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eduard
3 years ago
6

The sum of the measures of 2 angles is 90o. Angle C is 34o. Angle G is (3x-4)o. What is the value of x?

Mathematics
1 answer:
GenaCL600 [577]3 years ago
3 0

Answer:

the value of x will be -12

Step-by-step explanation:

hope it helps

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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.

4 0
3 years ago
(a²b²-c²)(a²b²+c²)<br>simplify​
liraira [26]

Answer:

a⁴b⁴ - c⁴

Step-by-step explanation:

The difference of squares formula states that (a - b)(a + b) = a² - b². In this case, a = a²b² and b = c² so a² - b² = (a²b²)² - (c²)² = a⁴b⁴ - c⁴.

6 0
3 years ago
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Given: M(-4,-1), B(-5,-3) find the midpoint
Dmitry [639]
\bf \textit{middle point of 2 points }\\ \quad \\&#10;\begin{array}{lllll}&#10;&x_1&y_1&x_2&y_2\\&#10;%  (a,b)&#10;M&({{ -4}}\quad ,&{{ -1}})\quad &#10;%  (c,d)&#10;B&({{ -5}}\quad ,&{{ -3}})&#10;\end{array}\qquad&#10;%   coordinates of midpoint &#10;\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)&#10;\\\\\\&#10;\left(\cfrac{{{ -5}}-4}{2}\quad ,\quad \cfrac{-3-1}{2} \right)
4 0
3 years ago
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Gareth has $2,000 to invest. Putting the money in a savings account at his local bank will earn him 2.2% annual interest and giv
strojnjashka [21]

Gareth has $2,000 to invest. Putting the money in a savings account at his local bank will earn him 2.2% annual interest.

Interest earned in local bank = 2000 * 22.2% = 2000 * 0.022 = 44

Putting the money in an online savings account will earn him 4.85% annual interest

Interest earned in online account = 2000 * 4.85% = 2000 * 0.0485 = 97

He will be charged $3 every time he makes an ATM withdrawal.

In online account, the interest is 97 . If he withdraws 18 times then

Total ATM fee is 18 * 3= 54 . so 97 - 54 = 43

43 is lower than 44 that is interest of local account.

Therefore, 18 ATM withdrawals make local savings account to be a better deal than the online savings account every year.

3 0
3 years ago
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3
Pavel [41]

Answer: three dimensional figure and plane.

Step-by-step explanation:

A cross section is the intersection between a (three dimensional figure) and also a (plane).

When an object is being cut straight, the shape that we get is referred to as the cross section. We should note that several parallel cross sections will be firmed when we cut a particular object into slices.

4 0
3 years ago
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