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Nezavi [6.7K]
2 years ago
14

Solve and show how you did: -2x + (12 - 9) = 2 + 9 + 2x

Mathematics
1 answer:
Norma-Jean [14]2 years ago
5 0
Remove parentheses
-2x + 12 - 9 = 2 + 9 + 2x

Simplify -2x + 12 -9 to -2x + 3
-2x + 3 = 2 + 9 + 2x

Simplify 2 + 9 + 2x to 2x + 11
-2x + 3 = 2x + 11

Add 2x to both sides
3 = 2x + 11 + 2x

Simplify 2x + 11 +2x to 4x + 11
3 = 4x + 11

Subtract 11 from both sides
3 - 11 = 4x

Simplify 3 - 11 to - 8
-8 = 4x

Divide both sides by 4
-8/4 = x

Simplify 8/4 to 2
-2 = x

Switch sides
x = -2
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Because 132/22=6 and 132-12/20=6
6 0
3 years ago
Talishas bedroom is a rectangular prism. The area of the floor is 156 square feet, and the height of the bedroom is 9 feet. What
andrew-mc [135]

Answer: 1404 cubic feet.

Step-by-step explanation:

Formula :

Volume of a rectangular prism is given by :

Volume= Area of the base x Height.

Given : Talishas bedroom is a rectangular prism.

The area of the floor = 156 square feet

The height of the floor = 9 feet

Then , the volume of Talishas bedroom =  Area of floor x Height

= 156 × 9=1404 cubic feet.

Hence, the volume of Talishas bedroom= 1404 cubic feet.

7 0
3 years ago
$9500 is invested, part of it at 11% and part of it at 8%. For a certain year, the total yield is $937.00. How much was invested
netineya [11]

Answer:

5900 at 11%

3600 at 8%

Step-by-step explanation:

x= invested at 11%

y= invested at 8%

x+y=9500

.11x+.08y=937

Mulitply the first equation by .11

.11x+.11y= 1045

Subtract this and the second equation

(.11x+.11y)-(.11x+.08y)=1045-937

.03y=108

y=3600

SOlve for x

x+3600=9500

x=5900

8 0
3 years ago
A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chose
Nookie1986 [14]

Answer:

The 95% confidence interval is given by (25.71536 ;28.32464)

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)  

Step-by-step explanation:

Notation and definitions  

n=50 represent the sample size  

\bar X= 27.2 represent the sample mean  

s=5.83 represent the sample standard deviation  

m represent the margin of error  

Confidence =88% or 0.88

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Calculate the critical value tc  

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by \alpha=1-0.88=0.12 and \alpha/2 =0.06. The degrees of freedom are given by:  

df=n-1=50-1=49  

We can find the critical values in R using the following formulas:  

qt(0.06,49)

[1] -1.582366

qt(1-0.06,49)

[1] 1.582366

The critical value tc=\pm 1.582366  

Calculate the margin of error (m)  

The margin of error for the sample mean is given by this formula:  

m=t_c \frac{s}{\sqrt{n}}  

m=1.582366 \frac{5.83}{\sqrt{50}}=14.613  

With R we can do this:

m=1.582366*(5.83/sqrt(50))

m

[1] 1.304639

Calculate the confidence interval  

The interval for the mean is given by this formula:  

\bar X \pm t_{c} \frac{s}{\sqrt{n}}  

And calculating the limits we got:  

27.02 - 1.582366 \frac{5.83}{\sqrt{50}}=25.715  

27.02 + 1.582366 \frac{5.83}{\sqrt{50}}=28.325

Using R the code is:

lower=27.02-m;lower

[1] 25.71536

upper=27.02+m;upper

[1] 28.32464

The 95% confidence interval is given by (25.71536 ;28.32464)  

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)  

6 0
3 years ago
Please solve for me. please be right
lesantik [10]

Answer:

4

Step-by-step explanation:

5+3÷5-3=8÷2=4

5 0
2 years ago
Read 2 more answers
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