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3 years ago

What is Omar's net income for October A. $1,000 B. $1,500 C. $ 2,500 D. $ 3,500

Mathematics

2 answers:

Jlenok [28]3 years ago

7 0

2,500 (income) - 1,000 (expenses)= 1,500 (net income)

Scilla [17]3 years ago

7 0

Total income : 2500 - total expenses : 1000 = net income of 1500

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There are two mixtures. One mixture contains 5% alchol and the other mixture contains 12% alchol. How much of each should be mix

hichkok12 [17]

Answer:

to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture that contains 5% alcohol and 285,7 gallons of mixture that contains 12% alcohol.

Step-by-step explanation:

According to the statement, there are two mixtures. One mixture contains 5% alcohol and the other contains 12% alcohol.

We want to make 1000 gallons with 10% alcohol, so we have the following system of equations:

A + B = 1000 gallons. [1]

0.05A + 0.12B = 0.1(1000) ⇒ 0.05A + 0.12B = 100 [2]

(Where 'A' represents the mixture that contains 5% alcohol and 'B' the one that contains 12% alcohol).

Solving the system of equations:

A + B = 1000 ⇒ A = 1000 - B [3]

[3] → [2]

0.05(1000 - B) + 0.12B = 100 ⇒ 50 - 0.05B + 0.12B = 100

⇒ 0.07B = 50 ⇒ B = 714.28 ≈ B=714.3 [4]

[4] → [1]

A + B = 1000 ⇒ A + 714.3 = 1000 ⇒ A = 285,7

Therefore, to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture 'A' and 285,7 gallons of mixture 'B'

4 0

3 years ago

The tables below show the values of Y for different values of X

pogonyaev

Answer:

Option D

Step-by-step explanation:

Rate of change of a linear function between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

Rate of change 'm' = $\frac{y_2-y_1}{x_2-x_1}$

From the given table,

Rate of change of the function between (-2, 6) and (-4, 9),

Rate of change 'm' = $\frac{9-6}{-4-(-2)}$

m = $\frac{3}{-2}$

Initial value = y-intercept

Let the equation of the line passing through a point (h, k) is,

y - k = m(x - h)

If a point (-2, 6) is lying on the graph of the function,

y - 6 = $-\frac{3}{2}(x+2)$

y = $-\frac{3}{2}x-3+6$

y = $-\frac{3}{2}x+3$

Y-intercept of the function = 3

Therefore, initial value of the function = 3

Option D is the answer.

3 0

2 years ago

George's page contains twice as many typed words as Bill's page and Bill's page contains 50 fewer words than Charlie's page. If

Deffense [45]

I think bills were 60 words because charlie was 210 so bill was 50 fewer so he is 60 and George will be twice as bills s his will be 80 words

5 0

3 years ago

In 1998, Cathy's age is equal to the sum of the four digits in the year of her birthday, then how old was Cathy in 1998?

ycow [4]

Answer:

<em>Cathy was born in 1980 and she was 18 years old in 1998</em>

Step-by-step explanation:

<u>Equations</u>

This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.

Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as

$x=1000a+100b+10c+d$

In 1998, Cathy's age was

$1998-(1000a+100b+10c+d)$

And it must be equal to the sum of the four digits

$1998-(1000a+100b+10c+d)=a+b+c+d$

Rearranging

$1998=1001a+101b+11c+2d$

We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus

$1998=1001+909+11c+2d$

Operating

$88=11c+2d$

If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]

c=8, d=0

Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18

5 0

3 years ago

How can $54,000 be invested part at 8% annual simple Interest and the remainder at 10% annual simple interest so that the intere

Nastasia [14]

Answer:

0.08x = $5400-0.1x Add 0.1x to both sides of the equation.

0.18x = $5400 Divide both sides by 0.18

x = $3000 and $54000-$3000 = $24000

$3,000 is invested at 8%

$2,400 is invested at 10%

Step-by-step explanation:

3 0

3 years ago