A high school decided to spend $ 750 on student academic achievement awards. At least 5 awards will be given, they should be equal in value, and each award should not be less than $ 50 . Write and sketch a function that models the relationship between the number a of awards and the cost c of each award. What are the domain and range of the function?
a. Which equation describes the relationship between a and c ?

The height of the candle which is a linear function with respect to time after 12 hours was 25.2 centimeters.

A linear function has a graph of a straight line.

Given that height of a candle is a linear function of the amount of time in hours it has been burning.

The slope(m) is = - 0.4 which is = -(4/10) = - (2/5).

The height of the candle after 19 hours is 22.4 centimeters, which can be written as two points (x,y) = (19,22.4).

Now to obtain the height of the candle first we have to form an equation of a line in slope intercept form to find y-intercept(b), which is,

y = mx + b.

22.4 = -(2/5).19 + b.

22.4 = -7.6 + b.

b = 22.4 + 7.6.

b = 30.

∴ y = -(2/5)x + 30.

Now to obtain the height of the candle after 12 hours we have to substitute 12 in x.

So, y = -(2/5)(12) + 30.

y = 25.2 centimeters.

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There are numerous videos and web sites that can show you the process of copying an angle. Some are animated. The best we can do here is show you a diagram with instructions. Of course, your curriculum materials already provide that

__

1. Set the compass to a convenient radius. Use that to draw an arc through rays ED and EF, using point E as the center.

2. Without changing the compass setting, draw a similar arc using S as the center, making sure it crosses the line containing S and extends far enough to accommodate the following steps. (In the attached, we show a full circle, because the tool we used won't draw an arc with a specific radius.)

3. Mark the points where the arc crosses ED as G, and where it crosses EF as H. Mark the point where the arc crosses the line containing S as I.

4. Set the compass radius to the distance GH. Using I as the center draw an arc with that radius so that it crosses the one made in step 2. Call that intersection point J. (Again, we have shown a circle because of the limitations of the tool being used for our diagram.)

5. Draw ray SJ to complete the angle copy.

Answer:

Step-by-step explanation: 23 is the median of the data set because it's the number in the middle.  

Median: 16, 18, 19,23, 24, 31, 32  

Mean: 16+18+19+23+24+31+32= 163 then divide by how many numbers you added by 163 divided by 7 equals 23.28571429. I'll just simplify it to 23.29 or rounding to tenths 23.3.

Answer:

Median = 23

Mean = 163/7 = 23.3 (1 d.p.)

Step-by-step explanation:

Given data set:

19, 18, 23, 24, 31, 32, 16

The middle value when all data values are placed in order of size.

Given data values in size order, from smallest to largest:

[tex]\sf 16, 18, 19, \boxed{\sf 23}, 24, 31, 32[/tex]

The middle value is 23, so the median of this data set is 23.

The sum of all data values divided by the total number of data values.

[tex]\begin{aligned}\implies \sf mean & =\sf \dfrac{19+18+23+24+31+32+16}{7}\\& = \sf \dfrac{163}{7}\\ & = \sf 23.28571429...\\ & = \sf 23.3\:(1\:d.p.)\end{aligned}[/tex]

Answer: n = 15/2

Step-by-step explanation:

Divide both sides n/10 = 3/34

Calculate n = 3/4 x 10

Answer is n = 15/2

Answer: The value of the triangle = 3.

               The value of the square = -2,

               The value of the star = 7

               The value of the rhombus = 18.

               The value of the circle  = 4,

               The value of the right angle triangle  = -5

Step-by-step explanation:

Define Linear equation:

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Given that,

Let us assume the values is,

(Option 1) : A shape puzzle is given that,

Let's assume, the triangle shape represents = a

Let's assume, the square shape represents = b

Let's assume, the star shape represents = c

The equation becomes,

clue 1 : 2a-1 = 5

clue 2 : a + b = 1

clue 3 : a-2b = c

First take, clue 1 :         2a-1 = 5

                                       2a = 5+1

                                        2a = 6

                                         a = 6/2

                                          a = 3

Therefore,       triangle (a) = 3

Take, clue 2 :                      a + b = 1

Replace 'a' value in this equation,

                                            a + b = 1

                                            3+b = 1

                                              b = 1-3

                                              b = -2

 Therefore,         square (b) = -2

Take clue 3 :                     a-2b = c

Replace with 'a' and 'b' values in this equation,

                                          a-2b = c

                                           3-2(-2) = c

                                            3+4 = c

                                              c = 7

Therefore,             star (c) = 7

we can substitute these values,

Then,      clue 1 : 2(3) -1 = 6-1 = 5

               clue 2 : 3 + (-2) = 3-2 = 1

               clue 3 : 3-2(-2) = 3+4 = 7

Thus, The value of the triangle = 3.

         The value of the square is = -2,

          The value of the star = 7

after using the concept of linear equation in two variables.

(Option 2) : A shape puzzle is given that,

Let's assume, the rhombus shape represents = x

Let's assume, the circle shape represents = y

Let's assume, the right angle triangle shape represents = z

The equation becomes,

clue 1 : x+2 = 5y

clue 2 : 3y = 12

clue 3 : 2y = x+2z

Take, clue 2 :                     3y = 12

                                            y = 12/3 = 4

Therefore,      circle (y) = 4

First take, clue 1 :         x+2 = 5y

                                      x+2=5(4)

                                      x+2=20

                                      x = 20-2 = 18

Therefore,       rhombus (x) = 18

Take clue 3 :                      2y = x+2z                

Replace with 'x' and 'y' values in this equation,

                                         2y = x+2z

                                         2(4) = (18)+2z

                                          2(4) = (18)+2z

                                           8 = (18)+2z

                                            8-18 = 2z

                                             -10 = 2z

                                              z = -10/2

                                              z = -5

Therefore,         right angle triangle (z) = -5

we can substitute these values,

Then,      clue 1 : 18+2=5(4)

                            20 = 20

               clue 2 : 3(4) = 12

                             12 = 12

               clue 3 : 2(4) = 18+2(-5)

                             8 = 18-10

                             10+8 = 18

                              18 = 18  

Thus, The value of the rhombus = 18.

         The value of the circle  = 4,

          The value of the right angle triangle  = -5

after using the concept of linear equation in two variables.

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The kilograms of apples and pears that the store rreceiv is 120kg and 108kg.

It should be noted that 40% of them are apples, 36% are pears. The percentage for peaches will be:

= 100 - (40% + 36%)

= 24%

The total fruit will be x. This will be:

24% of x = 72

0.24x = 72

x = 72/0.24

x = 300

Apples will be:

= 40% × 300

= 120kg

Pears = 36% × 300

= 108kg

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0.03337327...   is expression to four decimal places. e⁻³.

The significance of an exponential function

e⁻³ in your calculator, which gives you 0.03337327...

Since you need 4 decimal places, you need to look at the 5th decimal place. If it's 5 or more, you add 1 to the 4th decimal place. If it's less than 5, you leave the 4th decimal as it is.

In this case, the 5th decimal place is 7 and the 4th is 3. Since 7>5, the 4th decimal place changes from 3 to 4.

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With the formula d=vt+1/2at², we can prove that the acceleration of an object can be calculated with a=2d-2v t/t²

To solve this problem we must establish the equation, isolate the variable (a) following the rules of clearance and solve the operations:

d=vt+1/2at²

1/2at² = d - vt

at² = (d - vt)*2

at² = 2d - 2vt

a= (2d - 2vt) / t² verified

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer: x∈[0;+∞)

Step-by-step explanation:

[tex]|x|-6 > -16\\|x|-6+6 > -16+6\\|x| > -10\\[/tex]

As |x|≥0, hence: x≥0

Answer:

Dad: 312 miles

Mom: 62.4 miles

Sister: 105.6 miles

Step-by-step explanation:

Dad: 480 x .65 = 312

Mom: 312 x .2 = 62.4

Sister: 480 - 312 -62.4 = 105.6

Express 81 and 16 as a product of their prime factors. Apply the power rule for indices stating (a^m)^n = a^mn. Simplify the expression:

81=3x3x3x3 = 3^4

16 = 2x2x2x2 = 2^4

Thus, (3^4 x y^16 / 2^4 x X^12) ^ 1/2

3^4/2y^16/2 / 2^4/2 X^12/2

3^2 y^8 / 2^2 X^6 = 9y^8 / 4X^6

9y^8/4X^6 = (3/2)^2X^6y^8

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The solution of the given expression 3x⁻¹=24 is x = 1/8.

An exponent (also known as a power or degree) indicates the number of times the base is multiplied by itself. For example,'has an exponent of 5 and a base of. This means that variable would be multiplied 5 times by itself. This can also be thought of as to a fifth power.

Some properties of the exponents are given as-

Now, for the stated question;

The given expression is;

=> 3x⁻¹ = 24

Divide both sides by 3.

=> x⁻¹ = 8

Taking the reciprocal on both sides.

=> 1/x⁻¹ = 1/8

This 1/x⁻¹ can be written as x.

=> x = 1/8

Therefore, the value of the x for the given expression 3x⁻¹=24 is 1/8.

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Using the graph, the value of f(-3) is 2

From the question, we are to determine the value of the given function

The given function is f(-3)

To determine the value of f(-3) on the graph, we will trace from the point where x = -3 on the x-axis to the line of the function and then trace from the line to the y-axis. The value on the y-axis is the value of f(-3)

From the graph,

Tracing from the point where x = -3 to the line and then to the y-axis, we get y = 2

∴ f(-3) = 2

Hence, the value of f(-3) is 2

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Answer:

Given: two sides and a non-included angle

Step-by-step explanation:

This can sometimes result in 2 possible values when using the Law of Sines, since sin(180°-x)=sin(x)

The values of g(x) are:

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

given:

g(x) = -2 |x + 5| + 2

so, x= -4

g(-4)= -2|-4 + 5| +2

g(-4) = -2 +2

g(-4) = 0

at,  x= -3

g(-3)= -2|-3 + 5| +2

g(-3) = -4 +2

g(-3) = -2

x= -1

g(-1)= -2|-1 + 5| +2

g(-1) = -8 +2

g(-1) = -6

and,  x= 0

g(-4)= -2| 0+ 5| +2

g(-4) = -10 +2

g(-4) = -8

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The corresponding growth factor of +70% is 1.7

The formula for the annual rate of change is

                    1 ± r             (1)

where r = rate of change

and ± sign depends upon whether it is a growth or decay factor. If it is growth factor then it is plus sign otherwise negative sign.

According to the question we have been given the growth that is +70%. Since there is plus sign therefore it is a growth factor.

Thus, r = + 0.7

Putting this value in equation (1) we get

= 1 + 0.7

= 1.7

Hence the corresponding growth factor of +70% is 1.7

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The equation of the line will be y = 2x - 2.

A linear equation with a degree of one is referred to as a line equation. Two variables, x, and y are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.

The general form of the equation of the line is given as:-

y = mx + c

Given that the equation of the line is passing through the point ( -2,0) and the slope of the line is 2.

The equation of the line will be calculated as:-

y = mx + c

-2 = 0 + c

c = -2

y = mx + c

y = 2x - 2

Therefore, the equation of the line will be y = 2x - 2.

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The midpoint of diagonal AC is (5,-3).

Given A(3,-1) and C(7,-5)

Let the midpoint of diagonal AC be represented by P (say). Then the coordinate of P can be calculated by using the formula listed below:

let us suppose the coordinates of A be (a, b) and B be (c, d) and P is the midpoint of AC then the coordinate of P will be (a+c/2, b+d/2).

Now, by using the above formula, we get

x-coordinate of P be (3+7)/2 = 10/2 = 5

y-coordinate of P be (-1+(-5))/2 = -6/2 = -3

∴ The coordinate of midpoint of AC i.e., P be (5, -3).

Hence, the midpoint of diagonal AC is (5,-3).

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Answer:

-8

Step-by-step explanation:

(2)(-8)/2 convert it to a fraction and use fraction bar.

-16/2 = -8  Multiplication first then division

Note order of operations Division or multiplication which ever is first. also because the top of the fraction has parentherses do that first.

Answer:

b=10

Step-by-step explanation:

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The expected raise a union wage negotiator feels that   the union members will get is $1.22.

The probability of each pay raise is given below

P ($1.50 raise) = 0.40

P ($1.00 raise) = 0.30

P ($0.50 raise) = 0.20

P (no raise) = 0.10

The probability of each pay raise is then multiplied by the pay itself

Expected raise for each hour = $1.50(0.40) + $1.00(0.30) + $0.50(0.20) + $0.00(0.10)

E(x) = 0.6 + 0.52 + 0.1 + 0 (The probability of no pay at all gives 0 since the pay amount has no value)

E(x) = $1.22

Therefore, all together the union wage negotiator is able to predict a $1.22 pay raise for the workers for each time expected.

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0.04, 3/11, 0.35, 3/5 would be the solution

C.It is zero.

The net force is the sum of all of the forces exerted on an object.

Identifying Forces

Force is measured in newtons, which is shortened to N. Additionally, force will always have a direction, like 5N up or 3N to the left.

Sometimes force will be negative to represent direction. A force moving down or to the left might be negative because moving down or to the left on an axis moves towards negative numbers.

Net Force

As stated above, the net force is the sum of all of the forces acting on an object. For example, if one object is being moved 5N to the left and 4N to the right, the net force will be 1N to the left.

On the other hand, if the forces are balanced, like 5N on both the left and right, then the forces cancel out. This leaves a net force of 0.

From the situation described in the problem, we have that:

a) The system of inequalities is given by: s + a ≤ 800, 4s + 7a ≥ 3400.

b) The solution is graphed at the end of the answer.

c) Yes, the club could meet it's goal.

A system of inequalities is when multiple variables are related in a described situation, and then inequalities are built to find the interval ranges of each variable, according to the relations built.

In the context of this problem, the variables are given as follows:

The auditorium has 800 seats, hence:

s + a ≤ 800.

They have a goal of making at least $3400, hence, considering the price of the tickets, we have that:

4s + 7a ≥ 3400.

The graphical solution of the inequality is given by the painted region on the graph, and since point (200, 475) is inside the region, the club could meet it's goal.

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If a long run athlete can run 1/2 km in 3 minutes then he can run 10 km in an hour.

Given, a long distance athlete can run 1/2 kilometer in 3 minutes.

How much distance can he cover in an hour = ?

How quickly something or someone is moving is determined by their speed. If you know how far an object has traveled and how long it has taken, you can calculate its average speed. Speed equals distance times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

Time = 60 minutes.

we know that 3 minutes = 1/2 km

therefore, distance covered in an hour = 1/2 ÷ 3/60

= 1/2 × 60/3

= 1/2 × 20

= 10

distance covered in an hour = 10 km.

hence we get the distance covered by the athlete in an hour as 10 km.

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According to the solving this implies that the  1:3  ratio of 60 is 20.

A ratio expresses the number of times one number contains another. For example, if a dish of the fruit contains eight oranges and six lemons, the orange-to-lemon proportion is eight to six. Similarly, the lemonade and orange proportion is 6:8, while the orange to fruit weight ratio is 8:14.

Ratios are used to compare the two quantities by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.

Let us find 1/3 of 60.

We can write 1/3 of 60

= 1/3 × 60.

= 20.

According to the solving this implies that the  1:3  ratio of 60 is 20.

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Based on the dimensions of the rectangle and the dimensions of the sod, Jim will need to buy 87 pieces of sod to cover his backyard with sod.

First, find the area of the backyard which is shaped like a rectangle:

= 14⁵/₆ x 10²/₅

= 154.27 yards²

The area of a single sod is:

= 1¹/₃ x 1¹/₃

= 1.78 yards²

The number of sods needed is:

= 154.27 / 1.78

= 86.775

= 87 sods

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Answer:

30 c + 100 m = 700

c+ m = 14

Step-by-step explanation:

The product of the number of movies where the song was played (m) multiplied by the earnings per movie (30) plus the product of the number of commercials where the song was played (m) multiplied by the earnings per commercial, must be equal to $700.

30 c + 100 m = 700

The number of movies (m) plus the number of commercials (c) is equal to 14.

c+ m = 14

The system is:

30 c + 100 m = 700

c+ m = 14