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2 years ago

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In a certain year, there were 88 female officials in Congress, which is comprised of the House of Representatives and the Senate

. If there were 54 more female members of the House of Representatives than female senators, find the number of females in each house of Congress.

1 answer:

Ainat [17]2 years ago

3 0

Answer:

71 in House of Representatives
17 in Senate

Step-by-step explanation:

Let h and s represent the numbers in the House and Senate, respectively. Then we have ...

h + s = 88

h - s = 54

Subtracting the second equation from the first gives ...

(h +s) -(h -s) = (88) -(54)

2s = 34 . . . . . simplify

s = 17 . . . . . . . divide by 2

h = 88 -17 = 71 . . . . find the other value using the sum equation

There were 71 females in the House of Representatives, and 17 females in the Senate.

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Answer:

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So, given ordered pairs:

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So, we have given the domain which means the value of x we will put thses given values of x to find y

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So, given domain is: {-5,-1,0,2,10}

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when $x=2$

$y=-4(2)+1=-7$

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$y=-4(10)+1=39$

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(c) We have given a function $v(c)=98c$

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2 years ago

Researchers studying starfish collected two independent random samples of 40 starfish. One sample came from an ocean area in the

krek1111 [17]

Answer:

The test statistic for the appropriate test is $\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$ .

Step-by-step explanation:

The experiment conducted here is to determine whether there is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. north and south.

The hypothesis to test this can be defined as follows:

<em>H₀</em>: There is no difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ = <em>p</em>₂.

<em>Hₐ</em>: There is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ ≠ <em>p</em>₂.

The two-proportion <em>z</em>-test would be used to perform the test.

A sample of <em>n</em> = 40 starfishes are selected from both the ocean areas.

It provided that of the 40 starfish from the north, 6 were found to be over 8 inches in length and of the 40 starfish from the south, 11 were found to be over 8 inches in length.

Compute the sample proportion of starfish from north that were over 8 inches in length as follows:

$\hat p_{n}=\frac{6}{40}=0.15$

Compute the sample proportion of starfish from south that were over 8 inches in length as follows:

$\hat p_{s}=\frac{11}{40}=0.275$

The test statistic is:

$z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}$

Compute the combined proportion <em>P</em> as follows:

$P=\frac{X_{n}+X_{s}}{n_{n}+n_{s}}=\frac{6+11}{40+40}=0.2125$

Compute the test statistic value as follows:

$z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}$

$=\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$

Thus, the test statistic for the appropriate test is $\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$ .

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