We start by using the quotient rule to find the first derivative of f(x):
f'(x) = -(2(6+x))/((6+x)^2)^2 = -2/(6+x)^3
Next, we can use the formula for the geometric series with ratio r = -(x-(-6))/(-6) = (x+6)/6:
1/(6+x)^3 = (-1/6)(x+6)(-1/6)^n = (-1/6) * [(x+6)/6]^n
Therefore, we have:
f(x) = (-1/6) * [(x+6)/6]^n
Substituting in the value of n, we get the power series representation of f(x):
f(x) = (-1/6) * [(x+6)/6]^n = (-1/6) * [(x+6)/6]^0 + (-1/6) * [(x+6)/6]^1 + (-1/6) * [(x+6)/6]^2 + ...
Simplifying, we get:
f(x) = 1/36 - (x+6)/216 + (x+6)^2/1296 - (x+6)^3/7776 + ...
Therefore, the power series representation of f(x) centered at is:
f(x) = ∑ (-1/6) * [(x+6)/6]^n, n = 0 to infinity
f(x) = 1/36 - (x+6)/216 + (x+6)^2/1296 - (x+6)^3/7776 + ...
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A rectangular equation that is a function will be a function in any coordinate system. true or false ?
Answer:
True.
Step-by-step explanation:
In this true or false question, the answer is true.
Hope this helps!
Answer:
False
Step-by-step explanation:
Not every function in a rectangular plane will be a function in every plane. Hope this helps
Consider rolling a fair die thrice and tossing a fair coin sixteen times. Assume that all the tosses and rolls are independent. The chance that the total number of heads in all the coin tosses equals 12 is (
The probability that the total number of heads in all the coin tosses equals 12 is 0.0273.
Given a fair dice and tossing a fair coin sixteen times.
We have to find the probability that the total number of heads in all the coin tosses equals 12.
The probability lies between 0 and 1.
Probabiltiy of coming head when the coin is tossed 1 time is 0.5 and probability of coming tails is also 0.5.
Let X shows the sum of heads while tossing.
P(X=12)=?
We can find the probability using binomial theorem.
=[tex]16C_{12} (0.5)^{12} (0.5)^{2}[/tex]
We have to toss sixteen times and out of 16 times we need head 12 times.
=16!/12!4!*0.00024*0.0625
=1820*0.000015
=0.0273
Hence the probability that the total number of heads in all the coin tosses equals 12 is 0.0273.
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Find a linear inequality with the following solution set. Each grid line represents one unit.
The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.
How to derive the inequality that represents the image
Herein we have an representation of a inequality of the form y ≤ f(x), where f(x) is a linear function, that is, a first grade polynomial. By geometry we know that a equation of the line can be known from two distinct points set on Cartesian plane:
Slope
m = [- 4 - (- 2)] / [4 - (- 2)]
m = (- 2) / 6
m = - 1 / 3
Intercept (m = - 1 / 3, (x, y) = (4, - 4)
b = y - m · x
b = - 4 - (- 1 / 3) · 4
b = - 4 + 4 / 3
b = - 8 / 3
Then, we find that the inequality is:
y ≤ (- 1 / 3) · x - 8 / 3
8 / 3 ≤ (- 1 / 3) · x - y
(- 1 / 3) · x - y ≥ 8 / 3
The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.
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Right triangles \boxed{1}
1
start box, 1, end box, \boxed{2}
2
start box, 2, end box, and \boxed{3}
3
start box, 3, end box are given with all their angle measures and approximate side lengths.
Use one of the triangles to approximate the ratio \dfrac{WY}{WX}
WX
WY
start fraction, W, Y, divided by, W, X, end fraction.
Choose 1 answer:
Considering right-angled triangle XYW, an approximate ratio WY/WX is equal to: A. 0.34.
How to approximate the ratio WY/WX?Considering right-angled triangle XYW, we would apply the law of cosine to approximate the ratio WY/WX. Mathematically, the law of cosine is given by:
cos(θ) = Adj/Hyp
Where:
Adj is the adjacent side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.Substituting the given parameters into the formula, we have;
cos(θ) = WY/WX
cos(70) = 3.4/10
0.34 = 0.34.
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Complete Question:
Right triangles 1-2 and 3 are given with all their angle measures and approximate side lengths.
Use one of the triangles to approximate the ratio WY/WX
A. 0.34
B. 0.94
C. 1.06
D. 2.76
Which function in vertex form is equivalent to f(x) = x² + x +1?
○ f(x) = (x + 1/ 1³² + 1 ²1/0
3
4
○ f(x) = (x + 1)² + 2/1/2
○ f(x) = (x + ²/2 1²³ + ²/
4
5
f(x) = (x + 1/2-1² + ²/1/2
4
Answer:
[tex]\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]
Step-by-step explanation:
NOTE :
[tex]x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}[/tex]
………………………………………
f(x) = x² + x +1
[tex]=x^{2}+2\times \frac{x}{2} +1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]
What is 1 plus 1
Ok so what is 2 times 7
Alright what is 205 minus 306
Add all the answers together and multiply it by 5 then divide it by 1
Zoe says an equilateral triangle is always an acute triangle, but an acute triangle is never an equilateral triangle. Which statement explains whether Zoe is correct or not?
A. Zoe is not correct because equilateral triangles are acute triangles with three sides of equal length. Acute triangles can sometimes be equilateral triangles.
B. Zoe is not correct because equilateral triangles have three acute angles. Acute
triangles have three acute angles, so acute triangles are always equilateral triangles.
C. Zoe is correct because equilateral triangles have three sides of equal length, and acute triangles have three sides of different lengths.
D. Zoe is correct because equilateral triangles have three acute angles. Acute triangles have one acute angle, so an acute triangle cannot be an equilateral triangle.
HELP!
Answer:
Step-by-step explanation:
Discussion
She is correct.
An equilateral triangle is a specific acute triangle. An acute triangle can never be an equilateral triangle because it has 3 unequal angles. Your best choice is likely C, but none of the choices are first rate choices.
Answer: C
Can someone please explain how [tex](3^{\frac{1}{5} } )^{2}[/tex] can be written as the radical expression [tex]\sqrt[5]{9}[/tex] ???
We can to convert the expression [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression [tex]\sqrt[5]{9}[/tex]. by using the laws of indices.
What is a radical expression?A radical expression is an expression of the form ⁿ√x where it is called the nth root of x.
Now, to write [tex](3^{\frac{1}{5} } )^{2}[/tex] as the radical expression [tex]\sqrt[5]{9}[/tex], we use following laws of indices
The power law of indices. [tex](x^{\frac{1}{b} } )^{a} = (x^{a} )^{\frac{1}{b} }[/tex] and root law of indices [tex]x^{\frac{1}{a} } = \sqrt[a]{x}[/tex]So, [tex](3^{\frac{1}{5} } )^{2} = (3^{2} )^{\frac{1}{5} }[/tex]
[tex](3^{2} )^{\frac{1}{5} } = 9^{\frac{1}{5} } = \sqrt[5]{9}[/tex]
Thus, we can to convert the expression [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression [tex]\sqrt[5]{9}[/tex]. by using the laws of indices.
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Time Remaining
55:45
Circles C and D overlap. The distance from point C to point D is 7 centimeters.
What is the sum of the areas of circle C and circle D?
7Pi units squared
14Pi units squared
49Pi units squared
98Pi units squared
The sum of the areas of circle C and circle D is 98 units square. Option D
How to determine the areaIt is important to note that the if the circles overlap each other, then the most have the same radius
Also, the formula for area of a circle is given as;
Area = [tex]\pi r^2[/tex]
For Circle C
The value for π = 3. 142
radius = 7cm
Substitute the values into the formula
We have
Area = π × 7 × 7
Area = 49 π units square
For Circle D
Substitute the values into the formula
Area = [tex]\pi r^2[/tex]
Area = π × 7 × 7
Area = 49 π units square
Sum of the areas of circle C and circle D = area of circle C and area of circle D
Sum of the areas of circle C and D = 49π + 49 π
= 98 units square
The sum of the areas of the circles is 98 units square
Thus, the sum of the areas of circle C and circle D is 98 units square. Option D
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write [tex]sec^{2} x=\frac{1}{cos^2x}[/tex] in two equivalent forms.
write sec²x = 1/cos²x in two equivalent forms
sec²x = 1/cos²x
cos²x/cos²x = 1
sec²x = 1 + tan²x
i need help finding all of this stuff
Answer:
Axis Of Symmetry = -2
Vertex = (1,-2)
Min (0,-2)
Domain = All Real #'s
Range = Y is greater than or equal to -2
What is the value of z?
Answer:
(B). 25.25
Step-by-step explanation:
z + 54° + (3z + 1)° + 204° = 360°
4z + 259 = 360
z = 101 ÷ 4
z = 25.25 (B).
Sara's telephone service costs $31 per month plus $0.25 for each local call. Long-distance calls are extra. Last month, Sara's bill was $54.35, including $8.35 in long-distance charges. How many local calls did she make?
Answer:
60 local calls
Step-by-step explanation:
Total price minus the long-distance charges: 54.35 - 8.35 = $46.00
46 minus the fixed per month cost: 46-31 = $15
15 divided by the cost of each local call: 15/0.25 = 60 calls
The number of people in the world was 2.5 billion in 1950. The population has grown by 1.2% each year since then. Create a equation to model this situation using P to represent population (in billions) and y to represent years.
The equation which correctly models the situation in discuss is; P = 2.5(1.012)^y.
Which equation best models the situation?If follows from the task content that the situation given is that The number of people in the world was 2.5 billion in 1950.
Afterwards, The population has grown by 1.2% each year since then. Hence it follows that the function is an exponential one whose factor is; (100+1.2)%= 1.012.
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{10, 11, 12, ..., 55}
How many numbers in the above set are divisible by 2 but not by 10?
(A) 17
(B) 18
(C) 19
(D) 21
Considering concepts of divisibility, the amount of numbers in the set that are divisible by 2 but not by 10 is:
(C) 19.
What are the rules for division by 2 and by 10?Numbers that finish in 0, 2, 4, 6, and 8 are divisible by 2, that is, even numbers are divisible by 2.Numbers that finish in 0 are divisible by 10. Hence, every number that is divisible by 10 is also divisible by 2.The data-set has (55 - 10) + 1 = 46 numbers, hence 23 are divisible by 2. 20, 30, 40 and 50 are also divisible by 10, that is, 4 numbers have to be removed, hence the amount is:
23 - 4 = 19.
Which means that option C is correct.
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The price of a new television is $423. This price includes VAT in 17 1/2%.
a) Work out the cost of the television before VAT was added.
By the end of the year, the value of a television has fallen by 12% of its value at the start of that year. The value of a television was $423 at the start of the year.
b) Work out the value of the television at the end of the third year. Give your answer to the nearest penny.
The cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3
What is the meaning of VAT ?VAT is an acronym for Value Added Tax. This is a tax attach to goods and products.
Given that the price of a new television is $423. This price includes VAT in 17 1/2%.
a) The cost of the television before VAT was added is calculated below.
Let the initial cost = C
(17.5 + 100)/100 x C = 423
117.5/100 x C = 423
1.175C = 423
C = 423/1.175
C = $360
b. By the end of the year, the value of a television has fallen by 12% of its value at the start of that year. If the value of a television was $423 at the start of the year, the value of the television at the end of the third year will be calculated by using the formula
A = P(1 - R%)^3
Substitute all the parameters
A = 423(1 - 12/100)^3
A = 423 x [tex]0.88^{3}[/tex]
A = 288.3 dollars
Therefore, cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3
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Solve for x please anyone?
Answer: x=11
Step-by-step explanation:
The lines are parallel, which you can tell by the two arrows. 4x-8 is a corresponding angle to 3x+3, meaning they are congruent.
4x-8 = 3x+3
x=11
Answer:
x = 11
Step-by-step explanation:
these angles are corresponding angles so they are equal to each other.
4x - 8 = 3x + 3 Subtract 2x from both sides
x - 8 = 3 Add 8 to both sides
x = 11
Plug 11 back into the equations find the angle measurements
4(11) -8 = 36 degrees
3(11) + 3 = 36degrees
13. Rod earned $60 in one week working for a
lawn-care service. He worked for 6 hr. How
much did he earn per hour?
what are the more approprite measures of center and spread for this data set? select two choices: one for the center and one for the spread. please help asap!!
Based on the data set, B. Better measure of center: median. C. Better measure of spread: interquartile range (IQR).
What measures of center and spread are best?The measure of center should be the median because the mean will be affected by the outliers on the left side.
The IQR will be the best measure of spread because the standard deviation is also affected by the outliers.
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What is the area of parallelogram that has a base of 15 meters and a height of 9 meters
The area of the parallelogram is 135 square meters.
What is parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal).
Properties of parallelogram are-
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.The area of parallelogram = Base×Height
A = B×H
Calculation for the area of the given parallelogram.
The base is 15 meters.
The height is 9 meters
Area = 15×9
= 135
Therefore, the area of the parallelogram is 135 square meter.
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-9(z+8)=-9z-72
Llllllll
Answer:
true
-9(z+8)
-9*z +(-9)*8
-9z-72
Describe the sample variance using words rather than a formula. do the same with the population variance
A. The sample variance is the sum of the deviations from the mean divided by the number of measurements minus one. The population variance is the average of the distances of the measurements on all units in the population from the mean.B. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements. The population variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.C. The sample variance is the sum of the deviations from the mean divided by the number of measurements. The population variance is the sum of the deviations from the mean divided by the number of measurements minus one.D. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one. The population variance is the average of the squared distances of the measurements on all units in the population from the mean.
The option D is the correct option.
According to the statement
we have to define the sample variance in the words.
So,
The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.
and in the case of the population variance it becomes
The population variance is the average of the squared distances of the measurements on all units in the population from the mean.
This is the method by which we define the sample variance and population variance.
So, The option D is the correct option.
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what is the product of the fraction below x/x-5 * 2x/x+4
Answer:
A
Step-by-step explanation:
[tex]\frac{x}{x-5}[/tex] × [tex]\frac{2x}{x+4}[/tex] ( no factors cancel on numerator/ denominator )
= [tex]\frac{x(2x)}{(x-5)(x+4)}[/tex]
= [tex]\frac{2x^2}{x^2-x-20}[/tex]
Select the correct answer from each drop-down menu.
The hexagonal seating section in an auditorium has a small entrance at the front. A walkway leading from the entrance to the front of the stage is
30 ft long. What is the approximate area of the entrance and seating section combined?
30 ft
Each side of the hexagon is about oft long. The area of the seating section is about
ft². The area of the entrance and seating section combines is about
ft².
ft². The area of the entrance is about
Each side of the hexagon is about 105.219 ft².
The area of the seating section is about 631.315 ft². The area of the entrance and seating section combines is about 46.764ft².The area of the entrance is about 678. 078ft².What is the hexagon about?Note that:
A F: 30 ft long.
A O = 1/2 A F = 3ft
Δ C J X = 0 X = 1/2 (A F - A O)
= 1/2 (30-3)
= 13.5ft
Sin 60° =[tex]\frac{0x}{cx}[/tex]
cx = [tex]\frac{ox}{sn 60}[/tex]
= 15.558ft = CJ (Sides)
Hence: Each side of the hexagon is: 1/2 CJ x OX = 105.219 ft².
The area of the seating section is:
6 ( Each side of the hexagon )
= 6 x 105.219 ft².
631.315 ft².
The area of the entrance and seating section combines is:
CJ x AO = 46.764ft².
The area of the entrance is:
631.315 ft²+ 46.764ft².
= 678. 078ft².
Hence, Each side of the hexagon is about 105.219 ft².
The area of the seating section is about 631.315 ft². The area of the entrance and seating section combines is about 46.764ft².The area of the entrance is about 678. 078ft².Learn more about hexagon from
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Alan,becky and charlie share 72 sweets in the ratio 2:3:4. howmany sweets do they each receive?
Answer:
alan = 2 = 2x = 16
becky = 3 = 3x = 24
charlie = 4 = 4x = 32
Step-by-step explanation:
add 2 3 4 =
9
72 ÷ 9 = 8
alan = 2 = 2x = 16
becky = 3 = 3x = 24
charlie = 4 = 4x = 32
When a large cake is cut into piece that each weighs 3 ounces, it yields 120 pieces. How many pieces would the cake yield if it were cut into 2- ounce pieces instead
when the cake is cut into [tex]2[/tex] ounce pieces instead of [tex]3[/tex] pieces it yields [tex]180[/tex] pieces.
How to find large cake pieces ?
Given in the question when cake cuts into piece that each weight is [tex]3[/tex] ounce it yields [tex]120[/tex]
So original large cake weight is
[tex]w=120*3\\\\w=360[/tex]
So we can find cake pieces when cake cuts into weight [tex]2[/tex] each piece
[tex]pieces=\frac{360}{2}\\=180[/tex]
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Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
Based on the mean, standard deviation, and the graph, the indicated IQ score would be 115.
What is the indicated IQ score?First, find the z value:
P(Z<z) = 1 - tail value
= 1 - 0.1587
= 0.8413
According to the z-value, this gives a value of:
z = 1
The indicated IQ score is:
= mean + z value z standard deviation
= 100 + 1 x 15
= 115
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Answer:
x = 103.8
Step-by-step explanation:
Calc: [2nd] [VARS] [invNorm]
area: 0.6
z = .2533471011
x = u + (z × o)
x = 103.8
Clarice was late paying her credit card bill of $249. She was charged a 5% late fee. What was the amount of the late fee?
Answer:
You subtract 249 minus 5
You are hiking. The total weight of your backpack
and its contents is 13 3/8 pounds. You want to carry no more than
15 pounds. How many extra water bottles can you add to your
backpack if each bottle weighs 3/4 pound?
By statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .
What is the number of bottles we can add in the backpack ?It is given that the total weight of your backpack and its contents is 13 3/8 pounds.
Also given , we want to carry no more than 15 pounds.
Let the number of bottles we can carry be x.
Each bottles weigh 3/4 pounds.
Total weight of the bottles = 3x/4 pounds.
Thus, the total weight of the backpack is 13 3/8 + 3x/4 pounds .
Thus the statement equation formed is -
⇒ 107/8 + 3x/4 = 15
⇒ 3x/4 = 13/8
⇒ x = 13/6 = 2.166
∴ x ≈ 2
Therefore, by statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .
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The points (1, 5) and (0, –2) fall on a particular line. What is its equation in slope-intercept form?
Answer:
y = 7x - 2
Step-by-step explanation:
first we need the slope of the line.
the slope is expressed a the ratio (y coordinate change / x coordinate change) when we go from one point on the line to another.
so, let's say we go from (0, -2) to (1, 5), we see
x changes by +1 (from 0 to 1).
y changes by +7 (from -2 to 5)
so the slope is +7/+1 = 7
the slope-intercept form is in general
y = ax + b
a being the slope, b being the y-intercept (the y-value for x = 0).
the point (0, -2) gives us therefore the y-intercept directly : -2.
by using the already established slope and the point (0, -2) for the y-intercept the equation of our line is
y = 7x - 2