Ratio Word Problems
If a machine that runs 24 hours a day
can make 144 toy cars per day, how
many toy cars can it make per hour?

Answer:

165

Step-by-step explanation:

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

[tex]h(x)=ax(x-7)[/tex]             ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

[tex]4=a(3)((3)-7)[/tex]

[tex]4=a(3)(-4)[/tex]

[tex]\dfrac{4}{(3)(-4)}=a[/tex]

[tex]-\dfrac{1}{3}=a[/tex]

Putting [tex]a=-\dfrac{1}{3}[/tex], we get

[tex]h(x)=-\dfrac{1}{3}x(x-7)[/tex]              ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

[tex]h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)[/tex]

[tex]h(1.5)=-(0.5)(-5.5)[/tex]

[tex]h(1.5)=2.75[/tex]

Since h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.

Answer:

631.334460 ft

Step-by-step explanation:

i think

Answer:

32 feet

Step-by-step explanation:

Since we know that the formula for finding circumference is C = π · d, and π is equal to 3.14, we reverse the formula so it fits what information we have.

We know that C = 100.48 and we also know that π = 3.14 so all we have to find is the diameter.

To do this, you divide 100.48 by 3.14 to get 32 feet as your final answer.

Answer:

option 3

Step-by-step explanation:

not sure if right

A- x=A

B- x=27

C- x=3

D- x=4

E- x=17

ANSWER- A and C

Hope this Helped! :T

Answer:

Step-by-step explanation:

Given:

Conjugate of the given number is:

Divide the given number by its conjugate:

Correct choice is B

Answer:

-52

Step-by-step explanation:

-11 -14 are same sign is equal to plus ,,so that is answer -52 ...

Answer:

- 11 - 41

-52 is the right answer....

Answer:

6

Step-by-step explanation:

30%*20 = 6

I believe it would 18 ounces of chips for 3 cups of flour. If you take half of 12 ounces then you get 6 ounces per cup of flour. Adding 6 ounces to the 12 would get us the total of the 18 ounces.

Answer:

5/10 + 1/10 = 6/10 or if you simplify it 3/5

Step-by-step explanation:

1/2 = 5/10

1/10 = 1/10

5/10 + 1/10 = 6/10

6/10 = 3/5

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

Answer:

1/2 + 1/10 = 5/10+ 1/10 = 3/5

Step-by-step explanation:

Find the LCD of 2 and 10 (10)

Add the two together (6/10)

Reduce (3/5)

Have a good day :)

Answer:

I believe That the answer is c.

Step-by-step explanation:

The question shows what it should look like, and C matches the question.

Answer: C

Step-by-step explanation: not enough information

Answer:

bjbjy

Step-by-step explanation:

Answer: 1, 3, 5, 15.

Step-by-step explanation: Factors of 15: 1, 3, 5, 15

Answer:

£140

Step-by-step explanation:

Modal is the most common value in a sample, in this case it's 140

Answer:

Im sorry but your going to have to provide more information for me to answer my G!

Step-by-step explanation:

Answer:

f

Step-by-step explanation:

because 24 inches is 2 feet and 2 yards is is 6 feet

Answer:

B) 30.9

Step-by-step explanation:

So, because the radius is 6, we know the diameter is 12, meaning we know each side is 12, so the total area of the square is 144.

To find the area of a square we should use pi(r) ^2 which is pi(6) ^2 which is 113.09. to find the area of the shaded are we would subtract these. 144- 113.09 this gets us 30.91, this is closest to B) 30.9

Answer:

area = 32

perimeter = 30

Step-by-step explanation:

Formulas:

Area of a parallelogram: A = bh

Perimeter of a parallelogram: P = 2 ( b + s )

Where h = height s = slant height and b = base length

Define:

b = 8

h = 4

s = 7

Plug in given values into formulas and calculate

A = (8)(4)

8 * 4 = 32

A = 32

P = 2 ( 8 + 7 )

8 + 7 = 15

2(15) = 30

P = 30

Answer:

A 3/19

Step-by-step explanation:

There are 4 candies of each color. If you take out one yellow, you not only have three yellows; you have 19 candies. 3/19 is the answer.

Answer:

3/19

Step-by-step explanation:

There is an equal number of colored candies, in which there are 20 candies in all, and 5 colors:

20/5 = 4

Each color has 4 candies.

Savannah was able to obtain a yellow candy, and she does not replace it:

4/20 removing one yellow candy = 3/19

A) 3/19 is her chance of getting another yellow.

It's the one with the greater than or less than sign (the second option) because Logan wants to make money greater than or less than $1000

Answer:

7x+y=-5

Step-by-step explanation:

-y=7x+5

7x+y=-5

The variables on a scatter plot are related using the equation of a straight line graph; y = mx + c.

Since the options are unclear, I will try to help you as much as possible. A scatter plot is an arrangement in which one variable is plotted on the vertical axis and another is plotted on the horizontal axis.

The variables on a scatter plot are related using the equation of a straight line graph; y = mx + c. Using this relation, we can establish the equation of the scatter plot.

Learn more about scatterplot: https://brainly.com/question/15289741?

Answer:

h = 2A/b

Step-by-step explanation:

Area of a triangle, A = 1/2bh

Where,

b = base of the triangle

h = height of the triangle

Rearrange the formula to isolate h

A = 1/2bh

Multiply both sides by 2

2 * A = 2 * 1/2bh

2A = bh

Divide both sides by b

2A / b = bh / b

2A / b = h

Therefore,

h = 2A/b

Answer:

addition?

Step-by-step explanation:

Answer:

230 in.²

Step-by-step explanation:

20 · 10 = 200 in.²

5 · 6 = 30 in.²

200 in.² + 30 in.²

Answer:

230 sq in

Step-by-step explanation:

You can find entire area (20 x 16) and subtract out the area of the missing piece (15 x 6)

20 x 16 = 320

15 x 6 = 90

320 - 90 = 230

Answer:

[tex]47x^3\sqrt{5x}[/tex]

Step-by-step explanation:

The objective is to combine the terms to make one radical, so therefore we know that we will have to take a [tex]\sqrt{5}[/tex] out of the second radical [tex]\sqrt{180}[/tex].

If we divide 180 by 5, we will get 36, so now we have

[tex]\sqrt{180}=\sqrt{5}[/tex]×[tex]\sqrt{36}[/tex]

[tex]\sqrt{36}[/tex] can be simplied into just 6.

So now the expression becomes

[tex]-\sqrt{5x^7}+8x^2*6 \sqrt{5x^3}[/tex]

Then we can further simplify by moving the [tex]x^{2}[/tex] into the radical to get two common terms with [tex]\sqrt{5x^7}[/tex].

[tex]x^{2} =\sqrt{x^4}[/tex], so we now have

[tex]-\sqrt{5x^7}+ 8\sqrt{x^4} *6 \sqrt{5x^3}[/tex]

So then we can combine the two radicals to get the expression to

[tex]-\sqrt{5x^7}+48\sqrt{5x^7}[/tex]

We now see that we have two terms with a common radical, and coefficients of -1, and 48.

That allows us to simplify further to

[tex]47\sqrt{5x^7}[/tex]

Here, we can take out [tex]\sqrt{x^6}[/tex], which is [tex]x^3[/tex], and get the final simplied form to be

[tex]47x^3\sqrt{5x}[/tex]

Hope this helped.

Answer:

785.5ft

Step-by-step explanation:

Given data

Diameter= 250ft

Radius= D/2= 250/2= 125ft

The total steel required can be found from the Circumference

C= 2πr

C= 2*3.142*125

C= 785.5ft

Hence the total steel required is 785.5ft    

Answer:

-1.778

Step-by-step explanation:

The two lines cross at the point (-1.778,-4.333), but the x value is -1.778

Hope this helps