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Marat540 [252]
3 years ago
10

A line has a slope of 3, is increasing, and passes through the point (2,7). What is its y-intercept?

Mathematics
2 answers:
uysha [10]3 years ago
8 0
The y-intercept is 1.

First, we need to put this into point slope form which is y-7=3(x-2)

Next, multiply using the distributive property. y-7=3x-6

Lastly, we want to get y by itself so add 7 on both sides. y=3x+1.

Using the slope intercept form, y=mx+b where b is the y-intercept, we can see that the line will cross the y-axis at 1.

Hope this helps✨❤️
Anna71 [15]3 years ago
3 0
The y-intercept is 1
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3 years ago
A high school principal wishes to estimate how well his students are doing in math. Using 40 randomly chosen tests, he finds tha
ollegr [7]

Answer:

99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Step-by-step explanation:

We are given that a high school principal wishes to estimate how well his students are doing in math.

Using 40 randomly chosen tests, he finds that 77% of them received a passing grade.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                          P.Q. = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of students received a passing grade = 77%

           n = sample of tests = 40

           p = population proportion

<em>Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.</em>

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99  {As the critical value of z at 0.5%

                                           level of significance are -2.5758 & 2.5758}  

P(-2.5758 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 2.5758) = 0.99

P( -2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

P( \hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

<u>99% confidence interval for p</u> = [\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } , \hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }]

 = [ 0.77-2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } } , 0.77+2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } } ]

 = [0.5986 , 0.9414]

Therefore, 99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Lower bound of interval = 0.5986

Upper bound of interval = 0.9414

6 0
2 years ago
What is the length of a leg of a right triangle if the hypotenuse is 9 inches and the other leg is 8 inches.
adelina 88 [10]

Answer:

√17 or 4.12 inches

Step-by-step explanation:

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or 4.12 inches

5 0
3 years ago
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Fiesta28 [93]

Answer:

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Step-by-step explanation:

41 - 8m - 57 = 0

41- 8m = 57

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-8m = 16

m = -16/8

m = -2

8 0
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3 years ago
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