A theatre contains 441 seats and the ticket prices for a recent play were ​$60 for adults and ​$16 for children. If the total proceeds were ​$14,800 for a​ sold-out matinee, how many of each type of ticket were​ sold?

The measure of angles 1 and 2 are 16.5 and 73.5 respectively.

The sum of the two acute angles is complementary.

Let the complementary acute angles be x and y

Since they form a right angle triangle, hence;

x  + y = 90 ............................. 1

If the measure of one acute angle is 3 times the sum of the other acute angle and 8, this is expressed as x = 3(y + 8)

Substitute the value of x into the equation 1 as shown:

3(y+8) + y = 90

3y + 24 + y = 90

4y + 24 = 90

4y = 90 - 24

4y = 66

y = 66/4

y = 16.5

Get the other acute angle:

x = 90 - y

x = 90 - 16.5

x = 73.5 degrees

Hence the measure of angles 1 and 2 are 16.5 and 73.5 respectively.

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The required algebraic expression for the length of the blade is x = 14 - h.

Given that,

The knife shown below is 14 inches long.
To write an algebraic expression that represents the length of the blade (in inches).

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here let the length of the blade of the knife be x,
length of the knife handle be h
Here the total length of the knife is 14 inches
So,
The total length of the knife = length of the blade + length of the handle
14 = x + h
x = 14 - h

Thus, the required algebraic expression for the length of the blade is x = 14 - h.

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Answer:

[tex]\text{Growth in Kate}<\text{Growth in Mari}<\text{Growth in Kim}[/tex]

Step-by-step explanation:

We are given the following information in the question:

Growth in Mari =

[tex]2\displaystyle\frac{1}{4}\text{ inches} = \frac{2\times 4 + 1}{4} = \frac{9}{4} = 2.25\text{ inches}[/tex]

Growth in Kim =

2.4 inches

Growth in Kate =

[tex]2\displaystyle\frac{1}{8}\text{ inches}= \frac{2\times 8 + 1}{8} = \frac{17}{8} = 2.125\text{ inches}[/tex]

Growth in order from least to greatest:

[tex]2.125<2.25<2.4\\\text{Growth in Kate}<\text{Growth in Mari}<\text{Growth in Kim}[/tex]

If the CPI increased by 8.3%, therefore this means that there was a fractional increase of 0.083. So amount increased is:

CPI increase = 141 * 0.083 = 11.703

Therefore the end of year CPI is the sum of the original and the increase:

end of year CPI = 141 + 11.703 = 152.703

Answer:

152.703

Ten as 9 hundreds is 9 thousands.

Place value is the value of each digit in a number.

For example 5 in 350 is 5 tens or 50.

The given digit is 9 thousand which can be written as 9,000

It can be written as,

9,000 = 9 x 1000

or,9,000 = 9 x 10 x 100

So, for require 9 hundreds multiplying 9 by 100 in the above expression

9,000 = 10 x 900

which can be described as Ten as 9 hundreds is 9 thousand.

Hence, ten as 9 hundreds is 9 thousands

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10 as 9 hundreds  is 9 thousands.

Suppose a number 12345 is given this can be written as

10000 + 2000 + 300 + 40 + 5 if we sum up all these we will get back our given number.

Now if we are asked what is the place value of 2 & 4

So, the place value of 2 in the given number is 2000 & the place value of 4 is 40.

Place value is defined as the value based on the position of that number  whether it's in thousand's place or ten's or in 1's place.

In the given question

___ as 9 hundreds is 9 thousand

⇒ ____ as 900 is 9000

if we divide 9000/900 = 10 we will get our answer.

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The value of the 50 divided by 2.5 divided by 0.04 is equal to  500.

To calculate 50 divided by 2.5 divided by 0.04, should follow the order of operations,

which is parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).

However, there are no parentheses or exponents in this expression, so we can proceed directly to multiplication and division:

50 ÷ 2.5 ÷ 0.04

First, divide 50 by 2.5:

50 ÷ 2.5 = 20

Next, divide the result (20) by 0.04:

20 ÷ 0.04 = 500

Therefore, 50 divided by 2.5 divided by 0.04 equals 500.

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The function to find the number of rides Jay went on is [tex]\( 10.50 + 4.50x = 46.50 \)[/tex]

Let x be the number of rides Jay went on.

The cost of the entrance fee is $10.50, and the cost per ride is $4.50. The total amount Jay spent is $46.50. The equation representing this scenario is:

[tex]\[10.50 + 4.50x = 46.50\][/tex]

To find the number of rides, you can solve for x:

1. Subtract the entrance fee from the total amount:

  [tex]\[ 46.50 - 10.50 = 36.00 \][/tex]

2. Divide by the cost per ride:

 [tex]\[ \frac{36.00}{4.50} = 8 \][/tex]

So, Jay went on 8 rides.

The function to find the number of rides x is:

[tex]\[f(x) = 10.50 + 4.50x\][/tex]

Setting this equal to the total expenditure ($46.50), the function to find x is:

[tex]\[10.50 + 4.50x = 46.50\][/tex]

Answer: 36 Types

Step-by-step explanation:

3 designs and 6 color options so that would be

3 x 6 = 18

they also have the option of either long or short sleeve so that would be

18 x 2 = 36

Step-by-step explanation: Three consecutive odd integers are represents as follows.

X ⇒ first integer

X + 2 ⇒ second integer

X + 4 ⇒ third integer

Since the sum of these is 87, our equation reads X + X + 2 + X + 4 = 87.

Simplifying on the left, we get 3x + 6 = 87.

Subtracting 6 from both sides, 3x = 81.

Now divide both sides by 3 and x = 27.

Since x, our first odd integer is 27, our next consecutive odd integer will be X + 2 or 27 + 2 which is 29 and X + 4 would be 31.

The question involves setting up an equation to determine Clem Kadiddlehopper's current age based on his age in six years and 26 years ago. By solving the equation x + 6 = 5(x - 26), we find that Clem is currently 34 years old.

Explanation:

The question asks us to determine Clem Kadiddlehopper's current age based on information about his age in future and past years. Let's define Clem's current age as x years old.

In six years, he will be x + 6 years old. It is stated that in six years, Clem will be five times as old as he was 26 years ago. Since 26 years ago he was x - 26 years old, we can write the equation: x + 6 = 5(x - 26).

To find Clem's age, we will solve the equation:

Therefore, Clem Kadiddlehopper is currently 34 years old.

Answer:58 metric ton

Step-by-step explanation:

Given

Fifty eight thousand kilogram of solid waste

We need to convert it into metric tons

and we know 1 metric ton is equivalent to one thousand kilogram i.e. 1000 kg

so 58,000 kg is equivalent to 58 metric ton

Answer:

f⁻¹(x) = (1/2)x +5

Step-by-step explanation:

In y = f(x), swap the variables, then solve for y. The expression you get is f⁻¹(x).

... y = 2x -10

... x = 2y -10 . . . . . . swapped variables

... x +10 = 2y . . . . . add 10

... (1/2)x + 5 = y . . . . divide by 2

... f⁻¹(x) = (1/2)x + 5 . . . . . . rewrite using function notation

Final answer:

The region e refers to the inside of a cylinder defined by x² + y² = 16 and between the planes z = -4 and z = 1. It represents a three-dimensional space bounded both radially, by the cylinder, and vertically, by the planes.

Explanation:

The region described in the question is a cylindrical volume in three-dimensional space. To visualize this region, we remember that the cylinder is defined by the equation x2 + y2 = 16, which is the set of points in the xy-plane that are at a distance of 4 from the origin (since the radius is √16 = 4). This cylinder extends indefinitely in the positive and negative z-directions.

The planes z = -4 and z = 1 act as boundaries in the z-direction, trimming the cylinder down so that we're only considering the portion of the cylinder between these two planes. Thus the region e of interest is the set of points inside the cylinder that lie at a height between z = -4 and z = 1.

This type of region is common in problems involving volume calculations, especially when using integral calculus to determine the volume of the shape or when analyzing physical phenomena like fluid flow or electric fields within prescribed bounds.

The probability that a Poisson random variable X equals 2, given that its variance is 3, is approximately 0.2240.

The student asks about finding the probability that a Poisson random variable X takes on a value exactly equal to 2, given that the variance of X is 3. We know for a Poisson distribution, the variance is equal to its mean, which is denoted by λ (lambda). Therefore, λ = 3.

Using the formula for the Poisson probability mass function (PMF), P(X = k) = (e^(-λ) * λ^k) / k!, we can calculate P(X = 2). Substituting λ = 3 and k = 2, we have:

P(X = 2) = (e^(-3) * 3^2) / 2! = (0.0497871 * 9) / 2 = 0.224041.

We can round this probability to four decimal places:

P(X = 2) ≈ 0.2240.

Final answer:

To find out the total hardener needed for 15 containers of resin, multiply 15 by the amount per container, 50ML, which equals 750ML of hardener in total.

Explanation:

To calculate the total amount of hardener needed for 15 containers of resin, we use a simple multiplication. We have been given that each container requires 50ML of hardener. Therefore, we multiply the number of containers by the amount of hardener needed per container.

Calculation:
Number of containers × Amount of hardener per container = Total amount of hardener
15 containers × 50ML/container = 750ML

Thus, for 15 containers of resin, you would need to add a total of 750ML of hardener.