A container contains 145.2 ounces of lemonade. If the lemonade is poured equally into 15 cups, how many ounces will be poured into each cup?

A. 8.78
B. 9.12
C. 9.64
D. 9.68

Show answer.

Answer:

Measures of Central Tendancy

Mean: 429

Median: 344

Mode: 134,185,193,217,471,580,799,853

Range: 719

Step-by-step explanation:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is

[tex]\mu = \frac{{\sum}x}{N}[/tex]

The formula for the mean of a sample is

[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:

[tex]\frac{3432}{8} = 429[/tex]

The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:

[tex]134, 185, 193, 217, 471, 580, 799, 853[/tex]

Since there is an even number of data values in this data set, there are two middle numbers. With 8 data values, the middle numbers are the data values at positions 4 and 5. These are 217 and 471. The median is the average of these numbers. We have

[tex]{\frac{ 217 + 471 }{2}}[/tex]

Therefore, the median is

[tex]344[/tex]

The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, the mode(s) is/are

[tex]134,185,193,217,471,580,799,853[/tex]

We may conclude after answering the presented question that None of the given quotient equations are true.

What is an equation?

A formula is a statement that two expressions are equal. An equation consists of two sides separated by an algebraic equation (=).  

For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9."

The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements.

[tex]x^2 + 2x - 3 = 0.[/tex] Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.

None of the given quotients are true.

A. 1/2 ÷ 2 = 1/4, not 4.

B. 1/3 ÷ 4 = 1/12, not 4/3.

C. 1/2 ÷ 6 = 1/12, not 1/6.

D. 1/5 ÷ 2 = 1/10, not 10.

E. 1/8 ÷ 3 = 1/24, not 1/3.

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The variance of the number of citizens favoring the supermarket is 6.

To find the variance of the number of citizens favoring the supermarket, we need to use the binomial distribution formula:

Variance = n × p × (1 - p)

where n is the number of trials (25 in this case), p is the probability of success (0.6 in this case), and (1 - p) is the probability of failure.

Plugging in the values, we get:

Variance = 25 × 0.6 × (1 - 0.6)

Variance = 25 × 0.6 × 0.4

Variance = 6

The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, success or failure. In this case, the trials are the 25 citizens who were chosen, and the success is the event of favoring the supermarket, which has a probability of 0.6.

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It will take around 3.72 months to pay off the credit card debt.

The formula for APR is:

A = P * [tex](1 + r/n)^{nt}[/tex]

In which,

A = amount after compounding.

P = balance amount

r = rate of interest.

n = number of time compounded.

Initial balance: $30,000.

Payments per month = $200.

Expenses = $100

Balance amount = 30,000 - 12 *(200 - 100)

Balance amount = $28800

So, time taken for paying off credit card debt.

30,000 = 28800  [tex](1 + 0.24/1)^{1*t}[/tex]

[tex](1.24)^{t}[/tex] = 30,000 / 28800

[tex](1.24)^{t}[/tex] = 1.04

Solve by using logarithmic function.

t = ln (1.04) / 1.24

t = 0.31  year

t = 3.72 months

Thus, it will take around 3.72 months to pay off the credit card debt.

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Answer:

26° 180 -81 - 73 = 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

triangle= 180

81 + 73 = 154

180 - 154= 26

The type of transformation represented in the figure is the translation transformation i.e. (c) none of these

Given the triangles ABC and A'B'C'

The transformation between the triangles is translation

The translation transformation is a type of transformation that moves an object without changing its size, shape, or orientation.

This transformation involves sliding an object in a particular direction by a certain distance, either horizontally or vertically.

In this case, the direction is horizontally and vertically

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The total distance that the water tanker has covered in March of 2022 is given as follows:

1860 kilometers.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for this problem are given as follows:

Hence the total distance is then obtained as follows:

d = v x t

d = 60 x 31

d = 1860 kilometers.

The complete question is:

"Assuming that the water tanker travels an average of 60 kilometers a day, calculate the total distance that the water tanker has covered in March 2022​".

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There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Each classroom has 6 rows of 5 desks.

So the total number of desks in one classroom.

= 6 rows x 5 desks per row

= 30 desks

To find the total number of desks in 45 classrooms, we can multiply the number of desks in one classroom by the number of classrooms.

= 30 desks per classroom x 45 classrooms

= 1,350 desks

Therefore,

There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

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Answer:

Step-by-step explanation:

To find the utility-maximizing bundle of goods, we need to solve for the values of x and y that maximize U while still satisfying the budget constraint. The budget constraint can be written as:

2x + 4y = 24

or

x + 2y = 12

We can use the method of Lagrange multipliers to solve for the utility-maximizing values of x and y subject to this constraint. The Lagrangian function is:

L = 3x^(2/3)y^(-1/3) + λ(x + 2y - 12)

Taking partial derivatives with respect to x, y, and λ, we get:

dL/dx = 2x^(-1/3)y^(-1/3) + λ = 0

dL/dy = -x^(2/3)y^(-4/3) + 2λ = 0

dL/dλ = x + 2y - 12 = 0

Solving these equations simultaneously, we get:

x = 6

y = 3

So the utility-maximizing bundle is 6 units of x and 3 units of y.

To see if the individual is better off with the government intervention, we can plot the budget line and the indifference curve for the utility-maximizing bundle with and without the limit on x.

Without the limit, the budget line is the same as before (x + 2y = 12), and the indifference curve for the utility-maximizing bundle passes through the point (6, 3) on the graph.

With the limit, the budget line becomes x = 4, since the individual is prohibited from purchasing more than 4 units of x. The corresponding budget line has a slope of -1/2 and intercepts the y-axis at 6.

If we draw the indifference curve for the utility-maximizing bundle of (4,4), which lies on the budget line, we can see that the individual is not better off with the government intervention. This is because the slope of the budget line under the intervention is steeper, so the individual would have to give up more y than x to afford the same amount of utility. Thus, the individual would have to move to a lower indifference curve with lower utility.

Therefore, the individual is not better off with the government intervention.

Answer:

The given equation is 3 + 7x + 11 + 10x = y.

Simplifying the equation, we get:

y = 17x + 14

Comparing with the standard linear equation y = mx + b, we can see that:

m = 17

b = 14

Therefore, m = 17 and b = 14.

Answer:

Step-by-step explanation:

(x+3)^2=49

x+3=√(49)

x+3=√(7^2)

x+3=7

x+3-3=7-3

x+3=-√(49)

x+3=-7

x+3-3=-7-3

x = 4,-10

By rewritting the exponential equation, we can see that the correct options are B and C.

We know that the balance is modeled by the exponential equation below:

[tex]A = 328.23\times e^{0.045*(t - 2)}[/tex]

Now we want to see which of the other equations are equivalent to this one, so we need to rewrite this equation, so let's do that.

First we can rewrite the second part to get:

[tex]A = 328.23\times e^{0.045\times(t - 2)}\\\\A = 328.23\times(e^{-2*0.045*}\times e^{0.045\times t})\\\\A = 300\times e^{0.045\times t}[/tex]

So that is an equivalent equation.

We also can keep rewritting this to get:

[tex]A = 300\times e^{0.045\times t}\\\\A = 300\times(e^{0.045})^t\\\\A = 300\times(1.046)^t[/tex]

The correct options are B and C.

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the fraction of the class that are boys is 4/9. And the fraction of the class that are girls is 5/9.

What is ratio?

A ratio is a comparison of two or more quantities that are related in some way. It expresses the relationship between these quantities in terms of the number of times one quantity contains another. Ratios are usually expressed as a fraction, where the numerator represents the first quantity and the denominator represents the second quantity. For example, the ratio of boys to girls in a class of 40 students may be expressed as 2:3 or 2/3, meaning there are 2 boys for every 3 girls. Ratios can also be expressed in other forms, such as percentages or decimals. Ratios are commonly used in mathematics, science, engineering, and everyday life to compare quantities and make predictions or decisions.

A fraction is a number that represents a part of a whole or a ratio of two quantities. It consists of two numbers, a numerator and a denominator, separated by a line. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or in the comparison. Fractions are used in many areas, such as mathematics, science, engineering, cooking, and everyday life. They can be added, subtracted, multiplied, and divided, and can be converted to decimals or percentages.

a) The total ratio of boys to girls in the class is 4+5 = 9. Therefore, the fraction of the class that are boys is 4/9.

b) The question is unclear as it seems to be asking for the same answer as in part (a). If you meant to ask for the fraction of the class that are girls, you can use the same approach: the fraction of the class that are girls is 5/9.

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Answer:

Step-by-step explanation:

yes since they are both divisible by their denominators and equal the same thing

Answer:

yes, they are equivalent

Step-by-step explanation:

2/2 = (2/2)x(4/4) = 8/8 = 1

Answer:

This should be a permutation

Step-by-step explanation:

P (n, r) = n!/(n-r)!

P (12,5) = 12!/(12-5)!

P (12,5) = 12!/7!

P(12,5) = 95040

The volume of the cone is  2119. 5 cubic centimeters

The formula used for calculating the volume of a cone is expressed as;

V = πr² h/3

Given that the parameters are namely;

Now, substitute the values, we have;

Volume , V = 3.14 × 15² × 9/3

Divide the values, we have;

Volume = 3.14 × 225 × 3

Multiply the values, we get;

Volume, V = 2119. 5 cubic centimeters

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Answer:

Step-by-step explanation:

An example of an expression with 4 terms where 3 of them are like terms is:

$5x^2 + 7x - 2x^2 + 3x$

To rewrite this expression by combining like terms, we add the coefficients of the terms with the same variables raised to the same power. In this case, the two terms with $x^2$ are like terms, so we can add their coefficients:

$5x^2 - 2x^2 + 7x + 3x = 3x^2 + 10x$

The resulting expression has 2 terms.

The angle indicated by a green arc is 54 degrees.

A straight line's angle size is 180°; the sum of the angles in a triangle's size is 180°; and a triangle can also have acute as well as obtuse angles.

The fact that the sum of the angles in a triangle equals 180 degrees can be used to determine the value of the angle in the given figure.

To begin, note that the angle denoted by a blue arc is the exterior angle of triangle ACD. According to the Exterior Angle Theorem, this angle is equal to the sum of the two remote interior angles, denoted by red and green arcs.

So we have:

The blue arc angle is equal to the sum of the red and green arc angles.

We get the following equation when we plug in the given angle measurements:

98° = 44° + Green arc angle

We can simplify this equation as follows:

Green arc angle = 98° - 44° = 54°

The green arc represents an interior angle of triangle ABD. As a result, we can use the fact that the sum of a triangle's angles equals 180 degrees to calculate the value of this angle.

We currently have:

Green arc angle + 70° + 56° = 180°

We get the following by substituting the value we found for the green arc angle:

54° + 70° + 56° = 180°

We can simplify this equation as follows:

180° - 70° - 56° = 54°

As a result, the angle indicated by a green arc has the value:

It is 54 degrees outside.

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A square is not created when a plane slices through a cone.

What is square?

A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.

What is cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.

When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.

If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.

If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.

Therefore, a square is not created when a plane slices through a cone.

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Answer:

Experimental Procedure:

Materials:

Piece of wood

Electronic balance

Bunsen burner

Heat-resistant mat

Stopwatch or timer

Safety goggles

Lab coat

Safety Precautions:

Wear safety goggles and a lab coat to protect your eyes and clothing from any sparks or flames.

Place the heat-resistant mat under the Bunsen burner to prevent any accidental fires.

Use the Bunsen burner only under adult supervision.

Be cautious when handling hot objects, and allow them to cool before touching.

Procedure:

Measure the initial mass of the piece of wood using an electronic balance, and record it in a table.

Light the Bunsen burner, and place the piece of wood over the flame using tongs. Ensure that the wood is fully engulfed in the flame.

Use a stopwatch or timer to time how long the wood burns for (in this case, 15 minutes).

After 15 minutes, turn off the Bunsen burner and remove the piece of wood from the flame using tongs.

Allow the wood to cool, and then measure its final mass using the electronic balance, and record it in the table.

Calculate the difference between the initial and final mass of the wood, and record it in the table.

Repeat steps 1-6 three times to obtain three sets of data.

Calculate the average mass of the burned wood and compare it to the initial mass of the unburned wood to determine if the student's prediction was correct.

Conclusion:

If the average mass of the burned wood is less than the initial mass of the unburned wood, the student's prediction was correct, and he can conclude that the wood underwent a chemical change when it was burned. If the average mass is greater than or equal to the initial mass, the prediction was incorrect, and the student may need to revise his hypothesis or experimental design.

The resulting number is 12/5

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it

So, performing the operations,

15/16+15/16×3/5

= 15/16(1+3/5)

= 15/16(8/5)

= 120/80

= 3/2

Now,

3/2+3/2×3/5

= 3/2(1+3/5)

= 3/2(8/5)

= 24/10

= 12/5

Hence, the resulting number is 12/5

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Answer: 160

Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.

Answer: Sally will earn $4,830.00 in interest over 7 years.

Step-by-step explanation:

If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:

I = P * r * t

where:

I = the interest earned

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the time period, in years

In this case, we have:

P = $9,000 (the initial deposit)

r = 7% = 0.07 (the annual interest rate)

t = 7 (the number of years)

So, plugging in the values:

I = $9,000 * 0.07 * 7

I = $4,830.00

Therefore, Sally will earn $4,830.00 in interest over 7 years.

Answer:

112

Step-by-step explanation:

According to the circle graph, the mystery books make up 20% of all books sold. So, we can calculate the number of mystery books sold as follows:

Number of mystery books = 20% of 560

= (20/100) x 560

= 112

Therefore, the number of mystery books sold at the book fair was 112.

The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

What is a piecewise function ?

A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.

The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.

On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.

On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.

The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.

Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

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Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

Since "percent" is a slang term for "per hundred," when we discuss percentages, we are speaking to a fraction of a hundred. In a variety of contexts, including math, science, finance, and daily living, percentages are used. The percent sign (%) is commonly used to denote percentages. As an illustration, to determine what proportion of 50 apples are red, you would split the number of red apples by the total number of apples and multiply the result by 100.

given

If Jane had phoned 1,000 times and you had allowed 67% of those calls to go to voicemail, then 67% of those calls would have left voicemails for you.

You can multiply the overall number of calls by the proportion of calls that went to voicemail to determine how many voicemails you would have received:

1000 x 67% = 670

Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

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The complete question is :-  

Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail 67% of the time, how many voicemails would you have received if she left one each time?

Possible Answers:

3,700

57,000

67

None of the given answers

670

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

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Answer:

We can rewrite the function as:

f(x) = 3(8√3)^(2x) = 3(2^3√3)^(2x)

Using the properties of exponents, we can rewrite this as:

f(x) = 3(2^(3*2x)√3^(2x)) = 3(2^(6x)√(3^(2x)))

Therefore, the base of the exponent is 2.

The interest that is paid on the loan in 6 years will be $4,200.

The amount of interest that is saved is $2,100.

The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.

Simple interest = loan x time x interest rate

Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200

Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100

Interest saved = $4200 - $2100 = 2100

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