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Vlada [557]
3 years ago
9

Consider the figure below. Line FG is parallel to line JK.

Mathematics
1 answer:
Svet_ta [14]3 years ago
6 0

Answer:

A. a = 10

B. m<FNT = 120°

C. m<KTU = 60°

Step-by-step explanation:

A. (7a + 50)° and (14a - 20)° are corresponding angles. Therefore:

(7a + 50)° = (14a - 20)°

Use this equation to find the value of a

7a + 50 = 14a - 20

Combine like terms

7a - 14a = - 50 - 20

-7a = -70

Divide both sides by -7

-7a/-7 = -70/-7

a = 10

B. m<FNT = (14a - 20)° (alternate interior angles are congruent)

Plug in the value of a

m<FNT = 14(10) - 20

m<FNT = 140 - 20

m<FNT = 120°

C. m<KTU + (14a - 20)° = 180° (linear pair)

Plug in the value of a

m<KTU + 14(10) - 20 = 180

m<KTU + 120 = 180

m<KTU + 120 - 120 = 180 - 120

m<KTU = 60°

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4 years ago
Two factories I and II produce phones for brand ABC. Factory I produces 60% of all ABC phones, and factory II produces 40%. 10%
denpristay [2]

Answer:

0.3721 or 37.21%

Step-by-step explanation:

P(I) = 0.60; P(II) = 0.40;

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The probability that the phone came from factory II, given that is not defective, is determined by the probability of a phone from factory II not being defective divided by the probability of a phone not being defective.

P(II|not) = \frac{P(II)*P(not_{II})}{P(II)*P(not_{II})+P(I)*P(not_{I})}\\P(II|not) = \frac{0.40*0.80}{0.40*0.80+0.60*0.90}\\ P(II|not) =0.3721 = 37.21\%

The probability is 0.3721 or 37.21%.

4 0
3 years ago
Suppose you were looking at the histogram of the incomes of all of the households in the United States. Do you think that the hi
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Answer:

The histogram is right-skewed.

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Not many people earn a high income. So the proportions of people decreases as the income increases.

Most of the people earn a medium income. So the mode of the data would be somewhere in the start of the the distribution.

There are many households that earn a low income. But this proportion is not more than the proportion of people earning low income.

So the histogram for income distribution will have a long right tail with maximum data at the starting point.

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8 0
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x=\dfrac{y}{3}   ...(i)

x+y=y^2-5       ...(ii)

Put value of x from (i) in (ii)

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7 0
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σ = 0.988297

 

Going back to the confidence interval:

Confidence interval = 1.83 ± (2.58) (0.988297)

Confidence interval = 1.83 ± 2.55

Confidence interval = -0.72, 4.38

3 0
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