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In the 30-60-90 triangle below, side s has a length of and the hypotenuse has a length of

Zepler [3.9K]

Are there any dimensions on the triangle? or is it in terms of s? if so the answer would be 2s/sqrt(3) or you can rationalize the bottom and youd get 2sqrt(3)s/3

6 0

3 years ago

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A publisher reports that 75% of their readers own a particular make of car. A marketing executive wants to test the claim that t

Korolek [52]

Answer:

The p-value of the test is of 0.0536 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the executive's claim.

Step-by-step explanation:

A publisher reports that 75% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage.

At the null hypothesis, we test if the proportion is of 75%, that is:

$H_0: p = 0.75$

At the alternate hypothesis, we test if the proportion is different of 75%, that is:

$H_1: p \neq 0.75$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

75% is tested at the null hypothesis:

This means that $\mu = 0.75, \sigma = \sqrt{0.75*0.25}$

A random sample of 280 found that 70% of the readers owned a particular make of car.

This means that $n = 280, X = 0.7$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.7 - 0.75}{\frac{\sqrt{0.75*0.25}}{\sqrt{280}}}$

$z = -1.93$

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion differing from 0.75 by at least |0.7 - 0.75| = 0.05, which is P(|z| > 1.93), which is 2 multiplied by the p-value of z = -1.93.

Looking at the z-table, z = -1.93 has a p-value of 0.0268.

2*0.0268 = 0.0536.

The p-value of the test is of 0.0536 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the executive's claim.

5 0

3 years ago

1. The equation of the locus of a point which is always equidistant from the points (a + b, a - b) and (a - b, a + b) is a) x -

valina [46]

Answer:

c). y + x = 0

Step-by-step explanation:

The locus is a line perpendicular to the line connecting the 2 points and passing through the centre of the line.

The mid-point of the line connecting the given points is:

(a + b + a - b)/2 , (a - b + a + b) / 2

= (a, a)

It's slope = (a + b)- (a - b) / (a - b)- (a + b)

= 2b/ -2b

= -1

So the slope of the line we want is -1/(-1) = 1.

Using the point-slope form of a line:

y - y1 = m(x - x1)

y - a = 1(x - a)

y - a = x - a

x + y = 0

8 0

2 years ago

Gerard has $30 to spend on lunches this month. Lunch costs him $1.50 each day. After Gerard buys lunch for 8 days, which stateme

Harrizon [31]

What i did is that i did $1.50 time 8 = $12.00 and then do $30.00-12.00=$18.00

6 0

3 years ago

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Please help so I can watch Coop and Cami ask the world

MariettaO [177]

Step-by-step explanation:

Simple interest=principal x rate x time÷100

amount borrowed=$500

I=$500x7x6÷100

I=$210

therefore you will pay

amount borrowed+interest

$500+$210

$710

hope this is helpful

6 0

3 years ago