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3 years ago

6. Christopher wants to leave a 15% tip for his breakfast. His breakfast cost $23.00, how

Mathematics

1 answer:

Anestetic [448]3 years ago

7 0

Answer:

$3.45

Step-by-step explanation:

The tip is 15% of his breakfast, that means 15% of 23

That is 15%* 23= 15*23/100= 3.45 $

The tip is $3.45

Have a good day.

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-13m = 1 - 14m what is the answer

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Answer:

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If 2tanA=3tanB then prove that, tan(A+B)= 5sin2B/5cos2B-1

Fed [463]

By definition of tangent,

tan(A + B) = sin(A + B) / cos(A + B)

Using the angle sum identities for sine and cosine,

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

yields

tan(A + B) = (sin(A) cos(B) + cos(A) sin(B)) / (cos(A) cos(B) - sin(A) sin(B))

Multiplying the right side by 1/(cos(A) cos(B)) uniformly gives

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) tan(B))

Since 2 tan(A) = 3 tan(B), it follows that

tan(A + B) = (3/2 tan(B) + tan(B)) / (1 - 3/2 tan²(B))

… = 5 tan(B) / (2 - 3 tan²(B))

Putting everything back in terms of sin and cos gives

tan(A + B) = (5 sin(B)/cos(B)) / (2 - 3 sin²(B)/cos²(B))

Multiplying uniformly by cos²(B) gives

tan(A + B) = 5 sin(B) cos(B) / (2 cos²(B) - 3 sin²(B))

Recall the double angle identities for sin and cos:

sin(2x) = 2 sin(x) cos(x)

cos(2x) = cos²(x) - sin²(x)

and multiplying uniformly by 2, we find that

tan(A + B) = 10 sin(B) cos(B) / (4 cos²(B) - 6 sin²(B))

… = 10 sin(B) cos(B) / (4 (cos²(B) - sin²(B)) - 2 sin²(B))

… = 5 sin(2B) / (4 cos(2B) - 2 sin²(B))

The Pythagorean identity,

cos²(x) + sin²(x) = 1

lets us rewrite the double angle identity for cos as

cos(2x) = 1 - 2 sin²(x)

so it follows that

tan(A + B) = 5 sin(2B) / (4 cos(2B) + 1 - 2 sin²(B) - 1)

… = 5 sin(2B) / (4 cos(2B) + cos(2B) - 1)

… = 5 sin(2B) / (4 cos(2B) - 1)

as required.

5 0

2 years ago

A recent survey concluded that the proportion of american teenagers who have a cell phone is 0.27. the true population proportio

Jet001 [13]

Answer:

The mean for the sampling distribution of the sample proportion is 0.29

The standard deviation for the sampling distribution of the sample proportion is 0.01435

Step-by-step explanation:

The mean for the sampling distribution of the sample proportion is always equal to the true population proportion, in this case; p = 0.29

The standard deviation for the sampling distribution of the sample proportion is calculated as;

$\sqrt{\frac{p(1-p)}{n} }$

Using the given values;

p = 0.29

1 - p = 0.71

n = 1000

The standard deviation becomes;

$\sqrt{\frac{(0.29)(1-0.29)}{1000} } \\$

The s.d becomes 0.01435

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3 years ago