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gogolik [260]
3 years ago
13

The length of a rectangle is 3 more than twice its width. the perimeter is 48 feet. find the width.

Mathematics
1 answer:
zepelin [54]3 years ago
8 0
48 = 2l + 2w
l = 3w

48 = 2(3w) + 2w
48 = 6w + 2w
48 = 8w
6 = w

The width is 6 feet. The length is 18 feet. Hope this helps! :)

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A shipment of 12 microwave ovens contains three defective units. A vending company has ordered four units, and because each has
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Answer:a) 54/55

b) 100/110

c) 99/110

Step-by-step explanation:

a)Probability of ordering 4= 9/12×3/11×2/10×1/9 = 54/11880

Probability of 4 good units= 4 × 54/11880

= 216/11880

1/55

1-(1/55) = 54/55

b)Probability of 2 good units= 2 × 54/(11880)

= 108/11880

= 1/110

1- (1/110)= 100/110

c) Probability of exactly 2 units not good= 1 -(100/110) =99/110

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3 years ago
Hep I’m bout to fail if I don’t get this right will give brainless if correct
nalin [4]

Answer:

x = 4

ac = 56

Step-by-step explanation:

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7x - 6x = 3+ 1

6x + 3  + 7x + 1 = 56

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3 years ago
A bag contains 4 blue marbles and 2 yellow marbles. Two marbles are randomly chosen (the first marble is NOT replaced before dra
VMariaS [17]

Answer:

0.4 = 40% probability that both marbles are blue.

0.0667 = 6.67% probability that both marbles are yellow.

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If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

Step-by-step explanation:

To solve this question, we need to understand conditional probability(for the final question) and the hypergeometric distribution(for the first three, because the balls are chosen without being replaced).

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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)!}

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

What is the probability that both marbles are blue?

4 + 2 = 6 total marbles, which means that N = 6

4 blue, which means that k = 4

Sample of 2, which means that n = 2

This is P(X = 2). So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,6,2,4) = \frac{C_{4,2}*C_{2,0}}{C_{6,2}} = 0.4

0.4 = 40% probability that both marbles are blue

What is the probability that both marbles are yellow?

4 + 2 = 6 total marbles, which means that N = 6

2 yellow, which means that k = 2

Sample of 2, which means that n = 2

This is P(X = 2). So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,6,2,2) = \frac{C_{2,2}*C_{4,0}}{C_{6,2}} = 0.0667

0.0667 = 6.67% probability that both marbles are yellow.

What is the probability of one blue and then one yellow?

Total is 100%.

Can be:

Both blue(40%)

Both yellow(6.67%)

One blue and one yellow(x%). So

40 + 6.67 + x = 100

x = 100 - 46.67

x = 53.33

53.33% probability of one blue and then one yellow.

If you are told that both selected marbles are the same color, what is the probability that both are blue?

Conditional probability.

Event A: Both same color

Event B: Both blue

Probability of both being same color:

Both blue(40%)

Both yellow(6.67%)

This means that P(A) = 0.4 + 0.0667 = 0.4667

Probability of both being the same color and blue:

40% probability that both are blue, which means that P(A \cap B) = 0.4

Desired probability:

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.4667} = 0.8571

If you are told that both selected marbles are the same color, 0.8571 = 85.71% probability that both are blue

8 0
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Degger [83]

Answer:

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= x²+4x+4-6

= x²+4x-3

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UkoKoshka [18]

Answer:

x=y-48, y=x+48

Step-by-step explanation:

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