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Diano4ka-milaya [45]
4 years ago
11

Drag a statement or reason to each box to complete this proof. If −3(x+8)=−21, then x=−1.

Mathematics
2 answers:
Lelu [443]4 years ago
5 0

Answer:

Yes, it's true. X=-1

Step-by-step explanation:

We have,

-3(x+8)=-21

The objective is to discover which is the value of x, then first we need to divide both sides of the equation in -3,

\frac{-3(x-8)}{-3} =\frac{-21}{-3}

Now we can simplify and the result is,

x+8=7

Because \frac{-3(x+8)}{-3}=\frac{-3}{-3} (x+8)=x+8 and \frac{-21}{-3} =7

Then we have to sum (-8) in both sides of the equation,

x+8+(-8)=7+(-8)

And we have: x=-1

Luda [366]4 years ago
3 0
The answer is true because, you must use the distribute then add both sides by 24 then divide both sides by -3 and then you will come up with your answer x=-1 which means that statement is true

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In this triangle, cosA/cosB = <br><br><br> Random answers will be reported!
SOVA2 [1]

Answer:

cosA/cosB =  1

Step-by-step explanation:

We know that cos = Adjacent Side/hypothenuse.

Then Cos(A)= AC/AB = 3/4.24 = 0.707

Cos(B) = BC/AB = 3/4.24 = 0.707

Then cosA/cosB = 0.707/0.707 = 1

3 0
3 years ago
Read 2 more answers
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining.
strojnjashka [21]

Answer:

1. The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).

2. The point estimate for the true difference between the population means is of -1872.

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of Normal Variables:

When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 212 brakes using Compound 1 yields an average brake life of 47,895 miles. The population standard deviation for Compound 1 is 1590 miles.

This means that \mu_1 = 47895, \sigma_1 = 1590, n = 212, s_1 = \frac{1590}{\sqrt{212}} = 109.2

A sample of 180 brakes using Compound 2 yields an average brake life of 49,767 miles. The population standard deviation for Compound 2 is 4152 miles.

This means that \mu_2 = 49767, \sigma_2 = 4152, n = 180, s_2 = \frac{4152}{\sqrt{180}} = 309.47

True difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

This is the distribution 1 - 2. So

\mu = \mu_1 - \mu_2 = 47895 - 49767 = -1872

This is also the point estimate for the true difference between the population means, which is question 2.

s = \sqrt{s_1^2+s_2^2} = \sqrt{109.2^2+309.47^2} = 328.17

90% confidence interval

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.05 = 0.95, so Z = 1.645.

Now, find the margin of error M as such

M = zs = 1.645*328.17 = 539.84

The lower end of the interval is the sample mean subtracted by M. So it is -1872 - 539.84 = -2411.84

The upper end of the interval is the sample mean added to M. So it is -1872 + 539.84 = -1332.16.

The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).

5 0
4 years ago
Look at the quadratic equation below. x2 - 10x + 16 = -5 What is this quadratic equation written in standard form? A.5x2 + 10x -
ollegr [7]
Ax^2+bx+c=0 is the standard form, so we add 5 to both sides to get 

1*x^2+(-10)x+21=0
7 0
3 years ago
13 POINTS HELP ME PLEASE
My name is Ann [436]
X= 13.5

Every triangle equals 180 degrees. 23+23= 46. 46 - 1= 45. Then you solve the equation 10x+45=180 which would equal, 13.5.
8 0
3 years ago
Read 2 more answers
C2&gt;a2+b2 is it a obtuse right or acute
Alex Ar [27]

Answer:

obtuse

Step-by-step explanation:

When c, the hypotenuse, is greater than the legs (a and b), it's an obtuse triangle

7 0
3 years ago
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