Explain how to find the distance from (23,3) to (23,7) and from (23,3) and (4,3).

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) $P(140$

$P(0.036$

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:

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

$P(140< \bar X$

5 0

3 years ago

Toby the cat had quite a day. Toby caught 14 mice and ate 9 of them. How many mice does Toby still HAVE TO eat?

schepotkina [342]

Answer:

5

Step-by-step explanation:

14-9 = 5

3 0

3 years ago

Read 2 more answers

Frank wants to build a garden with the dimensions below.

dexar [7]

Given:
Length = x + x + 3 = 2x + 3
Width = 2 + x

Area = length * width
91 ft² = (2x + 3) (2+x)
91 = 4x + 2x² + 6 + 3x
0 = 2x² + 7x + 6 - 91
0 = 2x² + 7x - 85

(2x + 17) ( x - 5)

x = -17/2 or x = 5

Let x = 5 ;

length = 2x + 3 = 2(5) + 3 = 13
width = 2 + x = 2 + 5 = 7

Area = 13 x 7 = 91

Perimeter = 2(length + width)
Perimeter = 2(13 + 7)
Perimeter = 2(20)
Perimeter = 20 feet of fencing

7 0

3 years ago

Read 2 more answers

A box with an open top will be constructed from a rectangular piece of cardboard. The piece of cardboard is 10 inches wide and 1

kupik [55]

Answer:

Domain of the function is { x : x∈R, x>0 } or (0,∞).

Step-by-step explanation:

It is given that the dimensions of a rectangular piece of cardboard are

Length = 14 inch

Width = 10 inch

The box will be constructed by cutting out equal squares of side x at each corner and then folding up the sides. So the dimensions of the box are

Length = 14-2x inch

Breadth = 10- 2x inch

Height = x inch

The volume of cuboid box is

$V=length\times breadth \times height$

The volume function of the box is

$V=(14-2x)\times (10-2x)\times x$

$V=(14-2x)(10-2x)x$

The volume function is V=(14-2x)(10-2x)x.

It is a polynomial function and domain of a polynomial function is all real numbers.

Here, x represents the height of the box. So, value of x must be a positive real number.

Domain of the function is

Domain = { x : x∈R, x>0 }

It can be written as (0,∞).

Therefore, domain of the function is { x : x∈R, x>0 } or (0,∞).

5 0

3 years ago

Please help. I’ll mark you as brainliest if correct!!!!

aliya0001 [1]

Answer:

(-∞, -6] U [-2, ∞)

Step-by-step explanation:

To solve this, begin by factoring this quadratic equation into its factored form:

x² + 8x + 12 ≥ 0 becomes (x+6)(x+2) ≥ 0.

x = -6, and x = -2 are the zeros of this parabola. Therefore:

(-∞, -6] U [-2, ∞) are the parts of the graph above y = 0 because the graph

opens upward.

** Remember, when the '≥' sign is present, the

square brackets must be used.

8 0

3 years ago