Slope-Intercept Form of 3x – 4y – 16 = 0

Answer:

a) Due to the higher z-score, Ronald performed better relative to his peers on the test.

b) Ronald needed a grade of at least 732.5, and Rubin of at least 33.58.

c) 95% of the population fall between graded of 4.868 and 31.132 on the ACT.

95% of the population fall between graded of 304 and 696 on the SAT.

Step-by-step explanation:

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.

In this question:

(a) Relative to their peers who also took the tests, who performed better on his test? Explain.

We have to find whoever has the higher z-score.

Ronald:

Ronald scores 700 on the math section of the SAT exam. The distribution of SAT scores is approximately normal with a mean of 500 and a standard deviation of 100. So the z-score is found when [tex]X = 700, \mu = 500, \sigma = 100[/tex]. So

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

[tex]Z = \frac{700 - 500}{100}[/tex]

[tex]Z = 2[/tex]

Rubin:

Rubin takes the ACT math exam and scores 31 on the math portion. ACT scores are approximately normally distributed with a mean of 18 and a standard deviation of 6.7. So the z-score is found when [tex]X = 31, \mu = 18, \sigma = 6.7[/tex]. So

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

[tex]Z = \frac{31 - 18}{6.7}[/tex]

[tex]Z = 1.94[/tex]

Due to the higher z-score, Ronald performed better relative to his peers on the test.

(b) A certain school will only consider those students who score in the top 1% in the math section. What grades would Ronald and Rubin have to receive on their respective tests to be considered for admission?

They have to be in the 100 - 1 = 99th percentile, that is, they need a z-score with a pvalue of at least 0.99. So we need to find for them X when Z = 2.325.

Ronald:

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

[tex]2.325 = \frac{X - 500}{100}[/tex]

[tex]X - 500 = 232.5[/tex]

[tex]X = 732.5[/tex]

Rubin:

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

[tex]2.325 = \frac{X - 18}{6.7}[/tex]

[tex]X - 18 = 15.58[/tex]

[tex]X = 33.58[/tex]

Ronald needed a grade of at least 732.5, and Rubin of at least 33.58.

(c) Between what two grades does 95% of the population fall for the ACT and the SAT exams?

They fall between the 100 - (95/2) = 2.5th percentile and the 100 + (95/2) = 97.5th percentile, that is, they fall between X when Z = -1.96 and X when Z = 1.96.

ACT:

Lower bound:

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

[tex]-1.96 = \frac{X - 18}{6.7}[/tex]

[tex]X - 18 = -1.96*6.7[/tex]

[tex]X = 4.868[/tex]

Upper bound:

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

[tex]1.96 = \frac{X - 18}{6.7}[/tex]

[tex]X - 18 = 1.96*6.7[/tex]

[tex]X = 31.132[/tex]

95% of the population fall between graded of 4.868 and 31.132 on the ACT.

SAT:

Lower bound:

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

[tex]-1.96 = \frac{X - 500}{100}[/tex]

[tex]X - 500 = -196[/tex]

[tex]X = 304[/tex]

Upper bound:

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

[tex]1.96 = \frac{X - 500}{100}[/tex]

[tex]X - 500 = 196[/tex]

[tex]X = 696[/tex]

95% of the population fall between graded of 304 and 696 on the SAT.

Answer:

It should be C.

Step-by-step explanation:

Answer:

it is the first bubble the one you have already selected

Answer:

In order from top to bottom: 5^2, 125, 50

Step-by-step explanation:

1. (3+2) × 5 = 5 × 5 = 5^2

2. 5^3 = 5 × 5 × 5 = 125

3. 10^2 / 2 = 100/2 = 50

Answer:

10^2/2=50

5^3=125

(3+2)*5=5^2

Step-by-step explanation:

Answer:

y=1/7x+11/7

Step-by-step explanation:

I used mathaway

Answer:

[tex]f^{-1} (x)=\frac{x-3}{2}[/tex]

Step-by-step explanation:

y = f(x)

y = 2x+3

You need to switch the places of x and y, into this:

x = 2y + 3

Then solve for y:

2y = x-3

[tex]y=\frac{x-3}{2}[/tex]

[tex]f^{-1} (x)=\frac{x-3}{2}[/tex]

Answer:

[i] Area of Juan's garden:

Soln,

length(l)=16

width(w)=12

area(a)=?

Now,

a=l×w

=16×12

=192

[ii] Area of Matthew's garden:

Soln,

length(l)=18

width(w)=21

area(a)=?

Now,

a=l×w

=18×21

=378

So,the area ofJuan's garden=192

And

the area of Matthew's garden=378

Answer:

Look at the graph below, hope this helped.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The two unknown values of the triangle have to be the same.

Subtract 28 from 180 and you get 152

So each angle will be 76.

So now, 76 = -8 + 7x

Simplify and 84 = 7x

Now, x is equal to 12

Hope this helped! Please mark me as brainliest if you can!

Answer:

f(5) is equal to 5.

Step-by-step explanation:

You can see this by looking at 5 on the horizontal axis, and seeing where the graph crosses vertical line for that value.  If you look closely, you'll see that the x value of 5 has a y value of 5 as well.

Answer: It is C

Step-by-step explanation:

Good luck on your test or homework

Answer:

a number 12

Step-by-step explanation:

duh bro

Answer:

Interior Angle: 165°

Exterior Angle: 15°

Step-by-step explanation:

So first you have to find the sum of all interior angles of a polygon with 24 sides. This can be found using the formula:

sum = ( n - 2 ) * 180°     where 'n' is the number of sides.

When 'n = 24' then the sum is:

sum = ( 24 - 2 ) * 180°

Simplify and solve.

sum = 22 * 180°

sum = 3960°

Since there are 24 sides to the polygon, there are 24 interior angles. Assuming that this polygon is equilateral, you can surmise that:

Interior Angle = sum° / n   where n is the number of sides,

3960° / 24 = 165° = Interior Angle

Using that information, and combine it with the [Supplementary Angles Theorem] the exterior angle can be found by:

165° + x = 180°

Solve for x.

was divided into equal parts to make 7 loaves of bread. How can you mount of flour used for each loaf? select all that apply

Step-by-step explanation:

Answer:

B, C, F

Step-by-step explanation:

C = 3/8 divided 7 times 5.  3/8 lbs of flour in each was divided into equal parts to make 7 loaves. 3/8 divide by 7. Since there are 5 bags, times 5.

B = 3/8 times (for the five bags) times 5 divided by 7 samething from C.

F = You know the pattern now. Hint: B is the answer...

Answer:The total cost, C, is the sum of the cost to produce the centerpieces and the fixed cost. The equation for C is C = 8n + 500.

The total revenue, R, of Julio's floral business is the product of the cost per centerpiece and the number of centerpieces sold. The equation for R is R = 19.50n.

Step-by-step explanation:

Answer:

77.5

Step-by-step explanation:

Answer:

b = 39

Step-by-step explanation:

The two sides are equivalent so we can use this information to form an equation.

2b - 39 = b

-39 = -b

39 = b

Answer:

x=5

Step-by-step explanation:

hope this is correct have a wonderful day! <3

Answer:

x=5

Step-by-step explanation:

10+1.5x=3.5x

Subtract 3.5x from both sides.

10+1.5x−3.5x=0

Combine 1.5x and −3.5x to get −2x.

10−2x=0

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

−2x=−10

Divide both sides by −2.

x=  −2 /−10

​Divide −10 by −2 to get 5.

x=5

Answer:

You aren't posting pictures

Step-by-step explanation:

Answer:

540 pages

Step-by-step explanation:

100 pages = 50 mins

??? pages = 270 mins (converted 4hrs 30 mins to minutes)

Now you could cross multiply to find what the number of pages are:

100 pages x 270  mins = 50 mins x ??? pages

27000 = 50 mins x ??? pages

27000/50 = ??? pages

540 = ??? pages

So there are 540 pages in his favourite book.

Answer:

The fallacy can specifically be noted in this argument:

"You fell asleep and missed two important customer calls."

Step-by-step explanation:

In the previous argument we can see that the worker is being attacked directly, it is not being indicated with reasonable evidence when it was that he actually fell asleep, in what month, in what time, and how many times.

The area of figure will be;

⇒ 105.56 km²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The figure is shown.

Now,

The area of figure is find as;

Total area = (12 × 7) + (π × 4² / 4) + (3 × 3)

               = 84 + 3.14 × 4 + 9

               = 93 + 12.56

               = 105.56 km²

Thus, The area of figure will be;

⇒ 105.56 km²

Learn more about the area visit:

https://brainly.com/question/11564229

#SPJ1

Answer: There can be multiple combos.

Replace x with 10.

The exponent is now 0.1(10) = 1

Now you have 5000(1.181)^1

1.181^1 = 1.181

So now 5000 x 1.181 = 5,905

The answer is 5,905

Answer:

1.846=x

Step-by-step explanation:

SO to find X

We know perimeter is 16

So we have all the sides so add them all up

3x+3+8x-5+2(x-3)=16

Now distribute the possible things first

3x+3+8x-5+2x-6=16

Now combine like terms

13x-8=16

add 8 on both sides

13x=24

Since the problem asked for rounded to 3 decimal places

1.846

Answer:

yes the sum of any triangle is 180°

Step-by-step explanation:

I hope it's helps you

Answer:

y=-1 1/3+18

Step-by-step explanation:

isolate the y and divide both by 9

Answer:

[tex]\displaystyle no[/tex]

Step-by-step explanation:

SR is slightly longer than TS, so with that being stated, we cannot use this theorem for this triangle.

I am joyous to assist you at any time.