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1 year ago

Rhonda can travel 45 miles in 3 hours while on her skateboard. at this rate, how many hours does it take to travel 1 mile

Mathematics

1 answer:

Rasek [7]1 year ago

6 0

The question is relating Rhonda's distance travelled and time taken

If 45 miles = 3 hours

Then, 1 mile = 3/45 hours

$=\frac{1}{15}$

Therefore, it will take Rhonda 1/15 hours to travel 1 mile.

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△ABC has interior angles with measures 130°, x°, and 15°, and △DEF has interior angles with measures 35°, 15°, and y°. Using the

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It is y=130 because they are congruent

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3 years ago

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A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.93. Assume indepen

noname [10]

Answer:

There is a 99.99998% probability that at least one valve opens.

Step-by-step explanation:

For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 5, p = 0.93$

Calculate P(at least one valve opens).

This is $P(X \geq 1)$

Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:

$P(X = 0) + P(X \geq 1) = 1$

$P(X \geq 1) = 1 - P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.93)^{0}.(0.07)^{5} = 0.0000016807$

Finally

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000016807 = 0.9999983193$

There is a 99.99998% probability that at least one valve opens.

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3 years ago

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Express 2x^2+8x+3 in the form 2(x+p)^2+q

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Answer:

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add/subtract ( half the coefficient of the x- term)² to x² + 4x

= 2(x² + 2(2)x + 4 - 4) + 3

= 2(x + 2)² - 8 + 3

= 2(x + 2)² - 5

with p = 2 and q = - 5

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3 years ago

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Answer:

D) 3Log15^2

Step-by-step explanation:

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4) prove that using the formula (a - b)^2 = a^2 - 2ab + b^2

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