Answers
Answer:
Option 4 which is 1,430.
Step-by-step explanation:
Step 1
In this this step we will break up the terms in the summation symbol using the rules for manipulation summations.
[tex]\sum_{i=1}^{n}(aX^2_i+k)=\sum_{i=1}^{n}(aX)+\sum_{i=1}^{n}k\\\\\sum_{i=1}^{n}(aX^2_i+k)=a\sum_{i=1}^{n}X^2+nk.[/tex]
This means that for our case, the sum can be simplified to be,
[tex]\sum_{i=1}^{11}(3i^2_i-8)=3\sum_{i=1}^{11}i^2+11\times(-8)\\\\\sum_{i=1}^{11}(3i^2_i-8)=3\sum_{i=1}^{11}i^2-88[/tex]
Step 2
In this step we use the formula for the sum of the first n squares to evaluate the first part of the sum in step 2. The formula for the sum of the first n squares is,
[tex]\sum_{i=1}^{n}n^2=\frac{n(n+1)(2n+1)}{6} \\\\\implies\sum_{i=1}^{11}i^2=\frac{11(11+1)(2\times 11+1)}{6} =506[/tex]
Step 3
In this step we use the result from step 1 to evaluate the sum.[tex]3\sum_{i=1}^{11}i^2-88=3(506)-88=1,430.[/tex]
The correct answer is Option 4,which is 1,430.
Answer:
[tex]\boxed{\boxed{\sum_{i=1}^{11}(3i^2-8)=1430}}[/tex]
Step-by-step explanation:
The given expression is,
[tex]\sum_{i=1}^{11}(3i^2-8)[/tex]
[tex]=\sum_{i=1}^{11}(3i^2)-\sum_{i=1}^{11}(8)[/tex]
[tex]=3\sum_{i=1}^{11}(i^2)-\sum_{i=1}^{11}(8)[/tex]
we know that,
[tex]\sum_{i=1}^{n}i^2=\dfrac{n(n+1)(2n+1)}{6}[/tex] and
[tex]\sum_{i=1}^{n}c=cn,\text{ Where c is a constant}[/tex]
Hence,
[tex]3\sum_{i=1}^{11}(i^2)-\sum_{i=1}^{11}(8)=3\left(\dfrac{11(11+1)(2(11)+1)}{6}\right)-8(11)[/tex]
[tex]=3\left(\dfrac{11(12)(23)}{6}\right)-8(11)[/tex]
[tex]=3\left(506}\right)-8(11)[/tex]
[tex]=1518-88[/tex]
[tex]=1430[/tex]
Related Questions
help. Geometry. Branliest!!
Answers
1. Correct. The reflection happens over segment AB and then you translate 6 units to the right and 3 units up. This will move point A to D, B to F, C to E, to have the triangles line up perfectly.
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2. Problem 1 already confirmed the triangles are congruent based on how they line up perfectly. Another way to prove this is to either use the SAS (side angle side) or LL (leg leg) theorem. With SAS, we need a pair of congruent sides and a pair of angles, with the angles between the two sides. The horizontal and vertical sides can be easily measured. The angles between the two sides are 90 degree angles. Because we have right triangles, we can use LL which is really just a special case of SAS.
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3. Segment EF is 5 units. You can use the pythagorean theorem with a = 3 and b = 4 to solve a^2+b^2 = c^2 to get c = 5. Or you can use the fact that BC = 5 is given to us, so EF must also be 5 as well. This is because of the idea that if two triangles are congruent, then their corresponding pieces must be the same as well.
Real world example: imagine having 2 houses that are perfect clones of each other. If this is the case, then surely their front doors would be identical copies as well. In this analogy, a house is a triangle, while the front door is the segment.
I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?
Answers
The maximum number of trees the student can plant per row is 10. This is found by identifying the greatest common divisor of the total number of apple trees and peach trees he has which is 10.
Explanation:To solve this problem, you need to find the greatest common divisor of 50 (the number of apple trees) and 30 (the number of peach trees). The greatest common divisor is the highest number that can divide both numbers without a remainder.
Both 50 and 30 can be divided by 10 without any remainder, but they can't be divided evenly by any number higher than 10. Therefore, 10 is the greatest common divisor of 50 and 30.
In this context, being able to divide the number of trees evenly means that you can plant the same number of each type of tree in each row. So, given the total numbers of apple and peach trees, the maximum number of trees you can plant per row is 10.
Learn more about Greatest Common Divisor here:https://brainly.com/question/23270841
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To determine the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with uniformity, calculate the greatest common divisor (GCD) of the two quantities, which is 10. This means the maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.
The question involves finding the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with the same number and type of trees per row. To find this number, we need to determine the greatest common divisor (GCD) of the two quantities, which will tell us the largest number of trees that can uniformly fit into each row for both types of trees.
First, list the factors of 50 (1, 2, 5, 10, 25, 50) and the factors of 30 (1, 2, 3, 5, 6, 10, 15, 30).
Find the largest factor that appears in both lists. In this case, it is 10.
The maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.
Therefore, you can plant up to 10 trees per row for a neat and organized orchard layout.
I NEED HELP ASAP WILL MAKE BRAINLIEST!
In May, 2018 a store had a furniture with a listed price of $550, having a sales tax of 3% on the listed price. Next month the price increased by 33 1/3 %. What sales tax should be paid in dollars on the new price?
Answers
Answer:
$22
Step-by-step explanation:
Listed price = $550
Sales tax rate = 3%
The price increased by 33 1/3% or [tex]\frac{100}{3}[/tex]% in the next month
Now, Sales tax will be calculated on new price after increase price.
Price increase = \frac{100}{300}*550 = 183.33
New Price = 183.33+550 = 733.33
Since Sales tax =3% on 733.33
= \frac{3}{100}*733.33
= 21.99 =22(aprox)
Sales tax paid in dollars the next month after increase of price = $22
amina bought an air cooler for a AED 3300 including VAT of 5% find the price of the air cooler before VAT was added
Answers
Answer:
3142.86
Step-by-step explanation:
let the original price be 100%
Then the cost with 5% VAT is 105%
Divide the cost by 105 to find 1% and multiply by 100 for original cost
original cost = [tex]\frac{3300}{105}[/tex] × 100 = 3142.86
The depreciating value of a semi-truck can be modeled by y = Ao(0.85)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 15% per year.
An exponential function comes down from the positive infinity and passes through the points zero comma seventy five thousand. The graph is approaching the x axis.
What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $65,000?
Answers
$75,000.
The graph would have a y-intercept at 65,000
Answer:
75,000, and the graph would have a y-intercept of 65,000
Step-by-step explanation:
the person above said its true. good luck on the module 2 test guys!
which rate describes a unit price? $1.00 for 2 lemons $3.00 for every pound $4.00 for 3 slices of pizza $6.00 for every 6 bottle
Answers
Final answer:
A unit price is the price for one unit of an item. Among the options provided, $3.00 for every pound represents a unit price because it tells us the cost per single pound.
Explanation:
The question asks which rate describes a unit price. A unit price is the cost per single item or measure. It is calculated by dividing the total price by the number of units. In the context of the examples provided, a unit price is expressed as a cost for one lemon, one pound, one slice of pizza, or one bottle.
$1.00 for 2 lemons => $0.50 per lemon$3.00 for every pound => $3.00 per pound (this is a unit price)$4.00 for 3 slices of pizza => $1.33 per slice of pizza$6.00 for every 6 bottles => $1.00 per bottleTherefore, out of the provided options, $3.00 for every pound best represents a unit price as it is a rate describing the cost of one pound.
solve for x
(3x-6)(-x+3)-0
smaller x=?
larger x=?
Answers
3x - 6 = 0
and
-x + 3 = 0
So:
3x = 6 which means x = 2
and
3 = x.
The larger x is 3 and smaller x is 2.
Answer:
x=2 and x=3
Step-by-step explanation:
(3x-6)(-x+3)=0
We can use the zero product property to solve for x
3x-6 = 0 and -x+3 =0
3x-6 = 0
Add 6 to each side
3x-6+6 = 6
3x=6
Divide by 3
3x/3 =6/3
x =2
-x+3 =0
Add x to each side
-x+x+3 = +x
3 =x
Solve the following equation for b, a=b over 15
Answers
Answer:
15a=b
Step-by-step explanation:
so you have a=b/15.. we want b to be on its own.. you have to use inverse operations to get by by itself. so, we need to get rid of the 15.. it is being divided, so therefore multiply both sides by 15..
15a=b
What is the probability of someone being born on Feb.28 given that they were born in February?
Answers
Answer:
4/113
Step-by-step explanation:
1/28 for non leap years and 1/29 for leap years
However if u put those together it would be 4/113 overall
This is because every 4 years there are 113 days in February and 4 of those days will be the 28th.
Final answer:
The probability of someone being born on February 28th given that they were born in February is 1/28, assuming a non-leap year scenario.
Explanation:
The student is asking about the probability of being born on February 28th, given that they were born in February. Given that February usually has 28 days, except for leap years when it has 29 days, to find this probability, we consider a non-leap year scenario.
The total number of possible birth dates in February, in a non-leap year, is 28. Since being born on any given day in February is equally likely, the probability of being born on February 28th is simply 1 divided by the number of days in February.
Therefore, the probability is:
P(born on Feb. 28) = 1/28
3rs - 5cr - 15cs + 25c2
Answers
[tex]3rs-5cr-15cs+25c^2=r(3s-5c)-5c(3s-5c)\\\\=(3s-5c)(r-5c)\\\\Answer:\ \boxed{3rs-5cr-15cs+25c^2=(3s-5c)(r-5c)}[/tex]
A trick that I have learned, but does not apply to all equations, (some don’t work with this) is to multiply +25c by 2 to get =50c.
If we want to be 95% confident of our estimate, does the sample proportion obtained, 20 out of 50, fall within the margin of error developed from the simulation? Why or why not?
Answers
20/50 = 2/5 = 0.40 which is found in the dot plot given. Since this value is in the dot plot, this means that it is possible to obtain this value with a random simulation.
Answer: Yes, the sample proportion 20/50 falls within the margin of error.
Answer
20/50 = 2/5 = 0.40
Ok.
Which equation's graph has a steeper slope y=8x+4 or y=6x-4
Answers
Answer:
y=8x+4 has a steeper slope. itś slope is 8 while y=6x-4 has a slope of 6.
Step-by-step explanation:
The graph of the equation y=8x+4 is steeper because it has a higher slope.
What is the equation of a line?The equation of a line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The given equations are y=8x+4 and y=6x-4. Compare the equations with the standard form to find the slope.
y = mx + c
y=8x+4
y=6x-4.
The slope of the first equation is 8 and the other equation is 6.
Therefore, the graph of the equation y=8x+4 is steeper because it has a higher slope.
More about the equation of line link is given below.
https://brainly.com/question/21511618
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can anyone please solve this...............
Answers
Answer:
use photo math its helps alot
Step-by-step explanation:
Answer:
3 raise to 15
Step-by-step explanation:
If f(x)=4x-6 and g(x)=√x+2, what is (f°g)(7)
Answers
Answer:
[tex]4\sqrt{7} +2[/tex]
Step-by-step explanation:
fog =4[tex]\sqrt{x}[/tex]+8-6
= 4[tex]\sqrt{x}[/tex] +2
fog(7) = 4[tex]\sqrt{7}[/tex]+2
Greatest to least .01 1/8 .23 1/5
Answers
Answer:
0.23, 1/5, 1/8, 0.01
Step-by-step explanation:
1/8=0.125
1/5=2/10=0.2
0.01
0.125
0.23
0.2
0.0..., 0.1.., 0.2...
0.20 and then 0.23
Answer:
.23 ,1/5 , 1/8 ,.01
Step-by-step explanation:
.I will put them all in decimal form
.01 = .01
1/8 = .125
.23 = .23
1/5 = .2
largest to smallest
.23 >..2 < .125 < .01
Put them back in their original form
.23 >1/5 > 1/8 >.01
.23 ,1/5 , 1/8 ,.01
The local parts shop buys a machine that costs $500,000. Its value depreciates exponentially each year by 10%. what is the machines value after 5 years
Answers
Answer:
$250,000
Step-by-step explanation:
5 times 10% is 50%
50% of $500,000 is $250,000
Your answer is $250,00
I'm so confused. Please help I tried the first time got 50 some thing then 33 then 20.25. How do I do this?
Answers
Answer:
Basically, you have to think: more bricks : more time
more workers : less time
2,400 bricks 6 workers takes 18 hours
You now have to solve for 4,500 blocks and 10 workers
4,500 / 2,400 = 1.875 (times greater)
10 / 6 = 1.666666666 (times less)
So, we get 18 hours, multiply it by 1.875 and divide it by 1.666666666
which equals 20.25 hours
So, it seems you were correct on your third try.
Step-by-step explanation:
How to divide the polynomial using long division
Answers
[tex]\mathbb{ANSWER:}[/tex]
Refer to the attachment to view the answer.
4. What is the LCM of 4, 3, 10, and 8? *
80
240
120
30
5. Which statement is true? *
29/35 < 20/30
14/21 > 17/24
18/32 > 16/32
20/15 < 28/23
Answers
[tex]120[/tex]
And for 5 I’m thinking it’s the second choice
35/k = 7/3 i need this one done asap too lol
Answers
Answer:
k=15
Step-by-step explanation:
the product of three numbers is -216, but their sum is -18. What are these three numbers?
Answers
Answer:
-6, -6, & -6
Step-by-step explanation:
-6(-6)(-6) = -216
-6 + (-6) + (-6) = -18
does the equation 7x-4y=0 represent a direct variation? what is the constant of variation?
Answers
Yes, the equation 7x-4y=0 represents a direct variation with the constant of variation being 7/4.
The equation 7x-4y=0 does represent a direct variation. To see this, we can rearrange the equation into the form y = kx, which is the general form for direct variation. Solving for y, we divide both sides by -4 to get:
y = (7/4)x
Here, the coefficient of x, which is 7/4, is the constant of variation. Thus, in the given equation, the constant of variation is 7/4, meaning for every unit increase in x, y increases by 7/4 units. This proportional relationship where y varies directly as x, with a constant ratio of 7/4, confirms it's a direct variation.
The regular price of a jacket is $200. Today, the jacket is on sale. It is 20% off its regular price. The sales tax is 8%. If Steven buys the jacket today, how much will he pay?
Answers
Answer:
$172.80
Step-by-step explanation:
200*20%=40
200-40=160
160*0.08=12.8
12.8+160=172.80
Answer:
He pays $176
Step-by-step explanation:
First, to find 80% of 200, we can simply multiply 200 by .8.
200 x .8=160
Then, we add sales tax to that number. To find 8% of 200, multiply 200 by .08.
200 x .08=16
Then, add 16 to 160.
160+16= 176
Your answer is $176.
Hope this helps!
6. Maya is driving 120 miles to her grandmother’s house. She drives 35% of the distance before stopping for lunch. How far does she drive before lunch? (1 point)
Answers
Answer:
42 miles
Step-by-step explanation:
She drove 35% of 120 miles.
To find a percent of a number, multiply the percent by the number.
35% of 120 miles =
= 35% * 120 miles
= 0.35 * 120
= 42
Nancy is 5 years younger than her brother Stan. Last year she was twice as young as he was. How old is each of them now?
Answers
5 is 5 years
younger then Stan
And 5 is twice as
young as 10
Answer:
Nancy is 6 years old and Stan is 11 years old now.
Step-by-step explanation:
Let the present age of Stan be x.
Then age of Nancy = y
x - y = 5
Last year she was twice as young as he was
Age of Nancy last year = y-1
Age of Stan last year = x-1
2 × (y-1)= x-1
2y -2 = 5 + y -1
y = 6
x = y + 5 = 6 + 5 = 11
Nancy is 6 years old and Stan is 11 years old now.
How is the product related to the first factor?
4/9 × 7/3
The product is less than .4/9
The product is equal to .4/9
The product is greater than .4/9
The product is greater than .7/3
Answers
Answer:
5/5 austin
Step-by-step explanation:
I need help on 2,4,6 it will be worth a 10 points
Answers
Answer:
2 is 13
4 is 1
6 is 16
Step-by-step explanation:
Write y=-4/5x-2 in standard form using integers?
Answers
Answer:
4/5x + y = -2
Step-by-step explanation:
Answer:
4x+5y=-10
Step-by-step explanation:
We have to arrange [tex]y=\frac{-4}{5}x-2[/tex] in the standard form using integers.
The standard form of the equation of a line is represented as Ax+By=C, where A,B,C are integers and A≥0.
Therefore, multiplying the given equation by 5 on the both sides, we have,
[tex]5y=-4x-10[/tex]
On rearranging,we get,
[tex]4x+5y=-10[/tex]
Which is the required standard form using integers.
graph g(x) = x3 − x2 − 4x + 4
Answers
Answer:
In the attachment!!
Hope this helps!
A scatter plot was constructed and a line of best fit was drawn, 25x 80. What is the equation of this best line of fit?
Y=5x+5
y=x+5
Y=5x+25
Y=x+125
Answers
Answer:
y = 5x + 25
Explaination:
To get the equation of a line, first get the slope of the line.
Slope = (change in y)/(change in x)
= (60-30)/(7-1)
= 30/6
= 5
Now use one point in the line (4,45) and a general point (x,y).
Slope = (change in y)/(change in x)
5 = (y - 45)/(x - 4)
5(x - 4) = (y - 45)
5x - 20 = y - 45
y = 5x -20 + 45