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dsp73
2 years ago
13

An auto maker estimates that the mean gas mileage of its sports utility vehicle is at least 20 miles per gallon. A random sample

of 36 such vehicles had a mean of 18 miles per gallon and a standard deviation of 5 miles per gallon. At α = .01 can you reject the auto maker's claim?
Mathematics
1 answer:
Nady [450]2 years ago
7 0

Answer:

Yes, we reject the auto maker's claim.

Step-by-step explanation:

H0 : μ ≥ 20

H1 : μ < 20

Sample mean, xbar = 18 ;

Sample size, n = 36

Standard deviation, s = 5

At α = 0.01

The test statistic :

(xbar - μ) ÷ s /sqrt(n)

(18 - 20) ÷ 5/sqrt(36)

-2 /0.8333333

= - 2.4

Pvalue from test statistic : Pvalue = 0.00819

Pvalue < α

0.00819 < 0.01

Hence, we reject the Null

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Answer:

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Step-by-step explanation:

6(2a²b-3ab²-5ab³)

6a(2ab-3b²-5b³)

6ab(2a-3b-5b²)

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2 years ago
Con
mr Goodwill [35]

Answer:

The coordinates of E are E(x,y) = \left(\frac{9}{2}, 0 \right).

Step-by-step explanation:

The triangle ABC represents a right triangle as both sides AB and AC are orthogonal to each other. The side AB is in the y axis, whereas the side AC is in the x axis. The triangle is dilated with respect to the origin, in which point A is set.

Vectorially speaking, dilation is defined by the following operation:

P'(x,y) = O(x,y) + k\cdot [P(x,y) - O(x,y)] (1)

Where:

O(x,y) - Point of reference.

P(x,y) - Original point.

P'(x,y) - Dilated point.

k - Dilation factor.

By applying this operation, point B becomes point D:

B(x,y) = (0,4), D(x,y) = (0,6)

D(x,y) = (0,0) + k\cdot [(0,4)- (0,0)]

D(x,y) = (0,0) + k\cdot (0,4)

(0,6) = (0,0) +(0,4\cdot k)

(0, 6) = (0,4\cdot k)

k = \frac{3}{2}

Lastly, we transform point C into point E by applying the same operation: C(x,y) = (3, 0), O(x,y) = (0,0) and k = \frac{3}{2}

E(x,y) = (0,0) + \frac{3}{2}\cdot [(3,0)-(0,0)]

E(x,y) = \left(\frac{9}{2}, 0 \right)

The coordinates of E are E(x,y) = \left(\frac{9}{2}, 0 \right).

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