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The distance d of a particle moving in a straight line is given by d(t) = 2t3 + 5t – 2, where t is given in seconds and d is measured in meters. Find an expression for the instantaneous velocity v(t) of the particle at any given point in time.

Answers

Answer 1

Answer:

Answer:

6t^2 + 5

Step-by-step explanation:

i took the test and somehow got it correct:)

Answer 2

Answer:

Answer:

Step-by-step explanation:

hello,

$v(t)=(d(t))/(t)=2t^2+5-(2)/(t)$

hope this helps

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HOME Realty claims that it can sell a detached, residential house faster than any other realty company. With the aim of examining HOME's claim, you sample 20 customers who sold a detached, residential house through HOME and record the selling times (in days) of the houses. Your data are summarized below:Selling Time Frequency
0 10 3
10 20 4
20 30 6
30 40 4
40 50 3

Find the proportion of selling times in the sample that are less than 20 days claims that it can sell a detached, residential house faster than any other realty company.

Answers

Answer:

0.35

Step-by-step explanation:

Given the data:

Selling Time___ Frequency

0 10____________3

10 20__________ 4

20 30__________ 6

30 40__________ 4

40 50__________ 3

Proportion of selling time in sample above that are less Than 20 days :

Taking the sum of the frequency :

Hence, total frequency = (3 + 4 + 6 + 4 + 3) = 20

Selling time which is less Than 20 days :

(0 - 10) = 3

(10 - 20) = 4

Total = (3 + 4) = 7

Proportion = selling time less Than 20 days / total frequency

= 7 / 20

= 0.35

Say a business found that 29.5% of customers in Washington prefer grey suits. The company chooses 8 customers in Washington and asks them if they prefer grey suits. What assumption must be made for this study to follow the probabilities of a binomial experiment?

Answers

Answer:

The assumption that must be made for this study to follow the probabilities of a binomial experiment is that there must be only two outcomes of each trail in this study (meaning that it is either they prefer grey suits or they do not prefer grey suits). There must be no other option apart from those two options and each of the independent trails must be mutually exclusive, meaning that the two required options cannot occur together. It is either the first option (prefer grey suits) or the second option (do not prefer grey suits).

Step-by-step explanation:

If the ratio of boys to girls at the school is 2:5 and there are 40 boys how many girls are there?

Answers

The total number of students in school is 140 and number of girls at the school is equal to 100.

What do you mean by ratio ?

Ratio is the quantitative relationship between two values indicating how frequently one value contains or is contained within the other.

It is given that the ratio of boys to girls at the school is 2:5.

Let's assume the total number of students in school is x.

We now need to find the number of girls in the school but before that we must try to find the total number of students in the school.

Sum of ratios = 2 + 5 = 7

It is given that there are 40 boys in students.

2/7 of the total number of students are boys.

i.e., the expression can be written as :

2x / 7 = 40

2x = 40 × 7

2x = 280

x = 140

The total number of students in school is 140.

So , the number of girls in school is :

= 140 - 40

= 100

There are 100 girls in the school.

Therefore , the total number of students in school is 140 and number of girls at the school is equal to 100.

Learn more about ratios here :

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Answer:

100 girls

Step-by-step explanation:

The ratio of boys : girls is 2 : 5.

In other words, boys are 2 parts of the school while girls are 5 parts of the school.

Since there are 40 boys, 2 parts of the school is 40. Thus:

$2p = 40\np = 20$

1 part is 20.

Since there are 5 parts girls, there are

$5p = 5*20 = 100$

100 girls.

Answer: 100 girls

According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets returned (BusinessWeek, January 1 5, 2007). A Houston department store sampled 80 items sold in January and found that 12 of the items were returned.Construct a point estimate of the proportion of items returned for the population of sales transactions at the Houston store.

Answers

Using the sample proportion, it is found that the point estimate is of 0.15 = 15%.

What is a sample proportion?

A sample proportion is given by the number of desired outcomes divided by the number of total outcomes. It can also serve as the point estimate for the population proportion.

In this problem, 12 out of the 80 items sold were returned, hence:

12/80 = 0.15 = 15%.

The point estimate is of 0.15 = 15%.

More can be learned about point estimates at brainly.com/question/24651197

Answer:

a) $\hat p = (X)/(n)= (12)/(80)= 0.15$

b) $0.15 - 1.96 \sqrt{(0.15(1-0.15))/(80)}=0.072$

$0.15 + 1.96 \sqrt{(0.15(1-0.15))/(80)}=0.228$

And the 95% confidence interval would be given (0.072;0.228).

c) For this case since the confidence interval not contains the value 0.06 or 6% and since the lower limit for the confidence interval is higher than 0.06 (0.072>0.06), we have enough statistical evidence to support the conclusion that the true proportion of items returned is higher than 0.06 or 6% at a significance of 5%.

Step-by-step explanation:

Assumign the following question for the problem:

a. Construct a point estimate of the proportion of items returned for the population of sales transactions at the Houston store.

For this case the best estimate for the true proportion is given by the sample proportion:

$\hat p = (X)/(n)= (12)/(80)= 0.15$

b. Construct a 95% confidence interval for the porportion of returns at the Houston store.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The confidence interval would be given by this formula

$\hat p \pm z_(\alpha/2) \sqrt{(\hat p(1-\hat p))/(n)}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_(\alpha/2)=1.96$

And replacing into the confidence interval formula we got:

$0.15 - 1.96 \sqrt{(0.15(1-0.15))/(80)}=0.072$

$0.15 + 1.96 \sqrt{(0.15(1-0.15))/(80)}=0.228$

And the 95% confidence interval would be given (0.072;0.228).

c. Is the proportion of returns at the Houston store significantly different from the returns for the nation as a whole? Provide statistical support for your answer.

For this case since the confidence interval not contains the value 0.06 or 6% and since the lower limit for the confidence interval is higher than 0.06 (0.072>0.06), we have enough statistical evidence to support the conclusion that the true proportion of items returned is higher than 0.06 or 6% at a significance of 5%.

What is the value of the x-coordinate of point A?(a) sin(pi/5)
(b) cos (pi/5)
(c) sin (6pi/5)
(d) cos (6pi/5)
(e) sin (9pi/5)

Answers

The x - coordinate of the Point A is -

$$(√(5) +1)/(4)$

We have a Point A(x, y) on the graph.

We have to find out the x-coordinate of Point A(x, y).

Explain the resolution of Position vector of any point on the Cartesian coordinate.

For any position vector (say OA), having magnitude of 'M' Units, making an angle $$\theta$ with the x - axis, can be resolved along the x and y axes as -

OA = (M cos $$\theta$ ) $a_(x)$ + (M sin $$\theta$ ) $a_(y)$

According to the question, we have -

$$\theta =(\pi )/(5)$

We have to find the x - component of the position vector OA.

The circle has a radius of 1 units. Therefore, |OA| = 1

Assume that the x - coordinate of Point A is x.

Now -

x = |OA| cos ( $$(\pi )/(5)$ )

x = 1 x $(√(5) +1)/(4)$

x = $(√(5) +1)/(4)$

Hence, the x - coordinate of the PointA is -

$$(√(5) +1)/(4)$

To solve more questions on finding Coordinate Points, visit the link below -

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Step-by-step explanation:

You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test. (a) What is your expected score on the exam? (Hint: Your expected score is the mean value of the x distribution.) (b) Compute the variance and standard deviation of x. Variance = Standard deviation =

Answers

Answer:

a) 20

b) Variance 16, standard deviation 4

Step-by-step explanation:

For each question, there are only two possible outcomes. Either you guesses the answer correctly, or you do not. The probability of guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$