Answer:
Step-by-step explanation:
Since f(x) is a polynomial, it is a power series by itself with
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.
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, ∞).
The statements true about the the function f(x) = 2x2 – x – 6 are-
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-
More about vertex :
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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 do I need to d
Answer: 219,185
-Multiply the place values to find the answer,
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.
Answer:
Step-by-step explanation:
Confidence interval for population mean is given by :-
, where = Sample mean
z* = critical z-value.
= 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
Critical value for 95% confidence : z* = 1.96
So the 95% confidence interval becomes,
Hence, a 95% confidence interval for the mean monthly rent for unfurnished one bedroom apartments available for rent in this community=
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.
The probability that at least two out of the three workstations are available is 0.967.
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.
#SPJ3
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! :)
yards of purple fabric for the lining of the cap
How much more blue fabric than purple fabric should Jill buy?
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.