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A line with a slope of -2 passes through the point (4, 7). Write an equation for this line in point-slope form.

Answers

Answer 1

Answer:

Answer:

The equation in point-slope is $y-7=-2(x-4)$ .

Step-by-step explanation:

Point-slope is a specific form of linear equations in two variables:

$y-b=m(x-a)$

When an equation is written in this form, m gives the slope of the line and (a, b) is a point the line passes through.

We want to find the equation of the line that passes through (4, 7) and whose slope is -2. Well, we simply plug m = -2, a = 4, and b = 7 into point-slope form.

$y-7=-2(x-4)$

Answer 2

Answer:

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{7})~\hspace{10em} slope = m\implies -2 \n\n\n \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\n \cline{1-1} \n y-y_1=m(x-x_1) \n\n \cline{1-1} \end{array}\implies y-7=-2(x-4)$

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PLEASE HELP!!!Aidan is 5.5 ft tall and casts a shadow that is 9 ft long. He notices that a nearby tower casts a shadow that is 305 ft long.What is the height of the tower (h)?
Consider a disease whose presence can be identified by carrying out a blood test. Let p denote the probability that a randomly selected individual has the disease. Suppose n individuals are independently selected for testing. One way to proceed is to carry out a separate test on each of the n blood samples. A potentially more economical approach, group testing, was introduced during World War II to identify syphilitic men among army inductees. First, take a part of each blood sample, combine these specimens, and carry out a single test. If no one has the disease, the result will be negative, and only the one test is required. If at least one individual is diseased, the test on the combined sample will yield a positive result, in which case the n individual tests are then carried out. [The article "Random Multiple-Access Communication and Group Testing"† applied these ideas to a communication system in which the dichotomy was active/idle user rather than diseased/nondiseased.] If p = 0.15 and n = 5, what is the expected number of tests using this procedure? (Round your answer to three decimal places.)
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Use the number 7.14 to respond to the following:Identify the whole number.What is the farthest place value to the right?Write the decimal in word form.Write the decimal in expanded form.

Find the measure of <8

Answers

I’m pretty sure it’d be 72 degrees because they are alternate exterior angles

Three teams, A, B and C, play in a competition.games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 8 games.
In total, how many games have the three teams won?

Answers

Answer:

A = 24

B = 8

C = 6

Step-by-step explanation:

4:3 from B:C

8:6

8 games won by B and 6 games won by C.

3:1 from A:B

24:8

24 by A and 8 by B

Final answer:

Team A won 24 games, Team B won 8 games and Team C won 6 games. So, the total games won by all three teams is 38.

Explanation:

From the problem, we know that the ratio of games won by Team A to Team B is 3:1, and the ratio of games won by Team B to Team C is 4:3. We also know that Team B has won 8 games.

Since the ratio of Team B to Team A is 1:3, Team A must have won 3 times as many games as Team B. Therefore, Team A has won 3 * 8 = 24 games.

The ratio of games won by Team B to Team C is 4:3. This means Team B won 4 games for every 3 games Team C won. Since Team B won 8 games, Team C must have won 3/4 as many games as Team B. Therefore, Team C won 3/4 * 8 = 6 games.

So, in total, the three teams won 24 + 8 + 6 = 38 games.

Learn more about Ratio here:

brainly.com/question/32531170

#SPJ3

a softball league has 13 teams, if every team must play every other team in the first round of league play, how many games must be scheduled

Answers

Answer:

78 games

Step-by-step explanation:

Think of it this way. Let's name the teams Team 1 through Team 13. Team 1 needs to have 12 games to play each other team. Once those are scheduled, Team 2 needs to have 11 games scheduled to play all the other teams (remember their game against Team 1 was already scheduled). Team 3 needs to have 10 games scheduled to play all the other teams (remember their games against Team 1 and Team 2 have already been scheduled). This patten continues until you schedule a single game between Team 12 and Team 13. So the total number of games that need to be scheduled are:

12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 78

I don't know if the concept of triangular numbers has been touched on in your class, but if so, there is a much simpler way to calculate this using the triangular number formula with n = 12. The formula is:

T = (n * (n + 1)) / 2

So in this case:

(12 * (12 + 1)) / 2 = (12 * 13) / 2 = 6 * 13 = 78

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%.

On two investments totaling $6,000, Kevin lost 3% on one and earned 6% on the other. If his net annual receipts were $288, how much was each investment?

Answers

ANSWER:

$ 800 was invested in the account at 3%

$5200 was invested in the account at 6%

STEP-BY-STEP EXPLANATION:

We can establish the following system of equations thanks to the help of the statement:

Let x represent the amount invested in the investment that lost value

Let y represent the amount invested in the investment that gained

value.

$\begin{gathered} x+y=6000\rightarrow y=6000-x\text{ (1)} \n -0.03x+0.06y=288\text{ (2)} \end{gathered}$

We replace equation (1) in (2) and solve for x:

$\begin{gathered} -0.03x+0.06\cdot(6000-x)=288 \n -0.03x+360-0.06x=288 \n -0.09x=288-360 \n x=(-72)/(-0.09) \n x=800 \n \text{ Now, for y replacing in (1)} \n y=6000-800=5200 \end{gathered}$

Therefore, $ 800 was invested in the account the lost value, and $ 5200 was invested in the account that gained value.

A bookshelf is 3 feet long. Each book on the shelf is 3/4 inches wide. How many books will fit on the shelf? (Remember, there are 12 inches in a foot.)

Answers

Answer:

Step-by-step explanation:

3 feet is 36 inches. 3/4 of an inch is .75 inches. So you have a very simple equation of 36/.75=48

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