What's the common difference in −1,−4,−7,−10

The greatest common factor of the following monomials. 46x^5. 10x^3

Blizzard [7]

$46x^5 \times 10x^3$

$= 2x^3 (23x^2 \times 5)$

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Answer: GCF = 2x³
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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.

8 0

3 years ago

Let f(x)=2x-6. Solve f^-1(x) when x=2 -5 4 -2 7

ladessa [460]

Answer:

4.

Step-by-step explanation:

f^-1(x) is the inverse of f(x). That means that f(x) = 2x - 6 becomes...

x = 2y - 6

2y - 6 = x

2y = x + 6

y = 1/2x + 3.

When x = 2...

y = 1/2(2) + 3

= 1 + 3

= 4.

Hope this helps!

6 0

3 years ago

Solve the equation -[8x-(19x+1)]=1+(10x+7)

Olegator [25]

Answer:

x=7

Step-by-step explanation:

Let's solve your equation step-by-step.

−(8x−(19x+1))=1+10x+7

Step 1: Simplify both sides of the equation.

−(8x−(19x+1))=1+10x+7

11x+1=1+10x+7(Distribute)

11x+1=(10x)+(1+7)(Combine Like Terms)

11x+1=10x+8

Step 2: Subtract 10x from both sides.

11x+1−10x=10x+8−10x

x+1=8

Step 3: Subtract 1 from both sides.

x+1−1=8−1

x=7

Answer:

x=7

5 0

3 years ago

Anika wants to determine The maximum number of tulip bulbs (T) she can purchase if each bulb costs $1.50. She will also need to

PtichkaEL [24]

T( 1.50+ 1.25) + 10.00 < 20.00 2.75t + 10.00 < 20.00 2.75t < 10.00 T < 3.63 Partial bulbs and puts can't be bought, so Anika cannot spent the full $20.00. Therefore, t < 3 if t can be a whole number.

6 0

4 years ago

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