A simple random sample (SRS) of 100 of a certain popular car in 1997 found that 20 had a certain minor defect in the brakes. An

SRS of 400 of the same car in 1998 found that 50 had the minor defect in the brakes. Let p1 and p2 be the proportion of all cars of this model in 1997 and 1998, respectively,that contained the defect. A 90% confidence interval for p1−p2 is:

Mathematics

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Which functions represent the arithmetic sequence 8, 1.5, –5, –11.5 . . . ? Check all that apply. f(n) = –6.5n + 14.5 f(n) = –1.

PIT_PIT [12445]

To determine which functions depict the arithmetic sequence 8, 1.5, -5, -11.5,... follow these steps:

<span>f(n) = –6.5n + 14.5... correct
f(1) = 8
f(2) = 1.5
f(3) = -5
f(4) = -11.5

f(n) = –1.5n + 9.5... incorrect
f(1) = 8
f(2) = 6.5

f(n) = 6.5n + 1.5... incorrect
f(1) = 8
f(2) = 14.5

f(1) = 8, f(n + 1) = f(n) – 6.5... correct
f(2) = 8 - 6.5 = 1.5
f(3) = 1.5 - 6.5 = -5
f(4) = -5 - 6.5 = -11.5

f(1) = 8, f(n + 1) = f(n) – 1.5... incorrect
f(2) = 8 - 1.5 = 6.5

f(1) = 8, f(n + 1) = f(n) + 6.5... incorrect
f(2) = 8 + 6.5 = 14.5

The valid functions are:
</span>f(n) = –6.5n + 14.5 and f(1) = 8, f(n + 1) = f(n) – 6.5.

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1 month ago

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Mike earned x dollars the first week of his new job. He earned 5% more the second week than the first week. Which expression rep

zzz [12365]

The expression indicates that the total earnings of Mike over the two weeks amount to 2.05x dollars

Solution:

It is given that Mike earned x dollars during the first week at his new job,

While in the second week, he earned 5% more than the earnings of the first week.

To determine: Total earnings over the two weeks

From the information provided,

Earnings in the first week = "x" dollars

Earnings in the second week = 5% more than first week earnings

Thus,

Earnings in the second week = x + 5% of x

$\rightarrow x + 5 \% \times x\\\\\rightarrow x + \frac{5}{100} \times x\\\\\rightarrow x + 0.05x = 1.05x$

Therefore, earnings in the second week equal to 1.05x dollars

The total earnings over the two weeks:

Total earnings = Earnings from first week + Earnings from second week

$Total\ Amount = x + 1.05x = 2.05x$

Thus, the expression for the total earnings of Mike for both weeks is 2.05x dollars

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2 months ago

In the Ma-and-Pa grocery store, shelf-space is limited and must be used effectively to increase profit. Two-cereal items, Grano

Inessa [12570]

No. Allocate 2/3 of the space to Grano and 1/3 to Wheatie. This results in approximately 57% for Wheatie and 43% for Grano—meaning 60(.57)=34.2 ft² for Wheatie and 60(.43)=25.8 ft² for Grano. Therefore, there would be about 85.5 boxes of Wheatie and 129 boxes of Grano, leading to a total profit of 129(1)+85(1.35)=$243.75. The best choice would be to place 200 boxes of Grano and 50 boxes of Wheaties on the shelf. Allocating 40 ft² to Granos (200(.2)) and 20 ft² to Wheaties (50(.4)) means that 40/60=2/3=66.6% of the space would be for Granos, and 20/60=1/3=33.3% would be for Wheaties. The total profit would be 200(1)+50(1.35)=$267.5.

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2 months ago

Which expressions are equivalent to RootIndex 3 StartRoot 128 EndRoot Superscript x? Select three correct answers.

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Answer: