4. The sum of 50 consecutive positive even integers is 3250. What is the largest of these integers?
Answers
Answer:
114
Step-by-step explanation:
The question relates to the sum of an arithmetic progression, A. P.
The count of numbers added, n = 50
The sum of the numbers, Sₙ = 3,250
The formula for the sum of an A. P. is given as follows;
[tex]S_n = \dfrac{n}{2} \left[2 \cdot a + (n - 1)\cdot d\right][/tex]
[tex]S_n = \dfrac{n}{2} \left[a + a_n\right][/tex]
Where;
a = The first term of set of numbers
d = The common difference between consecutive numbers
n = The number of terms = 50
aₙ = The last term, the largest of the integers
Therefore, we get;
The common difference of consecutive even integers numbers, d = 2
Plugging in the values gives;
3,250 = (50/2) × (2·a + (50 - 1) × 2) = 25 × (2·a + 49 × 2)
2·a = (3,250/25) - 49 × 2 = 32
a = 32/2 = 16
From [tex]S_n = \dfrac{n}{2} \left[a + a_n\right][/tex], we have;
3,250/25 = 16 + aₙ
aₙ = 3,250/25 - 16 = 114
The largest of the integers, aₙ = 114.
Related Questions
What is the value of x in the equation 8x – 2y = 48, when y = 4?
Answers
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
[tex]8x – 2y = 48[/tex]
[tex]8x−2(4)=48[/tex]
[tex]8x−2 \times 4=48[/tex]
[tex]8x−8=48[/tex]
[tex]8x=48+8[/tex]
[tex]8x = 56[/tex]
[tex]x = \frac{56}{8} [/tex]
[tex]x = 7[/tex]
Hope it is helpful...Answer:b
Step-by-step explanation:
Sam is 34 years younger than Ashton. 4 years ago, Ashton's age was 3 times Sam's age. How old is Sam now?
Answers
Answer:
21years old
Step-by-step explanation:
Let Sam's age be x
Let Ashton present age be y
If Sam is 34 years younger than Ashton then;
x = y - 34 .... 1
If by 4 years ago, Ashton's age was 3 times Sam's age then;
Sam = x - 4
Ashton = y - 4
y-4 = 3(x-4)
y-4 = 3x - 12 ....2
Substitute 1 into 2;
y-4 = 3(y-34)-12
y-4 = 3y-102-12
y-4 = 3y - 114
y-3y = -114 + 4
-2y = -110
y = 110/2
y = 55
Since x = y- 34
x = 55-34
x = 21
Hence Sam will be 21years old now
Faith makes greetinli cards with colored paper. She plans to make 1/5 of the cards out of red paper. She
has 25 sheets of colored paper in all. If she uses all the colored paper she has, how many sheets are a
color other than red?
Answers
carlos has 4 tennis balls and 5 baseballs. what is the percentage of tennis balls?
Answers
Answer:
Its 80%
Step-by-step explanation:
4/5 * 100 = 80%
Answer:
80%
Step-by-step explanation:
4/5 * 100 = 80
At Fairview middle school 75 being members need to raise a total of $8250 for a trip so far they have is $3120 how much money in dollars per bandmember still needs to raised for the trip
Answers
Answer: 68.40$ per member left.
Explanation:
8250 = 75x + 3120
5130 = 75x
68.4 = x
El acero de alta resistencia es el principal material de los submarinos actuales, con un límite de profundidad de 250 a 400 m para que no haya ningún riesgo de explosión. Si se sabe que la distancia entre los 2 barcos es de 188 m y que las distancias de los barcos hasta el submarino son de 152 y 192 m respectivamente. Determina si el submarino corre algún riesgo de explosión, justificando la respuesta al mencionar la profundidad a la que se encuentra el submarino.
Answers
Bob eats 1/4 of a pie and later eats 2/5 of the pie. What fractions remains?
Answers
Answer:
9/20
Step-by-step explanation:
After Bob eats 1/4 of the pie, he has 3/4 left. 2/5 of 3/4 is the same as (2/5)*(3/4) because "of" is used as multiplication in math. (2/5)*(3/4)=6/20, so he ate 6/20 of the pie. To get the answer, you need to solve 1-(1/4+6/20)=
1-(5/20+6/20)=20/20-11/20=9/20. I hope this helps and sorry if I made a mistake. :)
A cone has a radius of 12 inches and a slant height of 20 inches. What is the approximate surface area of the cone?
Answers
Answer:
2009.6 in²
Step-by-step explanation:
The surface area, SA of a cone is obtained using the formular :
SA = πr² + πrl
Where ; r = Radius = 20 inches ; l = slant height = 12 inches
SA = π*20² + π*20*12
SA = 400π + 240π
Take π = 3.14
SA = (400*3.14) + (240*3.14)
SA = 1256 + 753.6
SA = 2009.6 in²
What is the area of this figure?
Enter your answer in the box
Answers
Answer:
and this is why I do not like math also all u got to do is count all the squares and the corners do not count as wholes u got to put two together and then it makes a whole
Step-by-step explanation:
its just that easy :D hope it was helpful
HELLLLLLP WILLGIVE 50 POINTS!A square is inscribed in a circle. If the area of the square is 9 in^2, what is the ratio of the circumference of the circle to the are of the circle?
Answers
Answer:
2√2/3Step-by-step explanation:
Area of the square is 9 in², so side of the square is:
a = √9 = 3 inThe diagonal of the square is the diameter of the circle.
d = 3√2Circumference of circle:
C = πd = 3√2πArea of circle:
A = πd²/4 = 18π/4 = 9/2πRatio of circumference to area:
C/A = 3√2π / (9/2π) = 2√2/3What is the basic difference between liability insurance and collision insurance?
a.
Liability insurance covers only medical injuries, and collision insurance covers only property damage.
b.
Liability insurance covers damage that you cause, and collision insurance covers damage done to your vehicle.
c.
Liability insurance is optional, but most states require collision insurance.
d.
Liability insurance protects against theft or vandalism, and collision insurance covers against accidents or crashes.
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
Hello There!!
Step-by-step explanation:
The answer is b. Liability insurance covers damage that you cause, and collision insurance covers damage done to your vehicle.
hope this helps,have a great day!!
~Pinky~
Answer:
B
Step-by-step explanation:
differentiate y=(5x-1)^1/2
Answers
Answer:
Df(1/5,+∞) or x>1/5 step by step
the rectangle with 2 row nd each raw has 6 square each sudw of square is 1 cm determine the perimeter of rectangle and area of square
Answers
Answer:
Perimeter of rectangle is 16 cm and the area of square is 1 cm^2
Step-by-step explanation:
Here, we want to get the perimeter of rectangle and area of square
From the question, the rectangle has 2 rows of 6 squares each; So we have the length as 2 cm and the width as 6 * 1 cm = 6 cm
So the rectangle is 6 cm by 2 cm
The perimeter of a rectangle is 2(l + b)
so, we have 2(6 + 2) = 2(8) = 16 cm
The area of the square is simply the side length raised to the power of 2
we have this as 1^2 = 1 cm^2
A triangular parcel of land has side lengths of 100, 580, and 600 feet. Approximate the area of the land. Round your answer to the nearest foot.
Answers
Answer:
28800 square feet
Step-by-step explanation:
We solve this using the Heron's formula
Area of a Triangle = √s(s - a)(s - b)(s - c)
s = a + b + c/2
s = 100 + 580 + 600/2 = 640
Area of the land(Triangle) = √640 × (640 - 100)(640 - 580)(640 - 600)
= √640 × (540) ×( 60) × (40)
= √(829440000)
= 28800 square feet
Therefore, the approximate the area of the land is 28800 square feet.
Hey could you please help me? thank you
Answers
Answer:
8
Step-by-step explanation:
c(w)= 200 * 1/5^2.
1/5 * 1/5 = 1/25
1/25 * 200 = 8
Hope this helps!
:)
what is the argument of 2-2i
Answers
Answer:
The argument of -2 -2i is either the negative angle from the positive real axis clockwise to the radial line, or the positive angle from the positive real axis counterclockwise to the radial line.
Pam's eye-level height is 324 ft above sea level, and Adam's eye-level height is 400 ft above sea level. How much farther can Adam see to the horizon? Use the formula d = StartRoot StartFraction 3 h Over 2 EndFraction EndRoot, with d being the distance they can see in miles and h being their eye-level height in feet. 1 mi StartRoot 6 EndRoot mi 19 mi 19 StartRoot 6 EndRoot mi
Answers
Answer:
B. StartRoot 6 EndRoot mi
√6 mi
Step-by-step explanation:
A. 1 mi
B. StartRoot 6 EndRoot mi
C.19 mi
D. 19 StartRoot 6 EndRoot mi
d = √(3h/2)
Where,
d = distance they can see in miles h = their eye-level height in feet
Pam:
h = 324 ft
d = √(3h/2)
d = √{(3 * 324)/2}
= √972/2
= √486
= √(81 * 6)
= √81 * √6
= 9√6 mi
Adam:
h = 400 ft
d = √(3h/2)
d = √{(3 * 400)/2}
= √1200/2
= √600
= √(100 * 6)
= √100 * √6
= 10√6 mi
How much farther can Adam see to the horizon?
Adam - Pam
= 10√6 - 9√6
= √6 mi
Let p(x)=3x-7. If p(x)=0,find x. A. -7
B.-4
C. 4
D. 7/3
E. The correct answer cannot be determined
Answers
Answer:
D
Step-by-step explanation:
0=3x-7
0=3x+7
7=3x/3
7/3=x
What is the factored form of x2 + 2xy − 8y2?
Answers
Answer:
(x+2y)(x−4y)
hope this helps!
Kelly's new snowboard is 120% longer than her old snowboard. If the new snowboard is 150 cm, how long is her old snowboard?
Answers
Which of the following would be the most logical first step to solving this
quadratic equation?
x2 - 5x + 6 = 0
A. Add -6 to both sides.
B. Take the square root of both sides.
C. Use the zero product rule to set up smaller equations.
D. Factor the left side.
Answers
Answer:
D)Factor the left side
Step-by-step explanation:
(x-2)(x-3)
ANSWER QUICK PLEASE
If 20.0 mL of a 5.0M HCl solution are required to neutralize 10.0 mL of a NaOH
solution, calculate the molarity of the NaOH solution.
Answers
20.0 mL of 5.0 M HCl solution contains
0.0200 L * 5.0 M = 0.10 mol
of HCl.
Mixing the HCl and NaOH solutions results in
HCl + NaOH ==> NaCl + H2O
which is to say 0.10 mol of HCl reacts with 0.10 mol of NaOH. If only 10.0 mL of NaOH solution is required, then its molarity x is such that
0.0100 L * x M = 0.10 mol => x = 10. M
James can write 6 paragraphs in 24 minutes.
Using the same unit rate, how many paragraphs can James write in 16 minutes?
Answers
Lets find out how many a minute. 3 in 12 minutes, 1 in 4 minutes, so 1/4th of a paragraph per minute.
Now 1/4 times 16 = 4. So he can write 4!
Brainliest or Heart if helpful!
Solve for the variable: p - 4.2 = 2. Show your work
Answers
Answer:
6.2
Step-by-step explanation:
P - 4.2 =2
we have to no separate the variables and constants
so , when we move 4.2 to the other side ( other side of 2) it will be something like this
p = 2+4.2
as you can wee when we moved 4.2 to the other side the operation changed from ,minuus to plus sign .
now just do what it says
formula :
=p-4.2=2
=p = 2+4.2
= 2+ 4.2= 6.2
so,
p=6.2
write the formula , I think no need to write explanation
Please help due at 9:36 please help
Answers
Answer:
I think it's 45, just guess bc ur in hurry
Step-by-step explanation:
What age bracket (s) has no participants?
Answers
Answer:
19-21 and 43-45
Step-by-step explanation:
Please find the attached question
Solution
As we can see in the image , it is the age group 19-21 and 43-45 which do not have any participants.
rest all age groups have some frequency values indicating that they have some participants.
what is the solution of 56= k-42
Answers
Answer:
k=98
Step-by-step explanation:
Let's solve your equation step-by-step.
56=k−42
Step 1: Flip the equation.
k−42=56
Step 2: Add 42 to both sides.
k−42+42=56+42
k=98
I Hope This Helps If Not Then Im Srry....
Here are front elevation,side elevation and plan of a 3d shape.
Answers
Find the median and range of the data.
5, 6, 16, 26, 2, 13, 26, 10, 30, 26, 27
Answers
Answer:
Step-by-step explanation:
arrange the data from ascending to descending order
2,5,6,10,13,16,26,26,26,27,30
Median=N+1/2 (N means no of data)
=11+1/2
=12/2
=6 th term
=16
rangle = highest value - lowest value
=30-2
=28
Tawana has $325.54 in her checking account. She must keep a balance of at least $300 to avoid a fee. She plans to write a check to pay her to pay her credit card bill of $125.43. how much must Tawana deposit in her checking account to maintain atleast the minimum balance?
hi
Answers
Answer: To pay her bill with the minimum balance to avoid the fee, she needs the total amountof $300+$125.43=$425.43. But she only has $325.54. So, the extra minimum amount she needs to deposit is 425.43-325.54=$99.89.
Hence, the answer is $99.89.
