tickets to the play cost $3 for children and $5 dollars for adults. for last bight performance there were 110 people in the audience and they made a total of 450 in ticket sales. how many children and how many adults attended the play (solve by substitution)

Answer:

This is a standard problem if GP (Geometric Progression) as the height of the ball is getting reduced by 25% every-time it touches the ground.

Step-by-step explanation:

The reason [tex]26^{23[/tex] x [tex]26^{15[/tex]  can be written as  [tex]26^{38[/tex] because both have same base and power get added.

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

We have [tex]26^{23[/tex] x [tex]26^{15[/tex]

Now, using the property of exponents and power if the base of number same and in relation of multiplication then the power get added.

So,  [tex]26^{23[/tex] x [tex]26^{15[/tex]

= [tex]26^{23 + 15[/tex]

and, 23+ 15 = 38

= [tex]26^{38[/tex]

So, the exponent can written with power of 38 as the power gets added.

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Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.

Start with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.

Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.

Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.

Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.

Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.

Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.

Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.

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Answer:(x,y)=(8/3+y/3,-3-y/2

Step-by-step explanation:

y=3x-8            3x+2y=2         next simplify

8/3+y/3           -x-2/3y=-2/3   multiply both sides by -1/3

x=8/3+y/3       -x-2/3y=-2/3   eliminate at least 1 variable

y=-3-y/2

ordered pair to the solution 0=0 & 2=2

2.5 is the length of segment AB.

What is  line segment ?

A line segment in geometry has two unique points on the line that define its boundaries. Or, a line segment is a section of the line that links two points, as another alternative.

                                   In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are fixed or identifiable.

          BD ║ AE

 Δ CBD ≈ ΔCAE by AA similarity corresponding sides are proportional .

       CB/CA = CD/DE  ⇒ CB/10 = EC - ED/16

  CB/10 = 16 - 4/16   ⇒  CB/10 = 12/16

  CB = 12 * 10/16  = 7.5

  AB= AC - CB = 10 - 7.5

  AB = 2.5

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The Answer Is A

Its hard to explain but the answer is A

Answer:

Step-by-step explanation:

3(x+5)<5(-x+18)

3x+3x5<5(-x)+5x8

3x+15<-5x+40

3x-(-5x)<40-15

3x+5x<25

8x<25

x<25/8

The t statistic table is the t-test table is used to evaluate proportions combined with z-scores.

In Statistics, a t-test, can be expressed similarly as a statistical hypothesis test where the test statistic maintains a student’s t-distribution, if the null hypothesis is set. Hence, we know we can use the t-test table here.

The t-test table is used to evaluate proportions combined with z-scores. This table is used to find the ratio for t-statistics. The t-distribution table displays the probability of t-values from a given value. The acquired probability is the t-curve area between the t-distribution ordinates, i.e., the given value and infinity.

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Answer: The final step in solving the inequality -2(5 - 4x) < 6x - 4 would be to isolate x on one side of the inequality. In the previous step (-6 < -2x), we have -2x on one side of the inequality and -6 on the other. To isolate x, we divide both sides of the inequality by -2:

-6 ÷ -2 < -2x ÷ -2

Since dividing by a negative number reverses the inequality direction, we get:

3 > x

So, the final solution to the inequality -2(5 - 4x) < 6x - 4 is x > 3. This means that all values of x that are greater than 3 satisfy the inequality.

Step-by-step explanation:

The system of equations are

a) Drama = ( 1/8 )s + 22

b) Baseball = ( 5/8 )s - 24

c) Dance = ( 1/8 )s + 27

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

Substituting the values in the equation , we get

Let the number of students be represented as s

a)

For Drama , it is 22 more than one​-eighth of the students

On simplifying the equation , we get

Drama = ( 1/8 )s + 22

b)

For Baseball , it is 24 fewer than five​-eighths of the students

On simplifying the equation , we get

Baseball = ( 5/8 )s - 24

c)

For Dance , it is 27 more than one​-eighth of the students

On simplifying the equation , we get

Dance = ( 1/8 )s + 27

Hence , the equations are solved

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The fraction of the box she puts in each bowl is, 1/10

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

To find the fraction of the box that Evangeline puts in each bowl, we need to divide the total amount of nuts in the box by the number of bowls.

The amount of nuts she has is 3/5 of a box.

To find the amount of nuts in each bowl, we need to divide 3/5 by 6:

(3/5) ÷ 6

To divide by a fraction, we can multiply by its reciprocal:

= (3/5) ÷ (6/1)

= (3/5) x (1/6)

Multiplying across, we get:

= (3/5) x (1/6)

= 3/30

= 1/10

Therefore, Evangeline puts 1/10 of the box in each bowl.

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The complete question:

Evangeline has 3/5 of a box of nuts. She uses it to fill 6 bowls. What fraction of the box does she put in each bowl.

Answer:

A metal disk 12cm in diameter and 5cm thick is melted down and cast into a cylindrical bar of diameter 5cm . How long is the bar

(D) Its mean is equal to its median is NOT a characteristic of a Normal curve.

While it is true that the mean and median are equal in a symmetrical distribution like the Normal curve, not all distributions with equal mean and median are symmetrical and Normal.

In a Normal distribution, the mean, median, and mode are equal and located at the center of the bell-shaped curve. However, in a skewed distribution, the mean and median may still be equal but the distribution will not be symmetrical or bell-shaped.

The most important continuous probability distribution in probability theory and statistics is known as the Normal Distribution, commonly known as the Gaussian Distribution.

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Answer:

12 carrots

Step-by-step explanation:

If there is 3 times as much cabbages as there is carrots, and there is 36 cabbages then you would do 36/3 because of the 3 times as much.  The answer would be 12 carrots.

36/3=12

Answer:

10 minutes

Step-by-step explanation:

21/6 will give us how much hot dogs in 1 minute

You then get 3.5 hot dogs per minute.

For 35 hot dogs do 35/3.5 which gives us the amount of time it wil take for Mika to eat 35 hot dogs

The residual value of Sally's leased car is 75%.

So, the answer is d. 75%.

To find the residual value of Sally's leased car, we can divide the value claimed by the leasing company by the original MSRP and multiply by 100 to express the answer as a percentage.

MSRP stands for Manufacturer's Suggested Retail Price. It is the price recommended by the manufacturer of a product for its retail sale.

Residual value refers to the estimated value of an asset at the end of its lease or at a specified future date. It is used in the context of lease financing or depreciation calculations and is usually expressed as a percentage of the original value of the asset. In the context of a car lease, the residual value refers to the estimated value of the car at the end of the lease term.

The residual value is:

= $28,500 / $38,000 * 100

= 75%

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The company's prime cost for January is 556000.

As per the data given:

Bodin Company manufactures finger splints for kids who get tendonitis from playing video games.

The firm had the following inventories at the beginning and end of the month of January.

                                            January 1                 January 31

The following additional data pertain to January operations.

Here we have compute the company's prime cost for January.

First add Raw materials, January 1 with Raw materials purchased and then subtract Raw materials, January 31 from this sum and then later add up the Direct labor to the result.

The final result will be the prime cost for January

Therefore the prime cost is 556000.

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The best conclusion is:

The bag contains more green Marbles than white marbles.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

The bag contains 10 green marbles and 20 white marbles.

The bag contains an equal amount of each color.

The bag contains more green than white marbles.

After 15 trials, Mark has drawn 10 green marbles and 5 white marbles

So, the Probability of Total green Marbles

= (10/15) x 30

= 20

Probability of Total White Marbles

= (5/15) x 30

= 10

So, The bag contains more green Marbles than white marbles.

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The solution of the system of equations is equal to (2, 3).

In Mathematics, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (2, 3).

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An expression which shows the money spent per test tube is u = 6/3.

Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the unit price, we would determine the unit rate for one pack of 3 test tubes by using the following mathematical expression;

Unit price = Cost of test tubes/Number of test tubes

Substituting the given parameters into the unit price formula, we have the following;

Unit price = $6/3

Unit price = $2.

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62kg is equivalent to approximately 136.7 pounds and both are unit of measurement of weight.

The conversion factor from kilograms to pounds is 2.20462. To convert kilograms to pounds, you simply multiply the weight in kilograms by this conversion factor.

Therefore, to convert 62kg to pounds, we can multiply 62 by 2.20462, which gives us approximately 136.7 pounds.

It's important to note that kilograms and pounds are both units of weight, but they are used in different parts of the world. Kilograms are the standard unit of weight in most countries, while pounds are commonly used in the United States and some other countries.

When traveling or communicating with people from different countries, it's important to be able to convert between different units of measurement.

Online converters or calculators can be useful tools to quickly and accurately convert between kilograms and pounds, or other units of measurement, as needed.

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Microeconomics is a branch of economics that focuses on the behavior of individuals and firms in making decisions regarding the allocation of limited resources

Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions about the allocation of limited resources, specifically focusing on the interaction of supply and demand in specific markets and how different factors influence the behavior of individuals and firms. It is concerned with the study of how people and firms make decisions about production, consumption, and distribution of goods and services.

Microeconomics analyzes how supply and demand in specific markets interact to determine the prices of goods and services. It also examines how different factors, such as taxes, government regulations, and technological changes, affect the behavior of individuals and firms.

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(1) The predetermined overhead rate is $10.50 per direct labor-hour.

(2) Mr. Wilkes' total job cost is $960.

(3) Speedy Auto Repairs would have charged Mr. Wilkes $1344 for the job.

1) To compute the predetermined overhead rate, we need to add the fixed and variable overhead costs, and then divide by the estimated direct labor-hours:

$114,000 + ($1.00 * 12,000) = $126,000

Predetermined overhead rate = $126,000 / 12,000 = $10.50 per direct labor-hour

2) To find Mr. Wilkes' total job cost, we need to add up the costs of the direct materials and direct labor, and then apply the predetermined overhead rate to the direct labor hours used:

Direct materials cost: $626

Direct labor cost: $292

Total direct costs: $626 + $292 = $918

Overhead cost: $10.50 * 4 = $42

Total job cost: $918 + $42 = $960

3) To find the selling price, we need to add a markup of 40% of the total job cost:

Total job cost: $960

Markup: 40% * $960 = $384

Selling price: $960 + $384 = $1344

So, Speedy Auto Repairs would have charged Mr. Wilkes $1344 for the job.

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Answer:

[tex]\huge\boxed{\sf 14\ times}[/tex]

Step-by-step explanation:

[tex]\displaystyle Probability = \frac{Possible \ no. \ of\ events}{Total \ number\ of \ events}[/tex]

If we roll a die 1 time, the probability of obtaining a 3 is:

= 1 / 6

Because a die has total 6 faces, out of which 3 is only 1.

But, if we roll it 84 times, it becomes:

= [tex]\displaystyle \frac{1}{6} \times 84[/tex]

= 84/6

[tex]\rule[225]{225}{2}[/tex]

The equation of a line perpendicular to line y = 8/3x-5 in slope-intercept form that contains point (-2, -2) is y = -3x/8 - 11/4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

8/3 × m₂ = -1

m₂ = -3/8.

At data point (-2, -2), a linear equation of this line can be calculated in point-slope form as follows:

y - (-2) = -3/8(x - (-2))

y + 2 = -3/8(x + 2)

y = -3x/8 - 3/4 - 2

y = -3x/8 - 11/4

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The requried area of the shaded region is 4.56 square centimeters.

The area of a circle is given by the pie times square of the radius.

Area of circle = πr²

Here,
A right triangle is inscribed in a circle where the diameter of the circle is the hypotenuse of the right triangle,
So from the figure,
The area of the shaded region is given by the difference between the semi-circle LMN and the area of the right triangle LMN

The diameter of the circle is given by trig ratios,
sin 45 = 4/d

d = 4√2 So the radius will be d = 2√2

Now,
As hypotenuse is the diameter of the circle,
So LM = MN

Now,
Area of shaded region = area of semi-circle - an area of a triangle
Area of shaded region = πr²/2 - 1/2 × base × height

Area of the shaded region = 3.14 × [2√2]²/2 - 1/2 × 4 × 4
Area of shaded region = 4.56 cm²

Thus, the requried area of the shaded region is 4.56 square centimeters.

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The prime factorization of 56 is the process of breaking 56 down into its prime factors. The prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.

One way to calculate the prime factorization of 56 is to use a factor tree. To begin, find two numbers that multiply together to equal 56. The two factors that multiply together to equal 56 are 8 and 7. Since 8 and 7 are both prime numbers, they can be written as the prime factors of 56: 56 = 8 x 7.In mathematical terms, the prime factorization of 56 can be expressed as 56 = 2 x 2 x 2 x 7, where 2 is multiplied by itself three times and then multiplied by 7. This is because 56 can also be written as 2 x 2 x 2 x 7, which is the same as 8 x 7.The prime factorization of 56 can also be expressed as the product of the prime exponents: 56 = 2^3 x 7^1. Here, 2 is raised to the third power, and 7 is raised to the first power. This expression is equivalent to 8 x 7.In summary, the prime factorization of 56 is 8 x 7, 2 x 2 x 2 x 7, or 2^3 x 7^1.

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Answer:

Below

Step-by-step explanation:

f(x) =  x^2+ 6x -5     Use Quadratic Formula with a = 1     b = 6      c = -5

to find :

x =  - 3 ± [tex]\sqrt{17}[/tex]

The average rate of change of f(x) over the interval is 15/7

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table, we have

f(-3) = -4

f(4) = 11

The average rate is then calculated as

Average rate = [f(4) - f(-3)]/[4 + 3]

Substitute the known values in the above equation, so, we have the following representation

Average rate = (11 + 4)/(4 + 3)

Evaluate

Average rate = 15/7

Hence, the average rate is 15/7

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Complete question

Find the average rate of change on the interval [-3, 4].

X f(x)

-3 -4

4 11