PLEASE HELP ME THIS IS IMPORTANT!! Ronnie, Bobby, and mike are singers from the group New Edition. They
are raising money for studio time. Ronnie raised $30 more than Mike, and
Bobby raised $12 less than Ronnie. They collected $432 in total. How
much did Ronnie collect? And how much did mike collect? Also how much did mike collect?

Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean of a population is 74 and the standard deviation is 15.

This means that [tex]\mu = 74, \sigma = 15[/tex]

Question a:

Sample of 36 means that [tex]n = 36, s = \frac{15}{\sqrt{36}} = 2.5[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 78. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{78 - 74}{2.5}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a pvalue of 0.9452

1 - 0.9452 = 0.0548

0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

Question b:

Sample of 150 means that [tex]n = 150, s = \frac{15}{\sqrt{150}} = 1.2247[/tex]

This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So

X = 77

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

[tex]Z = \frac{77 - 74}{1.2274}[/tex]

[tex]Z = 2.45[/tex]

[tex]Z = 2.45[/tex] has a pvalue of 0.9929

X = 71

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

[tex]Z = \frac{71 - 74}{1.2274}[/tex]

[tex]Z = -2.45[/tex]

[tex]Z = -2.45[/tex] has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c. A random sample of size 219 yielding a sample mean of less than 74.2

Sample size of 219 means that [tex]n = 219, s = \frac{15}{\sqrt{219}} = 1.0136[/tex]

This probability is the pvalue of Z when X = 74.2. So

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

[tex]Z = \frac{74.2 - 74}{1.0136}[/tex]

[tex]Z = 0.2[/tex]

[tex]Z = 0.2[/tex] has a pvalue of 0.5793

0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

Answer:

irrational number

Step-by-step explanation:

It is a non-recurring continuous decimal number

Answer:

Irrational and 3.14159

Step-by-step explanation:

t

Answer:

(1/6)2

Step-by-step explanation:

(1/6)2 has a value of 1/36

Answer: 4188790 cm^3

Step-by-step explanation:

To find Radius of sphere S we multiply 1/5 by 500.

1/5 x 500 = 100

We now have the radius of sphere S. Now we use the formula for a sphere and we get our answer.

4/3 \pi 100^2 = 4188790.205

Answer:

Polynomials are closed under addition and subtraction, which is fancy mathspeak that means that whenever we add or subtract two polynomials, we always get another polynomial. In that way, they behave a lot like the numbers you're probably already familiar with. Adding and subtracting:

And it works the same with polynomials!

Answer:

17

Step-by-step explanation:

divide by 5 both side and q will be:

q-2=15 then take 2 to the other side which will be positive . therefore

q=17

Answer:

Step-by-step explanation:

ΔABD ≅ ΔAEC because:

We have two sides and the included angle congruent - SAS

Corresponding parts of congruent figures are congruent:

Now, ∠CED is exterior angle and exterior angle is same as sum of non-adjacent interior angles:

Answer:

#3

Step-by-step explanation:

Answer:

EG and QM

Step-by-step explanation:

SAS or side angle side

so to start evaluate what u have already

EF =QN means that the two sides are congruent

then <MQN = <GEF

the angle Q is = to angle E

so fid the next two sides that fit the pattern or EG and QM

Answer:

16. y = 7x

17. y = x + 6

Answer:

Step-by-step explanation:

The x value comes first. The y value second. (alphabetical order).

A (-1,4)

B (2,3)

C (3,0)

The little lines through the 4 sides mean all the sides are the same length.

The area is side x side = 8 x 8 = 64 square cm.

Perimeter is the sum of the 4 sides = 8 + 8 + 8 +8 = 32 cm.

Answer:

Perimeter

P =a+a+a+a =4a

P = 4*8

P=32cm

Area

A = a*a = [tex]a^{2}[/tex]

A = [tex]8^{2}[/tex]

A = 64[tex]cm^{2}[/tex]

Answer:

sin2θ = [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

Since, sin2θ = 2sinθcosθ

From the triangle given in the picture,

Opposite side of angle θ = 2 units

Adjacent side of angle θ = 3 units

Hypotenuse = [tex]\sqrt{2^2+3^2}[/tex] = [tex]\sqrt{13}[/tex] [By Pythagoras theorem]

sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

       = [tex]\frac{2}{\sqrt{13}}[/tex]

cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

        = [tex]\frac{3}{\sqrt{13} }[/tex]

sin2θ = [tex]2\times (\frac{2}{\sqrt{13}})(\frac{3}{\sqrt{13}})[/tex]

         = [tex]\frac{12}{13}[/tex]

Answer:

We have 8 boys and 12 girls, and we have 5 boys that have a speaking part, and 7 of the 12 girls do not have a speaking part, so 5 girls have a speaking part, which makes 10 speaking parts out of 20 so we have [tex]\frac{10}{20} = \frac{1}{2}[/tex].

Hope this helps!

Answer:

Step-by-step explanation:

This math problem is only made difficult b/c they want you to figure out home many total kids have a speaking part in the play

5 boys do , but they give the mount of girls in a tricky way solve that part.  then mulitipy by 5 to make the totals from 100

20 total  kids

8 are boys

20-8 = 12

12 are girls

7 of those 12 do NOT speak in the play

12 - 7 = 5

5 girls speak in the play

5 boys + 5 girls = 10 kids speak in the play

you can probably figure out from   here...  1/2 of the kids speak .. that are in the play

so it's 50% as likely .. to pick someone that has a speaking part in the play as not

Answer: 120 kids were surveyed

              And 20 kids chose stuffed animal

Step-by-step explanation: hope this help

Answer:

120 were surveyed and about 16%(16.6666%) chose stuffed animal

Step-by-step explanation:

Answer:

-$9.6

Step-by-step explanation:

X : ___ 1000 ____600 ____300 ___200

P(x): __ 1/1000 _ 2/1000 _ 2/1000 _ 5/1000

Expected winning per ticket :

Σ(X * p(X)) = [(1000 * 1/1000) + (600 * 2/1000) + (300 * 2/1000) + (200 * 5/1000) - price per ticket

= 1 + 1.2 + 0.6 + 1 - 7

= 3.8 - 7

= - $3.2

Expextwd winning if 3 tickets Is purchased :

3 * - 3.2= - $9.6

Answer:

The answer is 20

Step-by-step explanation:

In ratio what you do one side you do on the other side 5:4=25:20

5×5=25

4×5=20

Answer:

subtract 2 on both sides

The arrays found here are as follows; red: 1 blue 2 yellow 7. green. 16

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

We are given that Max has 2 red tiles, 3 blue tiles, 4 yellow

tiles, and 8 green tiles.

We can see that 4 and 9 could be 1 array. 2 and 18 can be another array. 3 and 12 could be another one. 6 and 6 could be another array. Lastly, 1 and 36 could be an array.

There should be a total of 5 arrays. If we include the 1 and 36 array, then it's 5, I'd you don't include it, then it's 4 arrays.

Hence, there are  red: 1 blue 2 yellow 7. green. 16

Learn more about combinations and permutations here:

https://brainly.com/question/16107928

#SPJ2

Answer:

400

Step-by-step explanation:

8*20/2+16*20=400.

Answer:

all of the above

Step-by-step explanation:

Step-by-step explanation:

i think that it will be (D) all the above

Answer:

x=6,24

Step-by-step explanation:

Use the Theorem of Pythagoras.

H^2= S^2+ S^2

8^2= 5^2 + S^2

64-25 = S^2

39 = S^2

6,24= S

S is x therefore x = 6,24

Answer:

the answer is 14 for each person

Step-by-step explanation:

there are 5 apples. 10 mangos and 13 oranges so if yo add them all up its 28 and half of 28 is 14 so theres your answer.

im so so sorry i it does happen to be wrong.

Answer: 116.67

Step-by-step explanation:

30/100 * x = 35

3/10 * x = 35

3x = 350

x = 116.67

Answer:

a. Linear pair theorem

b. x = 40

Step-by-step explanation:

a. You can use linear pair theorem. That is, two angles on a straight line are supplementary. They sum up to 180°

b. Thus:

x + (4x - 20) = 180°

x + 4x - 20 = 180

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 200/5

x = 40