You and your friend skate at the same rate.You complete 5 laps in 7 minutes.How long does your friend take to complete 15 laps?

If cos theta=-3/5 in quadrant 2 what is sin theta? A:4/5 B:3/4 C:-3/4 D:-4/5

Scrat [10]

Answer: Choice A) 4/5

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Work Shown:

cos^2(theta) + sin^2(theta) = 1
(-3/5)^2 + sin^2(theta) = 1
9/25 + sin^2(theta) = 1
9/25 + sin^2(theta) - 9/25 = 1 - 9/25
sin^2(theta) = 1 - 9/25
sin^2(theta) = 25/25 - 9/25
sin^2(theta) = (25 - 9)/25
sin^2(theta) = 16/25
sqrt[sin^2(theta)] = sqrt[16/25]
sin(theta) = 4/5

The fact that sine is positive in quadrant 2 means that the result is positive.

8 0

3 years ago

8x+15≤51 slove.PLEASE HELP MEEEEEEEEEEEEEEE

inysia [295]

Answer:

x≤9/2

Step-by-step explanation:

8x+15≤51

Subtract 15

8x+15-15≤51-15

8x+≤36

Divide by 8

8x/8≤36/8

x≤9/2

7 0

3 years ago

Solve 7x - 2z = 4- xy for x.

ExtremeBDS [4]

Answer:

0

Step-by-step explanation:

7x + -2z = 4 + -1xy

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add 'xy' to each side of the equation.

7x + xy + -2z = 4 + -1xy + xy

Combine like terms: -1xy + xy = 0

7x + xy + -2z = 4 + 0

7x + xy + -2z = 4

Add '2z' to each side of the equation.

7x + xy + -2z + 2z = 4 + 2z

Combine like terms: -2z + 2z = 0

7x + xy + 0 = 4 + 2z

7x + xy = 4 + 2z

Reorder the terms:

-4 + 7x + xy + -2z = 4 + 2z + -4 + -2z

Reorder the terms:

-4 + 7x + xy + -2z = 4 + -4 + 2z + -2z

Combine like terms: 4 + -4 = 0

-4 + 7x + xy + -2z = 0 + 2z + -2z

-4 + 7x + xy + -2z = 2z + -2z

Combine like terms: 2z + -2z = 0

-4 + 7x + xy + -2z = 0

8 0

4 years ago

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection.

This means that,

Probability that at least one of them needs replacement at the first inspection =

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

5 0

3 years ago

Answer for brainliest!!! :> Three hens can lay 3 eggs in 3 days. How many hens would lay 3 eggs in 9 days?

marta [7]

It would still be the same 3 hens in 9 days.

6 0

3 years ago

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