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2 years ago

The sum of the measures of angles x and y is 120°. The measure of the angle x is 12 less than the measure of the angle y.

Mathematics

1 answer:

Maru [420]2 years ago

3 0

Answer:

Y-12 + y =120 take 12 to the other side get 2 y = 132

Y=66 so y-12=x

X=54

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5. The superintendent of the local school district claims that the children in her district are brighter, on average, than the g

anygoal [31]

Answer:

We conclude that children in district are brighter, on average, than the general population.

Step-by-step explanation:

We are given the following data set:

105, 109, 115, 112, 124, 115, 103, 110, 125, 99

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{1117}{10} = 111.7$

Sum of squares of differences = 642.1

$S.D = \sqrt{\frac{642.1}{49}} = 8.44$

We are given the following in the question:

Population mean, μ = 106

Sample mean, $\bar{x}$ = 111.7

Sample size, n = 10

Alpha, α = 0.05

Sample standard deviation, s = 8.44

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 106\\H_A: \mu > 106$

We use one-tailed(right) t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{111.7 - 106}{\frac{8.44}{\sqrt{10}} } = 2.135$

Now,

$t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = 1.833$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

We conclude that children in district are brighter, on average, than the general population.

4 0

2 years ago

8. Lisa types 6 pages in 36 minutes. Frank types 5 pages in 30 minutes. Do they type at the same rate? Use a proportion to expla

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Answer:

Yes

Step-by-step explanation:

Lisa and Frank type at the same rate.

They both type 1 page every six minutes.

Lisa types 6 pages every 36 minutes, and if we divide the minutes by the pages, we get

$\frac{36}{6} = 6$

And Frank types 5 pages ever 30 minutes, when we divide we get

$\frac{30}{5} = 6$

3 0

2 years ago

there are 100 movies at the store 30/100 are action movies 50/100 are comedies and 20/100 are adventure movies what part of the

pogonyaev

Answer:30 action and 50 comedies which is 80/100 or 80%/100%

Step-by-step explanation:

8 0

3 years ago

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10.20 to spend on a

JulijaS [17]

Answer:13 miles

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2 years ago

What is 6,4 rounded to the nearest whole number

Aleks04 [339]

6.4 rounded to the nearest whole number will be 6.

if the decimal was 5 or larger, it would’ve been 7.

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2 years ago