Answers
Let's see
[tex]\\ \rm\Rrightarrow {\displaystyle{\sum^{275}_{k=1}}}(-5k+12)[/tex]
[tex]\\ \rm\Rrightarrow (-5(1)+12)+(-5(2)+12)\dots (-5(275)+12)[/tex]
[tex]\\ \rm\Rrightarrow 7+5+3+2+1+\dots -1363[/tex]
So
a=7l=-1363n=275Sum:-
[tex]\\ \rm\Rrightarrow S_n=\dfrac{n}{2}[a+l][/tex]
[tex]\\ \rm\Rrightarrow \dfrac{275}{2}(7-1363)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{275}{2}(-1356)[/tex]
[tex]\\ \rm\Rrightarrow 275(-678)[/tex]
[tex]\\ \rm\Rrightarrow -186450[/tex]
Answer:
-186,450
Step-by-step explanation:
Sum of arithmetic series formula
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
where:
a is the first termd is the common difference between the termsn is the total number of terms in the sequence[tex]\displaystyle \sum\limits_{k=1}^{275} (-5k+12)[/tex]
To find the first term, substitute [tex]k = 1[/tex] into [tex](-5k+12)[/tex]
[tex]a_1=-5(1)+12=7[/tex]
To find the common difference, find [tex]a_2[/tex] then subtract [tex]a_1[/tex] from [tex]a_2[/tex]:
[tex]a_2=-5(2)+12=2[/tex]
[tex]\begin{aligned}d & =a_2-a_1\\ & =2-7\\ & =-5\end{aligned}[/tex]
Given:
[tex]a=7[/tex][tex]d=-5[/tex][tex]n=275[/tex][tex]\begin{aligned}S_{275} & = \dfrac{275}{2}[2(7)+(275-1)(-5)]\\& = \dfrac{275}{2}[14-1370]\\& = \dfrac{275}{2}[-1356]\\& = -186450\end{aligned}[/tex]
Related Questions
solve for x: 4x+1/2(2x+4) >12
Answers
Answer: x>2
Step-by-step explanation:
[tex]4x+\frac{1}{2} (2x+4) > 12[/tex]
Step 1: Simplify both sides of the inequality through the Distributive Property
[tex]4x+\frac{1}{2} (2x+4) > 12\\4x+(\frac{1}{2})(2x)+(\frac{1}{2})(4) > 12\\4x+x+2 > 12\\5x+2 > 12[/tex]
Step 2: Subtract 2 from both sides to isolate x
[tex]5x+2-2 > 12-2\\5x > 10[/tex]
Step 3: Divide both sides by 5 to full isolate x
[tex]\frac{5x}{5} > \frac{10}{5} \\x > 2[/tex]
Answer:
[tex]x > 2[/tex]
Step-by-step explanation:
[tex]4x+\frac{1}{2}(2x+4) > 12 < ==multiply\ the\ \#s\ in\ the\ parenthesis\ first\ using\ \frac{1}{2}\\\\4x+x+2 > 12 < ==combine\ any\ like\ terms\\\\5x+2 > 12 < ==subtract\ 2\ from\ both\ sides\\-2 \ \ \ \ \ -2\\\\5x > 10 < ==divide\ both\ sides\ by\ 5\\/5 \ \ \ \ /5\\\\x > 2[/tex]
This means that x can be any value that is greater than 2.
Hope this helps!
Find the supplement of an angle that measures 20 degrees.
Answers
180 - 20 = 160
160 is your answer.
for a craft project say that the length of a piece of red ribbon should be 7 inches longer than the length of a piece of blue ribbon. How long is the red ribbon if the length of the blue ribbon is x inches?
Answers
Answer:
If the blue ribbon is x inches and the red ribbon is that length and an additional 7 inches the red ribbon can be expressed as x + 7.
Find the area of the parallelogram
Answers
Answer:
A = 3484 ft²
Step-by-step explanation:
Area of a parallelogram is given by the formula:
A = bh (where b is the base length and h is the vertical height)
Substituting values given in the diagram gives us:
A = 67×52
A = 3484
Units will be ft² since it is area.
So our final answer is 3484 ft²
Brainliest if this helped and I hope you find the rest of your homework or task easy.
Jared lost a total of $96 over the last 12 months. What integer represents the mean number of dollars lost each month?
Answers
Answer:
-8
Step-by-step explanation:
To find mean, average, divide.
-96/12
-8
Hope this helps
100 points
The ratio of students polled in 6th grade who prefer lemonade to iced tea is 8:4. If there were 39 students in 6th grade polled, explain how to find the number of students that prefer lemonade and the number of students that prefer iced tea using a ratio table. If you wish, you may upload a copy of your ratio table.
Answers
Answer:
Step-by-step explanation:
So, the total unit number of sixth graders polled is 12.
39/12=3.25
So, you'd do 8x3.25=26 students like lemonade
13 students like iced tea
Find the volume of the prism or compound shape.
Answers
Since there are two “half spheres”, their area is: (113.04 x 2)in^3 = 226.08in^3.
Volume of a cylinder = (pi)(r^2)(height) = [(3.14)(9)(10)]in^3 = 282.6in^3.
Total volume = (282.6 + 226.08)in^3 = 508.68in^3.
The principal at mcdermott middle school is planning to survey students at his school, but only wants the survey to contain statistical questions. the following list contains survey questions that he is considering.
determine whether each question is a statistical question. type "yes" or "no" to indicate whether or not it is a statistical question.
what is the school's mascot?
how many minutes long is third period?
how many clubs do you participate in?
how many electives do you want to take next year?
Answers
what is the school's mascot? no
how many minutes long is third period? no
how many clubs do you participate in? yes
how many electives do you want to take next year? yes
what is an equation of the line that passes through the points (3,0) and (-6,-3)
Answers
Step-by-step explanation:
given ponts,
(3,0)=(x1,y1)
(-6,-3)=(x2,y2)
we know,
Eqn of any line joining two points be,
(y-y1)={(y2-y1)/(x2-x1)}*(x-x1)
y-0={(-3-0)/(-6-3)}*(x-3)
y=(1/3)*(x-3)
y=(x-3)/3
3y=x-3
0=x-3y-3
x-3y-3=0
Therefore it is required eqn
. mervin needs cash and he needs it now. he goes to advanced financial and takes out a loan of 300.00. advanced financial calls their loans mirco-loans and get to choose their own interest rates. if they set the rate at 70% per year, how much interest will mervin need to pay back in 5 months if interest compounds monthly? how much will he owe in 5 months using approximate equivalent growth?
Answers
Mervin's loan of $300 is an illustration of compound interest
The interest to pay back in 5 months is $74.2, and the amount to pay back in 5 months is $374.2
The interest to pay back in 5 monthsThe given parameters are:
Principal, P =$300.00Rate, r = 70%Time, t = 5 monthsThe compound interest is calculated as:
CI = P * (1 + r)^(t/12) - P
Substitute known values
CI = 300 * (1 + (0.70))^(5/12) - 300
Evaluate the expression
CI = 74.2
Hence, the interest to pay back in 5 months is $74.2
The amount to pay back in 5 monthsThe amount (A) is calculated using:
A = CI + P
This gives
A = 74.2 + 300
A = 374.2
Hence, the amount to pay back in 5 months is $374.2
Read more about compound interest at:
https://brainly.com/question/24924853
F(x)=3x^4-2x^3-12x^2-x; k=4
Answers
Answer:
444
Step-by-step explanation:
Find F * k given F(x) = 3x^4 - 2x^3 - 12x^2-x, k = 4
F * k = F( ( k ) ( x ) )
Help
Solve the quadratic equation by any means. Identify the method and complete the explanation of why you chose it. Irrational answers may be left in radical form.
5x2 + 16x + 3 = 0
Part a: factoring
Completing the swuares
Taking the square roots
Which one
Part b:
Why:
There are not many factors to check
It is not factorable
B is = to zero
Answers
Answer:
Factoring: [tex]x = -\frac{1}{5}, -3[/tex]
Step-by-step explanation:
A) You can factor the expression [tex]5x^2 + 16x + 3[/tex] into [tex](5x+1)(x+3)[/tex].
5x + 1 = 0 and x + 3 = 0
[tex]x = -\frac{1}{5}, -3[/tex]
B) I would use factoring because you can factor this expression, and you don't have to use completing the square
What is 4 2/5 divided by 1 1/10
Answers
Answer:
✓ 4 2/5 divided by 1 1/10= 4
Step-by-step explanation:
✓ Factor the numerator and denominator and cancel the common factors.
✓ Hopefully this helps you!
-Keira
When [tex]4\frac{2}{5}[/tex] is divided by [tex]1 \frac{1}{10}[/tex] we get the value 4.
Convert mixed numbers to improper fractions:
[tex]4\frac{2}{5}[/tex] = (4 × 5 + 2) / 5 = 22/5
[tex]1 \frac{1}{10}[/tex] = (1 × 10 + 1) / 10 = 11/10
Divide the two fractions:
(22/5) ÷ (11/10)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(22/5) × (10/11)
220/55
220/55 can be reduced by dividing both the numerator and denominator by their greatest common divisor, which is 5:
(220 ÷ 5) / (55 ÷ 5)
= 44/11
=4
To learn more on Division click:
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Part II: Analysis
5) How many seconds does the roller coaster last?
6) What is the roller coaster's starting height? How many seconds does it take the
roller coaster to reach maximum height?
7) Describe what the roller coaster is doing in the interval 7
8) Use your knowledge of function notation and piecewise functions to determine the
following:
a. f(10) =
i. Explain what this value means in real world context.
b. f(20) =
1. Explain what this value means in real world context.
c. If 16 seconds have passed since the roller coaster started, what is the height
of the roller coaster?
Bonus: When does the roller coaster reach 100 feet above the ground?
Answers
10 divided 20,then times mo 7 to 8
It’s easy yk bro i just need some helpp with it
Answers
Answer:
I think you need to link a picture or something
Step-by-step explanation:
Pls help! I really need help! This is my question..
A sample of iron has dimensions of 2 cm x 4 cm x 6 cm and a mass of 100g. What is the density of the sample?
Answers
Answer:
density= 2 and 1/2
Step-by-step explanation:
The formula to find density is: density=[tex]\frac{mass}{volume}[/tex]
so the mass is 100, and the volume is 2x4=8x6=48, 100/48 equals 2 and 1/2
please help me..... asap
Answers
Answer:
collect a sample bacteria from the lake
Answer:
A- collect a sample of bacteria from the lake.
Step-by-step explanation:
It will not help to get bacteria from a RIVER since the scientist wants to learn about the LAKE. Also, getting all the lake bacteria will cause no more bacterial life to thrive, which is bad- but just a single bacteria cell isn't good either since we don't know how it reproduces and one is usually not enough.
A submarine is at the surface of the ocean, preparing to dive. It submerges and dives to - 993 feet. Then, it ascends 308 feet to
void hitting an undersea cliff. What integer represents the submarine's position in feet (depth) after it ascends to avoid the cliff?
Answers
Answer:
-685
Step-by-step explanation:
hope I helped
To find the probability of two
independent events, you
their
probabilities.
A) add
B) subtract
C) multiply D) divide
Answers
Answer: You Multiply
Step-by-step explanation:
Which one is it
(1, 100)
(3, 49)
(4, 50)
(2, 74)
Answers
Answer:
(1, 100) » First one
(3, 49) » Third one
(4, 50) » Forth one
(2, 74) » Second one
Step-by-step explanation:
[tex]{}[/tex]
(1,100)
Jamie and Linda are having a contest to see whose photo will get more "likes" on social media.
Jamie's photo got 75 likes by the end of the first day and is getting 36 more likes each day.
Linda's likes can be modeled by the function f(x)=18(2)x.
Which statements are true? Select all that apply.
Hint: Use a table or graph to compare the number of likes that Jamie and Linda get. Remember that the value of the function at x=1 represents number of likes at the end of the first day.
Answers
Answer:
2) Jamie's photo gets more likes within the first three days than Linda's photo.
If x=y and y= 2, then 3x=
Answers
~Denki Kaminari here~
Answer:
6
Step-by-step explanation:
because x is equal to 1, and y is equal to 2, all we need to do is skip count 3 times by 2 and you get your answer: 6!
hope this helps :D
Answer:
6
Step-by-step explanation:
Given that x = y so that means if y and x are same and have same values. Therefore if y = 2 then x = 2.
So substitute x = 2 in 3x:
3(2) = 6
Therefore, the solution is 6
If someone could help me with this I would really appreciate it thank you !!
Answers
Answer:
It should be thirty if i read question properly
If want process pls comment
30 in
Explanation: 10/2 =5 4/2=2 6/2=3
5x2=10 10x3=30 in!
Write in standard form 8,00,000 + 60,000 + 3,000 + 400 +30 + 2 =
Answers
Answer:
863432
Step-by-step explanation:
Add all numbers You will get answer
Answer:
863432.00
Step-by-step explanation:
800000
60000
3000
400
30
2
--------------
863432
_______
i need help with this one! asap please!
Answers
Answer:
D. 60
Step-by-step explanation:
Height = constant / width
30 = c / 2
2* 30 = 60
c = 60
12 = c / 5
12 * 5 = 60
c = 60
10 = c / 6
10 * 6 = 60
c = 60
You received an $40,000 bonus, which was 18% of your salary. What is the percentage of your salary is this bonus?
Answers
Answer:
2.3% is the percentage of the Salary
Step-by-step explanation:
If ABCD is dilated by a factor of 1/2, the coordinate of D' would be:
Answers
Answer:
D'=(1,-1)
Step-by-step explanation:
If you dialate by 1/2 then all you have to do, is find half of point D. so point D sits at (2,-2) and half of 2 would be (1,-1).
The dilated coordinates of D(2,-2) = D'(1,-1).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
From the graph,
we interpreted the coordinates of D (2,-2).
Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
To find the dilation of transformation
The basic formula to find the scale factor of a dilated figure is:
Scale factor = coordinates of the new shape ÷ coordinates of the original shape.
That means,
multiply the factor to the coordinates.
D' = (2 x 1/2, -2 x 1/2)
D' = (1, -1)
Therefore, the coordinates after the dilation D' (1,-1).
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The function g(x) = (3-2). The function f(x) = g() +3.
The function f() is shifted horizontally
2 units to the left of g(3).
The function f() is shifted vertically
Answers
Answer:
Step-by-step explanation:
The answer
g(3)=3−23⋅(3)=3−2=1
Explanation:
show that
g(x)=3−23x
for g(3)g(3)=3−23⋅(3)=3−2=1
A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $327.50. The second order was for bushes and 2 trees, and totaled $142.96. Sam tried to use system of equation to solve the problem, if b represents brushes and t represent trees which system can Sam use
A
13b + 4t =327.50
6b + 2t = 142.96
B
13b + 2t =327.50
6b + 4t =142.96
C
13b + 4t = 142.96
6b + 2t = 327.50
D
4b + 13t = 327.50
2b + 6t = 142.96
Answers
The system of equations that Sam can use is given by:
A 13b + 4t =327.50, 6b + 2t = 142.96
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable b: Cost of a bush.Variable t: Cost of a tree.The first order was for 13 bushes and 4 trees, and totaled $327.50, hence:
13b + 4t = 327.50.
The second order was for 6 bushes and 2 trees, and totaled $142.96, hence:
6b + 2t = 142.96.
Which means that option A is correct.
More can be learned about a system of equations at https://brainly.com/question/24342899
PLEASE HELP
What is the product of (-a + 3)(a + 4)?
A. - a2 - a - 12
B. a2 - a + 12
C. - a2 - a + 12
D. a2 - a - 12
Answers
Answer:
-a^2-a+12
Step-by-step explanation:
Answer:
Option C.
[tex]-a^{2}-a+12[/tex]
Step-by-step explanation:
1. Distributive multiply
[tex]-a*(a+4)+3*(a+4)[/tex]
2. Distributive multiply
[tex]-a*a-a*4+3*(a+4)[/tex]
3. Multiply terms to exponential form
[tex](-1) *a^{2}-a*4+3*(a+4)[/tex]
4. Multiply constants
[tex]-a^{2}-4*a+3*(a+4)[/tex]
5. Distributive multiply
[tex]-a^{2}-4a+(3*a+3*4)[/tex]
6. Multiply constants
[tex]-a^{2}-4a+(3a+12)[/tex]
7. Reorder terms
[tex]-a^{2} -4a+(12+3a)[/tex]
8. Add terms
[tex]-a^{2}-a+12[/tex]
