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tangare [24]
1 year ago
13

Show that the equation x^3+7x-4=0 has a solution between x=0 and x=1

Mathematics
1 answer:
Aleksandr [31]1 year ago
3 0

Step-by-step explanation:

Using the Intermediate Value Theorem, the following is applied:

"If f(x) is a continuous on interval [a,b] and we have two points f(a) and f(b) then there must be some value c such that f(a)<f(c)<f(b).

So here there must be a c such that

f(0) < f(c) < f(1)

Note: F(c)=0, the questions that the function have a solution between 0 and 1, so that means we must have some value, c such that f(c)=0 that exists

Next, plug in the x values into the function

f(0)  =  - 4

f(1) =  {1}^{3}  + 7(1) - 4 = 4

Since cubic functions are continuous and -4<0<4, then there is a solution c that lies between f(0) and f(1)

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Pattern B starts at 0 and uses the rule Add 3.

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3 years ago
The probability distribution of the number of students absent on Mondays, is as follows: X 0 1 2 3 4 5 6 7 f(x) 0.02 0.03 0.26 0
alexgriva [62]

a) Add up all the probabilities f(x) where x>3:

f(4)+f(5)+f(6)+f(7)=0.35

b) The expected value is

E[X]=\displaystyle\sum_xx\,f(x)=3.16

Since X is the number of absent students on Monday, the expectation E[X] is the number of students you can expect to be absent on average on any given Monday. According to the distribution, you can expect around 3 students to be consistently absent.

c) The variance is

V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2

where

E[X^2]=\displaystyle\sum_xx^2\,f(x)=11.58

So the variance is

V[X]=11.58-3.16^2\approx1.59

The standard deviation is the square root of the variance:

\sqrt{V[X]}\approx1.26

d) Since Y=7X+3 is a linear combination of X, computing the expectation and variance of Y is easy:

E[Y]=E[7X+3]=7E[X]+3=25.12

V[Y]=V[7X+3]=7^2V[X]\approx78.13

e) The covariance of X and Y is

\mathrm{Cov}[X,Y]=E[(X-E[X])(Y-E[Y])]=E[XY]-E[X]E[Y]

We have

XY=X(7X+3)=7X^2+3X

so

E[XY]=E[7X^2+3X]=7E[X^2]+3E[X]=90.54

Then the covariance is

\mathrm{Cov}[X,Y]=90.54-3.16\cdot25.12\approx11.16

f) Dividing the covariance by the variance of X gives

\dfrac{\mathrm{Cov}[X,Y]}{V[X]}\approx\dfrac{11.16}{1.59}\approx0.9638

5 0
3 years ago
Write the number 1,700,000,000 in scientific notation.
Katyanochek1 [597]
The answer is B
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3 years ago
Kelly rode her bicycle for 35 minutes at a speed of 12 miles per hour. At that speed, how many miles did she ride?
ikadub [295]
It is 384 hope that helps!
3 0
3 years ago
You spend $3.50 on fruit. Apples cost $0.20 each while oranges cost $0.30 each. The equation models the situation, where x is th
Licemer1 [7]

Answer:

b. 11 apples; 1 orange

Step-by-step explanation:

We test each option, and see if the total is $3.50(what you spend). If the result is different, it is not a possible solution.

a. 1 apple; 11 oranges

1 apple for $0.20

11 oranges for $0.30 each

0.20 + 11*0.30 = $3.50

Possible solution

b. 11 apples; 1 orange

11 apples for $0.20 each

1 orange for $0.30

11*0.2 + 0.3 = 2.5

Not $3.5, so this is not a possible solution.

This is the answer

c. 7 apples; 7 oranges

7*0.2 + 7*0.3 = $3.5

Possible

d. 4 apples; 9 oranges

4*0.2 + 9*0.3 = $3.5

Possible

4 0
3 years ago
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