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Nimfa-mama [501]
2 years ago
13

Each side of a pentagon is 10 cm greater than the previous side. If the perimeter of this pentagon is 500 cm, find the lengths o

f the sides.
Mathematics
1 answer:
Vesna [10]2 years ago
8 0

Answer: See explanation

Step-by-step explanation:

The perimeter of a pentagon is gotten through the summation of its five sides. Let the first side be represented by x. Since each side of a pentagon is 10 cm greater than the previous side, then the sides will be:

First side = x

Second side = x + 10

Third side = x + 10 + 10 = x + 20

Forth side = x + 30

Fifty side = x + 40

Therefore,

x + (x + 10) + (x + 20) + (x + 30) + (x + 40) = 500

5x + 100 = 500

5x = 500 - 100

5x = 400

x = 400/5

x = 80

Therefore, the lengths will be:

First side = x = 80cm

Second side = x + 10 = 80 + 10 = 90cm

Third side = x + 20 = 80 + 20 = 100cm

Forth side = x + 30 = 80 + 30 = 110cm

Fifty side = x + 40 = 80 + 40 = 120cm

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Tom is incorrect

He keeps getting the same number of 1:6 on each roll.
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2 years ago
Which of the following expressions shows how to rewrite 5 − 6 using the additive inverse and displays the expression correctly o
Andru [333]

The correct display of the expression on a number line is number line (c)

<h3>How to determine the expression that shows how to rewrite 5 − 6 using the additive inverse?</h3>

The complete question is added as an attachment

The expression is given as:

5 - 6

Put 6 in a bracket.

So, we have:

5 - 6 = 5 - (6)

Express 6 as --6

So, we have:

5 - 6 = 5 - -(-6)

Rewrite as:

5 - 6 = 5 + (-6)

The above means that the arrow on the number line must start from 5 and moves in the negative direction in 6 units

The correct display of the expression on a number line is number line (c)

Read more about number lines at:

brainly.com/question/24644930

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7 0
1 year ago
The scientist performs additional analyses and observes that the number of major earthquakes does appear to be decreasing but wo
kifflom [539]

Answer:

Step-by-step explanation:

Hello!

A regression model was determined in order to predict the number of earthquakes above magnitude 7.0 regarding the year.

^Y= 164.67 - 0.07Xi

Y: earthquake above magnitude 7.0

X: year

The researcher wants to test the claim that the regression is statistically significant, i.e. if the year is a good predictor of the number of earthquakes with magnitude above 7.0 If he is correct, you'd expect the slope to be different from zero: β ≠ 0, if the claim is not correct, then the slope will be equal to zero: β = 0

The hypotheses are:

H₀: β = 0

H₁: β ≠ 0

α: 0.05

The statistic for this test is a student's t: t= \frac{b - \beta }{Sb} ~~t_{n-2}

The calculated value is in the regression output t_{H_0}= -3.82

This test is two-tailed, meaning that the rejection region is divided in two and you'll reject the null hypothesis to small values of t or to high values of t, the p-value for this test will also be divided in two.

The p-value is the probability of obtaining a value as extreme as the one calculated under the null hypothesis:

p-value: P(t_{n-2}\leq -3.82) + P(t_{n-2}\geq  3.82)

As you can see to calculate it you need the information of the sample size to determine the degrees of freedom of the distribution.

If you want to use the rejection region approach, the sample size is also needed to determine the critical values.

But since this test is two tailed at α: 0.05 and there was a confidence interval with confidence level 0.95 (which is complementary to the level of significance) you can use it to decide whether to reject the null hypothesis.

Using the CI, the decision rule is as follows:

If the CI includes the "zero", do not reject the null hypothesis.

If the CI doesn't include the "zero", reject the null hypothesis.

The calculated interval for the slope is: [-0.11; -0.04]

As you can see, both limits of the interval are negative and do not include the zero, so the decision is to reject the null hypothesis.

At a 5% significance level, you can conclude that the relationship between the year and the number of earthquakes above magnitude 7.0 is statistically significant.

I hope this helps!

(full output in attachment)

5 0
3 years ago
Drag each equation to show if it could be a correct first step to solving the equation 3(6+x)=24
kakasveta [241]

Use the distributive property.

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18 + 3x = 24

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x = 2

5 0
2 years ago
Read 2 more answers
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REY [17]

Answer:

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Step-by-step explanation:

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(h- -8)^2 + ( y - -1)^2 = 3^2

(h+8)^2 + ( y +1)^2 = 3^2

(h+8)^2 + ( y +1)^2 = 9

8 0
3 years ago
Read 2 more answers
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