To use the degree 2 Taylor polynomial centered at the origin for f, we first need to find the polynomial. The degree 2 Taylor polynomial for f centered at the origin is given by:
P(x) = f(0) + f'(0)x + (f''(0)/2)x^2
where f(0) = √4 = 2, f'(0) = 1/2(4+x)^(-1/2) evaluated at x=0 is 1/4 and f''(0) = (-1/2)(4+x)^(-3/2) evaluated at x=0 is -1/8.
So, we have:
P(x) = 2 + (1/4)x - (1/16)x^2
Now we can use P(x) to estimate the value of the integral I.
I = ∫20 f(x)dx ≈ ∫20 P(x)dx
= ∫20 (2 + (1/4)x - (1/16)x^2) dx
= 2x + (1/8)x^2 - (1/48)x^3 |[0,2]
= 4 + (1/2) - (1/12)
= 25/6
Therefore, I ≈ 25/6, which is closest to option (4) I ≈ 14/3.
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In the exponential function f(x) = 3^-x 2, what is the end behavior of f(x) as x goes to [infinity]?
For an exponential function [tex]f(x) = 3^{-x}2[/tex] as x goes to infinity, f(x) goes to zero.
We have been given an exponential function [tex]f(x) = 3^{-x}2[/tex]
We need to check the end behavior of f(x) as x goes to infinity.
Consider,
[tex]\lim_{x \to \infty} f(x)\\\\= \lim_{x \to \infty} 3^{-x}2\\\\=2\times \lim_{x \to \infty} 3^{-x}\\\\=2\times 3^{-\infty}\\\\=2\times 0\\\\=0[/tex]
This means, x [tex]\rightarrow[/tex] infinity, f(x) goes to 0
As x goes to infinity, f(x) goes to zero.
Therefore, for an exponential function [tex]f(x) = 3^{-x}2[/tex] as x goes to infinity, f(x) goes to zero.
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7. The table below shows the soft drinks preferences of people in two age groups.
Sprite
Lemonade
20
30
50
Under 21 years of age
Between 21 and 40
Totals
25
35
60
If one of the 110 subjects is randomly selected, find the probability that:
a) A person prefers to drink sprite
b) A person is between 21 and 40 years old.
c) A person drinks lemonade given they are between 21 and 40.
d) A person drinks Sprite given they are under 21 years of age.
Totals
45
65
110
The calculated probabilities are
0.54550.59090.46150.5556a. The probability of the people that prefer sprite isProbability = 60/110
= 0.5455
B. The probability that a person is between 21 and 40probability = 65/110
= 0.5909
C. Probability of drinking lemonade given that age is between 21 and 40Probability = 30/65
= 0.4615
d. Probability of sprite when under 2125/45
= 0.5556
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Alissa is analyzing an exponential growth function that has been reflected across the y-axis. She states that the domain of the reflected function will change because the input values will be the opposite sign from the reflected function. Simon disagrees with Alissa. He states that if an exponential function is reflected across the y-axis, the domain will still be all real numbers.
Which student is correct and why?
Alissa is correct because the domain will change from negative to positive x-values.
Alissa is correct because a reflection across the y-axis will change the possible input values of the reflected function.
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.
Neither student is correct.
Answer:
C) Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.================
The exponential growth function has:
Domain - all real numbers,Range - all real numbers excluding zero.When the function is reflected across the y-axis, we'll have no change to domain or range from what is described above.
Alissa is correct, the input values change to opposite, however the domain stays same - all real numbers.
It means Simon is correct with his statement.
The matching answer choice is C.
Answer:
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.
Step-by-step explanation:
Exponential Function
General form of an exponential function: [tex]f(x)=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Reflection in the y-axis
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
As the exponential function is a growth function, b > 1.
If the exponential growth function has been reflected in the y-axis, the x variable is negative:
[tex]\implies f(x)=ab^{-x}[/tex]
Regardless whether the initial value [tex]a[/tex] (y-intercept) is positive or negative, the domain of an exponential function is (-∞, ∞) so it is unrestricted.
Therefore, if the function is reflected across the y-axis, the output value for each input value will change, but the domain itself will not change and will still be all real numbers.
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Hank runs a successful hot dog stand right across from the arch at the University of Georgia in downtown Athens. Hank has to order his hot dogs, buns, mustard, relish, and all other condiments in bulk, as well as pay taxes, licensing fees, and other small business expenses. Therefore, Hank has a relatively large “sunk” cost associated with his business – it averages out to $950 per week just to keep the cart open. The cost of producing hot dogs is given by C(h) = 950 + .45(h). Where h is the number of hot dogs and C(h) is the cost. If he sold 100 hotdogs at $10.25 each, how much profit would he make for the week?
The profit he would make in one week is $30.
What is Hank's profit?Profit is the total revenue less total cost.
Total revenue = price of one hot dog x number of hotdogs sold
$10.25 x 100 = $1025
Total cost = 950 +( 0.45 x 100)
950 + 45 = 995
Profit = 1025 - 995 = $30
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Given that e parallel f and g is a transversal, we know that angle 4 is-congruent-to angle 5 by the alternate interior angles theorem. we also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the ________. therefore, angle 1 is-congruent-to angle 8 by the substitution property. corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem
∠5 ≅ ∠8 (vertically opposite angles)
Hence, ∠1 ≅ ∠8 by the transitive property.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line e and f are parallel lines cut by the the transversal g.
∠1 ≅ ∠4(vertically opposite angles)
Hence,
∠4 ≅ ∠8(corresponding angles)
Since, ∠1 ≅ ∠4
Then, by substitution,
∠1 ≅ ∠8 (transitive property)
∠5 ≅ ∠8 (vertically opposite angles)
Therefore, ∠1 ≅ ∠8 by the transitive property.
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This figure represents a design found in a glass panel. ABCD is a rectangle with
midpoints X, Y, Z, and W. Emily states that the quadrilateral formed by the segments
that join the midpoints of the sides is a rhombus. Do you agree with her? Explain why
or why not.
Answer: Yes
Step-by-step explanation:
Since ABCD is a rectangle, [tex]\angle AXY[/tex], [tex]\angle YBZ[/tex], [tex]\angle WCZ[/tex], and [tex]\angle WDX[/tex] are all right angles, and are thus all congruent because all right angles are congruent. Furthermore, because ABCD is a rectangle, we know that [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\overline{AD} \cong \overline{BC}[/tex]. Because we are given that X, Y, Z, and W are midpoints, using the fact that halves of congruent segments are congruent, we can conclude that [tex]\overline{AY} \cong \overline{YB} \cong \overline{CW} \cong \overline{WD}[/tex] and that [tex]\overline{AX} \cong \overline{XD} \cong \overline{BZ} \cong \overline{ZC}[/tex]. As a result, we can conclude that [tex]\triangle AYX \cong \triangle DXW \cong \triangle CWZ \cong \triangle BYZ[/tex] by SAS, and thus by CPCTC, [tex]\overline{AY} \cong \overline{XW} \cong \overline{ZW} \cong \overline{YZ}[/tex]. Therefore, since the quadrilateral formed by the midpoints has four congruent sides, it must be a rhombus.
Suppose you are asked to compare two functions, A and B. Function A written in slope-intercepts form, y= -3x + 4. Function B is graphed on the coordinate plane and has a greater rate of change but lower y-intercept than function A. Describe what is true about the graph of function B.
Answer:
Use the slope and one of the points to solve for the y-intercept (b). One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.
Step-by-step explanation:
The point M(-6, -4) is translated 2 units right. What are the coordinates of the resulting point, M'?
Answer:
(-4,-4)
Step-by-step explanation:
If the point is moved 2 units to the rights then we add 2 to the x value: -6+2 = -4
(-4,-4)
Select the correct answer from each drop-down menu. the endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5). the center of the circle is at the point , and its radius is units. the equation of this circle in standard form is .
The equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².
Based on the calculations, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5²
The equation of a circle.
Mathematically, the standard form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center.
r is the radius of a circle.
The midpoint of the given points represents the center of this circle:
h = (4 + 4)/2 = 4
k = (5.5 + 10.5)/2 = 8
Next, we would determine the radius by using the distance formula for coordinates:
r = √[(x₂ - x₁)² + (y₂ - y₁)²]
r = √[(4 - 4)² + (10.5 - 5.5)²]
r = √[0² + 5²]
r = √25
r = 5 units.
Therefore, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².
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Complete the following proof.
Prove: In an equilateral triangle the three medians are equal.
+a
e-(.*)-(
2a
P=
- (0 + 2ª + )-( ₂² )-(.)
?
2
0+
2-(+)-()
|− a)² + (
R-
C(a. b)
PC
=
(2a, 0)
√3 (with side - 2a)
QA-
- √(₁-2)* ·-(- -)
J(J
9a² 8²
a² (√3)²
B
(Height of equalateral A = b)
X
RB
a²3
√3
(²-²)² + (- - -)*
-J* · ·
()*(3
√√3
The median of an equilateral triangle are equal has been proved.
How to proof the triangle?The medians are given as AD, BE, and CF.
Let AB = AC = BC = x unit.
In triangles, BFC and CEB, we've
BF = CE.
ABC = ACB since they're both 60°
BC = BC
By SAS congruence,
BFC = CEB = BE = CF.
Similarly, we've AB = BE
Therefore, AD = BE = CF
median of an equilateral triangle are equal has been proved.
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what are the differences between cos(x) and cos^-1(x)
cos^-1(x) represents the inverse of cos(x).
Select the correct answer.
The parent function f(x)=√x is transformed to g(x) = 2f(x-3). Which is the graph of g(x)?
The function g(x) is a translation of 3 units to the right and a vertical dilation by scale factor k = 2 of f(x), the graphs of both functions can be seen in the image at the end.
Which is the graph of g(x)?We know that g(x) is a transformation of the parent function f(x) = √x, such that:
g(x) = 2*f(x - 3)
g(x) = 2*√(x - 3)
Then we can see that g(x) is a translation of 3 units to the right followed by a vertical dilation of scale factor 2 of the parent function f(x).
So to graph g(x) you first need to move the whole graph of f(x) 3 units to the right, and then apply a dilation vertically.
The graph of g(x) and f(x) can be seen in the image below:
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210÷[5+16÷2{6−18÷(7+2)}]−15
Answer:
[tex]-\frac{345}{37}[/tex]
Step-by-step explanation:
Just follow the order of operations
210÷[5+16÷2{6−18÷(7+2)}]−15
= 210÷[5+16÷2{6−18÷9}]−15 (calculate 7+2)
= 210÷[5+16÷2{6−2}]−15 (calculate 18÷9)
= 210÷[5+16÷2{4}]−15 (calculate 6-4)
= 210÷[5+16÷2×4]−15
= 210÷[5+8×4]−15 (calculate 16÷2)
= 210÷[5+32]−15 (calculate 8×4)
= 210÷[37]−15 (calculate 5+32)
= 210÷37−15
= 210÷37−(15×37)÷37 (put on the same denominator)
= 210÷37−555÷37 (calculate 15×37)
= (210−555)÷37
=-345÷37 (calculate 210-555)
Find the hourly rate of pay for each of the following jobs: a) Tamara owns a salon and earns R1050 for 6 hours and 15 minutes of work.
Answer:
₹168 per hour
Step-by-step explanation:
The hourly rate at which Tamara is paid can be found by dividing her ₹1050 pay by the 6:15 hours that she worked.
HoursWe know there are 60 minutes in an hour, so the fraction of an hour represented by 15 minutes is ...
(15 min)/(60 min/h) = (15/60) h = 1/4 h = 0.25 h
Added to the 6 whole hours Tamara worked, her pay is for 6.25 hours.
Hourly rateThe pay per hour is found by dividing pay by hours.
₹1050/(6.25 h) = ₹168/h
Tamara's hourly rate of pay is ₹168 per hour.
The step 2 of a certain construction is shown below. What construction is being performed?
bisect an angle
copy an angle
copy a segment
construct a right anglers
The construction that is performed based on the information given will be D. construct a right angle.
What is construction?It should be noted that construction simply means the accurate drawing of shapes, angles, and the line in geometry.
In this case, the construction that is performed based on the information given will be to construct a right angle.
It should be noted that a right angle has an angle of 90°.
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2/y = 4/2 find y
Answer is y=1 but how?
[tex] \frac{2}{y} = \frac{4}{2} [/tex]
[tex]4 = 4y[/tex]
[tex] \frac{4}{4} = y[/tex]
[tex]1 = y[/tex]
Hope it helps you any confusions you may ask!
Let's see
2/y=4/22/y=2y=2/2y=1Verified
Four different sets of objects contain 4,5,6, and 8 objects respectively. how many unique combinations can be formed by picking one object from each set?
A. 23
B. 141
C.960
D. 529
The number of unique combinations that can be formed by picking one object from each set is =960. That is option C.
Calculation of unique combinations of a number setNumber combination is a mathematical technique that shows the number of possible arrangements in a collection of items.
The first set of objects = 4. There are a total of 4 possibilities.
The second set of objects = 5. There are a total of 5 possibilities
Therefore from first and second set, the total number of possibilities = 4×5 = 20
For the whole set, the total possibilities;
= 4×5×6×8
= 960
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Which equation is equivalent to
f(x) = 16x4 -81 = 0?
✓(4x² +9)(4x² - 9) = 0 ✓
COMPLETE
Select all of the zeroes of the function.
O
2/3
DONE
The equivalent equation is (4x² + 9)(4x² - 9) and the zero's are x =± 3 / 2 and x = ± 3 / 2i
How to find equivalent equation?The equivalent equation can be found by factoring. Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.
Therefore,
f(x) = 16x⁴ - 81 = 0
Hence,
9 × 9 = 81
4x² × 4x² = 16x⁴
Therefore,
16x⁴ - 81 = (4x² + 9)(4x² - 9)
Hence,
The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).
The zero's of the function are as follows:
4x² = 9
x² = 9 / 4
x =± 3 / 2
4x² = -9
x² = - 9 / 4
x =√-9 / 2
x = ± 3 / 2i
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help!!!!>>>>>>>Explain the difference between perimeter
and volume.
a. Perimeter represents space inside a three-
dimensional object. You use volume to
measure the distance around an object.
b. You use perimeter to measure the distance
around an object. Volume represents space
inside a two-dimensional object.
c. Perimeter represents space inside a two
dimensional object. You use volume to
measure the distance around an object.
d. You use perimeter to measure the distance
around an object. Volume represents space
inside a three-dimensional object.
Someone help me with a step by step explanation to simplifying
100x(5 - 3p)
ty
Answer:
500x - 300xp.
Step-by-step explanation:
100x(5 - 3p)
First distribute the 100x over the parentheses:
= 100x*5 - 100x * 3p
Now simplify:
= 500x - 300xp.
match the graph with jts inequality
help helphelphelp help
Answer:
y<x
Step-by-step explanation:
Alright so you do know that the y=x has got the equal amount for both y and x right and it also is a bisector for the first and third area, that's that
the graph is show the same thing but with some blue area and the area show x values which less than y values sooo you answer is y<x
The number of jobs for nurses is expected to increase by 711,900 between 2010 and 2020. during the same decade, the number of jobs for physicians is expected to increase by 168,300. find the ratio of the increase in jobs for physicians to the increase in jobs for nurses.
The Ratio would be 43:100.
Lets simplify the problem,
Expected increase of nurses = 711900
Expected increase of physicians = 168300
Ratio = Expected increase of nurses / Expected increase of physicians
Ratio = 711900 / 168300
= 43/100
Ratio = 43:100
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The cost of 11 identical mobile phones is 91,300rs/-. what is the cost of 1 mobile phone?
The answer is 8300.
Divide 91300 by 11 you will get the answer.
Problem-solving is the act of defining trouble; figuring out the cause of the problem; figuring out, prioritizing, and choosing alternatives for an answer; and enforcing a solution.
Problem-fixing starts with identifying the difficulty. For instance, a teacher might want to discern the way to improve student performance on a writing talent test. To do that, the trainer will assess the writing checks looking for areas of development.
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Triangle M N O maps to triangle M prime N prime O prime.
In the diagram, triangle MNO maps to triangle M'N'O'.
Complete the statements.
Angle M corresponds to angle
Side
is the image of side NO.
Angle M corresponds to angle M' and
Side N'O' is the image of side NO
The vertices of each triangle must have a one-to-one correspondence. This phrase means that the measure of each side and angle of each triangle is equal to the side or angle of the other triangle.
Here it is given that Triangle MNO maps to triangle M'N'O'
We need to find that Angle M corresponds to which angle and the image of side NO
By one to one correspondence we get that
Angle M corresponds to angle M' and
Side N'O' is the image of side NO
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Tony is given _9 10 hour to mow a lawn. he only uses _ 2 3 of the given time to mow the lawn. how much time is left
[tex]\frac{7}{30}[/tex] units of time is left.
What is a fraction?A fraction is a component of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of pieces of a specific size, such as one-half, eight-fifths, and three-quarters.To find how much time is left:
Given - Tony is given [tex]\frac{9}{10}[/tex] hour to mow a lawn. he only uses [tex]\frac{2}{3}[/tex] the given time to mow the lawn.
Simplify subtract [tex]\frac{9}{10}[/tex] by [tex]\frac{2}{3}[/tex] as follows:
[tex]\frac{9}{10}-\frac{2}{3} =\frac{27-20}{30} =\frac{7}{30}[/tex]
Therefore, [tex]\frac{7}{30}[/tex] units of time is left.
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The three sides of a right triangle have integral lengths which form an arithmetic sequence. How many numbers between 1 and 2020 inclusive can be the side of the hypotenuse
There are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence. This can be obtained by forming the arithmetic sequence, equating by Pythagoras theorem and finding numbers divisible by the integral.
Find the value of hypotenuse?Let the arithmetic sequence be (a - d), a, (a+d)
Using Pythagoras theorem,
(a - d)² + a² = (a+d)²
a² -2ad + d² + a² = a² + 2ad + d²
2a² - 2ad + d² = a² + 2ad + d²
2a² - a² + d² - d² = 2ad + 2ad
a² = 4ad
a = 4d
Thus hypotenuse will be (a + d) = 4d + d = 5d
How many numbers between 1 and 2020 inclusive can be the side of the hypotenuse?Since the value of hypotenuse is 5d, the total numbers divisible by 5 between 1 and 2020 will be the number of possible sides of the hypotenuse.
There are 2020 numbers between 1 and 2020 inclusive
The numbers divisible by 5 = 2020/5 = 404
Hence there are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence.
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Pleassee help!!!
will give brainliest!!
The amplitude is 6 and vertical translation is 2. Therefore Option C is correct
For the transformation of y=f(x) to f(x)+k, for k>0, f(x) is moved k upwards and for transformation of f(x) to f(ax) it depends upon the value of a If |a|>1 then f(ax) is f(x) squashed horizontally by a factor of a and If 0<|a|<1 then f(x) is stretched horizontally by a factor of a.
So by the graph it is clearly visible that amplitude of the graph is 6 as the distance from the centre line (or the still position) to the top of a crest or to the bottom of a trough is 6 and the vertical translation is 2 as distance moved by the graph upwards is 2.
Thus the amplitude is 6 and vertical translation is 2.
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A right-angled triangle has a hypotenuse of length 8 and another side of length 3.
Find the length of the unknown side g.
Write each step of working as an equation and give the answer to two decimal places
Answer:
The file contains the solution to the above question
Prior to September, 2000, taxi fares from Washington DC to Maryland were described as follows: $2.00 up to and including 1⁄2 mile, $0.70 for each additional 1⁄2 mile increment.
- Describe the independent and dependent variables and explain your choices.
Answer:
See below.
Step-by-step explanation:
The $2 charge is independent of the miles driven. It cost $2 regardless of mileage. The $0.20.half mile is the dependent variable. The cost changes as a function of 1/2 miles driven.
Need help with Slope (find the slope of each line)these 8 problems show your work need ASAP
Answer:
17) 3
18) -5/4
19) 4/2 or 2
20) 1
21) 2/4 or 1/2
22) 4/7
23) -2/2 or -1
24) -1/3
Step-by-step explanation:
the easiest thing to do is go by rise over run and count the number of units, hope this helped!