some friends decided to equally split the cost of gas on their trip. the expression 3g4 represents how much money each person had to pay in dollars for g gallons of gas. what does the expression 3g in the numerator represent?

Answer:

1/8

Step-by-step explanation:

Answer:

25 miles per gallon

Step-by-step explanation:

Because if 2 gallons is 50 miles then one gallon has to be 25 miles per gallon

Answer:

3x-5

Step-by-step explanation:

Answer:

5 2/3

Step-by-step explanation:

because 17/3= 5 so 5 then they is 2 left so the answer is 5 2/3

The total number of attendees who attended the seminar was 97. While the total cost and revenue generated are given to be $1455 each. This problem is solved using the knowledge of linear equations.

What is a linear equation?

It is the equation in which the degree of a variable is always one i.e. the greatest power of a variable is one. Linear equations consist of two major types, linear equations in one variable and linear equations in two variables. The general form of a linear equation in one variable is ax + b = 0, while for two variables is ax + by + c = 0

Calculation of the total number of attendees of seminar and total revenue generated

Let us assume x as the number of attendees and C(x) as the cost function for the company

According to the given conditions,

C(x) = 11x + 388

As the company pays $11 for every person, thus the total amount for x attendees is given by 11x, further $388 is added up to attain overall dollars.

Further, let the revenue be R(x) being equal to $15 per person i.e.

R(x) = 15x

The company will be breaking even when the cost and revenue are the same, R(x) = C(x)

15x = 11x + 388

15x - 11x = 388

4x = 388

x = 97

Thus, the total number of people attending the seminar is 97.

Now, calculate the total expense, C(x) and revenue, R(x)

C(x) = 11(97) + 388

= $1455

R(x) = 15(97)

= $1455

The cost and revenue are $1455 for each.

Hence, the total number of attendees who attended the seminar is 97. Total cost and revenue are given to be $1455 each.

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Since the graph of g is translated vertically downward by 3 units, the graph of function h is equal to h(x) = 2x² - 10.

In Mathematics, there are different types of transformation and these include the following:

A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

Since the graph of g is translated vertically downward by 3 units, the graph of function h would be represented by the following expression:

Note: g(x) = 2x² - 7

h(x) = g(x) - 3.

h(x) = 2x² - 7 - 3.

h(x) = 2x² - 10.

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Total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

As given in the question,

Macro earns commission rate of 6% for the first $6500

And 9% on sales over $6500

Out of $10,500

For first $6500 Commission =(6500 × 6)/ 100

                                            = $390

For $ (10,500 - 6,500 = 4000) commission = (4000 × 9)/ 100

                                                                   = $360

Total graduated commission on sales of $10,500 = $( 390 + 360)

                                                                             = $750

Therefore, total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

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Answer:

We can now solve for B(x2, y2):

-14 = -3 + x2 and 16 = 6 + y2

-11 = x2 ... and... 10 = y2

Therefore B(x2, y2) = (-11, 10)

Step-by-step explanation:

The information illustrated about the statistics 201 is a sample.

A sample is an analytical subset of a larger population in statistics. Researchers can conduct their studies more quickly and with more manageable data by using samples. If the sample size is large enough, there won't be any bias, but getting such a sample might be costly and time-consuming.

The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.

Since there are many students, a sample will be used.

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For the following questions, would you collect information using a sample or population

a. statistics 201 is a course taught at a university. professor rauch has taught nearly 1500 students in the course over the past 5 years. you would like to know the average grade for the course

Answer:

21

Step-by-step explanation:

35x18 is 630/30 is 21.

The limit doesn't exist.

The value that a function (or sequence) approaches when the input (or index) gets closer to a particular value is known as a limit. Calculus and mathematical analysis are impossible without limits, which are also required to determine continuity, derivatives, and integrals.

In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the concept of a limit of a topological net.

A function's limit is typically expressed in formulas as

[tex]\lim_{x \to c } F(x) = L[/tex]

It is typically used to assign values to specific functions at locations where none are defined while maintaining consistency with existing values.

[tex]F(x) = -x+8 ,x\leq 0[/tex]

[tex]F(x) = 4x+9 , if x > 0[/tex]

[tex]\lim_{x \to 0^{+} } F(x) = \lim_{n \to 0^{+} } (4x+9) = 9[/tex]

[tex]\lim_{x \to 0^{-} } F(x) = \lim_{x \to 0^{-} } (-x+8) =8[/tex]

[tex]\lim_{x \to 0^{+} } F(x) \neq \lim_{x \to 0^{-} } F(x)[/tex]

So limit doesn't exist

For limit to exist

[tex]\lim_{x \to 0^{+} } F(x) = \lim_{x \to 0^{-} } F(x) = \lim_{x \to 0} f(x)[/tex]

must be satisfied

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The cargo plane flew approximately 1,760 km.

So, according to the information the equation formed will be:

Now, solve the equation for x:

Rounding off: 8

Therefore, the cargo plane flew approximately 1,760 km.

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Answer:

0=4    No solution

Step-by-step explanation:

you combine like terms like n, and n= 2n+8

then subtract 4 from both sides= 2n=2n+4

greatest to smallest :  [tex]= \sqrt[3]{88} ,\sqrt{19} ,\frac{28}{9}[/tex]

Fraction: A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator

Square root: In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = 16

Use this fraction calculator for adding, subtracting, multiplying, and dividing fractions. Answers are fractions in the lowest terms or mixed numbers in reduced form.

Input proper or improper fractions, select the math sign, and click Calculate. This is a fraction calculator with steps shown in the solution.

If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.

Solution :

[tex]\sqrt[3]{88} \\\sqrt[3]{2.2.2.11} \\2\sqrt[3]{11} \\\sqrt[3]{11} = 2.224\\2.2.224\\4.448 ...(1)\\\\\\\frac{28}{9} = 3.333 ...(2)\\\\ \sqrt{19} = 4.359 ...(3)\\\\Form 1 , 2 & 3 \\\\greatest number to smallest number = 4.448 , 4.359 ,3.333\\= \sqrt[3]{88} ,\sqrt{19} ,\frac{28}{9}[/tex]

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The geometric relationship between AP and PB such that M is the midpoint of AB and P is the midpoint of AM is PB = 3AP.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

Given that,

M is the midpoint of AB and P is the midpoint of AM

Let's suppose AP = x

Then,

AB = AM + MB

Since M is the midpoint so AM =

MB = AM

AB = AM + AM = 2AM

Since P is the midpoint of A and M

So,

AP = PM

AM = AP + PM

So,

AM = 2AP = 2x

So,

MB = 2x

So,

AP = x and PB = 3x

PB = 3AP

Hence "The geometric relationship between AP and PB such that M is the midpoint of AB and P is the midpoint of AM is PB = 3AP".

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4 liters of pure antifreeze is needed.

What is an linear equation in math?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term.

The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let the amount of pure antifreeze required be x + 10 liters. Thus, total solution amount will be

0.30 (10) + 1.00(x) = 0.50 ( x + 10 )

     3.00 + x = 0.50x + 5.00

     0.50x = 2.00

          x = 4

Thus, 4 liters of pure antifreeze is needed.

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The points X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below. From the obtained graph ∠XYZ is the obtuse angle.

The given coordinates are X(5,-3), Y(4,-1) and Z(6,-2).

We need to classify ∠XYZ whether it is right, acute, or obtuse.

A cartesian plane or coordinate plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.

Now, X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below:

The given points X(5,-3), Y(4,-1) and Z(6,-2) have positive x-coordinate and negative y-coordinate.

In the cartesian plane, the fourth quadrant positive x-coordinate and negative y-coordinate.

So, all points X(5,-3), Y(4,-1) and Z(6,-2) lie in the fourth quadrant.

From the graph, we can see that the two lines make an obtuse angle, which is more than 180° and less than 360°.

From the obtained graph ∠XYZ is the obtuse angle.

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the probability that a random selected student walks to the school is 19.5%, the correct option is D.

We want to find the probability that a random selected student walks to the school.

To find it, we just need to take the quotient between the number of students that walk to the school and the total number of students.

The number of students that walk to the school is:

42 + 36 = 78

The total number of students is:

85 + 77 + 30 + 47 + 42 + 36 + 44 + 39 = 400

Then the probability is:

P = 78/400 = 0.195

To get this in percentage form, we just multiply by 100%.

0.195*100% = 19.5%

The correct option is D.

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Answer:

20

Step-by-step explanation:

The additive inverse of the expression -3/w is 3/w.

A number is known as the additive inverse of another, if the sum of the two numbers comes out to be zero. For example- given a number 3, its additive inverse will be -3, as 3 + (-3) = 0. The additive inverse of 0 is 0 itself.

Here, we are given an expression -3/w, such that w ≠ 0

Let us assume that the additive inverse of -3/w is x

Then, the sum of -3/w and x must be equal to zero

⇒ -3/w + x = 0

adding 3/w to both sides

⇒ x = 3/w

Thus, the additive inverse of -3/w is 3/w.

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Answer:

d = √[(x2 x 2 − x1 x 1 )2 + (y2 y 2 − y1 y 1 )2]

Step-by-step explanation:

It would take 7 years for  the initial investment of $200 to become $350

Which calculator is appropriate in this case?

The best calculator which addresses the case at hand is a financial calculator, since it is mandatory we make use of calculator to determine the number of years it takes for initial investment of $200 to grow to $350 with 8% interest compounded continuously, bearing in mind that we need to convert the interest rate to a discrete rate

Rd = (e^(Rc) - 1)

Rd=discrete annual rate=unknown

e=exponential value=2.7182818

Rc=continuous rate=8%

Rd=(2.1782818^(8%))-1

Rd=1.083287067-1

Rd=8.3287067%

I/Y=8.3287067=annual interest rate without the % sign

PMT=0(no annual additional investment)

PV=-200(initial investment)

FV=350(future value of investment)

CPT(press compute)

N=7

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Answer:

Step-by-step explanation:

Based on the dimensions of the semicircle and the rectangle, the approximate area that Ysau paints is  514 ft²

First, find the area of the rectangle:

= 24 x 12

= 288 ft²

The area of the semi-circle is the area of a circle divided by two. The radius is half of the longer side of the rectangle:

= 24 / 2

= 12 ft

Area of the semicircle is:

= (22/7 x 12 x 12) / 2

= 226 ft²

The total approximate area is:

= 226 + 288

= 514 ft²

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Values at one, two and three standard deviations are 77.9, 82.8 and 87.7 respectively. Values at -1, -2 and -3 standard deviations are 68.1, 63.2 and 58.3 respectively.

The average grade given = 73

So, the mean, μ = 73

The standard deviation, σ = 4.9

We need to find the 1,2 and 3 standard deviations and -1, -2 and -3 deviations from the mean.

We use the formula z = μ + nσ to find the values at nth deviations.

When n = 1

z = 73 + 1 x 4.9 = 77.9

When n = 2

z = 73 + 2 x 4.9 = 82.8

When n = 3

z = 73 + 3 x 4.9 = 87.7

When n = -1

z = 73 -1 x 4.9 = 68.1

When n = -2

z = 73 - 2 x 4.9 = 63.2

When n = -3

z = 73 - 3 x 4.9 = 58.3

Hence, these are the required values.

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The expression equal to 8 × 10 5 squared is 64 × 10^10

Scientific notation is a mathematical way of expressing numbers that are too large or small to be written in decimal form.

Given the expression;

(8 × 10^ 5)²

expand the bracket

(8)² × (10)^ 5× 2

Find the squares

64 × 10^10

This is expressed as;

64 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10

Thus, the expression equal to 8 × 10 5 squared is 64 × 10^10

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The standard form is  [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125.

We have,

f ( x ) =  [tex]x^{2}[/tex]+ 9 x + 20        

g ( x ) = x + 5

Now we will simplify f ( x ) + g ( x ) f ( x ) + g ( x ).

On substituting the value of f ( x ) and g ( x ) in this equation, we get

( [tex]x^{2}[/tex]+ 9 x + 20 ) + ( x + 5) ( [tex]x^{2}[/tex]+ 9 x + 20 ) + ( x + 5)

Now we will simplify this equation,

( [tex]x^{2}[/tex]+ 10 x + 25 ) + ( [tex]x^{3}[/tex] + 9[tex]x^{2}[/tex] + 20x + 5[tex]x^{2}[/tex] + 45x + 100 )

⇒ [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125

The standard form is  [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125.

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Answer:

631%

Step-by-step explanation:

Answer:

631%

Step-by-step explanation:

When Mai-Lin's target heart rate is 153, then her age is 16 years.

From the information, the The American Heart Association suggests a target heart rate of T=0.75(220-a),

where T = person's target heart rate

a = his or her age.

Therefore, when the heart rate is 153, the age will be:

T = 0.75(220 - a)

153 = 165 - 0.75a

0.75a = 165 - 153

0.75a = 12

Divide

a = 12/0.75

a = 16

The person's age is 16 years.

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Answer:

77 degrees

Step-by-step explanation:

180 - 103