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3 years ago

Which inequality is equivalent to |x-4|<9

Mathematics

2 answers:

Lorico [155]3 years ago

8 0

Answer with explanation:

The Given Inequality is

|x-4|<9

Modulus of a number yields always a positive value.

→|x-4|= x-4, when, x-4≥0

That is , x≥4.

= -(x-4), when, x-4<0

means, x<4.

it can be Written as

→ -9<x-4<9

→ -9+4 < x -4+4 < 9+4

→ -5<x<13

→x∈(-5,13)

AnnyKZ [126]3 years ago

6 0

The answer is –9 < x – 4 < 9

option B in edg.

please give brainliest

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Alternative hypothesis: $\mu > 3.3$

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Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ 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)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case 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".

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

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

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Help

Vedmedyk [2.9K]

By pythagoreans' theorem,

Longer edge
= √(2² + 6²)
= √40

∴ The length of the longer edge is the square root of 40 feet.

Shorter edge
= √(1² + 3²)
= √10

Area = L × B
= √40 × √10
= 20 feet²

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