What is the GCF & LCM of 8 and 44

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Answer 1

Answer:

Answer: 44

Step-by-step explanation:

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jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 44 cm3. If nickel plating costs $1 per cm2 and silver plating costs $2 per cm2, find the dimensions of the box to minimize the cost of the materials. (Round your answers to two decimal places.) The box which minimizes the cost of materials has a square base of side length cm and a height of cm.

Answers

Answer:

The box which minimizes the cost of materials has a square base of side length 4.45cm and a height of 2.22 cm.

Step-by-step explanation:

Volume of the jewellery box=44cm³

The box has a square base and is to be built with silver plated sides and nickel plated top and base.

Therefore: Volume = Square Base Area X Height = l²h

l²h=44

h=44/l²

Total Surface Area of a Cuboid =2(lb+lh+bh)

Since we have a square base

Total Surface Area =2(l²+lh+lh)

The Total Surface Area of the box =2l²+4lh

Nickel plating costs $1 per cm³

Silver Plating costs $2 per cm³

Since the sides are to be silver plated and the top and bottom nickel plated:

Therefore, Cost of the Material for the jewellery box =1(2l²)+2(4lh)

Cost, C(l,h)=$(2l²+8lh)

Recall earlier that we derived:

h=44/l²

Substituting into the formula for the Total Cost

Cost, C(l)=2l²+8l(44/l²)

C=2l²+352/l

C=(2l³+352)/l

The minimum costs for the material occurs at the point where the derivative equals zero.

C'=(4l³-352)/l²

4l³-352=0

4l³=352

Divide both sides by 4

l³=88

l=4.45cm

Recall:

h=44/l²=44/4.45²=2.22cm

The box which minimizes the cost of materials has a square base of side length 4.45cm and a height of 2.22 cm.

What is a synthetic division used for

Answers

Answer:

pooping

Step-by-step explanation:

1.poop

2.wipe.

3.eat

4.sleep

Which phrase represents the algebraic expression 3d+7?

Answers

Answer:

3 multiplied by a variable d and add seven to it

Step-by-step explanation:

3 multiplied by a variable d and add seven to it.

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%.

Events A and B are mutually exclusive. Suppose event A occurs with probability 0.02 and event B occurs with probability 0.73. Compute the probability that B occurs or A does not occur (or both). Compute the probability that either B occurs without A occurring or A and B both occur

Answers

Answer:

1. The probability that B occurs or A does not occur (or both) is 0.73.

2. The probability that either B occurs without A occurring or A and B both occur is 0.73.

Step-by-step explanation:

It is given that the events A and B are mutually exclusive. It means the intersection of A and B is 0.

$P(A\cap B)=0$

Given information:

$P(A)=0.02$

$P(B)=0.73$

We get,

$P(A')=1-P(A)=1-0.02=0.98$

$P(B')=1-P(B)=1-0.73=0.27$

(1) We need to find the probability that B occurs or A does not occur (or both).

$P(B\cup A')+P(A\cap B)=P(B)+0$

$P(B\cup A')+P(A\cap B)=0.73+0$

$P(B\cup A')+P(A\cap B)=0.73$

Therefore the probability that B occurs or A does not occur (or both) is 0.73.

(2) We need to find the probability that either B occurs without A occurring or A and B both occur.

$P(B\cup A')+P(A\cap B)=P(B)+0$

$P(B\cup A')+P(A\cap B)=0.73+0$

$P(B\cup A')+P(A\cap B)=0.73$

Therefore the probability that either B occurs without A occurring or A and B both occur is 0.73.

Final answer:

For mutually exclusive events A and B, the probability that B occurs or A does not occur is approximately 1.45. The probability that either B occurs without A occurring or A and B both occur is 0.73 because A and B are mutually exclusive.

Explanation:

Events A and B are defined as mutually exclusive, which means they cannot occur at the same time. Hence, the probability that A and B both occur (referred to as P(A AND B)) is 0. In this question, for the first scenario, we need to compute the probability that B occurs or A does not occur which is denoted as P(B OR not A). Since events A and B are mutually exclusive, not A occurs with probability 1 - P(A) = 0.98. So, P(B OR not A) = P(B) + P(not A) - P(B AND not A) = 0.73 + 0.98 - (0.73 * 0.98) = 1.45 (approximately).

For the second scenario, we need to calculate the probability that either B occurs without A occurring or A and B both occur which is expressed as P((A and B) OR (B and not A)). But as we know P(A and B) = 0 for mutually exclusive events, there only remains P(B and not A). Again, as A and B are mutually exclusive, we can be sure that if B is happening, A is not, so the answer is P(B) = 0.73.

Learn more about Mutually Exclusive Events here:

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Im confused on how to label the thing as its not a perfect shape the question is basically in the photo

Answers

Answer:

Left function: f(x+3)

Right function: f(x)

Step-by-step explanation:

To translate a function, f(x-h) + k is used, where h is the horizontal and k is the vertical shift. Here, x+3 means the graph is shifted 3 units to the left, making it the left graph

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