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4 years ago

The sum of twice a number and 18 less than the number is the same as the difference between -30 and the number

Mathematics

2 answers:

maksim [4K]4 years ago

6 0

2x + x - 18 = -30 - x

Monica [59]4 years ago

6 0

Lets say the number is x. The formula would be:
2x + x - 18 = x -30
To find x, you have to get rid of everything els, so minus x from both sides.
2x - 18 = -30
Since -30 is the smallest number, you get rid of that next. Add 30 to both sides
2x + 12 = 0
Now get rid of +12 by doing -12.
2x = -12
divide both sides by 2 to get x by itself
x = -6.

To double check your answer, do the reverse. Substitute -6 iinto the equation wherever it says x.

2x + x - 18 = x -30 becomes (2 x -6) + (-6 - 18) = -6 - 30.
Use BIDMAS (Brackets Indices Division Multiplication Addition Subtraction) to get your answer. Brackets are first
-12 + -24 = -6 - 30
-36 = -6 - 30 which is basically -36 = -36

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3 years ago

It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportat

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State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 120 or not, the system of hypothesis would be:

Null hypothesis: $\mu = 120$

Alternative hypothesis: $\mu \neq 120$

Part 2

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{114-120}{\frac{22}{\sqrt{36}}}=-1.636$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(z$

Step-by-step explanation:

Data given and notation

$\bar X=114$ represent the sample mean

$\sigma=22$ represent the population standard deviation

$n=36$ sample size

$\mu_o =120$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part 1

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 120 or not, the system of hypothesis would be:

Null hypothesis: $\mu = 120$

Alternative hypothesis: $\mu \neq 120$

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".