A movie theater has 1,000 seats. There are 424 adults and 339 children sitting i seats. How many of the seats are empty

The complete table is as follows

x       y

0     -11/2

1     -3

2      -1/2

3      2

4      9/2

5      7

The table is completed by identifying the constant change

-11/2 + k = -3

k = -3 + 11/2

k = 5/2

This is used to complete the table as follows

For x = 1

-11/2 + 5/2 = -3

For x = 2

-3 + 5/2 = -1/2

For x = 3

-1/2 + 5/2 = 2

For x = 4

2 + 5/2 = 9/2

For x = 5

9/2 + 5/2 = 7

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Answer:

Volume = 1.9 in3

Step-by-step explanation:

If the perimeter of the square base is 5 inches, we have that:

Perimeter = 4 * side

5 = 4 * side

side = 1.25 in

Then, to find the volume of the pyramid, we can use the formula:

Volume = (1/3) * side^2 * height

So we have that:

Volume = (1/3) * 1.25^2 * 3.6

Volume = 1.875 in3

Rounding to nearest tenth, we have Volume = 1.9 in3

Answer: 1.875=1.9

Side length of base:{5}{4}=1.25 4 5  =1.25

A force of 4.05×10⁶ N was exerted on one side of the wall.

Force is an external agent capable of changing the state of rest or motion of a particular body. It has a magnitude and a direction.

The following data were obtained from the question:

Breadth (B) = 4 m

Length (L) = 10 m

Standard pressure (P) = 101325 Nm¯²

Next, we shall determine the area of the wall. This can be obtained as follow:

Area (A) = length (L) × breadth (B)

A = 10 × 4

A = 40 m²

Finally, we shall determine the force exerted on one side of the wall as follow:

Standard pressure (P) = 101325 Nm¯²

Area (A) = 40 m²

Pressure (P) = Force (F) /Area (A)

101325 = F/40

F = 101325 × 40

F = 4.05×10⁶ N.

Therefore, a force of 4.05×10⁶ N was exerted on one side of the wall.

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Answer:

(a) \(y = 4.5x + 22\) -- The equation

(b) 31 inches

Step-by-step explanation:

Given

See attachment

Solving (a): The equation of the trend line.

We start  by calculating the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where

\((x_1,y_1) = (0,22)\)

\((x_2,y_2) = (4,40)\)

So, we have:

\(m = \frac{40 - 22}{4 - 0}\)

\(m = \frac{18}{4}\)

\(m = 4.5\)

The equation is then calculated using:

\(y = m(x-x_1)+y_1\)

Where:

\((x_1,y_1) = (0,22)\)

\(m = 4.5\)

\(y = 4.5(x - 0) + 22\)

Open bracket

\(y = 4.5x - 0 + 22\)

\(y = 4.5x + 22\)

(b) The height of a 2 year old.

To do this, we substitute 2 for x in \(y = 4.5x + 22\)

\(y = 4.5 * 2 + 22\)

\(y = 9+ 22\)

\(y = 31\)

The prediction is 31 inches

Answer:

c. 4p+18

Step-by-step explanation:

-7d + 2d + 3d + 2d = 0

6p-3p+p = 4p

7-11+14+8 = 18

4p+18

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Answer:

false, true, fale

Step-by-step explanation: hi

The probability that 6 specified arrows hit the target is 0.321.

Probability means how likely an event is to occur. In many real-life situations, we may have to predict the outcome of events. We may or may not be fully aware of the outcome of the event. In this case, we say whether it will happen or not. The result often has good applications in sports, and business as a result of forecasting, and the result is also widely used in the field of new intelligence.

Given that:

She shoot 9 arrows,

the probability of each arrow being fitted 0.6.

Therefore,

The probability that 6 specified arrows hit the target is:

(⁸₄) ×(0.6)⁶ ×(0.4)⁶ = 0.321

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Answer:

Step-by-step explanation:

Therefore, Assuming that approximately 20% of the lake's trout population was marked, we can estimate that the lake contains approximately 250 trout.

To find the probability L(N) that 16 trout are marked in a sample of 80, we need to use the hypergeometric distribution formula. The formula is P(X=k) = [C(M,k) * C(N-M,n-k)] / C(N,n), where M is the total number of trout in the lake, N is the number of trout in the sample (80), k is the number of marked trout in the sample (16), and n is the sample size (50). Plugging in the values, we get P(X=16) = [C(M,16) * C(M-50,34)] / C(M,80). We don't know the exact value of N, but we can estimate it using the fact that 16 out of 80 trout were marked, which means that approximately 20% of the lake's trout population was marked. Therefore, we can estimate that the lake contains approximately 250 trout (i.e., 50 / 0.2). Writing the main answer in 2 lines: The probability L(N) that 16 trout are marked in a sample of 80 can be estimated using the hypergeometric distribution formula.

Therefore, Assuming that approximately 20% of the lake's trout population was marked, we can estimate that the lake contains approximately 250 trout.

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The first, second and third number is -4, 11 and 5.

An equation is formed from two or more numbers and variables, forming an expression through the use of mathematical operations of addition, subtraction, multiplication and division.

Let x represent the first number, y represent the second number and z represent the third number.

The sum of three numbers is 12. Hence:

x + y + z = 12      (1)

The sum of the first number and the second number is 2 more than the third number. Hence:

x + y = 2 + z     (2)

The second number minus the sum of the first number and third number is twice the third number. Hence:

y - (x + z) = 2z     (3)

From the 3 equations:

x = -4, y = 11 and z = 5

The numbers are -4, 11 and 5.

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Step-by-step explanation:

Create your own puzzle problem similar to the problem at the beginning of the lesson. Post your original puzzle on the discussion board.

Original problem: The sum of three numbers is 12. The sum of the first number and the second number is 2 more than the third number. The second number minus the sum of the first number and third number is twice the third number

Probability that a randomly selected point falls in the white area is; 84.1%

The formula for area of a circle is;

A = πr²

where r is radius.

Thus;

A_circle = π * 4² = 50.265 cm²

Now, formula for area of triangle is;

A_tria = ¹/₂ * base * height

A_tria = ¹/₂ * 4 * 4 = 8 cm²

Thus;

Area of white portion = 50.265 cm² - 8 cm²

Area of white portion = 42.265  cm²

Thus;

Probability that a randomly selected point falls in the white area is;

P(White area) = 42.265/50.265 = 0.8408

= 84.1%

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Answer:

x-axis

Step-by-step explanation:

The horizontal number line is called the x-axis. The vertical number line is called the y-axis. The point where the x- and y-axes meet is the origin.

Hope this helps! <3

The x-axis is the horizontal number line on the coordinate grid.

It is one of the two axes that form the Cartesian coordinate system, used to locate points in a two-dimensional plane. The x-axis runs horizontally from left to right, intersecting with the vertical y-axis at the origin (0,0). It acts as a reference line, assigning numerical values to the horizontal position of points on the grid.

The x-axis allows us to specify the x-coordinate of a point, which represents its horizontal distance from the origin. Positive values are to the right of the origin, while negative values are to the left. By combining the x-axis with the y-axis, we can precisely define the position of any point in the coordinate plane.

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Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

To determine the time Edna should leave, we need to subtract the travel time from the desired arrival time.

If Edna needs to be at Jake's party at 2:30 PM and it takes her 23 minutes to drive there, she should leave 23 minutes before 2:30 PM.

To calculate the departure time, we subtract 23 minutes from 2:30 PM:

2:30 PM - 23 minutes = 2:07 PM

Therefore, Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

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Answer:

1000grams= 1 kilogram

Step-by-step explanation:

Answer:

1000 grams = 1 Kilo

Comparing the equation with standard form we have the value of a = 2y, and b = -3, when 8y² - 12y + 4 is divided by 4y.

A quadratic equation has the conventional form ax² + bx + c, where an is the leading coefficient and a real integer that is not zero. Given that this equation has a degree of 2, it is referred to be a quadratic equation. Quad means square. A quadratic equation can be expressed in other ways than the traditional form.

The standard form of the quadratic equation is:

ax² + bx + c

The given equation is:

8y² - 12y + 4

When the equation is divided by 4y we have:

2y - 3 + 1/y

Comparing the equation with standard form we have the value of a = 2y, and b = -3.

Hence, the value of a and b are a = 2y, and b = -3. for the given equation.

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Answer: -45/4 = -11 1/4

Answer: 7 3/4 pounds

Step-by-step explanation:

Here's the correct question:

Last year, Bob's Market ordered 15 1/2 pounds of plums from a local orchard. This year, the market plans to order 1 1/4 times as many pounds of plums as were ordered last year. They want 2/5 of this order to be red plums. What is the total amount, in pounds, of red plums the market plans to order this year?

The amount of pounds of plum that is ordered this year will be:

= 15 1/2 × 1 1/4

= 31/2 × 5/4

= 19 3/8

Since they want 2/5 to be red plums, the total amount of red plums will then be:

= 2/5 × 19 3/8

= 2/5 × 155/8

= 310/40

= 7 3/4 pounds

Answer:

B. r = A-p/pt

Step-by-step explanation:

We can rearrange the equation to make \(r\) the subject of the equation:

\(A=p+prt\)

\(A-p = p+prt-p\)

\(A-p = prt\)

\(\frac{A-p}{pt} = \frac{prt}{pt}\)

\(r = \frac{A-p}{pt}\)

∴ Option B is correct

Hope this helps :)

Answer:

The formula for the volume of a cylinder is r^2piH.

Step-by-step explanation:

The process is to find the radius and square it, the radius is half of the top or bottom circle. And then you can get a calculator and multiply it by pi, or 3.14, or 3.141592653... Then you multiply it by the height. So the answer for this cylinder 200pi, or 628.3185307, you can round however you need to

UR WELCOME !!!!!

Answer:

different definitions

Step-by-step explanation:

ordering numbers can be seen as arranging the numbers by a certain characteristics. for example, you could order numbers from least to greatest

comparing numbers can be seen as looking into two or more numbers rather than the entire group of numbers. for example, if there were the numbers 1, 2, 3, 4, 5, 6, you could say that 2, 4, 6, are even numbers

comparing amounts could be determined by worth but not the numerical values. for example, you could have a gallon of milk and a quart of orange juice but just by the size of the container, a gallon of milk is bigger and holds more than a quart of orange juice

Answer:

the student in question bought 3 large notebooks and 3 small notebooks

Step-by-step explanation:

the easiest way to explain how to do this is by recognizing that the student bought $54 worth of notebooks- which is not divisible by 10 easily. that means, we should subtract 8 from 54 until we get a number that IS divisible

54 - 8 = 46 (one small notebook)

46 - 8 = 38 (two small notebooks)

3 8 - 8 = 30 (three small notebooks)

then, divide 30 by 10 to see how many large notebook the student bought.

30/10 = 3

the student in question bought 3 large notebooks and 3 small notebooks

Answer:

I believe what your problem is asking is to simplify \(xy + 2xy+x+3y\). If that is the case then the answer would be 3xy + x + 3y.

Step-by-step explanation:

Combine like terms.

Answer:

795

Step-by-step explanation:

First, we find the circumference of 1 ring.

c = 2πr

c = 2 × 3.14159 × 8.4 mm

c = 52.7787 mm

The circumference of 1 ring is the length of spooled gold used for 1 ring.

The spool has a total length of 42 m.

42 m × 1000 mm / 1 m = 42,000 mm

The spool has a total length of 42,000 mm.

Now we divide the length of the spool by the length of 1 ring.

42,000 mm / 52.7787 mm = 795.78

He can make 795 rings.

The three factors that determine the margin of error of a confidence interval for μ are the sample size (n), the standard deviation (σ) of the population, and the desired level of confidence (C).

1. Sample size (n): A larger sample size generally leads to a smaller margin of error because it provides more information about the population.
2. Standard deviation (σ): A smaller standard deviation results in a smaller margin of error since it indicates less variability in the population.
3. Level of confidence (C): A higher desired level of confidence, such as 95%, leads to a larger margin of error as it requires a wider interval to capture the true population mean with a higher degree of certainty.

Therefore, the margin of error of a confidence interval for μ depends on the sample size, standard deviation, and level of confidence. These factors affect the precision and reliability of the estimation.

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The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of the variable 'y' is given by the tangent of the angle 27°. Then we have

tan 27° = y / 350

y = 350 tan 27°

y = 178.3

The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

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The missing diagram is given below.

For the cyclic group G of order 5, \(x^n\) generates G if and only if n and 5 are co-prime (i.e., their greatest common divisor is 1).

For the cyclic group G of order 6,  \(x^n\)  generates G if and only if n and 6 are co-prime.

For a cyclic group G of order k (where k ≥ 2),  \(x^n\)  generates G if and only if n and k are co-prime.

In general, a cyclic group G is generated by an element x if and only if  \(x^n\)  generates G, where n is an integer between 0 and k-1 (inclusive) for a cyclic group of order k. This condition holds when n and k are co--prime, meaning they have no common factors other than 1. When n and k are co-prime, repeatedly applying the operation of multiplying x by itself (n times) will generate all the elements of G.

To determine whether  \(x^n\)  generates G, we need to check whether n and k are co-prime. If their greatest common divisor is 1, then  \(x^n\) generates G; otherwise, it does not.

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The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

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Answer:

-15

Step-by-step explanation:

if its just asking for what number would represent a loss of 15 it would be negative 15

i dont know if there's more to the problem or not

Answer:

-15

Step-by-step explanation:

This is because whatever much water was in the tank is now decreasing by 15, therefore, you can write it as -15,

hope this helps!

Answer:

Option B: 7x + y - 4 feet

Step-by-step explanation:  I got it right on the test. Trust me

The total perimeter of the triangular fence using the perimeter of a triangle formula is:

7x + y - 4 feet.

The perimeter of a form is the whole length enclosing it. It is the measurement of the perimeter or outline of any two-dimensional geometric shape. Many figures may have the same perimeter depending on their sizes.

The length that the shape's perimeter covers is known as the perimeter. Hence, the perimeter's units will be the same as its length units.

Now perimeter of a triangle =

Sum of all the sides of the triangular region:

= 4x + 5 + y -7 + 3x - 2

= 7x + y -4

Therefore, perimeter of the fence = 7x + y -4 feet.

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