Answer:
There are 1645 seats in the theatre.
Step-by-step explanation:
The first row has 13 seats and each row has 2 seats more than the previous one which means
13,15,17...
As the terms are increasing with the same difference, d=2 this forms an arithmetic sequence.
where
[tex]d = 2\\a_1 = 13\\a_2 = 15\\a_3 = 17[/tex]
The rule for an arithmetic sequence is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
Putting the value of a1 and d
[tex]a_n = 13+(n-1)(2)\\a_n = 13+2n-2\\a_n = 11+2n[/tex]
We have to find total seats in the theatre for that the 35th term of sequence is required as their are 35 rows.
So,
Putting n=35
[tex]a_{35} = 11+2(35)\\= 11+70\\=81[/tex]
Now we need to find the sum of the 35 terms
The formula for sum of arithmetic sequence is:
[tex]S_n = \frac{n}{2}(a_1+a_n)\\putting\ n=35\\S_{35} = \frac{35}{2}(a_1+a_{35})\\S_{35} = 17.5(13+81)\\S_{35} = 17.5(94)\\S_{35} = 1645[/tex]
Hence,
There are 1645 seats in the theatre.
Which expressions are equivalent to cos^2(105degrees) – sin^2(105°)? Check all that apply.
Edge 2020
Answer: it’s A B and E on edge <3 just did it
Step-by-step explanation:
Answer:
A
B
E
Step-by-step explanation:
A recipe calls for 3 cups of sugar for
every 1 cup of butter. How many cups
of butter does the recipe need for 4.5
cups of sugar?
Answer:
1.5 cups of butter
Step-by-step explanation:
3 : 1 <- this is our ratio
divide by 2
1.5 : 0.5 is our new ratio
equation: 1.5 * ? = 4
? = 3 cups of sugar
multiply the ratio by 3
1.5 : 0.5 = 4 : 1.5
we need 1.5 cups of butter for 4.5 cups of sugar
y = -6x
y = -8x + 6
?????
Answer:
x=3
Step-by-step explanation:
-6x=-8x+6
+8 +8
2x=6
2/2 6/2
x=3
in a survey of 3,000 people who owned a certain type of car, 1,800 said they would buy that type of car again. what percentage of the people surveyed were satisfied with the car
Answer:
Step-by-step explanation:
Iijuty
In two or more complete sentences write and solve an equation for the situation and explain how you will solve the equation. After an 8-week exercise program Grace lost 45 pounds. She now weighs 122 pounds. How much did Grace weigh before she started her exercise program?
Answer:
Grace weighed 167 pounds before she started her exercise program.
Step-by-step explanation:
Given,
Weight lost by Grace = 45 pounds
Weight of Grace after exercise weeks = 122 pounds
Let,
x represents the weight of Grace before she started the exercise program.
Loss means subtraction, therefore,
We will subtract the lost weight from original weight.
Original weight - Weight lost = Weight after exercise weeks
[tex]x - 45 = 122[/tex]
Adding 45 on both sides
[tex]x - 45+ 45= 122+45[/tex]
[tex]x=167 pounds[/tex]
Grace weighed 167 pounds before she started her exercise program.
Add or subtract Write in simplest form.
-11/15 - 1/15
Answer:
- 4/5
Step-by-step explanation:
Step 1:
- 11/15 - 1/15 Equation
Step 2:
- 12/15 Add the negative numbers
Step 3:
- 4/5 Convert
Answer:
- 4/5
Subtracting from a negative number is the same thing as adding them together.
Hope This Helps :)
If i start at the point (-3,2) and move 7 spaces to the right, what are the coordinates of the new plane? What Quadrant am I in?
Answer:
Your coordinates would be (4,2) and you would be in Quadrant 4
Step-by-step explanation:
-3+7 is 4 since going to the right goes towards the positive numbers while left is negative
Step-by-step explanation:
new Coordinates =(4,2)
You are in first quadrant
Is 42.7 less than or greater than 36.3
Answer:
Depends if it is negative or positive.
Step-by-step explanation:
If they are both positive then 42.7 would be greater than 36.3
Answer:
Its greater than. thats so ez XDDDDD
Step-by-step explanation:
42.7 is larger than 36.3
(4)2 -4(-5) (-1) Help Please For This
Answer:
-12
Step-by-step explanation:
first 4 times 2 is 8
so- 8-4(-5)(-1)
next negative four times negative 5 positive 20
so- 8+20(-1)
20 times negative 1 is -20 plus 8 is -12.
Write a ratio for 4 batches of this recipe
Answer:
wut recipe.........?
What percent of 200 is 16?,,,,
Answer:
8%
Step-by-step explanation:
To find the percent, divide 16 by 200, then multiply it by 100.
(16 / 200) x 100
0.08 x 100
= 8
So, 16 is 8% of 200
Helpppppppppppppppppp please
The rules of operations states that we deal with parentheses first. So, inside the parentheses, we have, 2 times 3. Multiply that. That gives us 6. So now, the equation looks like this:
(6)^2 + 5^2
Now we have to work with the exponents. So, square both numbers.
(6)^2 = 36
5^2 = 25
Now we have:
36 + 25
Now we add. 36 + 25 = 61
61 is your answer.
What is the factorization of the polynomial below?
9x2 - 16
use (a-b) (a+b )
(3x+4) (3x- 4)
[tex]\bigcirc [/tex](9x+4)(x-4)
[tex]\bigcirc [/tex](9x-4)(x-4)
[tex]\odot [/tex](3x+4)(3x-4)
[tex]\bigcirc [/tex](3x-4)(3x-4)
_____________________Calculations:-Let's Factorise:-[tex]{:}\leadsto [/tex] [tex]\sf 9x^2-16 [/tex]
Let's use algebraic identity for factorisation[tex]{\boxed{\sf (a+b)(a-b)=(a)^2-(b)^2}}[/tex]
Here see 16 is the square of 4 and 9x^2 is the square of 3x[tex]{:}\leadsto [/tex] [tex]\sf 3x^2-4^2 [/tex]
Now According to identity[tex]{:}\leadsto [/tex] [tex]\sf (3x+4)(3x-4)[/tex]
Hence the correct option is option C.1.name two acute angles in the figure
Answer:
There isn't a figure. But Acute angles are less than 90 degrees(they're small than an L). Remember it by saying "cute" things are small so acute
Step-by-step explanation:
I need the answer to this..please!!! Need the answer with the radius of 4 feet and the scale factor of 2.5. I need it in feet please- thank you.
Answer:
10 feet
Step-by-step explanation:
with the radius being 4 feet and the scaled factor being 2.5 times that. the new radius would be 10 feet.
Fiona wants to estimate the product (8.7)(3.0). Which expression shows each factor rounded to the nearest whole number?
(9)(4)
(9)(3)
(8)(3)
(8)(4)
Answer:
(9)(3)
Step-by-step explanation:
Round 8.7 to 9
And keep 3.0 as 3.
Answer:
B
Step-by-step explanation:
What’s the answer?!!?!?
Answer:
a) 25 in.
b) 13 in.
c) 4 in.
d) 61 in.
e) 30 weeks
Step-by-step explanation:
For a, b, c, and d, the equation to use is y = 3x + 4 and just plug in the given values for x (weeks) to receive y (inches of vine)
for e, use the same equation, but plug in 94 for y...
94 = 3x + 4 → 3x = 90 → x = 30
^^^^^^^^Help me please!!^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Answer:
3
Step-by-step explanation:
What is the difference of 8 in the number listed below?
48,567,879
(explanation to)
Answer:
because one of the eight is in million while the other in hundred
A school ordered 234 new pencils for the state tests. If they gave each student 6 pencils, how many students are in the school?
make it in partial quotients form
like for example here :
456 divide 2 =
2 x 200 = 400
456-400= 56
2 x 20 = 40
56 - 40 = 16
2 x 8 = 16
16 - 16 = 0
So , 456 divide 2 = 228 r. 0
There are 228 coins in each level
someone plz answer
Answer:
there will be 39 students in the school but not sure how to put it in partial quotients
A car has wheels with a 13 inch radius. If each wheel's rate of turn is 6 revolutions per second, find the angular speed in units of radians/second.
Answer:
Step-by-step explanation:
The expression for calculating the angular speed is expressed as
w = v/r
v is the linear speed
r is the radius
Given
v = 6rev/s
r = 13in
since 1rev = 2πrad
6rev = 12πrad
v = 12πrad/s
Substitute;
w = 12π/13
w = 12π/13 rad/seconds
Angular speed tails that how fast a object resolves. The angular acceleration is [tex]\dfrac{12\pi}{13}[/tex] radians/second.
To find the angular speed of the wheel, we need to know about the angular speed.
What is angular speed?Angular speed is the rate of change of angle with respect to time of an object. Angular speed tails that how fast a object resolves.
It can be given as,
[tex]\omega =\dfrac{v}{r}[/tex]
Here, [tex]v[/tex] is the linear velocity and [tex]r[/tex] is the radius.
Given information-
The radius of the wheels of the car is 13 inch.
The revolutions per second of the each wheel is 6 rpm.
As the wheel rotates at 6 revolutions per seconds. Thus its linear velocity is 6 rev/sec. The one rev/sec equals to the [tex]2\pi[/tex] rad.
Thus the linear velocity is,
[tex]v=6\times2\pi \\v=12\pi[/tex]
Put the values in the above formula,
[tex]\omega =\dfrac{12\pi}{13}[/tex]
Hence the angular acceleration is [tex]\dfrac{12\pi}{13}[/tex] radians/second.
Learn more about the angular speed here;
https://brainly.com/question/9684874
A man is 13 times as old as his son is. In 10 years he will be 3 times as old as his son is now. How old are they now?
Answer:
the son is 2
man is 26
+10 yrs
son=12
man=36
Step-by-step explanation:
Let the son's age be x.
Then the father's age is 13x.
In ten years their ages will be (x+10) and (13x+10).
(13x+10)=3(x+10)
13x+10=3x+30
10x=20
x=2
The son is 2 years old.
What is the area of the figure?
A. 40.0 yd2
B. 20.0 yd2
C. 21.1 yd
D. 22.0 yd
Answer:
B. 20 yd²Step-by-step explanation:
area of a triangle = 1/2 x base x height
= 1/2 x 5 x 8
= 20 yd²
The area of the figure is 20 yd²
What is an area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a figure of triangle with height = 8 yd and base = 5 yd
We know that,
The area of a triangle = 1/2 x base x height
= 1/2 x 5 x 8
= 20 yd²
Hence, The area of the figure is 20 yd²
For more references on the areas, click;
https://brainly.com/question/27683633
#SPJ2
Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below.
Find the coefficient of variation for each of the two sets of data, then compare the variation.
Bank A (single line): 6.6, 6.7, 6.7, 6.8, 7.0, 7.3, 7.5, 7.7, 7.8, 7.8Bank B (individual lines): 4.0, 5.5, 5.8, 6.2, 6.6, 7.6, 7.7, 8.5, 9.4, 9.7(Round to one decimal place as needed.)
Answer:
CV of Bank A = 6.4
CV of Bank B = 7.1
CV of Bank B is more than CV of Bank A
Step-by-step explanation:
Bank A
6.6, 6.7, 6.7, 6.8, 7.0, 7.3, 7.5, 7.7, 7.8, 7.8
[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{6.6+6.7+6.7+6.8+7.0+7.3+7.5+7.7+7.8+ 7.8}{10}\\Mean =7.19[/tex]
Standard deviation =[tex]\sqrt{ \frac{\sum(x-\bar{x})^2}{n}}=0.461[/tex]
[tex]CV = \frac{\sigma}{\bar{x}} \times 100\\CV = \frac{0.461}{7.19} \times 100=6.4[/tex]
Bank B
4.0, 5.5, 5.8, 6.2, 6.6, 7.6, 7.7, 8.5, 9.4, 9.7
[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{4.0+5.5+5.8+6.2+6.6+ 7.6+ 7.7+8.5+9.4+9.7}{10}\\Mean =7.1[/tex]
Standard deviation =[tex]\sqrt{ \frac{\sum(x-\bar{x})^2}{n}}=1.718[/tex]
[tex]CV = \frac{\sigma}{\bar{x}} \times 100\\CV = \frac{1.718}{7.1} \times 100=24.2[/tex]
CV of Bank A = 6.4
CV of Bank B = 7.1
CV of Bank B is more than CV of Bank A
what is the slope of (-7,-13) and (1, -5)
I think the slope is 1. hope that helps
Whats faster?
10 inches per minute or 1 cm per second?
Answer:
10 inches per minutes
Step-by-step explanation:
Inches are longer than Centimeters
Hope this helped, Have a Great Day!!
Answer:
1cm
Explanation:
Common factors and multiples mastery test
Answer:
Factors and multiples are different things.
But they both involve multiplication:
Factors are what we can multiply to get the number
Multiples are what we get after multiplying the number by an integer (not a fraction).
Example: the positive factors, and some multiples, of 6:
factors of 6: ..., 1, 2, 3, 6; multiples of 6: ... 0, 6, 12, 18, ...
Factors:
1 × 6 = 6, so 1 and 6 are factors of 6
2 × 3 = 6, so 2 and 3 are factors of 6
Multiples:
0 × 6 = 0, so 0 is a multiple of 6
1 × 6 = 6, so 6 is a multiple of 6
2 × 6 = 12, so 12 is a multiple of 6
and so on
(Note: there are negative factors and multiples as well)
Here are the details:
Factors
"Factors" are the numbers we can multiply together to get another number:
in 2x3=6, 2 and 3 are factors
2 and 3 are factors of 6
A number can have many factors.
Example: 12
3 × 4 = 12, so 3 and 4 are factors of 12
Also 2 × 6 = 12, so 2 and 6 are also factors of 12,
And 1 × 12 = 12, so 1 and 12 are factors of 12 as well.
AND because multiplying negatives makes a positive, −1, −2, −3, −4, −6 and −12 are also factors of 12:
(−1) × (−12) = 12
(−2) × (−6) = 12
(−3) × (−4) = 12
So ALL the factors of 12 are:
1, 2, 3, 4, 6 and 12
AND −1, −2, −3, −4, −6 and −12
Learn about Greatest Common Factor and how to find All Factors of a Number.
Multiples
A multiple is the result of multiplying a number by an integer (not a fraction).
Example: Multiples of 3:
Multiples of 3: ..., −9, −6, −3, 0, 3, 6, 9, ...
..., −9, −6, −3, 0, 3, 6, 9, ...
Example: 15 is a multiple of 3, as 3 × 5 = 15
Example: 16 is not a multiple of 3
Example: Multiples of 5:
Multiples of 5: ..., −15, −10, −5, 0, 5, 10, 15, ...
..., −15, −10, −5, 0, 5, 10, 15, ...
Example: 10 is a multiple of 5, as 5 × 2 = 10
Example: 11 is not a multiple of 5
Learn more about Least Common Multiple.
Multiples of Anything
We must multiply by an integer, but the number that is being multiplied can be anything.
Example: Multiples of π
..., −2π, −π, 0, π, 2π, 3π, 4π, ...
If the part is 63 and the percent is 90% what is the whole plz help
Answer:
70
Step-by-step explanation:
63/9 = 7
7 * 10 = 70
The function f(x) = 2.5x models the amount of water, in quarts, in a bucket after x seconds. Sally needs to fill a 55-quart bucket. Which is the most appropriate domain for the function?
Answer:
Domain: 0 ≤ x ≤ 22
Step-by-step explanation:
Given
f(x) = 2.5x
Required
Determine the domain of the function
From the question, we understand that the size of the bucket is 55 quarts
This means the maximum of the range is 55.
In other words, the maximum value of f(x) is 55
Substitute 55 for f(x) in f(x) = 2.5x
55 = 2.5x
2.5x = 55
Make x the subject
x = 55/2.5
x = 22
Also, we understand that x represents time and it's impossible to have a negative time.
So, the minimum value x can get is
x = 0
The domain can then be represented as:
Minimum ≤ x ≤ Maximum
This gives:
0 ≤ x ≤ 22
Answer:
Domain: 0 ≤ x ≤ 22
Step-by-step explanation:
Brendan and Marie are each assigned a paper for a class they share. Brendan decides to write 41 pages at a time while Marie decides to write 18 pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had?
Answer:
18+18=38, since they did the same number that's the least it could be