventy squares vertical-wise, thusly an 11 square would expect you to part 70 fifty-fifty, giving you 35, then, at that point, add this to 350 to get 385 as a result.

Answer:

The average speed on the return trip is 2.44 miles/h.                  

Step-by-step explanation:

To find the average speed we need to use the following equation:

\( \overline{v} = \frac{d}{t} \)

Where:

d: is the distance

t: is the time

Since the question is to find the average speed on the return trip, we will take the data of the time and speed of only the return trip.

\(\overline{v} = \frac{d}{t} = \frac{5 + 1/2}{2 + 1/4} = 2.44 miles/h\)                

Therefore, the average speed on the return trip is 2.44 miles/h.

I hope it helps you!

Answer:

15

Step-by-step explanation:

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(σ)= 1.55

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) =\(z_{\alpha /2}\frac{\sigma}{\sqrt n}\)

So n= \((z_{\alpha /2}\frac{\sigma}{ME})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

The given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n = \((2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(σ)= 2×1.55

Standard deviation of resistance(σ)= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n= \((2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5)^2

n=(15.996)^2

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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For the information given in the statement you have:

Then, the equation is

Now for the number of hip-hop songs, you can solve for x the equation

Then, the number of hip-hop songs is 12.

Therefore, the correct answer is B.

There are 82 people you should survey if you want to know, at a 98% confidence level, that the sample mean SAT score is within 50 points of the true mean SAT score.

We have,

a college board sample estimated the standard deviation of 2016 SAT scores to be 194 points.

We used the formula,

= x ± Z (α/2) × σ/√n

Here, α = 1 - 98% = 0.02

Z (α/2) = Z (0.02/2) = 2.326

Hence, We get;

Z (α/2) × σ/√n = 50

2.326 x 194 /√n = 50

√n = 2.326 x 194 / 50

n = 82

Therefore, There are 82 people you should survey if you want to know, at a 98% confidence level, that the sample mean SAT score is within 50 points of the true mean SAT score.

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Answer:

1. 32 * (-12) = negative

2. 4.75 * (-2.4) < 3 = negative

3. (-2.15) * (-14.6) = positive

4. (-2) (-3) × (-7) = negative

5. 10.5*(-2)*(-3.5) = positive

6. (-3.7)*(-2.6)*(-0.7)x4​ = negative

Based on the ratings system and the summarize() and mean() functions, the code chunk to add is summarize(mean(Rating)) and the mean rating is 3.185933.

To find the mean rating, the complete code should be trimmed_flavors_df %>% summarize(mean(Rating)).

This code would allow you to see the mean rating of your data by combining the summarize() and mean() functions such that you can display summary statistics.

Because of the "mean()" function, the statistic that will be displayed is the mean rating which in this case would be 3.185933.

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Answer:

2 cm

Step-by-step explanation:

\(\sqrt{4 cm^{2}} =2 cm\)

The proportion of the committee that is left-handed is 4/15, which is equivalent to 0.267 when rounded to three decimal places.

A proportion is a way of expressing the relationship between two quantities. It is often written as a fraction, where the numerator represents the quantity of interest, and the denominator represents the total quantity.

In this case, we are interested in the proportion of left-handed senators, so the numerator will be the number of left-handed senators, which is 4. The denominator will be the total number of senators in the committee, which is 15. Therefore, the proportion of left-handed senators can be written as:

4/15

This fraction can also be expressed as a decimal by dividing the numerator (4) by the denominator (15) using a calculator or long division. When rounded to three decimal places, the decimal equivalent of the fraction is:

0.267

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Given:

For the kiddie teacup ride at a carnival a person needs to be over 36 inches and at most 60 inches tall.

To find:

The inequality that describes all the heights that are eligible to ride.

Solution:

Let h represents the heights that are eligible to ride.

For the kiddie teacup ride at a carnival a person needs to be over 36 inches. It means, height should be greater than 36 inches.

\(h>36\)       ...(i)

For the kiddie teacup ride at a carnival a person needs to be at most 60 inches tall.

\(h\leq 60\)       ...(ii)

Using (i) and (ii), we get

\(36<h\leq 60\)

Therefore, the required inequality is \(36<h\leq 60\).

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766). The margin of error is approximately 0.0140.

To construct a confidence interval for the proportion of Americans who drink tea daily, we can use the formula:

Where,

p = the sample proportion

Z = the critical value corresponding to the desired confidence level

n = the sample size

Given:

Now, let's calculate the confidence interval and margin of error:

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766), with a margin of error of approximately 0.0140.

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Answer:

5) Slope(m): 2

y-intercept(b): (0, 4)

6) Slope(m): -1

y-intercept (b): (0, -6)

7) Slope(m): 5

y-intercept (b): (0, 8)

8) Slope(m): 7

y-intercept (b): (0, 1/2)

Step-by-step explanation:

in order to find the slope and y-intercept you need to rewrite the equation in y=mx+b.

in 5, the equation is -2x+y=4. we need to add 2x to both sides to get y=2x+4. now you can find your slope (2) and your y-intercept point (0, 4)

in 6, the equation is x+y=6. we need to subtract x from to both sides so we get y=-x+6. you would get a slope of -1 and a y-intercept point of (0, 6)

in 7, the equation is -5x=8-y. we need to add 5x to both sides to get 0=8-y+5x. then add y to both sides so we get the equation y=5x+8. you have a slope of 5 and a y-intercept point of (0, 8)

in 8, the equation 0=1-2y+14x. we need to add 2y to both sides and we get 2y=14x+1. since we need y to stand alone we need to divide both sides by 2. now we have y=7x+1/2. the slope is 7 and the y-intercept point is (0, 1/2)

Hope this helps!! :)

Answer:

DF=28 AC=64 CF=32

Step-by-step explanation:

Answer:

The solutions for both system of equations are as follows:

Step-by-step explanation:

The first set of equations is:

\(4x+6y=32\\3x-6y=3\\\)

It can clearly be seen that the coefficients of y are already same in magnitude with different signs so we have to add both equations

So adding both equations, we get

\(4x+6y+3x-6y = 32+3\\7x = 35\\\frac{7x}{7} = \frac{35}{7}\\x = 5\)

Putting x=5 in equation 1

\(4(5)+6y = 32\\20+6y = 32\\6y = 32-20\\6y = 12\\\frac{6y}{6} = \frac{12}{6}\\y = 2\)

The solution is (5,2)

The second set of simultaneous equations is:

\(-3x+5y=-113x+7y=-1\)

We can see that the coefficients of x in both equations are same in magnitude with opposite signs so

Adding both equations

\(-3x+5y+3x+7y = -11-1\\12y = -12\\\frac{12y}{12} = \frac{-12}{12}\\y = -1\)

Putting y= -1 in first equation

\(-3x+5(-1)=-11\\-3x-5=-11\\-3x=-11+5\\-3x=-6\\\frac{-3x}{-3} = \frac{-6}{-3}\\x = 2\)

The solution is: (2,-1)

Hence,

The solutions for both system of equations are as follows:

Answer: 1 & 6

Step-by-step explanation:

It x³ is positive, then x also has to be positive

Save works for negatives

x³ = 1

x = ∛1 = 1

x³ = 216

x = ∛216 = 6

(a) At the 0.05 significance level, the rejection region is t > 1.729. t = (4.6 - 5) / (2.2 / sqrt(20)) = -1.47 t < 1.729 and therefore p > 0.05, so we fail to reject the null hypothesis

(b) X ± t (s/√n)= 4.6 ± 2.093(2.2/√20) = 4.6 ± 1.85 = (2.75, 6.45)

(c)No, the results from the hypothesis test and confidence interval do not agree

(a) Georgianna's claim is that the average child takes at least five years of piano lessons in a small city famous for its music school. We want to test if the sample data provides enough evidence to support her claim.To assess Georgianna's assertion, we will use a hypothesis test.

(b) Constructing a confidence interval with a 95 percent confidence level, we get: X ± t (s/√n) where X = 4.6, s = 2.2, and n = 20.

We'll have to use the t-distribution since the sample size is small, and we'll require a critical value of t. We get 2.093 from the t-table with 19 degrees of freedom.X ± t (s/√n)= 4.6 ± 2.093(2.2/√20) = 4.6 ± 1.85 = (2.75, 6.45)

The following is the meaning of the 95% confidence interval: we can be 95% certain that the true mean number of years a child in the small city spends learning piano is between 2.75 and 6.45 years.

(c)No, the results from the hypothesis test and confidence interval do not agree. The hypothesis test failed to reject the null hypothesis, indicating that the sample provided insufficient evidence to back Georgianna's assertion that children in the city spent at least five years learning piano.

On the other hand, the confidence interval suggests that we can be 95 percent certain that the true mean number of years children in the city spend learning piano is between 2.75 and 6.45 years, which includes the five-year figure stated in the claim.

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Customer #2 has the smallest total bill, including tax and tip.

From the information, three business associates are at their favorite local café for lunch. They have finished their meals and just received their bills. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3.

For customer #1:

(1.06(12.95))(1.15) = 15.79;

The tip is 0.15(1.06(12.95)) = 2.06.

For customer #2:

1.06x = 11.65; x = 10.99; 20%

The tip = 0.2(10.99) = 2.20;

total = 11.65+2.20 = 13.85.

For customer #3:

1.06(11.50) + 0.18(11.50) = 14.26;

The tip is (0.18)(11.50) = 2.07.

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Three business associates are at their favorite local café for lunch. They have finished their meals and just received their bills. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3. Note: Sales tax is 6%, and tips are rounded to the nearest $0.25. Customer #1: The bill, before sales tax has been added, is $12.95. This customer plans to leave a 15% tip, calculated after the tax has been added. Customer #2: The bill, after sales tax has been added, is $11.65. This customer plans to leave a 20% tip, calculated before the tax was added. Customer #3: The bill, before sales tax has been added, is $11.50. This customer plans to leave an 18% tip, calculated before the tax is added.

1. Which customer has the smallest total bill, including tax and tip?

On a circle with center O, points P and A are marked such that the arc PA is a 46º arc. This implies that angle POA is half the measure of the intercepted arc PA, which is 23º. When segment PO is extended to meet the circle again at point T, the size of angle PTA is also 23º

In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Since arc PA is a 46º arc, angle POA, which intercepts arc PA, will have half that measure, which is 23º.

When segment PO is extended to meet the circle again at point T, we can observe that angle PTA is an inscribed angle. As a result, angle PTA will also have the same measure as its intercepted arc PT. Since point P lies on arc PT, which has a measure of 46º, angle PTA will also measure 46º.

This relationship between the intercepted arc and the inscribed angle is a fundamental property of circles. It allows us to determine the measure of an inscribed angle if we know the measure of its intercepted arc, and vice versa. In this case, the measures of both angle POA and angle PTA are determined by the 46º arc PA.

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In the context of a one-sample t-test described as t(15), the information provided refers to the degrees of freedom for the t-distribution, not the mean or sample size.

The answer is option d: the sample size used is 14. In a one-sample t-test, the notation t(df) represents the t-distribution with degrees of freedom (df). The degrees of freedom depend on the sample size and are calculated as df = n - 1, where n is the sample size. In this case, t(15) indicates that the test statistic follows a t-distribution with 15 degrees of freedom. To calculate the degrees of freedom, we subtract 1 from the sample size. Therefore, the sample size used in this one-sample t-test is 14.

The degrees of freedom are important because they determine the shape of the t-distribution and the critical values used in hypothesis testing. As the sample size increases, the t-distribution approaches a standard normal distribution. However, with smaller sample sizes, the t-distribution has thicker tails, allowing for greater variability and accounting for the additional uncertainty in estimating the population parameters.

Hence, it is crucial to correctly interpret the notation in a one-sample t-test, understanding that the number following "t" represents the degrees of freedom, not the mean or the sample size.

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This relationship holds true for all numbers that are multiples of 6.

The relationship between numbers divisible by 6, 2, and 3 can be explained as follows:Every number that is divisible by 6 is also divisible by both 2 and 3.

This relationship arises from the prime factorization of 6, which is 2 x 3. When a number is divisible by 6, it means that it can be divided evenly by 6 without leaving a remainder. Since 6 is composed of the prime factors 2 and 3, any number divisible by 6 must also be divisible by both 2 and 3.

In other words, if a number is divisible by 6, it implies that it is also divisible by 2 and 3 because the factors of 6 are included in its prime factorization. This relationship holds true for all numbers that are multiples of 6.

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The value of expression n + p - 2q when n = p = q is 0

In this question, we have been given an expression n+p-2q

We need to find the value of given expression when n=p=q

Consider given expression,

n + p - 2q

Substitute n = p

= p + p - 2q

= 2p - 2q

Now we substitute p = q in above expression,

= 2q - 2q

= 0

Therefore, the value of expression n + p - 2q when n = p = q is 0

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the required probability is 0.5668

Given that the distribution of the time it takes for the first goal to be scored in a hockey game is known to be extremely right-skewed with population mean 12 minutes and population standard deviation 8 minutes.

We need to find the probability

that in a random sample of 36 games, the mean time to the first goal is more than 15 minutes.To find this probability, we will use the z-score formula.z = (x - μ) / (σ / √n)wherez is the z-scorex is the sample meanμ is the population meanσ is the population standard deviationn

is the sample sizeGiven that n = 36, μ = 12, σ = 8, and x = 15, we havez = (15 - 12) / (8 / √36)z = 1.5Therefore, the probability that in a random sample of 36 games, the mean time to the first goal is more than 15 minutes is P(z > 1.5).We can find this probability using a standard normal table or a calculator.Using a standard normal table, we can find the area to the right of the z-score of 1.5. This is equivalent to finding the area between z = 0 and z = 1.5 and subtracting it from 1.P(z > 1.5) = 1 - P(0 < z < 1.5)Using a standard normal table, we find thatP(0 < z < 1.5) = 0.4332Therefore,P(z > 1.5) = 1 - 0.4332 = 0.5668Therefore, the probability that in a random sample of 3games, the mean time to the first goal is more than 15 minutes is 0.5668 (rounded to four decimal places).

Hence, the required probability is 0.5668.

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The probability that in a random sample of 36 games, the mean time to the first goal is more than 15 minutes is approximately 0.0122 or 1.22%.

The probability that in a random sample of 36 games, the mean time to the first goal is more than 15 minutes can be determined using the Central Limit Theorem (CLT).

According to the CLT, the distribution of sample means from a large enough sample follows a normal distribution, even if the population distribution is not normal. In this case, since the sample size is 36 (which is considered large), we can assume that the sample mean follows a normal distribution.

To find the probability, we need to standardize the sample mean using the population mean and standard deviation.

First, we calculate the standard error of the mean, which is the population standard deviation divided by the square root of the sample size. In this case, it would be 8 / √36 = 8 / 6 = 4/3 = 1.3333.

Next, we calculate the z-score, which is the difference between the sample mean and the population mean divided by the standard error of the mean. In this case, it would be (15 - 12) / 1.3333 = 2.2501.

Finally, we use the z-table or a calculator to find the probability associated with a z-score of 2.2501. The probability is the area under the standard normal curve to the right of the z-score.

Using a z-table, we find that the probability is approximately 0.0122. This means that there is a 1.22% chance that the mean time to the first goal in a random sample of 36 games is more than 15 minutes.

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Answer:it would be way over 100 because If you do the math it comes out as 312.73….. therefore it’s higher than 100 hope this helped hunny boo

Answer:

$26.00

Step-by-step explanation:

no explination :D

Answer:

the tax would be 26

Step-by-step explanation: