Write a linear function representing Xavier’s gross income (earnings before taxes) in terms of the number of hours (x) he works.














3

Answer: Let's use the following variables to represent the amount of vitamin C in an eight-ounce glass of each type of juice:

A: amount of vitamin C in an eight-ounce glass of apple juice (in milligrams)

O: amount of vitamin C in an eight-ounce glass of orange juice (in milligrams)

Using this, we can set up a system of two equations based on the given information:

Equation 1: A + O = 187.7 (total vitamin C in two glasses)

Equation 2: 3A + 4O = 651.4 (total vitamin C in three glasses of apple juice and four glasses of orange juice)

We can solve for one of the variables in terms of the other by rearranging Equation 1:

A = 187.7 - O

Substituting this expression for A into Equation 2, we get:

3(187.7 - O) + 4O = 651.4

Simplifying and solving for O, we get:

563.1 - 3O + 4O = 651.4

O = 88.3

Therefore, an eight-ounce glass of orange juice contains 88.3 milligrams of vitamin C. To find the amount of vitamin C in an eight-ounce glass of apple juice, we can substitute this value into Equation 1:

A + 88.3 = 187.7

A = 99.4

So, an eight-ounce glass of apple juice contains 99.4 milligrams of vitamin C.

Therefore, the amount of vitamin C in an eight-ounce glass of apple juice is 99.4 mg, and the amount of vitamin C in an eight-ounce glass of orange juice is 88.3 mg.

Step-by-step explanation:

Answer:

--------------------

The sum of (-2) and (-4) is:

The difference of (-2) and (-4) is:

The product of the sum and difference is:

The probability that Rebecka and Aaron both select a poodle is 0.09 or 9/100.

We have,

There are 3 poodles out of 10 puppies, so the probability that Rebecka selects a poodle is 3/10.

After Rebecka selects a poodle and it is replaced with another poodle, there are still 3 poodles out of 10 puppies.

This means,

The probability that Aaron selects a poodle, given that Rebecka selected a poodle, is also 3/10.

Now,

P(both select a poodle) = P(Rebecka selects a poodle) × P(Aaron selects a poodle | Rebecka selected a poodle)

= (3/10) × (3/10)

= 9/100

= 0.09

Therefore,

The probability that Rebecka and Aaron both select a poodle is 0.09 or 9/100.

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The length of the other two sides of triangle B are determined as:

9 cm and 12 cm.

When solving for the length of the side of triangles that are are similar, note that their sides have lengths that are proportional to each other.

Thus, since triangles A and B are similar, it means they will have side corresponding side lengths that are proportional, therefore:

Let x represent the length of the longest side of triangle B and y represent the medium side.

Therefore, we have:

4/6 = 6/y

4y = 36

4y/4 = 36/4

y = 9 cm

4/6 = 8/x

4x = 48

x = 12 cm

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The mean absolute deviation of the population is:

1.50 million

Mean absolute deviation (MAD) is a measure of the average absolute distance between each data value and the mean of a data set. The formula for MAD is:

MAD =∑|x-m|/n

∑ is known as Sigma and means to sum up

| | are vertical bars that mean absolute value

x is each value

m is the mean

n is the total number of data points in your data set

n = 10

m = (1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10

   = 25.4/10

   = 2.54

∑|x-m| = |1.5-2.54| + |3.8-2.54| + |1.3-2.54| + |1.6-2.54| + |2.9-2.54| + |1.4-2.54| +|0.9-2.54| + |2.3-2.54| + |8.4-2.54| + |1.3-2.54|

        = 1.04 + 1.26 + 1.24 + 0.94 + 0.36 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24

        = 14.96

MAD =∑|x-m|/n = 14.96/10 = 1.496

Rounding to the nearest hundredth:

MAD = 1.50

Therefore, the mean absolute deviation of the population is 1.50 million

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The number of more houses between the area 150m² and 200 m² than between 250m² and 300 m² is 8.

Histogram is a graphical representation of discrete or continuous data. In other words, it is a graphical representation of distribution of data.

Therefore, the histogram has number of houses on the y-axis and area on the x -axis,

The histogram relates the number of houses to the area of the houses in square metres.

Therefore, let's find how many more houses have an area between 150m² and 200 m² than between 250m² and 300 m²?

Hence,

Houses between 150m² and 200 m²  = 9

Houses between 250m² and 300 m² = 1

Finally,

difference between them = 9 - 1 = 8 houses

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Answer:

26

Step-by-step explanation:

I did this a year ago but I forgot my work sorry!

The distance between the boat and the diver is D = 276.5 feet

Given data ,

A scuba diver is 356 feet under the water's surface.

And the diver establishes a 39° angle of depression with her boat.

Therefore, using the trigonometric relationships, we can

tan θ = opposite / adjacent

On simplifying , we get

tan 39° = D / 356

Multiply by 356 on both sides , we get

D = 276.5 feet

Hence , the distance is therefore 276.5 ft.

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ln|sec(x)tan(x)| + C is the integral value of ∫sec²x/tanx dx

We can start by using the identity sec²(x) = 1 + tan²(x) to rewrite the integrand as:

sec²(x)/tan(x) = (1 + tan²(x))/tan(x)

= tan(x)/tan(x) + tan³(x)/tan(x)

= 1 + tan²(x)

Now we can make the substitution u = tan(x) to get:

∫sec²x/tanx dx = ∫(1 + tan²(x)) dx

= ∫(1 + u²) du

= u + (1/3)u³ + C

= tan(x) + (1/3)tan³(x) + C

= ln|sec(x)tan(x)| + C,

Therefore,  ln|sec(x)tan(x)| + C is the integral value of ∫sec²x/tanx dx

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Answer:

The range is the difference between the highest and lowest values in a set of data. In this case, the range is 15 - 1 = 14.

The interquartile range (IQR) is the difference between the third and first quartiles of a set of data. The first quartile (Q1) is the middle value of the lower half of the data, and the third quartile (Q3) is the middle value of the upper half of the data. In this case, the IQR is Q3 - Q1 = 12 - 5 = 7.

There are no outliers in this data set. An outlier is a data point that is significantly different from the rest of the data points. In this case, all of the data points are within 14 of the mean, which is 8.5. Therefore, there are no outliers.

Here is a summary of the range and IQR of the data set:

Range: 14

IQR: 7

Step-by-step explanation:

Answer: Range: 14 IQR: 7

Step-by-step explanation:

Answer:

----------------------------

Divide the total amount by the cost per piece:

Since the carpenter can only buy whole pieces of wood, they can buy 30 pieces.

The ratios with unit rates greater than 1 are:

3 1/5 pounds : 4 pounds

7 1/10 pounds : 9/10 pound

9/4 pounds : 3/4 pound

2 pounds : 1/3 pound.

A unit rate is the comparison of two quantities with a denominator of 1.

To determine if the unit rate is greater than 1, we need to compare the numerator to the denominator.

If the numerator is greater than the denominator, the unit rate is greater than 1.

Let's analyze each ratio:

3 1/5 pounds : 4 pounds:

The numerator (3 1/5) is greater than the denominator (4), so the unit rate is greater than 1.

7 1/10 pounds : 9/10 pound:

The numerator (7 1/10) is greater than the denominator (9/10), so the unit rate is greater than 1.

7/8 pound : 2 pounds:

The numerator (7/8) is less than the denominator (2), so the unit rate is not greater than 1.

9/4 pounds : 3/4 pound:

The numerator (9/4) is greater than the denominator (3/4), so the unit rate is greater than 1.

3 pounds : 1 1/2 pounds:

The numerator (3) is equal to the denominator (1 1/2), so the unit rate is not greater than 1.

2 pounds : 1/3 pound:

The numerator (2) is greater than the denominator (1/3), so the unit rate is greater than 1.

Therefore, the ratios with unit rates greater than 1 are:

7 1/10 pounds : 9/10 pound

9/4 pounds : 3/4 pound

2 pounds : 1/3 pound

3 1/5 pounds : 4 pounds

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The calculated full capacity of the tank is 90 liters

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

Proportion = 4/5

This is represented as

Size = 72 liters

Using the above as a guide, we have the following:

4/5 * x = 72 liters

Where

x = the full capacity of the tank

So, we have

x = 72 * 5/4

Evaluate

x = 90

Hence, the full capacity of the tank is 90 liters

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Based on proportions, if a lorry tank was ⁴/₅ full of petrol when the gauge indicates 72 liters, the full capacity of the tank is 90 liters.

Proportion refers to the fraction or portion of a whole value, quantity, or number.

Proportions are ratios equated to each other.

We can depict proportions using fractions, decimals, or percentages.

The fraction of the lorry tank of petrol = ⁴/₅ (0.80)

If ⁴/₅ = 72 liters, proportionately, the full tank = 90 liters (72 ÷ 0.80)

Thus, we can conclude that when the lorry tank is full the quantity of petrol in it is 90 liters.

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Assuming [tex]f(x)=x^2[/tex].

[tex]y=x^2\\x=-\sqrt y \vee x=\sqrt y[/tex]

Since [tex]x\geq0[/tex] only [tex]x=\sqrt y[/tex] is valid.

Therefore

[tex]f^{-1}(x)=\sqrt{x}[/tex]

Step-by-step explanation:

Note:

tanA=sinA/CosA i.e tan^2A=sin^2A/cos^2A

tanB=sinB/cosB

cos^2A+sin^2A=1

cos^2B+sin^2B=1

I hope this helps.

Answer:

1

Step-by-step explanation:

6c - 2c = 4

      4c = 4

        c = 4/4

        c = 1

The cost of covering 1 unit² should be $2.477 to be in the budget and the total area to be covered is 3027.22 ft².

Given is a blueprint we need to find area that be covered and then the cost of covering the area,

So, we will find the area by splitting the figure into different shapes,

So the area =

Ar(rectangle) + Ar(semicircle) + Ar(triangle) + Ar(square)

= 9×3 + 3.14×2²/2 + 1/2×3×1 + 3³

= 27 + 6.28 + 1.5 + 27

= 61.78 units²

Since 1 unit = 7 ft

So, 1 unit² = 49 ft²

therefore, 61.78 units² = 61.78 × 49 = 3027.22 ft²

Since our budget is $7500

Costing of covering the area = 3027.22 × x = 7500

x = $2.477

Hence the cost of covering 1 unit² should be $2.477 to be in the budget.

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Answer:

16 x 15 x 14 = 3,360

The vertices of the image after a dilation with the origin as its center and a scale factor of 2 are having coordinates A' = (12, 8), B' = (4, 8), C' = (12, -4) and D' = (4, -4)

To dilate a figure with the origin as the center, we only need to multiply each coordinate by the scale factor. In this case, the scale factor is 2.

So, for vertex A(6, 4), we have:

x-coordinate after dilation: 2 × 6 = 12

y-coordinate after dilation: 2 × 4 = 8

Similarly, for vertex B(2, 4), we have:

x-coordinate after dilation: 2 × 2 = 4

y-coordinate after dilation: 2 × 4 = 8

For vertex C(6, -2), we have:

x-coordinate after dilation: 2 × 6 = 12

y-coordinate after dilation: 2 × (-2) = -4

Finally, for vertex D(2, -2), we have:

x-coordinate after dilation: 2 × 2 = 4

y-coordinate after dilation: 2 × (-2) = -4

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Janna would be use 30 marshmallows and 45 graham crackers to make 15 s'mores.

Since, We know that;

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

We have to given that;

Janna wants to make s'mores at the backyard campfire.

The table below shows the parts of marshmallows to graham crackers to make s'mores.

S'mores  Marshmallows  Graham Crackers

4                   8                           12

15

That means, the rate is,

8/4 = 2 Marshmallows for each S'mores,

And 12/4 = 3 Graham Crackers for each S'mores.

Therefore, 30 marshmallows and 45 graham crackers to make 15 s'mores.

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Janna wants to make s'mores at the backyard campfire. The table below shows the parts of marshmallows to graham crackers to make s'mores.

S'mores Marshmallows Graham Crackers

4 8 12

15

At this rate, how many marshmallows and graham crackers will Janna use to make 15 s'mores?

Janna will use 17 marshmallows and 21 graham crackers to make 15 s'mores.

Janna will use 16 marshmallows and 24 graham crackers to make 15 s'mores.

Janna will use 25 marshmallows and 48 graham crackers to make 15 s'mores.

Janna will use 30 marshmallows and 45 graham crackers to make 15 s'mores.

Answer:

y = 4 - 1.25x

Step-by-step explanation:

5x + 4y = 16

subtract 5x from both sides

4y = 16 - 5x

divide all by 4

y = 4 - 1.25x

The absolute value function can be written as:

Here we have the function:

|7 - (12 - x)|

We can simplify this to get.

|7 - 12  + x| = |x - 5|

Now, if the argument is positive, then the function is equal to the argument.

If the argument is negative, the function is equal to minus the argument.

Then we can write:

if x  > 5, then |7 - (12 - x)| = x - 5

if x = 0, then |7 - (12 - x)| = 0

if x < 5, then |7 - (12 - x)| = 5 - x

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The factored form of the expression is  (x+3) (x-6), which is equivalent to choice C. x-6 , is one of the factors.

To factor a quadratic expression like this, we want to find two numbers that multiply to the constant term (-18) and add up to the coefficient of the x term (-3).

In this case, those numbers are -3 and 6, because (-3) * 6 = -18 and (-3) + 6 = 3.

Then, we can use those numbers to split the middle term into two terms:

x²-3x-18

=x²+3x - 6x-18

=x(x+3) -6(x+3)

=(x+3) (x-6)

So the factored form of the expression is (x+3) (x-6),

which is equivalent to choice C. x-6 , is one of the factors.

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The weights of equity, debt, and preferred stock, based on the market value of each component, of Linge burger Cheese Corporation, are as follows:

Firstly, we calculate the market value of each capital component and divide the result by the total market value of the firm.  This process determines the weights of equity, debt, and preferred stock.

The market value of equity is the number of shares outstanding multiplied by the current share price.

Number of shares outstanding = 6.4 million

Market value per share = $54

Common stock beta = 1.08

Market value = $345.6 million (6.4 million × $54)

Number of shares outstanding at $100 par value = 200,000

Market value per share  = $103

Market value = $20.6 million (200,000 × $103)

Number of bonds outstanding, par value $1,000 each = 120,000

Maturity period of bonds = 15 years

Market value per bond = 107 percent of par

Market value of debt = $128.4 million (120,000 × 1.07 × $1,000)

T-bill yields = 2.4%

Corporate tax rate = 22%

Total market value = $494.6 million ($345.6 million + $20.6 million + $128.4 million)

Weight of equity = 0.6987 or 69.87% ($345.6 million ÷ $494.6 million)

Weight of preferred stock = 0.0417 or 4.17% ($20.6 million ÷ $494.6 million)

Weight of debt = 0.2596 or 25.96% ($128.4 million ÷ $494.6 million)

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The total area of the regions between the curves is 389.0 square units

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

f(x) = x⁴ - 12x³ + 48x²

g(x) = 44x + 105

With the use of graphs, the curves intersect ar

x = -1 and x = 5

So, the area of the regions between the curves is

Area = ∫x⁴ - 12x³ + 48x² - 44x - 105

This gives

Area = ∫x⁴ - 12x³ + 48x² - 44x - 105

Integrate the expression

Area =  x * (x⁴ - 15x³ + 80x² - 110x - 525)/5

Recall that x = -1 and x = 5

So, we have

Area =  (-1) * ((-1)⁴ - 15(-1)³ + 80(-1)² - 110(-1) - 525)/5  - (5) * ((5)⁴ - 15(5)³ + 80(5)² - 110(5) - 525)/5

Evaluate

Area =  388.8

Approximate

Area =  389.0

Hence, the total area of the regions between the curves is 389.0 square units

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The retirement plans that potentially involve contributions from an individual's employer are I, III, and IV.

I - Traditional IRA: A Traditional IRA is an individual retirement account (IRA) that allows individuals to set aside money on a pre-tax basis. Contributions to a Traditional IRA may be made by an individual, or they may be made by an employer as part of an employee's retirement plan.

III - Pension Plan: A pension plan is a retirement plan organized by an employer that provides a guaranteed income to an employee after retirement. Employers typically make contributions to their employee's pension plan on their behalf.

IV - 401(k): A 401(k) is an employer-sponsored retirement savings plan. Contributions to a 401(k) plan can be made by an employee and their employer. Employers may match employee contributions, up to a certain percentage.

Therefore, the retirement plans that potentially involve contributions from an individual's employer are I, III, and IV.

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The equation represents a cosine function that is horizontally shifted, vertically shifted, and scaled with specific values for amplitude, period, phase shift, and midline adjustment.

The equation and description of the interactive widget graph. It appears that the equation you've shared represents a periodic function, specifically a cosine function, with some transformations applied to it.

The general form of a cosine function is given by:

f(x) = A * cos(Bx - C) + D

In your equation, the parameters have specific values:

A = 2

B = 5π/5 = π

C = 5/(2π) = 5/2π

D = -4

The parameter A determines the amplitude of the cosine function, which controls the vertical range of the graph. In this case, it is 2, so the graph will oscillate between 2 units above and 2 units below the midline.

The parameter B affects the period of the function. Since B = π, the period of the cosine function will be 2π/B = 2π/π = 2. This means that the graph completes one full cycle (i.e., goes through one peak and one trough) over an interval of length 2.

The parameter C introduces a phase shift or horizontal translation to the graph. The value of C, 5/2π, determines how much the graph is shifted horizontally. Specifically, it is shifted 5/(2π) units to the right.

The parameter D is the vertical shift or midline adjustment. With D = -4, the entire graph is shifted downward by 4 units.

The movable point mentioned in the widget likely allows you to change the value of x and observe how it affects the position of the extremum point and the intersection points with the midline.

Overall, the equation represents a cosine function that is horizontally shifted, vertically shifted, and scaled with specific values for amplitude, period, phase shift, and midline adjustment.

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Step-by-step explanation:

20+8+7+2=37

The domain of y = cot x is (d) all x ≠ kπ, where k is an integer

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

y = cot x

The domain of the function y = cot x is the set of input values the function can take

As a general rule

The function y = cot x is undefined at the points x = πk where x is an integer

This means that the domain of the function is the set of all real numbers except x = πk

Hence, the domain of y = cot x is (d)

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