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tigry1 [53]
3 years ago
12

Which of the following points lie in the solution set to the following system of inequalities?

Mathematics
1 answer:
emmasim [6.3K]3 years ago
6 0
<h3>Answer:</h3>

B. (5, -2)

<h3>Step-by-step explanation:</h3>

Try the points in the inequalities and see what works. Here, we evaluate the point in the first inequality, and if that works, then the second inequality.

A. 2 ≤ -(-5) -5 . . . ⇒ . . . 2 ≤ 0 . . . false

B. -2 ≤ 5 -5 . . . true

... -2 ≥ -(5) -4 . . . true . . . . . . selection B is a viable choice

C. we know from A that the first inequality will be satisfied

... -2 ≥ -(-5) -4 . . . ⇒ . . . -2 ≥ 1 . . . false

D. 2 ≤ 5 -5 . . . . false

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Please answer this correctly
DENIUS [597]

Answer:

The correct answer is

<u>379.94</u> cm^2

Use the equation pir^2 to find the area. If you need to find the radius make sure to divide the diameter my 2

Hope this helps! If u have anymore questions i'd love to help!

- Quinn

4 0
3 years ago
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A boat can travel 21mph in still water. If it travels 270 miles with the current in the same length of time it travels 108 miles
erica [24]

Answer: the speed of the current is 9 mph.

Step-by-step explanation:

Let x represent the speed of the current.

A boat can travel 21 mph in still water. If it travels 270 miles with the current. It means that the total speed with which the boat travelled with the current is (21 + x) mph.

Time = distance/speed

Time spent by the boat in travelling 270 miles is

270/(21 + x)

In the same length of time, it travels 108 miles against the current. It means that the total speed with which the boat travelled against the current is (21 - x) mph.

Time = distance/speed

Time spent by the boat in travelling 108 miles is

108/(21 - x)

Since the time is the same, then

270/(21 + x) = 108/(21 - x)

270(21 - x) = 108(21 + x)

5670 - 270x = 2268 - 108x

108x + 270x = 5670 - 2268

378x = 3402

x = 3402/378

x = 9

7 0
3 years ago
Suppose a bag contains many marbles, 54% of which are purple. You draw 5 marbles from the bag with replacement.
dolphi86 [110]

Part A

Use the binomial probability distribution formula.

p = 0.54 = probability of getting a purple marble

n = 5 = sample size

x = 2 = number of purple we want to get

P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}\\\\P(2) = \frac{5!}{2!(5-2)!}*0.54^2*(1-0.54)^{5-2}\\\\P(2) = 10*0.54^2*0.46^3\\\\P(2) = 0.283831776\\\\

The \frac{n!}{x!(n-x)!} portion is from the nCr combination formula. The exclamation marks indicate a factorial.

Alternatively, you could use Pascal's Triangle for that portion.

<h3>Answer: 0.283831776</h3>

This decimal value is exact. Round it however you need to.

============================================================

Part B

To find the expected value, aka the mean, we multiply the sample size and probability of getting a purple marble on any single selection.

n*p = 5*0.54 = 2.7

<h3>Answer: 2.7</h3>
6 0
2 years ago
Solve m=10x-1x for x
saveliy_v [14]

Answer:

x = 1/9m good luck........

6 0
3 years ago
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Which of the following is true for the relation f(x) = x2 + 8? Only the inverse is a function. Both the equation and its inverse
Alchen [17]

<u>ANSWER</u>

Only the equation is a function

<u>EXPLANATION</u>

f(x)=x^2+8 is graphed above with its inverse f^{-1}(x)=\pm \sqrt{x-8}.


We perform the vertical line test for both the equation and its inverse.


The equation f(x)=x^2+8 passed the vertical line hence it is a function.

However, f^{-1}(x)=\pm \sqrt{x-8} failed the vertical line test, hence it is not a function.


3 0
3 years ago
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