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Ulleksa [173]
1 year ago
6

50 points for this one

Mathematics
2 answers:
ss7ja [257]1 year ago
7 0

Answer:

-1, 0

Step-by-step explanation:

Hello!

We can test each solution for by substituting the value for x, and see if the inequality is true.

<h3>x = -1:</h3>
  • \frac{3(-1)^2}{(-1)^2+3} < 1
  • \frac34 < 1

This inequality is true.

<h3>x = -2:</h3>
  • \frac{3(-2)^2}{(-2)^2+3} < 1
  • \frac{12}{7} < 1

This inequality is not true because 12/7 is greater than 1.

<h3>x = 0:</h3>
  • \frac{3(0)^2}{(0)^2+3} < 1
  • 0 < 1

This is inequality is true.

<h3>x = 3:</h3>
  • \frac{3(3)^2}{(3)^2+3} < 1
  • \frac{27}{12} < 1

This inequality is not true because 27/12 is greater than 1.

The solutions that work are -1 and 0.

Georgia [21]1 year ago
6 0

Answer: A

Step-by-step explanation:

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A rectangular storage container with an open top is to have a volume of 10 m3. the length of this base is twice the width. mater
BartSMP [9]
Refer to the diagram shown below.

The volume of the container is 10 m³, therefore
x*2x*h = 10
2x²h = 10
h = 5/x²        (1)

The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²

The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x

The total cost is
C = 20x² + 180/x

The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
C'' = 40 + 360/x³
C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.

The total cost is
C = 20(1.651)² + 180/1.651 = $163.54

Answer: $163.54

7 0
2 years ago
Give a rule of the piecewise-defined function.
nataly862011 [7]

The equation of the piecewise function is f(x) = \left[\begin{array}{ccc}3&x \le -1\\-1&x > 2\end{array}\right

<h3>The piecewise function</h3>

On the graph, we have:

  • y = 3 for all x values not more than -1
  • y = -1 for all values greater than 2

Hence, the piecewise function is:

f(x) = \left[\begin{array}{ccc}3&x \le -1\\-1&x > 2\end{array}\right

<h3>The domain of the function</h3>

This is the set of input values

In (a), we have:

x ≤ -1 and x > 2

Hence, the domain is (∞, 3] u (2, ∞)

<h3>The range of the function</h3>

This is the set of output values

In (a), we have:

f(x) = 3 and f(x) -1

Hence, the range is [3] u (-1)

Read more about piecewise function at:

brainly.com/question/18859540

#SPJ1

5 0
1 year ago
A box is filled with 6 blue cards, 6 brown cards, and 3 green cards. A card is chosen at random from the box. What is the probab
Luden [163]

Answer:

60% chance of a blue or green card

6 0
2 years ago
Can anyone please help me with these questions please. thanks.
Pani-rosa [81]
1.) 3/4
2.) It snowed 1/4 more on Tuesday than it did on Monday.
3 0
3 years ago
Read 2 more answers
A college student is taking two courses. The probability she passes the first course is 0.73. The probability she passes the sec
zhenek [66]

Answer:

b) No, it's not independent.

c) 0.02

d) 0.59

e) 0.57

f) 0.5616

Step-by-step explanation:

To answer this problem, a Venn diagram should be useful. The diagram with the information of Event 1 and Event 2 is shown below (I already added the information for the intersection but we're going to see how to get that information in the b) part of the problem)

Let's call A the event that she passes the first course, then P(A)=.73

Let's call B the event that she passes the second course, then P(B)=.66

Then P(A∪B) is the probability that she passes the first or the second course (at least one of them) is the given probability. P(A∪B)=.98

b) Is the event she passes one course independent of the event that she passes the other course?

Two events are independent when P(A∩B) = P(A) * P(B)

So far, we don't know P(A∩B), but we do know that for all events, the next formula is true:

P(A∪B) = P(A) + P(B) - P(A∩B)

We are going to solve for P (A∩B)

.98 = .73 + .66 - P(A∩B)

P(A∩B) =.73 + .66 - .98

P(A∩B) = .41

Now we will see if the formula for independent events is true

P(A∩B) = P(A) x P(B)

.41 = .73 x .66

.41 ≠.4818

Therefore, these two events are not independent.

c) The probability she does not pass either course, is 1 - the probability that she passes either one of the courses (P(A∪B) = .98)

1 - P(A∪B) = 1 - .98 = .02

d) The probability she doesn't pass both courses is 1 - the probability that she passes both of the courses P(A∩B)

1 - P(A∩B) = 1 -.41 = .59

e) The probability she passes exactly one course would be the probability that she passes either course minus the probability that she passes both courses.

P(A∪B) - P(A∩B) = .98 - .41 = .57

f) Given that she passes the first course, the probability she passes the second would be a conditional probability P(B|A)

P(B|A) = P(A∩B) / P(A)

P(B|A) = .41 / .73 = .5616

4 0
3 years ago
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