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3 years ago

The perimeter of a rectangular painting is 310 centimeters. If the width of the painting is 64 centimeters, what is its length?

Mathematics

1 answer:

OlgaM077 [116]3 years ago

4 0

The length of the painting is 91 centimeters.

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Using the Principle of Mathematical Induction, prove that . n ^2 − n is even for n ≥ 1

Tamiku [17]

Base case: if n = 1, then

1² - 1 = 0

which is even.

Induction hypothesis: assume the statement is true for n = k, namely that k ² - k is even. This means that k ² - k = 2m for some integer m.

Induction step: show that the assumption implies (k + 1)² - (k + 1) is also even. We have

(k + 1)² - (k + 1) = k ² + 2k + 1 - k - 1

… = (k ² - k) + 2k

… = 2m + 2k

… = 2 (m + k)

which is clearly even. QED

8 0

3 years ago

Find the distance of a plane that travels at an average speed of 200mi/hr for 8.5 hours

asambeis [7]

Answer:

1800 mi

Step-by-step explanation:

Recall that (distance) = (rate)(time).

Here, (distance) = (200 mi/hr)(8.5 hr) = 1800 mi

6 0

3 years ago

20 points! I need the answer ASAP! Thanks!

serious [3.7K]

Answer: y=5/7x+2

Step-by-step explanation:

The y- intercept would be 2 since that is where the line goes through the y axis. Also if you use slope form you will see that the slope is 5/7.

5 0

3 years ago

Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students r

BaLLatris [955]

<h2>Answer with explanation:</h2>

Let p be the population proportion of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Given : Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Set hypothesis to test :

$H_0: p=0.39\\\\H_a :p\neq0.39$

Sample size : n= 1055

Sample proportion : $\hat{p}=\dfrac{466}{1055}=0.441706161137\approx0.44$

Critical value for 95% confidence : $z_{\alpha/2}=1.96$

Confidence interval : $\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}$

$0.44\pm (1.96)\sqrt{\dfrac{0.39(1-0.39)}{1055}}\\\\0.44\pm0.0299536805135\\\\0.44\pm0.03\\\\=(0.44-0.03, 0.44+0.03)\\\\=(0.41,\ 0.47)$

Since , Confidence interval does not contain 0.39.

It means we reject the null hypothesis.

We conclude that 95% confidence interval represents evidence that parents' attitudes toward the quality of education have changed.

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3 years ago

What is 1+1 Who ever awnser first get brainlyist

Bas_tet [7]

Answer:

Step-by-step explanation:

Hope this helps, been doing it all my life! :P

8 0

3 years ago

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