Complete the pattern _,_,_,0, 2, 4,6 A)-1, -2, -3 B) -2,-4, -6 C) -6, -4,-2

<img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7Bx%7D%5E%7B2%7D%20%2B%204x%20-%205" id="TexFormula1" title="f(x) = {x}^{2}

KATRIN_1 [288]

Answer:

$\dfrac{df^{1}(16)}{dx} = \pm \dfrac{1}{10}$

Step-by-step explanation:

$f(x) = x^2 + 4x - 5$

First we find the inverse function.

$y = x^2 + 4x - 5$

$x = y^2 + 4y - 5$

$y^2 + 4y - 5 = x$

$y^2 + 4y = x + 5$

$y^2 + 4y + 4 = x + 5 + 4$

$(y + 2)^2 = x + 9$

$y + 2 = \pm\sqrt{x + 9}$

$y = -2 \pm\sqrt{x + 9}$

$f^{-1}(x) = -2 \pm\sqrt{x + 9}$

$f^{-1}(x) = -2 \pm (x + 9)^{\frac{1}{2}}$

Now we find the derivative of the inverse function.

$\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2}(x + 9)^{-\frac{1}{2}}$

$\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2\sqrt{x + 9}}$

Now we evaluate the derivative of the inverse function at x = 16.

$\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{16 + 9}}$

$\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{25}}$

$\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2 \times 5 }$

$\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{10}$

4 0

3 years ago

A group of 3 adults and 10 children bought tickets to watch a dance

nignag [31]

Answer:

6

Step-by-step explanation:

guess and check 6(10)+((6+7)5)=125

7 0

3 years ago

estimate the perimeter of a school chalkboard, measuring 76 cm by 46 cm. Give your answer to the nearest ten

creativ13 [48]

Answer:

260

Step-by-step explanation:

76 rounded to 1 s.f. is 80

46 rounded to 1s.f. is 50

80+50+80+50= 260

Hope this helps!

3 0

3 years ago

Read 2 more answers

What is the measure of angle b

erma4kov [3.2K]

M∠b = 90° - 33° = 57° ← answer

4 0

3 years ago

Read 2 more answers

Based on a poll, 40% of adults believe in reincarnation. Assume that 4 adults are randomly selected, and find the indicated p

Anit [1.1K]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

$P(3) = 0.154$

b

$P(4) = 0.026$

c

$P( X \ge 3 ) = 0.18$

d

option C is correct

Step-by-step explanation:

From the question we are told that

The probability of success is p = 0.4

The sample size is n= 4

This adults believe follow a binomial distribution is because there are only two outcome one is an adult believes in reincarnation and the second an adult does not believe in reincarnation

The probability of failure is mathematically evaluated as

$q = 1 - p$

substituting values

$q = 1 - 0.4$

$q = 0.6$

Considering a

The probability that exactly 3 of the selected adults believe in reincarnation is mathematically represented as

$P(3) = \left n} \atop {}} \right. C_ 3 * p^3 * q^{n-3}$

substituting values

$P(3) = \left 4} \atop {}} \right. C_ 3 * (0.40)^3 * (0.60)^{4-3}$

Here $\left 4} \atop {}} \right.C_3$ means 4 combination 3 . i have calculated this using a calculator and the value is

$\left 4} \atop {}} \right.C_3 = 4$

So

$P(3) = 4* (0.4)^3 * (0.6)$

$P(3) = 0.154$

Considering b

The probability that all of the selected adults believe in reincarnation is mathematically represented as

$P(n) = \left n} \atop {}} \right. C_ n * p^n * q^{n-n}$

substituting values

$P(4) = \left 4} \atop {}} \right. C_ 4 * (0.40)^4 * (0.60)^{4-4}$

Here $\left 4} \atop {}} \right.C_3$ means 4 combination . i have calculated this using a calculator and the value is $\left 4} \atop {}} \right.C_4 = 1$

so

$P(4) = 1* (0.4)^4 * 1$

=> $P(4) = 0.026$

Considering c

the probability that at least 3 of the selected adults believe in reincarnation is mathematically represented as

$P( X \ge 3 ) = P(3 ) + P(n )$

substituting values

$P( X \ge 3 ) = 0.154 + 0.026$

$P( X \ge 3 ) = 0.18$

From the calculation the probability that all the 4 randomly selected persons believe in reincarnation is $p(4) = 0.026 < 0.05$

But the the probability of 3 out of the 4 randomly selected person believing in reincarnation is $P(3) = 0.154 \ which \ is \ > 0.05$

Hence 3 is not a significantly high number of adults who believe in reincarnation because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.

3 0

3 years ago