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3 years ago

Answer and explanation please. ty

Mathematics

1 answer:

larisa [96]3 years ago

6 0

Answer
0.47qt a sec
Reason
Convert the gallons to quart using the formula “q=4g”
q=4(7)= 28
So we learn that it’s 28 quarts a minute. To figure it out by the second divide by 60.
28 divided by 60 equals 0.4667
Round to the nearest hundredth and it equals
0.47
There for it is 0.47 quarts a second.

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Sum of 2 numbers is 42, and their difference is 8. What are the numbers?

Tems11 [23]

Answer:

25 , 17

Step-by-step explanation:

Let the unknown two numbers be x & y.

According to the question,

Sum of 2 numbers is 42.

x + y = 42 ⇒ ( 1 )

Their difference is 8.

x - y = 8 ⇒ ( 2 )

First let us find the value of x.

( 1 ) + ( 2 )

x + y + x - y = 42 + 8

2x = 50

Divide both sides by 2.

x = 25

And now let us find the value of y.

x + y = 42

25 + y = 42

y = 42 - 25

y = 17

Therefore, the two numbers are 25 , 17

Hope this helps you :-)

Let me know if you have any other questions :-)

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2 years ago

Read 2 more answers

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coldgirl [10]

Vertex is (-5,-10) y intercept of g is (0,-1) zeroes of h are x=-3,1

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2 years ago

Tracy needs to find the length and width of the equipment room where she works. The room is 2 meters longer than it is wide. The

Alekssandra [29.7K]

Answer:

The answer to your question is: width = 3 meters

Step-by-step explanation:

Data

Perimeter = 16 meters

The room is 2 meters longer than its width, then length = width + 2

Perimeter = 2 length + 2 width

16 = 2(width + 2) + 2 width

16 = 2 width + 4 + 2 width

16 = 4 width +4

16 - 4 = 4 width

12 = 4 width

12/4 = width

3 = width

length = 3 + 2 = 5 meters

8 0

3 years ago

A manufacturer produces crankshafts for an automobile engine. the crankshafts wear after 100,000 miles (0.0001 inch) is of inter

Daniel [21]

Part A:

Significant level:

α = 0.05

Null and alternative hypothesis:

h0 : μ = 3 vs h1: μ ≠ 3

Test statistics:

$z= \frac{\bar{x}-\mu}{\sigma/\sqrt{n}} \\ \\ = \frac{2.78-3}{0.9/\sqrt{15}} \\ \\ = \frac{-0.22}{0.2324} =-0.9467$

P-value:

P(-0.9467) = 0.1719

Since the test is a two-tailed test, p-value = 2(0.1719) = 0.3438

Conclusion:

Since the p-value is greater than the significant level, we fail to reject the null hypothesis and conclude that there is no sufficient evidence that the true mean is different from 3.

Part B:

The power of the test is given by:

$\beta=\phi\left(Z_{0.025}+ \frac{3-3.25}{0.9/\sqrt{15}}\right) -\phi\left(-Z_{0.025}+ \frac{3-3.25}{0.9/\sqrt{15}}\right) \\ \\ =\phi\left(1.96+ \frac{-0.25}{0.2324} \right)-\phi\left(-1.96+ \frac{-0.25}{0.2324} \right)=\phi(0.8842)-\phi(-3.0358) \\ \\ =0.8117-0.0012=0.8105$

Therefore, the power of the test if μ = 3.25 is 0.8105.

Part C:

The sample size that would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9 is obtained as follows:

$1-0.9=\phi\left(Z_{0.025}+ \frac{3-3.75}{0.9/\sqrt{n}}\right) -\phi\left(-Z_{0.025}+ \frac{3-3.75}{0.9/\sqrt{n}}\right) \\ \\ \Rightarrow0.1=\phi\left(1.96+ \frac{-0.75}{0.9/\sqrt{n}}\right)-\phi\left(-1.96+ \frac{-0.75}{0.9/\sqrt{n}} \right) \\ \\ =\phi\left(1.96+(-3.2415)\right)-\phi\left(1.96+(-3.2415)\right) \\ \\ \Rightarrow\frac{-0.75}{0.9/\sqrt{n}}=-3.2415 \\ \\ \Rightarrow\frac{0.9}{\sqrt{n}}=\frac{-0.75}{-3.2415}=0.2314 \\ \\ \Rightarrow\sqrt{n}=\frac{0.9}{0.2314}=3.8898$

$\Rightarrow n=(3.8898)^2=15.13$

Therefore, the sample size that would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9 is 16.

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3 years ago

To find the population of a city next year, we multiply its current population by 0.987. By what percent does the population dec

ololo11 [35]

Answer:

$1.3\%$

Step-by-step explanation:

$1 - 0.987 = 0.013$

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2 years ago