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olga55 [171]
4 years ago
9

The local skating rink pays Mary a fixed rate per pupil plus a base amount to work as a skating instructor. She earns $90 for in

structing 15 students on Monday afternoon. Last Friday, she earned $62 for working with 8 students. Lisa is also a skating instructor. She receives half the base amount that Mary does, but she is paid twice as much per student. Who would earn more money instructing a class of 20 students?
Mathematics
1 answer:
liq [111]4 years ago
6 0
The expressions for the payment made to Mary are,
         (Monday)      90 = 15m + b
         (Tuesday)     62 = 8m + b
where m and b are the fee per student and the base fee, respectively. Solving for m and b, the values are 4 and 30. 
The equation that represents Mary's earning is 
                                    y = 4x + 30
 For 20 students,
                                    y = 4(20) + 30 = 110
For Lisa's earnings,
                                     y = 8x + 15
Substituting 20,
                                    y  =8(20) + 15 = 175
Thus, Lisa would earn more than Mary by $65.
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Answer:

yes

Step-by-step explanation:

If the graph passes the horizontal-line test, then the function is one-to-one. Functions that are one-to-one have inverses that are also functions. Therefore, the inverse is a function.

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Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rect
Rudiy27

Full question :

Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 5, 7. Q is at 9, 7. R is at 9, 12. S is at 5, 12 . Rectangle JKLM with vertices J 4, 5. K is at 6, 5. L is at 6, 10. M is at 4, 10. Which statement is correct? The two tiles are not similar because segment PQ is to segment QR is 4:5 and segment JK is to segment LM is 2:1. The two tiles are not similar because segment SP is to segment SR is 5:4 and segment MJ is to segment ML is 5:2. The two tiles are similar because segment PQ is to segment QR is 4:5 and segment JK is to segment KL is also 4:5. The two tiles are similar because segment SR is to segment ML is 2:1 and segment PQ is to segment JK is also 2:1.

Answer:

The two tiles are not similar because segment SP is to segment SR is 5:4 and segment MJ is to segment ML is 5:2.

Step-by-step explanation:

Given vertices which will be our points on the graph to trace the rectangular shapes:

For the first rectangular shape PQRS

P(5,7)

Q(9,7)

R(9,12)

S(5,12)

For the second rectangular shape JKLM

J(4,5)

K(6,5)

L(6,10)

M(4,10)

From the above we can find that the two tiles are not similar if we calculate using their x, y coordinates points(vertices) on the graph.

We can see from the options given that only the second option is correct because:

Line SP ratio to line SR in rectangle PQRS= 5:4

since SP=12-7=5 and SR=9-5=4

Therefore SP:SR = 5:4

Line MJ ratio to line ML in rectangle JKLM= 5:2

Since MJ= 10-5=5 and ML= 6-4=2

Therefore MJ:ML =5:2

3 0
3 years ago
MAJORR HELP!!!
WINSTONCH [101]

Answer:

a)$1628.90

b)$1647.00

c)$1648.72

Step-by-step explanation:

The question is on compound interest.

The formula to apply here is;

A=P(1+\frac{r}{n} )^{nt}

where

  • P=principal /beginning amount
  • r=interest rate as a decimal
  • n=number of compoundings a year
  • t=total number of years

a) If compounded annually, n=1

p=$1000, r=5%=0.05 t=10

Amount will be;

A=1000(1+\frac{0.05}{1} )^{10} \\\\\\A=1000(1.05)^{10} \\\\\\A=1000*1.6289=1628.90

Amount=$1628.90

b) If compounded monthly, n=12

p=$1000, r=5%=0.05, t=10, n=12

A=1000(1+\frac{0.05}{12} )^{12*10} \\\\\\A=1000(1.0042)^{120} \\\\\\A=1000*1.647=1647

Amount=$1647.00

c)If interest compounded continuously, it means the principal is earning interest constantly and the interest keeps earning on the interest earned.Here the formula to apply is;

A=Pe^rt where e is the mathematical constant e=2.71828182846

Hence the amount will be;

A=Pe^{rt} \\\\\\A=1000*e^{0.05*10} \\\\\\A=1000*2.71828182846^{0.5} \\\\\\A=1648.72

Amount=$1648.72

8 0
3 years ago
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