MATHEMATICS
HIGH SCHOOL

B. c < 32

C. c > 32

D. c > 12

Answer: We want to simplify the inequality 1/4c < 8.

The c variable is being multiplied by 1/4. If we multiply each side by 4, we can get rid of the 1/4.

1/4c < 8

1/4c * 4 < 8 * 4

c < 8 * 4

c < 32

So, B. c < 32 is the answer.

The c variable is being multiplied by 1/4. If we multiply each side by 4, we can get rid of the 1/4.

1/4c < 8

1/4c * 4 < 8 * 4

c < 8 * 4

c < 32

So, B. c < 32 is the answer.

MIDDLE SCHOOL

Find two consecutive positive integers such that the sum of their squares is 181

Find two consecutive positive integers such that the sum of their squares is 181

consecutive positive integers: x and x+1

(x)²+(x+1)²= 181

x² +( x² +2x +1) =181 (expanded (x+1)²)

2x²+2x+1=181 (simplified)

2x²+2x+1-181=181-181 (subtraction property)

2x²+2x-180=0

Factor to solve for x

2x²+2x-180=0

2(x+10)(x-9)=0

2≠0

x+10=0

x+10-10=0-10

x=-10 number must be a positive integer, cannot use -10

x-9=0

x-9+9=0+9

x=9 we can use this one, it is positive

x=9 and x+1=9+1=10

two consecutive positive integers such that the sum of their squares is 181 are:

9 and 10

9²+10²=181

81+100=181

181=181

consecutive positive integers: x and x+1

(x)²+(x+1)²= 181

x² +( x² +2x +1) =181 (expanded (x+1)²)

2x²+2x+1=181 (simplified)

2x²+2x+1-181=181-181 (subtraction property)

2x²+2x-180=0

Factor to solve for x

2x²+2x-180=0

2(x+10)(x-9)=0

2≠0

x+10=0

x+10-10=0-10

x=-10 number must be a positive integer, cannot use -10

x-9=0

x-9+9=0+9

x=9 we can use this one, it is positive

x=9 and x+1=9+1=10

two consecutive positive integers such that the sum of their squares is 181 are:

9 and 10

9²+10²=181

81+100=181

181=181

HIGH SCHOOL

What is the standard form of (4,4), perpendicular to y = -4/9x

Y=9/4x-5 is the standard form.

COLLEGE

In 2012, New York Yankees baseball players earned an average salary of $6,186,321, with a standard deviation of $7,938,987. Assuming that these data are normally distributed, what was the salary of a player in the 53rd percentile?

Answer:

The salary of a player in the 53rd percentile was $6,781,745.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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 problem, we have that:

Assuming that these data are normally distributed, what was the salary of a player in the 53rd percentile?

This is the value of X when Z has a pvalue of 0.53. So X when Z = 0.075.

So

The salary of a player in the 53rd percentile was $6,781,745.

MIDDLE SCHOOL

algebraically determine the values of h and k to correctly complete the identity stated below : 2 x cubed - 10x squared + 11x - 7 = (x-4)(2x squared)+ hx+3(+k)

Answer:

The values for expression is h = - 2 and k = 5

Step-by-step explanation:

Given algebraic expression can be written as :

2 x³ - 10 x² + 11 x - 7 = ( x - 4 ) × ( 2 x² + h x + 3 ) + k

Now opening the bracket

Or, 2 x³ - 10 x² + 11 x - 7 = x × ( 2 x² + h x + 3 ) - 4 × ( 2 x² + h x + 3 ) + k

Or, 2 x³ - 10 x² + 11 x - 7 = 2 x³ + h x² + 3 x - 2 x² - 4 h x - 12 +k

Or , 2 x³ - 10 x² + 11 x - 7 = 2 x³ + ( h - 2 ) x² + ( 3 - 4 h ) x - 12 + k

Now, equating the equation both sides

I.e - 10 = ( h - 2 )

Or , h - 2 = - 10

I.e , h = - 10 + 2

∴ h = - 2

Again , 11 = ( 3 - 4 h )

or, 11 = 3 - 4 h

or, 11 - 3 = - 4 h

or, 8 = - 4 h

∴ h =

I.e h = - 2

Again

- 7 = - 12 + k

Or, k = - 7 + 12

∴ k = 5

Hence The values for expression is h = - 2 and k = 5 . Answer

MIDDLE SCHOOL

Find the value of y when x=-5 and y=7x

It would be -35 because 7 times 5 is 35 but the 5 makes the answer negative

Answer:(-35)

Step-by-step explanation:

Find the value of y when x=(-5) and y=7x

=7x(-5)

since multiplacation is addition multiple times it cold also be

(-5)+(-5)+(-5)+(-5)+(-5)+(-5)+(-5)+(-5)

=(-35)

MIDDLE SCHOOL

If A=1/2h(x+y), what is y in terms of A, h, and x?

Answer:

see explanation

Step-by-step explanation:

Given

A = h(x + y)

Multiply both sides by 2 to eliminate the fraction

2A = h(x + y) ( divide both sides by h )

= x + y ( subtract x from both sides )

y = - x

MIDDLE SCHOOL

4 L 342 mL + 2L 214 mL =

Let's convert the data into ml.

4l 342ml= 4342 ml

2l 214 ml= 2214 ml

4342+2214= 6556 ml

convert it to L= 6556 ml = 6 L 556 ml

4l 342ml= 4342 ml

2l 214 ml= 2214 ml

4342+2214= 6556 ml

convert it to L= 6556 ml = 6 L 556 ml

Your answer will be 6 L 556 ML

MIDDLE SCHOOL

2. Quan plans to spend less than $80 for buying groceries. He plans to spend $68.25 on food and spend the rest on juice. Each juice carton costs $3. He is curious how many juice cartons he can purchase before he runs out of money. (a) Use x to represent the number of juice cartons Quan can purchase and write an inequality that can be used to solve for x.

(b) Solve the inequality. Use the solution to determine the number of juice cartons Quan can purchase.

Answer:

a)

b)3

Step-by-step explanation:

Let x be the number of juice cartons.

Cost of 1 carton = $3

Cost of x cartons = 3x

He plans to spend $68.25 on food .

His total cost = 3x+68.25

He also plans He plans to spend $68.25 on food .

So, Equation becomes:

So, he can purchase 3 juice cartons.

Hence an inequality that can be used to solve for x is

Y=3X+68.25

80=3X+68.25

Subtract 68.25 from both sides

11.75=3X

Divide

11.75/3=3.91

He can't buy a portion of a juice but he doesn't have enough to buy 4

So he can afford 3 juice cartons

P.S. I do k12 also if that is what you are doing.

80=3X+68.25

Subtract 68.25 from both sides

11.75=3X

Divide

11.75/3=3.91

He can't buy a portion of a juice but he doesn't have enough to buy 4

So he can afford 3 juice cartons

P.S. I do k12 also if that is what you are doing.

HIGH SCHOOL

Write numerals for each of the italicized number word names found in these examples. Earth’s moon is (a) two million, one hundred fifty-five thousand, one hundred twenty miles across. The closest distance between Earth and the moon is (b) two hundred twenty-five million, sixty thousand miles. The farthest distance between them is (c) two hundred fifty-one million, seven hundred twenty thousand miles.

It is not really difficult writing numerals if you have only their word names - just make sure you know how many numbers a million consists of, a thousand, etc.

A. two million, one hundred fifty-five thousand, one hundred twenty =

2,155,120

B. two hundred twenty-five million, sixty thousand =

225,060,000

C. two hundred fifty-one million, seven hundred twenty thousand =

251,720,000

A. two million, one hundred fifty-five thousand, one hundred twenty =

2,155,120

B. two hundred twenty-five million, sixty thousand =

225,060,000

C. two hundred fifty-one million, seven hundred twenty thousand =

251,720,000

Answer:

(a)

2,155,120

(b)

225,060,000

(c)

251,720,000

Step-by-step explanation:

We have to write numerals for each of the italicized number word names found in these examples.

(a)

two million, one hundred fifty-five thousand, one hundred twenty =

2,155,120

( since 1 million could be represented as:

so 2 million could be written as:

similarly one hundred fifty-five thousand is written aS:

and one hundred twenty is written as 120.

Hence, the number two million, one hundred fifty-five thousand, one hundred twenty is written aS:

2,155,120 )

similarly we could proceed for (b) and (C) option.

(b)

two hundred twenty-five million, sixty thousand =

225,060,000

(c)

two hundred fifty-one million, seven hundred twenty thousand =

251,720,000