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andrezito [222]

2 years ago

9

Caleb has 20 more books than Danica. If Caleb gives Danica half of his books, Danica will have 4 more books than Caleb. How many

books did Caleb have to start with? E. 24 F. 34 G. 44 H. 55

1 answer:

wariber [46]2 years ago

3 0

Answer:

Option E: 24.

Step-by-step explanation:

When Caleb (C) has 20 more books than Danica (D), we have:

$C = 20 + D$ (1)

Now, when Caleb gives Danica half of his books:

$C' = C - \frac{C}{2}$ (2)

Danica will have 4 more books than Caleb, so:

$D' = D + \frac{C}{2}$ (3)

Also we have that:

$D' = C' + 4$ (4)

By entering equation (2) and equation (3) into equation (4) we have:

$D + \frac{C}{2} = C - \frac{C}{2} + 4$ (5)

From (1) we have:

$D = C - 20$ (6)

By entering (6) into (5):

$C - 20 + \frac{C}{2} = C - \frac{C}{2} + 4$

$C = 24$

And, from (6):

$D = C - 20 = 24 - 20 = 4$

Therefore, the correct option is E, Caleb had to start with 24 books.

I hope it helps you!

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<u>Solution- </u>

A researcher placed a petri dish with 32,000 bacterial cells. One hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. Another hour later, the number of cells had again halved.

This can be represented as exponential decreasing function,

$y=a(1 - r)^x$

Where,

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x = hours

Putting the values,

$\Rightarrow y=32000(1 - 0.5)^x$

$\Rightarrow y=32000(0.5)^x$

y-intercept means, where x=0, so

$\Rightarrow y=32000(0.5)^0\\\\\Rightarrow y=32000\times 1=32000$

The coordinate of this poin will be (0, 32000)

This means when x=0 or at the starting of the research, the number of bacteria cells was 32000.

After 3 hours, number of bacteria cells will be,

$\Rightarrow y=32000(0.5)^3$

$\Rightarrow y=32000\times 0.125$

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The coordinate of this point will be (3, 4000)

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2 years ago

Is rap music more popular among young Indians than among young Asians? A sample survey compared 634 randomly chosen Indians aged

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Answer:

Step-by-step explanation:

Confidence interval for the difference in the two proportions is written as

Difference in sample proportions ± margin of error

Sample proportion, p = x/n

Where x = number of successes

n = number of samples

For the indians,

x = 368

n1 = 634

p1 = 368/634 = 0.58

For the asians

x = 130

n2 = 567

p2 = 130/567 = 0.23

Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96

Margin of error = 1.96 × √[0.58(1 - 0.58)/634 + 0.23(1 - 0.23)/567]

= 1.96 × √0.00038422713 + 0.00031234568)

= 0.052

Confidence interval = 0.58 - 0.23 ± 0.052

Confidence interval = 0.35 ± 0.052

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2 years ago

For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: not all thr

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Answer:

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For other values of k, there is 1

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Step-by-step explanation:

We have 2 unknowns and 2 equations:

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If we multiply the E1 by 9 we obtain

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if we substract E3 with E2 we obtain

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Thus,

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That is, if 72-2k = 0, otherwise there is no solution. And 72-2k = 0 when k = 72/2 = 36.

If k is not 36, then

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Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by model

Ann [662]

Answer:

(1) The degrees of freedom for unequal variance test is (14, 11).

(2) The decision rule for the 0.01 significance level is;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The value of the test statistic is 0.3796.

Step-by-step explanation:

We are given that you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne's attire with those of Calvin Klein.

The following is the amount ($000) earned per month by a sample of 15 Claiborne models;

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The following is the amount ($000) earned by a sample of 12 Klein models;

$4.1, $2.5, $1.2, $3.5, $5.1, $2.3, $6.1, $1.2, $1.5, $1.3, $1.8, $2.1.

(1) As we know that for the unequal variance test, we use F-test. The degrees of freedom for the F-test is given by;

$\text{F}_(_n__1-1, n_2-1_)$

Here, $n_1$ = sample of 15 Claiborne models

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(2) The decision rule for 0.01 significance level is given by;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

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