Jack Roper is a college student. He pays $17,000 per year in tuition and books, $600 per month in rent, $400 per month for food, and $125 per month for on-campus parking. He gave up a job that pays $45,000 per year to attend college. Given this, the implicit cost of his education equals

The solution to the given equation 5x - 2 + x = 9 + 3x + 10 is x = 7.

Given the equation in the question;

5x - 2 + x = 9 + 3x + 10

Solve for x, first collect and add like terms

5x - 2 + x = 9 + 3x + 10

5x + x - 2 = 3x + 10 + 9

Add 5x and x

6x - 2 = 3x + 10 + 9

Add 10 and 9

6x - 2 = 3x + 19

Add 2 to both sides

6x - 2 + 2 = 3x + 19 + 2

6x = 3x + 21

Subtract 3x from both sides

6x - 3x = 3x - 3x + 21

3x = 21

Divide both sides by 3

3x/3 = 21/3

x = 21/3

x = 7

Therefore, the value of x is 7.

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Answer:

D.Sam he rides 14.5 meters per second which is over a meter per second faster than kevin

Step-by-step explanation:

Kevin:

Distance = 600m

Time = 45s

Speed = Distance/time = 600/45 = 13.33m/s

Sam:

Distance = 800m

Time = 55s

Speed = 800/55 = 14.54m/s

Therefore option D will be the answer

Answer:

60th term is 347

Step-by-step explanation:

This is an arithmetic sequence with common difference = -1 - (-7) = 5 - (-1) = 11 -5 = 6

The nth term for such a series is given by
aₙ = a₁ + d(n-1) where d = common difference and a₁ is the first term

Here d = 6, a₁ = -7

So

aₙ = -7 + 6(n-1)

aₙ = -7 + 6n-6

aₙ = 6n-13

60th term is

a₆₀ = 6(60) - 13 = 360 - 13 = 347

Answer:

15.4 min

Step-by-step explanation:

rate = liters/min = 2.5 l/min

time = liters/rate = 38.5 l / (2.5 l/min) = 15.4 min

As a result, the volume of the revolution solid is roughly -62.83π cubic units.

Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. To calculate the volume, multiply the length by the breadth by the height, which is 3x1x2, which is six. As a result, the fish tank has a volume of 6 cubic feet.

Here,

The region R is the upper half of a circle centered at the origin with a radius of 5. By the method of washers, the volume of the solid of revolution obtained by revolving R about the x-axis can be found by subtracting the volume of a cylinder of height "h" and radius "x" from the volume of a cylinder of height "h" and radius "sqrt(25-x²)".

The volume of a cylinder of height "h" and radius "r" is given by V = πr²h.

So, the volume of the solid of revolution can be expressed as:

V = ∫π(sqrt(25-x²)²- x²) dx from x=0 to x=5

Evaluating this integral, we get:

V = π(∫(25-x²)*0.5 dx - ∫x² dx) from x=0 to x=5

Using substitution and integrating, we can obtain the volume:

V = π * (5 * (2 * sqrt(25 - x²) - x²/2))

Evaluating the expression at x=5, we get:

V = π * (5 * (2 * sqrt(25 - 25) - 25/2))

V = π * (5 * (0 - 25/2))

V = -62.83π cubic units.

So, the volume of the solid of revolution is approximately -62.83π cubic units.

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Answer: The statement "d. The total cost is $4,950.00 since $27.50×180 = $4,950.00" is incorrect.

The first step is to convert the dimensions of the floor from feet to yards. Since 1 yard = 3 feet, the length of the floor is 15 feet / 3 feet/yard = 5 yards, and the width of the floor is 12 feet / 3 feet/yard = 4 yards. The total area of the floor is 5 yards * 4 yards = 20 square yards.

The total cost per square yard for carpet and installation is $27.50 + $4.15 = $31.65.

The total cost for carpet and installation for the entire floor is 20 square yards * $31.65/square yard = $633.00.

So, the statement "b. The total cost is $633.00 since $31.65×20 = $633.00" is correct.

Step-by-step explanation:

Answer: 35%

Explanation:

1 - 0.65 = 0.35

0.35 in percentage is 35%

Answer:

20%

Step-by-step explanation:

He spent (8500+ 1500) = 10 000   then sold it for 2000 MORE
Profit = 2000 / 10 000   * 100% = 20%

Graph A is not a function as its ordered pairs have the same first coordinate for different y coordinates.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is not a function if two distinct ordered pairs have the same first coordinate, (a, b), (a, c) is not a function.

The graph of A has an x value of - 3 and has different y values hence it is not a function.

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Answer:  A=78. 5 [tex]feet^{2}[/tex]

Step-by-step explanation:

[tex](3-2)^2+(7+5)(3-2)=(3-2)(3-2)+(7+5)(3-2)=(3-2)(3-2+7+5)=1*13=13[/tex]

Answer:

-22

Step-by-step explanation:

-9x^0-13

=-9×1-13

=-9-13

=-22

Answer:

-22

Step-by-step explanation:

To solve the expression

Let's start by finding the value of 'x'

[tex] - 9 {x}^{0} - 13[/tex]

Hint: Any number raised to power 0 is always 1.

Therefore x⁰ = 1

let's rewrite the expression by substituting where x is with 1

[tex] - 9(1) - 13[/tex]

[tex] - 9 \times 1 = - 9[/tex]

[tex] - 9 -13 = - 22[/tex]

Answer:

93cm

Step-by-step explanation:

6789 = 73 * length

length = 6789/73=93

Answer:

The length is 93 cm.

Step-by-step explanation:

We know that area is width times height. So, if we don't know what the length is,

Let x = the length

The equation would be

[tex]73x=6789\\[/tex]

We multiply 73 by x because of the formula talked about previously.

Now, lets  divide 73 on both sides

[tex]x = 93[/tex]

Answer:

27 and 13

Step-by-step explanation:

let the second number be x then the first number is x - 14

sum the 2 numbers and equate to 40

x - 14 + x = 40

2x - 14 = 40 ( add 14 to both sides )

2x = 54 ( divide both sides by 2 )

x = 27

x - 14 = 27 - 14 = 13

the first number is 27 and the second number is 13

The graph of the function g(x) = a |x| includes the point (1, 16). (-1, 16) is another point on the graph of the function.

Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function's domain and co-domain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.

Given that,

g(x) = a |x|

In a absolute value graph the value of y is the same in -x and x.

Then if the coordinates (x,y) one point is (1, 16), the graph have another point in (- 1, 16).

To find the value of a you use one of the points (x,y) in the general form of absolute value:

( 1 , 16) x = 1 f(x) = y = 16

16 = a | 1 |

As, |±a| = a

we get:

16 = a . 1

then, a = 16

The equation for the graph with points (1 , 16) and ( -1, 16) is:

g(x) = 16 |x|

a = 16

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Answer:

4/9

Step-by-step explanation:

If Jackie at 1/3, that means that 2/3 was left

2/3 x 2/3 = 4/9

Answer:

9

Step-by-step explanation:

Chebyshev's Theorem states that for any given sample, at least 1 - 1/k^2 of the data falls within k standard deviations from the mean.

Let's use k = 2. Then, at least 1 - 1/2^2 = 1 - 1/4 = 3/4 of the households should have between 3 - 2 = 1 and 3 + 2 = 5 televisions.

So, at least 12 * 3/4 = 9 of the households in the sample have between 1 and 5 televisions.

The minimum monthly income of full time worker  is $6112.

Full time worker = 4 weeks of 40 hour per week.

Part time worker = 2 weeks of 40 hour per week.

The full time hourly wage will be:

= $6112/(4 × 40)

= $6112/160

= $38.2

The part time hourly wage will be:

= $6112/(2 × 40)

= $6112/80

= $76.4

An additional child will impact the family budget as it will lead to lesser amount of money spent by each person.

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The sinusoidal function have the following features:

Amplitude: 1

Period: 2π

Frequency: ω = 2π / 2π = 1

Herein we find an example of a sinusoidal function, whose definition is shown below:

f(x) = A · sin (2π · x / T + Φ) + x'

Where:

The frequency (ω) is equal to the following formula:

ω = 2π / T

If we know that the sinusoidal function f(x) = sin (x + π / 2) - 2, then the amplitude, the period and the frequency, that is, the features of the sinusoidal function, are, respectively:

Amplitude: 1

Period: 2π

Frequency: ω = 2π / 2π = 1

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Answer:

  no

Step-by-step explanation:

You want to know if the equation y = 3x +1/5 represents a proportional relation.

A proportional relation has the equation ...

  y = kx

for some constant of proportionality k.

The added constant +1/5 in the given equation means the relation is Not Proportional.

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A) The events are not independent.

B) The events are independent.

There are 150 containers (the probabilities depend on that number), and we draw two of them.

In event A we draw one, then the number of containers after that will be 149.

Then the probabilities for event B (the second draw) are different, which means that the events are not independent.

B) If the containers are replaced, then the events are independent.

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As a result, the combo meal includes 4 onion rings and 8 pizza buns.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

Let x be the number of onion rings in the combination meal and y be the number of pizza rolls. We can write the following system of equations to represent the given information:

40x + 80y = 800 (the total calories of the meal)

y = x + 4 (the number of pizza rolls is 4 more than the number of onion rings)

We can substitute the second equation into the first equation to solve for x:

40x + 80(x + 4) = 800

40x + 80x + 320 = 800

120x = 480

x = 4

We can use this value to find y:

y = x + 4 = 4 + 4 = 8

So, the combination meal contains 4 onion rings and 8 pizza rolls.

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Answer:

Step-by-step explanation:

You want the primary trig functions of angle H in right triangle FGH with sides FG=12, GH=9, FH=15.

The mnemonic SOH CAH TOA is intended to help you with problems like this. Its purpose is to remind you that ...

With respect to angle H, the sides are ...

Then the values you want are ...

  sin(H) = 12/15 = 4/5

  cos(H) = 9/15 = 3/5

  tan(H) = 12/9 = 4/3

The value of the angle m/G is 118 degrees

It is important to note that the sum of the angles in a triangle is equivalent to 180 degrees.

From the information given, we have that;

Add the angles, we get;

8x + 14 + 3x - 6 + x + 16 = 180

collect like terms

8x + 3x + x = 180- 14 + 6 - 16

add or subtract like terms, we get;

12x = 156

Make 'x' the subject of formula by dividing both sides by the coefficient

x = 156/12

Divide the values

x = 13

m/G = 8(13) + 14

m/G = 118 degrees

Hence, the angle is 118 degrees

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The y - intercept of the graph is,  5

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 5) and (8, -2).

Now,

Since, The equation of line passes through the points (0, 5) and (8, -2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 2 - 5) / ( 8 - 0)

m = - 7 / 8

Thus, The equation of line with slope - 7/8 is,

⇒ y - 5 = - 7/8 (x - 0)

⇒ y - 5 = - 7/8x

⇒ y = - 7/8x + 5

Therefore, The y - intercept of the graph is,  5

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z-score for value 550 =  0.5

z-score for value 660 = 1.6

z-score for value 500 = 0

z-score for value 440 = -0.6

z-score for value 270 = -2.3

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

We are given a sample with a mean of 500 and a standard deviation of 100.

i.e.,  µ= 500 and  s= 100

The z score distribution is given by;

             Z =  (X-µ)/s ~ N(0,1)

where X represents the data values;

So, z score for value 550 is;

                z score =(550-500)/100  = 0.5

So, z score for value 660 is;

                z score = (660-500)/100  = 1.6

So, z score for value 500 is;

                z score = (550-500)/100  = 0

So, z score for value 440 is;

                z score =  (440-500)/100  = -0.6

So, z score for value 270 is;

                z score = (270-500)/100  = -2.3

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z-score for value 550 =  0.5

z-score for value 660 = 1.6

z-score for value 500 = 0

z-score for value 440 = -0.6

z-score for value 270 = -2.3

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

We are given a sample with a mean of 500 and a standard deviation of 100.

i.e.,  µ= 500 and  s= 100

The z score distribution is given by;

            Z =  (X-µ)/s ~ N(0,1)

where X represents the data values;

So, z score for value 550 is;

               z score =(550-500)/100  = 0.5

So, z score for value 660 is;

               z score = (660-500)/100  = 1.6

So, z score for value 500 is;

               z score = (550-500)/100  = 0

So, z score for value 440 is;

               z score =  (440-500)/100  = -0.6

So, z score for value 270 is;

               z score = (270-500)/100  = -2.3

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Answer:

  [9, 9+√18.25] ≈ [9, 13.272]

Step-by-step explanation:

You want the range of f(x)= 9+√(6+7x-x^2), determined algebraically.

The range is the set of values that f(x) may take on. It is the vertical extent of the graph. Here, it will be limited by the possible values the radical may have.

The expression under the radical is a quadratic that opens downward. It will have a maximum at its vertex, and a minimum usable value of 0.

The vertex of the quadratic can be found by putting it in vertex form:

  -x² +7x +6 = -(x² -7x) +6 = -(x² -7x +(7/2)²) +6 +(7/2)² = -(x -7/2)² +18.25

The maximum value the quadratic may have is 18.25.

Then the range of values that f(x) may have is ...

  9 +0 ≤ f(x) ≤ 9 +√18.25

The range is [9, 9+√18.25] ≈ [9, 13.272].

A. The probability that a randomly selected person aged 40 years or older is female and smokes is 0.05841.

B. No, it would not be unusual to randomly select a person aged 40 years or older who is female and smokes.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

When given an event A and an event B, the conditional probability that A will occur given than B has occurred is calculated using this formula -

P(A|B) = P(A and B) / P(B)

Let A be that the person is female and B be that they smoke. It is known that P(B) = 0.295 and let P(A|B) = 0.198.

Use the formula for conditional probability -

0.198 = P(A and B) / 0.295

P(A and B) = 0.198 × 0.295

P(A and B) = 0.05841

The probability that a person aged 40 years or older is female and smokes would happen is 0.05841, which is not less than the usual benchmark of 0.05 to be considered unusual.

Therefore, no, this would not be unusual.

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Suppose there is a 29.5% probability that a randomly selected person aged 40 years or older is a smoker. In addition, there is a 19.8% probability that a randomly selected person aged 40 years or older is a smoker. A. What is the probability that a randomly selected person aged 40 years or older is female and smokes? B. Would it be unusual to randomly select a person aged 40 years or older who is female and smokes?

One learning aid that  provides an interactive​ walk-through for solving the particular problem you are working on is "view an example"

It is also known as teaching aids, which are an essential part of any classroom. Teaching aids can help students improve their reading comprehension skills, illustrate or reinforce a skill or concept, differentiate instruction, and relieve anxiety or boredom by presenting information in a new and exciting way.

Teaching aids also engage students' other senses because there are no restrictions on what aids can be used to supplement a lesson. As technology advances, so do teaching aids, which are now classified as audio aids, visual aids, mechanical teaching aids, audio-visual aids, and more.

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