The function f(x)=101+25x2 is represented as a power series f(x)=∑n=0[infinity]cnxn. Find the first few coefficients in the power series. Some of the other problems only ask for the nonzero coefficients, but in this problem you are supposed to include those coefficents that are 0. Also, this problem is only asking for the coefficients of the power series. It does not want you to include the x's or the powers of x.

Answers

Answer 1
Answer:

Answer:

\large a_0=101,\;a_1=0,\;a_2=25,\;a_n=0\;for\;n>2

Step-by-step explanation:

Since f(x) is a polynomial, it is a power series by itself with

\large a_0=101,\;a_1=0,\;a_2=25,\;a_n=0\;for\;n>2

On the other hand, the representation of a function as a power series around a given point is unique. This means that these are the only possible coefficients of f as a power series around 0.


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On a coordinate plane, a parabola opens up. It goes through (negative 2, 4), has a vertex at (0.25, negative 6), and goes through (2, 0).Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Select two options.

The domain of the function is the set of all values x such that x is greater than or equal to one-quarter.
The range of the function is all real numbers.
The vertex of the function is (one-quarter, negative 6 and one-eighth).
The function has two x-intercepts.
The function is increasing over the interval (negative 6 and one-eighth, ∞).

Answers

The statements true about the the function f(x) = 2x2 – x – 6 are-

  • The vertex of the function is (one-quarter, negative 6 and one-eighth).
  • The function has two x-intercepts.

What is vertex of parabola?

The vertex of parabola is the point at the intersection of parabola and its line of symmetry.

Now the given function is,

f(x) = 2x^2 – x – 6

Also, it is given that the vertex is located at (0.25, -6)  and the parabola opens up, the function has two x-intercepts.

Comparing the given function with standard form,

f(x) = a x^2 bx + c

By comprison we get,

a = 2

b = -1

c = -6

Now, x-coordinate of vertex is given as,

x = -b/2a

put the values we get,

x = -(-1)/2*2

or, x = 1/4

Put the value of x in given function, so y-coordinate of the vertex is given as,

f(1/4) = 2(1/4)² - 1/4 - 6

        = -49/6

       = -6 1/8

Hence, The statements true about the the function f(x) = 2x2 – x – 6 are-

  • The vertex of the function is (one-quarter, negative 6 and one-eighth).
  • The function has two x-intercepts.

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Answer:

The vertex of the function is (one-quarter, negative 6 and one-eighth).

The function has two x-intercepts.

Step-by-step explanation:

The answer above is correct.

What is 743x295
What do I need to d

Answers

Answer: 219,185

-Multiply the place values to find the answer,

You want to rent an unfurnishedone-bedroomapartment for next semester. The mean monthlyrent for a random
sample of 10 apartments advertised in the localnewspaper is $580.
Assume that the standard deviation is$90. Find a 95% confidence
interval for the mean monthly rentfor unfurnished one bedroom
apartments available for rent in thiscommunity.

Answers

Answer: (\$524.22,\ \$635.78)

Step-by-step explanation:

Confidence interval for population mean is given by :-

\overline{x}\pm z^* (\sigma)/(√(n))

, where \overline{x} = Sample mean

z* =  critical z-value.

\sigma = Population standard deviation.

n= Sample size.

Let x be the denotes the monthly rent for unfurnished one bedroom  apartments available for rent in this community.

As per given , we have

n= 10

\overline{x}=\$580

\sigma=\$90

Critical value for 95% confidence : z* = 1.96

So the 95% confidence  interval becomes,

580\pm (1.96) (90)/(√(10))

=580\pm (1.96) (90)/(3.162278)

=580\pm (1.96)(28.46)

=580\pm 55.78

=(580-55.78,\ 580+55.78)=(524.22,\ 635.78)

Hence, a 95% confidence  interval for the mean monthly rent for unfurnished one bedroom  apartments available for rent in this community= (\$524.22,\ \$635.78)

There are three workstations available having steady-state probabilities of 0.99, 0.95, 0.85 of being available on demand. What is the probability that at least two of the three will be available at any given time?

Answers

Answer:

99.065% probability that at least two of the three will be available at any given time.

Step-by-step explanation:

We have these following probabilities:

99% probability of the first workstation being available

95% probability of the second workstation being available

85% probability of the third workstation being avaiable

Two being available:

We can have three outcomes

First and second available, third not. So

0.99*0.95*0.15 = 0.141075

First and third available, second not. So

0.99*0.05*0.85 = 0.042075

Second and third available, first not. So

0.01*0.95*0.85 = 0.008075

Adding them all

P(2) = 0.141075 + 0.042075 + 0.008075 = 0.191225

Three being available:

P(3) = 0.99*0.95*0.85 = 0.799425

What is the probability that at least two of the three will be available at any given time?

P = P(2) + P(3) = 0.191225 + 0.799425 = 0.99065

99.065% probability that at least two of the three will be available at any given time.

Final answer:

The probability that at least two out of the three workstations are available is 0.967.

Explanation:

We can find the probability that at least two out of the three workstations are available using the concept of complementary events. The probability of at least two workstations being available is equal to 1 minus the probability of none or only one workstation being available.

Let's calculate the probability of none or only one workstation being available:

Probability of none being available: 0.01 * 0.05 * 0.15 = 0.00075
Probability of only one being available: (0.99 * 0.05 * 0.15) + (0.01 * 0.95 * 0.15) + (0.01 * 0.05 * 0.85) = 0.03225

Now, subtracting this from 1:

1 - (0.00075 + 0.03225) = 0.967

Therefore, the probability that at least two out of the three workstations are available at any given time is 0.967.

Learn more about probability here:

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Using substitution, what is the first step to solve: x=6y+3 and x+2y=5.​

Answers

Answer:

Step-by-step explanation:

Remark

You could do it a very convoluted way or you could do it simply. The simple way, I think, is the one intended. The x on the second equation is sitting by it itself. So is it in the first equation. Put the x from the first equation into the second.

Solution

x=6y+3 ===> x+2y=5.​

6y + 3 + 2y = 5                        First Step

8y + 3 = 5                                Subtract 3 from both sides

8y = 5 - 3                                 Combine

8y = 2                                       Divide by 8

y = 2/8

y = 1/4

============================

x = 6y + 3

x = 6*(1/4) + 3

x = 6/4 + 3

x = 1.5 + 3

x = 4.5

Solution (4.5 , 0.25)

Answer:

x= 9/2 y=1,4

Step-by-step explanation:

Hope this helped you! :)

Jill is making a long cape. She needs 7 1/3 yards of blue fabric for the outside of the cape. She needs 6 2/3
yards of purple fabric for the lining of the cap
How much more blue fabric than purple fabric should Jill buy?

Answers

Answer: 2/3yards

Step-by-step explanation:

From the question, we are informed that Jill is making a long cape and that she needs 7 1/3yards of blue fabric for the outside of the cape and that she needs 6 2/3yards of purple fabric for the lining of the cap.

To calculate the yards of blue fabric that'll be needed more than purple fabric,, we subtract 6 2/3 from 7 1/3. This will be:

= 7 1/3 - 6 2/3

= 2/3

She needs 2/3yards of blue fabric more.