All categories

3 years ago

Bill paints murals. He recorded the total amount of white paint that he used for his murals each month in the table below.

Mathematics

2 answers:

inessss [21]3 years ago

8 0

Answer:

$\frac{8}{15}$ liters

Step-by-step explanation:

Bill paints murals. He recorded the total amount of white paint that he used for his murals each month in the table below.

March $1\frac{1}{4}$ liters of paint

April

May $\frac{4}{5}$ liters of paint.

In April Bill used $\frac{2}{3}$ of $\frac{4}{5}$

Therefore, he used in April

$\frac{2}{3}$ × $\frac{4}{5}$

= $\frac{8}{15}$ liters

In April Bill used $\frac{8}{15}$ liters of white paint.

kicyunya [14]3 years ago

6 0

Answer:

Step-by-step explanation:

2/3x4/5=8/15

You might be interested in

Be my friend with your Taurus or Leo. I love Tauars and leos! I'm a Pisces btw

barxatty [35]

Answer:

Well, I'm a Scorpio... why does the sign matter to you?

6 0

2 years ago

Read 2 more answers

A ship sails 250km due North qnd then 150km on a bearing of 075°.1)How far North is the ship now? 2)How far East is the ship now

olga_2 [115]

Answer:

1) 288.8 km due North

2) 144.9 km due East

3) 323.1 km

4) 207°

Step-by-step explanation:

Bearing: The angle (in degrees) measured clockwise from north.

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Cosine rule

$c^2=a^2+b^2-2ab \cos C$

where a, b and c are the sides and C is the angle opposite side c

-----------------------------------------------------------------------------------------------

Draw a diagram using the given information (see attached).

Create a right triangle (blue on attached diagram).

This right triangle can be used to calculate the additional vertical and horizontal distance the ship sailed after sailing north for 250 km.

Question 1

To find how far North the ship is now, find the measure of the short leg of the right triangle (labelled y on the attached diagram):

$\implies \sf \cos(75^{\circ})=\dfrac{y}{150}$

$\implies \sf y=150\cos(75^{\circ})$

$\implies \sf y=38.92285677$

Then add it to the first portion of the journey:

⇒ 250 + 38.92285677... = 288.8 km

Therefore, the ship is now 288.8 km due North.

Question 2

To find how far East the ship is now, find the measure of the long leg of the right triangle (labelled x on the attached diagram):

$\implies \sf \sin(75^{\circ})=\dfrac{x}{150}$

$\implies \sf x=150\sin(75^{\circ})$

$\implies \sf x=144.8888739$

Therefore, the ship is now 144.9 km due East.

Question 3

To find how far the ship is from its starting point (labelled in red as d on the attached diagram), use the cosine rule:

$\sf \implies d^2=250^2+150^2-2(250)(150) \cos (180-75)$

$\implies \sf d=\sqrt{250^2+150^2-2(250)(150) \cos (180-75)}$

$\implies \sf d=323.1275729$

Therefore, the ship is 323.1 km from its starting point.

Question 4

To find the bearing that the ship is now from its original position, find the angle labelled green on the attached diagram.

Use the answers from part 1 and 2 to find the angle that needs to be added to 180°:

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{Total\:Eastern\:distance}{Total\:Northern\:distance}\right)$

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{150\sin(75^{\circ})}{250+150\cos(75^{\circ})}\right)$

$\implies \sf Bearing=180^{\circ}+26.64077...^{\circ}$

$\implies \sf Bearing=207^{\circ}$

Therefore, as bearings are usually given as a three-figure bearings, the bearing of the ship from its original position is 207°

8 0

2 years ago

Read 2 more answers

3. Spiral Review: Solve the equation algebraically. Show all work. Circle your final solution.

AlexFokin [52]

Answer:

z=-13/7

Step-by-step explanation:

1. Add 3z(7z+5=-8)

2. Subtract 5(7z=-13)

3. Divide 7(z=-13/7)

3 0

3 years ago

A cookie recipe required 1 1/3 cups of sugar. If Mrs. Lee has 7 cups of sugar, how many recipes of cookies can she bake? Need an

Vitek1552 [10]

$\frac{21}{3} = 7 \: cups$

$\frac{21}{3} ÷ \frac {4}{3} = 5 \frac{1}{3}$

She can make 5 batches of cookies and have

$\frac{1}{3} \: cups$

left

3 0

3 years ago

Solve the proportion for the variable given. 4/6 = 9/x

Alexeev081 [22]

Answer: 6
Multiply 9 on both sides since the operation is division .

4/6=9/x
/9. /9
6=x

4 0

3 years ago