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3 years ago

Over the school holidays Brianna worked

Mathematics

1 answer:

labwork [276]3 years ago

6 0

Answer:

8 shifts.

Step-by-step explanation:

Brianna worked a total of 44 hours stacking shelves.

If she worked $5\frac{1}{2}$ hour shifts,

How many shifts did she work?

So 1 shift takes 5.5 hours

The number of shifts she worked in 5.5 hours is;

$\frac{44}{5.5} * 1$ = 8 shifts.

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Gabi wants to drive to and from the airport. She finds two companies near her that offer short-term car rental service at differ

lilavasa [31]

Answer:

The difference in per-mile costs for the two companies is $0.12

Step-by-step explanation:

Gabi sets up the equation $0.22m+7.20=0.1m+8.40$ to find out after how many miles, m, the companies will charge the same amount.

The first company charges $c_1=0.22m+7.20$ for m miles driven.

The second company charges $c_2=0.1m+8.40$ for m miles driven.

In both these functions, numbers 7.20 and 8,40 represent the initial fee the companies charge.

Numbers 0.22 and 0.1 represent per-mile costs.

Thus, the difference in per-mile costs is $0.22-0.1=0.12$

Another way to solve this problem is to find the cost per mile driven for each company:

1. Cost per-mile 1st company

$c_1(0)=0.22\cdot 0+7.20=7.20\\ \\c_1(1)=0.22\cdot 1+7.20=7.42\\ \\c_1(1)-c_1(0)-7.42-7.20=0.22$

2. Cost per-mile 2nd company

$c_2(0)=0.1\cdot 0+8.40=8.40\\ \\c_2(1)=0.1\cdot 1+8.40=8.50\\ \\c_2(1)-c_2(0)=8.50-8.40=0.1$

3. Difference:

$0.22-0.1=0.12$

6 0

3 years ago

A 10-ounce box of cereal costs $3. A 20-ounce box of the same cereal costs $5. A third box of the same cereal costs $8. Calculat

kogti [31]

Answer:

number of ounces in the third box = 32 ounces

Step-by-step explanation:

The number of ounces is directly proportional to the cost

Let O represent the number of ounces, C represent the cost

O∝C----------------Eqn 1

O = KC

K = O÷C = 20/5 = 4

Hence number of ounces in the third box = 4 × 8 = 32 ounces

7 0

4 years ago

Find the equation of the line between the points (10, – 5) and ( - 2,0).

Natali5045456 [20]

Answer <u>(assuming it can be in slope-intercept form)</u>:

$y = -\frac{5}{12} x-\frac{5}{6}$

Step-by-step explanation:

1) First, find the slope of the line between the two points by using the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(0)-(-5)}{(-2)-(10)} \\m = \frac{0+5}{-2-10} \\m=\frac{5}{-12}$

Thus, the slope of the line is $-\frac{5}{12}$ .

2) Next, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. Substitute values for $m$ , $x_1$ , and $y_1$ in the formula.

Since $m$ represents the slope, substitute $-\frac{5}{12}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:

$y-(0)=-\frac{5}{12} (x-(-2))\\y-0 = -\frac{5}{12} (x+2)\\y = -\frac{5}{12} x-\frac{5}{6}$

3 0

3 years ago

24. A tank can be filled by a pipe in 30 minutes and emptied by another pipe in 50 minutes. How many minutes will it take to fil

OleMash [197]

Answer:

75 minutes

Step-by-step explanation:

The rate at which the tank is filled up, F, and emptied, E, are respectively:

$F=\frac{V}{30}*60 = 2V/hour\\E=\frac{V}{50}*60 = 1.2V/hour$

Since V is the full volume of the tank, the time required to fill the tank if both pipes are open is given by:

$F-E=2V/hour-1.2V/hour = 0.8V/hour\\t= \frac{1}{0.8}=1.25\ hours = 75\ minutes$

It will take 75 minutes to fill the tank if both pipes are open.

4 0

3 years ago

The range of a projectile that is launched with an initial velocity v at an angle of a with the horizontal is given by R

lara31 [8.8K]

Answer:

$\theta=30.285^{\circ}$

Step-by-step explanation:

The range of a projectile is given by :

$R=\dfrac{u^2\sin2\theta}{g}$

Put R = 20 m, u = 15 m/s and finding the value of angle of projection

So,

$R=\dfrac{u^2\sin2\theta}{g}\\\\\sin2\theta=\dfrac{Rg}{u^2}\\\\\sin2\theta=\dfrac{20\times 9.8}{15^2}\\\\\sin2\theta=0.871\\\\2\theta=\sin^{-1}(0.871)\\\\2\theta=60.57\\\\\theta=30.285^{\circ}$

So, the required angle of projection is equal to $30.285^{\circ}$ .

3 0

3 years ago