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miss Akunina [59]

2 years ago

15

You buy a shirt for $19.95 and a pair of shorts for $35.95. Shirts are on sale for 25% off and shorts are on sale for 30% off. W

hat would you pay for the shirt and shorts after the discount?

1 answer:

harkovskaia [24]2 years ago

6 0

Discount on shirt, $D_s = 19.95\times 0.25=\$4.9875$ .

So, Price payed for shirt is :

$P=P_s-D_s\\\\P=19.95 - 4.9875\\\\P=\$14.9625$

Discount on shorts, $D_{sh}=35.95\times 0.30=\$10.785$

Discounted price :

$P=P_{sh}-D_{sh}\\\\P=35.95-10.785\\\\P=\$25.165$

Therefore, discounted price of shirt and shorts are $14.9625 and $25.165.

Hence, this is the required solution.

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2. When a large truckload of mangoes arrives at a packing plant, a random sample of 150 is selected and examined for

kirza4 [7]

a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).

b) The margin of error is: 2.45%.

c) The 90% confidence is the level of confidence that the true population percentage is in the interval.

d) The needed sample size is: 271.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions has the bounds given by the rule presented as follows:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

The variables are listed as follows:

$\pi$ is the sample proportion, which is also the estimate of the parameter.

z is the critical value.

n is the sample size.

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of $\frac{1+0.90}{2} = 0.95$ , so the critical value is z = 1.645.

The sample size and the estimate are given as follows:

$n = 150, \pi = \frac{15}{150} = 0.1$

The margin of error is of:

$M = z\sqrt{\frac{0.1(0.9)}{150}} = 0.0245 = 2.45\%$

The interval is given by the estimate plus/minus the margin of error, hence:

The lower bound is: 10 - 2.45 = 7.55%.

The upper bound is: 10 + 2.45 = 12.45%.

For a margin of error of 3% = 0.03, the needed sample size is obtained as follows:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.645\sqrt{\frac{0.1(0.9)}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.1(0.9)}$

$\sqrt{n} = \frac{1.645\sqrt{0.1(0.9)}}{0.03}$

$(\sqrt{n}})^2 = \left(\frac{1.645\sqrt{0.1(0.9)}}{0.03}\right)^2$

n = 271 (rounded up).

More can be learned about the z-distribution at brainly.com/question/25890103

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3 0

1 year ago

What is the length of line segment PQ? If you can please explain, thanks.

nydimaria [60]

Given:

Tangent segment MN = 6

External segment NQ = 4

Secant segment NP =x + 4

To find:

The length of line segment PQ.

Solution:

Property of tangent and secant segment:

If a secant and a tangent intersect outside a circle, then the product of the secant segment and external segment is equal to the product of the tangent segment.

$\Rightarrow NQ\times NP = MN^2$

$\Rightarrow 4\times (x+4) = 6^2$

$\Rightarrow 4x+16 = 36$

Subtract 16 from both sides.

$\Rightarrow 4x+16-16 = 36-16$

$\Rightarrow 4x =20$

Divide by 4 on both sides.

$$\Rightarrow\frac{4x}{4}=\frac{20}{4}$

$\Rightarrow x = 5$

The length of line segment PQ is 5 units.

5 0

3 years ago

Read 2 more answers

Prove: segment SD = segment PD

Elza [17]

Answer:

C

Step-by-step explanation:

SD is congruent to PD and both triangles share the same side with each other.

7 0

3 years ago

R + 8 > 21 what the ansr

Ksivusya [100]

Answer: r>13

Step-by-step explanation:

The sign is less than so r +8 has to be 20 or less.

3 0

2 years ago

The cost of an electrical gadget and the cost of a plumbing material were in the ratio 8:6 last year ,this year each cost was re

ELEN [110]

Answer:

P=25 q= -31

Step-by-step explanati

7 0

3 years ago