The theater sells two types of tickets: adult
tickets for $15 and child tickets for $13.
Last night, the theater sold a total of 340
tickets for a total of $4712. How many adult
tickets did the theater sell last night?

Answer:

40 km

Step-by-step explanation:

Divide the distance by the scale

12/3 = 4

Multiply that number by the 10 km

4 x 10 = 40

Answer:

  20.7°

Step-by-step explanation:

Bearing angle is measured clockwise from north. The geometry can be modeled by a right triangle with the sides equal to the distances north and east of town B. The tangent relation can be used to find the angle.

__

The attachment shows the geometry. The relevant angle relation is ...

  Tan = Opposite/Adjacent

  tanIβ) = 23/61 . . . . . where β is the bearing angle

The angle value can be found using the arctangent function.

  β = arctan(23/61) ≈ 20.659°

The bearing of A from B is about 20.7°.

Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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Answer:8/9 is the answer as the resulting quotient you get is 0.88.... And so on

Answer:

it is 0.888888.... is 8/9 or \(\frac{8}{9}\)

We have proved both statements, and hence we have proved that every nonzero element of Z_n has a multiplicative inverse if and only if n is prime.

Proof of Statement 1:

Let a be a nonzero element of Z_n. We need to show that a has a multiplicative inverse modulo n. Since n is prime, the only positive divisors of n are 1 and n.

Therefore, the greatest common divisor of a and n is 1 or n. If gcd(a, n) = 1, then by Bezout's identity, there exist integers x and y such that ax + ny = 1. This means that ax is congruent to 1 modulo n, and hence a has a multiplicative inverse modulo n. If gcd(a, n) = n, then a is a multiple of n, and hence a is congruent to 0 modulo n. Since a is nonzero, this is a contradiction.

Therefore, gcd(a, n) cannot be n, and hence a has a multiplicative inverse modulo n.

Proof of Statement 2:

Let n be a composite number, i.e., n = ab for some positive integers a and b, where 1 < a < n and 1 < b < n. Then the elements a and b are nonzero elements of Z_n, but they do not have multiplicative inverses modulo n.

To see this, suppose that a has a multiplicative inverse modulo n. Then there exists an integer x such that ax is congruent to 1 modulo n. This means that ax = kn + 1 for some integer k. Since n divides ab, we have ax = kab, and hence kab = kn + 1.

This implies that b divides kn + 1, or equivalently, kn is congruent to -1 modulo b. But since a and b are relatively prime, we also have an + bm = 1 for some integers m and n. Multiplying both sides by k and using kn = 1 - am, we get k = -akm + kbkn, or k(1 + am) = kbkn.

Since b divides k(1 + am), and b and k are relatively prime, we have b divides 1 + am. Therefore, -1 is congruent to kn is congruent to kab is congruent to a(1+am) modulo b. But this means that a has a zero divisor modulo b, which contradicts the fact that b is a nonzero element of Z_n.

Therefore, a does not have a multiplicative inverse modulo n. Similarly, we can show that b does not have a multiplicative inverse modulo n.

Therefore, if every nonzero element of Z_n has a multiplicative inverse, then n must be prime.

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Question

To prove that every nonzero element of Z_n has a multiplicative inverse if and only if n is prime,

If n is prime, then every nonzero element of Z_n has a multiplicative inverse.

If every nonzero element of Z_n has a multiplicative inverse, then n is prime.

Given the comopound inequality:

Let's graph the compound inequality.

Here x is greater than -1 but less than or equal to 7.

To graph the inequality, we have:

Also, x is less than or greater than 7, plot a closed dot on the point 7.

Then draw a straight line connecting both points.

Hence, we have the graph below:

Answer: 1 13/ 20

Step-by-step explanation:

first multiply 2 1/5 and 1 3/4 you will get 3 17/20then subtract from 3 17/20 - 2 1/5 you will get 1 13/20

Answer:

$73.37 is the new price.

Step-by-step explanation:

0.065 x 58 = 3.77

0.2 x 58 = 11.6

3.77 + 11.6 = 15.37

15.37 + 58 = 73.37

The quotient include the following: D. \(\frac{x(2x-3)}{7}\)

In Mathematics and Geometry, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

Based on the information provided above, we can logically deduce the following mathematical expression;

\(\frac{2x-3}{x} \div \frac{7}{x^2}\)

By rearranging the mathematical expression using the multiplication operation, we have:

\(\frac{2x-3}{x} \times \frac{x^{2} }{7}\\\\2x-3 \times \frac{x }{7}\\\\\frac{x(2x-3)}{7}\)

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Answer:

Step-by-step explanation:

Making x the subject of the formula;

y=x+z/a-x

Cross multiply

y(a-x) = x+z

ya - yx = x+z

Collect like terms

x+yx = ya - z

x(1+y) = ya - z

x = ya-z/1+y

Hence the value of x is ya-z/1+y

Answer:

\(\frac{ya-z}{1+y} = x\)

Step-by-step explanation:

\(y=\frac{x+z}{a-x}\)

Use cross multiplication

y ( a - x) =  x + z

Solve the brackets.

y a - y x = x + z

y a - y x - z = x

y a - z = x + y x

y a - z = x ( 1 + y )

Divide both sides by ( 1 + y ).

\(\frac{ya-z}{1+y} = x\)

Answer:

n

Step-by-step explanation:

The probability of drawing a red marble, regardless of the urn chosen, is: (1/6) * (1/100) + (1/6) * (2/5) + (1/6) * (2/5) + (1/6) * (1/2) + (1/6) * (1/2) + (1/6) * (1/2) = 7/30.

In the second part, Bayes' rule is used to determine the probability of drawing from each type of urn given that a red marble was drawn. Using the probabilities calculated earlier, we can apply Bayes' rule:

P(Urn 1|Red) = (P(Red|Urn 1) * P(Urn 1)) / P(Red)

P(Urn 2|Red) = (P(Red|Urn 2) * P(Urn 2)) / P(Red)

P(Urn 3|Red) = (P(Red|Urn 3) * P(Urn 3)) / P(Red)

P(Urn 4|Red) = (P(Red|Urn 4) * P(Urn 4)) / P(Red)

P(Urn 5|Red) = (P(Red|Urn 5) * P(Urn 5)) / P(Red)

P(Urn 6|Red) = (P(Red|Urn 6) * P(Urn 6)) / P(Red)

Substituting the known probabilities, we can calculate the chance of drawing from each type of urn given that a red marble was drawn.

In the last part, if all the marbles are combined into a single urn, the probability of drawing a red marble will be the sum of the red marbles divided by the total number of marbles. This probability can be calculated by adding the red marbles from each urn and dividing by the total number of marbles. However, the probability in part (a) is different from this because it considers the selection of each urn with equal likelihood, whereas in part (c), all marbles are combined into one urn.

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To simplify the indices expression x⁵y⁵z³, we can conclude that; A. bases are different, so this can't be done.

We want to simplify the indices given as;

x⁵y⁵z³

Now, we can see that the bases are different and as such it means they cannot be simplified using laws of indices on the exponents.

This is because when the bases are different, the expression cannot be factored with the exponents being added, subtracted, divided or multiplied.

Thus, we will conclude that the bases are different, so this can't be done.

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The true mean change in hemoglobin for women drinking tap and bottled water is not 0 g/dL.

a. The 95% confidence interval for the mean is (0.148, 0.772).

b. The standard error is 0.127.

c. The p-value is 0.002.

d. Using α = 0.05 and the p-value, the result of the hypothesis test is that we would reject the null hypothesis. We reject the null hypothesis because the p-value is less than α (0.002 < 0.05).

e. Based on our response to part d, we can conclude that the true mean change in hemoglobin for women drinking tap and bottled water is not 0 g/dL.

The 100-word short interpretation of the SAS output:

We can interpret that the true mean change in hemoglobin for women drinking tap and bottled water is not 0 g/dL.
The 95% confidence interval for the mean is (0.148, 0.772), which means that we are 95% confident that the true mean change in hemoglobin falls between these two values.

The standard error is 0.127, which means that the sample mean is expected to deviate from the true mean by 0.127 g/dL.

The p-value is 0.002, which is less than α (0.05), and we reject the null hypothesis.

Thus, we can conclude that the true mean change in hemoglobin for women drinking tap and bottled water is not 0 g/dL.

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Answer:

240

Step-by-step explanation:

\(L=\sqrt{{12}^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\)

\(SA=2x(5\times12\div2)+5\times6+12\times6+6\times13\)

\(=60+30+72+78\)

\(=240\)

I hope this helps you

:)

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is B.

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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The given function is f(x) = 15(1.02)^x, where x is the number of years from the date at which money is initially deposited.

This means that $15 were initially deposited into the account, and the amount grows at an annual rate of 2% (which is represented by 1.02 being raised to the power of x).

Therefore, the correct answer is: $15 were initially deposited into the account, which grows at an annual rate of 2%.

Hope I helped you...

Answer:

since total =10

Step-by-step explanation:

the probability =2/10=1/5

The solutions to the equation |-6x| = 24 are x = -4 and x = 4.

To solve the equation |-6x| = 24, we need to consider two cases: when -6x is positive and when -6x is negative.

Case 1: -6x is positive
In this case, we have -6x = 24. To solve for x, we divide both sides of the equation by -6: x = -4.

Case 2: -6x is negative
In this case, we have -(-6x) = 24, which simplifies to 6x = 24. To solve for x, we divide both sides of the equation by 6: x = 4.

Therefore, the solutions to the equation |-6x| = 24 are x = -4 and x = 4.

To check these answers, substitute them back into the original equation. For x = -4, |-6(-4)| = 24, which is true. For x = 4, |-6(4)| = 24, which is also true.

So, the solutions to the equation |-6x| = 24 are x = -4 and x = 4.

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Answer:

4.2 has a greater value

since 4.2 is greater than 3.6

Step-by-step explanation:

Since neither numbers are negative, the absolute value around the numbers do not change the values. So nothing changes and we know 4.2 is greater than 3.6

The corresponding point on the unit circle for the angle θ = 5pi/3  is given by: (0,5, -0.866).

What is the unit circle?

Basically, the unit circle is a circle with a radius of 1. It is used in trigonometry to help define and understand angles and their associated trigonometric values. The unit circle is centered at the origin (0, 0) of the coordinate plane, and each point on the circle is defined by its distance from the origin and its angle from the positive x-axis.

What is area of circle ?

The area of circle can be defined as the product of pi and square of radius of a given circle.

In this problem, we have that θ = 5pi/3 , hence:

cos θ = 0.5

sin θ = -0.866

Thus the point is (0,5, -0.866).

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The area of a rectangle is given by:

Answer:

y - 7 = - 1(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 1 and (a, b) = (4, 7) , thus

y - 7 = - (x - 4)

The equation of line in the point-slope form is y = -1x + 11

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be P = P ( 4 , 7 )

Let the slope of the line be m = -1

So , the equation of line is given by the formula

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = -1 ( x - 4 )

On simplifying the equation , we get

y - 7 = -1x + 4

Adding 7 on both sides of the equation , we get

y = -1x + 11

y = -x + 11

Therefore , the value of A is y = -x + 11

Hence , the equation of line is y = -x + 11

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The correct answer is b. Expected value. The mean of a discrete random variable generalizes the concept of expected value. The expected value of a discrete random variable is the weighted average of all possible outcomes, where the weights are the probabilities associated with each outcome.

It represents the long-term average value that we would expect to observe if we repeated the random experiment multiple times.

In the context of a discrete random variable, the mean (or expected value) is calculated by multiplying each possible value of the variable by its corresponding probability and summing them up. It provides a measure of central tendency and represents the average value we would expect to obtain from the random variable over a large number of trials.

The population mean (mean of a variable) refers to the average value of a variable in the entire population, not specifically related to a random variable. The sample mean is the average value of a variable calculated from a sample of observations. The distribution of a discrete random variable refers to the pattern of probabilities associated with each possible outcome of the variable.

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In a transportation problem, the activities correspond to the shipping lanes while the supply of each activity is the quantity shipped.

In the transportation problem, activities are the shipping lanes that are taken to transport goods from sources to destinations.

The quantities to be shipped are known as supplies or availabilities. The transportation problem is a linear programming problem that is used to determine how to allocate resources to obtain a minimum cost or maximum profit.The transportation problem is one of the most widely used problems in linear programming. It is used to solve many real-world problems such as supply chain management, production planning, and logistics.

In the transportation problem, we are given a set of sources and a set of destinations. The supply and demand at each source and destination are also given. The objective is to minimize the total cost of transporting the goods from sources to destinations while satisfying the demand and supply constraints.

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Answer:

a) 2^1

b) 2^3

Step-by-step explanation:

a) (16*2^3)/64=(2^4*2^3)/2^6=2^(4+3-6)=2^1

b) 64/2^3=2^6/2^3=2^(6-3)=2^3

Answer:

\(a. \: \: {2}^{1} \\ b. \: \: {2}^{3} \)

Step-by-step explanation:

\(a. \: \: \frac{16 \times {2}^{3} }{64} \\ \frac{ {2}^{4} \times {2}^{3} }{ {2}^{6} } \\ \frac{ {2}^{4 + 3} }{ {2}^{6} } \\ \frac{ {2}^{7} }{ {2}^{6} } \\ {2}^{7 - 6} \\ {2}^{1} \\ \)

\(b. \: \: 64 \div {2}^{3} \\ {2}^{6} \div {2}^{3} \\ {2}^{6 - 3} \\ {2}^{3} \)

Answer:

x=4

Step-by-step explanation:

\(2(x+5)=x+14\)

\(2x+10=x+14\)

\(2x-x+10=x-x+14\)

\(x+10=14\)

\(x+10-10=14-10\)

\(x=4\)

Answer:

Step-by-step explanation:

2x + 10 = x + 14

2x = x + 4

x = 4