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egoroff_w [7]
3 years ago
12

Identify each x-value at which the slope of the tangent line to the function f(x) = 0.2x^2 + 5x − 12 belongs to the interval (-1

, 1).

Mathematics
2 answers:
zhuklara [117]3 years ago
5 0

Answer:

Step-by-step explanation:

Hello, the slope of the tangent is the value of the derivative.

f'(x) = 2*0.2x + 5 = 0.4x + 5

So we are looking for

-1\leq f'(x) \leq 1 \\ \\ -1\leq 0.4x+5 \leq 1 \\ \\ -1-5=-6\leq 0.4x \leq 1-5=-4 \\ \\ \dfrac{-6}{0.4}\leq 0.4x \leq \dfrac{-4}{0.4} \\\\ \boxed{-15 \leq x\leq -10}

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

DIA [1.3K]3 years ago
3 0

Answer:

Step-by-step explanation:

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The Statistical Abstract of the United States published by the U.S. Census Bureau reports that the average annual consumption of
ololo11 [35]

Answer:

Hence,

a) The probability that the sample average would be less than 90 pounds is 0.0210.

b) The probability that the sample average would be between 98 and 105 pounds is 0.5045.

c) The probability that the sample average would be less than 112 pounds is 0.9935.

d) The probability that the sample average would be between 93 and 96 pounds is 0.1341.

Step-by-step explanation:

a) P(X < 90) = P(Z < (90 - 99.9) / (30\sqrt(38)))

                     = P(Z < -2.03) = 0.0210

b )P(98 < x

                              = P(-0.39 < Z < 1.05) = 0.5045

c ) P(X < 112) = P(Z < (112 - 99.9) / (30\sqrt(38)))

                        = P(Z < 2.49) = 0.9935

d )P(93 < x < 96) = P((93 -99.9) / (30 \sqrt(38)) < Z < (96 -99.9) / (30 \sqrt(38)))

                            = P( -1.42 < Z < -0.8 )

                            = 0.2119 - 0.0778 = 0.1341

8 0
3 years ago
Help is needed please help
Anna007 [38]

You have to do Pythagorean theorem:

a^{2} +b^{2}  = c^{2}

"a" and "b" are the legs. In this case 7 is a leg and x is a leg

"c" is the hypotenuses, which is 19 here

so...

a = 7

b = x

c = 19

Plug the numbers above into the equation:

7^{2} + x^{2} = 19^{2}

49 +x^{2} = 361

Isolate x by subtracting 49 to both sides:

(49-49) + x^{2} = 361 - 49

x^{2} = 312

To solve for x you have to take the square root to both sides of the equation:

\sqrt{x^{2} } = \sqrt{312}

x = 17.6635

x = 17.7

Hope this helped!

6 0
3 years ago
If Judy completes a puzzle by herself, it takes her 3 hours. Working with Sal, it only takes them 2 hours.What is the missing va
aliina [53]

Answer:

It means the Judy's rate to complete the puzzle is \frac{1}{3}.

Step-by-step explanation:

If Judy completes a puzzle by herself, it takes her 3 hours.

Working with Sal, it only takes them 2 hours

We have been given the rates of time taken by Judy and Sal to complete a puzzle.

We can see from our given table that Sal's rate is r. We are told that Judy completes a puzzle by herself, it takes her 3 hours. working with Sal, it only takes them 2 hours.

It is given that Judy completes a puzzle by herself, it takes her 3 hours.

so part of puzzle completed by Judy in one hour would be\frac{1}{3}

Therefore, the part of puzzle completed by Judy in one hour is \frac{1}{3}.

8 0
3 years ago
Read 2 more answers
Ben is repackaging a 45 pound bag of Rice into 8 smaller Bags so much rice is going to be in each smaller bag
natka813 [3]

Answer:

5.625

Step-by-step explanation:

45 ÷ 8 = 5.625

6 0
3 years ago
What's 12748 rounded to the nearest thousand
FinnZ [79.3K]
12748 rounded to the nearest thousand is 13000
8 0
3 years ago
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