Review the graph of piecewise function g(x).

A dump truck brought 1⁄3 of a ton of rock on the first trip, 1⁄2 of a ton on the second trip, but on the third trip, had to take

Allisa [31]

Answer:

1/30 of a ton

Step-by-step explanation:

Write this as an expression:

1/3 of a ton and 1/2 of a ton were taken to the site.

4/5 of a ton were remove from the site.

Amount of a ton at the site = $\frac{1}{3}+ \frac{1}{2}- \frac{4}{5}$

Solve the equation by finding common denominators (when the bottom numbers are the same).

$(\frac{1}{3}+ \frac{1}{2})- \frac{4}{5}$ Focus on the first part. The least common multiple (LCM) of 3 and 2 is "6", which will become the denominator.

For 1/3 to become ?/6, multiply top and bottom by 2.

For 1/2 to become ?/6, multiply top and bottom by 3.

$(\frac{2}{6}+ \frac{3}{6})- \frac{4}{5}$

Now we can add the numerators together over the same denominator.

$\frac{5}{6}- \frac{4}{5}$

Do the same thing as before and change the denominators. The LCM of 6 and 5 is "30".

For 5/6 to become ?/30, multiply top and bottom by 5.

For 4/5 to become ?/30, multiply top and bottom by 6.

$\frac{25}{30}- \frac{24}{30}$

Subtract the numerators:

$\frac{1}{30}$ Answer in tons

Therefore there was 1/30 of a ton of rock left at the construction site.

7 0

2 years ago

Read 2 more answers

In the number 409.21 what digit is in the ones place

Orlov [11]

Answer: The number before the decimal

Step-by-step explanation:

5 0

3 years ago

Autum school holding a voleturing challeng. Students are encouraged to volunteer for at least 1 1/2 hours per week. Volenteers a

Pani-rosa [81]

Given :

Challenge given is to volunteer for about 1 1/2 hours per week .

Autum did at a rate of 6 3/4 hours per week .

To Find :

The comparison ( ratio ) her volunteers rate with the challenge rate .

Solution :

Simplifying challenge rate in in normal fraction , $1\dfrac{1}{2}=\dfrac{2+1}{2}=\dfrac{3}{2}$ .

Also , simplifying her rate , $6\dfrac{3}{4}=\dfrac{(6\times 4)+3}{4}=\dfrac{27}{4}$ .

Now , ratio of his work by challenge is :

$R=\dfrac{\dfrac{27}{4}}{\dfrac{3}{2}}\\\\\\R=\dfrac{27\times 2}{4\times 3}\\\\R=\dfrac{9}{2}$

Therefore , the ratio is 9/2 or 4 1/2 .

Hence , this is the required solution .

8 0

3 years ago

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if you have installed 4000 linear feet of 8 inch water pipe how much will it hold when full? (answe is 10,543) i need help writi

GuDViN [60]

Answer:

$768,000\pi\ in^{3}$

Step-by-step explanation:

we know that

The volume of a cylinder (water pipe) is equal to

$V=\pi r^{2}L$

In this problem we have

$r=8/2=4\ in$ -----> the radius is half the diameter

$L=4,000\ ft$ ----> convert to inches

$L=4,000*12=48,000\ in$

$V=\pi (4^{2}48,000)=768,000\pi\ in^{3}$

3 0

3 years ago

Alicia drives her car 287.5 miles in 5 hours. What is the constant of proportionality that relates the total number of miles, y,

Sphinxa [80]

Answer:

57.5

Step-by-step explanation:

The constant of proportionality is "k" in the equation ...

y = kx

It can be found from values of x and y using ...

k = y/x

For the given values, it is ...

k = (287.5 mi)/(5 h) = 57.5 mi/h

The constant of proportionality relating miles to hours is 57.5.

5 0

3 years ago