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3 years ago

What is the equation of the line in the following graph? 1)y=x+2

Mathematics

1 answer:

Levart [38]3 years ago

8 0

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have two points (2, 0) and (-2, -4). Substitute:

$m=\dfrac{-4-0}{-2-2}=\dfrac{-4}{-4}=1$

Therefore we have the equation of a line

$y=1x+b\to y=x+b$

Put the coordinates of the point (2, 0) to the equation:

$0=2+b$ subtract 2 from both sides

$-2=b\to b=-2$

Answer: $\boxed{y=x-2}\to\boxed{3)}$

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An environmental scientist wants to use a 95% confidence interval to estimate the mean number of hours per day her solar panel r

MissTica

Answer:

a) The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

b) The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

Step-by-step explanation:

We have the standard deviation for the sample. So we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 48 - 1 = 47

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 47 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 2.0117

The margin of error is:

M = T*s = 2.0117*2.3 = 4.6

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 7.1 - 4.6 = 2.5 hours of sunlight per day

The upper end of the interval is the sample mean added to M. So it is 7.1 + 4.6 = 11.7 hours of sunlight per day

a) Compute the 95% confidence interval for the mean.

The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

b) Explain your confidence interval from part (a) in context.

The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

6 0

3 years ago

In APQR, the measure of ZR=90°, RQ = 55, PR = 48, and QP = 73. What ratio represents the sine of ZQ?

Irina18 [472]

To find the angle Q we can us the sin law so:

$\frac{\sin (Q)}{48}=\frac{\sin (90)}{73}$

So we can solve for Q so:

$\begin{gathered} \sin (Q)=\frac{48}{73} \\ \measuredangle Q=\sin ^{-1}(0.6) \\ \measuredangle Q=36.87 \end{gathered}$

5 0

1 year ago

A metal worker has several 1-kilogram bars of a metal alloy that contain 23% copper and several 1-kilogram bars that contain 79%

astraxan [27]

Answer:

30 each of 23% bars and 18 each of 79% bars

Step-by-step explanation:

If x is the number of 1 kg 23% copper bars, and y is the number of 1 kg 79% copper bars, then:

x + y = 48

0.23x + 0.79y = 0.44(48)

Substituting and solving:

0.23x + 0.79(48-x) = 0.44(48)

0.23x + 37.92 - 0.79x = 21.12

16.8 = 0.56x

x = 30

y = 48 - x

y = 18

You need 30 each of 23% bars and 18 each of 79% bars.

4 0

3 years ago

Smallest of 3 consecutive positive intergers if the product of the smaller two intergers is 5 less than 5 times the largest inte

amm1812

What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)

Three consecutive integers are . . . x, x+1, and x+2

The smallest two are . . . x and x+1
 Their product is . . . . . x(x+1)

5 times the largest one is . . . 5(x+2)
 5 less than that is . . . . . . 5(x+2)-5

Now, the conditions of the problem say that x (x + 1) = 5 (x+2) - 5
THAT's the equation we have to solve, to find 'x' .

 Eliminate parentheses: x² + x = 5x + 10 - 5
 Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: x² - 4x - 5 = 0

You could solve that by factoring it, or use the quadratic equation.

Factored, it says that (x + 1) (x - 5) = 0

From which x = -1
 and x = +5

We only want the positive results, so our three consecutive integers are

 5, 6, and 7 .

To answer the question, the smallest one is 5 .

Check:

 5 x 6 ? = ? (7 x 5) - 5

 30 ? = ? (35) - 5

 30 = 30

 yay !

6 0

3 years ago

Kelly earned $20 for babysitting. She has also earned money by doing chores for 5 weeks. Altogether, she has earned $100. How mu

NikAS [45]

Answer: 16

Step-by-step explanation:

i did the math trust me

3 0

3 years ago

Read 2 more answers