What is the cost of a $1200 washing machine after a discount of one fifth the original price

1 and 2 are a linear pair, and 2 and 3 are vertical angles. m 2=(5+4 y) and m 3=(6 y-25). what is m 1

poizon [28]

Vertical angles are equal to each other:
    ∠2    =    ∠3
   5 + 4y = 6y - 25
→ 30 = 2y
→    15 = y

∠2 = 5 + 4y = 5 + 4(15) = 5 + 60 = 65

linear pairs equal 180:
   ∠1 + ∠2 = 180
→ ∠1 + 65 = 180
→ ∠1 = 115

5 0

3 years ago

It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 househo

BartSMP [9]

Complete Question

It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 households in Iowa City is taken, would you be surprised to find that fewer than 3% of households in the sample recycle their garbage? Use the fact that p-hat has an approximately normal distribution.

Group of answer choices

A I would not be surprised because there are lots of lazy students in Iowa City.

B I would not be surprised because 3% is not that far away from 9%.

C I would be surprised because Iowa City is a very clean community which means lots of people recycle their garbage.

D I would be surprised because if the 9% average is true, the chance of a sample proportion being less than 3% is very small (only 1%). Who cares? It's only garbage!

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

The sample size is n = 120

The mean of the proportion is p = 0.09

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{p(1-p)}{n} }$

=> $\sigma = \sqrt{\frac{0.09(1-0.09)}{120 } }$

=> $\sigma = 0.02612$

Generally the chance that fewer than 3% of households in the sample recycle their garbage is mathematically represented as

$P(X < 0.03) = P( \frac{X - p}{\sigma} < \frac{0.03 -0.09}{0.02612} )$

$P(X < 0.03) = P( Z < -2.297 )$

From the z-table

$P( Z < -2.297 ) = 0.01$

=> [tex]P(X < 0.03) = 0.01/tex]

=> [tex]P(X < 0.03) = 1\% /tex]

4 0

3 years ago

Find the 4th term of a proportion whose 1st, 2nd, and 3rd terms are 5, 10, and 7 respectively

fomenos

12 is the 4th term? Dont quote me on that though. I am 90% sure.

6 0

3 years ago

What is the square root of 8 rounded to the nearest tenth?

frozen [14]

Square Root of 8 to the nearest tenth, means to calculate the square root of 8 where the answer should only have one number after the decimal point.

Here are step-by-step instructions for how to get the square root of 8 to the nearest tenth:

Step 1: Calculate

We calculate the square root of 8 to be:

√8 = 2.82842712474619

Step 2: Reduce

Reduce the tail of the answer above to two numbers after the decimal point:

2.82

Step 3: Round

Round 2.82 so you only have one digit after the decimal point to get the answer:

2.8

To check that the answer is correct, use your calculator to confirm that 2.82 is about 8.

8 0

3 years ago

Consider the hypotheses below. Upper H 0: mu equals 50 Upper H 1: mu not equals 50 Given that x overbar equals 60, s equals 1

Neko [114]

Answer:

We conclude that $\mu\neq$ 50.

Step-by-step explanation:

We are given that x bar = 60, s = 12, n = 30, and alpha = 0.10

Also, Null Hypothesis, $H_0$ : $\mu$ = 50

Alternate Hypothesis, $H_1$ : $\mu$ $\neq$ 50

The test statistics we will use here is;

T.S. = $\frac{Xbar-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, X bar = sample mean = 60

s = sample standard deviation = 12

n = sample size = 30

So, Test statistics = $\frac{60-50}{\frac{12}{\sqrt{30} } }$ ~ $t_2_9$

= 4.564

At 10% significance level, t table gives critical value of 1.311 at 29 degree of freedom. Since our test statistics is more than the critical value as 4.564 > 1.311 so we have sufficient evidence to reject null hypothesis as our test statistics will fall in the rejection region.

P-value is given by, P( $t_2_9$ > 4.564) = less than 0.05% {using t table}

Here also, P-value is less than the significance level as 0.05% < 10% , so we will reject null hypothesis.

Therefore, we conclude that $\mu\neq$ 50.

7 0

3 years ago