There are a total of 180 seats in the theater
How to determine the number of seats?The theatre illustrates an arithmetic sequence, with the following parameters:
Number of rows = 18
Let the number of seats per row be n.
So, we have:
Total = 18n
When there are 3 fewer rows, the total number of seats is:
Total = (18 - 3) * (n + 6)
This gives
Total = 15* (n + 6)
Substitute Total = 18n in Total = 15* (n + 6)
18n = 15* (n + 6)
Open the bracket
18n = 15n + 90
Subtract 15n from both sides
3n = 30
Divide both sides by 3
n = 10
Substitute n = 10 in Total = 18n
Total = 18 *10
This gives
Total = 180
Hence, there are 180 seats in the theater
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Find the fourth derivative of f(x) = 3x^-1 ƒ(4) (x) =
[tex]f(x) = 3x^{-1}\\\\f'(x) = 3(-1) x^{-1-1} = -3x^{-2}\\\\f''(x) = -3(-2)x^{-2-1} = 6x^{-3}\\\\f'''(x) = 6(-3)x^{-3-1}=-18x^{-4}\\\\f''''(x) = -18(-4)x^{-4-1} = 72x^{-5}[/tex]
[tex]\text{The fourth derivative of f(x) is}~ 72x^{-5}.[/tex]
14 boys and 16 girls in class
What is the ratio of girls to the total number of students in class? Write ratio in 3 ways
Answer:
1) 16 : 30
2) 8 : 15
3) [tex]\displaystyle \frac{8}{15}[/tex]
Step-by-step explanation:
Boys = 14
Girls = 16
Total students:
= 14 + 16
= 30
Ratio of Girls to total number of students in class:
= 16 : 30
÷2 ÷2
= 8 : 15
= [tex]\displaystyle \frac{8}{15}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Suzy drove to a hair appointment at 50mph. Her average speed on the return home was 40mph. The return home took 1/4hr longer because of heavy traffic. How far did she travel to her hair appointment?
Since Suzy return took 1/4 hr longer, how far Suzy travelled to her appointment is 50 mi
To answer the question, we need to know what distance travelled by Suzy is
Distance between Suzy's home and hair appointmentThe distance between Suzy and her appointment is d = vt where
v = Suzy's speed = 50 mph and t = time it takes to teach her appointment.So, d = 50t (1)
Now, since Suzy returns home at a speed of v' = 40 mph and takes her 1/4 hr longer to return home,her return time is , t' = (t + 1/4) h
Since the distance she ruturns home is the same, we also have that
d = v't'
= 40(t + 1/4) (2)
Equating (1) and (2), we have
50t = 40(t + 1/4)
50t = 40t + 10
50t - 40t = 10
10t = 10
t = 10/10
t = 1 hr
How far Suzy travelled to her appointmentSubstituting t = 1 into d = 50t, we have
d = 50(1)
d = 50 m
So, how far Suzy travelled to her appointment is 50 mi
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Find the area of each. Round your answer to the nearest tenth. 28) 2.6 cm
Answer:
Here is the answer...hope it helps
A password is 4 characters long and must consist of 3 letters and one number. if letters cannot be repeated and the password must end with a number, how many possibilities are there? a. 175,760 b. 158,184 c. 156,000 d. 140,400 please select the best answer from the choices provided a b c d
The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The possibility of selecting the password = 26 * 25 * 24 * 10 = 156000
The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000
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Use the axiomatic approach for vectors to prove the distributive law of vectors
Step-by-step explanation:
Find the HCF of 9m 80cm 8m 40cm 4m 20cm
The bottom of a circular swimming pool with a diameter of 40feet is made up of blue tiles . How many square feet is that
Answer:
radius = 40 / 2 = 20ft
Circle area = πr² = π × 20² = 1256.6 sq. ft
PLEASE EXPLAIN I NEED THIS
Find the Area and circumference of each circle below.
Answer:
2: area is ≈153.93804 and circumfrence is ≈43.9823
3: area is ≈706.85835 and circumfrene is ≈94.24778
Step-by-step explanation:
The formula for area is A = pi r^2
for 2 you would plug 7 in for r, then square it, then multiply it by pi.
for 3 you would divide the diameter, 30, by 2 to get r (15), then square it then multiply by pi.
The formula for cirumfrence is C = 2 pi r
for 2 you would multiply 7 by 2, then multiply that by pi
for 3 you dont need to do much since the diameter (30) is already 2r. Basically all you need to do for that one is multiply 30 by pi
Can you help me please
From the figure given above, angel < ABE = 40°
Calculation of unknown angleThe angle of a straight line = 180°
That is angle <ABC = 180°
If <EBC is = 140°
Therefore, <ABE = 180 - 140
= 40°
Therefore, from the figure given above, angel < ABE = 40°
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Solve for x. Enter your answer in interval
notation using grouping symbols.
x² + 2x ≥ 15
Answer:
[tex](x−3)(x+5) .....is.. the.. factorised.. form.. of.. the.. expression[/tex]
Step-by-step explanation:
[tex]x^2 + 2x > =15 \\x^2 + 2x - 15 > = 0 \\(x + 4)(x - 2) < 0 , \\{x + 4 < 0 and .x - 2 > 0} or {x + 4 > 0 ,\\and .x - 2 < 0} , \\{x < -4 and .x > 2} or {x > -4 and. x < 2},\\ Discard .x < -4 and. x > 2 because. it. has. no. solutions,\\ leaving .just x > -4 and .x < 2 , -4 < x < 2[/tex]
What is the value of x in the triangle?
Answer:
3 = x
Step-by-step explanation:
Well, the two unknown sides share the same size due to the same angle, so now, using the fact we only have the info about one side, we need to do a reverse pythagorean theorem.
[tex]c^{2} = a^{2} + b^{2}[/tex]
Our a and b are the same, so I will change them to "x" and combine them.
[tex]c^{2} = 2(x)^{2}[/tex]
Now we plug in our "c" and square it ("C" in this case is: [tex]3\sqrt{2}[/tex] )
[tex]18 = 2(x)^{2}[/tex]
[tex]9 = x^{2}[/tex]
3 = x
I really need help on this
Answer:
y=4
Step-by-step explanation:
steps
3×9+4y=43
4y=43-27
4y=16
Divide both side by 4
4y/4=16/4
y=4
1
James purchases a rare coin for $450. The coin appreciates at a rate of 1.2% each year. How much will the coin be worth after 25 years?
Select the reason why these triangles are
similar. If they are not, select "Not similar."
2.5
1
0.5
2.25
A. AA
B. SAS
C. SSS
D. Not similar
Answer:
D
Step-by-step explanation:
1/2 is not equal to 1/2.5 is not equal to 0.5/2.25.
Which of these ordered pairs is a solution to the linear inequality 3y – 2x ≥ 8?
(3, 1)
(1, 3)
(2, –4)
(–4, 2)
Answer:
(-4 , 2)
Step-by-step explanation:
Linear inequality:3y - 2x ≥ 8
The ordered point (-4 ,2) satisfies the inequality. So, (-4,2) is the solution for the equation.
3*2 - 2*(-4) ≥ 8
6 + 8 ≥ 8
14 ≥ 8
The amount of bacteria in a culture doubles every minute. The culture starts with
20 bacteria.
a. Write an equation modelling the number of bacteria, y, after x minutes.
Answer:
exponential function, x = time in minutes, y = number of bacteria
Step-by-step explanation:
y = 20 × (2)^x
If a = 11 cm, b = 29 cm, c = 15 cm, and d = 17 cm, what is the area of the poster?
Answer:
multiply them all together
How many students were surveyed?
Answer:
20
Step-by-step explanation:
count the dots
Answer:
20 students
Step-by-step explanation:
You just need to count the number of dots.
hope this helps
have a good day
Type the correct answer in each box.
A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ____? units. The point (-7, __?) lies on this circle.
Answer:
the answer is 5 and (-7,5)
Step-by-step explanation:
The radius is 5, and the points (-7, 5) and (-7, -1) both lie on the circle.
Given that:
The points at which the circle is centered are (-3,2)
Passing points = (1,5)
The radius is calculated using the distance formula:
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
Substituting the coordinates, we have:
d =[tex]\sqrt{({1 - (-3))^2 + (5 - 2)^2[/tex]
= [tex]\sqrt{(1 + 3)^2 + (5 - 2)^2[/tex]
=[tex]\sqrt{(4^2 + 3^2)[/tex]
= [tex]\sqrt{(16 + 9)[/tex]
= 5
Therefore, the radius of the circle is 5 units.
The equation of a circle with center (h, k) and radius r is given by:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Substituting the values, we have:
[tex][-7 - (-3)]^2 + (y - 2)^2 = 5^2[/tex]
[tex](-7 + 3)^2 + (y - 2)^2 = 25[/tex]
[tex](-4)^2 + (y - 2)^2 = 25[/tex]
[tex]16 + (y - 2)^2 = 25[/tex]
[tex](y - 2)^2 = 9[/tex]
Taking the square root of both sides, we have:
y - 2 = ±3
Solving for y, we have two possible values:
y - 2 = 3
y = 5
y - 2 = -3
y = -1
The points (-7, 5) and (-7, -1) both lie on the circle.
Thus, the radius is 5, and the points (-7, 5) and (-7, -1) both lie on the circle.
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Which ordered pair is a solution of the equation?
4x -1 = 3y + 5
(2,3)
(3,2)
(1,1)
(9,10)
Answer:
(3, 2)
(9, 10)
Step-by-step explanation:
Ordered pairs (3, 2) and (9, 10) is the solution of the equation 4x -1 = 3y + 5
4x -1 = 3y + 5 (given)Lets us check for (3, 2)L.H.S. = 4x - 1 = 4(3) - 1 = 12 - 1 = 11 (plug x = 3)R.H.S. = 3y + 5 = 3(2) + 5 = 6 + 5 = 11 (plug y = 2)-> L.H.S. = R.H.S.-> Ordered pair (3, 2) is a solution of the given equation.Similarly, ordered pair (9, 10) is also a solution of the given equation because L.H.S and R. H.S. are equal to 35 on plugging x = 9 and y = 10.1. Answer the following questions on the number given below. 12,34 761 (a) What is this number called?
Step-by-step explanation:
one million, two hundred thirty-four thousand, seven hundred sixty-one
How do I solve this ?
Answer:
The theoretical probability of rolling a 4 on any given roll for a six-sided die is [tex]\frac{1}{6}[/tex], The experimental probability of rolling a 4 is [tex]\frac{6}{25}[/tex].
Step-by-step explanation:
help will mark Brainliest!!
Answer:
1/20
Step-by-step explanation:
1/4 = 0.25
0.25 / 5 = 0.05
0.05 as a fraction = 5/100
simplified
5 / 5 = 1
100 / 5 = 20
1/20
Simplify (2x^2y)^5. This needs to be simplified
Answer:
32x^10y
Explanation -
You want to use distributive property. Take 2x^5 and the Exponent 2y^5
It should look like this
For Halloween, Sue wears a monocle that, its packaging claims, has a circumference of
18.212 centimeters. What is the monocle's radius?
Use 3.14
the measure of the radius is 2.9
Sophia is 12 years old. Her Uncle Reynald tells her that if she adds 5 to her age, multiplies the sum by 3, and then subtracts 4 from the product, she will find his age. She tells him that his age equals the expression 12 + 5 × 3 − 4 . Is Sophia correct? Choose the correct answers from the drop-down menus. Sophia is Choose... . Her uncle's actual age is Choose... .
Answer:
Yes, Sophia is correct
Step-by-step explanation:
The expression is correct and if you solve it, you get 23 which should be her uncle's age.
1 Which expression is equivalent to
12x - 3x?
A x(123)
(B) 8x
© 3(3x - x)
(D 9
If your options are:
A. x(12-3)
B. 8x
C. 3 (3x-x)
D. 9
Then the following is true.
Answer: (A) x(12-3)
First, we will simplify the given expressions;
A. x(12-3) = 12x - 3x
B. 8x = 8x
C. 3 (3x-x) = 9x - 3x
D. 9 =9
This means the answer to your question is;
A. x(12-3)
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CAN ANYONE PLEASE HELP!’
Answer:
130 cm³
Step-by-step explanation:
Volume of the pyramid = 1/3 × base area × height
Calculating base area;
Area = length × width
= 8 × 7
= 56 cm²
Now, Volume = ⅓ × 56 × 7
= ⅓ × 392
= 130.6 cm³.
Algebra 1 is all about equations and functions. First, you learned about Linear Functions then Quadratic Functions. Next, you learned about Rational Functions (indirect variation), then Exponential and then Radical Functions. Before Algebra 1 comes to a close, it is good to review these functions and compare them side by side.
Complete the table below. The table is created for you in the Word or PDF Worksheet. If you don't have Microsoft Word, download the PDF and create the worksheet in an application of your choice, complete the worksheet and upload it as a PDF.
All images should be original. Graphed them using a digital calculator such as Desmos.
Resources: Desmos User Guide
Export a graph from Desmos by choosing 'Share' and then 'Export', or you can 'Print' them as a PDF. Alternatively, you can take a screenshot of your graph. You can insert the image into this table or give your image files a distinct name and upload them with this worksheet. You can upload them as a PDF, or you can use an image file format - PNG, JPG or GIF files.
Linear Quadratic Rational Exponential Radical
Parent Function:
Notation
----------------------------
Parent Function:
Graph
----------------------------
Translation:
Graph a function which extends
through quadrant 1, 2, and 4.
If it is not possible to graph
through these quadrants,
chose one or two quadrants and explain the choice.
-------------------------------------
Write the function notation
for the above function
-------------------------------------
Domain and Range of
translated function
Reflection: Write a paragraph summarizing what you learned from this activity.
Answer:
Algebra is simple and the answer is infinity due to there being over one million diffrent possoblitlitys, We know that because of albert ienstine so the answer has been solved.
Step-by-step explanation: