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Masteriza [31]
2 years ago
13

A worker is installing blue and white square tiles in a kitchen. Blue tiles have different lengths than white tiles. A row of 8

blue tiles and 16 white tiles has a length of 39 inches. A row of 40 blue tiles and 8 white tiles has a length of 42 inches. Write a system of equations that represents in inches the relationship between the length of a blue tile and the length of a white tile.
Mathematics
1 answer:
sertanlavr [38]2 years ago
5 0

8x+16y = 39 and 40x+8y = 42 are the system of equations that represents in inches the relationship between the length of a blue tile and the length of a white tile.

<u>Step-by-step explanation</u>:

Let 'x' be the inches of a blue tile.

Let 'y' be the inches of a white tile.

8x+16y = 39  -------(1)

40x+8y = 42  -------(2)

Multiply eqn(2) by 2 and subtract it from eqn(1)

    8x+16y = 39

(-) <u>80x+16y = 84</u>

  <u>-72x = -45       </u>

⇒ x = -45/-72

⇒ x = 5/8

∴ Blue tile is 5/8 inches.

substitute x=5/8 in eqn(1)

⇒ 8(5/8) + 16y = 39

⇒ 16y = 39-5

⇒ y =34/16

⇒ y = 17/8

∴ White tile is 17/8 inches.

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There is enough evidence to support the claim that the proportions are not equal. (P-value: 0.048).

Step-by-step explanation:

The question is incomplete:

<em>"A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are different."</em>

This is a hypothesis test for the difference between proportions.

The claim is that the proportions are not equal.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0

The significance level is 0.05.

The sample 1, of size n1=1000 has a proportion of p1=0.031.

p_1=X_1/n_1=31/1000=0.031

The sample 2, of size n2=1200 has a proportion of p2=0.018.

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As the P-value (0.048) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportions are not equal.

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