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3 years ago

Solve (x + 5 < 4) ∩ (x - 3 > -6).

Mathematics

1 answer:

LenaWriter [7]3 years ago

3 0

Answer:

$\large\boxed{-3$

Step-by-step explanation:

$x+5-3\\\\x-3\to-3$

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What is the factored form of 8x^2 + 12x

Crazy boy [7]

The answer is the following:

4x(2x+3)

hope it helped :)

6 0

3 years ago

Read 2 more answers

Stacy rolls a pair of six-sided fair dice.

insens350 [35]

Answer:

Pr(the sum of the numbers rolled is either a multiple of 3 or an even number)= $\frac{2}{3}$

Step-by-step explanation:

Let A be the event "sum of numbers is multiple of 3"

and B be the event "sum is an even number".

As our dice has six sides, so the sample space of two dices will be of 36 ordered pairs.

|sample space | = 36

Out of which 11 pairs have the sum multiple of 3 and 18 pairs having sum even.

So Pr(A)= $\frac{11}{36}$

and Pr(B)= $\frac{18}{36}$

and Pr(A∩B) = $\frac{5}{36}$ , as 5 pairs are common between A and B.

So now Pr(A or B)= Pr(A∪B)

= Pr(A)+Pr(B) - Pr(A∩B)

= $\frac{11}{36}$ + $\frac{18}{36}$ - $\frac{5}{36}$

= $\frac{24}{36}$

= $\frac{2}{3}$

7 0

3 years ago

The solutions to the equation 2x2+x-1=2 are X= -3/2 or x=

Brilliant_brown [7]

Answer:

positive 3/2

Step-by-step explanation:

3 0

3 years ago

Nitella [24]

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

<h3>How to find the production level that'll maximize profit?</h3>

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

C(x) = 12000 + 400x − 2.6x² + 0.004x³

C'(x) = 400 − 5.2x + 0.012x².

Also, revenue, R(x) = x × P(x)

Revenue, R(x) = x(1600 − 8x)

Revenue, R(x) = 1600x − 8x²

Next, we would differentiate the revenue function to derive the marginal revenue:

R'(x) = 1600 - 8x

At maximum profit, the marginal revenue is equal to the marginal cost:

1600 - 8x = 400 − 5.2x + 0.012x

1600 - 8x - 400 + 5.2x - 0.012x² = 0

1200 - 2.8x - 0.012x² = 0

0.012x² + 2.8x - 1200 = 0

Solving by using the quadratic equation, we have:

x = 220.40 or x = -453.73.

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

Read more on maximized profit here: brainly.com/question/13800671

#SPJ1

6 0

2 years ago

Give the product in simplest form: (pic below)

stellarik [79]

Answer:

26/3

Step-by-step explanation:

First, you need to turn the fractions from mixed form to improper fractions.

3 1/4 x 2 2/3

13/4 x 8/3

= 26/3

4 0

2 years ago