A theater can seat 864 people. The number of rows is 5 less than the number of seats in each row. How many rows of seats are there?

Answers

Answer 1

There should be 27 rows of 32 seats.

Answer 2

Final answer:

To determine the number of rows in a theater that can seat 864 people, with the number of rows being 5 less than the number of seats per row, we set up the equation x(x-5)=864. Solving this quadratic equation, we find that there are 31 rows of seats.

Explanation:

To solve for the number of rows in the theater, let's denote the number of seats in each row as x and the number of rows as x - 5. Since the product of the number of seats in each row and the number of rows will give us the total seating capacity, we can write down the equation:

x(x - 5) = 864

Expanding the equation, we get:

x2 - 5x - 864 = 0

Using the quadratic formula or factoring, we find that x = 36. Therefore:

The number of rows is x - 5 = 36 - 5 = 31.

So, the theater has 31 rows of seats.

Related Questions

what's the closest number to 27.8 * 9.8

Answers

280...round each number to the nearest whole number (27.8=28 and 9.8=10) then multiply and you will get 280

27.8 * 9.8 = 272.44

Closest whole number = 272.

I don't get why price(max)=$80
Can someone help me

Answers

check the picture below.

as a matter of elasticity, if you sell 100 popsicles for $1, you get a revenue of $100.

However, if your price goes to $5 per popsicle, then folks will begin to find it too expensive and won't be buying 100, but just 15, so, even though $5 is a higher price, 5 * 15 is a much smaller revenue than 1 * 100.

Jennifer's grandmother buys carrots at the farm stand. She and her 3 grandchildren equally share the carrots. The total weight of the carrots she bought is 28 kilograms. How many kilograms of carrots will Jennifer get ?

Answers

since they share it equally
28/4=7

How many times dose 63 go into 272? THANK YOU SO MUCH FOR ANSWERING,IF YOU DID!!!!!!!

Answers

Let's write this problem as an expression: 272 ÷ 63
Now, it is just division, and we can divide the two numbers to get 4.317...
However, the question only asks for how many times 63 goes into 272, so the answer would be that 63 goes into 272 four times. Hope this helps and have an awesome day!

Integers contain the whole numbers.true or false

Answers

True, Integers mean "whole", and it cannot be a fraction or decimal

hope this helps

true , hope this helps :)

Can someone please solve this?

Answers

multiplicity of a root means, is there that many times.

[tex]\bf \begin{cases} x=3\implies &x-3=0\\ x=2\implies &\begin{cases} x-2=0\\ x-2=0\\ x-2=0 \end{cases} \end{cases} \\\\\\ (x-3)(x-2)~~(x-2)(x-2)=\textit{original polynomial} \\\\\\ (x^2-5x+6)~~(x^2-4x+4)=y \\\\\\ x^4-4x^3+4x^2-5x^3+20x^2-20x+6x^2-24x+24=y \\\\\\ 1x^4-9x^3+30x^2-44x+24=y[/tex]

Write the equation for the following relation. Include all of your work in your final answer. Submit your solution. P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}

Answers

First, we will notice that while the value of x increases by 1, the corresponding value of y increases by 4. This means that this is a linear relation.

The general equation for linear equations is : y = mx + c where m is the slope and c is the y-intercept

To get the slope, we will need to use two points. Let's take the first and the last points: (1,0) and (4,12)
The slope is calculated as: (y2-y1) / (x2-x1)
Use the chosen points to substitute in the equation and get the slope as follows:
m = (12-0) / (4-1) = 12/3 = 4

Now, the equation of the line became: y = 4x + c

The given points all satisfy the equation of the line, we can use any of them to substitute in the equation and get the value of c.
For instance, I will use the first point: (1,0)
y = 4x + c
0 = 4(1) + c
c = -4

The equation of the line is:
y = 4x - 4

The table shows the steps for solving the given inequality for x.

−3(4−6x)
Select the reason for each step from the drop-down menus.

Answers

step        justification

- 3 (4 - 6x) < x + 5

- 12 + 18x < x + 5                 distributive property (to solve the left side)

-12 + 17x < 5                        subtraction property of equality (to transpose x
                                             from right to left side)

                                              subtraction of like terms (18x - x = 17x)

17x < 17                                addition property of equality (to tranpose - 12
                                              from left to right side)

                                              addition of like terms (12 + 5 =17)

x < 1                                  division property of equality

Answer:step justification

- 3 (4 - 6x) < x + 5

- 12 + 18x < x + 5 distributive property (to solve the left side)

-12 + 17x < 5 subtraction property of equality (to transpose x

from right to left side)

subtraction of like terms (18x - x = 17x)

17x < 17 addition property of equality (to tranpose - 12

from left to right side)

addition of like terms (12 + 5 =17)

x < 1 division property of equality

Step-by-step explanation:

what square root lies between 17 and 18

Answers

easy
if x is the number
sqrt x is between 17 and 18

17<√x<18
squaer the whole thing
289x could be 300
it could be sqrt of 300
√300=10√3

one is 10√3

The ordered pair (2, 1) is a solution of a direct variation equation. Write the equation and identify the constant of variation.

Answers

A direct variation equation takes the form "b = ka," where the k is the constant of variation. In this case, 1 (b) is one-half as large as 2 (a), so the constant will be 0.5. This would allow the equation to be written as "b = 0.5a," and the constant of variation in this equation is 0.5.

If each weighs 2/3 pound, how many potatoes are there in a 50-pound case?

Answers

The number of potatoes that are there in a 50-pound case are 75 potatoes.

In Mathematics and Euclidean Geometry, an expression simply refers to a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Since each potato weighs 2/3 pound, the number of potatoes that are there in a 50-pound case can be modeled by the following expression;

Number of potatoes = 50 ÷ 2/3

Number of potatoes = 50 × 3/2

Number of potatoes = 150/2

Number of potatoes = 75 potatoes.

how many square inches does an "11x13" area encompass

Answers

143 square inches

Answer:

143 square inches

Step-by-step explanation:

The area of encompass is given by 11 * 13 inches.

Here the length = 11 inches and the width = 13 inches.

The length and width have different numbers, so the given figure is a rectangle.

Area of a rectangle = length * width

Area of the figure = 11*13

= 143 square inches

The unit for the area is "square"

The units are given in inches, therefore, it is 143 square inches.

Verify the identity Cotx/tanx+cotx = 1-sin^2x

Answers

[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\\\\ -------------------------------\\\\ \cfrac{cot(x)}{tan(x)+cot(x)}=1-sin^2(x) \\\\\\ \textit{doing the left-side}\implies \cfrac{\frac{cos(x)}{sin(x)}}{\frac{sin(x)}{cos(x)}+\frac{cos(x)}{sin(x)}}\implies \cfrac{\frac{cos(x)}{sin(x)}}{\frac{sin^2(x)+cos^2(x)}{cos(x)sin(x)}}[/tex]

[tex]\bf \cfrac{\frac{cos(x)}{sin(x)}}{\frac{1}{cos(x)sin(x)}}\implies \cfrac{cos(x)}{\underline{sin(x)}}\cdot \cfrac{cos(x)\underline{sin(x)}}{1}\implies cos^2(x)\implies 1-sin^2(x)[/tex]

Two pounds of bananas cost $1.16 what would be the cost of 5pounds s of bananas

Answers

If 2 lb of bananas cost $1.16, then each pound costs $0.58.

0.58 * 5 = 2.9

So 5 lb of bananas will cost $2.90.

Hope this helps!

The cost of 5 lbs of bananas would be $2.90.

Suppose △DEF≅△MNO.
Which congruency statement is true?

A) DF≅NO
B) DE≅MN
C) EF≅MN
D) EF≅MO

Answers

the answer is b. would u like to see steps or are you good?

Final answer:

When triangles are congruent, their corresponding sides and angles are the same. Hence in congruent triangles △DEF and △MNO, side DF is congruent to side MN, thus option B) DE≅MN is the correct answer.

Explanation:

In the case of congruent triangles, the corresponding sides and angles are essentially the same. Therefore, we must match up the corresponding sides. A correct statement would be that side DF, from the first triangle, is congruent to side MN, from the second triangle. Hence the correct option is B) DE≅MN.

Additionally, DE would be congruent to MN, and EF would be congruent to NO, completing the congruence between triangles △DEF and △MNO.

Learn more about Congruent Triangles here:

https://brainly.com/question/22062407

#SPJ2

Plot the x- and y-intercepts to graph the equation. y=−12x−3

Answers

x-intercept: (1/4) ,0
y-intercept: (0, -3)

Keywords

x-intercept, y-intercept, linear equation, graphing tool

we know that

The y-intercept is the value of y when the value of x is equal to zero

The x-intercept is the value of x when the value of y is equal to zero

In this problem we have

[tex]y=-12x-3[/tex]

Step 1

Find the x-intercept

For [tex]y=0[/tex]

find the value of x

[tex]0=-12x-3[/tex]

[tex]12x=-3[/tex]

[tex]x=-0.25[/tex]

The x-intercept is the point [tex](-0.25,0)[/tex]

Step 2

Find the y-intercept

For [tex]x=0[/tex]

find the value of y

[tex]y=-12*0-3[/tex]

[tex]y=-3[/tex]

The y-intercept is the point [tex](0,-3)[/tex]

Step 3

With the point [tex](-0.25,0)[/tex] and the point [tex](0,-3)[/tex]

Plot the linear equation

Using a graphing tool

see the attached figure

therefore

the answer in the attached figure

Complete the sentence using one of the words below in 10/6 the 10 is the

Answers

The 10 Is The Numerator

Find the maximum and minimum values of the function.
y=7cosx

Answers

The Maximum and Minimum can not be determined on this problem because it isn't a quadratic function. Graphed, the highest point is 7 and lowest is -7 in a repeated mountain shape. Hope this helps.

The range of cos x is -1 to + 1

So maximum of 7 cos x = 7 and minimum is -7.

Stuck on this question. Any help would be appreciated.

Answers

Solving the 2nd equation for r results in
10-2h
r = --------------
5
(10-2h)^2
Then r^2 = ----------------
25

Substitute this r and this r^2 into the first equation and simplify. This will result in a formula for V as a function of h (V in terms of h).

2x^5+12x^4+16x^3-12x^2-18x=0

Answers

[tex]2x^5+12x^4+16x^3-12x^2-18x=0 [/tex]

State the slope and the y-intercept of each given graph plz help i really dont know how to do this

Answers

For graph 1, the y-intercept is (0,1) and the slope is 1.
For graph 2, the y-intercept is (0,4) and the slope is -1.
For graph 3, the y-intercept is (0,-4) and the slope is -2.
For graph 4, the y-intercept is (0,-3) and the slope is 3/2.
For graph 5, the y-intercept is (0,4) and the slope is 2.
For graph 6, the y-intercept is (0,3) and the slope is -3/2.

(By the way, since the graphs aren't labeled as numbers, I went from left to right, and then down, and then left to right again).

Now, here's the explanation:

Solving for y-intercept is easier than it sounds. All you need to do is mark the point where the line crosses the y-axis (vertical axis).

Solving for slope is just rise/run. For example, in graph one, the points on the line went up one and then to the right one.

So, 1/1 = 1.

When a slope moves down or to the left, it will be negative. However, that's only if the rise OR run is down/left. If both are negative, the two will cancel each other out to make a positive.

Hope this helped!!

if today is wednsday what day will it be in 100 days and why

Answers

the day would be friday because there are 7 days in a week and in fourteen weeks on wednesday would be 98 days so add two more days which would be friday which is also 100 days

Bonswa. How are you today?

We know that every week (every seven days) it will be Wednesday if today is Wednesday. So, how may weeks are in 100 days? 14. Why? Because 14(7) = 98. So, in order to get to 100 we must add 2. So what is Wednesday plus two more days? Friday. So if today is Wednesday it will be Friday in 100 days. Why? Well, that's how our calendar is set up.

tep 1: –10 + 8x < 6x – 4 Step 2: –10 < –2x – 4 Step 3: –6 < –2x Step 4: ________

Answers

Step 4: 3>x. (The sign flips because you divided a negative)
I hope this helps love! :)

Y=2x^2-x-10 write in intercept form

Answers

y-intercept: Let x = 0 and solve for y. Then y =2(0)^2 -(0) - 10 = -10. The y-intercept is (0,-1).

x-intercept: Let y = 0 and solve for x.
Then 0 = 2x^2 - x - 10. a=2, b= -1 and c = -10.
-(-1) plus or minus sqrt[ (-1)^2 - 4(2)(-10)
Then x = ------------------------------------------------------------
2(2)
1 plus or minus sqrt(81) 1 plus or minus 9
x = ----------------------------------- = ---------------------------
4 4

Calculate the 2 x-values. Let's call them "a" and "b." Then the x-intercepts (there are 2) are

(a, 0) and (b, 0)

Use addition to simplify the expression 6/x+6/3x . show all the steps necessary to write the expression with a common denominator and to simplify the expression

Answers

Common Denominator is 3x

we write 6/x as 18/3x So we have

18/3x + 6 /3x = 24/3x

simplifyiby dividing numerator and denominator by 3:-

Answer is 8/x

What is the number 0.093 expressed in Scientific notation?
A. 9.3 * 10^2
B. 0.93 * 10^1
C. 9.3 * 10^-3
D. 9.3 * 10^-2

Answers

0.093 expressed in Scientific
=
9.3 x 10^-2

answer
D. 9.3 * 10^-2

Option D is correct. 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex].

To express the number 0.093 in scientific notation, we need to determine the coefficient and exponent.

0.093 can be written as 9.3 multiplied by a power of 10.

Since 0.093 is less than 1, the exponent should be negative.

To shift the decimal point to the right to form the original number, we move it three places to the right:

[tex]0.093 \rightarrow 9.3 \times 10^{-2}[/tex]

Therefore, 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex], option D is correct.

To learn more on Number system click:

https://brainly.com/question/1763119

#SPJ6

Sampling is ordinarily used when the number of items comprising the population is relatively small.

Answers

I believe this statement is false, and that sampling is used when the number of items in a population are fairly large. One would use a sample to represent some form of measurement or test so that it can be applied to the larger number of same objects.

A new iPhone user receives an average of 4.2 phone calls per hour. The calls occur randomly in time so if X = the number of calls received in an hour, then we can assume that X has a Poisson distribution with parameter λ = 4.2. Let Y = the number of phone calls received in a day. Assume all necessary independence in the following.
a. Y also has a Poisson distribution. What is the λ for Y?

b. What is the standard deviation of X?

c. What is the standard deviation of Y?

d. What is the probability that no calls are received in an hour?

e. What is the probability that more than 120 calls are received in a day?

f. What is the probability that Y is between 90 and 110 inclusive? (i.e. 90 ≤ Y≤110)

g. What is the variance of square root of 2Y?

h. Assume this distribution holds for all hours and days and that one call is independent from another. What is the probability that 120 or fewer calls are received for every day of this week? (Assume appropriate independence

Add any comments below.

Answers

Part A:

Given that Y is the number of phone calls received in a day and that a new iPhone user receives an average of 4.2 phone calls per hour.

Thus, the average number of phone calls received in a day is 4.2 * 24 = 100.8

Therefore, the λ for Y is 100.8

Part B:

The standard deviation of a Poisson distribution is given by

[tex]\sigma=\sqrt{\lambda}[/tex]

Thus, the standard deviation of X is given by

[tex]\sigma=\sqrt{4.2}=2.05[/tex]

Therefore, the standard deviation of X is 2.05.

Part C:

The standard deviation of Y is given by

[tex]\sigma=\sqrt{100.8}=10.04[/tex]

Therefore, the standard deviation of X is 10.04.

Part D:

The probability of a Poisson distribution is given by

[tex]P(X=x)=e^{-\lambda} \frac{\lambda^x}{x!} [/tex]

where, x is the number of occurence of the event in the given period.

Thus, the probability that no calls are received in an hour is given by

[tex]P(X=0)=e^{-4.2} \frac{(4.2)^0}{0!} =0.015[/tex]

Therefore, the probability that no calls are received in an hour is 0.015

Part E:

We approximate the Poisson distribution using Normal distribution by noting that for a Poisson distribution

[tex]\mu=\lambda \\ \\ \sigma^2=\lambda \\ \\ \sigma=\sqrt{\lambda}[/tex]

The probability of a normal distribution is given by

[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]

Thus, the probability that more than 120 calls are received in a day is given by

[tex]P(X\ \textgreater \ 120)=1-P(X\leq120) \\ \\ =1-P\left(z\leq \frac{120-100.8}{10.04} \right)=1-P(z\leq1.912) \\ \\ =1-0.97208=0.0279[/tex]

Therefore, the probability that more than 120 calls are received in a day is 0.0279

Part F:

We also approximate this using Normal distribution

The probability of a normal distribution between two value (a, b) is given by

[tex]P(a\ \textless \ X\ \textless \ b)=P\left(z\ \textless \ \frac{b-\mu}{\sigma} \right)-P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]

Thus, the probability that Y is between 90 and 110 inclusive is given by

[tex]P(90\leq X\leq 110)=P\left(z\leq \ \frac{110-100.8}{10.04} \right)-P\left(z\leq \frac{90-100.8}{10.04} \right) \\ \\ =P(z\leq0.916)-P(-1.076)=0.82025-0.14103=0.67922[/tex]

Therefore, the probability that Y is between 90 and 110 is 0.67922

Part G:

The variance of aY is given by

[tex]Var(aY)=a^2Var(Y)[/tex]

Thus, the variance of [tex] \sqrt{2} Y[/tex] is given by

[tex]Var( \sqrt{2} Y)=( \sqrt{2} )^2Var(Y)=2(100.8)=201.6[/tex]

Therefore, the variance of [tex] \sqrt{2} Y[/tex] is 201.6

Part H:

We approximate this using Normal distribution

The probability of a normal distribution is given by

[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]

Thus, the probability that 120 or fewer calls are received in a day is given by

[tex]P(X\leq120)=P\left(z\leq \frac{120-100.8}{10.04} \right) \\ \\ =P(z\leq1.912)=0.97208[/tex]

Since, this distribution holds for all hours and days and one call is independent from another. Assuming that there are seven days in a week.

The probability that 120 or fewer calls are received for every day of this week is given by

[tex](0.97208)^7=0.8202[/tex]

Therefore, the probability that 120 or fewer calls are received for every day of this week is 0.8202

Simplify 3 + c (8n + 4) + 9n

A. 49n + 20
B. 3+33n
C. 25n + 11
D. 19n + 7

Answers

c is the answer to your question

Well first you need to distribute the (c) to the 8n+4. So then you you would get 8nc+4c+9n+3. Not unless that (c) is suppose to be a number.

the sum of 2 3/5 + (-1/5) write in simplest form

Answers

The answer is 2 2/5. Need an explanation

2 2/5 that’s the answer

Other Questions

32 gal/min = what qt/h Why does the radley place fascinate scout, jem, and dill in to kill a mockingbird? why cant body builders swim please give reasons. Which describes the role of a vassal? to give the king a fiefdom, to work the land, to pay homage to a knight, to be ready to serve in a standing army, to function as liege-lord to knights please help Hace unos anos, mientras (yo estar) en la escuela primaria, me enferme gravementeA. estoyB. esteC. estaba D. estuve A homeowner installs an electrical heated mirror into the shower room. When a person has a shower, the heated mirror does not go misty but stays clear, why? Read this excerpt from "Teens Migrating to Twitter" by Jennifer C. Kerr and answer the question that follows: Twitter is booming as a social media destination for teenagers who complain about too many adults and too much drama on Facebook, according to a new study published Tuesday about online behavior. It said teens are sharing more personal information about themselves even as they try to protect their online reputations. Teens told researchers there were too many adults on Facebook and too much sharing of teenage angst and inane details like what a friend ate for dinner. "The key is that there are fewer adults, fewer parents and just simply less complexity," said Amanda Lenhart of the Pew Research Center, one of the study's authors. "They still have their Facebook profiles, but they spend less time on them and move to places like Twitter, Instagram and Tumblr." In the poll, 94 percent of teens who are social media users have a profile on Facebook flat from the previous year. Twenty-six percent of teen social media users were on Twitter. That's more than double the figure in 2011 of 12 percent. "Facebook just really seems to have more drama," said 16-year-old Jaime Esquivel, a junior at C.D. Hylton High School in Woodbridge, Va., in an interview. Esquivel said he still checks his Facebook account daily but isn't using it as regularly as in the past. He sees teens complaining on Twitter, too, so Esquivel has been using the photo-sharing service Instagram more often, posting a couple of pictures each day and communicating with friends. Facebook purchased Instagram last year. In what may be a concern to parents, more than 60 percent of the teens with Twitter accounts said their tweets were public, meaning anyone on Twitter friend, foe or stranger can see what they write and publish. About one-quarter of kids said their tweets were private and 12 percent said they did not know whether their tweets were public or private. Source: Kerr, Jennifer C. "Teens Migrating to Twitter." 21 May 2013: n. pag. AP Images. Web. 17 Jan. 2014. Based on this excerpt, this article would be most useful in answering which of the following research questions? What is the most popular topic of conversation on teenagers' Twitter feeds? Why do parents spend less time communicating on Twitter than their children? When is the best time to access social media sites like Twitter? How does Twitter affect the safety and security of teenagers? what is the solution to this equation? 4x^2+98=0 What kind of government existed in the novel 1984? how did orwell portray the state in 1984? An ideal gas undergoes an adiabatic process and does 25 joules of work on its environment. What is the change in internal energy? a.50 joules b. 25 joules c. 0 joules d. -25 joules An officer approaches a group of teenagers standing in a parking lot, drinking beer. she checks them for gang symbols and calls into the station to ascertain if any of them have active warrants. this officer typifies which officer style? Which of the following reactions shows that the rate of the appearance of D is twice the disappearance of A and one third the disappearance of B? "what happens to the neurons in your brain every time you learn something new?" What is someone who is willing to invest in a risky venture on the chance of making a large profit called? Last year, there were 12,000 students at a local college. There were 2000 more female students than male students. How many male and female students attended the college? if *(pic below)* complete the following statementf(6)=___ Explain why the graph shown may be misleading. (please help) Why did Spain explore and colonize the American southwest? The strongest conditioning occurs during acquisition when a previously neutral stimulus is presented Which angle is the included angle for DE and FE ?DEF Steam Workshop Downloader