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3 years ago

The maximum point of the function f (x) = -2x2 + 4x + 6 is: please help me

Mathematics

1 answer:

Arisa [49]3 years ago

7 0

Step-by-step explanation:

By Completing the Square,

$\begin{align}f(x)&=-2x^2+4x+6\\&=-2(x^2-2x)+6\\&=-2(x^2-2x+1)+8\\&=-2(x-1)^2+8 \end{align}$

Since the first tern is at most zero, the maximum value occurs when

$x=1, f(x)=8$

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3 years ago

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.42 and a standard deviation of 1.52.

Roman55 [17]

Answer:

The percentage of the women have size shoes that are greater than

9.94 is 16%

Step-by-step explanation:

* Lets revise the empirical rule

- The Empirical Rule states that almost all data lies within 3 standard

deviations of the mean for a normal distribution.

- 68% of the data falls within one standard deviation.

- 95% of the data lies within two standard deviations.

- 99.7% of the data lies Within three standard deviations

* The empirical rule shows that

# 68% falls within the first standard deviation (µ ± σ)

# 95% within the first two standard deviations (µ ± 2σ)

# 99.7% within the first three standard deviations (µ ± 3σ).

* Lets solve the problem

- The shoe sizes of American women have a bell-shaped distribution

with a mean of 8.42 and a standard deviation of 1.52

∴ μ = 8.42

- The standard deviation is 1.52

∴ σ = 1.52

- One standard deviation (µ ± σ):

∵ (8.42 - 1.52) = 6.9

∵ (8.42 + 1.52) = 9.94

- Two standard deviations (µ ± 2σ):

∵ (8.42 - 2×1.52) = (8.42 - 3.04) = 5.38

∵ (8.42 + 2×1.52) = (8.42 + 3.04) = 11.46

- Three standard deviations (µ ± 3σ):

∵ (8.42 - 3×1.52) = (8.42 - 4.56) = 3.86

∵ (8.42 + 3×1.52) = (8.42 + 4.56) = 12.98

- We need to find the percent of American women have shoe sizes

that are greater than 9.94

∵ The empirical rule shows that 68% of the distribution lies

within one standard deviation in this case, from 6.9 to 9.94

∵ We need the percentage of greater than 9.94

- That means we need the area under the cure which represents more

than one standard deviation (more than 68%)

∵ The total area of the curve is 100% and the area within one standard

deviation is 68%

∴ The area greater than one standard deviation = (100 - 68)/2 = 16

∴ The percentage of the women have size shoes that are greater

than 9.94 is 16%

8 0

3 years ago