Find $(-1)^{-10} (-1)^{-9} (-1)^{-8} \cdots (-1)^9 (-1)^{10}$. (The dots $\cdots$ mean that there are 21 numbers being added, one for each integer from $-10$ to 10.)
The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1
Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]
here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.
We need to find the sum.
We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1
We know that the formula of the sum of n-terms of a geometric sequence is:
[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]
For n = 21, r = -1 and a1 = 1
[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]
Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1
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Daily Question 8/4/20: Cities A, B, C, D, and E are connected by roads AB, AD, AE, BC, BD, CD, and DE (see figure). How many different routes are there from A to B that use each road exactly once?
Geometrically there are 16 different routes from A to B that use each road exactly once.
What is geometry?
The area of mathematics known as geometry is concerned with the dimensions, sizes, forms, and angles of a wide range of everyday objects. Geometry comes from the Ancient Greek terms "geo" and "metron," which both imply "measuring."
Keep in mind that cities C and E can be excluded from the count of paths because there is only one road that can lead out of either city if a path enters it. The geometric diagram is shown below.
Now move on to the casework. It's important to keep in mind that there are two routes from A to D, D to A, B to D, and D to B.
Case 1: A⇒D: If the path from D leads back to A, the subsequent path must go to B⇒D⇒B. The path ADABDB has 2×1×2=4 possible outcomes. The path must continue with either BDAB or BADB if it leads from B to D. There are 8 possibilities as 2×2×2=8. Therefore, there are 4+8=12 potential outcomes in this scenario.
Case 2: A⇒B: BDADB must be the next step on the path. There are 2×2=4 options in this situation.
Combining the two situations results in 12+4=16.
Therefore, there are 16 different routes.
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Please help
Find the value of x
Find the measure of the two marked angles
PLEASE ALSO FIND X
The value of x is 8 and the measure of the two marked angles is 60°.
Which angles are corresponding and adjacent?When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.
we know that ,
10x-20=7x+4 (it is corresponding opposite angle)
3x=24
x=8
the value of x is 8.
the measure of the two marked angles is 10*8-20= 80°-20°= 60°.
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HELP
i been trying for a while and cant get it
The ordered pair for the function y = -(x/3) + 2 is (-3, 3), (0, 2), (3, 2) and (6, 0)
What is an equation?An equation is used to show the relationship between numbers and variables.
The standard form of a linear equation graph is:
y = mx + b
Where m is the slope of the line and b is the y intercept.
Given the function:
y = -(x/3) + 2
At x = -3:
y = -((-3)/3) + 2 = 3
At x = 0:
y = -(0/3) + 2 = 2
At x = 3:
y = -(3/3) + 2 = 1
At x = 6:
y = -(6/3) + 2 = 0
The value of y when x = -3 is 3
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difference between -0.4 and 44.4
Answer:
44.8
Step-by-step explanation:
44.4 - (-0.4) = 44.8
True or false:
If f(x) is a cubic function
and f(1) = 0, f(3) = 0 and
ƒ(4) = 0,
then f(5)=8
Answer:
FALSE
Step-by-step explanation:
It is not necessarily true that ƒ(5)=8 just because ƒ(1)=0, ƒ(3)=0, and ƒ(4)=0. In fact, it is possible for ƒ(x) to be a cubic function and for ƒ(5) to equal any number, depending on the specific form of the function and the values of its coefficients.
3 A sphere is increasing in volume at the rate of 20 in3/s. At what rate is the radius of the sphere increasing when the radius is 4 in.? A.0.982 inls B.0.424 inls C.0.995 inls D.0.025 inls
The rate of increase of the radius is 0.025 in/sec.
What is a sphere?A three-dimensional object with a sphere-like shape. A sphere has no vertices or edges, unlike other three-dimensional shapes. The distances between each point on its surface and its center are equal.
In other words, the distance between any two points on the surface and the sphere's center is equal. The formula for the Volume of the sphere is given by
Volume of sphere = (4/3)πr³
Where, r = radius of the sphere
Here we have
A sphere is increasing in volume at the rate of 20 in³/s.
Here we need to find at what rate the radius of the sphere increases when the radius is 4 in.
Let v = Volume of the sphere at time t
=> Change in Volume = dv/dt = 20
r = Radius of the sphere at time t
As we know, the Volume of the sphere, v = (4/3)πr³
Differentiate the Volume of the sphere with respect to t
=> dv/dt = (4/3)3πr³⁻¹)(dr/dt)
=> dv/dt = 4πr² (dr/dt)
=> 20 = 4πr² (dr/dt)
=> 5 = πr² (dr/dt)
Given that radius, r = 4
=> 5 = π4² (dr/dt)
=> 5 = (22/7) 64 (dr/dt)
=> 5 = 3.14(64) (dr/dt)
=> dr/dt = (5/3.14 × 64)
=> dr/dt = 0.024880573
=> dr/dt = 0.025
Therefore,
The rate of increase of the radius is 0.025 in/sec.
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eight more than the product of a number 9 is equal to 7
Answer:
The equation you have provided is 8 + 9x = 7, where x is the unknown number.
To solve for x, you can first subtract 8 from both sides of the equation to get
9x = -1
Then divide both sides by 9
x = -1/9
So the number x is -1/9, which means that the product of x and 9 is equal to -1.
Keep in mind that this is not a natural number and it is not possible to represent the solution as a whole number.
Step-by-step explanation:
the diagram shows 2 mathematically similar vases. vase A has height 20cm and volume 1500^3. vase B has volume 2592cm^3. calculate h, the height of vase b.
The height of vase b is 34.56 cm.
What is volume?In mathematics, volume is the space taken by an object.
V=pi*r²*h
Here, given that,
vase A has height 20cm =H
and volume 1500^3. =V
And, A & B similar vases.
Again, vase B has volume 2592cm^3 =v
let, h, the height of vase b.
both radius are equal
so, we get, V/pi*H = v/pi*h
i.e. 1500/20=2592/h
so, h= 34.56 cm
Hence, the height of vase b is 34.56 cm.
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The table shows the relationship between the participants walking and running for the week's cross-country practices. Walk (laps) 3 B 15 Run (laps) 5 10 D Total (laps) A C 40 At this rate, how many laps will the participants walk if the total distance is 16 miles? How many miles will they run? They will walk 6 laps and run 10 laps for a total of 16 miles. They will walk 9 laps and run 7 laps for a total of 16 miles. They will walk 10 laps and run 6 laps for a total of 16 miles. They will walk 5 laps and run 11 laps for a total of 16 miles.
At the given rate, we can say that they will walk 6 laps and run 10 laps for a total of 16 miles.
What is a direct proportional relationship?In a direct proportional relationship, we can say that the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:
y = kx.
For the first question, we have that out of a total distance of 8 miles, and we can see that;
Walk is 3/8 of the distance.
Run is 5/8 of the distance.
Thus, the proportional relationships for the distances are given as follows:
Walked = 3/8 x Total Distance.
Ran = 5/8 x Total Distance.
We are told that the total distance is 16 miles and so;
Walked: 3/8 * 16 = 6 laps
Ran: 5/8 * 16 = 10 laps
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find the area of the rectangle whose lengths 16cm and breadth is 8cm
Answer: Breadth? Did you mean width? If so, the answer is 128cm
Step-by-step explanation:
Area = Width x Length
8x16=128
Jon flips a coin and writes down H if heads comes up or T if tails comes up. He does this 3 times. If the order of the results matters, how many possible outcomes are there?
Answer:
There are always two possible outcomes H (heads) and T (tails) but the possible combination outcomes are HH, TT, HT, and TH
Step-by-step explanation:
It is just my common sense~
There is 8 possible outcomes.
Marissa is skateboarding on a straight stretch of sidewalk. In 3.0 minutes, she travels 486 meters. What is the magnitude of her velocity during this stretch?
Marissa velocity while skateboarding is 162 meters per minute
What is an equation?An equation is used to show the relationship between numbers and variables.
Velocity is the ratio of displacement to time taken. It is a vector quantity (has magnitude and direction) and it is given by:
Velocity = displacement / time
Marissa travels 486 meters in 3 minutes, hence:
Velocity = displacement / time
Velocity = 486 m / 3 min = 162 meters per minute
The velocity is 162 meters per minute
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Answer: The correct answer is 2.7m/s
Step-by-step explanation:
I took the test
I NEED HELPPPPPPPPPPPPP
Answer:
y= 12
Step-by-step explanation:
3(-12)-24
-36-24
-12
Evaluate 5c+cd5c+cd5, c, plus, c, d when c=\dfrac15c=
5
1
c, equals, start fraction, 1, divided by, 5, end fraction and d=15d=15
Answer:
the value is 4
Step-by-step explanation:
Please help ASAP
Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
Step-by-step explanation:
I'm assuming that its 23 to the power x since you said it is an exponential equation.
as for the hint there is no specific base specified so I'll do the best I can with the answer.
Angie can begin solving by applying log to the base 23 on both sides. when this is done, Angie will be left with:
[tex] log_{23}( {23}^{x} ) = log_{23}(6) [/tex]
and as we know the power rule in logarithms allows us to remove the power within the expression.
hence, we'll get:
[tex]x log_{23}(23) = log_{23}(6) [/tex]
furthermore, if we have the same number and base within a logarithmic expression it will simply become 1 giving us the final answer:
[tex]x = log_{23}(6) [/tex]
if the question that I've answered is different to yours please let me know and I'll make sure to fix it.
hope this helps :)
1. Which word doe not have a imilar meaning to - condemn
critique
diparage
criticize
cenure
Among the given four options, the word that doesnot have similar meaning to condemn is "critique".
What is the meaning of word condemn?The word "condemn" means to express strong disapproval or criticism of something or someone, often in a formal or official manner. It can also mean to pronounce a judgment of guilt, especially in a court of law. It implies a severe judgment or punishment. Condemn also implies the declaration of something being morally wrong or unacceptable. It is a strong word that carries a sense of condemnation or blame.
Make two sentences using the word condemn.The sentences are given below:
The judge condemned the defendant for his crimes, sentencing him to life in prison.The community condemned the company for their unethical business practices and called for a boycott.The word that does not have a similar meaning to "condemn" is "critique".
"Condemn" means to express strong disapproval of something or someone, often in a formal or official manner.
"Criticize" means to express disapproval or to find fault with something or someone
"Censure" means to express strong disapproval or criticism of something or someone, typically in a formal or official manner.
"Disparage" means to speak or write about in a negative way; to belittle or criticize.
"Critique" means to evaluate (a work of art, literary work, etc.) in terms of its strengths and weaknesses; to give an analysis or evaluation of something."Critique" is different because it is an analysis or evaluation of something, whereas the other words are about expressing disapproval or criticism.
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A sphere has a radius of 24 centimeters. What is its volume?
V
=
Cm^3
Hello there!
Answer:
[tex]V = 18432\pi[/tex] or approximately 57876.48
Step-by-step explanation:
[tex]V = \frac{4}{3} \pi R^{3}[/tex]
R = 24
[tex]V = \frac{4}{3} \pi *24^{3} = 18432\pi[/tex]
if [tex]\pi =3.14[/tex] then:
[tex]V = 57 876.48[/tex]
Find the area of a table top that is 3 1/3 feet by 2 feet
6.666666666666666 (6.6 repeating, I just don’t know how to use the sign online)
I multiplied 3 1/3 by 2
Reasonable Time: Algorithms with a polynomial efficiency or lower (constant, linear, square, cube, etc.) are said to run in a reasonable amount of time. Unreasonable Time: Algorithms with exponential or factorial efficiencies are examples of algorithms that run in an unreasonable amount of time. Your school is considering running the group raffle at an upcoming assembly to give away a prize. Write a brief explanation of what advice you would give them.
Unreasonable Time is the nest option for running the group raffle at an upcoming assembly to give away a prize.
As given that;
Reasonable Time: Algorithms with a polynomial efficiency or lower (constant, linear, square, cube, etc.) are said to run in a reasonable amount of time.
Unreasonable Time: Algorithms with exponential or factorial efficiencies are examples of algorithms that run in an unreasonable amount of time.
Your school is considering running the group raffle at an upcoming assembly to give away a prize.
We have to write a brief explanation of what advice you would give them.
We can use the unreasonable time because running the group raffle at an upcoming assembly to give away a prize cannot complete their work is the given amount of time.
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Solve for m/IGH if m/FGH = 141° and m/FGI = 72°.
F
Answer: m/IGH =
O
G
Submit Answer
H
attempt 1 out of 2/ problem 1 out
Answer:
Step-by-step explanation:
m∡IGH = ? m∡FGH = 141 degrees and m∡FGI = 72 degrees
therefore, m∡IGH = m∡FGH - m∡FGI = 141 - 72 = 69 degrees
−321⋅35⋅7⋅15 what is this properties
The dots in the expression - 321⋅35⋅7⋅15 represents multiplication.
What are some alternative names for arithmetic operations?Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
From higher classes, we write a dot sign in between two terms to represent that the terms are being multiplied.
Given, - 321⋅35⋅7⋅15 this represents multiplication between the numbers
- 321, 35, 7, and 15.
The result of this product is,
- 321×35×7×15
= - 1,179,675.
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a man left 1/2 of his money to his first son 3/8 to his second son, the rest 80,000 to his third son.how much did he he leave to his second son
As per the given conditions in the question, the amount of money that the second son was left with by the man is 2,40,000.
How do you add two fractions with different denominators?To add two fractions with different denominators, you must first find a common denominator. A common denominator is a number that is divisible by both denominators of the fractions. Once you have a common denominator, you can add the numerators of the fractions together and place the sum over the common denominator. Then simplify the fraction if possible.
What is the reciprocal of a fraction?The reciprocal of a fraction is another fraction whose numerator and denominator are flipped. For example, the reciprocal of the fraction 2/3 is 3/2. The product of a fraction and its reciprocal is always equal to 1. To find the reciprocal of a fraction, simply swap the numerator and denominator.
Considering the conditions given in the question,let us suppose that the third son was left with x part of the money,
so we can use the equation,
part of money left for fist son + part of money left for second son + part of money left for third son = total part of money
or, 1/2 + 3/8 + x = 1
therefore, x = 1/8
Also we know that the third son was left 80,000 ,
so 1/8 of total money = 80,000
therefore, total money = 80000 * 8 =6,40,000
Now the amount left for the second son is , 3/8 of total money
which is equal to , 3/8 of 6,40,000 = 2,40,000
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How fast is a motorcycle that is going 6 miles in 4 minute?
Answer:90
Step-by-step explanation:
Jonathan opened an auto repair shop. In the first month, 11 cars were serviced at his shop. After the first month, the total number of cars serviced at Jonathan's shop increased by 9 cars per month.
How many total cars were serviced at Jonathan's shop at the end of the 7th month?
Answer:
65 cars
Step-by-step explanation:
3x+2y=2 in slope intercept form!!!
Answer:
[tex] \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}[/tex]
Step-by-step explanation:
Slope-intercept is in form of y = mx + b where m is slope and b is y-intercept. We simply solve for y in term of x and then we will obtain the slope-intercept form.
Given the linear equation:
[tex] \displaystyle{3x + 2y = 2}[/tex]
First, subtract both sides by 3x:
[tex] \displaystyle{3x + 2y - 3x= - 3x + 2} \\ \\ \displaystyle{2y = - 3x + 2}[/tex]
Then divide both sides by 2:
[tex] \displaystyle{ \dfrac{2y}{2} = \dfrac{ - 3x + 2}{2}} \\ \\ \displaystyle{ y = \dfrac{ - 3x + 2}{2}}[/tex]
Separate fractions (Simplify):
[tex] \displaystyle{ y= \dfrac{ - 3x}{2} + \dfrac{2}{2}} \\ \\ \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}[/tex]
And we have finally converted the equation to slope-intercept form.
This question has two parts. First, answer Part A. Then answer part B. Part A Based on the text what inference can be made about laughter? Part B Drag "yes" or "no" to each box to show whether or not the piece of evidence supports the answer to part A
Part A: Based on the text, an inference that can be made about laughter is that it can be a positive response to a situation or a way of expressing joy.
What is inference?Inference is the process of drawing conclusions from given facts or evidence. It involves making a logical guess or assumption based on the available information. Inference requires the use of critical thinking to draw conclusions that are most likely to be accurate.
Part B:
Yes - Laughter is described as a response to a situation and can be a way of expressing joy.
No - There is no evidence that laughter is a negative response to a situation.
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a builder wishes to fence in 60,000m of land in a rectangular shape. for security reasons, the fence along the front part of the land will cost 20 per meter, while the fence for the other three sides will cost 10 per meter. how much of each type of fence should the builder buy to minimize the cost of the fence
The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.
To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.
To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length) + 2(width)
Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:
2x + 2y = 60,000
To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:
60,000 - x = 3x + 2y
The total length of the three sides that are not the front is 3x + 2y.
Now we can calculate how much the builder will pay for each type of fence:
Cost of front fence = $20/m * x = $20xCost of other three sides = $10/m * (3x + 2y) = $30x + $20yTotal cost of the fence = $20x + $30x + $20y = $50x + $20y
To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.
However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:
x meters of $20/m fence for the front side3x + 2y meters of $10/m fence for the other three sides.This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.
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Select all ratios equivalent to 2:14. A3:21b.1.2.c
16:112
The ratios equivalent to 2:14 are 3:21 and 16:112. Option A &C
What is equivalent ratios?Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.
2:14 = 2/14
Reducing 2/14 to the lowest terms = 1/7
2:14 is equivalent to 1:7
3:21 = 3/21 = 1/7
Reducing 3/21 to the lowest terms = 1/7
3:21 is equivalent to 1:7
1:2 = 1/2
1:2 is not equivalent to 1:7
16:112 = 16/112 = 1/7
Reducing 16/112 to the lowest terms = 1/7
16:112 is equivalent to 1:7
Hence, 2:14, 3:21 and 16:112 are all equivalent ratios
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Sasha is a journalist for an online school magazine. She wants to know what topic readers are not interested in for the next publication
Sasha puts a survey on the magazine's website and considers the first 25 responses. Are conclusions drawn from this sample likey to be true for all readers of the magazine?
Answer:
Step-by-step explanation:
No, some people don't like certain things. It like saying that you pick five random people who are at a science fair and ask them if they like science, the answer would be yes, but if you went to Walmart and asked five random people if they liked science your answers would most likely end up being no. It's the same way looking at the magazines.