A line with a positive slope is perpendicular to one of the lines shown. What is its slope? Use the graph shown below.

a) The median number of hours per week these Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k is 5.75 hours.

The median is a central value or a middle value in a distribution. The number of values in a dataset is an important factor that determines the calculation of the median. It is a value that cuts the data set into two equal parts.

The data set consists of 20 Year 12 students. Sort the data in ascending order (or descending order) and find the middle value. Then, use the formula for calculating the median. 

a)The number of hours per week the Year 12 students spend doing homework is given as:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Arrange the data in ascending order:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Now count the data, which gives us 20 numbers. The middle value is the 10th and the 11th numbers, which are both 4.

So the median of the number of hours per week Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k can be found using the following formula:

100% - 10% = 90%

So, 90% of students study for k hours or less.

So, the value of k can be found using the median. The median value is 4 hours, and 90% of students are studying for k hours or less. Therefore, 10% of students study for more than k hours.

k = 10% more than the value of the 90th percentile value, which is given by: k = 5.5 + ((8-5.5)/10)*1 = 5.5 + 0.25 = 5.75 hours.

Therefore, 10% of Year 12 students spend more than 5.75 hours per week doing homework.

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441

Step-by-step explanation:

420-5%=399 so the diference is 21 so 21+420=441

Answer:

1. y= -2/5x+3

2. y= 3x-2

3. y= -1/2+0

Step-by-step explanation:

The formula for a linear equation is y=mx+b with

m=slope

and b= the y-intercept.

The measures of angles A and B must be complementary (add up to 90°) and differ by 90°If sin A = cos B, then we can use the trigonometric identity sin A = cos (90° - A) to get:

sin A = cos B

sin A = sin (90° - B)

Setting the two expressions for sin A equal to each other, we have:

cos B = sin (90° - B)

Using the trigonometric identity sin (90° - x) = cos x, we can write:

cos B = cos (90° - B)

This means that either:

B = 90° - A

or

B = A + 90°

In other words, the measures of angles A and B must be complementary (add up to 90°) and differ by 90°.

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Answer:

Step-by-step explanation:

m≥150

draw a solid dot (since it is greater than or equal to) starting at 150 and continue to the end of the number line.

Answer:

B. m is greater than or equal to 150

Step-by-step explanation:

if he has to drive at least 150, then he must drive 150 miles or more

Answer:

C

Step-by-step explanation:

trust

Answer:

5)7:8=180

84:96=180

6)4:5=90

40:50=90

7)a). q=135

p=45

b).a=70

b=110

supplementary angle=sum of two angle 180°

complementary angle=sum of two angle 90°

Answer:

The two angle 7 and 8 —> 7x and 8x

Sum of two supplementary angle is 180°

7x +8x =180

15x =180

x= 180/15

x = 12°

7x =7(12)= 84°

8x = 8(12)= 96°

The angles; 84° , 96°

The two angle 4 , 5 —> 4x and 5x

Sum of two complimentary angle is 90°

4x+5x =90

9x =90

x=90/9

x=10

4x—> 4(10) = 40°

5x —> 5(10) = 50°

The angles; 40° , 50°

q= 135 ( Vertically Opposite angles)

q+p = 180

135+p=180

p=180-135

p = 45°

_______o_____o_____

a= 70° ( Alternate angles)

a+ b = 180

70 + b = 180

b =180 - 70

b = 110

So ; angle a=70° , b = 110°

I hope I helped you^_^

Answer:

Check below:

Step-by-step explanation:

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs so that you can factor out a common factor from each pair.

3x² + 6x + 4x + 8

(3x² + 6x) + (4x + 8)

Step 2: Factoring out the common factors

Factor out the common factors from each pair separately.

3x(x + 2) + 4(x + 2)

Step 3: Factoring out the common factor from the resulting expression

Notice that we have a common factor, (x + 2), in both terms.

(x + 2)(3x + 4)

Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).

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Using proportions, it is found that the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.

The Ruiz family is exchanging Euros for USD dollars, considering the following currency rate:

1 euro = 1.35261 USD.

Considering that the amounts in USD are rounded to the nearest hundredth, the use the following rule

1 euro - 1.35 USD.

It asks if the Ruiz family will be getting the most accurate answer.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, we suppose a 1000 euros amount, them:

Hence the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.

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Answer:

3x 2 +7 = 13 + 5x3+10= 38

Step-by-step explanation:

38 is your answer. Hope I helped.

Answer: So you need to do the slope-intercept form  for y = mx+b so that you can find the slope of m.

Step-by-step explanation:

-y  =  3  −  2 x

Multiply each term:

1 y = 3⋅ −1 + (−2x)⋅ −1

y = 3. −1 + (−2x)⋅ −1

y=−3+(−2x)⋅−1

y=−3+2x

y=2x−3

Answer:

yes

Step-by-step explanation:

From the calculation that we have done;

Angle B =   80.2°

Angle C = 59.8°

Side c =  20.3

The sine rule, often referred to as the law of sines, is a geometrical concept that links the sines of a triangle's opposite angles to the lengths of its sides. It claims that for all triangle sides and angles, the ratio of a side's length to the sine of its opposite angle is constant.

We have to apply the sine rule in the calculation;

We know that;

a/Sin A = b/SinB

Hence;

15/Sin 40 = 23/SinB

15 Sin B = 23Sin 40

B = Sin-1( 23Sin 40/15)

B = 80.2°

Angle C =

180 - (80.2 + 40)

= 59.8°

Then Side c

c/Sin 59.8 = 15/Sin 40

cSin40 = 15 Sin 59.8

c = 15 Sin 59.8/Sin 40

= 12.96/0.64

= 20.3

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Answer:

  -425

Step-by-step explanation:

You want the sum of the first 8 terms of the geometric series with first term 5 and common ratio -2.

The sum is given by the formula ...

  Sn = a1·(r^n -1)/(r -1) . . . . . . a1 = first term, r = common ratio

The sum of 8 terms of the given series is ...

  S8 = 5·((-2)^8 -1)/(-2 -1) = 5(255/-3) = -1275/3 = -425

The sum of 8 terms is -425.

Answer:

12:5:18

Step-by-step explanation:

60:25:90

12:5:18

Answer:

(4, 5)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

3x + 3y = 27

x - 3y = -11

Step 2: Solve for x

Step 3: Solve for y

The correct response is D. a segment of a line that goes on forever in one direction from one terminal.

A line is a one-dimensional, perfectly straight shape that extends forever and is infinitely thin in both directions. A line may be referred to as a straight line or, more formally, a right line (Casey 1893), to stress that there are no "wiggles" throughout its entire length. When two points are connected with the smallest possible distance between them and both ends stretched to infinity, a line is the shape that results. Despite the fact that lines don't have a clear beginning or finish, they are represented in our daily lives by things like railroad tracks and freeways. Any section of a line with two fixed endpoints is referred to as a line. Line segments make up a line.

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Answer:

slope intercept form or an linear equation.

The equation that Rae should use to determine the width of a pen is 280 = w(w + 6)

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilateral are kite, rhombus, rectangle, square, parallelogram.

A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other. Each angle measure 90 degrees and diagonals bisect each other.

The area of rectangle is:

area = length * width

Let w represent the width of the rectangle

Given that length is 6 feet longer than the width, length = w + 6. Hence:

Area = length * width

substituting:

280 = w(w + 6)

w² + 6w - 280 = 0

The equation is 280 = w(w + 6)

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Answer:

a) (2x+7)(x-4)

b) x = -7/2 and x = 4

Step-by-step explanation:

a) (2x  ?)(x  ?)

set up the above and considered factors of 28 that, when paired with 2, would give me -1x and -28  → (1·28, 2·14, 4·7)

after trial-and-error, found that 4 and 7 worked (used un-FOIL)

b) 2x + 7 = 0

2x = -7

x = -7/2

*********

x-4 = 0

x = 4

Answer:

Tn = 75+25n

Step-by-step explanation:

The balance are in arithmetic progression

$100, $125, $150...

The formula for calculating the nth term of the sequence is expressed as;

Tn = a+(n-1)d

a =100

d = 125 - 100 = 150 - 125

d = 25

n is the number of terms

Substitute

Tn = 100+(n-1)*25

Tn = 100 + 25n-25

Tn = 75+25n

Hence the nth term of the sequence is Tn = 75+25n

The means to study and analyze economic phenomena, formulate economic models, make predictions, and derive policy recommendations.

1. Importance of studying mathematics in economics:

a. Modeling and Analysis: Mathematics provides the tools and techniques for constructing models that represent economic phenomena.

These models help economists analyze and understand complex economic systems, predict outcomes, and make informed decisions.

b. Quantitative Analysis: Economics involves analyzing numerical data and making quantitative assessments. Mathematics equips economists with the necessary skills to handle and manipulate data, perform statistical analysis, and draw meaningful conclusions from empirical evidence.

c. Logical Reasoning and Problem Solving: Mathematics trains students to think critically, logically, and abstractly. These skills are essential in economics, where students need to formulate and solve economic problems, derive solutions, and interpret results.

2. Mathematical tools used in economics:

a. Calculus: Calculus plays a crucial role in economics by providing techniques for analyzing and optimizing economic functions and models. Concepts such as derivatives and integrals are used to study economic relationships, marginal analysis, and optimization problems.

b. Linear Algebra: Linear algebra is employed in various economic applications, such as solving systems of linear equations, representing and manipulating matrices, and analyzing input-output models.

c. Statistics and Probability: Statistics is used to analyze economic data, estimate parameters, test hypotheses, and make inferences. Probability theory is essential in modeling uncertainty and risk in economic decision-making.

d. Optimization Theory: Optimization theory, including linear programming and nonlinear optimization, is used to find optimal solutions in various economic problems, such as resource allocation, production planning, and utility maximization.

e. Game Theory: Game theory is a mathematical framework used to analyze strategic interactions and decision-making among multiple agents. It is widely applied in fields such as industrial organization, microeconomics, and international trade.

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Answer:

-1

Step-by-step explanation:

3-1=2

2-1=1

Answer:

2 pizzas

Step-by-step explanation:

5 7/8 - 4 1/16=

5 14/16 - 4 1/16 ==> make the denominators equal to each other so they can be easily subtracted in the next step

5 + 14/16 - (4 + 1/16)=

5 + 14/16 - 4 - 1/16 =

5 - 4 + 14/16 - 1/16 =

1 + 13/16 = 1 13/16 which is approximately 2 pizzas

A graph which represents this situation include the following: B. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this scenario, the y-intercept of this equation can be calculated as follows;

y = 30 + 10x

y = 30 + 10(0)

y = 30

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The LP problem is to maximize the objective function 10x+15y subject to the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. By graphing the constraints and identifying the feasible region, we can determine the optimal solution.

To find the optimal solution for the LP problem, we first graph the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. These constraints represent the inequalities that the variables x and y must satisfy. We plot the lines 2x+5y = 40 and 6x+3y = 48 on a graph and shade the region that satisfies both constraints.

The feasible region is the area where the shaded regions of both inequalities overlap. We then identify the corner points of the feasible region, which represent the extreme points where the objective function can be maximized.

Next, we evaluate the objective function 10x+15y at each corner point of the feasible region. The point that gives the highest value for the objective function is the optimal solution.

By solving the LP problem graphically, we can determine the corner point that maximizes the objective function. The optimal solution will have specific values for x and y that satisfy the constraints and maximize the objective function 10x+15y.

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Answer:

The answer is below

Step-by-step explanation:

The question is not complete, what are the coordinates of point Q and R. But I would show how to solve this.

The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at (\(x_1,y_1\)) and B(\(x_2,y_2\)) is given by the formula:

\(x=\frac{a}{a+b}(x_2-x_1)+x_1\\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1\)

If point Q is at (\(x_1,y_1\)) and S at (\(x_2,y_2\))  and R(x, y) divides QS in the ratio QR to RS is 3:5, The coordinates of R is:

\(x=\frac{3}{3+5}(x_2-x_1)+x_1=\frac{3}{8}(x_2-x_1)+x_1\\ \\y=\frac{3}{3+5}(y_2-y_1)+y_1=\frac{3}{8}(y_2-y_1)+y_1\)

Let us assume Q(−9,4) and S(7,−4)

\(x=\frac{3}{8}(7-(-9))+(-9)=\frac{3}{8}(16)-9=-3\\\\y=\frac{3}{8}(-4-4)+4=\frac{3}{8}(-8)+4=1\)

Answer: It’s 2.6

Step-by-step explanation:

The written form of the quotient as a simplified fraction as required in the task content is; Choice Choice B; 18 1/2.

It follows from the task content that the quotient as given in the task content is; 851/46.

On this note, it follows that the result of the division is; 18 with a remainder of 23.

Hence, we have; 18 23/46 which is equivalent to 18 1/2.

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Answer:

(2x+1)(x+1)

Step-by-step explanation:

got it right on my quiz and also there is 2 reds= 2x on the bottom and 1 red=x and the yellow is the +1

The product represented by these algebra tiles is (2x+1) (x+1).

Suppose the blue tiles are x.

Suppose  the red tiles are 1.

Therefore,

length = 2 blue tiles + 1 red tile

= 2x+1

Breadth = 1 blue tile + 1 red tile

= x+1

Therefore, product represented by these algebra tiles is (2x+1) (x+1).

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The Perimeter of the hexagon that Pete made by putting the trapezoids together is 22 inches.

To find the perimeter of the hexagon formed by putting the trapezoids together, we need to add up the lengths of all the sides.

Let's analyze the given trapezoids:

Trapezoid 1: It has two parallel sides measuring 3 inches and 5 inches, and two non-parallel sides measuring 3 inches each.

Trapezoid 2: It also has two parallel sides measuring 3 inches and 5 inches, and two non-parallel sides measuring 3 inches each.

When we put these trapezoids together to form a hexagon, we can observe that the parallel sides of the trapezoids become consecutive sides of the hexagon.

Since the hexagon has six sides, we need to consider the lengths of all six sides. By examining the trapezoids, we can determine that the lengths of the sides are as follows:

Side 1: 5 inches (one of the sides of the trapezoid)

Side 2: 3 inches (one of the sides of the trapezoid)

Side 3: 3 inches (one of the sides of the trapezoid)

Side 4: 3 inches (one of the sides of the trapezoid)

Side 5: 3 inches (one of the sides of the trapezoid)

Side 6: 5 inches (the other side of the trapezoid)

To find the perimeter, we add up the lengths of all six sides:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4 + Side 5 + Side 6

        = 5 + 3 + 3 + 3 + 3 + 5

        = 22 inches

Therefore, the perimeter of the hexagon that Pete made by putting the trapezoids together is 22 inches.

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