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3 years ago

Geometry ∠1 and ∠2 are vertical angles. If m∠1 = 17x + 1 and m∠2 = 20x – 14, find m∠2.

Mathematics

1 answer:

stiv31 [10]3 years ago

7 0

Answer:

m∠2= 86

Step-by-step explanation:

since they are vertical angles, that means they are both equal to eachother.

so lets set them equal!

17x+1=20x-14

17x+15=20x

15=3x

x=5

now input x into m∠2

m∠2 = 20(5) – 14 = 86

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Vera_Pavlovna [14]

I think you times them

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2 years ago

Boxes of raisins are labeled as containing 22 ounces. Following are the weights, in the ounces, of a sample of 12 boxes. It is r

ZanzabumX [31]

Answer:

A 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

Step-by-step explanation:

We are given the weights, in the ounces, of a sample of 12 boxes below;

Weights (X): 21.88, 21.76, 22.14, 21.63, 21.81, 22.12, 21.97, 21.57, 21.75, 21.96, 22.20, 21.80.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean weight = $\frac{\sum X}{n}$ = 21.88 ounces

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 0.201 ounces

n = sample of boxes = 12

$\mu$ = population mean weight

Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.796 < $t_1_1$ < 1.796) = 0.90 {As the critical value of t at 11 degrees of

freedom are -1.796 & 1.796 with P = 5%}

P(-1.796 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.796) = 0.90

P( $-1.796 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.796 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.796 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.796 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.796 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.796 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $21.88-1.796 \times {\frac{0.201}{\sqrt{12} } }$ , $21.88+1.796 \times {\frac{0.201}{\sqrt{12} } }$ ]

= [21.78, 21.98]

Therefore, a 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].

8 0

2 years ago

There are two balance beams at the gym.one is 15 feet long ,theother is 162 inches long.which beam is longer?

Oduvanchick [21]

12 inches = 1 foot

Let x=length of 2nd balance beam in feet

by ratio and proportion

1/12 = x/162

multiply noth sides by 162 to isolate x

(1/12)(162) = (x/162)(162)

162/12 = x

13.5 = x

Source -->https://socratic.org/questions/at-the-gym-one-balance-beam-is-15-feet-long-while-the-other-is-162-in...<--

can you help me? brainly.com/question/3131429

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2 years ago

Read 2 more answers

What is the average rate of change for this function for the interval fron x=2 to x=4

mezya [45]

Subtract the two Y values of X = 2 and X = 4 to find the total difference, then divide by the difference between X=2 and X =4

When X = 2 Y = 9
When X = 4 Y = 64

Difference between the two Y values = 64 -9 = 55
Difference between the two X values = 4-2 = 2

The rate of change = difference in Y divided by difference in X:

55/2 = 27.5

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3 years ago

6x-4y=8 solve for variable x

Radda [10]

6x - 4y = 8...solve for x
6x = 4y + 8
x = (4/6)y + 8/6
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2 years ago