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SpyIntel [72]
1 year ago
5

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)

So

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.

5 0
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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2x² + 8x + 3

To obtain the required form use the method of completing the square.

The coefficient of the x² term must be 1, thus factor 2 out of 2x² + 8x

= 2(x² + 4x) + 3

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

4 0
3 years ago
What is log Subscript 15 Baseline 2 cubed rewritten using the power property?
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Answer:

D) 3Log15^2

Step-by-step explanation:

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Complete the square to form a perfect square trinomial x^2-14x+
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Answer: x^2 - 14x + 49

Explanation:

1) Divide the coefficient of x by 2:

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2) so you have to add 7^2 = 49

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3) that trinomial is equivalent to:

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

(x - 7)^2  = x^2 - 14x + 49

Then you have to add 49 to complete the square. and form a perfect square trinomial.
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3 years ago
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