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satela [25.4K]
3 years ago
5

Solve for all values of x for -2|x+9|-6=-24

Mathematics
1 answer:
DerKrebs [107]3 years ago
5 0
-2(x+9)-6=-24
-2x-18-6=-24
2x=0
x=0

2(x+9)-6=-24
2x+18-6=-24
2x=-36
x=-18
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Given: Angle 2 is 65 degrees. What is the angle measurement of Angle 4. Explain the angle relationship used and show your work.
lesya [120]

Answer:

\angle 4 = 115^{\circ}

\angle 3 = 65^{\circ}

\angle 7 = 65^{\circ}

Step-by-step explanation:

Given

\angle 2 = 65^{\circ}

See attachment

Solving (a): \angle 4

To solve for \angle 4, we make use of:

\angle 2 +\angle 4 = 180^{\circ}

The relationship between both angles is that they are complementary angles

Make \angle 4 the subject

\angle 4 = 180^{\circ} - \angle 2

Substitute 65^{\circ} for \angle 2

\angle 4 = 180^{\circ} - 65^{\circ}

\angle 4 = 115^{\circ}

Solving (b): \angle 3

To solve for \angle 3, we make use of:

\angle 3 =\angle 2

The relationship between both angles is that they are complementary angles

\angle 3 = 65^{\circ}

Solving (c): \angle 7

To solve for \angle 7, we make use of:

\angle 7 = \angle 3

The relationship between both angles is that they are alternate exterior angles.

So:

\angle 7 = 65^{\circ}

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3 years ago
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Answer:

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3 years ago
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3 years ago
The Westbrook Pharmaceutical Company manufactures atorvastatin pills, designed to lower cholesterol levels. Listed below are the
Sloan [31]

Solution :

Given :

$\mu = 24$

n = 15

$\overline x = 24.89$

s = 0.5902

The hypothesis :

$H_0 : \mu = 25$

$H_a : \mu \neq 25$

This is a 2 tailed test.

The significance level is $95 \% \ ( \alpha =0.05)$

The test statistic :

$Z=\frac{\overline x - \mu}{\frac{\sigma}{\sqrt n}}$

$Z=\frac{24.89-25}{\frac{0.5902}{\sqrt 15}}$

   = -0.72

The p value : The p value for Z = -0.72 is 0.4716

The critical value : the critical value at α = 0.05 is +1.96 to -1.96

The decision rule :

If $Z_{observed} > Z_{critical}$ or if $Z_{observed} < -Z_{critical}$, then reject $H_0$.

Also if p value is less than α, then reject $H_0$.

The decision :

Since the Z falls in between +1.96 and -1.96, we fail to reject the $H_0$. Also since p value is greater than α, we fail to reject  $H_0$.

The conclusion :

There is not sufficient evidence at the 95% significance level to warrant rejection of the claim that the pills come from a population in which the amount of the atorvastatin is equal to 25 mg.

Now calculating the mean and the standard deviation :

$\text{Mean} = \frac{\text{sum of observation}}{\text{total observations}}$

Standard deviation = $\sqrt{\text{variance}}$

Variance = $\frac{\text{sum of squares(SS)}}{n-1}$

Where, SS = $\sum (X - \text{mean})^2$

X                   Mean                 $(X-\text{mean})^2$

24.1               24.89                    0.62

24.4              24.89                     0.24

24.3              24.89                    0.35

24.9             24.89                       0

24.1              24.89                    0.62

24.2             24.89                    1.72

24.1              24.89                    0.04

26.2             24.89                    0.04

25.1              24.89                   0.24

25                24.89                    0.01

24.7             24.89                    0.04

25.1             24.89                    0.04

25.3             24.89                   0.17

25.5             24.89                   0.37

25.5            24.89                   0.37

n                                                   15

Sum                                           373.3

Average                                    24.89

SS                                              4.8775

Variance = $\frac{SS}{n-1}$                       0.348392857

Standard deviation                    0.5902      

3 0
3 years ago
I Have To Show My Work Help I'm Stuck
Katena32 [7]
The answer is 64.5

1/4 of 86, divide 86 by 4 is 21.5. Then u multiply that by 3 since this is only 1/4. You would get a result of  64.5.


Eric is 64.5 inches tall :)
8 0
3 years ago
Read 2 more answers
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