The top of a 230 foot vertical tower is to be anchored by cables that make an angle with a measure of 50 degrees with the ground.
How long must each cable be? ____ feet   
How far from the base of the tower should the anchors be placed? _____ feet   
​

Answer:

a) P(X > 207.50) = 0.0808

b) P(X-bar > 193.5) = 0.7734

c) It matters only in sampling distribution when we does not know the shape of distribution.

Step-by-step explanation:

Given - The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 8.9 cm.

To find - a. Find the probability that an individual distance is greater than 207.50 cm.

              b. Find the probability that the mean for 20 randomly selected distances is greater than 193.50 cm.

              c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30 ?

Proof -

Given that,

μ = 195 cm

σ = 8.9 cm

a)

P(X > 207.50) = 1 - P(X < 207.5)

                       = 1 - P(Z < [tex]\frac{207.5 - 195}{8.9}[/tex] )

                       = 1 - P(Z < 1.4)

                       = 1 - 0.9192

                       = 0.0808

⇒P(X > 207.50) = 0.0808

b)

n = 20

μₓ- = μ = 195

σₓ⁻ = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{8.9}{\sqrt{20} }[/tex] = 1.99

Now,

P(X-bar > 193.5) = 1 - P(X-bar < 193.5)

                          = 1 - P(Z < [tex]\frac{193.5 - 195}{1.99}[/tex] )

                          = 1 - P(Z < -0.75)

                          = 1 - 0.2266

                          = 0.7734

⇒P(X-bar > 193.5) = 0.7734

c)

Given that If the population is normally distributed , then the sample does not have to be greater than 30.

It matters only in sampling distribution when we does not know the shape of distribution.

Answer:

88°

Step-by-step explanation:

Because, vertically opposite angles are equal

Answer: D

Step-by-step explanation: on The graph it shows the height of the ball after 3 bounces is 4 feet

Answer:

8

Step-by-step explanation:

Answer:

What is the Greatest Common Factor of 8 and 16? Greatest common factor (GCF) of 8 and 16 is 8.

Answer:

Step-by-step explanation:

A = (7 + 4)(24) ÷ 2 = 132 units²

Answer:

5 less than y isn’t up there but if you mean 5 minus y it’s the second one, and y minus 5 is the first

Step-by-step explanation:

Answer:

9/15 will become 3/5 and 6/15 will become 2/5.

Answer:

Step-by-step explanation:

Let the speed of Baba Yaga is x

The distance to Bald Mountain:

The distance she actually travelled is less by 40 km:

The time she spent:

Solve for x to find the speed:

Solving the quadratic equation we get:

Answer:

21+10.5 which would equal 31.5

Step-by-step explanation:

Answer:

21+10.5 which would equal 31.5

Step-by-step explanation:

Answer:

Answer is Complementary.

Step-by-step explanation:

This is because complementary angles add up to 90 degrees. In this example, the angles are exactly 45 degrees. Therefore, because there are two angles 45 * 2 is 90. Answer is B.

Answer:

D. vertical

Step-by-step explanation:

We can rule out A and B because they wont equal 180 or 90 they will be somewhere in between. We can rule out C because those are acute angles. So we are left with D. These angles are vertical because they are opposite angles made by two intersecting lines and they have equal values.

Answer:

A) x > -5

Step-by-step explanation:

Answer:

Step-by-step explanation:

n o The angle terminates in Quadrant II In degrees, the reference angle for the given angle is 30°.

Answer:

A

Step-by-step explanation:

That's your answer...

dang u fail gonna fail i feel baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad.......

just look at the one that has the letter x going up it is c or d

Answer:

[tex]P(X = x) = C_{8,x}.(0.4)^{x}.(0.6)^{8-x}[/tex]

In which x is the number of which we want to find the probability.

Step-by-step explanation:

For each traffic fatality, there are only two possible outcomes. EIther it involved an intoxicated or alcohol-impaired driver or nonoccupant, or it didn't. Traffic fatalities are independent of other traffic fatalities, which means that the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability is .40 that a traffic fatality involves an intoxication or alcohol-impaired driver or nonoccupant.

This means that [tex]p = 0.4[/tex]

Eight traffic fatalities

This means that [tex]n = 8[/tex]

Find the probability that the number which involve an intoxicated or alcohol-impaired driver or nonoccupant is

This is P(X = x), in which x is the number of which we want to find the probability. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = x) = C_{8,x}.(0.4)^{x}.(0.6)^{8-x}[/tex]

Based on the binomial probability principle, the probability involving the number of non-occupant is [tex] P(x = k) = 8Ck \times 0.40^{k} \times 0.60^{8-k} [/tex]

Let :

Using the binomial probability relation :

Substituting the values into the relation :

[tex] P(x = k) = nCk \times 0.40^{k} \times 0.60^{n-k} [/tex]

Hence, the required probability expression is [tex] P(x = k) = 8Ck \times 0.40^{k} \times 0.60^{8-k} [/tex]

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Answer:

interesting

Step-by-step explanation:

very interesting

Answer:

That is a ratio. Like for every 5 blue cards there are 7 red cards, read the context and you'll be able to see the ratio.

Step-by-step explanation:

Hope this helps :)

Answer

A triangle can be constructed if we are given 2 sides and an angle. For these ... AB=4 cm, Angle A =30˚, AC=5 cm. 2.) BC=3 cm, Angle B=80˚, BA=6 cm ... Angle A=20˚, AC=6.5 cm, Angle C=90˚ ... Angle A=25˚, Angle B=120˚, Angle C=35˚.

Step-by-step explanation:

Answer: 6%

Step-by-step explanation: Step 1: We make the assumption that 2000 is 100% since it is our output value.

Step 2: We next represent the value we seek with x.

Step 3: From step 1, it follows that 100%=2000$.

Step 4: In the same vein, x%=120.

Step 5: This gives us a pair of simple equations:

100%=2000(1).

x%=120(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

[tex]\frac{100\%}{x\%}=\frac{2000}{120}[/tex]

Step 7: Taking the inverse (or reciprocal) of both sides yields

[tex]\frac{x\%}{100\%}=\frac{120}{2000}[/tex]

[tex]\Rightarrow x=6\%[/tex]

Therefore, 120 is 6% of 2000$.

Answer:

A. help him/her

funny story, i once got into trouble for defending my friend from being bullied and the person doing the bullying didn't get punished smh

Answer:

a

Step-by-step explanation:

duhh

Answer:

5

Step-by-step explanation:

The value of the interquartile range of the data below is 5.

The difference between the third and the first quartile is defined by the interquartile range. There are so three quartiles.

The first quartile, also known as the lower quartile, is marked by Q1, the second quartile by Q2, and the third quartile, sometimes known as the upper quartile, is denoted by Q3. The lower quartile less the upper quartile equals the interquartile range.

From the Plot we can write

Minimum = 27

Lower quartile = 32

Median = 36

Upper Quartile = 37

Maximum = 40

So, Interquartile range (IQR)

= Third Quartile (Q3) - First Quartile (Q1)

= 37 - 32

= 5

Learn more about IQR here:

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Answer:

A = 81

Step-by-step explanation:

When there is a number above the other. You will need to multiply it.

There is   a 4 so its 4 times.

-3 x -3 = 9

9 x -3 = -27

-27 x -3 = 81

------

When you multiply a negative number by a negative number it will be a positive.

If you multiply a positive number by a negative it will be negative.

Answer:

n divided by 6 (n/6)

Step-by-step explanation:

The mathematical expression for 'the quotient of 6 and a number (n)' is, 6/n or (6 ÷ n).

Used the concept of mathematical expression which can be stated that,

A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

Given that,

The algebraic expression is,

''The quotient of 6 and a number (n).''

Now, the mathematical expression for 'the quotient of 6 and a

number (n)' is,

6 ÷ n

= 6 / n

So, the mathmatical notation is 6/n.

To learn more about the divide visit:

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Answer:

e

Step-by-step explanation:

e

Answer:

6

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Answer:

Option 1

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

The area of one of the four triangles is [tex]\frac{1}{2}\times 5 \times 7 = 17.5[/tex]. So together the area of all the four traingles is [tex]4\times 17.5 = 70[/tex]

Answer:

8n < 72

Step-by-step explanation:

Eight times a number (n) is less than 72.

Answer:

32/24 is equivalent to 12/19

yes

Answer:

the first one

Step-by-step explanation:

y-y1=m(x-x1)

y-20=12(x-3)

[tex]y-20+20=12\left(x-3\right)+20[/tex]

simplify:

[tex]y=12x-16[/tex]