Tion? What is/are the given in the problem? What are you going to solve? How can you do

Y=-1/2x+11 that passes through (4,-8)

kompoz [17]

A line in point-slope form has the equation

y = mx + b

where m=slope (increase in y for unit increase in x), and

b=y-intercept (value of y where line cuts y-axis)

The original line is

y=(-1/2)x + 11

so

slope = m = -1/2

Any line perpendicular to a line with slope m has a slope of m1=-1/m

So the slope m1 of the required line

m1 = -1 / (-1/2) = +2

and the required line therefore has an equation of

y=2x+b

Knowing that the line passes through P1=(x1, y1)=(4,-8), we can find b using the point slope form of a line with slope m : (y-y1) = m(x-x1)

where m=+2 as found above.

Substituting values, m=+2, x1=4, y1= -8

y-(-8) = +2(x--4)

simplify

y+8 = 2x-8

=>

y=2x-16 (in point slope form)

8 0

3 years ago

Part B: In complete sentences, explain how a circle can be used to find the circumcenter of the triangle graphed below.

Karo-lina-s [1.5K]

Answer:

Step-by-step explanation:

Part B:

The center of the circumscribed circle around a triangle is equidistant from vertices of that triangle. To find the circumcenter need to draw at least two perpendicular bisectors to the sides of the given triangle. Point of intersect of them is center of the circumscribed circle.

Part C:

Coordinates of the midpoint of line BC ( y = - 1 ) are

( $\frac{-6+2}{2}$ , $\frac{-1-1}{2}$ ) = ( - 2 , - 1 ) and the equation of the line ⊥ to BC is x = - 2

Because BC is ║ to x-axis and m∠A is 90° , the center of the circle is midpoint of BC and r = $\frac{BC}{2}$ = 4

3 0

1 year ago

Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement

Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.173, n = 120$ . So

$\mu = E(X) = np = 120*0.173 = 20.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14$

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34 - 20.76}{4.14}$

$Z = 3.2$

$Z = 3.2$ has a pvalue of 0.9993

X = 21

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{21 - 20.76}{4.14}$

$Z = 0.06$

$Z = 0.06$ has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

6 0

3 years ago

What is the surface area of a rectangular prism with a height of 8 yd, length of 5.6 yd, and width of 2.3 yd?

sammy [17]

Answer:

152.16 yd²

Step-by-step explanation:

2(8 x 5.6) + 2(8 x 2.3) + (2.3 x 8) = 152.16 yd²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

4 0

2 years ago

Read 2 more answers

Given PA=13 in. and CB=15 in. What is CA ?

alexandr1967 [171]

Triangles CPA and CPB are both right triangles. They share a leg, so that leg in one triangle is congruent to that leg in the other triangle. We are given that PA is congruent to PB by the hash marks on the diagram. Thus two legs and an included angle are congruent between the triangles.

... ∆CPA ≅ ∆CPB by the SAS postulate

Then side CA ≅ CB = 15 in, because corresponding parts of congruent triangles are congruent (CPCTC).

... CA is 15 in.

8 0

2 years ago

Read 2 more answers

Tion?What is/are the given in the problem? What are you going to solve?How can you do​

Tion?What is/are the given in the problem? What are you going to solve?How can you do