How to solve it and the answer

Answer:

If ticket sales were $3,000 for 400 tickets then 280 students attended the play.

Step-by-step explanation:

The solutions to the equation -b² + 2b = 0 are b = 0 and b = 2.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), which are connected by an equals sign (=). The expressions on each side of the equals sign can be made up of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation can be solved to find the value of the variable(s) that makes both sides of the equation equal.

To find the solution of -b²+ 2b = 0, we can use algebraic manipulation as follows:

-b² + 2b = 0

Factor out -b:

-b(b - 2) = 0

From this equation, we see that either -b = 0 or b - 2 = 0:

-b = 0 or b - 2 = 0

Solving for b in each case, we get:

-b = 0 --> b = 0

b - 2 = 0 --> b = 2

Therefore, the solutions to the equation -b² + 2b = 0 are b = 0 and b = 2.

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Therefore, the graph of the given set is: closed circles on 1 and 4 with a line segment between.

A common form for an algebraic expression is one of the following: addition, subtraction, multiplication, or division. Simplify the values to determine the result.

The expression (x I x ≤ 1) U (x I x ≥ 24) represents the set of all values of x that are less than or equal to 1 or greater than or equal to 24.

the graph of this set will have a closed circle at x=1 and a closed circle at x=24

The arrows pointing outward indicate that the set continues indefinitely in both directions.

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Answer:

hm

Step-by-step explanation:

The reason why it is possible to draw two different rectangles that have an area of 30 square inches is that there are multiple pairs of whole numbers that multiply to 30. For example, a rectangle with dimensions 5 inches by 6 inches has an area of 30 square inches, and so does a rectangle with dimensions 2 inches by 15 inches.

However, the number 7 is a prime number, which means it can only be divided evenly by 1 and itself. Therefore, the only way to get an area of 7 square inches for a rectangle is by multiplying 1 and 7, which means the dimensions of the rectangle would be 1 inch by 7 inches. Since there are no other pairs of whole numbers that multiply to 7, it is not possible to draw two different rectangles with an area of 7 square inches.

Answer:

C

Step-by-step explanation:

using the sine ratio and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 5[tex]\sqrt{2}[/tex]

The smaller number is 6 .

The larger number is 22

Let's let x be the smaller number and y be the larger number.

From the problem, we know that one number is eight less than five times the other, so we can write:

y = 5x - 8

We also know that the sum of the two numbers is 28, so we can write:

x + y = 28

Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.

Let's solve the first equation for x

x = (y + 8)/5

Now we can substitute this expression for x into the second equation:

(y + 8)/5 + y = 28

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 8 + 5y = 140

Combining like terms, we get:

6y + 8 = 140

Subtracting 8 from both sides, we get:

6y = 132

Dividing both sides by 6, we get:

y = 22

Now we can use the equation y = 5x - 8 to solve for x:

22 = 5x - 8

Adding 8 to both sides, we get:

30 = 5x

Dividing both sides by 5, we get:

x = 6

Therefore, the smaller number is 6 and the larger number is 22.

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Answer:

Adult tickets: 145

Child tickets: 290

Step-by-step explanation:

Let x = adults; y = children

[tex]\left \{ {{x + y=435} \atop {6.50x+2.50y=1667.50}} \right.[/tex]

=> x = adults = 145

    y = children = 290

The correct Repeating or Non-repeating decimals are-

Repeating - 2.23(bar) , 3.426(bar) , 4.321321....

Non-repeating - 1.01011

As fractions and decimals both represent portions of a whole, many decimals can be expressed as fractions. "Rational numbers" are defined as decimals that can be expressed as fractions. "Irrational numbers" are decimals that cannot be expressed as a fraction.

Repeating decimals: The decimals which will not end and the number will repeat again and again.

Repeating - 2.23(bar) , 3.426(bar) , 4.321321....

Non-repeating: These decimals will not have the repeating numbers after the decimal poins.

Non-repeating - 1.01011

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a. The converse, inverse and contrapositive are "If you cannot attend this movie, then you are under age 17.", "If you are over age 16, then you can attend this movie." and  "If you can attend this movie, then you are not under age 17."

The original statement is an example of a conditional statement, which is a statement of the form "if A, then B." The part that comes after "if" is called the hypothesis, and the part that comes after "then" is called the conclusion.

To find the converse of the statement, we switch the hypothesis and conclusion. The converse of a conditional statement may or may not be true. In this case, the converse is not true.

To find the inverse of the statement, we negate both the hypothesis and conclusion. The inverse of a conditional statement may or may not be true. In this case, the inverse is not true.

To find the contrapositive of the statement, we switch and negate both the hypothesis and conclusion. The contrapositive of a conditional statement is always true if the original statement is true. In this case, the contrapositive is true.

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The ratio between yellow to red is 1 to 2 or 1:2. Answer: not listed.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

First, we can use the given information to find the ratio between green and yellow:

6 yellow = 5 green

=> green/yellow = 6/5

Next, we can use the given information to find the ratio between purple and green:

4 green = 3 purple

=> purple/green = 4/3

Finally, we can use the given information to find the ratio between red and purple:

5 purple = 2 red

=> red/purple = 5/2

To find the ratio between yellow and red, we can combine these ratios and simplify:

green/yellow = 6/5

=> yellow/green = 5/6

purple/green = 4/3

=> green/purple = 3/4

red/purple = 5/2

=> purple/red = 2/5

yellow/green * green/purple * purple/red = yellow/red

(5/6) * (3/4) * (2/5) = 1/2

Therefore, the ratio between yellow to red is 1 to 2 or 1:2. Answer: not listed.

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The answer is 1,764 in^2

Answer: option (a) and option (e).

Step-by-step explanation:

Answer:

(a) and (e) are correct

Step-by-step explanation:

(a) x² + (y - 3)² = 6²

(b) x² + (y - 5)² = (√6)²

(c) (x - 4)² + y² = 6²

(d) (x + 6)² + y² = 12²

(e) x² + (y + 8)² = 6²

The general equation of a circle is:

(x - a)² + (y - b)² = r², where (a, b) represents the x-y coordinates of the centre, and r represents the radius.

Hence, by process of elimination, the options that have a diameter of 12 units and therefore, a radius of 6 units, are (a), (c), and (e).

Therefore, the correct choices are (a), and (e), as (c) has a circle centre of (4,0) and does not lie on the y-axis.

Answer:

6xy^2 + 9(xy)^2.dy/dx

Step-by-step explanation:

d/dx(3x^2.y^3)=

3y^2.d/dx(x^2) + 3x^2.d/dx(y^3)      [Using uv rule, d/dx(uv)=u.dv/dx +v.du/dx]

= 3y^2.2x + 3x^2.3y^2.dy/dx

= 6xy^2 + 9(xy)^2.dy/dx

Answer:

a) 5x/16

b) x = 32

Step-by-step explanation:

a) x/8 + 3x/16 can be simplified by getting a common denominator. x/8 can be changed like this:

x/8 × 2/2 is 2x/16

now we have:

2x/16 + 3x/16

= 5x/16

b) solve x/8+3x/16=10

change the left side of the equation as in part a.

5x/16 = 10

multiply both sides of the equation by 16

5x = 160

divide by 5

x = 32

Answer:

7 batches

hope this helps

Step-by-step explanation:

1 n (batches of dumpling wrappers) = 3 cups flour

n = 21 / 3

n = 7

The chef can make 7 batches of dumpling wrappers :D.

Standard deviation does not mean independent events.

No, the standard deviation is a measure of the spread or variability of a set of data. It measures how much the individual data points in a dataset deviate from the mean or average of the dataset.

Independence, on the other hand, refers to the relationship between two or more events, where the occurrence of one event does not affect the probability of the other event occurring.

Standard deviation is not directly related to the concept of independence. However, when calculating the standard deviation of a dataset, it assumes that each data point is independent and identically distributed. This means that the value of one data point does not affect the value of another data point, and that each data point is drawn from the same underlying distribution.

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we can replace the second occurrence of x = -2 with x = 1:

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

For the table to be a function, each x-value must correspond to a unique y-value. To determine the missing x-value, we need to find if there are any repeated x-values with different y-values.

The x-value 3 is paired with y-values -3 and -1, which means that the table is not a function. Therefore, we need to replace one of the x-values that appears twice with a different value.

Since x = 0 is already paired with y = 5, we cannot use 0 as the replacement. The only other x-value that appears more than once is x = -2. Therefore, we can replace one of the occurrences of x = -2 with a different value.

For example, we can replace the second occurrence of x = -2 with x = 1:

x    y

3   -3

1    4

-2  -1

-2  -2

0    5

Now each x-value corresponds to a unique y-value, so the table represents a function.

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Answer:

Ten times greater

Step-by-step explanation:

700 x 10 = 7000

Answer:

it will be ten times greater

Step-by-step explanation:

Answer: Since we know that cos A = 3/10, we can use the Pythagorean identity to find sin A:

sin^2 A + cos^2 A = 1

sin^2 A = 1 - cos^2 A

sin A = sqrt(1 - cos^2 A)

Substituting cos A = 3/10, we get:

sin A = sqrt(1 - (3/10)^2)

sin A = sqrt(1 - 9/100)

sin A = sqrt(91)/10

Since we also know that tan A < 0, we know that the sine and tangent of A have opposite signs, and therefore sin A is negative.

Therefore:

sin A = -sqrt(91)/10

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

To find out how many bunches of each flower the shop should order, we need to calculate the percentage of customers who preferred each flower, and then use that percentage to estimate the number of bunches needed for each flower.

First, we need to calculate the total number of customers who were surveyed:

Total customers surveyed = 8 + 4 + 8 + 20 = 40

Next, we can calculate the percentage of customers who preferred each flower:

Percentage of customers who preferred daisy = (8/40) x 100% = 20%

Percentage of customers who preferred gardenia = (4/40) x 100% = 10%

Percentage of customers who preferred mum = (8/40) x 100% = 20%

Percentage of customers who preferred rose = (20/40) x 100% = 50%

Now, we can use these percentages to estimate how many bunches of each flower to order.

Let's assume that each bunch contains 10 flowers (this is just an example, the actual number may vary):

Number of bunches of daisy to order = 20% of 50 bunches = 10 bunches

Number of bunches of gardenia to order = 10% of 50 bunches = 5 bunches

Number of bunches of mum to order = 20% of 50 bunches = 10 bunches

Number of bunches of rose to order = 50% of 50 bunches = 25 bunches

So, the shop should order 10 bunches of daisy, 5 bunches of gardenia, 10 bunches of mum, and 25 bunches of rose to meet the expected demand on Sunday.

a) The angular velocity of the wheel is approximately 1.0667 radians per second. b) The wheel will spin at approximately 10.16 revolutions per minute.

Angular velocity is a measure of how quickly an object rotates or revolves around a fixed point, such as an axis or a center of rotation. It is a vector quantity that describes the rate of change of an object's angular position with respect to time, and is usually expressed in units of radians per second (rad/s) or degrees per second (deg/s).

a) To find the angular velocity of the wheel, we can use the formula:

angular velocity = linear velocity / radius

In this case, the linear velocity of the hamster is 16 centimeters per second, and the radius of the wheel is 15 centimeters. So, we have:

angular velocity = 16 / 15

angular velocity = 1.0667 radians per second

Therefore, the angular velocity of the wheel is approximately 1.0667 radians per second.

b) To find the speed of the wheel in revolutions per minute, we need to convert the angular velocity from radians per second to revolutions per minute. There are 2π radians in one revolution, and 60 seconds in one minute. So, we can use the following formula:

angular velocity (in revolutions per minute) = angular velocity (in radians per second) * 60 / 2π

Plugging in the angular velocity we found in part (a), we get:

angular velocity (in revolutions per minute) = 1.0667 * 60 / 2π

angular velocity (in revolutions per minute) ≈ 10.16 revolutions per minute

Therefore, the wheel will spin at approximately 10.16 revolutions per minute.

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A41 represents the element at the line 4 and column 1, which is the same for B41.

When two matrices are added or subtract, we add or subtract the elements at the same position.

The elements are:

Hence:

When a matrix is multiplied by a constant, each element is multiplied by a constant, hence:

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Okay, here are the steps to find the probability the randomly selected pitcher is left-handed:

1) There are 1 left-handed starter, 4 right-handed starters, 2 left-handed relievers and 1 right-handed reliever.

2) In total, there are 1 + 4 + 2 + 1 = 8 pitchers.

3) Of the 8 pitchers, 1 + 2 = 3 are left-handed.

4) So the probability the randomly selected pitcher is left-handed = (3/8) = 3/8 = 0.375

Therefore, the probability that the randomly selected pitcher from the team is left-handed is 0.375.

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the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $[tex]570.[/tex]

To calculate the total cost of the car rental, we need to first determine the rental rate for a compact car for 8 days, including the optional insurance.

The daily rental rate for a compact car is $ [tex]56,[/tex] and the optional insurance costs $10 per day. Therefore, the total daily cost of renting a compact car with insurance is:

[tex]56 + 10 = 66[/tex]

To determine the total cost of renting the compact car for 8 days, we simply multiply the daily cost by the number of days:

[tex]66 \times 8 = $528[/tex]

Next, we need to determine the cost of gasoline if Nate returns the car without a full tank. The gasoline charge is $ [tex]3.50[/tex] per gallon, but we don't know how many gallons Nate will need to fill up the tank.

If we assume that a compact car has a gas tank capacity of around 12 gallons, and that Nate will need to refill the tank to its full capacity, then the gasoline charge would be:

$[tex]3.50 \times 12 = $42[/tex]

Finally, we can calculate the total cost of the rental, including the optional insurance and the gasoline charge if Nate returns the car without a full tank:

$[tex]528 + $42 = $570[/tex]

Therefore, the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $[tex]570[/tex].

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The statement that describes the mean number of hours worked through which the relation is satisfied is The mean is the highest number or hours worked by any students in the group

What about mean?

In mathematics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is often called the arithmetic mean, and it is calculated by adding up all the values in the set and then dividing the result by the total number of values.

The formula for the mean is:

mean = (sum of all values) / (total number of values)

For example, suppose we have a set of four numbers: 2, 5, 8, and 11. To find the mean of this set of numbers, we add them up and divide by the total number of values:

mean = (2 + 5 + 8 + 11) / 4

mean = 26 / 4

mean = 6.5

Therefore, the mean of this set of numbers is 6.5. The mean is a commonly used measure of central tendency in statistics and data analysis, and it provides a way to summarize the general trend or average of a data set.

According to the given information:

Mean of the given condition is,

⇒    [tex]\frac{3 + 5 + 4 + 4 + 2 + 5}{6}[/tex]

⇒    [tex]\frac{23}{6}[/tex]

⇒    3.83 mean of the given condition.

So, it indicate that The mean is the highest number or hours worked by any students in the group.

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a) The degree of the interpolant is 3.

b) Required system of equations are

[tex]a_0 + 3a_1 + 9a_2 = 4 \\ a_0 + 5a_1 + 25a_2 = 80 \\ a_0 + 7a_1 + 49a_2 = 188 \\ a_0 + 10a_1 = 245 \\ a_0 + 13a_1 = 305 \\ a_0 + a_1 + a_2 + a_3 = 9 \\ a_0 + 2a_1 + 4a_2 + 6a_3 = 15 \\ a_0 + 4a_1 + 16a_2 + 36a_3 = 87 \\ a_0 + 6a_1 + 36a_2 + 216a_3 = 279[/tex]

c) Required Vandermonde matrix corresponding to the system of equations are [ 1 3 9; 1 5 25; 1 7 49], [1 10; 1 13], [1 1 1 1; 1 2 4 6; 1 4 16 36; 1 6 36 216].

a) How to determine the degree of the interpolant?

To determine the degree of the interpolant, we count the number of data points in each set, subtract one, and take the minimum of the resulting values. This is because a polynomial of degree n can exactly interpolate n+1 distinct data points.

For the first set, we have 3 data points, so the interpolant can have degree at most 2.

For the second set, we have 2 data points, so the interpolant can have degree at most 1.

For the third set, we have 4 data points, so the interpolant can have degree at most 3.

b) How to find the interpolant for each set?

To find the interpolant for each set, we need to solve a system of equations. Let f(x) be the interpolant for each set, and let [tex]x_i[/tex] be the x-coordinate of the ith data point, and yi be the corresponding y-coordinate. Then we need to find the coefficients [tex]a_0, a_1, ..., a_n[/tex] such that [tex]f(x_i) = a_i(x_i)^n + a_{i-1}(x_i)^{(n-1)} + ... + a_1 \times x_i + a_0 = y_i[/tex] for i = 1, 2, ..., m, where m is the number of data points in the set. This gives us m equations in n+1 unknowns.

For the first set,

[tex]a_0 + 3a_1 + 9a_2 = 4 \\ a_0 + 5a_1 + 25a_2 = 80 \\ a_0 + 7a_1 + 49a_2 = 188[/tex]

For the second set,

[tex]a_0 + 10a_1 = 245 \\ a_0 + 13a_1 = 305[/tex]

For the third set,

[tex]a_0 + a_1 + a_2 + a_3 = 9 \\ a_0 + 2a_1 + 4a_2 + 6a_3 = 15 \\ a_0 + 4a_1 + 16a_2 + 36a_3 = 87 \\ a_0 + 6a_1 + 36a_2 + 216a_3 = 279[/tex]

c) The Vandermonde matrix corresponding to the system of equations is an m x (n+1) matrix V, where the ith row is [tex] [x_i^n, x_i^{(n-1)}, ..., x_1, 1] [/tex] for i = 1, 2, ..., m. The columns of the matrix correspond to the coefficients of the interpolant.

For the first set,

V = [ 1 3 9; 1 5 25; 1 7 49]

For the second set,

V = [1 10; 1 13]

For the third set,

V = [1 1 1 1; 1 2 4 6; 1 4 16 36; 1 6 36 216]

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