Which is the solution to the equation -3x-4=5(x+4)

Mathematics

2 answers:

Lorico [155]3 years ago

6 0

Step 1. Expand

-3x - 4 = 5x + 20

Step 2. Add 3x to both sides

-4 = 5x + 20 + 3x

Step 3. Simplify 5x + 20 + 3x to 8x + 20

-4 = 8x + 20

Step 4. Subtract 20 from both sides

-4 - 20 = 8x

Step 5. Simplify -4 - 20 to -24

-24 = 8x

Step 6. Divide both sides by 8

-24/8 = x

Step 7. Simplify 24/8 to 3

-3 = x

Step 8. Switch sides

x = -3

ratelena [41]3 years ago

4 0

X=-3..................

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The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

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The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305$