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3 years ago

Margaret drove to a business appointment at 30 mph. Her average speed on the return trip was 20 mph. The return trip took

Mathematics

1 answer:

Firlakuza [10]3 years ago

5 0

Margaret drove 30 miles one way and 30 miles back, totaling 60 miles.

Given that Margaret drove to a business appointment at 30 mph, and her average speed on the return trip was 20 mph, and the return trip took 1/2 hr longer because of heavy traffic, to determine how far did she travel to the appointment the following calculation must be performed:

30 - 20 = 10
10 = 0.5 hours = 30 minutes
30 = 1
20 = 0.666
1 = 1
1.333 = 1.5
1 = 30 x 2 = 60

Therefore, Margaret drove 30 miles one way and 30 miles back, totaling 60 miles.

Learn more in brainly.com/question/24268730

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A survey of 2306 adult Americans aged 18 and older conducted by Harris Interactive found that 417 have donated blood in the past

disa [49]

Answer:

a) p = 0.1808

b) Since 341.54 ≥ 10. Therefore the requirements for constructing a confidence interval for p is satisfied.

c) The interval is (0.1676, 0.194)

d) We are 90% confident that the population proportion of adult Americans who have donated blood in the past two years is between 0.1676 and 0.194

Step-by-step explanation:

Given that:

n = 2306 and x =417

a) Obtain a point estimate for the population proportion (p) is the ratio of sample successes to sample size.

Therefore: p = x / n = 417 / 2306 = 0.1808

p = 0.1808

b) requirements for constructing a confidence interval for p is given by:

np(1-p) ≥ 10

Therefore: np(1-p) = 2306(0.1808)(1 - 0.1808) = 341.54 ≥ 10

Since 341.54 ≥ 10. Therefore the requirements for constructing a confidence interval for p is satisfied.

c) c = 90% = 0.9

α = 1 - 0.9 = 0.1

α / 2 = 0.1 /2 = 0.05

From the probability table, $z_{\frac{\alpha}{2} } = 1.645$

Margin of error (e) = $z_{\frac{\alpha}{2} } \sqrt{\frac{p(1-p)}{n} } =1.645* \sqrt{\frac{0.1808(1-0.1808)}{2306} }=0.0132$

The boundaries are (p - e, p + e) = (0.1808 - 0.0132, 0.1808 + 0.0132) = (0.1676, 0.194)

The interval is (0.1676, 0.194)

d) We are 90% confident that the population proportion of adult Americans who have donated blood in the past two years is between 0.1676 and 0.194

6 0

3 years ago

Read 2 more answers

I really need help with this! Thank you!!

photoshop1234 [79]

<h3>Answer:</h3>

x = 13; NP = 2 18/23 ≈ 2.8; NL = 5 5/23 ≈ 5.2
D. x = 17, y = 5

<h3>Step-by-step explanation:</h3>

1. In order for this problem to be workable, we need to assume PQ ║ ML. Then ΔPNQ ~ ΔLNM and ∠L = ∠P = 60°.

... ∠L = 60°

... (3x+21)° = 60°

... 3x = 39 . . . . . . . divide by °, subtract 21

... x = 13 . . . . . . . . .divide by 3

The side lengths of similar triangles are proportional, so we have ...

... (3.2 cm)/y = (6 cm)/(8-y)

Multiplying by the product of the denominators, and dividing by (cm), we have ...

... 3.2(8 -y) = 6y

... 3.2×8 = 9.2y . . . . . add 3.2y

... y = 3.2×8/9.2 = 64/23 = 2 18/23 ≈ 2.78 = NP

Then ...

... 8-y = NL ≈ 5.22

In summary: x = 13; NP ≈ 2.8; NL ≈ 5.2

_____

2. If we assume figures ABCD and PSRQ are similar, we can find the values of the variables. We assume ∠C ≅ ∠R, so ...

... 4x +27° = 95°

... 4x = 68° . . . . . subtract 27°

... x = 17° . . . . . . . divide by 4

___

AB/AD = PS/PQ . . . . . corresponding sides of similar figures are proportional

... 4y/(3y-5) = 10/5 . . . . . units of ft cancel

... 5×4y = 10(3y -5) . . . . . multiply by 5(3y-5)

... 20y = 30y -50 . . . . . . simplify

... 50 = 10y . . . . . . . . . . . add 50-20y

... 5 = y . . . . . . . . . . . . . . divide by 10

Using this value of y, we have ...

AB = 4y ft = 20 ft; AD = (3y-5) ft = 10 ft. Both these values are double the corresponding lengths on PSRQ.

In summary, x = 17°, y = 5. . . . . . (note that the ° symbol is appropriate for x)

_____

You should have your teacher show you how to work these problems <em>using only the given information</em>.

In the second problem, you cannot start with the assumption that the figures are similar, as that is what you're being asked to prove. Please note, too, that two sides and one angle of a quadrilateral are insufficient to show similarity.

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Answer:

x = m - z

Step-by-step explanation:

z = m - x

Add x to both sides.

x + z = m

Subtract z from both sides.

x = m - z

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