-12/5+3/10/11/14-(-9/14)

Determine, using the intermediate value theorem, if the function F(x)=x^3+2x-1 has a zero on the interval [0,1]. Justify your an

SSSSS [86.1K]

Plug x = 0 into the function

f(x) = x^3 + 2x - 1

f(0) = 0^3 + 2(0) - 1

f(0) = -1

Note how the result is negative. The actual number itself doesn't matter. All we care about is the sign of the result.

Repeat for x = 1

f(x) = x^3 + 2x - 1

f(1) = 1^3 + 2(1) - 1

f(1) = 2

This result is positive.

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We found that f(0) = -1 and f(1) = 2. The first output -1 is negative while the second output 2 is positive. Going from negative to positive means that, at some point, we will hit y = 0. We might have multiple instances of this happening, or just one. We don't know for sure. The only thing we do know is that there is at least one root in this interval.

To actually find this root, you'll need to use a graphing calculator because the root is some complicated decimal value. Using a graphing calculator, you should find the root to be approximately 0.4533976515

7 0

3 years ago

What is the measure of angle x?

aivan3 [116]

Answer:

83 is the measure of x.

Step-by-step explanation:

A triangle is equal to 180 degrees. So 180 - 53 - 44 = 83.

4 0

2 years ago

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The Washington, DC, region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure

Ilia_Sergeevich [38]

Answer:

a) 0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b) 0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c) The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

Step-by-step explanation:

For each home, there are only two possible outcomes. Either it goes into foreclosure, or it does not. The probability of a home going into foreclosure is independent of other homes. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?

The foreclosure rate is 1.31% for the Washington, DC area, which means that $p = 0.0131$

We wanto to find, with $n = 100$ :

$P(X < 2) = P(X = 0) + P(X = 1)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{100,0}.(0.0131)^{0}.(0.9869)^{100} = 0.2675$

$P(X = 1) = C_{100,1}.(0.0131)^{1}.(0.9869)^{99} = 0.3551$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.2675 + 0.3551 = 0.6226$

0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?

Foreclosure rate of 0.87% for the nation, which means that $p = 0.0087$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{100,0}.(0.0087)^{0}.(0.9913)^{100} = 0.4174$

$P(X = 1) = C_{100,1}.(0.0087)^{1}.(0.9913)^{99} = 0.3663$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.4174 + 0.3663 = 0.7837$

0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c. Comment on the above findings.

The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

7 0

3 years ago

You need to write 0.63 as a fraction. How do you choose the denominator?

Tamiku [17]

I would use 100 as the denominator because it can not be simplified as a whole number

7 0

3 years ago

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9) Tony the Tiger spent $95 on 5 sweaters that each cost the

Shalnov [3]

Answer:

5 sweaters cost = $95