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Alex_Xolod [135]

3 years ago

8

John wants to make two frames for his artwork. One frame requires 3 1/2 feet of molding the other requires 4 2/3 feet of the sam

e kind of molding. If he already has 8 3/5 feet of molding in his workshop, does he need to buy any more.

1 answer:

Damm [24]3 years ago

4 0

no because if you make each fraction equal , the first would be 3 3/6 feet of molding and the other would be 4 4/6 feet and if you add those together you would get 8 1/6 which is less than 8 3/5

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Calculate the Social Security and Medicare tax that would be applied to an annual salary of $235,430. Use $106,800 for maximum t

Artemon [7]

<span>Social Security tax is a percentage that both employees and employers must contribute 6.2% of employee compensation, for a total of 12.4%. The social security that would be applied to an annual salary of $235,430 using $106,800 as the maximum taxable income is 12.4% of $106,800 = 0.124 x $106,800 = $13,243.20 The Medicare payroll tax is 2.9%. It applies only to earned income, which is wages you are paid by an employer, plus tips. You're responsible for 1.45% of the tax, and it's deducted automatically from your paycheck. Your employer pays the other 1.45% The Medicare tax that would be applied to an annual salary of $235,430 using $106,800 as the maximum taxable income is 2.9% of $106,800 = 0.029 x $106,800 = $3,097.20 </span>

5 0

3 years ago

5x+7 but the given x=6

lions [1.4K]

Answer:

37

Step-by-step explanation:

5 x 6 = 30

30+7=37

8 0

2 years ago

Read 2 more answers

A company makes steel rods shaped like cylinders. Each rod has a diameter of 4 centimeters and a height of 60 centimeters. If th

gavmur [86]

Answer:

See below.

Step-by-step explanation:

1) Please check the number of volume of steel. It should be 54,259.2

${cm}^{3}$

. Not 54,259.2 cm. Right?

2) If so,

First

The volume of single rod

$= \pi \times ( { \frac{4}{2} })^{2} \times 60= \pi \times {2}^{2} \times 60= 4\pi \times 60= 4 \times 3.14 \times 60= 753.6 {cm}^{3}$

The number of rods

$= \frac{54259.2}{753.6} = 72$

5 0

3 years ago

Kasey needs 1.5 cups of milk and 4 cups of sugar to make 12 muffins. She plans to make 36 muffins . How many fl oz of sugar does

Masja [62]

Answer:

12 cups of milk

Step-by-step explanation:

36/12= 3

4 x 3= 12

So the Answer is 12 cups of milk

4 0

3 years ago

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.† (a) For

SpyIntel [72]

Answer:

a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring

b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

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

$Z = \frac{X - \mu}{\sigma}$

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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.71$

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?

Here $n = 16$ , we want $P(X \geq 13)$ . So

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 13) = C_{16,13}.(0.71)^{13}.(0.29)^{3} = 0.1591$

$P(X = 14) = C_{16,14}.(0.71)^{14}.(0.29)^{2} = 0.0835$

$P(X = 15) = C_{16,15}.(0.71)^{15}.(0.29)^{1} = 0.0273$

$P(X = 16) = C_{16,16}.(0.71)^{16}.(0.29)^{0} = 0.0042$

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) = 0.1591 + 0.0835 + 0.0273 + 0.0042 = 0.2741$

0.2741 = 27.41% probability that at least 13 believe global warming is occurring

(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?

Now $n = 160$ . So

$\mu = E(X) = np = 160*0.71 = 113.6$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{160*0.71*0.29} = 5.74$

Using continuity correction, this is $P(X \geq 110 - 0.5) = P(X \geq 109.5)$ , which is 1 subtracted by the pvalue of Z when X = 109.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{109.5 - 113.6}{5.74}$

$Z = -0.71$

$Z = -0.71$ has a pvalue of 0.2389

1 - 0.2389 = 0.7611

0.7611 = 76.11% probability that at least 110 believe global warming is occurring

3 0

3 years ago