MATHEMATICS COLLEGE

The design of a concrete mix requires 2,314 lb/yd3 of gravel having a moisture content of 3.5% and absorption of 4.2%, and 899 lb/yd3 of sand having a moisture content of 5.7% and absorption of 1.4%, and 244 lb/yd3 of free water. What is the weight of the mixing water per cubic yard that should be used at the job site?

Answers

Answer 1

Answer:

Answer:

Weight of mixing water=224.541 lb

Step-by-step explanation:

Taking 1 cubic yard of concrete

Mass of gravel = 2314 lb

Moisture content = 3.5% Absorption 4.2%

Extra water needed = (4.2-3.5)*2314/100= 16.198 lb

Mass of sand= 899 lb

Moisture content = 5.7% Absorption =1.4%

Water released = (5.7-1.4)*899/100= 38.657 lb

Free water = 244 lb

Weight of mixing water = free water + extra water needed-water released = 244+16.198-38.657=224.541 lb

Weight of mixing water=224.541 lb

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Jenny drove 715 miles in 11 hours.At the same rate, how long would it take her to drive 325 miles?

Answers

5 hours

715/11 = 65
325/65 = 5

Suppose 41%41% of American singers are Grammy award winners. If a random sample of size 860860 is selected, what is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%5%?

Answers

Answer:

99.72% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{(p(1-p))/(n)}$

In this question:

$n = 860, p = 0.41$

$\mu = 0.41, s = \sqrt{(0.41*0.59)/(860)} = 0.0168$

What is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%?

This is the pvalue of Z when X = 0.41 + 0.05 = 0.46 subtracted by the pvalue of Z when X = 0.41 - 0.05 = 0.36. So

X = 0.46

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (0.46 - 0.41)/(0.0168)$

$Z = 2.98$

$Z = 2.98$ has a pvalue of 0.9986

X = 0.36

$Z = (X - \mu)/(s)$

$Z = (0.36 - 0.41)/(0.0168)$

$Z = -2.98$

$Z = -2.98$ has a pvalue of 0.0014

0.9986 - 0.0014 = 0.9972

99.72% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%.

a tree needs to be stake with four wires, each wire is attached to the trunk 6 feet above the ground, and then anchored to the ground 8 feet from the base of the tree. How many feet of the wire is needed for 5 trees???

Answers

Answer:

Step-by-step explanation:

A student purchases school supplies at a store where the sale tax is 7%. The pre-tax price of the supplies is $48. What is the total cost of the supplies?

Answers

$51.36

$1.07 * 48 = 51.36$
to add 7% to the pre-price, simply multiply the pre-price by 1.07, do this to automatically get the total. I personally see % as decimals so that helps me figure out where to start.

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Answers

Answer:

y = -7/5x - 6.7

Step-by-step

y = -7/5x + 6. A Line that is parallel will always have the same slope. The slope is m. m in this situation = -7/5x. A lines equation is y = mx + b. m = -7/5. y = -7/5x + b. Now to find b we can substitute the given point which goes through the new line, (2, -6). In this point x =2 and y = -6. Now substitute the x and y values into our equation. y = -7/5x + b is now -6 = -7/5(2) + b. -7/5(2) = -7/10. -6 = 7/10 + b. Subtract 7/10 from -6. Its -6 and 7/10 or -6.7 . -6.7 = b. b = -6.7. Now substitute the b value into the equation. y = -7/5x -6.7.

Please Help !!!The line above goes through points (-5,5) and (0,3). What is the slope-intercept form of the equation of the line above?

A. y = (-5/2)x - 3

B. y = (-2/5)x + 3

C. y = (-2/5)x - 3

D. y = (2/5)x + 3

Answers

Answer:

Step-by-step explanation:

The equation we must find is in y = mx + b form. We are given that it intercepts (0,3), so the y-intercept it 3 and b = 3. We can find the slope with the two points we are given: m = (3-5)/(0(-5)) = -2/5. Substituting these values, we find: y = (-2/5)x + 3

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