Solve the system of equations by substitution. Show your work.
y = 2x - 1
6x - 2y = 24

Answer:

1. mean: 51.68, median: 51

2. 100 numbers (n represents how many numbers are in the set)

3. Interquartile range: 54 (subtract Q1 from Q3)

Answer:

The cost of the car with sales tax would be $23,406.38.

Step-by-step explanation:

You can calculate this by adding the sales tax to the cost of the car:

$21,500 * 8.25% = $1,786.25

$21,500 + $1,786.25 = $23,286.25

The x-intercepts of the quadratic function can be found by setting y to 0 and solving for x. The x-intercepts are -9, -3.5 and 3.5

The line of symmetry of a quadratic function, represented by the equation y = ax^2 + bx + c, is x = -b/(2a).

Since the line of symmetry of the given function is x = -3.5, we have -b/(2a) = -3.5, so b/(2a) = 3.5.

The zeros of a quadratic function are given by the solutions of the equation y = 0, which is equivalent to ax^2 + bx + c = 0.

Since the function has a zero at x = -9, the equation becomes -9 = -9a^2 - 9b + c, or 9a^2 + 9b - c = 0.

We can use the equation b/(2a) = 3.5 to find a in terms of b, which can then be used to solve for c.

Substituting b/(2a) = 3.5 into 9a^2 + 9b - c = 0 gives us 9a^2 + 9(2a * 3.5) - c = 0.

Simplifying the right-hand side gives us 9a^2 + 63a - c = 0.

So, c = 9a^2 + 63a.

The x-intercepts are given by the solutions of the equation ax^2 + bx + c = 0, so to find them, we can substitute the values of a, b, and c into this equation.

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The standard form for this number is 7.1509 x [tex]10^4[/tex].

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(9 × 1) + (5 × 1100) + (6 × 11,000)

The standard form for this number is written with a decimal number greater than 1 but less than 2 with an exponent of 10.

Now,

= 9 + 5500 + 66,000

= 71509

= 7.1509 x [tex]10^4[/tex]

Thus,

The standard form is 7.1509 x [tex]10^4[/tex].

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Answer:

71509

Step-by-step explanation:

If there is an inflation rate of 2%, then the cost of  $60 pair of shoes in 5 years is,  $66.245

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

Rate of inflation = 2%

The cost of pair of shoes = $60

Cost after 5 years = ?

After 1 year cost will be,

⇒  $60 +  2% of original cost

2% of original cost =  (60 x 2)/100

                               =   0.02 x 60

⇒   $60 + $0.02 x 60

⇒   $60(1 + 0.02)

After 2 year cost will be,

⇒ $60(1 + 0.02) +  2% of cost after 1 year

2% of original cost =  ( 60(1 + 0.02) x 2)/100

                               =   0.02 x 60(1 + 0.02)

⇒   $60(1 + 0.02) + $0.02 x 60(1 + 0.02)

⇒   $60(1 + 0.02)(1 + 0.02)

Similarly, After 5 years,

⇒ $60(1 + 0.02)(1 + 0.02)(1 + 0.02)(1 + 0.02)(1 + 0.02)

⇒ $ 60 x 1.02⁵

⇒ $ 60 x 1.104

⇒ $ 66.245

Hence, the cost will be  $66.245

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Answer: (a) The probability that all three have type B+ blood is (0.11) * (0.11) * (0.11) = 0.001331 = 0.1331% (rounded to six decimal places).

(b) Find the probability that exactly two of the three have type B+ blood.

The probability that exactly two of the three have type B+ blood can be found using the formula for combinations: C(3,2) * (0.11)^2 * (0.89)^1, where C(3,2) represents the number of ways to choose 2 people out of 3, (0.11)^2 is the probability of both of those people having type B+ blood, and (0.89)^1 is the probability of the third person not having type B+ blood. So, C(3,2) * (0.11)^2 * (0.89)^1 = 3 * 0.11^2 * 0.89 = 0.3027 (rounded to four decimal places).

(c) Find the probability that exactly one of the three has type B+ blood.

The probability that exactly one of the three has type B+ blood can be found using the formula for combinations: C(3,1) * (0.11)^1 * (0.89)^2, where C(3,1) represents the number of ways to choose 1 person out of 3, (0.11)^1 is the probability of that person having type B+ blood, and (0.89)^2 is the probability of the other two people not having type B+ blood. So, C(3,1) * (0.11)^1 * (0.89)^2 = 3 * 0.11 * 0.89^2 = 0.2613 (rounded to four decimal places).

(d) Find the probability that none of the three has type B+ blood.

The probability that none of the three has type B+ blood is (0.89)^3 = 0.696731 = 69.6731% (rounded to four decimal places).

Step-by-step explanation:

The equation of line passes through the point (-8, 7) will be;

⇒ y = - 9x - 65

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;

The point on the line are (-8, 7).

And, The parallel line is,

⇒ y = - 9x + 8

Now,

Since, The equation of line passes through the point (- 8, 7).

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

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

y = -9x + 8

m = dy/dx = - 9

m = - 9

Thus, The equation of line with slope - 9 is,

⇒ y - 7 = - 9 (x - (-8))

⇒ y - 7 = - 9 (x + 8)

⇒ y - 7 = - 9x - 72

⇒ y = - 9x - 72 + 7

⇒ y = - 9x - 65

Therefore, The equation of line passes through the point (-8, 7) will be;

⇒ y = - 9x - 65

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Answer: [tex]x=20, y=26[/tex]

Step-by-step explanation:

Opposite sides of a parallelogram are congruent.

The general term formula for the Fibonacci sequence would be   [tex]F_n=\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n - (\frac{1-\sqrt{5}}{2})^n)[/tex].

What is a Fibonacci Sequence?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, starting from 0 and 1. The sequence goes as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on.

The Fibonacci sequence is given by

                              [tex]F_n-F_{n-1}-F_{n-2}=0[/tex]

So its characteristic polynomial is

                               [tex]x^2-x-1=0[/tex]

The roots of this are

                            [tex]\alpha=\frac{1+\sqrt{5}}{2}\\\\\beta=\frac{1-\sqrt{5}}{2}[/tex]
Each with multiplicity one. Hence,

                      [tex]F_n=A\alpha^n + B\beta^n\\\\\For $ F_1=1 $ $and $ $ F_2=1$\\\\A=1/\sqrt{5} \\\\B=-1/\sqrt{5}[/tex]

Thus,

                   [tex]F_n=\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n - (\frac{1-\sqrt{5}}{2})^n)[/tex]

Hence, the general term formula for the Fibonacci sequence would be   [tex]F_n=\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n - (\frac{1-\sqrt{5}}{2})^n)[/tex].

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Answer:

adult tickets purchased = 9

student tickets purchased = 3

Step-by-step explanation:

a = # of adult tickets purchased

s = # of student tickets purchased

(1)   a + s = 12

(2)  $5a + $3s = $54

solve equation (1) for s:

s = 12 - a    now substitute this into equation (2) so you have an expression all in terms of a

$5a + $3(12 - a) = $54    solve for a

5a + 36 - 3a = 54

2a = 54 - 36 = 18

a = 18/2 = 9     substitute this into equation (1) and solve for s

9 + s = 12

s = 12 - 9 = 3  

Answer:

Step-by-step explanation:

The number of students should be in the class should be considered as the 36.

Calculation of the number of students:

Since

there are between 25 and 43 students in a class

the ratio of boys to girls is 5 : 7

So here the total ratio should be like

= 5 + 7

= 12

So here the number of students should be divisible by 12

So, it should be 36

The value of fractions after subtraction is,

⇒ - (y² - 10y - 12) / (y - 4) × 1 / (y + 2)

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

⇒ y/ (y + 2) is subtracted from 6 / (y - 4).

Now, We can subtract as;

⇒ 6 / (y - 4) - y / (y + 2)

⇒ 6 (y + 2) - y (y - 4) / (y - 4) (y + 2)

⇒ (6y + 12 - y² + 4y) / (y - 4) (y + 2)

⇒ (- y² + 10y + 12) / (y - 4) (y + 2)

⇒ - (y² - 10y - 12) / (y - 4) (y + 2)

⇒ - (y² - 10y - 12) / (y - 4) (y + 2)

⇒ - (y² - 10y - 12) / (y - 4) × 1 / (y + 2)

Thus, The value of fractions after subtraction is,

⇒ - (y² - 10y - 12) / (y - 4) × 1 / (y + 2)

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Step-by-step explanation:

since you don't show us f(x) here, I can only tell you in general :

when you are asked for something like f(2), it means that x = 2, and that you have to replace all "x" in the f(x) definition by "2". and then you take the calculator, if necessary, and calculate.

The two expressions are equivalent is equal to 2y+19.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

(y+10)+y+9

⇒ y+y+10+9

⇒2y+19

using addition we get this.

now, we have,

and 2 (y+7)+5

⇒2y +14+5

⇒2y+19

using  multiplication & then addition , we get, this.

Hence, the two expressions are equivalent is equal to 2y+19.

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The suitable inequalities that can shown the shaded region are

2x-y≤0 and 2x-4y≤0

Inequality can be viewed from different perspectives, all of which are related. Most common metric is Income Inequality, which refers to the extent to which income is evenly distributed within a population.

From the graph, the first line cuts the x-axis at point 2 and touches the y-axis at -1

This forms the inequality 2x-y≤0 and

the second graph/line cuts the x-axis at point 2 and the y-axis at point -4 making the inequality 2x-4y≤0

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The linear equation that models the population is:

p(t) = 2200*t - 4356000

And in 2010 the population was 66000.

We know that the population grows linearly.

Remember that the general linear equation can be written as:

y = a*t +b

Where a is the slope and b is the y-intercept.

And if the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the points (2005, 55000) and (2008, 61600)

Then the slope is:

a = (61600 - 55000)/(2008 - 2005)

a = 2200

Then the line is something like:

y = 2200*t + b

To find the value of b we can replace the values of the point (2005, 55000), then we will get:

55000 = 2200*2005 + b

55000 - 2200*2005 = b

-4356000 = b

The linear equation is

p(t) = 2200*t - 4356000

The population in 2010 is:

p(2010) = 2200*2010 - -4356000 = 66000

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The amount invested at each rate of 2% and 7% respectively is $12000 and $2000

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent the amount invested at 2% by x and the amount invested at 7% by y

therefore x+y = 14000 equation 1

2x/100 + 7y/100 = 380

multiply through by 100

2x + 7y = 38000 equation 2

using elimination method

2x + 2y = 28000 equation 3

2x + 7y = 38000 equation 4

subtract equation 3 from 4

5y = 10000

divide both sides by 5

y = 10000/5

y = $2000

substitute 2000 for y in equation 1

x+2000 = 14000

x = 14000-2000

x = $12000

therefore the amount invested at 2% rate is $12000 and at 7% rate is $2000

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The correct measures of these two angles are, 30°  and 150°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

We know that, a ray is a line that continues on forever inn one direction with a point at it's start.

here, we have,

He also wants the measure of ∠A to be five times the measure of ∠D.

Let the smaller side is x then other side is 5x,

so, we get,

x+5x=180°[interior property]

on solving we get

6x=180°

x=30°

therefore, the other side is 5x

                                             =5*30°

                                             =150°

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Probability that both donators are O blood type = 0.0203

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x.

The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given,

A group of 46 people where 7 of them are O blood type

Probability of one donator to be O blood type

= No. of People with O blood type/total People in the group

= 7/46

No. of people left in the group left after choosing one donator = 46 - 1 = 45

No. of People left with O Blood type = 7 - 1 = 6

Probability of 2nd donator to be O blood type = 6/45

Probability that both are O blood type = 7/46 × 6/45

                                                                = 42/2070

                                                                = 0.0203

Hence, there is probability of 0.0203 that both donators are of O blood type.

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The following statements about the data above which is true is that the estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A which is denoted as option B.

This is information that has been translated into a form that is efficient for movement or processing.

From the table we can deduce that the number of employees who vited for coffee is higher in Group B than A and is therefore the reason why it was chosen as the correct choice.

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The number of classes who took test are 12.

A division is a process of splitting a specific amount into equal parts.

Given that Junior high classes of 20 students each met in the cafeteria to take achievement tests.

Exactly 8 students sat at each table and 30 tables were used,

We have to find the number of classes who took the tests.

8 students sat at each table and 30 tables were used then 30×8 students were sitting =240 students.      

Every class is made of 20 students so to know how many classes took the test make 240/20  which gives you 12 classes

Hence, the number of classes who took test are 12.

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The expression that can be used to find the area of the shaded portion will be C. 2/3 × 9² × π

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

In this situation, the circle has a radius of 9 inches and is divided into 6 equal parts. the area of a single section of the circle is equal to 13.5(pie) square inches.

The expression that can be used to find the area of the shaded portion will be:

= 4/6 × πr²

= 4/6 × 9² × π

= 2/3 × 9² × π

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The measure of angle W in the kite WXYZ is 115°

A kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides.

Given that, In kite WXYZ, m ∠ x = 90° and m ∠ z =40°.

Please refer to figure attached,

We know that, in a kite, it has two opposite and equal angles.

According to figure, here,

m ∠ W = m ∠ Y

Let m ∠ W = m ∠ Y = x

Also, the sum of interior angles of quadrilateral = 360°

Therefore,

x + x + 90° + 40° = 360°

2x = 360° - 130°

2x = 230°

x = 115°

Thus, m ∠ W = m ∠ Y = 115°  

Hence, the measure of angle W in the kite WXYZ is 115°

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Answer:

2/8 + 3/8 = 5/8

Step-by-step explanation:

Total: 8 marbles

Yellow: 3

Green: 2

8 - 3 - 2 = 3

Blue: 3

Fraction of yellow: 3/8

Fraction of green: 2/8

Fraction of yellow and green:

2/8 + 3/8 = 5/8

The speed of the train in miles per hour is equal to 120 miles per hour.

In Mathematics, speed can be defined as the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using this unit of measurement;

Mathematically, the speed of this train can be calculated by using this formula;

Speed = total distance/time

Speed = (450 + 270)/6

Speed = 720/6

Speed = 120 miles per hour.

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Answer:

B

Step-by-step explanation:

orignal height：length＝1：3

for B＝3：9 same as 1：3

The required average mark for a one-hour exam is given as 81, as per the given condition.  

The average of the values is the ratio of the total sum of values to the number of values.

To find the student's grade, we need to calculate the average of all the exams. The total number of 1-hour exams is 4 + 2 = 6, so the total number of hours of exams is 6 * 1 hour = 6 hours.

First, we find the average of the four 1-hour exams: (63 + 78 + 95 + 90) ÷ 4 = 316 ÷ 4 = 79.

Next, we add the final exam grade, which counts as two 1-hour exams, to find the total number of exam points: 79 * 4 + 85 * 2 = 316 + 170 = 486.

Finally, we divide the total number of points by the total number of hours of exams to find the average exam grade: 486 ÷ 6 = 81.

So, the student's average exam grade is 81.

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