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3 years ago

Suppose f is a one-to-one function with f(2)=8 and f’(2)=4. What is the value of (f^-1)’(8)?

Mathematics

1 answer:

yuradex [85]3 years ago

5 0

Answer:

1/4

Step-by-step explanation:

The tangent line to f(x) at x=2 goes through the point (2, 8) and has slope 4.

The inverse function f⁻¹(x) is a reflection of the function f(x) across the line y=x. The corresponding tangent line will go through point (8, 2) and have slope 1/f'(2) = 1/4 at that point. That is, ...

(f⁻¹)'(8) = 1/f'(f⁻¹(8)) = 1/f'(2) = 1/4

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Which of the following choices is equivalent to -9x > -27?

Llana [10]

Answer:

-9x>-27

x<-27/-9

x<3

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example : -x<-3 (×-1)

x>3

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2 years ago

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At a miniature golf course, after every 5 th visit you receive a free beverage. After every 12 th visit you receive a free game.

Airida [17]

Answer:

60th visit

Step-by-step explanation:

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3 years ago

Y=3x+5 6x - 2y = -10

klasskru [66]

Answer:

Parallel?

Step-by-step explanation:

6x = 2y + 10

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3 years ago

HELPP WITH MATH PLEASSS 11-12

evablogger [386]

Answer:

11. Not enough information

12. You can say DB = DC by SAA congruence rule and CPCTC (Corresponding parts of congruent triangles are congruent)

Step-by-step explanation:

For 12, you can say ΔABD≅ΔACD because they have a side in common (AD) and they have 2 congruent angles. Thus, you can use the SAA congruence criterion. Then, you can use CPCTC (Corresponding parts of congruent triangles are congruent) to say that DB = DC.

Hope this helps :)

4 0

2 years ago

1. (5pt) In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also,

gladu [14]

Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

$\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988$

The combined proportion is:

$\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989$

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

$Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}$

$=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78$

Compute the p-value as follows:

$p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075$

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

$=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\$

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

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3 years ago