Solve the equation 3(2x + 1) = 2x

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.

4 0

3 years ago

Three fences on a ranch measure 15/16 miles 7/8 miles and 7/16 miles which is the best estimate of the total length of all three

gizmo_the_mogwai [7]

2.25.....
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....
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6 0

3 years ago

The gross weight of a package and its contents is 11 pounds 5 ounces. If the packaging weighs 1 pound 15 ounces, what's the net

umka21 [38]

11 lbs 5 oz - 1 lb 15 oz...we are gonna have to borrow...there is 16 oz in a lb.
11 lbs 5 oz....we r going to borrow 1 lb from the right side and add it to the left side making it 10 lbs and 21 oz...u see what I did...I borrowed 1 lb from the right side and added 16 oz to the left.Now we can subtract.

10 lbs 21 oz - 1 lb 15 oz = 9 lbs 6 oz <== ur answer

3 0

3 years ago

Read 2 more answers

Answer ASAP, Will give brainliest

erastova [34]

Answer:

Step-by-step explanation:

1) ABCD is a trapezium. AB ║ CD

∠ADC + ∠DAB = 180° { Co interior angles}

110° + ∠DAB = 180

∠DAB = 180 -110

∠DAB = 70°

2) Sum of all angles of trapezium = 360°

∠A + ∠B + ∠DCB + ∠D = 360

70° + 50° + ∠DCB + 110° = 360

230 + ∠DCB = 360

∠DCB = 360 - 230

∠DCB = 130°

3) For finding the height, use Pythagorean theorem

height² + base² = hypotenuse²

height² + 6² = 10²

height² + 36 =100

height² = 100 - 36

height² = 64

height = √64

height = 8 m

4) a = AB = x m

b = 9 m

h = height = 8 m

Area of trapezium = 120 m²

$\frac{(a+b)*h}{2}\\\\$ = 120

$\frac{(x+9)*8}{2} =120\\\\\\(x +9)*4 = 120$

x + 9 = 120/4

x + 9 = 30

x = 30 - 9

x = 21 m

AB = 21m

7 0

3 years ago

If a car travels 350 miles in 2.5 hours, how far does it travel in one hour?

algol13

It travels 140 miles per 1 hour

8 0

3 years ago

Solve the equation 3(2x + 1) = 2x - 9 for x.