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3 years ago

-x+ 2y = 10 -3x+By = 11

Mathematics

2 answers:

adoni [48]3 years ago

8 0

Answer:

change the equation into one variable.

2 y equals 10 + x

y equals 5 + x by 2

now put that into the second equation

-3x + b parentheses 5 + x / 2 equals 11

-3x+b(5+ x/2)

-3x + b5 + bx/2 = 11

Sav [38]3 years ago

7 0

Answer:

Would be the answer -3x + b5 + bx/2 = 11.

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Answer:

Step-by-step explanation:

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8 + 4 = 12

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2 years ago

The perimeter of the square is equal to the perimeter of the triangle. What are the side lengths of each figure? square: ? units

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Answer:

Square= 12 units

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Step-by-step explanation:

It is a square, so all sides are the same. That means 3x+3 equals 4x. What number can be subsituted into x to equal 4? If x is 3, then 3x+3 would be 3(3)+3. It equals 12. 4 times 3 is also 12. It works! That also means the square's side is 12 units.

Square= 12 units

So, x=3

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Triangle short side= 10 units

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2 years ago

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Two angles are complementary. Angle A Is (2x+20) and angle B is (3x+10). Find the value of x and the measure of each angle

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3 years ago

Simplify 2x - 8x - 6y + 9 -14 + x + 11y. Thanks!

yarga [219]

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3 years ago

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A student carried out an experiment to determine the amount of vitamin C in a tablet sample. He performed 5 trials to produce th

ivolga24 [154]

Answer:

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

P-value = 0.166.

Step-by-step explanation:

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

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\$

Then, we can perform the hypothesis t-test for the mean.

The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.

Then, the null and alternative hypothesis are:

$H_0: \mu=500\\\\H_a:\mu< 500$

The significance level is 0.05.

The sample has a size n=5.

The sample mean is M=496.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1$

The degrees of freedom for this sample size are:

$df=n-1=5-1=4$

This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

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2 years ago