A miner earns a wage of $28.42 per hour, plus an allowance of $9.97 per hour for working underground in confined spaces. If the miner works from 8.30am to 4.00pm each day from Monday to Friday, calculate his yearly income

Answer:

The solution to the system of equations is:

The graph is attached below.

Step-by-step explanation:

Given the system of equations

[tex]2y = 2x - 8[/tex]

[tex]2x + y = 5[/tex]

Let us solve the system of equations using the elimination method

[tex]\begin{bmatrix}2y=2x-8\\ 2x+y=5\end{bmatrix}[/tex]

Arrange equation variables for elimination

[tex]\begin{bmatrix}2y-2x=-8\\ y+2x=5\end{bmatrix}[/tex]

Multiply y + 2x = 5 by 2:  2y + 4x = 10

[tex]\begin{bmatrix}2y-2x=-8\\ 2y+4x=10\end{bmatrix}[/tex]

subtracting the equations

[tex]2y+4x=10[/tex]

[tex]-[/tex]

[tex]\underline{2y-2x=-8}[/tex]

[tex]6x=18[/tex]

solve 6x = 18 for x

[tex]6x=18[/tex]

Divide both sides by 6

[tex]\frac{6x}{6}=\frac{18}{6}[/tex]

simplify

[tex]x=3[/tex]

For 2y - 2x = -8  plug in x = 3

[tex]2y-2\cdot \:3=-8[/tex]

[tex]2y-6=-8[/tex]

Add 6 to both sides

[tex]2y-6+6=-8+6[/tex]

Simplify

[tex]2y=-2[/tex]

Divide both sides by 2

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

Simplify

[tex]y=-1[/tex]

Therefore, the solution to the system of equations is:

The graph is attached below.

Answer:

it would be 2m and 5n

Step-by-step explanation:

because 4 * 2 is 8 for m

and 4*5 is 20 for n

Answer:

4(2m - 5n)

4×2m - 4×5n

8m-20n

Therfore ans are 2m and 5 n

Answer:

3.5%

Step-by-step explanation:

Given data

A=$6225

P=$5000

T= 7years

R=???

Simple interest

A=P(1+rt)

substitute

6225=5000(1+7r)

6225=5000+35000r

collect like terms

6225-5000=35000r

1225=35000r

r= 1225/35000

r=0.035

Hence the rate is 0.035*100= 3.5%

Answer:71

Step-by-step explanation:1775/25

Answer:

71 bags

Step-by-step explanation:

Each bag: 20 pennies

Pennies count: 1775

Final Answer: 71 bags

Explain:

1775 / 25 = 71

Answer:

The variables in a study of a cause-and-effect relationship are called the independent and dependent variables. The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.

Step-by-step explanation:

Answer:

go to photo math on your phone it will help you and please give me brainleist

Step-by-step explanation:

a^n + a^n+1

rewrite a^n+1 as a^1 a^n

now you have a^n + a^1a^n

Factor out the common term to get the final answer:

a^n (1+a)

Answer:d

Step-by-step explanation:

distrubition lol

Given:

The LCM of two numbers is 14 times their HCF.

The sum of LCM and HCF is 600.

One number is 280.

To find:

The other number.

Solution:

Let HCF of two numbers be x.

The LCM of two numbers is 14 times their HCF.

LCM = 14x

The sum of LCM and HCF is 600.

[tex]14x+x=600[/tex]

[tex]15x=600[/tex]

[tex]x=\dfrac{600}{15}[/tex]

[tex]x=40[/tex]

So, HCF = 40 and the LCM is

[tex]LCM=14(40)[/tex]

[tex]LCM=560[/tex]

We know that, if a and b are two numbers, then

[tex]a\times b=LCM(a,b)\times HCF(a,b)[/tex]

One number is 280.

[tex]280\times b=560\times 40[/tex]

[tex]b=\dfrac{560\times 40}{280}[/tex]

[tex]b=2\times 40[/tex]

[tex]b=80[/tex]

Therefore, the other number is 80.

Answer:

Step-by-step explanation:

No, the answer is y=-0.30x2-0.48x+15.83

Answer:

$1932

Step-by-step explanation:

12x 7 = 84

84% of 2300 = 1932

Answer:

42 - 22 = 20

Mary has 20 more peanuts than Frank.

Answer:

20

Step-by-step explanation:

42-22=20

Answer:

2 or b

Step-by-step explanation:

Answer:

2,560

Step-by-step explanation:

multiplication

Answer: 13.64%

Step-by-step explanation:

Alyssa estimates that the gym can hold 660 students even though it can hold 750.

Her percent error is calculated by:

= (Actual seats - Estimated seats) / Estimated seats

= (750 - 660) / 660

= 90 / 660

= 0.1364

= 13.64%

Answer: 15

Step-by-step explanation:

Answer:

x=4.464974

Step-by-step explanation:

Answer:

Rate of the Eastbound train is 93 mph.

Step-by-step explanation:

Let the speed of the Eastbound train = x miles per hour

And the speed of the West bound train = y mph

Eastbound train travels 14 mph slower than the westbound train,

So the equation will be,

y - x = 14 ----------(1)

If these trains are 400 miles apart after 2 hours,

Distance traveled by the Eastbound train = Speed × Time

                                                              = 2x miles

Distance traveled by the Westbound train = 2y miles

Trains are 400 miles apart after 2 hours,

So the equation will be,

2y + 2x = 400

x + y = 200 ----------(2)

By adding equation (1) and equation (2)

(y - x) + (x + y) = 14 + 200

2y = 214

y = 107 mph

From equation (1)

107 - x = 14

x = 107 - 14

x = 93 mph

Therefore, rate of the Eastbound train is 93 mph.

Total number of orders served by Maya, Ahmad and Joe on Moday = 75

Let the number of orders Maya served be x.

Then :

Number of orders Joe served = 2x

Number of orders Ahmad served = x - 5

This can be written in an equation as :

[tex] \tt \: 2x + x - 5 + x = 75[/tex]

[tex] = \tt 4x - 5 = 75[/tex]

[tex] = \tt 4x = 75 + 5[/tex]

[tex] = \tt 4x = 80[/tex]

[tex] = \tt \: x = \frac{80}{4} [/tex]

[tex] = \tt \: x = 20[/tex]

Which means :

Number of orders Joe served :

= 2 × 20

= 40

Thus, Joe served 40 orders.

Number of orders Maya served = 20

Number of orders Ahmad served :

= 20 - 5

= 15

Thus, Ahmad served 15 orders.

Answer:

1. 12/1= rate of change

Step-by-step explanation:

1.

1 mile= 30 seconds

(1,30)

6 miles= 1 1/2 minutes

6 miles=90seconds

(6,90)

Formula: y2-y1/x2-x1

90-30/6-1

60/5

12/1= rate of change

hope its right

Answer:

x=3

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Would it be b) 15/7

Step-by-step explanation:

Answer:

8[tex]\pi[/tex]

Step-by-step explanation:

area=[tex]\pi[/tex][tex]r^{2}[/tex]

[tex]\pi[/tex][tex]4^{2}[/tex]

16[tex]\pi[/tex]

since it is a semicircle, cut that number in half.

Answer:

25.12units squared

Step-by-step explanation:

A = [tex]\frac{\pi r^2}{2}[/tex] or [tex]\frac{3.14r^2}{2}[/tex]

r = 4

3.14 x 4^2 = 50.24

50.24/2 = 25.12

Answer: $43.13

Step-by-step explanation:

The cost of a gallon of gasoline is $3.45.

Jenny bought 12.5 gallons of said gasoline. Her total cost is therefore:

= Cost of a gallon * number of gallons purchased

= 3.45 * 12.5

= $43.13

Answer:

43.14

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

the two numbers that satisfy the requirements for this is 2 and 3, so the answer i put is the sum of the square of the two numbers.

Answer:

let two number be x and y

by question

x+y=5….....(1)

xy=6

x=6/y.........(2)

putting the value of x in equation 1

6/y+y=5

6+y²=5×y

y²-5y+6=0

y²-3x-2x+6=0

(y-3)(y-2)=0

either

y=3

or

y=2

:.required no is 2 and 3

Answer:

12 x1/4 or 12x.25=3

Step-by-step explanation:

you can pick between 1/4 or 0.25 they both equal 3

Answer:

$45

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW;

For a walk-a-thon a sponsor committed to give you a flat fee of $5 plus $2 for every mile you walk. If you walk for 20 miles, what is the total amount you will collect from your sponsor at the end of the walk-a-thon?

$5 was given for participants of the walk-a-thon.

$2 was given for every miles won

Then, for "y" number of miles, the the amount that can be won is ( 2×y)= 2y

The Total amount that can be given

= (5 + 2y)

Where "y" is the miles value

Then, if you walk for 20 miles, The Total amount that can be given

= 5 + 2(20)

= 5+ 40

= $45

Answer:

18

Step-by-step explanation:

1/3(x-9)=3

x-9=3/(1/3)

x-9=(3/1)/(1/3)

x-9=(3/1)(3/1)

x-9=9/1

x-9=9

x=9+9

x=18