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3 years ago

Given the function h(x)=-x^2-5x+14 determine the average rate of change of the function over the interval -9

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

8 0

Answer:

The average rate of change of the function over the interval is of 6.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function h(x) over an interval [a,b] is given by:

$A = \frac{h(b)-h(a)}{b-a}$

In this question:

Over the interval [-9,-2], so $a = -9, b = -2, b - a = -2 -(-9) = 7$

The function is:

$h(x) = -x^2 - 5x + 14$

$h(-9) = -9^2 -5(-9) + 14 = -81 + 45 + 14 = -22$

$h(-2) = -2^2 -5(-2) + 14 = -4 + 10 + 14 = 20$

Then

$A = \frac{h(-2)-h(-9)}{7} = \frac{20-(-22)}{7} = \frac{42}{7} = 6$

The average rate of change of the function over the interval is of 6.

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Andreyy89

Answer:

$88 \: {in}^{2}$

Step-by-step explanation:

Area of the figure = Area of rectangle with dimensions 16 in and 4 in + Area of two right triangles with base (7 - 4 = 3) 3 in and height 8 in

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7 0

3 years ago

In a list of households, own homes and do not own homes. Five households are randomly selected from these households. Find the p

hichkok12 [17]

Answer:

The probability of success for this case would be:

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Let X the random variable of interest, on this case we now that:

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The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want this probability:

$P(X=3)$

And uing the probability mass function we got:

$P(X=3)= 15C3 (0.6)^3 (1-0.6)^{15-3}= 0.00165$

Step-by-step explanation:

Adduming the following info: In a list of 15 households, 9 own homes and 6 do not own homes. Five households are randomly selected from these 15 households. Find the probability that the number of households in these 5 own homes is exactly 3.

Round your answer to four decimal places

P (exactly 3)=

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

The probability of success for this case would be:

$p =\frac{9}{15}= 0.6$ representing the proportion of homes that are own homes

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=15, p=0.6)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want this probability:

$P(X=3)$

And uing the probability mass function we got:

$P(X=3)= 15C3 (0.6)^3 (1-0.6)^{15-3}= 0.00165$

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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kolbaska11 [484]

Answer:

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Step-by-step explanation:

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+ 12x^2 -22xy + 8x

_________________

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8 0

3 years ago