Answers
Answer:
1806 seats.
Step-by-step explanation:
From the question given above, the following data were obtained:
Row 1 = 24 seats
Row 2 = 27 seats
Row 3 = 30 seats
Total roll = 28
Total number of seat =?
From the above data, we can liken the roll to be in arithmetic progress.
Also, we are asked to determine the total number of seats in the theater.
Thus the sum of the sequence can be written as:
Roll 1 + Roll 2 + Roll 3 +... + Roll 28 i.e
24 + 27 + 30 +...
Thus, we can obtain obtained the total number of seats in the theater by applying the sum of arithmetic progress formula. This can be obtained as follow:
First term (a) = 24
Common difference (d) = 2nd term – 1st term
Common difference (d) = 27 – 24 = 3
Number of term (n) = 28
Sum of the 28th term (S₂₈) =?
Sₙ = n/2 [2a + (n –1)d]
S₂₈ = 28/2 [2×24 + (28 –1)3]
S₂₈ = 14 [48 + 27×3]
S₂₈ = 14 [48 + 81]
S₂₈ = 14 [129]
S₂₈ = 1806
Thus, the number of seats in the theater is 1806.
Related Questions
the graph of a quadratic function is shown on the grid. which function is the best represented by this graph?
Answers
Answer:
Step-by-step explanation:
It is H
Function for the graph of the parabola given in the picture attached will be Option (H). f(x) = x² - 6x
Equation of a parabola in vertex form: Equation of a parabola in vertex form is given by,
y = a(x - h)² + k
Here, (h, k) is the vertex of the parabola
Given in the graph,
Vertex of the parabola → (3, -9) Parabola passes through the origin (0, 0).Equation of the graph with vertex (3, -9) will be,
y = a(x - 3)² - 9
Since, the parabola passes through (0, 0),
0 = a(0 - 3)² - 9
0 = 9a - 9
a = 1
Substitute the value of 'a' in the equation of the parabola,
y = 1.(x - 3)² - 9
y = x² - 6x + 9 - 9
y = x² - 6x
Hence, the function representing the graph will be f(x) = x² - 6x
Learn more to get the equation of a parabola here,
https://brainly.com/question/22649174?referrer=searchResults
PLEASE HELP FAST ASAP WILL GIVE BRAINLIEST
Find the value of AD.
Answers
Complete the table.
y = f(g(x))
u = g(x)
y = f(u)
y = 8 tan(itx5) u =
I
y = 8 tan u
Answers
9514 1404 393
Answer:
u = x +14 u = πx^5Step-by-step explanation:
I find it easiest to match the patterns. You could also work this by finding inverse functions.
1.
[tex]y=u^{-1/2}\\\\y=\dfrac{1}{\sqrt{u}}=\dfrac{1}{\sqrt{x+14}}\\\\u=x+14 \qquad\text{match radical contents}[/tex]
__
2.
[tex]y=8\tan{u}=8\tan{(\pi x^5)}\\\\u=\pi x^5 \qquad\text{match tangent arguments}[/tex]
What is the value of -4^2+(5-2)(-6)?
O-34
O-2
O 10
O 34
Answers
The value of -4² + (5-2) (-8) is -34.
What is Integer?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
We have expression as -4² + (5-2) (-8)
Now, solving the terms in the expression
-4² = -(4 x 4)= -16
and, (5-2) (-6)
= 3 (-6)
= -18
So, the value of -4² + (5-2) (-6)
= -16 - 18
= -34
Learn more about Integer here:
https://brainly.com/question/15276410
#SPJ1
Can some one help meeee
Answers
Answer:
With what? there is nothing here
Step-by-step explanation:
NEED BY TODAY PLEASE GET RIGHT
Answers
30 + (-15) + (-10) + [-5] = 0
A manager purchased a total of 25 short sleeved and long sleeved shirts. Each short sleeved shirt costs $15 and each long sleeved shirt
costs $20. If the manager spent a total of $425, how many short sleeved shirts did the manager buy?
Answers
Steps:
Use system of equations where x is short sleeved and y is long sleeved.
x+y=25
15x+20y=425
Make the coefficient of x the same in both equations.
Solve by elimination
15x+15y=375
-15x+20y=425
=-5y=-50
Divide both sides by -5 to isolate x
= y=10
This is the number of long sleeved shirts the manager bought.
Substitute y into the second equation to find the number of short sleeved shorts the manager bought.
15x+20(10)=425
= 15x+200=425
= 15x=225
= x=15
So the final answer is that the manager bought a total of 15 short sleeved shirts and 10 long sleeved shirts.
Help me out here please I need some help here
Answers
3/10 * 4/1 = 12/10
Simplify:
12/10 -> 6/5 -> 1 1/5
Thus D, 1 1/5 loaves remain at the end of the picnic.
The value of a video game decreased by 30%. If the original cost was $45.00, what is the current value of the
video game?
Answers
Answer:
$31.50
Step-by-step explanation:
If the value fell by 30%, then the game is worth 70% of its' original value. So:
45 x 70%=45 x .7=31.5......................
The given expression represents the area. Find the side length of the square.
Answers
9514 1404 393
Answer:
(4x +5)
Step-by-step explanation:
The square of a binomial is ...
(a +b)² = a² +2ab +b²
We assume that the given trinomial is a perfect square, so we can find the terms of the squared binomial by looking at the square roots of the first and last terms:
√(16x²) = 4x
√25 = 5
So, our first choice of side length for the square is ...
s = (4x +5) . . . . . side length of the square
__
Using the above identity, we can verify that the square of this gives the right area:
A = s² = (4x +5)² = (4x)² +2(4x)(5) +5²
A = 16x² +40x +25 . . . . . . as required
What is the quotient of 2 ÷2/3 plz help
Answers
Answer:
3
Step-by-step explanation:
2/(2/3)=(2/1)/(2/3)=(2/1)(3/2)=6/2=3
Answer:
3, I think (hope this helps)
Step-by-step explanation:
х
У
о
12
1
8
N
4
3
о
4
4
Answers
Answer:
13
Step-by-step explanation:
Sorry im in 5th grade.
Am I correct? I would like to know, thanks!
Answers
Answer:
a) <CA
b) im not sure about this one
Step-by-step explanation:
Help ASAP Please
t=[tex]\frac{(y+v)r}{7}[/tex]
solve for R
Answers
Answer: (7t)/(y+v)
All work is in the picture below:
3x-2/4 -2x-5/3 = 1+x/6 i wil mark brainliest plz solve this equation with explanation
Answers
Answer:
x is equal to 19/5 which can also be expressed as [tex]3\frac{4}{5}[/tex], or 3.8
Step-by-step explanation:
[tex]3x - 2/4 - 2x - 5/3 = 1 + x/6\\\\x - x / 6 = 1 + 2/4 + 5/3\\\\5x/6 = 6/6 + 3/6 + 10/6\\\\\frac{5}{6}x = 19/6\\\\x = \frac{19}{6} * \frac{6}{5}\\\\x = \frac{19}{5}[/tex]
Answer:
x = 12
Step-by-step explanation:
Solve:
[tex]\displaystyle \frac{3x-2}{4}-\frac{2x-5}{3}=\frac{1+x}{6}[/tex]
To eliminate denominators, we multiply all terms by the LCM of 4,3, and 6 = 12.
Multiply by 12:
[tex]3(3x-2)-4(2x-5)=2(1+x)[/tex]
Operating:
[tex]9x-6-8x+20=2x+2[/tex]
[tex]9x-8x-2x=6-20+2[/tex]
Simplifying:
-x=-12
x = 12
2.85 tons when rounded to the nearest hundreds
Answers
Answer:
2.861
Step-by-step explanation:
I need help!!! Please figure it out and type it out.
Answers
Answer:
the mean number is 2.7
Step-by-step explanation:
if you add up the frequency of books then divide by 20 you get 2.7
Ghidu it g get stuck didjdgef
Answers
Answer:
It would be a
Step-by-step explanation:
the difference is 4/8 but simplified it is 1/2
Choose the inequality that represents the following graph.
Answers
Hope this helps!
Answer:
0>0
Step-by-step explanation:
Michael has credit card debt of $75,000 that has an 12% APR, compounded monthly. The minimum payment only the requires him to pay the interest on his debt. He receives an offer for a credit with an APR of 4% compounded monthly. If he rolls over his debt onto his card and makes the same monthly payment as before, how long will it take him to pay off his credit card debt?
Answers
Answer: 122 months.
Step-by-step explanation: The first step is to calculate the minimum monthly payment using the debt balance of $75,000 and 12% APR compounded monthly,which = $75,000 × 12% / 12 = $750 . The second step is to use the same $750 as payment, and using a discount rate of 4%/12, calculate the number of months required to pay off the present value (PV) of $75,000 , which = 122 months.
one - step adding/ subtraction equation / multiplication/ division problems
The height of the water in an above ground pool is 36 inches. The pool needs to be drained. As the water drains, the height of the water changes at a rate of -1/2 inch per minute. Write and solve and equation to find out how many minutes it will take to drain the pool.
Answers
Answer:
It would take x = 72 minutes to drain the pool.
Step-by-step explanation:
We know that the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
where m is the rate of change or slope and b is the y-intercept
Let 'y' be the height of the water poolLet 'x' be the time in the minute of the water poolAs the height of the water of the pool is 36 inches, meaning the basic condition of the pool states that the ground pool is 36 inches.
Thus,
y-intercept = b = 36As the water drains, the height of the water changes at a rate of -1/2 inch per minute.
Thus, the rate of change or slope = m = -1/2Thus, using the equation
[tex]y = mx+b[/tex]
substituting m = -1/2 and b = 36
[tex]y\:=\:-\frac{1}{2}x+36[/tex]
We know that when the pool drains, the height of water reduces to zero.
Thus, substituting y = 0 in the equation
[tex]0=-\frac{1}{2}x+36[/tex]
switching sides
[tex]-\frac{1}{2}x+36=0[/tex]
subtract 36 from both sides
[tex]-\frac{1}{2}x+36-36=0-36[/tex]
[tex]-\frac{1}{2}x=-36[/tex]
Multiplying both sides by -2
[tex]\left(-\frac{1}{2}x\right)\left(-2\right)=\left(-36\right)\left(-2\right)[/tex]
[tex]x=72[/tex]
Therefore, it would take x = 72 minutes to drain the pool.
Felicia paid $125 to join a tennis club. She pays an additional $5 every time she uses on of the tennis club occurs.
State what x and y represent in context
What is the y-intercept for the question and explain what it represents in context
Answers
You can model the situation you described as
[tex]y=125+5x[/tex]
Where [tex]y[/tex] represents the money spent, and [tex]x[/tex] the number of uses.
The [tex]y[/tex] intercept is 125, which represents the money spent without using the club even once. In fact, to find it you set [tex]x=0[/tex], i.e. zero usage.
The area of a rectangular field is 200 m²and its perimeter is 60 m. Find the lengthand width of the field.
Answers
Answer:
length: 20m
width: 10m
(or vice versa)
Step-by-step explanation:
By substituting each of the values (20 meters for length and 10 meters for width), you will receive answers that satisfy each of the given traits of the rectangle:
200=20x10
200=200
60=2(20)+2(10)
60=40+20
60=60
Here are three symbols.
<
>
=
Write one of these symbols in each box to make four true state
Answers
Step-by-step explanation:
4 + 9 = 3 ^ {2}
13=3^{2}
13=9
Answer:
a. <
b. =
c. =
d. >
these are correct I guess
5/6 × 1/5= 1/6. How the answer came 1/6? Explanation needed.
Answers
Answer:
see below
Step-by-step explanation:
5/6 × 1/5= 1/6
Rewrite the fractions
5/5 * 1/6 = 1/6
1 * 1/6 = 1/6
1/6 = 1/6
Answer:
below
Step-by-step explanation:
[tex] \frac{5}{6} \times \frac{1}{5} [/tex]
divided 5 by 5
[tex] 5 \div 5 = 1 [/tex]
multiply 1 by 1/6
[tex] 1 \times \frac{1}{6} [/tex]
hence,
[tex] = \frac{1}{6} [/tex]
48 girls and 64 boys belong to the Twelve Mile Coulee School choir. The choir teacher plans to arrange the students into equal rows (the same number of students in each row). Only girls or boys will be in each row. What is the greatest number of students that could be in each row?
Answers
Answer:
16 students
Step-by-step explanation:
48+64=112
the highest number that can go into 112 equally is 16 so htere would be 7 rows and 16 students in each row
3 1 R7 12 8 27 - 2 4 1 2 O 00 7 4 0 7
Answers
correct sirrrrr
Graph the line that passes through the two lines (1,5/2), (-1/2,-1/4)
Answers
Answer:
Image below
Step-by-step explanation:
Graph of a Line Given Two Points
We are given the points (1,5/2), (-1/2,-1/4).
A straight line is entirely defined by two points. We have to plot them and join them with a straight line ending in arrows.
The point (1,5/2) is converted to decimal as (1,2.5)
The point (-1/2,-1/4) is also converted to decimal: (-0.5,-0.25)
This helps to define the divisions of each axis and properly draw the line.
Please refer to the image below.
how do you graph x ≥ 6 and
x ≥ -0.6
on a line graph
Answers
Step-by-step explanation:
A line graph, or a number line, has the numbers on different points along the graph. It's a little hard to explain since I can't draw one, but for x>=6, jut plot 6 on the number line as normal. Then since it could be equal to six, put a closed circle (if it wasn't equal to then it would be an open circle).
Now since x is greater than, draw an arrow to the right (since the numbers increase the farther right you go). The follow the same idea for the other one.
Answer:
Look at the Picture.
Step-by-step explanation:
*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^
Since the greater than sign is used, the circle will be filled in.
Since x is greater than the number, the line arrow will go in the direction of the number that is greater than it.
*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^
#teamtrees #WAP (Water And Plant)
Which of these angles are the alternate interior angles theorem?
ECA = BAD
CAE=BAD
ECA=BDA
ECA=DBA
Answers
Answer:
C. ECA = BDA
Step-by-step explanation:
An angle is said to be produced whenever two or more lines meet at a point. An interior angle is an angle form within two lines meeting at a point. Then, alternate interior angles are internal angles that are equal due to alternate theorem. These angles should have equal measures.
From the given question, the alternate interior angles by the theorem is;
ECA = BDA
By the alternate interior angle theorem, the alternate interior angles are ECA and BDA. This implies that the measure of <ECA should be equal to the measure of <BDA.