how can equations help you model the relationship between two quantities

Answer:

0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution, the central limit theorem, and subtraction of normal variables:

Normal probability distribution

When the distribution is normal, we use 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

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.

Subtraction of normal variables:

When we subtract two normal variables, the mean is the subtraction of the mean of each variable, while the standard deviation is the square root of the sum of each variance.

Method A:

One student: N(75,30), so [tex]\mu = 75, \sigma = 30[/tex]

Samples of 100 students: [tex]n = 100, s = \frac{30}{\sqrt{100}} = 0.3[/tex]

Method B:

One student: N(74,40), so [tex]\mu = 74, \sigma = 40[/tex]

Samples of 100 students: [tex]n = 100, s = \frac{40}{\sqrt{100}} = 0.4[/tex]

What is the probability that the mean score for the B group will be at least five points higher than the mean score for the A group?

This is the probability that B - A >= 5. So

[tex]\mu_{B-A} = \mu_B - \mu_A = 74 - 75 = -1[/tex]

[tex]s_{B-A} = \sqrt{s_A^{2}+S_B^{2}} = \sqrt{(0.3)^2+(0.4)^2} = 0.5[/tex]

We have to find 1 subtracted by the pvalue of Z when X = 5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{5 - (-1)}{0.5}[/tex]

[tex]Z = 12[/tex]

[tex]Z = 12[/tex] has a pvalue of 1

1 - 1 = 0, so

0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group

Answer:

30

60

90

120

180

210

240

hope it helped have a good day mate

Answer:

Step-by-step explanation:

-6=3/2z

-12z=3

z=-4

Answer: 30 drinks

Step-by-step explanation:

From the question, we are informed that Colin made 4 drinks in 12 minutes during his training. This shows that a drink is made in (12/4) = 3 minutes.

Since he will work for 90 minutes, the number of drinks that he will make will be:

= 90/3

= 30 drinks

Answer:

[tex] \frac{1}{2} {x}^{2} + 10 + \frac{1}{4} x[/tex]

Step-by-step explanation:

[tex] \frac{1}{2} {x}^{2} + 2 + \frac{1}{4} x + 8[/tex]

[tex]2 + 8 = 10[/tex]

[tex] \frac{1}{2} {x}^{2} + 10 + \frac{1}{4} x[/tex]

Answer:

$247.94

Step-by-step explanation:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answer:

m=2

Step-by-step explanation:

5-1/3-1

4/3-1

4/2

2

I hope this helps

Answer:

x = -4

Step-by-step explanation:

8x - 3 = 5(2x + 1)

8x - 3 = 10x + 5

8x - 10x = 5 + 3

-2x = 8

x = 8/-2

x = -4

Answer:

$27 is left over.

Step-by-step explanation:

If you divide 36 by 4, you can find out what 1/4 of 36 is. 36/4 = 9

This $9 is how much he gave away to his brother. In order to find out how much he has leftover for himself, subtract the $9 from the $36.

36-9 = 27.

Therefore, Aaron has $27 leftover for himself.

Answer:

c.

Step-by-step explanation:

4/3 pi r²

4/3 × 3.142 or 22/7 × 3.5²

Answer:

2400

Step-by-step explanation:

150 times 4 = 600 times 4 = 2400

Answer:

30 minutes

Step-by-step explanation:

150 sec. x 4 = 600 sec.

600 sec. per mile

600 sec. x 3 = 1800 sec.

1800 sec. / 60 sec. = 30 min.

Answer:

5/11

Step-by-step explanation:

&add up the decimals I think

Answer:

$6.39

Step-by-step explanation:

b= batch

1b=$0.71

9b=?

9b=9($0.71)

9b=$6.39

Answer:

D.

Step-by-step explanation:

This is the only one that sounds correct

Answer:

i  cant read it oh i zoomed in B

Step-by-step explanation:

Answer:

im not sure i understand the question

Step-by-step explanation:

80.50 plus........plus what?

i am confusion

Answer:gd

Step-by-step explanation:

Vygfy

Answer:

y = (7w - 3m) / 3a

Step-by-step explanation:

w = 3/7ay + 3/7m

multiply each side by 7 to eliminate fractions

7w = 3ay + 3m

3ay = 7w - 3m

y = (7w - 3m) / 3a

Answer:

x = 4

Step-by-step explanation:

Given:

(√x + 2)(√x - 2) = 0

Required:

Find x

SOLUTION:

√x(√x - 2) + 2(√x - 2) = 0 (distributive property)

x - 2√x + 2√x - 4 = 0

x - 4 = 0

x - 4 + 4 = 0 + 4

x = 4

Answer:

c

Step-by-step explanation:

if the sides are in proportion set the proportions

6.21/ 5.4 = x/2.6; cross multiply

5.4*x = 6.21 *2.6; divide by 5.4

x= 2.99

Answer:

y=3/4x-2

Step-by-step explanation:

Answer:

y=3/4x-2

Step-by-step explanation:

y-intercept: -2

slope: 3/4

Answer:

it is 100000000 i think i am not sure either

The value of 4ˣ for x = -2  and x = 3 is 0.0625 and 64 respectively.

The formula for an exponential function is f (x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given function 4ˣ

when x = -2

4ˣ = 4⁻²

using a⁻ⁿ = 1/aⁿ

4⁻² = 1/4² = 1/16

4⁻² = 0.0625

and x = 3

4ˣ = 4³

4³ = 4 x 4 x 4 = 64

Hence the values are 0.0625 and 64 for x = -2 and 3.

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Answer:

384 square meters.

Step-by-step explanation:

Given that a cube has a lateral surface area of 64 square meters, to find the total surface area of the cube, the following calculation must be performed, knowing that the formula to calculate the area of a cube is to multiply by 6 (the number of sides of the cube) the area of one of its sides:

A x 6 = X

64 x 6 = X

384 = X

Thus, the area of the cube is 384 square meters.

Answer:

Definitely 3/4!

Step-by-step explanation:

Option A = 7.5

Option B = 66.6%

Option C = 75% (because 25 times 4 is equal to 100%, so 25 times 3 would be 75)

Option D = 6/10 or 60%

The values that are equivalent to 75% are A) 75/100 (0.75) and C) 3/4.

To determine whether these values are equivalent, let's evaluate each expression and compare the results.

A) 75% can be written as a decimal by dividing 75 by 100:

75% = 75/100 = 0.75

B) 2/3 is already in fractional form and cannot be simplified further.

C) 3/4 is also in fractional form and cannot be simplified further.

D) 3/5 is in fractional form and cannot be simplified further.

Now let's compare the decimal equivalents:

0.75 = 75/100

2/3 = 0.666...

3/4 = 0.75

3/5 = 0.6

Comparing the decimal values, we can see that A) 0.75 and C) 0.75 are equivalent, as they both represent 75% in decimal form.

However, B) 2/3 and D) 3/5 do not equal 0.75 and are therefore not equivalent to 75%.

Hence, the values that are equivalent to 75% are A) 75/100 (0.75) and C) 3/4.

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Answer:

N

Step-by-step explanation:

Yeah cos it's like n ya know ueuehd

Answer:

X=3

Step-by-step explanation:

3 is in the middle of the figure.

I hope this helps!

Answer:

ehjrbbvhbvebvuhbdhvhdhsduhsdbrhw

Step-by-step explanation: