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3 years ago

Out of -1.81 , 1 3/4 , -1.3 , -1 4/5 is the least or greatest

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

5 0

Answer:

-1.81 is the least and 1 3/4 is the greatest

Step-by-step explanation:

1 3/4 is also 1.75 -1 4/5 is also -1.8

Ordered from least to greatest:

-1.81, - 1 4/5, -1.3, 1 3/4

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A train travels at a constant rate of 55 miles per hour.

patriot [66]

Answer:

55miles per hour

Step-by-step explanation:

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3 years ago

What is the area of the following circle

Alex17521 [72]

Answer:

Area = 153.86

Step-by-step explanation:

Formula: A = $\pi r^{2}$

diameter (d) = 14

radius = d / 2

radius is 14 / 2 = 7

A = $\pi (7)^{2}\\\pi 49\\49\pi \\49(3.14) = 153.86$

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1 year ago

if the equation x^2 +(k+2)x+2k=0 has equal roots,then the value of k is .....a.2 b.-2 c 1/2 d.none

blsea [12.9K]

Answer:

k=2

Problem:

if the equation x^2 +(k+2)x+2k=0 has equal roots,then the value of k is ..

Step-by-step explanation:

Since the coefficient of x^2 is 1, we can use this identity to aid us: x^2+bx+(b/2)^2=(x+b/2)^2.

So we want the following:

[(k+2)/2]^2=2k

Apply the power on the left:

(k+2)^2/4=2k

Multiply both sides by 4:

(k+2)^2=8k

Expand left side:

k^2+4k+4=8k *I used identity (x+c)^2=x^2+2xc+c^2

Subtract 8k on both sides:

k^2-4k+4=0

Factor using the identity mentioned a couple lines above:

(k-2)^2=0

Since zero squared is zero, we want k-2=0.

Adding both sides by 2 gives k=2.

8 0

3 years ago

4x + 15 - 3x + 10 simpllify the expression pleas give answer and how to do it

dexar [7]

Answer:

x + 25

Step-by-step explanation:

First, group terms that are similar:

4x - 3x + 15 + 10

Next subtract the similar terms:

4x - 3x = 1x

Simplify 1x:

1x = x

Add the other numbers:

15 + 10 = 25

Final product:

x + 25

8 0

2 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