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3 years ago

Candace is knitting a scarf. The scarf is 4.6 feet long. if she knits another 1.75 feet, how long will the scarf be?

1 answer:

7 0

All we need to do for this one is add. She is adding on to the length, so we need to add the length before she added on to the length that she did add on.
4.6+1.75=6.35
The scarf will be 6.35 ft long.

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2 years ago

For positive acute angles A and B, it is known that tan A = 35/12 and sin B = 20/29. Find the value of sin(A - B ) in the simple

almond37 [142]

Answer:

$\displaystyle \sin(A-B)=\frac{495}{1073}$

Step-by-step explanation:

We are given that:

$\displaystyle \tan(A)=\frac{35}{12}\text{ and } \sin(B)=\frac{20}{29}$

Where both A and B are positive acute angles.

And we want to find he value of sin(A-B).

Using the first ratio, we can conclude that the opposite side is 35 and the adjacent side is 12.

Then by the Pythagorean Theorem, the hypotenuse is:

$h = \sqrt{35^2 + 12^2} =37$

Using the second ratio, we can likewise conclude that the opposite side is 20 and the hypotenuse is 29.

Then by the Pythagorean Theorem, the adjacent is:

$a=\sqrt{29^2-20^2}=21$

Therefore, we can conclude that:

So, for A, the adjacent is 12, opposite is 35, and the hypotenuse is 37.

For B, the adjacent is 21, opposite is 20, and the hypotenuse is 29.

We can rewrite sin(A-B) as:

$\sin(A-B)=\sin(A)\cos(B)-\cos(A)\sin(B)$

Using the above conclusions, this yields: (Note that since A and B are positive acute angles, all resulting ratios will be positive.)

$\displaystyle \sin(A-B)=\Big(\frac{35}{37}\Big)\Big(\frac{21}{29}\Big)-\Big(\frac{12}{37}\Big)\Big(\frac{20}{29}\Big)$

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$\displaystyle \sin(A-B)=\frac{735-240}{1073}=\frac{495}{1073}$

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3 years ago

A true-false question is to be posed to a husband and wife team. Both the husband and the wife will give the correct answer with

marysya [2.9K]

Answer:

Choose either strategy both are equally successful

Step-by-step explanation:

Given:-

- The probability of success for both husband (H) and wife (W) are:

P ( W ) = 0.8 , P ( H ) = 0.8

Find:-

- Which of the following is a better strategy for the couple?

Solution:-

Strategy 1

- First note that P ( W ) & P ( H ) are independent from one another, i.e the probability of giving correct answer of husband does not influences that of wife's.

- This strategy poses an event such that either wife knows the answer and answer it correctly or the husband knows and answers in correctly.

- We will assume that probability of either the husband or wife knowing the answer is 0.5 and the two events of knowing and answering correctly are independent. So,

P ( Wk ) = P (Hk) = 0.5

- The event P(S1) is:

P(S1) = P ( Hk & H ) + P ( Wk & W )

P(S1) = 0.5*0.8 + 0.5*0.8

P(S1) = 0.8

- Hence, the probability of success for strategy 1 is = 0.8

Strategy 2

- Both agree , then the common answer is selected otherwise, one of their answers is chosen at random.

- The success of strategy 2, will occur when both agree and are correct, wife is correct and answers while husband is not or husband is correct and he answers.

- The event P(S2) is:

P(S2) = P ( H & W ) + P ( H / W' & Hk ) + P ( H' / W & Wk )

P(S2) = P ( H & W ) + P ( H / W') P ( Hk ) + P ( H' / W) P (Wk)

P(S2) = P ( H & W ) + P ( H / W')*0.5 + P ( H' / W)*0.5

P(S2) = 0.5* [ P ( H & W ) + P ( H / W') ] + 0.5* [ P ( H' / W) + P ( H & W )]

P(S2) = 0.5*P(H) + 0.5*P(W)

P(S2) = 0.5*0.8 + 0.5*0.8

P(S2) = 0.8

- Hence, the probability of success for strategy 2 is = 0.8

Both strategy give us the same probability of success.

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3 years ago