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2 years ago

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the volume of a rectangle prism with square bases is 5880 cubic inches. it has a height of 30 inches. find the side length of th

e square base.

1 answer:

Delicious77 [7]2 years ago

8 0

A prism with square bases is just a square prism.

The volume of a rectangular prism is equal to its width times its length times its height. Since the base is a square, we can just say it's equal to the base squared times the height. Let's set up a formula, plug and chug.

$V = b^2h \\ 5880 = 30b^2 \\ 196 = b^2 \\ \sqrt{196} = b \\ \boxed{14 = b}$

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Solve for x7(x 2) (x 5)44O -16

babymother [125]

7(x + 2) = 6(x + 5)

7x + 14 = 6x + 30 |subtract 14 from both sides

7x = 6x + 16 |subtract 6x from both sides

x = 16

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2 years ago

PLS HELP BRAINLIEST WILL BE GIVEN :D

disa [49]

Answer:

56

Step-by-step explanation:

By tracing the lines on the tree diagram, we see the probability of both being red is 0.5 × 0.6 = 0.3.

The probability of both being blue is 0.5 × 0.4 = 0.2.

So we would expect to get both blue 2/3 of the times we get both red.

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X = 56

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2 years ago

A 10-pound block of ice melts at a rate of 3% per hour. Find the weight of the block of ice after 1 day.

mylen [45]

Answer:

The weight of the block of ice after 1 day is of 4.81 pounds.

Step-by-step explanation:

Equation for exponential decay:

The equation that models an amount after t hours, subject to exponential decay, is given by:

$A(t) = A(0)(1 - r)^t$

In which A(0) is the initial amount and r is the decay rate, as a decimal.

A 10-pound block of ice melts at a rate of 3% per hour.

This means that $A(0) = 10, r = 0.03$

So

$A(t) = A(0)(1 - r)^t$

$A(t) = 10(1 - 0.03)^t$

$A(t) = 10(0.97)^t$

Find the weight of the block of ice after 1 day.

One day has 24 hours, so this is A(24).

$A(24) = 10(0.97)^{24} = 4.81$

The weight of the block of ice after 1 day is of 4.81 pounds.

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2 years ago

The arrivals of clients at a service firm in Santa Clara is a random variable from Poisson distribution with rate 2 arrivals per

ICE Princess25 [194]

Answer:

1.76% probability that in one hour more than 5 clients arrive

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

The arrivals of clients at a service firm in Santa Clara is a random variable from Poisson distribution with rate 2 arrivals per hour.

This means that $\mu = 2$

What is the probability that in one hour more than 5 clients arrive

Either 5 or less clients arrive, or more than 5 do. The sum of the probabilities of these events is decimal 1. So

$P(X \leq 5) + P(X > 5) = 1$

We want P(X > 5). So

$P(X > 5) = 1 - P(X \leq 5)$

In which

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353$

$P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707$

$P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707$

$P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1804$

$P(X = 4) = \frac{e^{-2}*2^{4}}{(4)!} = 0.0902$

$P(X = 5) = \frac{e^{-2}*2^{5}}{(5)!} = 0.0361$

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.1353 + 0.2702 + 0.2702 + 0.1804 + 0.0902 + 0.0361 = 0.9824$

$P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9824 = 0.0176$

1.76% probability that in one hour more than 5 clients arrive

8 0

2 years ago

Read 2 more answers

— 7х + Зу = 2<br> Which ordered pair is a solution of the equation

lidiya [134]

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2 years ago