All categories

3 years ago

Solve for x -6x + 14<-28 AND 3x + 28 < 25

Mathematics

1 answer:

MAVERICK [17]3 years ago

7 0

Answer:

Treat the lesser than sign as an equal sign. What you do to one side, you do to the other. Isolate the variable x. Do the opposite of PEMDAS.

PEMDAS = Parenthesis, Exponents ( & roots), Multiplication, Division, Addition, Subtraction.

Solve -6x + 14 < -28

First, subtract 14 from both sides:

-6x + 14 (-14) < -28 (-14)

-6x < -42

Next, divide -6 from both sides to isolate the variable x. Note that when you divide (or multiply) by a negative number, you must flip the greater than or less than sign.

(-6x)/-6 < (-42)/-6

x > (-42)/(-6)

x > 7

x > 7 is your answer.

Solve 3x + 28 < 25

First, subtract 28 from both sides.

3x + 28 (-28) < 25 (-28)

3x < -3

Isolate the variable x. Divide 3 from both sides. Note that because you aren't dividing by a negative number (rather a positive 3), you do not flip the sign.

(3x)/3 < (-3)/3

x < (-3)/(3)

x < -1

x < -1 is your answer.

You might be interested in

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 420 gram setting. It is

anastassius [24]

Answer:

$t=\frac{424-420}{\frac{26}{\sqrt{61}}}=1.202$

$p_v =2*P(t_{(60)}>1.202)=0.234$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the true mean is NOT different from 420. So the specification is satisfied.

Step-by-step explanation:

Data given and notation

$\bar X=424$ represent the sample mean

$s=26$ represent the sample standard deviation

$n=61$ sample size

$\mu_o =420$ represent the value that we want to test

$\alpha=0.01$ 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)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is different from 420 or not, the system of hypothesis would be:

Null hypothesis: $\mu = 420$

Alternative hypothesis: $\mu \neq 420$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-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".

Calculate the statistic

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

$t=\frac{424-420}{\frac{26}{\sqrt{61}}}=1.202$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=61-1=60$