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Nataly [62]
3 years ago
10

A school group has $140 to spend. Write and solve an inequality that represents the cost to rent the main hall, where h represen

ts the number of hours the group can rent the room.
Mathematics
1 answer:
lisov135 [29]3 years ago
6 0

Answer:

a. 15h + 40 ≤ 140

b. h ≤ 6.6

<em>Note: The question is missing a table. The table is shown in the attachment below.</em>

Step-by-step explanation:

a. The school group has $140 to spend, and so can only spend an amount less than or equal to $140 when renting the main hall.

The cost of renting the main includes an hourly rate of $15 and a set-up fee of $40.

Let  h represent the number of hours the group can rent the hall.

Cost of renting the main hall, C is given by:

15h + 40 ≤ 140

b. Solution of the inequality:

15h + 40 ≤ 140

15h ≤ 140 - 40

15h ≤ 100

h ≤ 100/15

h ≤ 6.6

Therefore, the main hall can only be rented for a maximum of 6.6 hours or less

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A population of rabbits is described by the function R(t) = 100(2t/5), where t is measured in months and R is measured in rabbit
Savatey [412]

Answer and Step-by-step explanation: The graph is shown in the attachment.

a. ΔR on [1,2] is mathematically expressed as:

ΔR = R(2) - R(1)

which means difference of population of rabbits after 2 months and after 1 month.

R(1) = 100(\frac{2}{5}.1 )

R(1) = 100(\frac{2}{5} )

R(2) = 100(\frac{2}{5}.2 )

R(2) = 100(\frac{4}{5} )

\Delta R = 100(\frac{4}{5} )-100(\frac{2}{5} )

\Delta R = 100[\frac{4}{5} - \frac{2}{5} ]

\Delta R= 40

Difference of rabbits between first and second months is 40.

b. R(0) = 100(\frac{2}{5} .0)

R(0) = 0

Initially, there no rabbits in the population.

c. R(10) = 100(\frac{2}{5}.10 )

R(10) = 400

In 10 months, there will be 400 rabbits.

d. R(t) = 500

500=100(\frac{2}{5}.t )

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3 0
3 years ago
Theo earns a base salary plus commission. At the end of September, he was paid $3,835.25 based on his monthly sales of $12,850.
hodyreva [135]

Theo's base salary  using a simultaneous equation approach is $2,996.22 .

In order to determine the base salary of Theo, we can express the two earnings and sales amounts using simultaneous equation, that we would solve to arrive at the base salary

Bear in mind that total earnings are determined as base salary plus commission

Let X be the base salary

Let R be the rate of commission

commission =sales*rate of commission

When earnings were $3,835.25 and sales is $12,850, we have the below equation:

X+(12,850*R)=3,835.25

X+12850R=3,835.25  .................... equation (1)

When earnings were $3,641 and sales is $9,875, we have the below equation:

X+(9,875*R)=3641

X+9875R=3641 .........................  equation (2)

subtract equation 2 from 1

2975R=194.25

R=194.25/2975

R=commission rate=6.52941176470588%

substitute for R in equation 1 to arrive at X(base salary)

X+(12850*6.52941176470588%)=3,835.25

X=3,835.25-(12850*6.52941176470588%)

X=base salary=$2,996.22

Find further guide on simultaneous equation in the link below:

brainly.com/question/6597041

#SPJ1

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