MATHEMATICS
COLLEGE

Answer: 4 gallons=32 pints

:) :) :)

:) :) :)

MIDDLE SCHOOL

7) Convert this fraction to a percentage: 95/200 8) Convert this percentage to a decimal: 99.99%

Answer:

The fraction would be 47.5%

The percentage would be 0.9999 or 0.99

Step-by-step explanation:

Answer:

0.99%

Step-by-step explanation:

MIDDLE SCHOOL

There are 25 students in a class at the beginning of the school year and the average number of siblings for each student is three. A new student with eight siblings joins the class in November does the average number of siblings that each student has go up?

Answer: Yes. The new average is 3

Step-by-step explanation:

25 students at 3 siblings each = 75 siblings

26 students has 75 siblings + 8 siblings = 83 siblings

New average is 83 siblings ÷ 26 students = 3.19 siblings per students

MIDDLE SCHOOL

If sine theta equals one over three, what are the values of cos θ and tan θ? cosine theta equals plus or minus four over three, tangent theta equals plus or minus one over two

cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four

cosine theta equals plus or minus four over three, tangent theta equals negative one over two

cosine theta equals plus or minus two times square root of two over three, tangent theta equals negative square root of two over two

Answer:

cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four

Step-by-step explanation:

Given:

sinθ=1/3

θ=19.47 degrees

then

cosθ= cos(19.47)=0.942 = 2(√2/3)

tanθ=tan(19.47)=0.35= √2/4

Hence option two is correct:cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four!

Answer:

So second choice.

Step-by-step explanation:

I'm going to use a Pythagorean Identity, name the one that says:

.

We are given: .

Inserting this into our identity above gives us:

Time to solve this for the cosine value:

Subtract 1/9 on both sides:

Square root both sides:

9 is a perfect square but 8 is not.

8 does contain a factor that is a perfect square which is 4.

So time for a rewrite:

So without any other give information we can't know if cosine is positive or negative.

Now time for the tangent value.

You can find tangent value by using a quotient identity:

Multiply top and bottom by 3 get's rid of the 3's on the bottom of each mini-fraction:

Multiply top and bottom by sqrt(2) to get rid of the square root on bottom:

Simplifying:

HIGH SCHOOL

What is the solution to the following system of equations? y = -x2 - 5x - 4

y = -x2 + 9x - 18 (2 points)

(-1, -10)

(1, -10)

(-1, 10)

(1, 10)

The correct answer is option B. i.e. (1,-10) two equations are y = -x^2 - 5x - 4 and y = -x^2 + 9x - 18. Now, equating both the equations we get, -x^2 - 5x - 4 = -x^2 + 9x - 18 or 14 x= 14 or x = 1. Now, y = -1 -5 -4 = -10.

Answer:B

Step-by-step explanation: no cap