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3 years ago

7

Which statements apply to the expression ? Check all that apply. The base is . The base is 3. The exponent is 3. The expanded fo

rm is . The expanded form is .

2 answers:

julsineya [31]3 years ago

8 0

Answer:

a b e f are the anwser

Step-by-step explanation:

SpyIntel [72]3 years ago

3 0

there is no expanded form

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Calculate the value of the sample variance. Round your answer to one decimal place. 9_5,9_5,2,9_5

Ugo [173]

Answer:

$s^2 = 0.01$

Step-by-step explanation:

Given

Values: 9/5, 9/5, 2, 9/5

Required

Calculate the sample variance

Sample variance is calculated using:

$s^2 = \frac{\sum (x_i - \overline x)^2}{n - 1}$

First, we calculate the mean

$\overline x = \frac{\sum x}{n}$

$\overline x = \frac{9/5 + 9/5 + 2 + 9/5}{4}$

$\overline x = \frac{7.4}{4}$

$\overline x = 1.85$

$s^2 = \frac{\sum (x_i - \overline x)^2}{n - 1}$ becomes

$s^2 = \frac{(9/5 - 1.85)^2+(9/5 - 1.85)^2+(2 - 1.85)^2+(9/5 - 1.85)^2}{4 - 1}$

$s^2 = \frac{(-0.05)^2+(-0.05)^2+(0.15)^2+(-0.05)^2}{4 - 1}$

$s^2 = \frac{0.0025+0.0025+0.0225+0.0025}{3}$

$s^2 = \frac{0.03}{3}$

$s^2 = 0.01$

<em>Hence, the variance is 0.01</em>

5 0

3 years ago

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

Someone please help me I’m so confused!!!

QveST [7]

Answer:

number one. 186 $in^{2}$ number two. 36 $cm^{2}$

Step-by-step explanation:

FOR NUMBER ONE:

the area of a trapezoid formula is $\frac{a+b}{2} h$ where a and b are the bases and h is the height. so we have to add in the numbers into the formula

$\frac{12+15}{2} * 6\\$ = <em>81</em>

and the paralellogram formula is b×h. where b is the base and h is height

15 × 7 = <em>105</em>

so the area of the figure is 81 + 105 is 186 in^2

FOR NUMBER TWO:

the area of the square formula is $s^{2}$ . where s is the side

4^2 = <em>16</em>

and for the paralellogram is b × h

4 × 5 = <em>20</em>

so the area of the figure is 16 +20 = 36 in^2

hope this helps! ;)

5 0

3 years ago

A number is randomly selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. A is represented by the event that the number picked is grea

fomenos

P(A) = P(8) + P(9) + P(10) = 3/10 so P(A complement) = 1 - P(A) = 1 - 3/10 = 7/10 - D

7 0

4 years ago

Read 2 more answers

Why is it so expensive to buy organic food

Jet001 [13]

A few reasons are:
1) They contain very little to no chemicals
2) It takes more work to grow, care for, and harvest
3) Majority of farmers produce organic food as a living so it has to be more expensive if they actually want to make a profit

6 0

4 years ago