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ale4655 [162]
2 years ago
15

Question 6 of 6

Mathematics
1 answer:
Bezzdna [24]2 years ago
6 0

\huge \boxed { \sf \: Answer}

We have to use the formula:

(ab) ^{n}  =  {a}^{n}  {b}^{n}

So,

(5 \times 9) ^{12}  \\  =  {5}^{12} . 9^{12}

Also, it will be

45^{12}

Hope you could understand.

If you have any query, feel free to ask.

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An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and
egoroff_w [7]

Answer:

a) P(140

P(0.036

P(0.036

b) P(140< \bar X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(139,28.1)  

Where \mu=139 and \sigma=28.1

We are interested on this probability

P(140

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(140

And we can find this probability like this:

P(0.036

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(0.036

Part b

For this case we select a sample size of n =32. Since the distribution for X is normal then the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu=139, \frac{\sigma}{\sqrt{n}}=\frac{28.1}{\sqrt{32}}=4.97)

And the new z score would be:

Z=\frac{\bar X -\mu}{\sigma_{\bar x}}

P(140< \bar X

P(140< \bar X

5 0
3 years ago
PLEASE HELP:
Lady bird [3.3K]

Answer: (A) The image of JKL after a 90° counterclockwise about the origin is shown in figure 1. (B) The image of JKL after a reflection across the y-axis is shown in figure 2.

Explanation:

(A)

From the given figure it is noticed that the coordinate points are J(-4,1), K(-4,-2) and L(-3,-1).

If a shape rotate 90 degree counterclockwise about the origin, then,

(x,y)\rightarrow (-y,x)

J(-4,1)\rightarrow J'(-1,-4)

K(-4,-2)\rightarrow K'(2,-4)

L(-3,-1)\rightarrow L'(1,-3)

Therefore, the vertex of imare are  J'(-1,-4),  K'(2,-4) and  L'(1,-3). The graph is shown in figure (1).

(B)

If a figure reflect across the y-axis then,

(x,y)\rightarrow (-x,y)

J(-4,1)\rightarrow J''(4,1)

K(-4,-2)\rightarrow K''(2,-4)

L(-3,-1)\rightarrow L''(3,-1)

Therefore, the vertex of imare are  J''(4,1),  K''(2,-4) and  L''(3,-1). The graph is shown in figure (2).

8 0
3 years ago
F (x) = x+2 +9<br> What is the inverse
Sindrei [870]

Answer: The inverse is f^-1 (x) = x - 11

8 0
3 years ago
Pls help quick. will give brainliest
olya-2409 [2.1K]

Answer:

113.04

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Both circle A and circle B have a central angle measuring 50°. The area of circle A's sector is 36π cm2, and the area of circle
slega [8]

Answer:

A) 3/4

Step-by-step explanation:

Given: Both circle A and circle B have a central angle measuring 50°.

           The area of circle A's sector is 36π cm2.

            The area of circle B's sector is 64π cm2.

We know, area of the circle= \pi r^{2}

lets assume the radius of circle A be "r_1" and radius of circle B be "r_2"

As given, Area of circle A and B´s sector is 36π and 64π repectively.

Now, writing ratio of area of circle A and B, to find the ratio of radius.

⇒\frac{\pi r_1^{2}  }{\pi r_2^{2} }  = \frac{36\pi }{64\pi }

Cancelling out the common factor

⇒ \frac{r_1^{2}  }{r_2^{2} }  = \frac{36 }{64}

⇒ (\frac{r_1  }{r_2} )^{2} = \frac{36 }{64}

Taking square on both side.

Remember; √a²= a

⇒ (\frac{r_1  }{r_2} ) =\sqrt{ \frac{36 }{64}}

⇒ (\frac{r_1  }{r_2} ) = \frac{6}{8}

⇒\frac{r_1  }{r_2}  = \frac{3}{4}

Hence, ratio of the radius of circle A to the radius of circle B is 3:4 or 3/4.

5 0
3 years ago
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