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3 years ago

Lines c and d are parallel lines cut by transversal p.

Mathematics

1 answer:

lilavasa [31]3 years ago

5 0

Answer:

Option (B).

Step-by-step explanation:

Here there are two parallel lines c and d cuts by a transversal p.

The angles are formed as shown in diagram.

Here,

$\angle 1 = \angle 7 (alternate)\\\\\angle 2 = \angle 6 (corresponding)\\\\\angle 3 = \angle 5 (alternate)\\\\\angle 5 = \angle 7 (alternate)$

So, the option (B) is correct.

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Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Norm

Vlad1618 [11]

Answer:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

Step-by-step explanation:

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".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma)$

The distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar x =512$ represent the sample mean

$\sigma=100$ represent the population standard deviation

n= 100 sample size selected.

The confidence interval is given by this formula:

$\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$ (1)

The marginof error for this case is given by Me=25.76. And we know that the formula for the margin of error is given by:

$Me=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

$25.76=z_{\alpha/2} \frac{100}{\sqrt{100}}$

And we can find the critical value $z_{\alpha/2}$ like this:

$z_{\alpha/2}=\frac{25.76(\sqrt{100})}{100}=2.576$

And we know that on the right tail of the z score =2.576 we have $\alpha/2$ of the total area. We can find the area on the right of the z score using this excel code:

"=1-NORM.DIST(2.576,0,1,TRUE)" or using a table of the normal standard distribution, and we got 0.004998= $\alpha/2$ , so then $\alpha=0.00498*2=0.009995 \approx 0.01$ , and then we can find the confidence like this:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

8 0

3 years ago

For what values of $x$ is it true that $x^2 - 5x - 4 \le 10$? Express your answer in interval notation.

dybincka [34]

Answer:

x ∈ [-2, 7]

Step-by-step explanation:

The given equation ...

x^2 -5x -4 ≤ 10

can be rewritten as ...

x^2 -5x -14 ≤ 0

and factored as ...

(x +2)(x -7) ≤ 0

Clearly, the "or equal to" condition will be met when x=-2 and x=7. For values of x between these numbers, one factor is negative and the other is positive. Hence the product will be negative. So, numbers in that interval are the solution set.

x ∈ [-2, 7]

5 0

3 years ago

sally gave her brother 3.95 in quarters and dimes. if the number of quarters is 6 more then the number of dimes, how many quarte

iragen [17]

Let q be the number of 25 cent coins.
Let d be the number of 10 cent coins.
0.25q+0.10d= 3.95...(1)
q-d=6...(2)

(2)-> q-d= 6
q-d+d= 6+d
q= 6+d...(2a)

(2a)-> (1) 0.25q+0.10d=3.95
0.25(6+d)=0.10d= 3.95
1.95+0.25d+0.10d= 3.95
0.35d= 3.95-1.5
0.35d/0.35= 2.45/0.35
d= 7...(3)

(3)->(2) q-d= 6
q-7= 6
q=6+7
q= 13
There are 13 quarters and 7 dimes.

7 0

3 years ago

Find the value of x so that the line through the pair of points has the given slope.

MatroZZZ [7]

1 is the answer b/c that's the only number it goes too

3 0

3 years ago

The length of a rectangle is three times its width. if the area of the rectangle is 300 yd2 , find its perimeter.

Svetradugi [14.3K]

Let, width = x
Length = 3x

It is given that, 3x * x = 300
3x² = 300
x² = 300 / 3
x = √100
x = 10
& 3x = 3(10) = 30

Perimeter = 2(l + w)
P = 2(10 + 30)
P = 2(40) = 80

In short, Your Answer would be 80 Yards

Hope this helps!

4 0

3 years ago