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____ [38]
2 years ago
14

During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea

should the caterer bring if there are 16 cups in one gallon?
gallons
Mathematics
2 answers:
allsm [11]2 years ago
8 0
The answer is 30.
There are 16 cups in a gallon. And 120 minutes in 2 hours. so multiple 
16*120 which is 480. Then divide 480/120 and get 30 as your answer
Nostrana [21]2 years ago
8 0

we know that

An average of 4 cups of tea are poured per minute

Step 1

Find the number of cups that are poured in two hours by proportion

Remember that

2\ hours=120\ minutes

\frac{4}{1} \frac{cups}{minute} =\frac{x}{120}\frac{cups}{minutes} \\ \\x=120*4 \\ \\x=480\ cups

Step 2

Convert cups to gallons by proportion

Remember that

16\ cups=1\ gallon

\frac{1}{16} \frac{gallon}{cups} =\frac{x}{480} \frac{gallons}{cups} \\ \\x=480/16 \\ \\x=30\ gallons

therefore

the answer is

30\ gallons

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Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.
TiliK225 [7]

we know that

For a polynomial, if x=a is a zero of the function, then (x−a) is a factor of the function. The term multiplicity, refers to the number of times that its associated factor appears in the polynomial.

So

In this problem

If the cubic polynomial function has zeroes at 2, 3, and 5

then

the factors are

(x-2)\\ (x-3)\\ (x-5)

Part a) Can any of the roots have multiplicity?

The answer is No

If a cubic polynomial function has three different zeroes

then

the multiplicity of each factor is one

For instance, the cubic polynomial function has the zeroes

x=2\\ x=3\\ x=5

each occurring once.

Part b) How can you find a function that has these roots?

To find the cubic polynomial function multiply the factors and equate to zero

so

(x-2)*(x-3)*(x-5)=0\\ (x^{2} -3x-2x+6)*(x-5)=0\\ (x^{2} -5x+6)*(x-5)=0\\ x^{3} -5x^{2} -5x^{2} +25x+6x-30=0\\ x^{3}-10x^{2} +31x-30=0

therefore

the answer Part b) is

the cubic polynomial function is equal to

x^{3}-10x^{2} +31x-30=0

7 0
2 years ago
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Which shows the four-term polynomial and factored form of x2 + 6x-27?
blsea [12.9K]

Answer:

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Step-by-step explanation:

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2 years ago
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Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers have maintained careful records
madreJ [45]

Answer:

For this case we have the following info related to the time to prepare a return

\mu =90 , \sigma =14

And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the standard deviation would be:

\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2

And the best answer would be

b. 2 minutes

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

For this case we have the following info related to the time to prepare a return

\mu =90 , \sigma =14

And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the standard deviation would be:

\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2

And the best answer would be

b. 2 minutes

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The circumference of Mars is 7.00 x 107. Which planet is larger, and by how many feet? Write the answer in both standard and sci
Rasek [7]

Answer:

34

Step-by-step explanation:

the....

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What is the following difference?
Svetllana [295]

Answer:

  -7ab\sqrt[3]{3ab^2}

Step-by-step explanation:

Remove perfect cubes from under the radical and combine like terms.

  2ab\sqrt[3]{192ab^2}-5\sqrt[3]{81a^4b^5}=2ab\sqrt[3]{4^3\cdot 3ab^2}-5\sqrt[3]{(3ab)^3\cdot 3ab^2}\\\\=(8ab -15ab)\sqrt[3]{3ab^2}=\boxed{-7ab\sqrt[3]{3ab^2} }

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