Leave your answer in terms of pi. Find the circumference.

What is the slope of a line perpendicular to the line whose equation is 4x−10y=404x−10y=40. Fully simplify your answer.

Anna007 [38]

Answer:

$- \frac{5}{2}$

Step-by-step explanation:

4x -10y= 40

Let's rewrite this equation in the slope-intercept form (y= mx +c) so that we can obtain it's slope.

10y= 4x -40

Divide both side by 10:

$y = \frac{2}{5} x - 4$

The product of the gradients of perpendicular lines is -1.

⅖(gradient of line)= -1

Gradient of perpendicular line

$= - 1 \div \frac{2}{5}$

$= - 1 \times \frac{5}{2}$

$= - \frac{5}{2}$

5 0

3 years ago

SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school are given below

kvasek [131]

Answer:

The value of test statistics is 25.

Step-by-step explanation:

We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;

380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560

Let $\sigma$ = population standard of the reading and writing section SAT score of the students in this school

So, Null Hypothesis, $H_0$ : $\sigma \leq$ 100 {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}

Alternate Hypothesis, $H_A$ : $\sigma$ > 100 {means that the reading and writing section SAT score of the students in this school is higher than 100}

The test statistics that would be used here is One-sample Chi-square test statistics;

T.S. = $\frac{(n-1)s^{2} }{\sigma^{2} }$ ~ $\chi^{2} __n_-_1$

where, $s^{2}$ = sample variance = $\frac{\sum (X-\bar X)^{2} }{n-1}$ = 13135.8

n = sample of 11th-grade students = 20

So, the test statistics = $\frac{(20-1)\times 13135.8^{2} }{100^{2} }$

= 24.96 ≈ 25

Hence, the value of test statistics is 25.

5 0

3 years ago

4(3-2x)=4(x-6) what is x

erastova [34]

Here are the steps
(4*3)+(4*-2x)=(4x)+(4*-6)
...12+-8x=16x-24x
...-8x+24x-16x=-12
0x=-12
x=-12/0
dividing by 0.
so there is no solution.

3 0

3 years ago

A tower casts a shadow 11 feet long the distance from the top of the tower to the end of the the shadow is 61 feet how many feet

Jobisdone [24]

This is very easy!! I have attached a picture I have drawn if you are a visual learner... well, everything else like computations is here.
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This is the PYTHAGOREAN THEOREM!!
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If you don't know, it says that the lengths of the legs squared added together all equal the hypotenuse squared in a right triangle!!
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And if you want to know why the "triangle" has a right angle... well, are towers slanted? I mean, other than the Leaning Tower of Pizza. I mean Pisa.
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So... we plug it in!!
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Formula: a^2 + b^2 = c^2.
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Plug it in: 11^2+ 61^2 = c^2
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c^2 = 3842.
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So now what?
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SQUARE ROOT OF EVERYTHING!!
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c = √3842.
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So? c = approximately 61.984.
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Hope I helped!!

8 0

3 years ago

I need help with this

Nana76 [90]

Answer: -0.5

Step-by-step explanation:

We can see that at x=0 that Y=2, when x=2, y=1, so we do the x1 - x2 = -2 and y1-y2 = 1

Then we do 1 / -2 = -0.5

The average rate of change is -0.5

3 0

3 years ago