Members of the theater club sold tickets for the spring
musical. On Friday night, they made $125 in presales a
sold 120 tickets at the door. For the Saturday night sho
they earned $180 in presales and sold 110 tickets at the
door, If the theater club earned the same amount each
night, what is t, the cost per ticket?

Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

The measurement that is closest to the volume of the cylinder in cubic feet is: 15.7 Feet. (Option B)

Recall that volume is

V = πr²h

Given:

h = 5 feet

r = 2/2 = 1

Hence

V = 5 x 1 x 22/7

= 15.7142857143

Hence, the cylinders volume in cubic feet is given as:

\($\approx$\) 15.7 ft

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Answer: 15.7 ft3

Step-by-step explanation:

Answer:

n = 17-13

Step-by-step explanation:

n+13=17

Subtract 13 from each side

n+13-13 = 17-13

n = 17-13

Approximately 17 students who took the optional class passed their driver's test.

Let's solve this problem step by step.

We are given the following information:

28 out of 75 students who took the optional class passed their driver's test.

8 out of 15 students overall passed their driver's test.

3 out of 5 students took the optional class.

To find the number of students who took the optional class and passed, we need to calculate the intersection of these two groups.

First, let's calculate the total number of students who took the optional class:

Total students who took the optional class = (3/5) \(\times\) Total number of students

Total students who took the optional class = (3/5) \(\times\) 75 = 45

Now, let's calculate the total number of students who passed their driver's test:

Total students who passed their driver's test = (8/15) \(\times\) Total number of students

Total students who passed their driver's test = (8/15) \(\times\) 75 = 40

Next, let's find the number of students who both took the optional class and passed their driver's test.

This can be found by taking the intersection of the two groups:

Number of students who took the optional class and passed = (28/75) \(\times\)Total students who took the optional class

Number of students who took the optional class and passed = (28/75) \(\times\)45 = 16.8 (approximated to the nearest whole number).

Therefore, approximately 17 students who took the optional class passed their driver's test.

It's important to note that since we're dealing with whole numbers, the approximated answer is 17, as we cannot have a fraction of a student.

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Answer:

Step-by-step explanation:

The equation is number of muffins left = 34 - 17 And the solution is number of muffins left = 17

Let's define the variables:

M = Number of muffins Mary baked originally (34 muffins)

G = Number of muffins given to her neighbour (17 muffins)

The equation that represents the number of muffins Mary had left after giving some to her neighbour is:

Number of muffins left = Original number of muffins - Number of muffins given

M - G

Substitute the values:

Number of muffins left = 34 - 17

Solving this equation:

Number of muffins left = 17

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Answer:

51

Step-by-step explanation:

Answer:

25 hits

Step-by-step explanation:

you would divide 1000 by 40 and get 25

The correct option of the given question is option (c)  fissure.

When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is c. fissure.

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The main term to reference in the index when coding the phrase "supravesical fissure of urinary bladder" is c. fissure.

In medical coding, the index is typically organized alphabetically based on the main terms or significant words within medical terminology. In this case, "fissure" is the main term that represents the specific condition or anatomical feature being coded.

The other terms, such as "urinary," "bladder," and "supravesical," provide additional context but are not the primary focus when searching for the appropriate code in the index.

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Answer:

the sample space for the first and second cow walking out of the barn is {HH, HG, GH, GG}

Step-by-step explanation:

The sample space for the first and second cow walking out of the barn is the set of all possible combinations of the first and second cow. Since there are two types of cows (Holstein and Guernsey), and the order in which the cows walk out of the barn matters, the sample space has four possible outcomes:

The first cow is a Holstein and the second cow is a Holstein: HH

The first cow is a Holstein and the second cow is a Guernsey: HG

The first cow is a Guernsey and the second cow is a Holstein: GH

The first cow is a Guernsey and the second cow is a Guernsey: GG

The sample space for the 1st and 2nd cow walking out of the barn is {HH, HG, GH, GG}.

A sample space is the set which contains all the possible outcomes of a random experiment. Usually, it is represented using the letter S.

Discrete or finite sample spaces contain finite number of elements.

Event is the subset of sample space.

Here, there are two kind of elements in the experiment, H and G.

So there are 4 possible outcomes.

Holstein walk out of the barn first and then Holstein = HH

Holstein walk out of the barn first and then Guernsey = HG

Guernsey walk out of the barn first and then Holstein = GH

Guernsey walk out of the barn first and then Guernsey = GG

Hence the sample space for this random experiment is  {HH, HG, GH, GG}.

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Answer:

12 pens

Step-by-step explanation:

25% basically means 25/100 which is simplified to 1/4. Now if 3 pens are 1/4 of all the pens, then you multiply 3 by 4 to give you 12 pens in all.

Answer:

Alex has 12 pens altogether !

Step-by-step explanation:

- 25% = 25/100

- 25% × 4 = 100%

- 3 × 4 = 12

The probability that a randomly selected customer had at least one order in the previous month or uses express shipping is 0.9242.

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to measure the likelihood or chance of an event occurring, ranging from impossible (0 probability) to certain (1 probability).

The basic concept of probability involves determining the ratio of the number of favorable outcomes to the total number of possible outcomes. This ratio is expressed as a fraction, decimal, or percentage.

For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2 or 0.5 or 50%, and the probability of getting tails is also 1/2 or 0.5 or 50%.

P( at least one order in the previous month or uses express shipping)

=P(at least one order in the previous month) + P(uses express shipping) - P(at least one order in the previous month and uses express shipping)

\(\frac{107+63}{211} +\frac{131}{211} -\frac{65+41}{211}\)

= 0.9242

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option C is correct......

Answer;

WUV = 36

Explanation:

Here is what we get when we draw the figures

Now we know that the sum of the interior angles of a triangle must equal 180 degrees; therefore,

Also, angle y and VWX are supplementary; therefore,

Now, solving for y in the above gives

Putting this value of y in the first equation gives

Expanding and simplifying the left-hand side gives

Subtracting 214 from both sides gives

Finally, dividing both sides by -3 gives

With the value of x in hand, we now find the measurement of WUV:

Hence, WUV = 36,

Answer: 28x+8y+2 .

= -2 (-14x-4y-1)

= 28x + 8y + 2

Step-by-step explanation:

Answer: 28x + 8y + 2

Step-by-step explanation:

-2(3x+12y-5-17x-16y+4)

= -2(3x-17x+12y-16y-5+4)

= -2(-14x-4y-1)

= -2(-14x) -2(-4y) -2(-1)

= 28x+8y+2

There are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

To find the number of unique 4-digit integers (excluding leading zeros) where the sum of the digits is 6, we can use a combinatorial approach.

Let's consider the four digits as four distinct positions: A, B, C, and D. The sum of the four digits is 6, so we need to distribute these six units among these four positions.

We can solve this problem using stars and bars. Imagine we have six stars (representing the six units) and three bars (representing the three dividers between the positions). The bars help us separate the units into four distinct positions.

For example, if we have the configuration "* | * * | * * | *," it represents the digits 1, 2, 2, and 1. The sum of these digits is 6.

The number of ways to arrange the six stars and three bars is given by the binomial coefficient (6 + 3 choose 3). Using the formula for combinations, we have:

(6 + 3) C 3 = (9 C 3) = 9! / (3! * (9 - 3)!) = 84.

So, there are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

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Answer:

100 CD's

Step-by-step explanation:

250-175 is 75. and if yu subtract 175 by 75, you get 100. so 100 CD's

Answer:

7√3

Step-by-step explanation:

A company received 15 funding applications and want to select 8 of them to be funded. The number of different lists of successful applications is 6,435

Suppose we have n objects in total and we want to select r objects among total objects, the number of ways they can be selected is given by the combination formula:

ⁿCr = n! / [r! (n-r)!]

Data from the problem:

n = total applications = 15

r = number of selected applications = 8

Hence, the number of different lists of successful applications is:

¹⁵C₈ = 15! / [8! (15-8)!]

       = 15! / [8! 7!]

       = 6,435

Thus, the number of different lists can be selected is 6,435

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Answer: O A. f-¹(x)=√x - 2 + 3

Step-by-step explanation: ( x ) = 3 x + 2 f(x)=3x+2 f(x)=3x+2f, left parenthesis, x, right parenthesis, equals, 3, x, plus, 2.

Answer:

(a) angle ACB is not proper way

Answer:

A.

Step-by-step explanation:

We can read the angle with the labels found in answers B, C and D.

1. The solutions to the equation x³ ≡ 1 (mod 30) are x ≡ 1, 11, or 19 (mod 30).

2. The equation x³ + 8x - 5 ≡ 0 (mod 125) has a unique solution, which is x ≡ 48 (mod 125).

1. To find the solutions to the equation x³ ≡ 1 (mod 30), we need to find values of x that satisfy the congruence relation. Since 30 can be factored as 2 * 3 * 5, we can solve the congruence modulo 2, 3, and 5 separately.

For the congruence modulo 2, we have x³ ≡ 1 (mod 2). The only possible value for x modulo 2 is x ≡ 1 (mod 2) since any other value cubed will give an odd result.

For the congruence modulo 3, we have x³ ≡ 1 (mod 3). By trying out values of x modulo 3, we find that x ≡ 1 (mod 3) and x ≡ 2 (mod 3) satisfy the congruence.

For the congruence modulo 5, we have x³ ≡ 1 (mod 5). By trying out values of x modulo 5, we find that x ≡ 1 (mod 5), x ≡ 4 (mod 5), and x ≡ 6 (mod 5) satisfy the congruence.

Now, we can use the Chinese Remainder Theorem to find the values of x modulo 30 that satisfy all the congruences. The solutions are x ≡ 1, 11, or 19 (mod 30), as these values satisfy all the individual congruences.

In summary, the solutions to the equation x³ ≡ 1 (mod 30) are x ≡ 1, 11, or 19 (mod 30).

2. To find the solution to the equation x³ + 8x - 5 ≡ 0 (mod 125), we can use the concept of polynomial congruences. We want to find a value of x that satisfies the congruence relation.

We start by trying out values of x modulo 125 and calculate the corresponding value of the polynomial. By doing so, we find that x ≡ 48 (mod 125) is the only value that makes the polynomial congruent to zero modulo 125.

To verify this, we substitute x ≡ 48 (mod 125) into the equation x³ + 8x - 5 and calculate the result modulo 125:

(48)³ + 8(48) - 5 ≡ 110592 + 384 - 5 ≡ 110971 ≡ 0 (mod 125)

Since the result is congruent to zero modulo 125, x ≡ 48 (mod 125) is indeed a solution to the equation.

In conclusion, the equation x³ + 8x - 5 ≡ 0 (mod 125) has a unique solution, which is x ≡ 48 (mod 125).

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Answer:

The quotient of 24 and d would be \(\frac{24}{d}\)

Step-by-step explanation:

Quotient is the answer of a division problem. So, you would divide 24 by d.

The equivalent effective bi-weekly rate is approximately 0.01456%.

To find the equivalent effective bi-weekly rate, we need to convert the given nominal rate \(i^{(2)} =1.45000\%\) to the effective rate for a bi-weekly period.

The formula to convert a nominal rate to an effective rate is \(i^{(m)} =(1+r/m)^{m}-1\), where \(i^{(m)}\) is the effective rate, r is the nominal rate, and m is the number of compounding periods per year.

In this case, we have a nominal rate \(i^{(2)}\) that corresponds to a semi-annual compounding (2 periods per year). We can plug the values into the formula and calculate the effective rate \(i^{(bi-weekly)}\) for a bi-weekly period.

\(i^{(bi-weekly)}=(1+1.45000/2/100)^{2}-1\)

Calculating the expression:

\(i^{bi-weekly}=(1+0.00725)^{2} -1\\i^{bi-weekly}= 1.0145640625-1\\i^{bi-weekly}= 0.0145640625\)

The equivalent effective bi-weekly rate is approximately 0.01456%.

Among the given options, none of them match the calculated value exactly.

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We will investigate how to use the difference of two squares theorem to determine a solution to the equation.

The equation at hand is as follows:

We will move all the terms on the left hand side of the " = " sign as follows:

The difference of two squares theorem states that:

We see from the above form that we have the following:

Using the difference of two squares formulation we can re-write as a multiple of two factors:

Then the factorized equation becomes:

The solution of the equation becomes:

We can condense our solution in the form:

Answer:

Your parents took your family out to dinner. Your parents wanted to give the waiter a 15% tip. If

the total amount of the dinner was $42.00, what should be paid to the waiter

.06 x 860 =51.60 of tax.

Total for Stereo is 911.60

The equation for the demand curve is Q = a - bP, where Q represents the quantity demanded, P represents the price of the product, a represents the intercept of the demand curve, and b represents the slope of the demand curve.

The equation for the demand curve is a fundamental concept in economics that helps us understand the relationship between the price of a product and the quantity of the product that consumers are willing to buy at that price.

The equation is typically expressed as:

Q = a - bP

The equation shows that as the price of a product increases, the quantity demanded decreases, and vice versa. This is known as the law of demand. It reflects the inverse relationship between price and quantity demanded.

The demand curve is downward sloping because of this inverse relationship. It slopes downwards from left to right, indicating that as the price decreases, the quantity demanded increases, and as the price increases, the quantity demanded decreases.

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The number of each type of coins are as follows:

q = 15 quarters.

d = 30 dimes.

n = 25 nickels.

In order to solve this word problem, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let d represent the number of dimes.

Let q represent number of quarters.

Let n represent number of nickels.

Let T represent total number of coins.

Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.

Translating the word problem into an algebraic equation, we have;

Dimes; d = 2q     .....equation 1.

Nickels; (70 - (q + 2q)) = (70 - 3q)     .....equation 2.

Total coins; T = n + d + q

0.5(70 - 3q) + 2q(0.1) + q(0.25) = 8.00

Multiplying all through by 100, we have:

5(70 - 3q) + 2q(10) + q(25) = 800

350 - 15q + 20q + 25q = 800

350 + 30q = 800

30q = 800 - 350

30q = 450

q = 450/30

q = 15 quarters.

For the number of dimes, we have:

Dimes, d = 2q

Dimes, d = 2(15)

Dimes, d = 30 dimes.

For the number of nickels, we have:

Nickels, n = (70 - 3q)

Nickels, n = (70 - 3(15))

Nickels, n = (70 - 45)

Nickels, n = 25 nickels.

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Answer:

A

Step-by-step explanation:

The answer is negative so that eliminates one

and the greater sign is opposite of b so that makes the answer A!

Answer:

(x - 4)

Step-by-step explanation:

Given

x² + 2x - 24

Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (+ 2)

The factors are + 6 and - 4, since

6 × - 4 = - 24 and 6 - 4 = + 2, thus

x² + 2x - 24 = (x + 6)(x - 4) ← in factored form

Thus the other factor is (x - 4)

The solution is Option D.

The equation x² + 2x - 24 = 0 has the factors as ( x + 6 ) and ( x - 4 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

x² + 2x - 24 = 0   equation (1)

The equation can be factorized as

x² + 6x - 4x - 24 = 0

Taking x as the common factor , we get

x ( x + 6 ) - 4 ( x + 6 ) = 0

So , the equation will be

( x + 6 ) ( x - 4 ) = 0

Therefore , the factors of x are -6 and 4

Hence , the factors of the equations are ( x + 6 ) and ( x - 4 )

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