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3 years ago

12a+6b equivalent expression

Mathematics

1 answer:

patriot [66]3 years ago

5 0

Answer:

$6(2a+b)$

Step-by-step explanation:

The given expression is

$12a+6b$

To find the equivalent expression of the given one, we just have to factor.

In this case, the only thing we can do to rewrite is to extract the common greatest factor, which is 6

$12a+6b\\6(2a+b)$

Therefore, the equivalent expression is

$6(2a+b)$

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A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name br

Marianna [84]

Answer:

The calculated value |Z| = |-2.5| >2.326 at 0.05 level of significance

The alternative hypothesis is accepted at a 0.05 level of significance

The manager of Publix in Clemson believes 64% is too high for his own store

Step-by-step explanation:

Step:-1

Given that the consumer Reports showed that 64% of supermarket shoppers.

Given that the population proportion

P = 0.64

Given that random sample size 'n' = 100

Given that 52 believe the supermarket brands were as good as the national brands.

sample proportion

$p^{-} = \frac{x}{n} = \frac{52}{100} = 0.52$

Step:-2

Null hypothesis: The manager of the Publix in Clemson believes 64% is too low for his own store

μ < 0.64

Alternative Hypothesis:H₁:μ > 0.64

Test statistic

$Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }$

$Z = \frac{0.52-0.64}{\sqrt{\frac{0.64 X 0.36}{100} } }$

Z = -2.5

Level of significance = 0.05

Z₀.₀₅ = 2.326

The calculated value |Z| = |-2.5| >2.326 at 0.05 level of significance

Final answer:-

The null hypothesis is rejected at a 0.05 level of significance

The alternative hypothesis is accepted at a 0.05 level of significance

3 0

3 years ago

The blood platelet counts of a group of women have a boll-shaped distribution with a mean of 261.1 and a standard deviation of 6

alexandr402 [8]

The variable is

X: blood platelet count of a woman

This variable has a bell shaped distribution (Normal)

With mean μ=261.1 and standard deviation σ=64.3

The platelet count within 3 standard deviations of the mean can be calculated as

μ±3σ

You can symbolize it as

μ-3σ ≤ X ≤ μ+3σ

According to the empirical rule of the normal distribution you know that under any bell shaped distribution:

Between μ ± σ you'll find the 68% of the distribution

Between μ ± 2σ you'll find the 95% of the distribution

Between μ ± 3σ you'll find the 99% of the distribution

So following this rule you'll find 99% of the women with platelet count within 3 standard deviations of the mean.

3% of the population is found between a vertain interval, the rest 97% is separated in equal tails around this interval.

Divide 0.97 by 2

0.97/2= 0.485

Each tail contains 0.485 of the distribtuion.

a and b represent the values within you'll find 3% of the population.

Until a you'll find 0.485 of the population and until b you'll find 0.485+0.03=0.515

To calculate both unknown values you have to use the standard normal distribution. This distribution is centered in zero, the left tail is negative and the right tail is positive.

a and b are at a equal distance from the mean but with different sign, so you only have to calculate on and then you invert the sign to get the other one.

I'll calculate the positive value:

Z= (X- μ )/σ~N(0,1)

P(Z≤ b)=0.515

Look in the body of the Z-table, rigth or positive entry and reach the margins for the value:

b= 0.038

Then using the values of the mean and the standard deviation you can calculate the corresponding valueof platelet count:

b= (X- μ )/σ

0.038= (X- 261.1 )/64.3

0.038*64.3=X-261.1

2.4434+261.1=X

X=263.5434=263.5

a=-b=-0.038

a= (X- μ )/σ

-0.038= (X- 261.1 )/64.3

-0.038*64.3=X-261.1

-2.4434+261.1=X

X=258.6566= 258.7

3% of the populations platelet count is between 258.7 and 263.5.

3 0

1 year ago

Choose the correct definition of a sampling distribution. The sampling distribution of a statistic of size isa.the distribution

sweet-ann [11.9K]

Answer:

The answer is Option D:

"The distribution of all values of the statistic resulting from all samples of size taken from the same population."

Step-by-step explanation:

First, is a distribution of all values. It has to include all the possible values of the statistic with its associated probability.

Second, is a distribution of a statistic because we are talking about sample results.

Third, it has to be taken from the same population and have to have the same sample size.

3 0

3 years ago

How do you solve this absolute value equatuon? 4|x - 1| - 7 = -3

MatroZZZ [7]

4|x - 1| - 7 = -3 |add 7 to both sides

4|x - 1| = 4 |divide both sides by 4

|x - 1| = 1 ⇔ x - 1 = 1 or x - 1 = -1 |add 1 to both sides

x = 2 or x = 0

Answer: B.

3 0

3 years ago

Please help a step by step would be nice answer is also ok

nasty-shy [4]

I would choose A I’m not to sure tho

6 0

3 years ago