Answer:
Lf(x) = Lg(x) = Lh(x) = 1 - 2x
value of the functions and their derivative are the same at x = 0
Step-by-step explanation:
Given :
f(x) = (x − 1)^2,
g(x) = e^−2x ,
h(x) = 1 + ln(1 − 2x).
a) Determine Linearization of f, g and h at a = 0
L(x) = f (a) + f'(a) (x-a) ( linearization of f at a )
for f(x) = (x − 1)^2
f'(x ) = 2( x - 1 )
at x = 0
f' = -2
hence the Linearization at a = 0
Lf (x) = f(0) + f'(0) ( x - 0 )
Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x
For g(x) = e^−2x
g'(x) = -2e^-2x
at x = 0
g(0) = 1
g'(0) = -2e^0 = -2
hence linearization at a = 0
Lg(x) = g ( 0 ) + g' (0) (x - 0 )
Lg(x) = 1 - 2x
For h(x) = 1 + ln(1 − 2x).
h'(x) = -2 / ( 1 - 2x )
at x = 0
h(0) = 1
h'(0) = -2
hence linearization at a = 0
Lh(x) = h(0) + h'(0) (x-0)
= 1 - 2x
Observation and reason
The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0
What is the answer
5 10 25 100 × ÷ ÷
Answer: 1/50, or 0.02
Step-by-step explanation:
I'm assuming this is 5*10/25/100. if you just follow the equation, you get 50/25/100, which is 2/100, or 1/50.
Given that Z1 = 1 + i and Z2 = 3 - 4i, find z1z2
Answer:
7-i
Step-by-step explanation:
It is asking for the product of the given complex numbers.
Z1Z2 means Z1 times Z2
(1+i)(3-4i)
You can do the whole foil thing here since we are multiplying a pair of binomials. But all you are doing when you do that is multiplying every term in the first ( ) to every term in the second ( ).
1(3)+1(-4i)+i(3)+i(-4i)
Simplify each term. That is, perform the multiplication in each term:
3-4i+3i-4i^2
Combine like terms and also replace i^2 with (-1):
3-1i-4(-1)
Multiplication identity property used:
3-i+4
Combine like terms:
7-i
ANSWER ASAPPPP PLS
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2
3
4
5
6
Answer:
I'm going to help you figure this out because I am actually on the same assignment. If you do not understand what it is asking, it is not asking you to break down the function notation, it is simply asking you to substitute (X) with 2,3,4,5,and 6 and then to solve it on each line
Points A, B, C, and D lie on a line in that order. If AD/AC = 2/1 and AD/AB = 3/1, what is the value of AC/BD?
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Answer:
3/4
Step-by-step explanation:
It might be easier to start by expressing the ratios with AD as the denominator.
AD/AC = 2/1 ⇒ AC/AD = 1/2
AD/AB = 3/1 ⇒ AB/AD = 1/3
From the latter, we have ...
(AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD
Then the desired ratio is ...
AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)
AC/BD = 3/4
Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(-4, -33) (1, 2) (9, 162)
HELP PLZ
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Answer:
y = x^2 +10x -9
Step-by-step explanation:
Quadratic regression generally requires the use of "technology" to aid in finding the equation of the curve of best fit. Use the technology you've been introduced to.
__
When only a few data points are provided, I prefer to use the Desmos graphing calculator. It shows the equation to be ...
y = x^2 +10x -9
A carpet expert believes that 9% of Persian carpets are counterfeits. If the expert is right, what is the probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%
Answer:
0.0060 = 0.6% probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A carpet expert believes that 9% of Persian carpets are counterfeits.
This means that [tex]p = 0.09[/tex]
Sample of 686:
This means that [tex]n = 686[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{0.09*0.91}{686}} = 0.0109[/tex]
What is the probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%?
Proportion lower than 9% - 3% = 6% or higher than 9% + 3% = 12%. The normal distribution is symmetric, thus these probabilities are equal, so we can find one of them and multiply by 2.
Probability it is lower than 6%
p-value of Z when X = 0.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0109}[/tex]
[tex]Z = -2.75[/tex]
[tex]Z = -2.75[/tex] has a p-value of 0.0030
2*0.0030 = 0.0060
0.0060 = 0.6% probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%
Type the correct answer in each box. The volume of a cube is given by and the total surface area of a cube is given by , where s is the side length of the cube. If the side length of a cube is 5 inches , the volume of the cube is ____ cubic inches and its total surface area is ____ square inches.
Answer:
hope this will help you a lot
is 7/4 bigger than -4 / 7
Answer:
7/4 is larger than -4/7
Step-by-step explanation:
7/4 is greater than a whole. 4/4 = 1 whole and the fraction is 7/4. -4/7 is smaller than a whole and is a negative number.
Therefore 7/4 is bigger
Hope this helps!
Answer:
yes 7/4 is bigger than -4/7
Step-by-step explanation:
its bigger because its positive!
in a school there are 650 girls. It is 26% of the whole students, how many boys are there in the school?
Answer:
Step-by-step explanation:
Frt7v6c87buhinjomp,l.;
In a box of chocolates, 12 of the chocolates are wrapped in red foil. That is 30% of the chocolates in the box. How many chocolates are there?
Answer:
The answer is 40 chocolates in the box in total
Ted is not particularly creative. He uses the pickup line "If I could rearrange the alphabet, I'd put U and I together." The random variable x is the number of women Ted approaches before encountering one who reacts positively. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
No, the sum of all the probabilities is not equal to 1.
Step-by-step explanation:
Given
[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} & {P(x)} & {0.001} & {0.007} & {0.033} & {0.059} \ \end{array}[/tex]
Required
Determine if the given parameter is a probability distribution
For a probability distribution to exist, the following must be true;
[tex]\sum P(x)=1[/tex]
So, we have:
[tex]\sum P(x) = 0.001 + 0.007 + 0.033 + 0.059[/tex]
[tex]\sum P(x) = 0.1[/tex]
Hence, it is not a probability distribution because the sum of all probabilities is not 1
A charity raffle prize is $1,000. The charity sells 4,000 raffle tickets. One winner will be selected at random. At what ticket price would a ticket buyer expect to break even
Answer:
0.25
Step-by-step explanation:
Given that :
Charity raffle price = $1000
Amount of ticket sold = 4000
Only one winner is to be selected ;
Point ticket buyer is expected to break even :
Probability of winning = 1 / number of ticket sold = 1 / 4000 = 0.00025
P(winning) * raffle price = 0.00025 * 1000 = 0.25
Which value is in the domain of f(x)?
f(x) =
2x+5, |-6 < xso
- 2x + 3, 0 < x 34
N
-7
-6
5
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Answer:
4
Step-by-step explanation:
The function definition tells you its domain is ...
-6 < x ≤ 4
Values -7, -6, and 5 are not in this domain.
Of the listed values, only 4 is in the domain.
Help! This is timed!
Answer: 5 ft i think so
Use the Pythagorean theorem
Evaluate 19C1 PLEASE HELP
Answer:
[tex]{19}C_1=19[/tex]
Step-by-step explanation:
We need to find the value of [tex]{19}C_1[/tex].
C stands for combination.
The formula of combination is as follows :
[tex]nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Here,
n = 19 and r = 1
So,
[tex]nC_r=\dfrac{19!}{1!(19-1)!}\\\\nC_r=\dfrac{19!}{1!\times 18!}\\\\nC_r=\dfrac{19\times 18!}{1!\times 18!}\\\\nC_r=19[/tex]
So, the value of [tex]{19}C_1[/tex] is 19.
Answer:
Your answer will be 19C1 =19
If the fixed cost is 9000 per year. Variable costs are estimated to be Tk. 60.75 / item. The firm wants to break even if 80 items are sold per year. What should be the unit price of the item?
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Answer:
Tk 173.25
Step-by-step explanation:
The firm will break even if its cost is equal to its revenue. That is, the price of each item sold must equal the cost of producing it. To cover the fixed cost, a share of it must be added to each of the items sold. Then the break-even price for 80 items is ...
price = variable cost + share of fixed cost
price = Tk 60.75 +9000/80 = Tk 60.75 +112.50 = Tk 173.25
Sketch the graph of each line.
7) 2x - y = -4
Answer:
check the attachment
Step-by-step explanation:
2x - y = - 4
- y = - 4 - 2x
y = 2x + 4
slope of the line = 2 with y - intercept 4
if triangle TAN has vertices T(0, 2), A(-1,3), and N(-2,-4), which of the following coordinates is N' of the dilation from the origin using the scale factor 3?
Answer:
(-6,-12)
Step-by-step explanation:
A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.
[tex] - 2 \times 3 = - 6[/tex]
[tex] - 4 \times 3 = - 12[/tex]
So our new coordinates is
(-6,-12)
Answer:
(-6,-12)
Step-by-step explanation:
A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.
So our new coordinates is
(-6,-12)
Step-by-step explanation:
Which of the following as describes the slope of the line below ? Help pls
Answer:
I think C
Step-by-step explanation:
Sorry if its wrong
How long will it take 500 dollars to double if it is invested at 7% interest compounded semi-annually
Answer:
11 half years
Step-by-step explanation:
The formula for compound interest is
A = P(1+r/n)^(nt), with r representing the interest rate, n being the number of times interest is applied over the time period, and t being the amount of time periods.
If we make the time period a half year (so interest is compounded once per time period), n=2. Then, our interest rate is 7%, or 0.07 (to convert from percent to decimal, simply divide by 100). Our starting amount is 500, and we want it to double, making it 1000. Our formula is thus
1000 = 500 (1+0.07)^(t)
divide both sides by 500
2 = (1+0.07)^(t)
2 = (1.07)^(t)
Using logarithms, we can say that
[tex]log_{1.07} 2 = t[/tex]
and using a calculator, we get
10.24 = t
Since interest is only compounded once per time period, though, we have to round up to make sure it doubles, so t = 11
How many fourths are in 3 4 ?
O 4 Over 16
O One-half
O 3
O 4
Answer:
⭕ 3hope it helps much
What is the approximate percent change in temperature that went down from 120 degrees to 100 degrees?
Answer:
17%
Step-by-step explanation:
change in temprature=100-120=-20
% chsnge in temp.=-20/120 ×100=-50/3 %=-16.66666...≈-17%
negative sign shows temperature is coming down.
I need help finding this solution.
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Answer:
-16∛2
Step-by-step explanation:
It can be helpful to have some familiarity with the cubes of small integers. For example, ...
2³ = 8
6³ = 216
With this in mind you recognize the expression as ...
3∛((-6)³(2)) +∛((2³)(2))
= 3(-6)∛2 +2∛2
= (-18 +2)∛2
= -16∛2
PLEASE I NEED HELP!!!!!
Find the volume of this sphere.
Use 3 for TT.
L-r=3ft
V [?]ft3
V = Tr3
Answer:
113.1 =VOLUME , 4/3 X 3.14 (3) ^3 = 113.1
Express each ratio as a fraction in its lowest terms.
18 hours to 2 days
Answer:
3/8.
Step-by-step explanation:
First convert days to hours:
2 days = 2 * 24 = 48 hours.
The greatest common factor of 18 and 48 = 6 so the required fraction is
18/48
= (18/6) / (48/6)
= 3/8.
HELP BRAINLIEST?? ALL THE TUTORS ARE TAKEN
Answer:
The slope of the green line is 3
Step-by-step explanation:
The lines are perpendicular, so the slopes are negative inverses
-1/(-1/3)
3
Match the number of significant figures to the value or problem.
1
?
0.008
4
?
54
3
?
1002. 43.2
2
?
1.068
Answer:
answer is 1 2 3 and 4 respectively of given match the following
Draw a line representing the “rise” and a line representing “run” of the line. State the slope of the line in simplest form
Answer: The rise and run is the two point between each other on a line for example 1/2 rise over run. 1 is rise and 2 is run so y=mx +b the slope is m and the y int is b so
Y= 1/2x + 3 the 3 is going to be on the Y acis not the X its important not to mix the two. In other words go to 0,0 make a line go up.. the from 0,0 go doen the same length
Step-by-step explanation:
What is the length of an arc with a central angle of 2/3pi radians and a radius of 24 centimeters?
Use 3.14 for pi.
Enter your answer, as a decimal, in the box.
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Answer:
50.24 cm
Step-by-step explanation:
Fill in the given numbers and do the arithmetic.
s = rθ
s = (24 cm)(2/3π) = (24 cm)(2/3)(3.14) = 50.24 cm
Convert the equation (y + 2) = –1/3(x – 4) to the point-slope form. Then fill in the blanks below to describe how to graph the equation. Plot the point _______, move _______ unit(s) down, and _______ unit(s) over to find the next point on the line.
A. (–2, 4), one, three
B. (4, –2), one, three
C. (2, 4), one, three
D.(4, –2), three, one
Answer:
A. (–2, 4), one, three
Step-by-step explanation:
For a linear equation:
y = a*x + b
the point-slope form is:
(y - y₁) = m*(x - x₁)
Where we know that this line has the slope m, and passes through the point (x₁, y₁)
In this case, the equation:
(y + 2) = –1/3(x – 4)
is already in the point-slope form.
here we have:
y₁ = -2
x₁ = 4
then the point is (-2, 4)
m = -(1/3)
m = -1/3 means that when we move 3 units to the right, we need to move one unit down. (or the inverse, we can move one unit down and 3 to the right)
So, to complete the statement we have:
plot the point (-2, 4), move one unit down, and three units over to find the next point on the line.
The correct option is A.