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masha68 [24]
1 year ago
12

Which expression gives the length of the transverse axis of the hyperbola

Mathematics
1 answer:
klio [65]1 year ago
7 0

Answer:

Option (B)

Step-by-step explanation:

From the picture attached,

F1 and F2 are the focii of the hyperbola.

Point P(x, y) is x units distant from F1 and y units distant from the other focus F2.

By the definition of a hyperbola,

"Difference between the distances of a point from the focii is always constant and equals to the measure of transverse axis."

Difference in the distances of point P from focii F1 and F2 = (x - y) units

This distance is equal to the length of the transverse axis = (x - y) units

Therefore, Option (B) will be the answer.

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Two production lines produce the same parts per week of which 100 are defective. Line 2 produces 2,000 parts per week of which 1
Vikentia [17]

Answer:

(a) 0.0833 or 8.33%

(b) 0.40 or 40%

Step-by-step explanation:

Parts line one (n1) = 1,000 parts

Defects line one (d1) = 100 parts

Parts line two (n2) = 2,000 parts

Defects line two (d2) = 150 parts

Total number of parts (n) = 3,000 parts

a. Probability of a randomly selected part being defective:

P(d) = \frac{d_1+d_2}{n_1+n_2}=\frac{100+150}{1,000+2,000}\\P(d) =0.0833=8.33\%

The probability is 0.0833 or 8.33%

b. Probability of a part being produced by line one, given that it is defective:

P(1|d)=\frac{P(1\cap d)}{P(1\cap d)+P(2\cap d)}\\P(1|d)=\frac{\frac{100}{3,000} }{\frac{100}{3,000}+\frac{150}{3,000}}\\P(1|d)=0.4 = 40\%

The probability is 0.40 or 40%.

5 0
1 year ago
After working satisfactorily for 6 months, Dave received a 7% raise. His original gross monthly salary was $1083.34. What is Dav
Dmitriy789 [7]

Answer:

Step-by-step explanation:

His original gross monthly salary was $1083.34. This means that the total amount that he earned that he earned in the first 6 months would be

6 × 1083.34 = $6500.4

After working satisfactorily for 6 months, Dave received a 7% raise. The amount by which it was raised would be

7/100 × 6500.4 = $455.00

His salary for the next 6 months would be

6500.4 + 455.00 = $6955.40

Dave's gross annual salary would be

6955.40 + 6500.4

= $13455.8

7 0
1 year ago
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Two pounds of sugar cost $1.40. How much sugar do you get per dollar? Round your answer to the nearest hundredth, if necessary.
Vsevolod [243]

Answer:

1.429 lbs per dollar of sugar

Step-by-step explanation:

multiply by 5 get 10 lbs of sugar for 7 dollars divide by 7 get 1.4285 round up

5 0
2 years ago
Which is a solution to the equation? (x −2)(x + 5) = 18 x = −10 x = −7 x = −4 x = −2
Leona [35]

Answer:

Solutions:

x=-7

x=4

Step-by-step explanation:

(x-2)(x + 5) = 18

Expanding the factored form:

x^2+5x-2x-10=18

x^2+3x-28=0

Factoring the second-degree polynomial:

(x+7)(x-4)=0

This is true for

x=-7 \text{ or } x=4

4 0
1 year ago
In a survey of 200 people, 37% had a son, 31% had a daughter, and 23% had both a son and a daughter. What is the conditional pro
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About 46 people because that is 23% of 200
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