The equation of a circle is x2 + 8x + y2 - 12y = 144. What are the coordinates of the center and the length of the radius of the circle?

9514 1404 393

Answer:

  8 inches

Step-by-step explanation:

The product of length, width, and height is the volume.

  V = LWH

  H = V/(LW) = 64/(2·4) = 8

The height of the new box should be 8 inches.

To create a box that is 2 inches wide, 4 inches long, and has a volume of 64 cubic inches, the box should be made 8 inches tall.

The question asks how tall a new box should be if it is 2 inches wide, has a length of 4 inches, and must have a volume of 64 cubic inches. To find the height of the box, we use the formula for the volume of a rectangular prism (box), which is Volume = length × width × height.

Given the volume (V) is 64 cubic inches, the width (w) is 2 inches, and the length (l) is 4 inches, we can rearrange the formula to solve for the height (h):

h = V / (l × w)
= 64 / (4 × 2)
= 64 / 8
= 8 inches

Therefore, to create a new box with the specified dimensions and volume, Vector should make the box 8 inches tall.

Answer:

150

Step-by-step explanation:

Answer: You would pay $150

Step-by-step explanation: Take 25 times 4, then add on the additional fee.

Data for complete question is attached.

Answers

Therefore .

A. The regression equation is

y = beta0 + beta1+ ∈

B. From the given output regression line

y= 2.478+7.717x

The question addresses using a simple linear regression model to determine the relationship between two variables, and how to interpret the parameters of that model, as well as the significance of the correlation coefficient in the context of a hypothetical student protest situation.

The subject of this question is about linear regression analysis in mathematics, particularly in the context of statistical analysis. The question demonstrates the application of a simple linear regression to decipher the relationship between the duration of student sit-ins (independent variable) and the number of arrests (dependent variable).

Answer:

The 95% confidence interval for the mean is (3.249, 4.324).

We can predict with 95% confidence that the next trial of the paint will be within 3.249 and 4.324.

Step-by-step explanation:

We have to calculate a 95% confidence interval for the mean.

As the population standard deviation is not known, we will use the sample standard deviation as an estimation.

The sample mean is:

[tex]M=\dfrac{1}{15}\sum_{i=1}^{15}(3.4+2.5+4.8+2.9+3.6+2.8+3.3+5.6+3.7+2.8+4.4+4+5.2+3+4.8)\\\\\\ M=\dfrac{56.8}{15}=3.787[/tex]

The sample standard deviation is:

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{15}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{14}\cdot [(3.4-(3.787))^2+(2.5-(3.787))^2+(4.8-(3.787))^2+...+(4.8-(3.787))^2]}\\\\\\[/tex][tex]s=\sqrt{\dfrac{1}{14}\cdot [(0.15)+(1.66)+(1.03)+...+(1.03)]}[/tex]

[tex]s=\sqrt{\dfrac{13.197}{14}}=\sqrt{0.9427}\\\\\\s=0.971[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=3.787.

The sample size is N=15.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.971}{\sqrt{15}}=\dfrac{0.971}{3.873}=0.2507[/tex]

The t-value for a 95% confidence interval is t=2.145.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.145 \cdot 0.2507=0.538[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 3.787-0.538=3.249\\\\UL=M+t \cdot s_M = 3.787+0.538=4.324[/tex]

The 95% confidence interval for the mean is (3.249, 4.324).

To estimate a 95% prediction interval, calculate the sample mean and standard deviation, then use the t-distribution to apply the formula that includes the t-value for 95% confidence level and the sample size.

To find a 95% prediction interval for the drying time for the next trial of latex paint, we need to use the measurements provided with the assumption that they represent a random sample from a normally distributed population.

However, before we can provide the prediction interval, we must first calculate the sample mean and the sample standard deviation from the given data. With those, we can then use the t-distribution to find the prediction interval, which will take the form of:

Sample Mean ± (t-value * Sample Standard Deviation * √(1 + 1/n))

Where 'n' is the number of observations and the t-value is determined from the t-distribution table for (n-1) degrees of freedom at the 95% confidence level.

Once calculated, this interval estimates the range within which we can expect the drying time for the next trial of paint to fall, with 95% confidence.

Answer:

1 Lawn per 3 Hours

Step-by-step explanation:

In 'Lawns : Hours' the work that she has done = 4 : 12 = 1 : 3

With this workout, we can conclude that Maya mowed 1 Lawn every 3 Hours.

Maya's rate of mowing is 3 hours per lawn, calculated by dividing the total time spent (12 hours) by the number of lawns mowed (4 lawns).

Maya mowed 4 lawns in 12 hours, so to find her rate of mowing in hours per lawn, we divide the total hours by the number of lawns mowed. The calculation is 12 hours / 4 lawns, which equals 3 hours per lawn. Therefore, Maya's mowing rate is 3 hours per lawn.

Answer:

300tan43 - 300tan40

Step-by-step explanation:

Use tangent to find the height of the building:

tan40 = b/300

b = 300tan40

The use tangent to find the height to the top of the antenna:

tan43 = a/300

a = 300tan43

The antenna height = a - b

Answer:

Lacrosse = 62 students

Swimming = 62 students

Soccer = 124 students

Football = 186 students

Step-by-step explanation:

Based on the information, we can draw some equations

1.    Lacrosse = Swimming

2.   Soccer = 2 * Lacrosse

3.   Football = 3 * Swimming

4.   Football + Soccer + Swimming + Lacrosse = 434

Lets solve for once sport at a time, I will start with Football.

I will put equation 1, 2 and 3 into equation 4

3Sw + 2L + L + L = 434

We can now again put equation 1 into the new equation 4

3L + 2L + L + L = 434

Simplify

7L = 434

L = 434 ÷ 7

L = 62 students

Since L = Sw, 62 students did swimming also

We can put L into equation 2 to solve for So

So = 2 * 62

So = 124 students

And now we can put Sw into equation 3 to solve for F

F = 3 * 62

F = 186 students

Answer:

4283.46 billion

Step-by-step explanation:

According to the information of the problem

[tex]\hat{Y} = 20.46 + 4.06(X)[/tex]

Therefore you are looking for

[tex]\hat{Y} = 20.46 + 4.06(1050) = 4283.46[/tex]

Answer:

Step-by-step explanation:

The question is incomplete since they do not give information about the Car type 3.

We will do it in a generic way, we will say that the Car type 3 has a mean of M and a standard deviation SD.

We would be:

P (CT3 <550) = P [z <(550 - X) / SD]

Now if we give it values, for example that X = 600 and SD = 120

It would remain:

P (CT3 <550) = P [z <(550 - 600) / 120]

P (CT3 <550) = P [z <-0.42]

We look for this value in the normal distribution table (attached) and it shows us that the probability is approximately 0.3372, that is, 33.72%

What you need to do is replace the X and SD values of theCar type 3 in the equation above how I just did and you will get the result.

The dot product of u = 9i+4j and v = 3i- j is 23.

The dot product of two vectors can be calculated by multiplying their corresponding components and then summing them up. In this case, the dot product of u = 9i+4j and v = 3i- j is:

u · v = (9)(3) + (4)(-1) = 27 - 4 = 23

So, the dot product of u and v is 23.

Answer:

You have to break apart the shape into individual shapes to find the volume of each one. Then you add.

hope this helped :)

Answer:

A. [tex]\frac{64}{25}[/tex] ​, because probability values cannot be greater than 1.

C. -1.5, because probability values cannot be less than 0.

Step-by-step explanation:

Probability is the extent to which an event is likely to happen. It ranges from 0(impossible) to 1(certain). Probability values can be written in decimal form or in fractional form.

The following numbers could not be used to represent the probability of an event.

A. [tex]\frac{64}{25}[/tex] ​, because probability values cannot be greater than 1.

C. -1.5, because probability values cannot be less than 0.

The range of g(x) = 3|x-1|-1 is (-∞,∞).

The range is "set of all y-coordinates of the function's graph".

According to the question,

g(x) = 3 |x-1| - 1

To find range of linear polynomial 3|x-1|-1  put any value in right 'x' we can able to get any value 'y' in the set (-∞.∞).

Hence, the range of g(x) = 3|x-1|-1 is (-∞,∞).

Learn more about range here

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Answer:

irrational

Step-by-step explanation:

because √3 is irrational

Answer:

irational

Step-by-step explanation:

Answer:

a) Null hypothesis:[tex]\mu = 140[/tex]  

Alternative hypothesis:[tex]\mu \neq 140[/tex]  

b) [tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]  

c) The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]

Now we can calculate the p value, since we are conducting a two tailed test:

[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]  

Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes

Step-by-step explanation:

Information provided

[tex]\bar X=170[/tex] represent the sample mean   in minutes

[tex]s=80[/tex] represent the standard deviation

[tex]n=64[/tex] sample size  

[tex]\mu_o =140[/tex] represent the value to verify

[tex]\alpha[/tex] represent the significance level

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Part a

We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average (140 minutes), the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 140[/tex]  

Alternative hypothesis:[tex]\mu \neq 140[/tex]  

Part b

Since we don't know the population deviation the statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]  

Part c

The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]

Now we can calculate the p value, since we are conducting a two tailed test:

[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]  

Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes

The null hypothesis that the average internet usage in Soddy-Daisy is not significantly different from the U.S. average is rejected based on a computed z-score of 3, which falls outside the critical z-score values for a 95% confidence level. Therefore, the average internet usage in Soddy-Daisy is significantly different from the U.S. average.

This problem pertains to the domain of statistical hypothesis testing. Let's first set up the null and alternative hypotheses:

For the second part, we need to compute the test statistic. The formula for the test statistic (z) in this context is z = (x - μ) / (σ/√n), where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

So, (170-140) / (80/√64) = 30 / (10) = 3. The z score is 3.

For the final part of your question, with 95% confidence, the critical z-score values are -1.96 and +1.96. Since our observed z-score of 3 is outside this range, we reject the null hypothesis. Therefore, we can conclude that the average internet usage in Soddy-Daisy is significantly different from the U.S. average.

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Answer:

  C. 1175

Step-by-step explanation:

At 3 liters per minute, the amount leaked in 27 minutes is ...

  (3 L/min)(27 min) = 81 L

Then the amount remaining is ...

  1256 L - 81 L = 1175 L

There will be 1175 liters in the barrel after 27 minutes.

u = 2i - 6j

v = 3i + 9j

Take the dot product:

u • v = (2i - 6j) • (3i + 9j)

u • v = (2i • 3i) + (2i • 9j) + (-6j • 3i) + (-6j • 9j)

u • v = 6 (i • i) + 18 (i • j) - 18 (j • i) - 54 (j • j)

The dot product is defined so that for the orthogonal unit vectors i and j, we have i • i = j • j = 1, and i • j = 0. So the above reduces to

u • v = 6 + 0 - 0 - 54

u • v = -48

Answer:

The s-score corresponding to a score  of 54 is 4.67

Step-by-step explanation:

In a certain normal distribution of scores:

Mean = [tex]\mu = 40[/tex]

Standard deviation = [tex]\sigma = 3[/tex]

We are supposed to find  the z-score corresponding to a score  of 54.

Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]

x=54

Substitute the values

So,[tex]Z= \frac{54-40}{3}[/tex]

Z=4.67

So, Option A is true

Hence the s-score corresponding to a score  of 54 is 4.67

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Eric and Joshua are playing ping pong and pool. Joshua believes he has a good chance of beating Eric in at least one of the games. The probability Joshua beats Eric in ping pong is 0.48. The probability Joshua beats Eric in pool is 0.46. Joshua is willing to assume the probability of Eric winning a game of ping pong is independent of him winning a game of pool.

Find the probability:

The probability that Joshua beats Eric in ping pong AND pool?

The probability that Joshua beats Eric in ping pong OR pool?

Answer:

P(pp & pool) = 22%

There is 22% probability that Joshua beats Eric in ping pong AND pool.

P(pp OR pool) = 50%

There is 50% probability that Joshua beats Eric in ping pong OR pool.

Step-by-step explanation:

The probability Joshua beats Eric in ping pong is given by

P(pp) = 0.48

The probability Joshua beats Eric in pool is given by

P(pool) = 0.46

The probability that Joshua beats Eric in ping pong AND pool is given by

P(pp & pool) = P(pp)×P(pool)

P(pp & pool) = 0.48×0.46

P(pp & pool) = 0.22

P(pp & pool) = 22%

Therefore, there is 22% probability that Joshua beats Eric in ping pong AND pool.

The probability that Joshua beats Eric in ping pong OR pool is given by

P(pp OR pool) = P(pp)×0.52 + P(pool)×0.54

Where 0.52 is the probability that Eric beats Joshua in the ping pong match (1 - 0.48 = 0.52)

Where 0.54 is the probability that Eric beats Joshua in the pool match (1 - 0.46 = 0.54)

P(pp OR pool) = 0.48×0.52 + 0.46×0.54

P(pp OR pool) = 0.25 + 0.25

P(pp OR pool) = 0.50

P(pp OR pool) = 50%

Therefore, there is 50% probability that Joshua beats Eric in ping pong OR pool.

To calculate the probability of Joshua beating Eric in at least one game of ping pong or pool, taking into account the probabilities for each game.

Probability plays a key role in analyzing the chances of events happening. In this case, we have two independent events: winning ping pong and winning pool. The probability of Joshua winning at least one game can be calculated using the probabilities given for each game.

Calculate the probability of Joshua winning both games: 0.48 × 0.46 = 0.2208

Subtract this value from 1 to find the probability of Joshua winning at least one game: 1 - 0.2208 = 0.7792

Therefore, Joshua has a 77.92% chance of beating Eric in at least one of the games.

Answer:

The   95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

(48.937 , 50.863)

Step-by-step explanation:

Explanation:-

Given data random sample of 46 bins, the sample mean amount was 49.9 pounds and the sample standard deviation was 3.641

The sample size 'n' =46

mean of the sample x⁻ = 49.9

Standard deviation of the sample S = 3.641

Confidence intervals:-

The   95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

Degrees of freedom = n-1  = 46-1 =45

The tabulated value   t₀.₉₆ =   1.794 ( from t-table)

[tex](49.9 - 1.794 \frac{3.641}{\sqrt{46} } ,49.9+ 1.794 \frac{3.641}{\sqrt{46} })[/tex]

(49.9 -0.9630 , 49.9+0.9630)

(48.937 , 50.863)

Conclusion:-

The   95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

(48.937 , 50.863)

Answer:

74.1 or 74

Step-by-step explanation:

Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for the step by step solution of the given problem.

Answer:

11-5 = 6

Step-by-step explanation:

Answer:

A Reflection on Edg

Step-by-step explanation:

Answer:B reflection

Step-by-step explanation:

edg 2022

Answer:

[tex]1/6[/tex]

Step-by-step explanation:

When we say, the difference of scores should be more than 3 it means that the difference can be 4 or 5.

Case 1: The difference of scores is 4.

The possible outcomes can be [tex](1,5), (5,1), (2,6) \text{ and }(6,2).[/tex] i.e. 4 number of cases are possible.

Case 2: The difference of scores is 5.

The possible outcomes can be [tex](1,6) \text{ and } (6,1)[/tex]. i.e. 2 number of cases.

Here, total number of favorable cases are 4 + 2 = 6.

Total number of cases, when two fair dice are rolled, are 36.

These cases are:

[tex][(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),\\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\..\\(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)]}[/tex]

Formula:

[tex]\text{Probability of an event = } \frac{Number\ of\ favorable\ cases}{Total\ number\ of\ cases}[/tex]

Hence, the probability that the difference of scores is more than 3, at the roll of 2 dice, is [tex]\frac{6}{36}[/tex] i.e. [tex]\frac{1}{6}[/tex].

Hence, the required probability is [tex]\frac{1}{6}[/tex].

Answer:

Reject null hypothesis ([tex]H_0[/tex]) since the​ P-value is less than the significance level.

Step-by-step explanation:

We are given that it has long been stated that the mean temperature of humans is 98.6 degrees F. ​However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degrees F.

The sample data resulted in a sample mean of 98.2 degrees F and a sample standard deviation of 0.9 degrees F.

Let [tex]\mu[/tex] = mean temperature of humans.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu\geq[/tex] 98.6°F      {means that the mean temperature of humans is more than or equal to 98.6°F}

Alternate Hypothesis, [tex]H_A[/tex] : p < 98.6°F    {means that the mean temperature of humans is less than 98.6°F}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                        T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean temperature = 98.2°F

            [tex]\sigma[/tex] = sample standard deviation = 0.9°F

            n = sample of healthy adults = 56

So, test statistics  =   [tex]\frac{98.2-98.6}{\frac{0.9}{\sqrt{56} } }[/tex]  ~ [tex]t_5_5[/tex]

                               =  -3.326

The value of t test statistics is -3.326.

Now, P-value of the test statistics is given by following formula;

         P-value = P( [tex]t_5_5[/tex] < -3.326) = 0.00077 or 0.08%

Since, P-value of the test statistics is less than the level of significance as 0.08% < 1%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean temperature of humans is less than 98.6°F.

To determine if the mean human temperature is less than 98.6°F, we conducted a left-tailed t-test using the provided sample data. We calculated the t-test statistic and then used it to find the p-value. We then used the p-value to make our final decision on whether to reject or fail to reject our null hypothesis.

In this scenario, we are performing a hypothesis test about the average human temperature. Let's formulate our hypothesis first:

We will conduct a left-tailed t-test because we are testing whether the average human temperature is less than a stated value.

Given the data: the sample size n = 250, the sample mean (x_bar) = 98.2 F, and the standard deviation (s) = 0.9 F.

To calculate the t-test statistic, use the formula: t0 = (x_bar - μ) / (s/√n)

For getting the p-value, you would use a statistical table or software with the above t statistic and degree of freedom (which is n-1 in this case).

In the end, if your p-value is less than the significance level (α = 0.01 in this case), we reject the null hypothesis, if not, we fail to reject the null hypothesis.

If the P-value is less than α, we would conclude that the research may be correct, and the average human temperature is indeed lower than 98.6 F (37.0 °C).

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Answer:

-1/4

Step-by-step explanation:

The slope is found by

m = (y2-y1)/(x2-x1)

    = (-1-2)/(7- -5)

    = (-1-2)/(7+5)

     = -3/12

     = -1/4

A Markov chain is used to model this situation. The transition matrix based on the given probabilities will be [[0.9, 0.1],[0.4, 0.6]]. Also, to calculate the probability of being in a high-volume state two weeks from now given that it is in a high-volume state now, we square the matrix and look at the upper-left entry.

A Markov process, in particular, a Markov chain, is a stochastic process that undergoes transitions from one state to another on a state space following the Markov property, stating that future states depend only on the current state and not on events that occurred before it. The transition matrix in these cases provides the probabilities between state transitions.

Given the data:

Based on these probabilities the transition matrix will be of the form:

[[0.9, 0.1],[0.4, 0.6]].

To find the probability that the volume will be high two weeks from now, we will need to square the matrix as we are considering two steps ahead. The top left element of the resulting matrix will give the desired probability. In general, the i,j-th entry of the square of a transition matrix gives the 2-step transition probability from state i to state j.

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Answer:

2646/100 or 260  46/100 or 260 23/50

Answer:

He lost $5.

Step-by-step explanation:

When the customer gives him the $20, the salesman does not gain any money because it is fake.

Then, he gets real money summing up to $20. So he gains that, but then gives $5 away. Now he has $15.

Then, the lady tells him the $20 bill is fake, so he must give the lady $20. So, 15 - 20 = -5. He lost $5.

Answer: He lost $35. $15 for the pair of shoes and $20 for having to repay the joined store for the counterfit money.

Step-by-step explanation: