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DIA [1.3K]
3 years ago
5

the point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the stand

ard form of the equation for this line?
Mathematics
1 answer:
Olin [163]3 years ago
8 0
                   y - 1 = 0.25(x - 12)
                   y - 1 = 0.25(x) - 0.25(12)
                   y - 1 = 0.25x - 3
                     + 1             + 1
                        y = 0.25x - 2
          -0.25x + y = 0.25x - 0.25x + 2
          -0.25x + y = 2
    -1(-0.25x + y) = -1(2)
-1(-0.25x) - 1(y) = -2
           0.25x - y = -2
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2x + 2y - x - (8 + 1)?
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Answer:

x + 2 y − 9

Step-by-step explanation:

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2 years ago
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Suppose $200 is invested at the annual interest rate 6% compounded continuously what is the amount in the account after years ?
Setler [38]
The amount in the account after years is 12
6 0
3 years ago
A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. A previous study indicates that the propo
never [62]

Answer:

A sample of 997 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

A previous study indicates that the proportion of left-handed golfers is 8%.

This means that \pi = 0.08

98% confidence level

So \alpha = 0.02, z is the value of Z that has a p-value of 1 - \frac{0.02}{2} = 0.99, so Z = 2.327.  

How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?

This is n for which M = 0.02. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.02 = 2.327\sqrt{\frac{0.08*0.92}{n}}

0.02\sqrt{n} = 2.327\sqrt{0.08*0.92}

\sqrt{n} = \frac{2.327\sqrt{0.08*0.92}}{0.02}

(\sqrt{n})^2 = (\frac{2.327\sqrt{0.08*0.92}}{0.02})^2

n = 996.3

Rounding up:

A sample of 997 is needed.

3 0
3 years ago
40. In a statistics class of 30 students, there were 13 men and 17 women. Two of the men and three of the women received an A in
Harrizon [31]

Answer:

a) 56.67% probability that the student is a woman

b) 16.67% probability that the student received an A

c) 63.33% probability that the student is a woman or received an A.

d) 83.33% probability that the student did not receive an A.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We have that:

30 students

13 men

17 women

2 men that got an A and 11 men that did not get an A.

3 women that got an A and 14 women that did not get an A.

a. Find the probability that the student is a woman.

30 students, of which 17 are women.

P = \frac{17}{30} = 0.5667

56.67% probability that the student is a woman

b. Find the probability that the student received an A.

30 students, of which 5 received an A

P = \frac{5}{30} = 0.1667

16.67% probability that the student received an A

c. Find the probability that the student is a woman or received an A.

30 students, of which 17 are women and 2 are men who received an A. So

P = \frac{19}{30} = 0.6333

63.33% probability that the student is a woman or received an A.

d. Find the probability that the student did not receive an A.

30 students, of which 25 did not receive an A.

P = \frac{25}{30} = 0.8333

83.33% probability that the student did not receive an A.

7 0
3 years ago
Use the data in LAWSCH85 for this exercise. (i) Using the same model as in Problem 4 in Chapter 3, state and test the null hypot
natka813 [3]

Answer:

Step-by-step explanation:

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The hypothesis that rank has no effect on log (salary) is H0:B5 = 0. The estimated equation (now with standard errors) is

               Log (salary) =    8.34 +    .0047 LSAT +   .248 GPA +   .095 log(libvol)

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                                         +     .038 log(cost)    – .0033 rank

                                              (.032)                    (.0003)

                   n = 136,    R2 = .842.

The t statistic on rank is –11(i.e. 0.0033/0.0003), which is very significant. If rank decreases by 10 (which is a move up for a law school), median starting salary is predicted to increase by about 3.3%.

(ii) LSAT is not statistically significant (t statistic ≈1.18) but GPA is very significance (t statistic  ≈2.76). The test for joint significance is moot given that GPA is so significant, but for completeness the F statistic is about 9.95 (with 2 and 130 df) and p-value ≈.0001.

6 0
3 years ago
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