All categories

2 years ago

A school graduation class wants to hire buses and vans for a trip to Jasper National Park. Each bus

Mathematics

1 answer:

BARSIC [14]2 years ago

6 0

Let the school hire x buses and y vans.

A bus can hold 40 students and 3 teachers.
A van can hold 8 students and 1 teacher.

The number of students riding in buses and vans is at least 400, therefore
40x + 8y ≥ 400 (1)

The number of teachers riding in buses and vans is at most 36, therefore
3x + y ≤ 36 (2)

Write (1) and (2) as
y ≥ 50 - 5x (3)
y ≤ 36 - 3x (4)

The equality portion of the solution of (3) and (4) is
36 - 3x = 50 - 5x
2x = 14
x = 7 => y = 36 - 3*7 = 15

A graph of the inequalities indicates the acceptable solution in shaded color, as shown below.

The minimum cost of renting buses and vans is
7*$1200 + 15*$100 = $9900

Answer: The minimum cost is $9,900

You might be interested in

Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus \$6$6dollar sign, 6 for each ho

Margarita [4]

For this case, the first thing we must do is define variables.

We have then:

t: number of hours

F (t): total charge

We write the function that models the problem:

$F (t) = 6t + b$

Where,

b: represents an initial fee.

We must find the value of b.

For this, we use the following data:

Her total fee for a 4-hour job, for instance, is $ 32.

We have then:

$32 = 6 (4) + b$

From here, we clear the value of b:

$32 = 24 + b$

$32-24 = b$

$b = 8$

Then, the function that models the problem is:

$F (t) = 6t + 8$

Answer:

the function's formula is:

$F (t) = 6t + 8$

7 0

2 years ago

A fuel is purified by passing it through a clay pipe. Each foot of the clay pipe removes a fixed percentage of impurities in the

creativ13 [48]

The amount of pollutants.

8 0

2 years ago

which of the following is equivalent to 3 sqrt 32x^3y^6 / 3 sqrt 2x^9y^2 where x is greater than or equal to 0 and y is greater

Nutka1998 [239]

Answer:

$\frac{\sqrt[3]{16y^4}}{x^2}$

Step-by-step explanation:

The options are missing; However, I'll simplify the given expression.

Given

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$

Required

Write Equivalent Expression

To solve this expression, we'll make use of laws of indices throughout.

From laws of indices $\sqrt[n]{a} = a^{\frac{1}{n}}$

So,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ gives

$\frac{(32x^3y^6)^{\frac{1}{3}}}{(2x^9y^2)^\frac{1}{3}}$

Also from laws of indices

$(ab)^n = a^nb^n$

So, the above expression can be further simplified to

$\frac{(32^\frac{1}{3}x^{3*\frac{1}{3}}y^{6*\frac{1}{3}})}{(2^\frac{1}{3}x^{9*\frac{1}{3}}y^{2*\frac{1}{3}})}$

Multiply the exponents gives

$\frac{(32^\frac{1}{3}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

Substitute $2^5$ for 32

$\frac{(2^{5*\frac{1}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

From laws of indices

$\frac{a^m}{a^n} = a^{m-n}$

This law can be applied to the expression above;

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$ becomes

$2^{\frac{5}{3}-\frac{1}{3}}x^{1-3}*y^{2-\frac{2}{3}}$

Solve exponents

$2^{\frac{5-1}{3}}*x^{-2}*y^{\frac{6-2}{3}}$

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$

From laws of indices,

$a^{-n} = \frac{1}{a^n}$ ; So,

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$ gives

$\frac{2^{\frac{4}{3}}*y^{\frac{4}{3}}}{x^2}$

The expression at the numerator can be combined to give

$\frac{(2y)^{\frac{4}{3}}}{x^2}$

Lastly, From laws of indices,

$a^{\frac{m}{n} = \sqrt[n]{a^m}$ ; So,

$\frac{(2y)^{\frac{4}{3}}}{x^2}$ becomes

$\frac{\sqrt[3]{(2y)}^{4}}{x^2}$

$\frac{\sqrt[3]{16y^4}}{x^2}$

Hence,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ is equivalent to $\frac{\sqrt[3]{16y^4}}{x^2}$

8 0

2 years ago

You just obtained a credit card. You immediately purchase a digital camera for $160. Your credit limit is $4000. Let’s assume th

attashe74 [19]

Every month your balance includes the original amount (100%) and the added the monthly interest (1.42%) so each month the balance will be 101.42% of pior month's balance move the decimal point two points two places to the left to make that into a decimal

So the answer is 101.42

8 0

2 years ago

What angle does an arc 6.6cm in length subtends at the centre of a circle of radius 14cm. Use π = 22/7)

aniked [119]

Answer:

STEP 1: Find the circumference:

Circumference = 2πr

Circumference = 2π(14) = 28π cm

............................................................................................

STEP 2: Find the length of the arc:

Length of the arc = 36/360 x 28π

Length of the arc = 8.8 cm

.............................................................................................

Answer: The length of the arc is 8.8 cm

............................................................................................

hope it helpssss

Mark it as brilliant answer plzzz

ФωФ

4 0

2 years ago

Read 2 more answers