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VladimirAG [237]
3 years ago
6

Janice receives $.40 per pound for 1 to 99 pounds of aluminum cans he recycles. he receives $.50 per pound if you are cycles mor

e than 100 pounds. is the amount of money Janice receives a function of the weight of the cans here cycles? Explain your reasoning.
Mathematics
1 answer:
Ilya [14]3 years ago
5 0

Answer:

M=\left\{\begin{matrix}0.4x &x\leq99 \\ 0.5x &x>100 \\ \end{matrix}\right.

Step-by-step explanation:

<u>Function modeling</u>

Real-life situations often require the help of mathematics to model numerically what happens when the variables involved can change. It could even be used to predict some expected outcomes from those models.

The problem states Janice receives $.40 per pound when he recycles less or equal than 99 pounds of aluminum. If x is the number of recycled pounds, then the amount of money he receives is

M=0.4x

We also know that if he recycles more than 100 pounds of aluminum, the pay increases to $0.5 per pound. In that case, the amount of money is

M=0.5x

This is a case where the function is defined differently depending on the conditions of the input variable x. It's called a piecewise function. The function can be written as

M=\left\{\begin{matrix}0.4x &x\leq99 \\ 0.5x &x>100 \\ \end{matrix}\right.

Note the function is not well constructed because there is a gap for x=100 where M is not defined. If we establish that for 100 pounds the payment is $0.5, then the second piece would include x=100

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1. 4x + 5y
kvv77 [185]
<h3><u>Solution</u><u> </u><u>:</u><u>-</u><u> </u></h3>

  • When x = 6 and y = 1.

1) 4x + 5y

→ 4*6 + 5*1

→ 24 +5 = 29

2) 2x (20-y)

→ 2*6 (20-1)

→ 12 *19 = 228

3) x ÷ 3 + y

→ 6 ÷ 3 + 1

→ 2 +1 = 3

4) 4y ÷ 2 + (8x + 10)

→ 4*1 ÷ 2 +(8*6+10)

→ 2 + (48+10)

→ 2 + 58

→ 60

5 ) 5. Patty made $34 baby sitting on each of 3 weekends. If she spent $50 on gifts for her family, how much money does she have left?

Money made each weekend = $34

Money made in 3 weekend = $34*3 =$102

Money spent = $50

Therefore ,

→Money left = Money made in 3 weekends - Money spent

→ Money left = $102 - $50 = $52

6.Carlos solved 20-(2x6) + 8 divide 4 = 29. Is this the correct answer? ( In attachment it's written 29 and not 28 .)

Given equation is ,

→ 20 - (2 × 6) + 8 ÷ 4 = 29

Solve inside the brackets ,

→ 20 - 12 + 8 ÷ 4

Perform division ,

→ 20 -12 + 2

Perform addition ,

→ 22 - 12

Perform subtraction,

→ 10

<u>No , he is wrong the answer should have been 10 but he got 29 .</u>

<em>I </em><em>hope</em><em> this</em><em> helps</em><em> </em><em>.</em>

8 0
2 years ago
The sum of a number and 6 is greater than or equal to -4
olga2289 [7]
N is greater than or equal to -10
4 0
3 years ago
Plz help me and answer!
Yuri [45]

Answer:

(3,4)

Step-by-step explanation:

A function can't have the x repeat so the only possible answer is (3,4)

4 0
3 years ago
Read 2 more answers
Q18. The sum of the first N terms of an arithmetic series, S, is 292 The 2nd term of S is 8.5 The 5th term of Sis 13 Find the va
Gelneren [198K]

Step-by-step explanation:

Sn= a+[n-1]d

S2= a+[2-1]d

8.5 = a+d _______Equation 1

S5 = a+[5-1]d

13=a+4d ________Equation 2

Subtract Equation 1 from Equation 2

13=a+4d

-

8.5= a+d

________

4.5= 3d

d=1.5

Substituting d=1.5 in equation 1

8.5=a+1.5

a=8.5-1.5

a=7

Sum of terms of an A.P =

Sn= n/2[2a+(n-1)d]

292= n/2[2×7+(n-1)d]

292=n/2[14+(n-1)1.5

292×2=n[14+(n-1)1.5]

584=n[14+1.5n-1.5]

584= 14n+1.5n²-1.5n

584= 1.5n²+12.5n

1.5n²+12.5n-584

1.5n²-24n+36.5n-584

1.5n(n-16)+36.5(n-16)

(1.5n+36.5)(n-16)

**n-16=0

n=16

3 0
1 year ago
A student bought 11 pencils and a pad of paper. The pencils each cost the same amount. The pad of paper cost $4.99. The student
AleksAgata [21]
No lo se wey, espero estes bien :D
3 0
3 years ago
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