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Tanya [424]
3 years ago
6

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

back 4⁄5 of a ton. What was the total weight of the rock left at the construction site?
Mathematics
2 answers:
Allisa [31]3 years ago
7 0

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 <u>common denominators</u> (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 <u>1/3 to become ?/6</u>, multiply top and bottom by 2.

For <u>1/2 to become ?/6</u>, 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 <u>5/6 to become ?/30</u>, multiply top and bottom by 5.

For <u>4/5 to become ?/30</u>, 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.

bija089 [108]3 years ago
5 0
Larry received 1/3 pound of candy from his grandmother and 2/5 pound of candy from his best friend. Larry's sister ate 1/2 pound of Larry's candy. How many pounds of candy does Larry have left?
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Answer:

The probability that the mean of this sample is less than 16.1 ounces of beverage is 0.0537.

Step-by-step explanation:

We are given that the average amount of a beverage in randomly selected 16-ounce beverage can is 16.18 ounces with a standard deviation of 0.4 ounces.

A random sample of sixty-five 16-ounce beverage cans are selected

Let \bar X = <u><em>sample mean amount of a beverage</em></u>

The z-score probability distribution for the sample mean is given by;

                          Z  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean amount of a beverage = 16.18 ounces

           \sigma = standard deviation = 0.4 ounces

           n = sample of 16-ounce beverage cans = 65

Now, the probability that the mean of this sample is less than 16.1 ounces of beverage is given by = P(\bar X < 16.1 ounces)

   P(\bar X < 16.1 ounces) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{16.1-16.18}{\frac{0.4}{\sqrt{65} } } ) = P(Z < -1.61) = 1 - P(Z \leq 1.61)

                                                    = 1 - 0.9463 = <u>0.0537</u>

The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9591.

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3 years ago
Convert 330 litres per hour into millilitres per minute (ml/min).
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2 years ago
If a bird is on the ground, 7 ft away from a 10 ft tall tree, then what is the angle (to the
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Answer:

The angle is 55°

Step-by-step explanation:

To find the angle at which a bid is looking up on top of a tree that is 10feet tall if the bird is on the ground 7 feet away from the tree, we will follow the steps below:

we will use trigonometric ratio to find the angle

SOH CAH TOA

sinФ = opposite / hypotenuse

cosФ = adjacent / hypotenuse

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from the diagram below, opposite = 10 feet   and   adjacent = 7 feet

the best trig.ratio to use is tan

tanФ = opposite /adjacent

tanФ = 10 /7

tan Ф =1.42857

to get the value of  Ф, we will take the tan⁻¹  of both-side

tan⁻¹ tan Ф = tan⁻¹ 1.42857

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3 years ago
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Outside a home, there is a 10-key keypad with the letters A, B, C, D, E, F, G, H, I, and J that can be used to open the garage i
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Answer:

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Since every letter can only be used once, the second letter can only be 9 possible letters.

E.G.: If the first letter is A, the second letter is B-J.

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In math form, figuring out the possible combinations would be written out as so:

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An easier way to write this out would be using "10!", which stands for "10 Factorial"

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