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In-s [12.5K]
3 years ago
14

Write a polynomial f(x) that satisfies the given conditions.

Mathematics
1 answer:
patriot [66]3 years ago
6 0

Answer:

f(x) = (x-4)(x-\frac{1}{2})^2 = x^3-5x^2+4.25x -1

Step-by-step explanation:

Recall, if we have a polynomial of the form (x-a)^k \cdot (x-b)^m, then we say that a is a zero of multiplicity k and b is a zero of multiplicty m. For example, in the polynomial of the form (x+5)^10(x-2)^3 -5 is a zero of multiplicity 10 and 2 is a zero of multiplicity 3. If we want to know the degree of the polynomial,  just add the multiplicity of both zeros (13 in our example).

In this case, we know that the degree of our polynomial should be at least 3(multiplicity 2 and multiplicity 1). So, lets take the polynomial of the form

f(x)=(x-a)(x-b)^2).

In here, a is a zero with multiplicity 1 and b is a zero with multiplicity 2. We are also given that

f(0) = -1 = (0-a)(0-b)^2 = -a\codt b^2.

Which implies that 1 = a\cdot b^2. Since the square of any number is a positive number, it must happen that a>0. So, we have that

b= \pm \sqrt[]{\frac{1}{a}}.

We can choose any value of a and solve for b. Let us choose a=4. So we can have b=1/2 or b=-1/2. Let's use b=1/2. So our polynomial would be

f(x) = (x-4)(x-\frac{1}{2})^2 = x^3-5x^2+4.25x -1

which we can easily check that f(0)=-1.

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g Minimizing the sum of the squared deviations around the line is called: predictor regression. mean squared error technique. le
Alex787 [66]

Minimizing the sum of the squared deviations around the line is called Least square estimation.

It is given that the sum of squares is around the line.

Least squares estimations minimize the sum of squared deviations around the estimated regression function. It is between observed data, on the one hand, and their expected values on the other. This is called least squares estimation because it gives the least value for the sum of squared errors. Finding the best estimates of the coefficients is often called “fitting” the model to the data, or sometimes “learning” or “training” the model.

To learn more about regression visit: brainly.com/question/14563186

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3 0
1 year ago
Dr. gavin is conducting a 2 x 4 independent-groups factorial design. how many interactions will dr. gavin need to examine?
Sholpan [36]
For the answer to the question above, I believe the answer is simply <u><em>8.
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2 groups divided into four participants. So all in all people needed is 8.
I hope this helped you. Have a nice day!
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8 0
2 years ago
2) A pair of socks is purchased for $3.00 it is then sold for $4.00 What is the percent of change that
Veronika [31]

Answer:

5% change

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
There are many square prisms with volume 125 in. Let w represent the side length of the square base and h represent the height i
iogann1982 [59]

Answer:

5in by 5in by 5in

Step-by-step explanation:

We are not told wat to find but we can as well find the dimension of the prism that will minimize its surface area.

Given

Volume = 125in³

Formula

V = w²h ..... 1

S = 2w²+4wh ..... 2

w is the side length of the square base

h is the height of the prism

125 = w²h

h = 125/w² ..... 3

Substitute eqn 3 into 2 as shown

S = 2w²+4wh

S = 2w²+4w(125/w²)

S = 2w²+500/w

To minimize the surface area, dS/dw = 0

dS/dw =4w-500/w²

0= 4w-500/w²

Multiply through by w²

0 = 4w³-500

-4w³ = -500

w³ = 500/4

w³ =125

w = cuberoot(125)

w = 5in

Get the height

125 =w²h

125 = 25h

h = 125/25

h = 5in

Hence the dimension of the prism is 5in by 5in by 5in

5 0
2 years ago
(a) A lamp has two bulbs, each of a type with average lifetime 1400 hours. Assuming that we can model the probability of failure
Temka [501]

Answer:

For first lamp ; The resultant probability is 0.703

For both lamps; The resultant probability is 0.3614

Step-by-step explanation:

Let X be the lifetime hours of two bulbs

X∼exp(1/1400)

f(x)=1/1400e−1/1400x

P(X<x)=1−e−1/1400x

X∼exp⁡(1/1400)

f(x)=1/1400 e−1/1400x

P(X<x)=1−e−1/1400x

The probability that both of the lamp bulbs fail within 1700 hours is calculated below,

P(X≤1700)=1−e−1/1400×1700

=1−e−1.21=0.703

The resultant probability is 0.703

Let Y be a lifetime of another lamp two bulbs

Then the Z = X + Y will follow gamma distribution that is,

X+Y=Z∼gamma(2,1/1400)

2λZ∼

X+Y=Z∼gamma(2,1/1400)

2λZ∼χ2α2

The probability that both of the lamp bulbs fail within a total of 1700 hours is calculated below,

P(Z≤1700)=P(1/700Z≤1.67)=

P(χ24≤1.67)=0.3614

The resultant probability is 0.3614

8 0
2 years ago
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