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liraira [26]
3 years ago
12

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

swer and find the indicated zero, if it exists.
Mathematics
1 answer:
SSSSS [86.1K]3 years ago
7 0

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.

---------------------------

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

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suppose X and Y are independent random variables, both with normal distributions. If X has a mean of 45 with a standard deviatio
djyliett [7]

Answer:

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

\mu_X = 45, \sigma_X = 4, \mu_Y = 35, \sigma_Y = 3

What is the probability that a randomly generated value of X is greater than a randomly generated value of Y

This means that the subtraction of X by Y has to be positive.

When we subtract two normal variables, the mean is the subtraction of their means, and the standard deviation is the square root of the sum of their variances. So

\mu = \mu_X - \mu_Y = 45 - 35 = 0

\sigma = \sqrt{\sigma_X^2+\sigma_Y^2} = \sqrt{25} = 5

We want to find P(X > 0), that is, 1 subtracted by the pvalue of Z when X = 0. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{0 - 10}{5}

Z = -2

Z = -2 has a pvalue of 0.0228

1 - 0.0228 = 0.9772

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

4 0
3 years ago
I can Multiply a 11x6 matric by a 6x7 matrix. The resulting matrix will be ??? Can somebody help me
Bumek [7]

Answer:

The resulting matrix will be 11 * 7

Step-by-step explanation:

Given

Matrices 11 * 6 multiplied by 6 * 7

Required

The dimension of the resulting matrix

When a matrix a * b is multiplies by a matrix b * c, the resulting matrix will be: a * c

In this case:

a * b = > 11 * 6

b * c => 6 * 7

So, the resulting matrix will be:

a * c => 11 * 7

3 0
3 years ago
Find the point where the line crosses the x-axis. y = –5x + 5
Ronch [10]
Every point on the x-axis has y-coordinate 0.
Let y = 0, and solve for x.

y = -5x + 5

0 = -5x + 5

5x = 5

x = 1

The line crosses the x-axis at x = 1.
8 0
3 years ago
Solve 1/4 divided by 3
zysi [14]

The anwser is 0.083 a bunch of threes follow but the aren't important all you need to do is round which that should be rounded enough.

6 0
3 years ago
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WILL GIVE BRAINIEST ANSWER!!! TUVW has vertices T(1,-3),U(3,-1),V(6,-4),and W(4,-6).Determine if quadrilateral TUVW is a paralle
Arte-miy333 [17]
Plotting the 4 points and doing visual inspection will tell us if the quadrilateral is a parallelogram. We can also do analytical techniques which are to determine the slope and the distance between the points. Doing either of these two will give us
<span>B. Yes,TUVW quadrilateral s a parallelogram because there are two pairs of parallel sides.
</span>
4 0
3 years ago
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