Use the approach in Gauss's problem to find the sums of the arithmetic sequences below
(do not use formulas).
>
c. 3+ 6 + 9 + ... + 300
Answers
Answer:
15150 is the required sum.
Step-by-step explanation:
Gauss method of summing sequences like this is to add the first term to the last term, the second term to the second to the last term and so on until you get to the middle. By doing this, you will always get the same sum. Then you divide the number of terms by two, because you are technically adding the first half of the sequence to the second half. You then multiply the sum of each pair that gave the same number with the number of terms that has been divided by 2. For this problem we have:
3 + 300 = 303
6 + 297 = 303
9 + 294 = 303
and so on.
100÷ 2 = 50.
Therefore we have 50 * 303 = 15150 is the required sum.
Related Questions
32 to the power of negative 4 fifths
Answers
Answer:
0.0625
Step-by-step explanation:
hope this helps :)
A rectangle has an area of 18 square centimeters.
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
B
C
1 cm and 18 cm
2 cm and 9 cm
3 cm and 6 cm
4 cm and 5 cm
Answers
Answer:
1 cm and 18 cm
2 cm and 9 cm
3 cm and 6 cm
Step-by-step explanation:
We need to find the factors of 18
which are; 1,18; 2,9; 3,6
So therefore we'd pick:
1 cm and 18 cm
2 cm and 9 cm
3 cm and 6 cm
с
If 2x – 3y = 2 and xy = 8 then find the value of 4x2 +9y2.
(d) If 4x – 5y = 6 and xy = 8 then find the value of 16x2 + 25y2.
Answers
Answer:hmmmmm
Step-by-step explanation:
If each rabbit consumes 10 pounds of rabbit food each year, then how much rabbit food is consumed in 10 years
Answers
Answer:
100 pounds in 10 years
Step-by-step explanation:
10 pounds per year for 10 years
We simply multiply 10 pounds to 10 years to get 100 pounds
-Chetan K
somebody please help meeeeeeeeee
Answers
The value of x is given as follows:
x = 22.
What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.The two triangles in this problem are similar, hence the proportional relationship for the side lengths is given as follows:
x/18 = 11/9
9x = 11 x 18
x = 11 x 2
x = 22.
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Help please! I need an explanation but I dont understand this!!!!!!!
Answers
Answer:
its to small
Step-by-step explanation:
Decide whether the rates are equivalent. Maria saves $50 in 4 months.
Ralph saves $60 in 5 months
Answers
Answer:
The rates are not equivalent since Maria saves $0.50 more per month than Ralph.
Step-by-step explanation:
We can determine if two rates are equivalent by comparing the rates at which they save per month.
Maria's savings per month:
Both 50 and 4 can be divided by 2, which gives us 25/2. As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.
Ralph's savings per month:
Both 60 and 5 can be divided by 5, which gives us 12. Thus, Ralph saves $12 per month.
Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.
Lunch trays are stacked in
4 stacks with 25 trays in
each stack. How many
lunch trays are in the stacks
altogethere Show your
work.
Answers
Answer:
4 stacks and 25 in each stack
its asking you what is the total so
25*4=100
so 100 trays altogether
Answer:
100
Step-by-step explanation:
25+25+25+25
50+50
100
Find the following images in width and circumference
Answers
Step-by-step explanation:
hey guys how do you put a picture like you did ?
Find the length of x??
Answers
Answer:
8 meters.
Step-by-step explanation:
the formula for the hypotenuse of a right triangle is: \(a^2 + b^2 = c^2\). Where C= hypotenuse and a and b = other sides. We can sub in a and c to get \(6^2 + x^2 = 10^2\\\). Simplify to \(36+x^2=100\). Subtract 36 from both sides to get x^2 = 64. \(\sqrt{64} =8\)
A glass holds 1over6 liter of liquid.How many glasses of liquid are in 4 liters
Answers
Answer:
24 glasses
Step-by-step explanation:
If a glass holds 1/6 liters of liquid, that means that 6 of them can hold one liter
1/6 * 6 = 1
and if 6 of them can hold 1 liter, that means 24 of them can hold 4 liters
6 * 4 = 24
Solve for x
x^2 - 8x = -3
Answers
The solutions for the quadratic equation:
x^2 - 8x = -3
Are:
x = 7.6x = 0.4How to solve the quadratic equation?Here we want to solve the quadratic equation:
x^2 - 8x = -3
First we can move all the terms to the left side so we get:
x^2 - 8x + 3 = 0
Using the quadratic formula (or Bhaskara's formula) we can get the solutions for x as:
\(x = \frac{8 \pm \sqrt{(-8)^2 - 4*¨1*3} }{2*1} \\\\x = \frac{8 \pm 7.2 }{2}\)
Then the two solutions for the quadratic equation are:
x = (8 + 7.2)/2 = 7.6
x = (8 - 7.2)/2 =0.4
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Graph the solution to the equations below. y = 1 4 x + 2 and y = −2x −7
Answers
Answer the question with explanation;
Answers
Answer:
The statement in the question is wrong. The series actually diverges.
Step-by-step explanation:
We compute
\(\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=\lim_{n\to\infty}\left(\frac{n^2}{n^2+2n+1}\cdot\frac{1/n^2}{1/n^2}\right)=\lim_{n\to\infty}\frac1{1+2/n+1/n^2}=\frac1{1+0+0}=1\ne0\)
Therefore, by the series divergence test, the series \(\sum_{n=1}^\infty\frac{n^2}{(n+1)^2}\) diverges.
EDIT: To VectorFundament120, if \((x_n)_{n\in\mathbb N}\) is a sequence, both \(\lim x_n\) and \(\lim_{n\to\infty}x_n\) are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.
Answer:
\(\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2} = \text{div}\)
General Formulas and Concepts:
Calculus
Limits
Special Limit Rule [Coefficient Power Method]: \(\displaystyle \lim_{x \to \pm \infty} \frac{ax^n}{bx^n} = \frac{a}{b}\)Series Convergence Tests
nth Term Test: \(\displaystyle \sum^{\infty}_{n = 1} a_n \rightarrow \lim_{n \to \infty} a_n\)Integral Test: \(\displaystyle \sum^{\infty}_{n = a} f(n) \rightarrow \int\limits^{\infty}_a {f(x)} \, dx\)P-Series: \(\displaystyle \sum^{\infty}_{n = 1} \frac{1}{n^p}\)Direct Comparison Test (DCT)Limit Comparison Test (LCT)Alternating Series Test (AST)Ratio Test: \(\displaystyle \sum^{\infty}_{n = 0} a_n \rightarrow \lim_{n \to \infty} \bigg| \frac{a_{n + 1}}{a_n} \bigg|\)Step-by-step explanation:
*Note:
Always apply the nth Term Test as the first test to use for convergence.
Rules:
If \(\displaystyle \lim_{n \to \infty} S_n = 0\), then the nth Term Test is inconclusive.If \(\displaystyle \lim_{n \to \infty} S_n = l\) (some number l), then the series is divergent by the nth Term Test.Step 1: Define
Identify
\(\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2}\)
Step 2: Find Convergence
Substitute in variables [nth Term Test]: \(\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2} \rightarrow \lim_{n \to \infty} \frac{n^2}{(n + 1)^2}\)Expand: \(\displaystyle \lim_{n \to \infty} \frac{n^2}{(n + 1)^2}= \lim_{n \to \infty} \frac{n^2}{n^2 + 2n + 1}\)Evaluate limit [Special Limit Rule - Coefficient Power Method]: \(\displaystyle \lim_{n \to \infty} \frac{n^2}{(n + 1)^2} = 1\)Compute [nth Term Test]: \(\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2} = \text{div}\)∴ by the nth Term Test, the series diverges.
Topic: AP Calculus BC (Calculus I + II)
Unit: Convergence Tests
Help me pleaseeeeeeeeee
Answers
Answer:
y = 3x + 4
Step-by-step explanation:
✔️First, find the slope using any two given pairs form the table, say (2, 10) and (5, 19):
Slope (m) = ∆y/∆x = (19 - 10) / (5 - 2) = 9/3
m = 3
✔️Find y-intercept (b) by substituting (x, y) = (2, 10) and m = 3 into y = mx + b
10 = 3(2) + b
10 = 6 + b
10 - 6 = b
4 = b
b = 4
✔️Write the equation by substituing m = 3 and b = 4 into y = mx + b
y = 3x + 4
Can someone help meh???
Answers
Answer:
-3, -3
Step-by-step explanation:
It would just be the opposite of the point(look at it as a mirror).
Hope this helps! :)
Solve for x round to the nearest tenth of a degree if necessary. HURRYYYY TY
Answers
The value of x is 58.51 degree.
We have,
Perpendicular= 8
Base = 4.9
Using trigonometry
tan x = Perpendicular/ Base
tan x = 8/4.9
tan x= 1.63265306122449
x = 58.51253064
Thus, the value of x is 58.51 degree.
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Quadrilateral QRST is dilated by a factor of 2 with the center of dilation at the origin. What are the coordinates of quadrilateral Q'R'S'T'?
A) Q' (4, 4), R' (-4, 4), S' (-4, -4), T' (4, -4)
B) Q' (-1, 1), R' (1, 1), S' (1, -1), T' (-1, -1)
C) Q' (-4, 4), R' (4, 4), S' (4, -4), T' (-4, -4)
D) Q' (-3, 3), R' (3, 3), S' (3, -3), T' (-3, -3)
Answers
Answer:
C) Q' (-4, 4), R' (4, 4), S' (4, -4), T' (-4, -4)
Step-by-step explanation:
Original:
Q = (-2, 2)
R = (2, 2)
S = (2, -2)
T = (-2, -2)
After multiplying each coordinate by 2:
Q' = (-4, 4)
R' = (4, 4)
S' = (4, -4)
T' = (-4, -4)
Which expression is equal to 2rad-28
Answers
How many pounds of a chicken feed that is 40% corn must be mixed with 270 lb of a feed that is 80% corn to make a chicken feed that is 70% corn?
Answers
We have to add 90 pounds of chicken feed that is 40 % to make a chicken feed that is 70 % corn.
How many chicken feed must be added to a given blend?
In this problem we have to prepare a chicken feed with a given concentration by blending two chicken feeds with different concentration. The addition of chicken feed needed can be determined by weighted averages:
(70 / 100) · (270 + x) = (80 / 100) · 270 + (40 / 100) · x
0.7 · (270 + x) = 0.8 · 270 + 0.4 · x
189 + 0.7 · x = 216 + 0.4 · x
0.3 · x = 27
x = 90
We have to add 90 pounds of chicken feed that is 40 % to make a chicken feed that is 70 % corn.
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what is 750× 2
what is the square root of 90
Answers
Square root of 90 can be written as 3 multiplied by Square root of 10
PLEASE HELP
Order cube root of fifty-eight, thirty-two over seven, square root of twenty-eight from greatest to least.
square root of twenty-eight, thirty-two over seven, cube root of fifty-eight
thirty-two over seven, square root of twenty-eight, cube root of fifty-eight
cube root of fifty-eight, square root of twenty-eight, thirty-two over seven
thirty-two over seven, cube root of fifty-eight, square root of twenty-eight
Answers
Answer:
sqrt28, 32/7, cubrt58
Step-by-step explanation:
It says to order "greatest to least" so that means the biggest number goes first, then smaller next, and the smallest goes last.
sqrt25 is 5 and sqrt28 would be a little bigger, so 5.something. (you can find exactly on a calculator, but we don't need exact)
28/7 is 4 and 35/7 is 5. So 32/7 is in between, so like 4.something.
cuberoot27 is 3 and cuberoot64 is 4. So cuberoot58 is in between, it is 3.something.
So in order from big to small is
5...
4...
3...
which is
sqrt28,
32/7
cubrt58
The order from greatest to least will be the square root of twenty-eight, thirty-two over seven, and cube root of fifty-eight. Then the correct option is A.
What is descending order?It is the order of the numbers in which the biggest number comes first and then followed by the next number and then the last number will be the smallest one.
Order cube root of fifty-eight, thirty-two over seven, square root of twenty-eight from greatest to least.
∛58, 32/7, and √28
The expression is converted into decimal form, then we have
∛58, 32/7, and √28
3.87, 4.57, and 5.29
Then the order of the numbers from greatest to least will be
√28 > 32/7 > ∛58
The order from greatest to least will be the square root of twenty-eight, thirty-two over seven, and cube root of fifty-eight. Then the correct option is A.
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Which one is this please help thank u
Answers
Answer:
isosceles
Step-by-step explanation:
Two sides are the same length as indicated by the lines on the sides.
This tells use that the triangle is isosceles
Answer:
Hi, this an isoceles triangle
Step-by-step explanation:
An isoceles triangle has 2 equal sides
A right angled one has a right angle (90 degrees)
An equilateral traingle has all of his sides equal
A scalene has all of his sides different.
So this must be an isoceles triangle because there is basically a proof of the two equal sides (the bars).
Hope its clear!
The following question has two parts. First answer part A. Then,
answer part B
In math class, Alyssa's average test score is 90.125.
Part A
What is 90.125 written in expanded form?
х
A 9 x 10+1x1+2 x + 5 x
1
100
X B. 9x1+1x D + 2 x
100
+5
1,000
C. 9 x 10+1 x 1 + 2 x 100 + 5 x 1000
х
D. 9x1+1 100 + 2 x 1000 + 5 x
10.000
Answers
2) Corresponding angles are congruent L1 II L2 (2x + 20) (3x - 10)
Answers
Given angles are corresponding angles, they are congruent (have the same measure):
\((2x+20)=(3x-10)\)Use the equation above to solve x;
\(\begin{gathered} 2x+20=3x-10 \\ \\ \text{Subtract 3x in both sides of the equation:} \\ 2x-3x+20=3x-3x-10 \\ -x+20=-10 \\ \\ \text{Subtract 20 in both sides of the equation:} \\ -x+20-20=-10-20 \\ -x=-30 \\ \\ \text{Multiply both sides of the equation by (-1):} \\ (-1)(-x)=(-1)(-30) \\ \\ x=30 \end{gathered}\)You use the value of x=30 to find the measure of corresponding angles:
\(\begin{gathered} 2x+20 \\ 2(30)+20=80 \end{gathered}\)Then, the meaure of the corresponding angles is 80°Stacy Arrington is paid $.73 for sewing a
jacket collar, $.86 for a sleeve with cuffs,
and $.94 for a lapel. One week she sewed
318 jacket collars, 112 sleeves with cuffs,
and 37 lapels. Find her gross earnings.
Answers
Answer:
Her gross earnings for that week were $ 363.24.
Step-by-step explanation:
Since Stacy Arrington is paid $ 0.73 for sewing a jacket collar, $ 0.86 for a sleeve with cuffs, and $ 0.94 for a lapel, and one week she sewed 318 jacket collars, 112 sleeves with cuffs, and 37 lapels, to find her gross earnings you must perform the following calculations:
(318 x 0.73) + (112 x 0.86) + (37 x 0.94) = X
232.14 + 96.32 + 34.78 = X
363.24 = X
Therefore, her gross earnings for that week were $ 363.24.
Which statement is the inverse of the conditional statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
Answers
The inverse of the given statement will be- Option 3, If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
Here, we are given a statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
According to the statement,
if B bisects AC ⇒ AB = BC
then, B is the midpoint.
The inverse of this will be-
if B is the midpoint of AB ⇒ AB = BC
then, B bisects AB
This can be written as-
If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
Thus, option 3 is the correct answer.
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Your question was incomplete. Check below for full content-
Which statement is the contrapositive of the conditional statement:
Which statement is the inverse of the conditional statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
1. If point B is not the midpoint, then point B does not bisect line segment AC into two congruent segments.
2. Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint.
3. If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
4. If point B does not bisect line segment AC into two congruent segments, then point B is not the midpoint.
is the following statement true or false? all other things being equal, outliers tend to have a greater effect on the value of the mean, as compared to the value of the median.
Answers
All other things being equal, outliers tend to have a greater effect on the value of the mean, as compared to the value of the median. The given statement is true.
What is the mean and median?
Outliers are values that are significantly different from the other values in a data set, and their presence can greatly affect the value of measures of central tendency, such as the mean and the median.
The mean is a measure of central tendency that is calculated as the sum of all the values in a data set divided by the number of values. The presence of outliers can greatly affect the mean because outliers can have a large impact on the sum of the values in the data set. For example, if a data set has a few very large outliers, the mean will be pulled up to be much higher than the median, which represents the midpoint of the data set.
On the other hand, the median is a measure of central tendency that is calculated as the middle value of a data set when the values are arranged in order. The median is not as sensitive to outliers as the mean because outliers do not affect the median unless the number of outliers is so large that it changes the value of the middle value.
Hence, all other things being equal, outliers tend to have a greater effect on the value of the mean than on the value of the median.
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Kelly weekly salary of 300 plus a 20 commission her sales Create a table values when yKelly's weekly pay is the amount of sales Kelly makes in a week. From the tablewrite an equation and create a Braph the equation picture your work in the space below. Amount of sales In the weekweekly
Answers
Help I will give brainliest
Answers
the inequality is 8 (w+18) ≤ 19
Answer: -15.625
Step-by-step explanation:
Let w represent the number:
8 (w + 18) ≤ 19
\(\frac{8\left(w+18\right)}{8}\le \frac{19}{8}\)
\(w+18\le \frac{19}{8}\)
\(w+18-18\le \frac{19}{8}-18\)
\(w\le \:-\frac{125}{8}\)
-125/8 or -15.625
Check:
\(8\left(-15.625+18\right)\le \:19\)
\(8\cdot \:2.375 \leq 19\)
\(19 \leq 19\)
Therefore, the number is -15.625