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Ksivusya [100]
3 years ago
7

Solve the inequality. Graph the solution. 7z< -28

Mathematics
1 answer:
Zepler [3.9K]3 years ago
6 0

Answer: The answer is -9

Step-by-step explanation:

7z<-28= -9

Because we take the -28 and add 19 because that's the common denominator and we come up with -9

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Determine if events A and B are mutually exclusive.
gladu [14]

Answer:

A) Not mutually exclusive

Step-by-step explanation:

Given

P(A) = \frac{1}{4}

P(B) = \frac{3}{5}

P(A\ or\ B) = \frac{7}{10}

Required

Determine if they are mutually exclusive or not

Mutually exclusive are defined by:

P(A\ or\ B) = P(A) + P(B)

So, we have:

P(A\ or\ B) = \frac{1}{4} + \frac{3}{5}

Take LCM

P(A\ or\ B) = \frac{5+12}{20}

P(A\ or\ B) = \frac{17}{20}

By comparing:

P(A\ or\ B) = \frac{17}{20} ---- Calculated

P(A\ or\ B) = \frac{7}{10} ---- Given

We can conclude that A and B are not mutually exclusive because:

\frac{17}{20} \ne \frac{7}{10}

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timothy's video game the levels starts with 30 aliens each worth five points Timothy already shot 6 of them how many more points
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2 years ago
The rate at which rain accumulates in a bucket is modeled by the function r given by r(t)=10t−t^2, where r(t) is measured in mil
mars1129 [50]

Answer:

36 milliliters of rain.

Step-by-step explanation:

The rate at which rain accumluated in a bucket is given by the function:

r(t)=10t-t^2

Where r(t) is measured in milliliters per minute.

We want to find the total accumulation of rain from <em>t</em> = 0 to <em>t</em> = 3.

We can use the Net Change Theorem. So, we will integrate function <em>r</em> from <em>t</em> = 0 to <em>t</em> = 3:

\displaystyle \int_0^3r(t)\, dt

Substitute:

=\displaystyle \int_0^3 10t-t^2\, dt

Integrate:

\displaystyle =5t^2-\frac{1}{3}t^3\Big|_0^3

Evaluate:

\displaystyle =(5(3)^2-\frac{1}{3}(3)^3)-(5(0)^2-\frac{1}{3}(0)^3)=36\text{ milliliters}

36 milliliters of rain accumulated in the bucket from time <em>t</em> = 0 to <em>t</em> = 3.

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