Fair Race UNIT NAME: FUNCTIONS
Directions: Follow the instructions below to design a fair race for the new video game Animal Tracks. 1. Choose two animals with different speeds. You can choose from the chart that starts at the bottom of this page or do research to choose your own. 2. Design a fair race in which the two animals have an equal chance of winning if they race at their top speed. Here are a few tips for your design: a. The race is fair if the two animals could finish the race in the same amount of time. b. You can give the slower animal a shorter distance to race. c. Since this is a video game, the race does not need to be realistic—it can be any length, and the animals can run at a constant speed. 3. Write a system of two linear equations showing the distance each animal can travel to model the fair race. Be sure to define all variables. 4. Graph the system to prove that the two animals have an equal chance of winning the race. Explain how the graph proves the race is fair. Your equations, graph, and explanation for your race design will be submitted as your portfolio assessment.

Animal Speed (mph) cheetah 70 lion 50 coyote 43 rabbit 35 kangaroo 30 squirrel 12 chicken 9 antelope 61 elk 45 ostrich 40 giraffe 32

Animal Speed (mph) elephant 25 pig 11 mouse 8

I need help wiith 3. Write a system of two linear equations showing the distance each animal can travel to model the fair race. Be sure to define all variables. I choose The mouse and squirrel ....can i get help on the equuations? Can someone explain it to me?

Answer:

8x - 5y = 11---->8x - 5y = 11

4x - 3y = 5---->-8x + 6y = -10

-------------------

y = 1, x = 2

{(2, 1)}

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

Number of times a die rolled = 500

Number of times an odd number occurs =325

so, the experimental probability would be

[tex]\dfrac{325}{500}\\\\=0.65[/tex]

And we know that

Number of outcomes in a die = 3

Number of total outcomes = 6

So, The theoretical probability would be

[tex]\dfrac{3}{6}=\dfrac{1}{2}=0.5[/tex]

So, The experimental probability is larger than the theoretical probability.

Hence, Second option is correct.

Answer:

A) 5

B) 200

C) 25.5

D) 14/3

E) 77 1/2

Step-by-step explanation:

We have been given a function [tex]f(x)=10.25x[/tex], where, [tex]f(x)[/tex] represents the amount of money earned after x hours.

We are asked to choose the elements of the domain of the function.

Since the x represents time in hours, so negative numbers wouldn't be domain of the given function. as times cannot be negative.

Therefore, options A, B, C ,D and E are correct choices.

Answer:

The first 5 is the right answer

Step-by-step explanation:

your answer will be 2 hours and 10 minutes

mark brainliest

Answer:

2 10

Step-by-step explanation:

210

Final answer:

Different pairs of numbers can add up to 24.

Explanation:

The sum of two numbers that equals 24 depends on the specific values of the two numbers. However, here are a few examples:

12 + 12 = 24

20 + 4 = 24

15 + 9 = 24

These examples show that different pairs of numbers can add up to 24. The sum can be found by adding the two numbers together.

Answer:

The standard form of the given number is [tex]8.73\times 10^{16}[/tex].

Step-by-step explanation:

Standard form of a number is a easy ways to write very small numbers and very large numbers.

In the standard form the number is written as the number lies between 1 to 10 and multiple of power of 10.

The given number is

[tex]8.73e16[/tex]

It can be written as

[tex]8.73e16=87300000000000000[/tex]

[tex]8.73e16=8.73\times 10^{16}[/tex]

Therefore the standard form of the given number is [tex]8.73\times 10^{16}[/tex].

Answer:

All of the above

Step-by-step explanation:

A 15 kg box has more inertia than a 10 kg box. --TRUE

Inertia is a property of matter related to its mass. The more mass an object has, the greater its inertia. S o the statement is correct since 15 kg is greater in mass than 10 kg therefore it has more inertia.

Forces occur in equal and opposite force pairs.  -- TRUE  

This statement is correct and is known as Newton's third law. Which tells us that for every force of action there is  a reaction force that is equal in magnitude but opposite in direction.

Objects in motion will keep moving at the same velocity unless acted upon by an outside force.  -- TRUE  

This is Newton's first law of motion, it tells us that an object will retain its state of rest or movement as long as there is no resulting force  or external force acting on it.

There are two cases here:

Case 1: First card chosen is a queen

Case 2: First card chosen is not a queen.

Adding both the cases, we get 1722117221 = 452452 = 113113

In a simpler case: Think about it this way: Shuffle a deck of cards randomly. The probability of drawing a queen as your second card is the same as the probability that the second card in the deck is a queen, which is clearly 4/52.

The most reasonable prediction of the number of seventh grade students in her school who would choose summer as their favorite season is 75.

To predict the number of seventh-grade students in Laticia's school who would choose summer as their favorite season, we can use the fact that she surveyed 25% of the seventh-grade students and found that 51 of them chose summer.

First, we need to find out how many seventh-grade students there are in total. Since Laticia surveyed 25%, we can set up a proportion:

[tex]\[\frac{51}{25\%} = \frac{x}{100\%}\][/tex]

Solving for x, the total number of seventh-grade students, we get:

[tex]\[x = \frac{51 \times 100\%}{25\%} = 204\][/tex]

Now, since 51 students chose summer as their favorite season out of 204 seventh-grade students, to find out how many students might choose summer if all seventh-grade students were surveyed, we can set up another proportion:

[tex]\[\frac{51}{204} = \frac{y}{100\%}\][/tex]

Solving for y, the number of students who might choose summer if all seventh-grade students were surveyed:

[tex]\[y = \frac{51 \times 100\%}{204} = 25\%\][/tex]

This comes out to (y = 51), which means if all seventh-grade students were surveyed, we could reasonably predict that 51 of them would choose summer as their favorite season. Therefore, option B) 75 is the most reasonable prediction.

Final answer:

The scale factor for the scale drawing of a car with a scale of 1 inch : 3 feet is 1:36, or the fraction 1/36.

Explanation:

The student has a scale drawing of a car with a scale of 1 inch : 3 feet. To find the scale factor for this drawing, you need to convert feet into inches since the scale is given in inches to feet. There are 12 inches in a foot, so 3 feet is the same as 36 inches. Therefore, the scale for the car drawing is 1 inch on the drawing for every 36 inches of the actual car.

The scale factor is the ratio of the dimension in the drawing to the actual dimension of the object. In this case, the scale factor is 1:36, which can be written as the fraction 1/36. This means that every inch on the scale drawing represents 36 inches on the actual car.

Answer:

Given the system of equations:

[tex]y = 6x+6[/tex]         .....[1]

[tex]y = -x^2+5x+6[/tex]      .....[2]

Equate these two equations we have;

[tex]-x^2+5x+6 = 6x+6[/tex]

Subtract 6 from both sides we have;

[tex]-x^2+5x= 6x[/tex]

Subtract 6x from both sides we have;

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

⇒[tex]-x(x+1) = 0[/tex]

By zero product property we have;

⇒x = 0 and x+1= 0

⇒x = 0 and x=-1

Substitute these values in [1] we have;

For x = 0

y = 6(0)+6 = 6

for x = -1

y =6(-1)+6 = -6+6=  0

Therefore, the solutions of the given systems are, (0, 6) and (-1, 0)

Final answer:

To calculate i^3, we use the powers of i, where i = √-1. We find that i² = -1, and thus i³ = i² × i = -1 × i = -i.

Explanation:

The value of i to the power of 3, denoted as i3, can be determined by understanding the fundamental properties of the imaginary unit i, where i is defined as i = √-1. To find i3, we start by considering the powers of i:

i1 = i,

i2 = -1,

i3 = i2 × i = -1 × i = -i,

i4 = (i2)2 = (-1)2 = 1.

Therefore, the value of i3 is -i.

Answer:

61 sales.

Step-by-step explanation:

Let x represent present sales.

We have been given that you need to increase your sales by 35% this month. You are currently at 45 sales.

To find the number of sales to meet the goal, we will find 35% of 45 and add to 45 as:

[tex]\text{The number of sales to meet the goal}=45+\frac{35}{100}*45[/tex]

[tex]\text{The number of sales to meet the goal}=45+0.35*45[/tex]

[tex]\text{The number of sales to meet the goal}=45+15.75[/tex]

[tex]\text{The number of sales to meet the goal}=60.75[/tex]

[tex]\text{The number of sales to meet the goal}\approx 61[/tex]

Therefore, you need to make 61 sales to meet you goal.

Answer:

Four songs

Step-by-step explanation:

1. Change into y-intercept form.

y = 3.25/1x + 18

y = 2.00/1x + 23

2. Graph them!!

the outcome is ( 4, 31 )

So 4 songs for $31.00

Answer:$18.84. I hope this helps. Have a great day!♡

Step-by-step explanation:

The expression that represents the length of one side of the square is (x+2)

In mathematics, a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface.

Given,

Area of the square = [tex]x^{2} +4x+4[/tex]

Area of the square = l × l

were l is the length

Then,

[tex]x^{2} +4x+4=(x+2)(x+2)[/tex]

Hence, The expression that represents the length of one side of the square is (x+2)

Learn more about polynomial and area here

https://brainly.com/question/22576901

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Answer:

  √25

Step-by-step explanation:

  √25 = √(5²) = 5 . . . . a rational number

The other roots are not the roots of perfect squares, so are irrational.