The first and second term of a linear sequence (A.p) are 3 and 8 respectively. Determine the least number of terms of the A.P that must be added so that the sum is greater than 250.
We are to find the number of terms in the AP that has a sum greater than 250
The number of teams in the AP which has a sum greater than 250 is at least 11 terms
First term, a = 3
second term, a + d = 8
so
common difference, d = 8-3
= 5
let
n = number of terms in the AP
The sum of n terms is 250
Sum = n/2{2a + (n - 1)d}
250 = n/2{2*3 + (n-1)5 }
250 = n/2{6 + 5n - 5}
250 = n/2(1 + 5n)
500 = n + 5n²
5n² + n - 500 = 0
Solve quadratically using formula
n = -b ± √b² - 4ac / 2a
= -1 ± √1² - 4(5)(-500) / 2(5)
= -1 ± √1 - (-10000) / 10
= -1 ± √1 + 10000 / 10
= -1 ± √10001 / 10
= -1 + √10001 / 10 or -1 - √10001 / 10
= -1/10 + √10001/10
or
-1/10 - √10001 / 20
= 9.9005 or -10.1005
The value of n must be positive and a whole value
Therefore,
n = 9.9005
Approximately, n = 10
The number of teams in the AP which has a sum greater than 250 is at least 11 terms
Read more:
https://brainly.com/question/24321873
3. You bought a shirt at regular price for $22 and a pair of jeans that are marked $42 but
are 25% off. How much will you pay with tax?
Answer:3
Step-by-step explanation:
I need this ASAP!!!! PLZ HELP!!! 20 points!!
7. You are on a field trip. You have to travel 73 miles to reach
your destination. You have traveled 29 miles so far. How
much further do you have to travel?
10 marbles.
Answer:
44
Step-by-step explanation:
Take the miles you already traveled and subtract it from the total.
73-29=44
Find the probability of prime or cube between 1 to 39
Answer: List of prime numbers before 39: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.
Step-by-step explanation:
Answer:
la numerencia es
Step-by-step explanation:
39 1 5 68
16. Which situation can be represented by y = 60x – 20?
A. The time remaining in minutes, y, for x hours after 20 minutes have past.
B. The cost, y, of buying x pairs of jeans for $60 with a 20% off coupon.
C. The cost, y, after buying raffle tickets for $40 each.
D. The number of seconds, y, in an x minute commercial if you skip the first 20 minutes.
Answer:
A is the right answer. so right it
1. The quotient of a number and 6 is 12.
Answer:
2 is your answer
Step-by-step explanation:
6x2=12
Answer:
72
Step-by-step explanation:
[tex] \frac{x}{6} = 12 \\ x = 12 \times 6 \\ x = 72[/tex]
exponential functions
Answer:
An exponential function is a Mathematical function in form f (x) = ax.
[tex]f(x) = ax[/tex]
Step-by-step explanation:
where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
NoTe: The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
if u need any help, just tell me know
Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.
1.Write the linear equation that models the equation?
2.What is the cost per T-shirt?
3.What is the standard shipping and handling bag?
Step-by-step explanation:
Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.
Then we have to writer a linear equation, for which I got: y-27/4x+25. We also had to find the cost per t-shirt, for which I got: $31.75. The last part I don't understand, however: fidn the shipping and handling charge.
The second word problem is:
It costs Consolidated Cereals Corporation $1050 to produce 100 boxes of corn flakes and $1250 to produce 500 boxes. I found the cost function: c(x)=1/2x+1000 but don't know how to determine the fixed cost and the variable cost per box (mainly because I have no idea what those are.)
Cost= m x+b
x is the cost per shirt, b is the handling charge
295=40m+b
565=80m+b
subtract the first equation from the second:
370=40x solve for m, the cost of each shirt. Then solve for b, put all that into y= mx+b
One the second question,
Cost= variable cost * n + Fixedcosts or
cost= n*v+F
1250=500v+f
1050=100v+f
subtract the second equation from the first
200=400v solve for v, and it is 1/2 dollar. Solve for f, the fixed cost, and it looks as if it is 1000 dollars.
What’s equivalent too -4+y+4y-5x+2x-3
Hey there!
-4 + y + 4y - 5x + 2x - 3
COMBINE the LIKE TERMS
= (-5x + 2x) + (y + 4y) + (-4 - 3)
= -3x + 5y - 7
Answer: -3x + 5y - 7
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Please walk me through how to solve these problems. If you can only solve one that’s fine, I just don’t know where to start. (This is geometry)
Answer:
5,-0.5 is the answer to the fist one
Step-by-step explanation:
they want you to give the middle point of the line segment when you have graphed the two end points,... find the coordinates of the point the would be in the middle,... Best of luck,... Chow
evaluate the following 1340five minus 242five
Answer:
13405 -- 2425 = 10980
Step-by-step explanation:
Answer:
-----> 13405-2425= 10980
A recipe for fluffy slime calls for 3 3/4 cups of shaving
cream, 1/2 cup of glue, 1/2 teaspoon of baking soda
and 1 1/2 tablespoons of saline solution; this is
enough for 2 people. How much shaving cream
would you need if you were making enough slime
for ten people?
Answer:
75/4 cups (or 18-3/4 cups)
Step-by-step explanation:
2 people ---> requires 3 3/4 cups (or 15/4 cups) of shaving cream
10 people ----> requires 5 times the amount of shaving cream needed for 2 people
Hence shaving cream is needed for 10 people
= 5 x 3 3/4 cups
= 5 x 15/4 cups
= 75/4 cups (or 18-3/4 cups)
lemme know if it helped <3. and lemme me know if it's right :) .!
a= r/2L solve for r, please help me!!
Answer:
r = 2L * a
Step-by-step explanation:
a= r/2L
then:
2L * a = 2L*r/2L
r = 2L * a
RS = 3y + 3, ST = 2y + 7, and RT=-10y-10
-1/2x3/5 divided by (-51/40)
plz help me simplify this
-4/17
Step-by-step explanation:
-1/2×3/5÷-51/40
= -1/2×3/5×40/51
=-4/17
Brianna has saved $600 to buy a new tv If the tv cos $1800 and she saves $20 a week
60 days or 8.5 weeks
Step-by-step explanation:
1800-600=1200
1200/20=60
60/7=8.5
Which of the following is equivalent to 6.32x10^-3?
A. 0.632
B. 0.0632
C. 0.00632
D. 0.000632
Answer:
c. 0.00632
Step-by-step explanation:
Since 10 is raised to a negative 3, this means that the zeros come before the non-zero digits
a) When I add 8 the answer is 30.
Answer:
if we add 8 then the answer will be 30"
because
if 22is added 8 then it became 30
22+8= 30
simple
5. Based on the graph of the trigonometric function,
what is the amplitudes
Answer:
[tex]\displaystyle 3[/tex]
Explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A|[/tex]
AND
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A|[/tex]
Accourding to the graph AND the above information, your amplitude is three units. This means each crest is extended three units beyond the midline of [tex]\displaystyle y = 0,[/tex] the centre of your graph, also known as the vertical shift. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
Now, just in case you wanted to know the equation(s) of this graph, look below:
[tex]\displaystyle y = 3sin\:(\frac{\pi}{2}x + \frac{\pi}{2}) \\ y = 3cos\:\frac{\pi}{2}x[/tex]
I am delighted to assist you at any time.
Samantha's car used 3 gallons to travel 51 miles. At what rate does the car use gas, in miles per gallon?
Answer:
17 miles per gallon
Step-by-step explanation:
Divide 51 by 3. Here's a better way to understand it:
Create a ratio to represent miles to gallons: 51-to-3
To find the ratio of miles per gallon, it's implying x miles for 1 gallon. To get this x value, you divide both sides by 3.
51/3 = 17miles/gallon
The owner of a pool cleaning business wants to know how much time, on average, his workers
spend cleaning a pool. Last week, 7 employees each worked a 6-hour shift. In all, they cleaned
42 pools. Which is the most appropriate unit in which to calculate an answer to his question?
A. pools per employee
B. pools per day
C. employees per pool
D. hours per pool
Answer:
C. employees per pool...
WILL.MARK BRAINLEST. ( The length of a rectangular garden is 5m longer than its breadth .If its perimeter is 150 m,find the area of the garden ) step by step
Answer:
1400m^2
Step-by-step explanation:
Let the breadth of the garden be a, therefore the length of the garden is (a+5).
The perimeter of the garden is the sum of all its sides, therefore:
Perimeter = a + a + (a+5) + (a+5) = 150
Simplifying the LHS of the equation:
4a +10 = 150
Subtracting 10 from both sides of the equation:
4a = 140
Dividing both sides by 4:
a = 35 = breadth
Therefore the length of the garden = (a + 5) = 40
Recall that the area of the garden is its length multiplied by its breadth, therefore:
Area = 35*40 = 1400
Answer:
area=1400
Step-by-step explanation:
length(l)=x+5
breadth(b)=x
Perimeter=2(l+b)
150 =2(x+5+x)
150 =2x+10+2x
150-10=4x
140=4x
x=35
therefore breadth=35
length=40
area=l*b
=35*40
=1400
YO I NEED HELP PLEASE!!
1. The sum of 6 times a number n and 4 times a number n is -30.
What is the number?
2. Four less than the product of 6 and a number n is -30.
What is the number? _____
3. Four less than the product of 6 and a number n is -30.
What is the number? _____
Answer:
1. n = -3
6n + 4n = -30
10n = -30
n = -3
Need help with 10 and 11
reflect point (-3,1) in the line y=5
Answer:
6 (4757)
Step-by-step explanation:
Simple interest on a certain sum is 16 by 25 of the sum. find the rate of interest and time is the both are numerically equal.
Answer:
hence rate of interest is 8% and time 8 years
Step-by-step explanation:
2a + 9 = 4 then a = _______
Answer:
[tex]a=\frac{-5}{2}[/tex]
Step-by-step explanation:
[tex]2a+9=4[/tex]
[tex]2a=4-9[/tex]
[tex]2a=-5[/tex]
[tex]a=\frac{-5}{2}[/tex]
I need help plzzzz and thx
Answer:
The answer is
x=³√6
semoga membantu
The perimeter of a rectangular deck measured 130 m. What are the possible
dimensions of the deck?
Answer:
The possible dimensions of the deck can be anything that adds up to be 130 m.
Step-by-step explanation:
The perimeter could be 1m x 64m.
Two sides would be 1m each (so 2m total) and the other two sides would be 64m each (128m total). 2 + 128 = 130m.
The perimeter could be 15m x 50m.
Two sides would be 15m each (so 30m total) and the other two sides would be 50m each (100m total). 30 + 100 = 130m.