Alex can earn $15 an hour mowing neighborhood lawns on weekends. If Alex decides to spend an hour mowing rather than watching a football game, his opportunity cost of mowinf lawns is:
a. The $15 he earns
b. The enjoyment he would have received from watching the football game during that time.
c. The $15 he earns minus the enjoyment he would have received from watching the football game during that time.
d. The $15 he earns plus the enjoyment he would have received from watching the football game during that time.
e. Nothing because he would have received $15 worth of enjoyment from watching the football game during that time

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin x= -3/√13

So, B = √13 - 9 = √4 =2

cos x= 2/ √13

So, sin 2x= 2 sin x cos x =2 (-3/√13 )(2/√13 ) = -12/√13

and, cos 2x= 1- 2 sin²x

                  = 1- 2( -3/ √13 )²

                  = -5/ √13

and, tan 2x = sin 2x/ cos 2x = 5/12

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a) The step in which McKenna made her first mistake is given as follows: Step 4.

b) The correct simplified expression in standard form is given as follows: -15a - 15.

The expression in this problem is defined as follows:

3 − 5(3a + 6)

On the third step, the expression is given as follows:

3 + (−5)(3a + 6)

And on the fourth step, the expression is given as follows:

−2(3a + 6).

This is where the mistake happened, as the multiplication takes precedence over the subtraction.

Then to obtain the correct expression the first step is applying the distributive property, as follows:

3 − 5(3a + 6) = 3 - 15a - 18.

Then the like terms 3 and -18 are combined to obtain the correct simplified expression, as follows:

3 - 15a - 18 = -15a - 15.

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Using monthly payment formula, the principal of the facility paying a monthly payment of $8750 for 25 years at a rate of 5.50% is $1,424,878.39

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.

The formula to calculate the monthly payment of a facility is;

A = P[(r(1 + r)ⁿ] / [(1 + r)ⁿ - 1]

Substituting the values into the formula and solving for p

P = $1,424,878.39

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Answer: x=5

Step-by-step explanation:

isolate x

8x-4+4=36+4

8x=40

x=5

Answer:

x=5

Step-by-step explanation:

You would first want to add 4 to both sides. Then divide 40 and 8 by 8 and you get x=5.

Following values can be filled in the table:

(0,-3), (-1,0), (1,-8), (-2,1), (2,-15)

It can be solved using the concept of graph plotting and function.

What is graph?

When a set of points are connected together to form a strcture then the structure is known as graph. The set of ponts is known as ordered pair.

Consider the eqution.

[tex]y=-2(x+2)^2-3[/tex]

Substitute the simplest value x = 0 and find the value of y.

[tex]y=-2(0+2)^2-3\\=-11\\[/tex]

Now, substitute x = -1 and find the value of y.

[tex]y=-2(-1+2)^2-3\\=-5\\[/tex]

Now, substitute x = 1 and find the value of y.

[tex]y=-2(1+2)^2-3\\=-21\\[/tex]

Now, substitute x = -2 and find the value of y.

[tex]y=-2(-2+2)^2-3\\=-3\\[/tex]

Now, substitute x = 2 and find the value of y.

[tex]y=-2(2+2)^2-3\\=-35\\[/tex]

Hence, following values can be filled in the table:

(0,-11), (-1,-5), (1,-21), (-2,-3), (2,-35)

It can be solved using the concept of graph plotting.

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A has the larger standard devlation.

What is standard devlation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

We are given two plots of normal distributions A and B.

The mean of a normal distribution is located at the center of the plot.

Since the centers of both of the normal distributions A and B seems to be aligned, therefore, they both seems to have equal means.

The standard deviation basically determines the shape of the distribution.

As you can see, the normal distribution A is more spread out and thus has a larger standard deviation than normal distribution B.

Therefore, the two correct options are

• The means of A and B are equal.

• A has larger standard deviation.

Complete question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

Select all that apply:

A has the larger mean.

B has the larger mean.

The means of A and. Q jual.

A has the larger standard devlation.

B has the larger standard deviation.

The standard deviations of A and B are equal.

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The baby is 105.6  ounces or 6.96 pounds lighter than an average baby.

Weight is the measurement of Gravitational force on an object. It can be zero as in the space.

We are given in the question that A baby weighed only 14.4 ounces at birth the weight of an average baby is 7lb 8 ounces.

1 lb = 16 ounce

Therefore an average baby weight = 7 x 16 + 8 = 120 ounces

The baby weight is just 14.4 ounces

Hence, the baby is 120 - 14.4 = 105.6 ounces lighter than an average baby.

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Let no of level in one day is x. So, Zoe can play x= 12 level in a day.

The likelihood might be between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. In a sample space, each occurrence has a probability of one overall. the possibility that two or more events will follow one another. Since there are two or more of them, the events are either dependent or independent events. A dependent event—also referred to as a conditional event—is one in which the occurrence of the first event affects the occurrences that follow. The total number of outcomes will differ.

Probability = Possible outcomes/total outcomes

Factors of 12 can be written as:

1 * 12 = 12

2 * 6 = 12

3 * 4 = 12

For this question look for factors of 12-These would be

1 and 12 (1 x 12 = 12)

2 and 6 (2 x 6 = 12)

3 and 4 (3 x 4 = 12)

Hence Zoe could either play

1 level each day for 12 days

2 levels each day for 6 days

3 levels each day for 4 days

4 levels each day for 3 days

Or...

12 levels in one day

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Answer:

Step-by-step explanation:

1:Pl 2:Th 3:Th 4:P 5:P 6:Pl 7:Pl 8:Th 9:Th 10:Th 11:Pl 12:P  

There you go, the numbers go down. So Iowa is 1 and so on, I don't know if they are all right but I did my best.

Answer:

OD 4x³, x², 3x, 6

Step-by-step explanation:

The solution of the system of equation are;

⇒ x = - 2

⇒ y = 0

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ 5x - 4y = - 10

⇒ - 4x + 5y = 8

Now,

Find the solution as;

The system of equation are,

⇒ 5x - 4y = - 10  ..(i)

⇒ - 4x + 5y = 8   ..(ii)

Multiply by 4 in equation (i) + Multiply by 5 in equation (ii);

⇒ 20x - 16y + (- 20x + 25y) = - 40 + 40

⇒ 9y = 0

⇒ y = 0

And,  - 4x + 5y = 8

⇒ - 4x + 0 = 8

⇒ x = - 2

Thus, The solution of the system of equation are;

⇒ x = - 2

⇒ y = 0

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The values of x where f(x) is 0 to determine a function's zeros.

The set of all x for which the f(x) graph crosses the x-axis is the solution of f(x) = 0. The set of all x for which the graph of f is strictly above the x-axis is the solution of f(x) > 0

In general, finding the zeros of the function f(x) involves setting the function to zero. The zeroes of the function are the values of x that correspond to the set equation. Find the values of x where f(x) = 0 to determine a function's zeros.

f ( x)=- 3 is a horizontal line that connects to the x-axis, hence there is no x-intercept and the y-intercept is ( 0, -3).

The y-intercept is ( 0, -3)

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Answer:

250 meters per minute.

Step-by-step explanation:

1 km = 1000 m

15 km = 15*1000 = 15000 m

1 hour = 60 min

Then:

15km/h = 15000km/60minutes

= 250 meter per minute

Answer:250 meters / minute

Step-by-step explanation:1 km/h = 16.66667 m/min

The mean of the data is x(bar) = 41.396

The Median of the data is  $40.76

The mode of all the values are appearing once and therefore there is no mode for the phone bill.

Now, According to the question:

Given the data:

$35.34, $42.09, $39.43, $38.87, $43.39, $49.26

Mean is the average of the data computed as x(bar) = Σ[tex]x_i[/tex] /n where [tex]x_i[/tex]

are the data points and n is the number of data points

x(bar) = 35.34 + 42.09 + 39.43 +38.87 +43.39 + 49.26 /  6

x(bar) = 248.38 /6

x(bar) = 41.396

The median is the data point that lies in the middle of the data set when the data is arranged in ascending or descending order.

Thus,

Ascending order:

$35.34, $38.87, $39.43, $42.09, $43.39, $49.26

The median lies between $39.43 and $42.09 and to get it, we find the average of the two numbers

Median = (39.43 + 42.09)/ 2

Median = $40.76

→ Mode is the value in a data set that is repeated most frequently. In the given data, all the values are appearing once and therefore there is no mode for the phone bill.

Hence, The mean of the data is x(bar) = 41.396

The Median of the data is  $40.76

The mode of all the values are appearing once and therefore there is no mode for the phone bill.

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The value of P = $7,000,r = 3.2%, n = 4, and money after 7 years will be $8749.6954.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

(A)

As per the given,

Principle amount P = $7,000

Rate of interest r = 3.2%

Number of times interest applied per time period n = 4 (Quarterly)

(B)

Time period T = 7 year

Total amount S(7) = 7,000(1 + 0.032/4)^(4 x 7)

S(7) = $8749.6954

Hence "The value of P = $7,000,r = 3.2%, n = 4, and money after 7 years will be $8749.6954".

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Answer: The bisector of [tex]\angle BAC[/tex]

Step-by-step explanation:

This is a standard construction.

The option that shows that Wesley will save enough money for his vacation is D. Multiply 30 × 12 to get 360. Then divide 360 ÷ 7 to get 51 R3. Wesley will have $51 for each.day plus $3 left over.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this situation, Wesley wants to have at least $50 to spend each day of his 7-day vacation. He plans to save $30 each month for 12 months.

This will be illustrated thus:

(30 × 12) / 7

= 51 R 3

This shows that he'll have enough money. The correct option is D.

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To factor the expression 54a⁶b²+ 9ab², you can use the fact that a common factor of 54a⁶b² and 9ab² is ab².

Thus, you can rewrite the expression as:

ab²(54a⁶ + 9)

You can then factor the expression inside the parentheses using the fact that 3 is a common factor of both 54 and 9:

ab²(3 * 18a⁶ + 3 * 3)

This can be simplified as:

ab²(6a⁶ + 9)

This expression is completely factored and cannot be further simplified. Therefore, the completely factored form of the expression is:

ab²(6a⁶ + 9)

You can make a chart in PowerPoint or Excel. If you have lots of data to chart, create your chart in Excel, and then copy it into your presentation. This is also the best way if your data changes regularly and you want your chart to always reflect the latest numbers. In that case, when you copy and paste the chart, keep it linked to the original Excel file.

To create a simple chart from scratch in PowerPoint, click Insert > Chart and pick the chart you want.

1. Click Insert > Chart.

2.Click the chart type and then double-click the chart you want.

3.In the worksheet that appears, replace the placeholder data with your own information.

4.When you insert a chart, small buttons appear next to its upper-right corner. Use the Chart Elements Chart Elements button button to show, hide, or format things like axis titles or data labels. Or use the Chart Styles Customize the Look of Your Chart button button to quickly change the color or style of the chart.

What is excel ?

Excel is a spreadsheet program from Microsoft and a component of its Office product group for business applications. Microsoft Excel enables users to format, organize and calculate data in a spreadsheet.

The main uses of Excel include: Data entry. Data management. Accounting.

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Answer: C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Well, there are the same amount of numbers in each equation. You can take the a from both equations, raise it to the second power, then do the same to the b. The addition sign will automatically disappear because you've added the two components together. You'll use subtraction to get your answer. I think.

Answer:

A)  Pam had less water left over than apple juice.

Step-by-step explanation:

Given amounts of drinks left over:

To compare the amounts of drinks left over, convert the fractions into equivalent fractions that have the same denominator.

The denominators of the three fractions are 2, 5 and 10.

The lowest common multiple of the denominators is 10.

Therefore, rewrite the first two fractions so that their denominators are also 10.

[tex]\textsf{Soda}: \quad \dfrac{1}{2}=\dfrac{1 \cdot 5}{2 \cdot 5}=\dfrac{5}{10}[/tex]

[tex]\textsf{Water}: \quad \dfrac{1}{5}=\dfrac{1 \cdot 2}{5 \cdot 2}=\dfrac{2}{10}[/tex]

Therefore, as:

then:

Therefore, Pam had less water left over than apple juice.

Answer:

a) Pam had less water than apple juice.

★ Water < Soda < Apple juice

Step-by-step explanation:

Converting the fraction into decimals,

→ Soda left = 1/2 = 0.5 litres

→ Water left = 1/5 = 0.2 litres

→ Apple juice left = 8/10 = 0.8 litres

Let's order them in ascending order,

→ 0.2 < 0.5 < 0.8

→ 1/5 < 1/2 < 8/10

→ Water left < Soda left < Apple juice left

Now the applicable options is,

→ Pam had less water than apple juice.

Hence, option (a) is correct answer.

A linear equation to find p, Laredo's population for any year after 1990 is 5441t + 123000.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given:

t = the number of years after 1990.

So, for 1990, t = 0. So the coordinate is (0, 123000).

For 2007, t = 17. So the coordinate is (17, 215500).

Slope = (215500 - 123000)/17

Slope = 5441

P = 5441t + b,

b = 123000

P = 5441t + 123000

Hence,  a linear equation to find p, Laredo's population for any year after 1990 is 5441t + 123000.

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The number of possible paint jobs that can be done on the 4 cars can be determined by permutation (15,4). That is option B.

Permutation is defined as the various number of ways a data set can be arranged to arrive at a definite value.

the number of colours offered by the paint shop = 15

The number of cars the need a new paint job = 4

To find the possible number of colour that can be used permutation (15,4) is carried out.

That is,

= 15!/(15-4)!

= 15!/11!

= 15×14×13×12×11×10×9×8×7×6×5×4×3×2×1/11×10×9×8×7×6×5×4×3×2×1

or 15×14×13×12×11!/11!

= 15×14×13×12

= 32,760

Therefore, there would be 32,760 possible paint jobs that can be carried out on the 4 cars.

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By using the formula for slope, it can be calculated that

The slope of the given line is 10

What is slope of a line?

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan \theta[/tex]

If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], slope is calculated by the formula

Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here, the line passes through (2, 3) and (3, 13)

Slope = [tex]\frac{13 - 3}{3-2}[/tex]

Slope = 10

So the slope of the given line is 10

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Step-by-step explanation:

[tex] {x}^{2} - 14x = 164[/tex]

[tex] {x}^{2} - 14x + 49 = 213[/tex]

[tex](x - 7) {}^{2} = 213[/tex]

[tex](x - 7) = \sqrt{213} [/tex]

[tex](x - 7) = - \sqrt{213} [/tex]

[tex]x = 7 + \sqrt{213} [/tex]

[tex]x = 7 - \sqrt{213} [/tex]

Determining whether each statement implies correlation or causation between two variables is as follows:

Correlation indicates that one independent variable causes another dependent variable to change.

Causation indicates that one dependent variable or event is the direct result of the occurrence of the other event or independent variable.

Causation shows cause and effect - unlike correlation which points out two events simultaneously occur or two variables change at the same time.

Thus, correlation is a test of association in relationship, while causation focuses on cause and effect.

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The gradient of the line is 4/30 and it means that the amount for each unit of electricity used is 4/30

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

From the graph, we have the following ordered pairs

(0, 0) and (30, 4)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0) and (30, 4)

The gradient of the line is then calculated using the following slope equation

gradient = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (30, 4)

Substitute the known values in the above equation

So, we have the following equation

gradient  = (4 - 0)/(30 - 0)

Evaluate

gradient  = 4/30

Hence, the gradient of the line is 4/30

Generally, slope or gradient means rate

This means that the gradient of this line represent the rate

i.e. the amount for each unit is 4/30

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