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Dennis_Churaev [7]

3 years ago

8

Four sisters bought a present for their mother. They received a 10% discount on the original price of the gift. After the discou

nt was taken, each sister payed $9. What was the original price of the gift

1 answer:

Orlov [11]3 years ago

4 0

Answer:

$40

Step-by-step explanation:

x is the original price of the gift

(10% of x) is the value of the discount

(10% of x) = 10/100 . x = 0.1 x

0.1 x is the value of the discount

x - (10% of x) is what was paid, after the discount

x - 0.1 x = 0.9 x

0.9 x is what was paid

4 children paid $9/each

4 times $9 = $36

$36 is the total amount that was paid by the children

$36 = 0.9 x

$36 / 0.9 = x

x = $36 / 0.9 = 360 / 9

x = 40

;-)

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A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex

Olenka [21]

Answer:

a

The 90% confidence interval that estimate the true proportion of students who receive financial aid is

$0.533 < p < 0.64$

b

$n = 1789$

Step-by-step explanation:

Considering question a

From the question we are told that

The sample size is n = 200

The number of student that receives financial aid is $k = 118$

Generally the sample proportion is

$\^ p = \frac{k}{n}$

=> $\^ p = \frac{118}{200}$

=> $\^ p = 0.59$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

=> $E = 1.645 * \sqrt{\frac{0.59 (1- 0.59)}{200} }$

=> $E = 0.057$

Generally 90% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.533 < p < 0.64$

Considering question b

From the question we are told that

The margin of error is E = 0.03

From the question we are told the confidence level is 99% , hence the level of significance is

$\alpha = (100 - 99 ) \%$

=> $\alpha = 0.01$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the sample size is mathematically represented as

$[\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [\frac{2.58}{0.03} ]^2 * 0.59 (1 - 0.59 )$

=> $n = 1789$

8 0

3 years ago

Find the Factor of 6x 2 - 17x + 5.

nydimaria [60]

6x² -17x +5 = (6x² - 2x) - (15x + 5) (factoring by grouping)

2x (3x -1) - 5(3x - 1)

(2x -5) (3x - 1) is your final answer

hope this helps

5 0

3 years ago

Read 2 more answers

50% of all the cakes jenny baked that week were party cakes,1/5 were fruit cakes, and the remainder were sponge cakes. what perc

irina1246 [14]

Answer:

30%

Step-by-step explanation:

1/5 = 20%

so, 50 - 20 = 30

7 0

3 years ago

Josh is building a sandbox for his little sister. He uses these plans, which have a scale of 2 in. : 3 ft.

skelet666 [1.2K]

Answer:

Width of 6ft and length of 9ft

Step-by-step explanation:

The sandbox has a ratio of 2:3. If you plug the numbers in with the ratio, you can find the actual dimensions.

Let x be the length

Let y be the width

(Length)

2in / 3ft = 6in / (x)ft

2in / 3ft = 6in / <u><em>9ft </em></u>

(Width)

2in / 3ft = 4in / (y)ft

2in / 3ft = 4in / <em><u>6ft</u></em>

6 0

3 years ago

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nikitadnepr [17]

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Comparing the test statistic Z = -5.47 with the rejection region Z < -2.5758 and Z > 2.5758. we find the test statistic lies in the rejection region. Therefore the evidence does not indicate that the average body temperature for healthy humans is different from 98.6◦.

7 0

3 years ago