We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of Pomona College looked at the exam scores of all 346 students who took his statistics class over a 10-year period. The least-squares line for predicting final-exam score from mid-term exam score was γ=46.6 + 0.41x.
Octavio scores 10 points above the clas mean on the midterm. How many points above the class mean do you predict that he will score on the final. (Hint: what is the predicted final-exam score for the class mean midterm score of x-bar?) This is an example of regression to the mean, the phenomenon that gave "regression" its name: students who do well on the midterm will on average do less well on the final, but still above the class mean.)

Answer:

lol no34532534

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

We have to prove that:

[tex]\rm\longmapsto \dfrac{ \sin(x) - 2 \sin^{3} (x) }{2 \cos^{3} (x) - \cos(x) } = \tan(x) [/tex]

Taking LHS, we get:

[tex]\rm = \dfrac{ \sin(x) - 2 \sin^{3} (x) }{2 \cos^{3} (x) - \cos(x) }[/tex]

We can take sin(x) as common from numerator part. We get:

[tex]\rm = \dfrac{ \sin(x) \{1- 2 \sin^{2} (x) \}}{2 \cos^{3} (x) - \cos(x) }[/tex]

Similarly, we can take cos(x) as common from first two terms. We get:

[tex]\rm = \dfrac{ \sin(x) \{1- 2 \sin^{2} (x) \}}{ \cos(x) \{ 2 \cos^{2} (x) -1\}}[/tex]

[tex]\rm = \dfrac{ \sin(x) }{ \cos(x) } \cdot \dfrac{\{1- 2 \sin^{2} (x) \}}{\{ 2 \cos^{2} (x) -1\}}[/tex]

As we know that:

[tex]\rm\longmapsto \dfrac{ \sin(x) }{ \cos(x) } = \tan(x) [/tex]

We get:

[tex]\rm = \tan(x) \cdot \dfrac{\{1- 2 \sin^{2} (x) \}}{\{ 2 \cos^{2} (x) -1\}}[/tex]

Now, we will expand the terms in fraction:

[tex]\rm = \tan(x) \cdot \dfrac{\{1- \sin^{2} (x) - { \sin }^{2}(x) \}}{\{\cos^{2} (x) + \cos^{x}(x) -1\}}[/tex]

As we know that:

[tex]\rm \longmapsto \sin^{2}(x)+cos^{2}(x)=1[/tex]

[tex]\rm \longmapsto\cos^{2}(x)=1-sin^{2}(x)[/tex]

[tex]\rm \longmapsto\cos^{2}(x) - 1=-sin^{2}(x)[/tex]

Now substitute the values in the expression, we get:

[tex]\rm = \tan(x)\cdot \dfrac{ \cos^{2} (x)-{ \sin }^{2}(x)}{\cos^{2} (x) - \sin^{2} (x) }[/tex]

[tex]\rm = \tan(x)\cdot1[/tex]

[tex]\rm = \tan(x)[/tex]

Here, we notice that LHS = RHS

Proved.

Answer:

10 feet tall

Step-by-step explanation:

(Triangle problem was answered in a previous question)

So like before, we have a ratio: 1.5inches:2.5feet

We have a starting value as well: 6 inches

All we have to do is convert from inches to feet (not with a real life equation, but with the given equation)

To begin, dvide 6 by 1.5

6inches/1.5inches = 4 (The units canceled out during division)

Not multiply by the ratio:

4 * 2.5feet = 10 feet (It takes the units in feet)

Therefore, the tree is actually 10 feet tall.

Answer:

1/12 pounds of strawbebbies left.

Step-by-step explanation:

Answer:

I think it's b.

Step-by-step explanation:

b. ,. ....

Answer:

aaaaaaaa nad its by

Step-by-step explanation:

============================================================

Explanation:

Let's say that this tub is 72 gallons. I picked this number since 12*6 = 72. You can pick any number you want, but I picked this number so we end up with whole number results as shown below.

Tap X can fill the 72 gallon tub in 12 minutes. Its rate is 72/12 = 6 gallons per minute. Tap Y has a rate of 12 gallons per minute because 72/6 = 12.

Add the two unit rates: 6+12 = 18

If the two taps are opened at the same time, then they will work at a rate of 18 gallons per minute.

Let x be the number of minutes. The expression 18x represents how much of the tub is full after x minutes. Set this equal to the 72 we started with earlier and solve for x.

18x = 72

x = 72/18

x = 4

It will take 4 minutes if both taps are running at the same time.

Answer:

Ой ну не знаю очень сложный вопрос

Answer:

is this what your looking for?

Answer:

it's C. 3/40

Step-by-step explanation:

ghjfrukkbf

Answer:

Step-by-step explanation:

The cubes have sides of 2 cm, 3 cm and 4 cm respectively.

Their face area of the cubes is 4 cm², 9 cm² and 16 cm² respectively.

Total surface area of each cube is:

Total of three cubes:

When you glue the cubes together you lose an area equal to double face area of the smaller cube from the total surface area.

Possible decrease, provided full faces area covered:

The least possible surface area is:

3Cubes :

Soo :

Volume - 1 = 6 × 2² = 6 × 4 = 24cm²

Volume - 2 = 6 × 3² = 6 × 9 = 54cm²

Volume - 3 = 6 × 4² = 6 × 16 = 96cm²

[tex] \: [/tex]

surface area = 174 - 2(3² + 2²)

surface area = 174 - 2(9 + 4)

surface area = 174 - 2(13)

surface area = 174 - 26

serface area = 148cm²

[tex] \: [/tex]

-HayabusaBrainly

Answer:

what the hell

Step-by-step explanation:

Step-by-step explanation:

oh, come on, just multiplication.

7.5×10⁴ years is 7.5×10000 =75000 years.

0.005 inches per year for 75000 years means

0.005 × 75000 = 5 × 75 = 375 inches.

Answer:

[tex]\huge\boxed{\sf \frac{7}{40} }[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{5} \times \frac{7}{8} \\\\= \frac{1 \times 7}{5 \times 8} \\\\= \frac{7}{40} \\\\Hence, this \ is \ the \ simplest \ form.\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

7/40

Step-by-step explanation:

7 cant go into 40 so it just stays as 7/40

Answer:

The greatest common factor is surprisingly 6.

All three numbers can be divided by 6 and it is the highest value that can be taken from all three numbers.

Step-by-step explanation:

Hope this helps.

<3

Answer:

the GCF of those numbers is 6.

Step-by-step explanation:

One way to solve this is to list the factors of them, then find the greatest one that they share.

42: 1, 2, 3, 6, 7, 14, 21, 42

12: 1, 2, 3, 4, 6, 12

6: 1, 2, 3, 6

If we look at them, notice that six is in all of them. All of them have factors of six. Can we go any higher than that? No because six is the greatest factor of six, so we can't go any higher and still have all of them share a GCF. So your answer is 6.

Answer:1 mile traveled at the rate of 200 miles in 60 minutes. ... Therefore, it would take 18 seconds to travel 1 mile going at a speed of 200 miles per hour!

Step-by-step explanation:

Answer:

[tex]\sf\bold \longmapsto \: Tan \: P = \frac{15}{8} [/tex]

Step-by-step explanation:

We know,The formula of Tan ∅ is–

[tex]\sf\longmapsto \: \tan = \frac{opposite}{adjacent} [/tex]

Therefore,Tan P will be Option D

[tex]\sf\longmapsto \: \frac{15}{8} [/tex]

Answer:

43%

Step-by-step explanation:

mark me as brainliest please

Answer:

$395.55

Step-by-step explanation:

45%+10%=55%

100%-55%=45%

Since 45% is 45/100 in fractions, use that x 879 for the final price.

45/100x879=395.55

Hope this helps! Thanks.

Answer:

435.11

Step-by-step explanation:

First find the sale price of the computer. Then take the additional 10% off of the sale price.

[tex]\huge\fbox\orange{S} \huge\fbox\red{C}\huge\fbox\blue{R}\huge\fbox\green{O}\huge\fbox\gray{L}\huge\fbox\purple{L>}[/tex]

[tex]\huge\underline\mathtt\colorbox{cyan}{2.49 cubed=15.438249}[/tex]

[tex]\huge\underline\mathtt\colorbox{red}{2.98 cubed=26.463592}[/tex]

Answer:

11

Step-by-step explanation:

4-1=3/11-7=4

The parabola crosses the x-axis at x = 1 and x = -3.

x - 1 = 0

x = 1

x + 3 = 0

x = -3

b = 3

Hope this helps!! :)

Answer:

Step-by-step explanation:

The ratio of height to shadow length will be proportional.

2.6 / 1.26 = h / 37.25

h = 37.25(2.6)/1.26 = 76.865079...

h = 76.9 m

Answer:

26200

Step-by-step explanation:

exactly 262200

Step-by-step explanation:

Let's first find the slope

(-5-2)/(5--1) = -7/6

the equation should be

[tex]y = \frac{ - 7}{6} x + c[/tex]

To find c, we replace X with -1 and Y with 2

c= 5/6

So the equation is

[tex]y = \frac{ - 7}{6} x + \frac{5}{6} [/tex]

And if you multiply everything by 6 you get

6y = -7x +5