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3 years ago

5

Determine which consecutive integers do not have a real zero of f(x)=x^3-4x^2-4x+15 between them. a. (4,5) b. (1,2) c. (-2,-1) d

. (-3,-2)

2 answers:

Crank3 years ago

5 0

Answer:

(-3,-2)

Step-by-step explanation:

on edge. sorry Im late

ollegr [7]3 years ago

4 0

(-3,-2)
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5,5,3 Is this a triangle? Explain.

Vlad1618 [11]

Problem 1

Answer: <u>Yes</u> a triangle can be formed with side lengths 5,5,3

--------------------

Explanation:

Take any two sides and add them up. If we get a sum larger than the third side, then a triangle is possible. This is the triangle inequality theorem.

5+5 = 10 is larger than 3

5+3 = 8 is larger than 5

This shows a triangle is possible. The triangle is isosceles because two sides are the same length.

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

Problem 2

Answer: <u>Yes</u> a triangle can be formed with side lengths 8,8,8

--------------------

Explanation:

This triangle is equilateral because all sides are the same length.

Take any two sides, add them up, and you'll find the sum is larger than the third side.

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

Problem 3

Answer: <u>No</u> a triangle cannot be formed with sides 7,8,15

--------------------

Explanation:

Yes it is true that

8+15 = 23 is larger than 7

7+15 = 22 is larger than 8

but

7+8 = 15 is not larger than 15

So this means a triangle is not possible.

Imagine you had 3 strips of paper that were 7 inches, 8 inches and 15 inches long. The 7 and 8 inch strips add to 15 inches, but those two smaller strips only form a straight line. We cannot pull them so a triangle forms. If we did, then the third side would be smaller than 15 inches. This is one way to get hands on to see why the triangle inequality theorem works.

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

Problem 4

Answer: <u>Yes</u> a triangle is possible with side lengths 5,6,10

--------------------

Explanation:

Same idea as before. We can take any two sides, add them, and get a sum larger than the third side. A triangle is possible.

5+6 = 11 is larger than 10
6+10 = 16 is larger than 5
5+10 = 15 is larger than 6

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2 years ago

Which number line plots the integers -12,-3,and 7 <br><br>not sure

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Answer:

the first one I think

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A picture shows the net of the lateral surface of the cone. Which statement about this cone is NOT true?

Archy [21]

Answer:

The area of the net is not π • 9^2

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3 years ago

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Quality control is an important issue at ACME Company which manufacturers light bulbs. In order to conduct testing of the life h

mrs_skeptik [129]

Answer: 3424.28

Step-by-step explanation:

Given data : 378, 361, 350, 375, 200, 391, 375, 368, 321

Number of data values = 9

Mean : $\overline{x}=\dfrac{\sum^n_{i=1} x_i}{n}$

$\\\\=\dfrac{378+361+350+375+200+391+375+368+321}{9}\\\\=\dfrac{3119}{9}\approx346.56$

Variance = $\dfrac{\sum^n_{i=1} (x_i-\overline{x})^2}{n-1}$

$\sum^n_{i=1} (x_i-\overline{x})^2 = (31.44)^2+(14.44)^2+(3.44)^2+(28.44)^2+(-146.56)^2+(44.44)^2+(28.44)^2+(21.44)^2+(-25.56)^2\\\\=27394.2224$

Variance = $\dfrac{27394.2224}{8}=3424.2775\approx3424.28$

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3 years ago

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work pro

olchik [2.2K]

Answer:

0.756

Step-by-step explanation:

It is given that a machine has four components, A, B, C, and D.

$P(A)=P(B)=0.93, P(C)=0.95,P(D)=0.92$

If these components set up in such a manner that all four parts must work for the machine to work properly.

We need to find the probability that the machine works properly. It means we have to find the value of $P(A\cap B\cap C\cap D)$ .

If two events X and Y are independent, then

$P(X\cap Y)=P(X)\times P(Y)$

Assume the probability of one part working does not depend on the functionality of any of the other parts.

$P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)$

Substitute the given values.

$P(A\cap B\cap C\cap D)=0.93\times 0.93\times 0.95\times 0.92$

$P(A\cap B\cap C\cap D)=0.7559226$

$P(A\cap B\cap C\cap D)\approx 0.756$

Therefore, the probability that the machine works properly is 0.756.

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2 years ago