Show mathematically why the ratio 15:10 is not equal to 10:15

Answer:

1. It is not appropriate to use the normal curve, since np = 7.4 < 10.

2. The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.

Step-by-step explanation:

Binomial approximation to the normal:

The binomial approximation to the normal can be used if:

np >= 10 and n(1-p) >= 10

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

The proportion of U.S. adults with high blood pressure is 0.2. A sample of 37 U.S. adults is chosen.

This means, respectively, that [tex]p = 0.2, n = 37[/tex]

Is it appropriate to use the normal approximation to find the probability that more than 48% of the people in the sample have high blood pressure?

np = 37*0.2 = 7.4 < 10

So not appropriate.

It is not appropriate to use the normal curve, since np = 7.4 < 10.

Part 2:

Now n = 82, 82*0.2 = 16.4 > 10, so ok

Mean and standard deviation:

By the Central Limit Theorem,

Mean [tex]\mu = p = 0.2[/tex]

Standard deviation [tex]s = \sqrt{\frac{0.2*0.8}{82}} = 0.0442[/tex]

Find the probability that more than 32% of the people in this sample have high blood pressure.

This probability is 1 subtracted by the pvalue of Z when X = 0.32. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.32 - 0.2}{0.0442][/tex]

[tex]Z = 2.72[/tex]

[tex]Z = 2.72[/tex] has a pvalue of 0.9967.

1 - 0.9967 = 0.0033

The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.

Answer: 16%

Step-by-step explanation:

168.2 - 145 = 23.2

23.2/145 = 0.16

0.16 as a percent is 16%

The percentage change of the height is A = 16 %

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Christian's height increased by

168.2 - 145 = 23.2 cm

To find the percentage increase, we need to divide the increase by the original height and then multiply by 100:

Percentage increase = (23.2 / 145) x 100%

Percentage increase = 0.16 x 100%

Percentage increase = 16%

Hence , Christian's height increased by 16%

To learn more about percentage click :

https://brainly.com/question/12861068

#SPJ3

Answer:

Step-by-step explanation:

Find attached the second one

Answer: I cant see the picture

Step-by-step explanation:

Answer:

lol

no

ask

it teacher of it school

Answer:

x=-4

Step-by-step explanation:

Answer:

624

Step-by-step explanation:

I hope it helps i did the test  btw <3

Answer:

624

Step-by-step explanation:

I also did that same exact test. K12 right? That is what I go to. Anyway that answer is correct. Your welcome!

Answer:

14

Step-by-step explanation:

-21+-13+20=14

This is true because when subtracting negatives by negatives you pretty much add them and then when you add a positive to a negative you are technically removing the negative by the amount you are adding.

In short its kind of like using inverse operation in a way.

Hope this helps and have a nice day

Also may I please have a brainliest!!!

Answer:

$7

Step-by-step explanation:

Recognize our numbers, I always say

14, 8, 56

"For every $14, he saves 8."

14-6=8

"He earned $56 babysitting..."

What times eight can give us 56?

56 divided by 8=7

8x7=56

Hope this helps!

Can I get brainliest please?

Answer: 15 Dogs

Step-by-step explanation:

1.) Set up a ratio!

6 Dogs =    ?

4 Hours    10 Hours

2.) Cross Multiply

6x10=60

60/4= 15

Answer:

It is an Irrational Number

Answer:

Sorry this is so late but for those that need it. The answer is 4.8

Step-by-step explanation:

In order to get this i set up my equation like so.

0.60*(0.5*16)=y

Why I did it like this is because for every 0.5 thats half a mile so 8 miles times 2 to get the half miles was 16.

After figuring out that i started my equation and got

0.60*8=y

Then to finish it and get $4.8 Donated.

Hope this helped

A brainliest is always appreciated.

Answer:

70in.

Step-by-step explanation:

1 foot is the equivalent to 12 inches. So 6 feet is 6×12. ... So now we have  72 and 70 inches.

Answer:

6 ft is more then 70 in.

Step-by-step explanation:

6 ft is more then 70 in. because 6ft is 72 in. therefore 6ft. is more then 70 in.

HOPE THIS HELPS

Answer:

0.6864 = 68.64% probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios

Step-by-step explanation:

The cars are chosen without replacement, so the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[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]

48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed.

This means that [tex]N = 48, k = 12[/tex]

8 cars received.

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

What is the probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios

This is

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,48,8,12) = \frac{C_{12,0}*C_{36,8}}{C_{48,8}} = 0.0802[/tex]

[tex]P(X = 1) = h(1,48,8,12) = \frac{C_{12,1}*C_{36,7}}{C_{48,8}} = 0.2655[/tex]

[tex]P(X = 2) = h(2,48,8,12) = \frac{C_{12,2}*C_{36,6}}{C_{48,8}} = 0.3407[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0802 + 0.2655 + 0.3407 = 0.6864[/tex]

0.6864 = 68.64% probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios

Answer:2

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

Given

The given side lengths are not clear enough:

So, I will give a general explanation.

From the question, we understand WXYZ is dilated to produce W'X'Y'Z

This implies that the sides of WYZY is multiplied by the scale factor (k) to give W'X'Y'Z'

i.e.

[tex]ZW *k =Z'W'[/tex]

Divide both sides by k to get side length ZW

[tex]ZW = \frac{Z'W'}{k}[/tex]

Assume that:

[tex]k = 4[/tex] and

[tex]Z'W' = 28[/tex]

[tex]ZW = \frac{Z'W'}{k}[/tex]

[tex]ZW = \frac{28}{4}[/tex]

[tex]ZW = 7[/tex]

Apply these steps and you will get your answer

Answer:

Area of square= side*side

So we will have,

14*14

= 196cm²

Answer:

5/11

Step-by-step explanation:

35 to 77 simplified is 5/11

35 ÷ 7

---------

77 ÷ 7

Therefore, 35/77 simplified to lowest terms is 5/11.

Hope that helps

And if wrong sorry

Answer:

just add them

Step-by-step explanation:

Answer:

According to the table in both equation u can see the similar variables x=1, y=3

Step-by-step explanation:

Please I don't have graph with me

Answer:

Volume = 126 cm^2

Step-by-step explanation:

You don't exactly know what the base looks like, but it doesn't matter. The volume of a Prism is Base * height.

Solution

V = Base (which is the Cross sectional Area) * Length

V = 21 cm^2 * 6 cm

V = 126 cm^2

Answer:

i did it .but not sure.thanks.

Answer:

3x + 472

Step-by-step explanation:

Answer:

3x + 472

Step-by-step explanation:

We have the expression 3x + 235 + 237 and are asked to find the answer.

We are not solving for x, neither are we doing anything complicated, we need to focus on like terms, which are certain numbers having different symbols, in which they can only be added with the numbers with the same symbols as them.

In this equation, we have two terms, variables and constant. We can only add the constants because once again, you cannot add two terms that don't have the same symbol.

Therefore :

3x + 235 + 237

235 + 237

472.

The answer is 3x + 472

Answer:

n + 0.5 = p

Step-by-step explanation:

I'm not sure how you format it so the AI would understand.

Answer and Step-by-step explanation:

With the distributive property, the 8 will distribute itself to the a and the 4, resulting in 8a + 32.

#teamtrees #PAW (Plant And Water)

The question is incomplete. Here is the complete question.

To set up a game of billiards, the first player moves the balls contained within a triangular rack as shown. What happens to the distance between each billiard during this rigid transformation?

A. The distance remains constant throughout the transformation.

B. The distance decreases at the start and increases after all motion stops.

C. The distance stays the same at the start but decreasesexactly when motion ends.

D. The distance increases at the start and then decreases as the rack gets further from the player.

Answer: A. The distance remains constant throughout the transformation.

Step-by-step explanation: In a rigid motion, all moving points in the plane are moving in way such tha:

1)  relative distance between them stays the same and

2) relative position of the points stays the same

There are four types of rigid motions: translation, rotation, reflexion and glide reflection.

Translation: every point or object is moved by the same amount and in the same direction;

Rotation: the object rotates by the same amount around a fixed point;

Reflexion: the object exchange points from one side of a line with points on the other side of the line at the same distance from the line;

Glide Reflection: is a mirror reflection followed by a translation parallel to the mirror.

In the game of billiards, because all the balls are inside the triangular rack, the distance, and also the position, between them stays the same, limited by the rack. Since they are moving by the same amount in the same direction, the rigid transformation is a translation.

Therefore, the distance of the balls in the triangular rack remains constant throughout the transformation.

Answer:

im pretty sure its y=1/3x

Step-by-step explanation:

rearrange for y to be subject

its perpendicular so then the gradient will be the negative reciprocal (-1 / -3= 1/3) so thats your new gradient

then when you substitute the (3,-1) into that equation get -1=1 + c so then c is 0  and your whole equation is y=1/3x

Answer:

x=5.6  y=4.8

Step-by-step explanation:

Answer:

I need to know how much each bag costs. And how many pounds they are. If you can add that I can give you and answer.

Step-by-step explanation: