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zhuklara [117]
3 years ago
6

What is the solution set of the quadratic equation - 2(2x-7)^2 = - 8​​

Mathematics
1 answer:
barxatty [35]3 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

Given

- 2(2x - 7)² = - 8 ( divide both sides by - 2 )

(2x - 7)² = 4 ( take the square root of both sides )

2x - 7 = ± \sqrt{4} = ± 2 ( add 7 to both sides )

2x = 7 ± 2

2x = 7 - 2 = 5 or 2x = 7 + 2 = 9 ( divide both sides by 2 )

x = \frac{5}{2}

x = \frac{9}{2}

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What percentage of the shape is green?
Reika [66]

Answer:

2/5 or 40% of the shape is green

Step-by-step explanation:

the shape is divided into 5th and since 2 of the five spaces are green, 2/5th or 40%

7 0
2 years ago
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The value of y varies directly as x, with a constant of variation of -8. What is the value of y when x is 7?
slega [8]

Answer:

y = -56

Step-by-step explanation:

The equation for direct variation is

y = kx  where k is the constant of variation

y = -8 x

We know x =7

y = -8*7

y = -56

6 0
3 years ago
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carol is excited to get a new kitten from the animal shelter. the kitten had an $299 adoption fee. carol had $50 off coupon for
Molodets [167]

Answer:

1 month

Step-by-step explanation:

249 is the amount she spends for buying the kitten, (299-50=249) which she only has to pay once.

20 is the amount she has to spend every month, the rate of change.

The problem can be modeled with the general equation:

y = 20x + 249

In this equation, x the the time in months and y is the amount of money spent.

Substitute 250 for y.

y = 20x + 249

250 = 20x + 249    <= isolate x to get the number of months

1 = 20x

x = 1/20

Carol will only spent money every month, not for 1/20 of a month.

It will only take Carol 1 month to spent $250.

Check answer:

Substitute x for 1

y = 20x + 249

y = 20(1) + 249

y = 269

269 is more than 250 already.

3 0
2 years ago
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The thickness of a plastic film (in mils) on a substrate material is thought to be influenced by the temperature at which the co
statuscvo [17]

Answer:

Step-by-step explanation:

Hello!

The objective is to test if rising the process temperature reduces the thickness of the plastic film that coats a substrate material To do so, two samples of substrates are coated at different temperatures:

Sample 1

X₁: Thickness of the plastic film after the substrate is coated at 125F

n₁=11

X[bar]₁= 101.28

S₁= 5.08

Sample 2

X₂: Thickness of the plastic film after the substrate is coated at 150F

n₂= 13

X[bar]₂= 101.70

S₂= 20.15

Does the data support this claim? Use the P-value approach and assume that the two population standard deviations are not equal.

Now if the higher the heat, the thinner the thickness of the plastic coating, then the average thickness of the coating done at 150F should be less than the average thickness of the coating done at 125F, symbolically: μ₂ < μ₁

Then the hypotheses are:

H₀: μ₂ ≥ μ₁

H₁: μ₂ < μ₁

α:0.05 (there is no α level stated so I've chosen the most common one)

Assuming that both variables have a normal distribution since the population standard deviations are not equal, the statistic to use is the Welch's t-test:

t= \frac{(X[bar]_2-X[bar]_1)-(Mu_1-Mu_2)}{\sqrt{\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} } } ~~t_w

t_{H_0}= \frac{(101.7-101.28)-0}{\sqrt{\frac{(20.15)^2}{13} +\frac{(5.08)^2}{11} } } = 0.072

This test is one-tailed to the left, meaning that you'll reject the null hypothesis at small values of t. The p-value is also one-tailed and has the same direction as the test. To calculate it you have to first calculate the degrees of freedom of the Welch's t:

Df_w= \frac{(\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} )^2}{\frac{(\frac{S^2_1}{n_1})^2 }{n_1-1}+\frac{(\frac{S^2_2}{n_2} )^2}{n_2-1}  }

Df_w= \frac{(\frac{5.08^2}{11} +\frac{20.15^2}{13} )^2}{\frac{(\frac{5.08^2}{11})^2 }{10} +\frac{(\frac{20.15^2}{13} )^2}{12} } = 13.78

The distribution is a Student's t with 13 degrees of freedom, then you can calculate the p-value as:

P(t₁₃≤0.072)= 0.4718

Using the p-value approach, the decision rule is:

If the p-value ≤ α, the decision is to reject the null hypothesis.

If the p-value > α, the decision is to not reject the null hypothesis.

The p-value is greater than the significance level, so the decision is to nor reject the null hypothesis.

Using a significance level of 5%, there is no significant evidence to support the claim that the average thickness pf the plastic coat processed at 150F is less than the average thickness pf the plastic coat processed at 125F.

I hope you have a SUPER day!

4 0
3 years ago
Find last year’s salary if, after a 3% pay raise, this year’s salary is $30,900
Liono4ka [1.6K]
Your answer is $30,000.
The way I have answered this is quite strange, but I'll do my best to explain it. So because we know that $30,900 is 3% than last year, we can call it 103%. This allows us to form a ratio and therefore find 100%.
30,900 : 103
÷ 103
300 : 1
× 100
30,000 : 100
Which means $30,000 is 100%, or 3% less than $30,900. I hope this helps! Let me know if it was confusing or anything :)
5 0
3 years ago
Read 2 more answers
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