Answer:
The seating capacity of the auditorium is 2,340.
Step-by-step explanation:
This question relates to an Arithmetic Progression (AP).
An Arithmetic Progression (AP) is a sequence of numbers in which the differences of every two consecutive numbers or terms are constant or the same.
Therefore, the seating capacity can be calculated using the an arithmetic progression (AP) formula as follows:
Seating capacity = (n / 2) * (2a_1 + (n - 1)d) ...................... (1)
Where;
n = number of rows = 30
a_1 = Number seats in the first row = 20
d = Common difference = 24 - 20 = 28 - 24 = 4
Substituting the values into equation (1), we have:
Seating capacity = (30 / 2) * ((2 * 20) + ((30 - 1) * 4))
Seating capacity = 15 * (40 + (29 * 4))
Seating capacity = 15 * (40 + 116)
Seating capacity = 15 * 156
Seating capacity = 2,340
Therefore, the seating capacity of the auditorium is 2,340.
Martin Lukarevski, a super-hard problem published by Cambridge:
Let m be an arbitrary integer and let k=3m+1. Find all integer solutions x and y of the equation
(x + y − k)(x + y + k)=1+xy.
Answer:
Yagub Muallim is watching, grave is loading .
Step-by-step explanation:
Which are are solutions for x^2 + 5x – 1 > 6
Answer:
it might be b and d
Step-by-step explanation:
What addition statement does this show?
A. 10 + 3 = 13
B. 10 + (–3) = 7
C. –10 + 3 = –7
D. –10 + (–3) = –13
please answer as soon as you can!<3
Answer:
I think the answer is A sorry if I am wrong
Step-by-step explanation:
Answer:
The answer is b
Step-by-step explanation:
10 + (-3) = 7
how long is a meter
you can not use google
1 km=1000 m
1 m=100 cm
please mark as brainliest
Lorena compró en una tienda una remera, un pantalón y una cartera. Se sabe que el pantalón cuesta $400 más que la remera, y la cartera cuesta 5 veces el valor de la remera. Si por los tres objetos pagó, en total, $2850, ¿cuál es precio de cada uno?
Responder:
Costo de la camisa = $ 350
Pantalón = $ 750
Billetera = $ 1750
Explicación paso a paso:
Artículos comprados :
Camiseta (t); pantalones (p); y billetera (w)
El pantalón cuesta 400 más que la camisa
La billetera cuesta 5 veces el valor de la camisa
Importe total pagado = 2850
Sea el costo de la camiseta = x
Costo del pantalón = x + 400
Costo de la billetera = 5x
La suma del costo debe dar el monto total pagado:
x + x + 400 + 5x = 2850
7x + 400 = 2850
7x = 2850 - 400
7x = 2450
x = 350
Por lo tanto,
Costo de la camisa = $ 350
Pantalón = x + 400 = 350 + 400 = $ 750
Billetera = 5x = 350 * 5 = $ 1750
A man walks around a circular park 4 times in 12 minutes. The radius of the park is 49m. Find the speed of the man in km/ h.
Write an informal proof to show triangles ABC and DEF are similar.
A.) 12
B.) 10
C.) 6
D.) 8
Answer:
a
Step-by-step explanation:
Rounding decimals. 0.01426; thousandths
Answer:
0.014
Step-by-step explanation:
how many solutions does -2 + x -3 = 2x + 5 -x have?
Answer:
No solutions
Step-by-step explanation:
Mr. Thompson plans to invest $7,500 in a savings account that earns 2.75% simple annual interest. If he makes no other deposits or withdrawals, how much money will Mr. Thompson's account be worth after 10 years.
Answer:
Mr. Thompson's account be worth $9,562.50 after 10 years
Step-by-step explanation:
Simple Interest
Interest is calculated on the original principal only of a loan or on the balance of an account.
Unlike compound interest where the interest earned in the compounding periods is added to the new principal, simple interest only considers the principal to calculate the interest.
The interest earned is calculated as follows:
I=P.r.t
Where:
I = Interest
P = initial principal balance
r = interest rate
t = time
Mr. Thompson plans to invest P=7,500 in a savings account that earns r=2.75% = 0.0275.
The interest earned in t=10 years is calculated now:
I=7,500*0.0275*10
I=2,062.50
Now we add the interest to the principal:
A = $7,500 + $2,062.50
A = $9,562.50
Mr. Thompson's account be worth $9,562.50 after 10 years
Complete the steps to find the value of x.
2xº
1282
What does ø mean ? Can someone explain it based off the problem in the photo ?
Answer:
It means something mathematical
Step-by-step explanation:
The slashed zero glyph is often used to distinguish the digit "zero" ("0") from the Latin script letter "O" anywhere that the distinction needs emphasis, particularly in encoding systems, scientific and engineering applications, computer programming (such as software development), and telecommunications.
A rental car cost 36 for one day plus additional 0.42 per mile. Simplify the expression 36 + 0.42( 78) to determine the cost of renting a car and driving it 78 miles
A. 68.76
B.70.08
C. 93.12
D. 2,808.42
Answer:
The Answer is A
Step-by-step explanation: What you do is multiply 0.42 by 78 since that is what it costs per mile which is 32.76.
And then you add 36 and you get 68.76
PLEASE HELP I DONT WANT TO FAIL
Complete the equation of the line through (3,-8)(3,−8)left parenthesis, 3, comma, minus, 8, right parenthesis and (6,-4)(6,−4)left parenthesis, 6, comma, minus, 4, right parenthesis.
Answer:
[tex]y = \frac{4}{3}x - 12[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (3,-8)[/tex]
[tex](x_2,y_2) = (6,-4)[/tex]
Required
Determine the equation
First, we need to determine the slope (m):
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-4 - (-8)}{6 -3}[/tex]
[tex]m = \frac{-4 +8}{3}[/tex]
[tex]m = \frac{4}{3}[/tex]
Next, we determine the line equation using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = \frac{4}{3}[/tex]
[tex](x_1,y_1) = (3,-8)[/tex]
[tex]y - (-8) = \frac{4}{3}(x - 3)[/tex]
[tex]y +8 = \frac{4}{3}(x - 3)[/tex]
[tex]y +8 = \frac{4}{3}x - 4[/tex]
[tex]y = \frac{4}{3}x - 4 - 8[/tex]
[tex]y = \frac{4}{3}x - 12[/tex]
The equation of the line that passes through (3, -8)(6, -4) is y = - 1 / 2 x - 1
The slope intercept equation is as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
The line passes through (3, -8)(6, -4)
m = -4 - 3 / 6 + 8 = -7 / 14 = - 1 / 2
y = - 1 /2 x + b
let's find b using (6, -4)
-4 = - 1 /2 (6) + b
-4 + 3 = b
b = -1
Therefore,
y = - 1 / 2 x - 1
learn more:
Fredrick manages a band and sing leads vocal the band charges $700 per concert Frederick receives 175 of that money and he shares the rest equally among the other five members of the band how much money does each of the five band members receive per concert
Answer:
Each will receive $105Step-by-step explanation:
Step one:
given data
we are told that the total amount made is $700
If Frederick receives $175 from the amount made the balance left to share is
=700-175
=$525
Step two:
Hence the five band members will share $525
each of them will receive
=525/5
=$105
Formula One race cars can reach speeds of approximately 100 meters per second. What is this speed in meters per minute?
0.6 meters per minute
1.67 meters per minute
600 meters per minute
6,000 meters per minute
Answer:
6,000 meters per minute
Step-by-step explanation:
Answer:
D. 6,000 meters per minute
Step-by-step explanation:
It's right on edg 2020
hope it helps (;
Have a good day and good luck !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which situation could be represented by the equation 38.25 = 3x?
A group of 3 friends each had $38.25. What is x, the total amount of money the friends had all together?
A group of friends had $38.25. They decided to triple their money by working for a neighbor. What is x, the total amount of money the friends had all together after working for a neighbor?
A group of 3 friends had $38.25 all together. Each friend had the same amount of money. What is x, the amount of money each friend had?
A group of friends had $38.25. They earned $3 more. What is x, the amount of money the friends have all together?
Answer:
A
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
(-20, -3) U (0,00)
what is the inequality notation?
Answer:
-20 < x < -3
Step-by-step explanation:
*math*
what is the answer
9x plus 2 (2x+3)
Step-by-step explanation:
=9x+2(2x+3)
=9x+4x+6
=13x+6 I hope so,
please help me this question
Step-by-step explanation:
Please mark me as the brainliest answer
Answer:
x^3 - 7x^2 + 72
Step-by-step explanation:
you just subtract both equations
Carter can bake 11 cookies with each scoop of flour. With 4 scoops of flour, how many cookies can Carter bake?
Answer:
44 cookies
Step-by-step explanation:
1 scoop = 11 cookies
11 cookies * 4 scoops = 44 cookies
The equation F= 9/5 C+32 relates temperature measured in degrees Celsius, C , to degrees Fahrenheit, F. Determine whether there is a proportional relationship between C and F.
Answer:
The relationship between F and C is proportional
Step-by-step explanation:
The relationship between Celsius and Fahrenheit temperatures is a direct proportionality. Both scales have their ice and steam points as well as their fundamental intervals.
When the temperature in Celsius increases, the temperature in Fahrenheit increases and vice versa.
Can Somebody Help With Geometry?
Answer:
SAS
Step-by-step explanation:
II side (given)
Angles between the congruent sides (vertically opposite angle)
III side (given)
Hence by, SAS the Triangles are congruent.
3.
Lakpa buys 20 items for Rs 6000. He sells them at Rs 390 each. Calculate:
(a)
His total profit on the deal.
(b)
His percentage of profit on the deal
y+4= 2/3 (x+3) written in standard form
I will give brainliest
4 = u/10
what is the value of u?
WILL MARK brainiest answer
Answer:
i Think it would be B
Step-by-step explanation:
Choose the correct answer below for the following problem:
(‒489) + (‒764) =
A.
‒1,253
B.
275
C.
1,253
D.
‒275
Step-by-step explanation Answer:
A -1253
-489-764 = -1253
what is the equation of a line that passes through (4,6) and is parallel to y=2x+2 ?
Answer:
y=2x-2
Step-by-step explanation:
my work is in the picture I attached. lmk if you'd like me to explain more
Answer:
y = 2x - 2
Step-by-step explanation:
let equation of the line be y = mx + c
since it is parallel to y = 2x + 2, gradient/slope of the two lines would be the same
therefore, m = 2
since it passes through (4, 6),
sub (4, 6):
6 = 2(4) + c
c = -2
therefore equation of the line is y = 2x - 2