Write and solve the following expression:<br><br>The sum of 7 and twice a number is 15

I need help for this one do I add them up and equal them to 180?

nikitadnepr [17]

The measure of angle 1 is 210 degrees.

You'll have to draw an auxiliary line in between the two parallel lines.

Then, you'll have to find out the angle measures next to 100 and next to 50. Since a line is 180°, then the angle measures next to 100 and 50 are 80 and 130 respectively.

Then, since you have an auxiliary line, you can use the rule of alternate interior angles of parallel lines being equal.

Then from there just add up 80 and 130 to get you 210.

7 0

3 years ago

PLEASE DONT SKIP THIS I NEED HELP<br><br> Can someone please explain how to solve this problem?

Setler [38]

I would say 168 because if you throw a dice with 6 sides a thousand 1000 you will most likely get one certain side 168 times.

7 0

2 years ago

Factor completely. 2ay 2 5ay - 3a

stiv31 [10]

Hello,

2ay²+5ay-3a=a(2y²+5y-3)
=a(2y²+6y-y-3)=a(2y(y+3)-(y+3))
=a(y+3)(2y-1)

8 0

3 years 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

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

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