Answer:
This sum is the sum of an arithmetic sequence. There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.
A nice approach for this sequence is the following. Notice that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.
There are n of these pairs. So the desired sum is n x (first number + last number). But the first number is 1 and the last on is 2n. Thus the desired sum is n(1 + 2n).
Hope this helps!!
Mark Brainleast!!!!!!!!!!!
Consider the set {1, 2, 3, 4, ..., m} where m is some natural number, i.e. a positive whole number.
Now let's say we wanted to add everything in that set.
What we can do is write out the terms
1, 2, 3, 4, ..., m
then just underneath, we write the reverse of that set
m, ..., 4, 3, 2, 1
Here's an example of what I mean. I'll use m = 7
[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}\end{array}[/tex]
For each column, add straight down
The third row will be nothing but 8's
[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}8 & 8 & 8 & 8 & 8 & 8 & 8\\\cline{1-7}\end{array}[/tex]
We can see there are seven copies of '8' being added here, so the sum of all the numbers in the set {1,2,3,4,5,6,7} is 8*7 = 56. But wait, we double-counted each item when we formed the second row. So we must divide by 2 to fix the double-counting error.
Therefore, 1+2+3+4+5+6+7 = 56/2 = 28 instead.
-----------------------------
That previous example showed that adding from 1 to 7 means we have 7 copies of (1+7). In other words, 7 copies of 8 being added.
We could write that as 7(1+7)
Then divide that by 2 to fix the double-counting error.
We have 7(1+7)/2
Now imagine that we applied all of what was mentioned to the set {1,2,3,4,5,6,7,8}. Instead of 7's, we use 8's this time to get 8(1+8)/2
Then we can extend it out to the set {1,2,3,4,..., m} and we get the formula m(1+m)/2
We have m copies of (1+m) being added; hence the m(1+m). Don't forget to divide by 2 to fix the double-counting error.
-----------------------------
The key takeaway here is that summing 1+2+3+4+...+m gets us m(1+m)/2
In this case, m = 2n because we want the first 2n natural numbers.
Therefore,
m(1+m)/2
2n(1+2n)/2
n(1+2n)
n(2n+1)
represents the sum 1+2+3+...+n+...+2n
-----------------------------
Try out a value like n = 5 to find that 2n = 2*5 = 10, and,
1+2+3+4+5+6+7+8+9+10 = 55
also
n(2n+1) = 5(2*5+1) = 5*(11) = 55
Showing that the formula works for n = 5. I'll let you try other values of n.
64.89% of 407.68cm
Give your answer rounded to 2dp
Answer: 264.54cm
Step-by-step explanation:
407.68x0.6489=264.543552264.543552 rounded to 2 decimal points is 264.54A recipe for muffins calls for 1 1 over 3 cups of milk. a recipe for bread calls 2 over 3 cup of milk how much more milk is needed for the muffin recipe than the bread recipe
Answer:
The Muffin Recipe calls for 3 more cups of Milk than the Bread Recipe.
Step-by-step explanation:
11/3=
3[tex]\frac{2}{3}[/tex]
2/3
We can see that the difference is GREAT. So, now, let's subtract.
[tex]3\frac{2}{3} -\frac{2}{3} =3[/tex]
So hence, the Muffin Recipe calls for 3 more cups of Milk than the Bread Recipe!
----------------------------------------------------------------------------------------------------------"The beautiful thing about learning is that no one can take it away from you!"
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Have a great night!
~ms115~
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The muffin recipe requires 2/3 cup more milk than the bread recipe.
What is subtraction?Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.
To find out how much more milk is needed for the muffin recipe than the bread recipe,
we need to calculate the difference between the amount of milk required for each recipe.
The muffin recipe calls for 1 1/3 cups of milk, which is equivalent to 4/3 cups of milk.
The bread recipe calls for 2/3 cup of milk.
To find the difference between the two amounts of milk, we can subtract the milk required for the bread recipe from the milk required for the muffin recipe:
4/3 - 2/3 = 2/3
Therefore, 2/3 is the required fraction.
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when I think of a number, double it , then add seven , I get 23. Determine the number I first thought of
Answer:
8
Step-by-step explanation:
2x + 7 = 23
2x = 16
X = 8
i do not know this answer
Answer: awnser is m= 1/6
Step-by-step explanation: m = add the terms which is -1 -5m-4+6 m= 1-5m
step 2 then rerange the terms to m= 1-5m to m = 5m + 1
step 3 add 5m to both sides m= -5m+1 to m + 5m= -5m + 1 + 5m
step 4 simplify and combine like terms 6m= 1
step 5 divide both sides by the same factor 6m= 1 6m/6 = 1/6
step 6 simplify Cancel terms that are in both the numerator and denominator so it is m= 1/6 is the correct awnser mark me brainliest please
(100 POINTS AND BRAINLIEST) Please use the answers that are given. Using the following data, calculate the mean absolute deviation
What is the mean absolute deviation for these data?
A: 9
B: 5.4
C: 5
D: 2.6
Answer:
There isn't any data, maybe you could put the rest of the question in the comment area.
Please help will give brainliest
Which of the following are tangent to circle A? Select all that apply
see picture
Answer:
RS RT ST
Step-by-step explanation:
This is due to the facts that tangency means having contact at a single point or along a line without crossing. so the first 3 options are correct
Find the area of the following triangle. Show each of the math steps that you use to find the area. Then explain how to go about finding the area of this particular triangle (explain each one of the steps that you showed with your math).
Right angled triangle
Base=B=2.4cmHeight=H=1.8cmArea:-
[tex]\\ \rm\rightarrowtail \dfrac{1}{2}BH[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{1}{2}(2.4)(1.8)[/tex]
[tex]\\ \rm\rightarrowtail 1.2(1.8)[/tex]
[tex]\\ \rm\rightarrowtail 2.16cm^2[/tex]
What is the measure of each angle in the circle?
40°
60°
45°
36°
Answer:
i think it would be 45
hope im right
if not i can change it
Step-by-step explanation:
Answer:
45°
Step-by-step explanation:
The circle is divided into 8 equal arcs, each arc measuring an angle of:
360/8 = 45°
Hope this helps
Please Help!!! Will Mark Brainliest!
Step-by-step explanation:
from my side it's blury, try to send it again
Abebi surveyed how many miles the students in her Algebra 1 class travel to get to school, and ended up with the following set of data: 4.75, 2.25, 3, 3.5, 1.75, 2.25, 1.5, 5, 4.5, 2.25, 2, 3, 2.65, 4.8, 3.5\
Match the measures of central tendency to the correct values.
Hint:
MEAN = Sum of the data/# of data values
MEDIAN = middle data value when values are listed least to greatest
MODE = value appearing the most times
RANGE = difference between the largest and smallest values
Answer:
Mean: 3.1
Median: 3
Mode: 2.25 appears 3 times
Range: 5 - 1.5 = 3.5
Mean = (4.75+2.25+3+3.5+1.75+2.25+1.5+5+4.5+2.25+2+3+2.65+4.8+3.5)/16
= 3.56625
Median = 3.50
Mode = 2.25
Range = 9.10
This is a 30-60-90 triangle.
What is the measure of x?
Rationalize the denominator.
[?]
х
X=
7
Answer:
x = [tex]\frac{2\sqrt{21}}{3}[/tex]
Step-by-step explanation:
For a 30-60-90 triangle:
Short leg = sLong leg = s√3Hypotenuse = 2sThus:
Short leg = √7/√3 = (√21)/3Long leg = √7Hypotenuse = x = 2(√21)/3Answer:
2 21 3
Step-by-step explanation:
How would you expand log412 so that it can be evaluated, given log43 ≈ 0.792? Log Subscript 4 Baseline 3 times log Subscript 4 Baseline 4 StartRoot a squared + b squared EndRoot log 3 + log 4 log Subscript 4 Baseline 3 + log Subscript 4 Baseline 4 log 3 times log 4
Answer: log412 = 1.792
Step-by-step explanation:
log412 = log4(3 x 4)
log4(3 x 4) = log4(3) + log4(4)
log4(4) = 1
log4(3) = .792
1 + .792 = 1.792
log412 = 1.792
Evaluate (2 minus 5 i) (p + q) (i) when p = 2 and q = 5 i.
29 i
29 i - 20
- 21 i
29
Find the volume of a cone that has a diameter of 14 feet and a height of 11 feet. Use 3.14 for pi
Answer:
564.15 cubic ft[tex] \: [/tex]
Step-by-step explanation:
In the question, it is given that a cone has a diameter of 14 feet and a height of 11 feet and we have to find the volume of the cone.
[tex] \: [/tex]
To Find the volume of the cone, we must know this formula :
[tex] \\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { Volume_{(cone) }= \dfrac{1}{3} \: \pi {r}^{2}h }}}}}}} \\ \\[/tex]
Where,
r refers to the radius of the cone. As the diameter is 14 ft, therefore the radius will 7 ft.h refers to the height of the cone.Now, we will substitute the values in the formula :
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times {(7)}^{2} \times 11 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 49 \times 11 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 539 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 1692.46 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1692.46}{3} }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \: \: \underline{ \boxed{ \frak{564.15 } }} }}}}}}} \: \: \bigstar \\ \\[/tex]
Therefore,
The volume of the cone is 564.15 ft³ .Step-by-step explanation:
Given :-
Height of cone :- 11 feet Diameter of cone :- 14 feet , radius = 7 feetTo Find :-
Volume of coneSolution:-
Formula for volume of cone = 1/3πr²h
putting the known values ,Volume = 1/3×3.14×7²×11 cubic ft.
Volume = 564.15 cubic ft.
How would we add -3 + (-9) on the number line?
Answer:
-12
Step-by-step explanation:
1. Create an Equation
-3-9
2. Solve
-3-9 <=== subtract -3 and -9 together to get your answer
-12
3. Check
-12+3 <=== create this equation or this one ===> -12+9 to check if we calculated correctly
-12+3= -9 -12+9= -3
this shows the answer is corrrect
Q: Ribbon cost $1.44 for 3 m.
(1) What is the cost per meter?
(2) How much would 5 m of ribbon cost?
(3) How much ribbon could you buy for $12?
Answer:
1.44 divided by 3m will give $0.48/5 times 0.48 gives 2.412 times three divided by 1.44 gives$.25Pls help !!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
D. Rhombus.
Step-by-step explanation:
This will be a quadrilateral with 4 equal sides.
The oppsoite angles will be equal but they will not be 90 degrees as each triangle of the 3 dimensional figure is an equilateral triangle.
Therfore the cross section is a rhombus.
What is the volume of the rectangular prism below in cubic inches?
Answer:
24
Step-by-step explanation:
The volume formula is all the dimensions multiplied together, or lengthxwidthxheight.
So, you do 1x1x2 which is 2 feet. HOWEVER, it is looking for CUBIC INCHES, not cubic FEET.
There are twelve inches in a foot so 2x12=24 inches.
prove it equals 1
(Tanx - Cotx) + Sinx.Cosx
Step-by-step explanation:
(sinx/cosx - cosx/sinx) + sinxcosx
sin²x - cos²x = 1
I can't prove
I only know sin²x + cos²x = 1 : )
Past experience shows that Mr.Reisman will have 3 left-handed students in ever class of 25 math students. If Mr.Reisman teaches 125 students in one day, what is the most likely total number of left-handed students in his classes?
Answer:
15 students
Step-by-step explanation:
125/25=5
5x3=15
Im so desperate
ms. davis sold $309.00 of books. at the end of the day, she earned $27.81 in commission for those sales. what is ms. davis' commission rate?
question 8 options:
11%
9%
3.4%
2.81%
so Ms. Davis gets hmmm say "x" percent from sales as her commission, and we know she did in sales $309 and made $27.81.
if we take 309 to be the 100%, and x% of that is 27.81, what's "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 309 & 100\\ 27.81& x \end{array} \implies \cfrac{309}{27.81}=\cfrac{100}{x} \\\\\\ 309x=2781\implies x=\cfrac{2781}{309}\implies x=9[/tex]
a
С
b
60°
45°
Find a, b, and c.
Answer:
Step-by-step explanation:
The measures of the bases of a trapezoid are 14 and 20. What is the measure of the median of the trapezoid?
The median of the trapezoid is = 17
calculation of the median of a trapezoidA trapezoid is a quadrilateral with one pair of opposite sides parallel. It has parallel sides which are known as the bases.
The base of the trapezoid(B1) =14
The base of the trapezoid (B2) = 20
To calculate the median = half the sum of the base of the trapezoid given.
Therefore,
14+20/2
34/2= 17
Therefore, the median of the trapezoid is = 17
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What is the length of a car if the length on the scale madel car is 17 cm and the scale is 2 cm : 50 cm?
Answer:
x= 425
Step-by-step explanation:
In parallelogram crhs, the measure of angle c is 48.Find the measure of angle h?
Answer:
48°
Step-by-step explanation:
we know that opposite angle of parallelogram is equal
so,
angel C is equal to opposite angle H
H = 48
angle C = 48°
angle R = 132°
angle H = 48° (opposite of angle C)
angle S = 132°(opposite of angle R)
Mark me Brainiest please
express the following rational algebraic expression to its simple form.show your solution
1. 25 ׳y³/ 75 ×⁴y⁴
express the following rational algebraic expression to its simple form.show your solution
1. 25 ׳y³/ 75 ×⁴y⁴
Answer
1/3×yPLEASE HELP WILL GIVE BRAINLIEST!!!!
Answer:
Its The 3rd one you are correct in picture
Step-by-step explanation:
Element x decays radioactively with a half life of 12 minutes. if there are 580 grams
of element x, how long, to the nearest tenth of a minute, would it take the element to
decay to 68 grams?
Answer:
37.1
Step-by-step explanation:
37.1
Write and solve an equation to find the value of x
Answer:
Equation: x+90=7x
Answer: x=15
Step-by-step explanation:
By looking at the image, I can tell that both of those angles are vertical.
Vertical angles mean that both of the angles would be equal. Therefore, we can set x+90 = 7x
You then subtract x from both sides, leaving us with 90 = 6x
From there, divide both sides by 6 to isolate 6 to 1, and you are left with 15= x or x=15, giving you your answer and equation.
The value of x is 15.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given that the two angle measures (x + 90)° and 7x°.
And both the angle measures are formed by opposite angles,
so,
x + 90 = 7x
Taking like terms to one side,
we get,
7x - x = 90
6x = 90
Divide by 6, and we get,
x = 90/6
x = 15
Therefore, x = 15°.
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What is the area of this figure?
18 ft
3 ft
15 ft
12 ft
9 ft
3 ft
square feet
Submit
Answer: Times it
Step-by-step explanation:
Answer:
90 square feet
Step-by-step explanation:
area of this figure = area of 1 rectangle + area of 2nd rectangle
= L×B + l × b
= 18 × 3 + 12 × 3
= 54 + 36
= 90 feet²
