Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order. What is the sample space showing the possible orders of the other three runners? S = {FGI, GFI, IFG} S = {FGI, FIG, GFI, GIF} S = {FGI, FIG, GFI, GIF, IFG, IGF} S = {FGI, FIG, GFI, GIF, HFG, HGI, IFG, IGF}

Answers

Answer 1

the Different possibilities in which the three players are placed are as follows ;
F can come first then the possibilities of other 2 players are ;
FGI and FIG
G can come first then the possibilities of other 2 players are ;
GIF and GFI
Next If I comes first then the possibilities are
IGF and IFG

Therefore sample space for all the possibilities as noted above are;
S = {FGI, FIG, GFI, GIF, IFG, IGF}

Answer 2

The sample space or sets showing the possible orders of the other three runners is S = {FGI, FIG, GFI, GIF, IFG, IGF}.

What are Sets?

Sets are the collection of well-defined elements. A set is represented by a capital letter symbol and the number of elements in the finite set is shown as curly bracket {..}.

Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team.

Haley is the first runner in the relay. The other runners can run in any order.

The sample space or sets showing the possible orders of the other three runners will be

S = {FGI, FIG, GFI, GIF, IFG, IGF}

Thus, the correct option is C.

More about the sets link is given below.

https://brainly.com/question/8053622

Related Questions

Jalen plots two integers on a horizontal number line. The leftmost integer is negative. Which must be true of the second integer?
The second integer is negative.
The second integer is positive.
The second integer is greater than the first integer.
The second integer is less than the first integer.

Answers

The second integer is greater than the first integer

Answer:

c)The second integer is greater than the first integer

Step-by-step explanation:

In mathematics, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.

A number line can be extended infinitely in any direction and is usually represented horizontally, with 0 in the middle and negative numbers on the left and positive numbers to the right of zero.

Thus a number line can be used to represent both positive and negative rational numbers as well as integers.

The numbers to the left are less than that to the right

Hence here the option c) is right

what the circumstances of a circle with a diameter of 12ft

Answers

Circumstances?
I have seen a circle about that size used for a labyrinth at a church.

Circumference is found by multiplying the diameter by pi.
(12 ft)*π ≈ 37.7 ft

vita wants to center a towel bar on her door that is 27 1/2 inches wide . she determines that the distance from each end of the towel bar to the end of the door is 9 inches. write and solve an equation to find the length of the towel bar

Answers

The length of the towel bar is 9.5 inches.

Explanation

Suppose, the length of the towel bar is [tex]x[/tex] inches.

The distance from each end of the towel bar to the end of the door is 9 inches. So, the total width of the door will be: [tex][x+(9*2)] = (x+18)inches[/tex]

Given that, the width of the door is [tex]27\frac{1}{2}[/tex] inches or 27.5 inches. So, the equation will be........

[tex]x+18=27.5\\ \\ x=27.5-18= 9.5[/tex]

Thus, the length of the towel bar will be 9.5 inches.

Final answer:

Vita can center the towel bar on her 27 1/2-inch wide door by ensuring it is 9.5 inches long. This is done by deducting the combined distances from the ends of the towel bar to the door edges (18 inches) from the total width of the door.

Explanation:

Vita wants to find the length of the towel bar that she wants to center on a door that is 27 1/2 inches wide, with the distance from each end of the towel bar to the end of the door being 9 inches. To solve for the length of the towel bar, we denote the length of the towel bar by x. Then, we can set up an equation where the sum of the distances from both ends of the towel bar to the door edges and the length of the towel bar itself equals the width of the door.

The equation will be:

9 inches + x + 9 inches = 27 1/2 inches

We combine the known distances to simplify the equation:

18 inches + x = 27 1/2 inches

To find x, we subtract 18 inches from both sides of the equation:

x = 27 1/2 inches - 18 inches

Converting 27 1/2 inches to a decimal, we have 27.5 inches. Thus:

x = 27.5 inches - 18 inches

x = 9.5 inches

Therefore, the length of Vita's towel bar should be 9.5 inches long to be centered on her 27 1/2-inch wide door.

mrs. west is 14 years younger than her aunt. if mrs. west’s age in years is as much below 60 as her aunt’s age is over 40, how old is each?

Answers

Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.

Let's represent Mrs. West's age as W and her aunt's age as A.

Given that Mrs. West is [tex]14[/tex] years younger than her aunt, we can write the equation:

[tex]W=A-14[/tex]

Also, it's given that Mrs. West's age is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex] . This can be represented as:

[tex]W=60-(A-40)[/tex]

Simplify the equation:

[tex]W=60-A+40\\W=100-A[/tex]

Now, we have two equations for [tex]W[/tex]:

[tex]W=A-14\\W=100-A[/tex]

Since both equations equal [tex]W[/tex], we can set them equal to each other:

[tex]A-14=100-A[/tex]

Now, solve for A:

[tex]A+A=100+14\\2A=114\\A=57[/tex]

Now, plug the value of [tex]A[/tex] into either equation to find [tex]W[/tex]:

[tex]W=57-14\\W=43[/tex]

So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.

COMPLETE QUESTION:

Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], how old is each?

a puppy weighs 9/10 pound. it's mother weighs 8 times as much. how much does the mother weigh?

Answers

the answer would be 72/10 or 7 2/10

The answer would be 7 2/10 or 72/10 or 7.2

which is smaller, half of 36 or one-seventh of 42

Answers

half of 36 = 36/2 = 18

one seventh of 42 = 42/7 = 6

one seventh of 42 is smaller than half of 36 by 12

hope this helps

what is -10+2 because this is really confusing to me.

Answers

-8 hope this helps btw i am a pro at this kinda stuff lol have a nice day

If you need explaining think of it as....a number line. Zero is in the middle with negative numbers going down the left and positive numbers going down the right. Put a mark on -10 and move to the right 2 times. That would give you an answer of -8.

Hope this helps!
Let me know if i'm wrong.

if 5 lemons cost £1 and a bag of 4 oranges cost £1.80, how much more does one orange cost than the lemon?

Answers

One orange costs 0.45 so a lemon costs 55 cents more than one orange

One lemon cost 20 cents and one orange cost 45 cents then 45-20 is 25 cents

The dimensions of an office conference room are 10 feet by 18 feet. If the conference room blueprint dimensions are 5 centimeters by 9 centimeters, what is the scale of the blueprint?
A. 1 centimeter = 9 feet
B. 1 centimeter = 2 feet
C. 1 centimeter = 5 feet
D. 1 centimeter = 10 feet

Answers

1 centimeter = 2 feet

In certain county, the number of charter schools is 4vless than twice the numbervof alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?

Answers

Let us assume that the number of alternative schools in the county are x in number.

It is given that the number of charter schools is 4 less than twice the number of alternative schools. So we can write, the number of charter schools is 4 less than twice of x. In equation form this can be written as:

Number of Charter Schools = 2x - 4

It is given that number of charter schools is 48. So we can write:

48 = 2x - 4
2x = 52
x = 26

x was the number of alternative schools. Therefore, there are 26 alternative schools in the county.

1. Let's call the number of carter school: "x" and "y" the number of alternative school. Then, you have that:
- The number of charter schools is 4 less than twice the number of alternative schools.
- There are 48 charter schools in the country.
2. So, you have:
x=2y-4 (i)
x=48 (ii)
3. Then, when you substitute x=48 into the equation (i), you obtain:
x=2y-4
48=2y-4
4. Now, you must clear "y, as below:
48+4=2y
2y=52
y=52/2
y=26

How many alternative schools are in the county? The answer is: There are 26 alternative schools.

Gabriela buys a basketball for $78 and a soccer ball for $32 she must pay 8.5% sales tax. What is the total amount she must pay?

Answers

Hello!

Add the costs of the basketball and the soccerball together:

78 + 32 = 110

Next, Gabriella must pay 8.5% sales tax. Sales tax is money collected by the government, so it is added onto the purchase.

First, we must find what 8.5% of 110 is. To do that, convert the percentage to a decimal by dividing it by 100, then multiply the total cost of the two balls by the decimal.

8.5% ÷ 100 = 0.085

110 × 0.085 = 9.35

Finally, add the sales tax to the cost of the two balls:

110 + 9.35 = 119.35

ANSWER:

The total amount Gabriella will pay is $119.35.

Final answer:

To find the total amount Gabriela must pay for the basketball and soccer ball including sales tax, add the cost of the items, convert the tax rate to a decimal, calculate the tax amount, and then add it to the subtotal for a total of $119.35.

Explanation:

To calculate the total amount Gabriela must pay after purchasing a basketball for $78 and a soccer ball for $32 with an 8.5% sales tax, we need to follow these steps:

Firstly, we calculate the subtotal by adding the price of the basketball and the soccer ball: $78 + $32 = $110.

Next, we convert the sales tax rate from a percentage to a decimal by dividing by 100: 8.5% ÷ 100 = 0.085.

Then, we calculate the total sales tax by multiplying the subtotal by the sales tax rate: $110 × 0.085 = $9.35.

Lastly, we add the sales tax to the subtotal to find the total amount Gabriela must pay: $110 + $9.35 = $119.35.

Therefore, after including the sales tax, the total amount Gabriela must pay is $119.35.

Which function is the inverse of f(x)=4x-1?

Answers

The function f⁻¹(x) = x/4 + 1/4 is the inverse of f(x)=4x-1

What is a function?

The function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable). In maths and the physical sciences, functions are indispensable for formulating physical relationships.

The function is given as f(x)=4x-1

To determine the inverse of a function, switch the places of x and y (or f(x)).

f(x) = 4x - 1

y = 4x - 1

Switch the variables;

x = 4y - 1

Now, convert the equation back into y = mx + b form.

x + 1 = 4y

y = x/4 + 1/4

f⁻¹(x) = x/4 + 1/4

Learn more about function here:

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11x−6y=5 −4x−6y=13 How many solutions does this system have

Answers

x=1.2 therefore the system only has ONE solution.

Each morning, the employees in an office drink at least 73 cups of coffee. Write an inequality that represents this situation. Let c represent the number of cups of coffee.
An inequality is???????

Answers

Is at least. No more than 73 but can be equal to 73
73 less than equal C
73< C
-
I don’t have that sign on my phone.

What is the first derivative of 3\sqrt[3]{x^4}-12\sqrt[3]{x}?

Answers

[tex]\bf y=3\sqrt[3]{x^4}-12\sqrt[3]{x}\implies y=3x^{\frac{4}{3}}-12x^{\frac{1}{3}} \\\\\\ \cfrac{dy}{dx}=3\left( \frac{4}{3}x^{\frac{1}{3}} \right)-12\left( \frac{1}{3}x^{-\frac{2}{3}} \right)\implies \cfrac{dy}{dx}=4x^{\frac{1}{3}}-4x^{-\frac{2}{3}} \\\\\\ \cfrac{dy}{dx}=4\sqrt[3]{x}-\cfrac{4}{\sqrt[3]{x^2}}[/tex]

2 times 2 plus 10 plus 200 plus 56

Answers

2×2 + 10 + 200 + 56
The order of operations requires the multiplication be done first.
= 4 + 10 + 200 + 56
The addition is done left to right.
= 14 + 200 + 56
= 214 + 56
= 270

Answer:

270

Step-by-step explanation:

2*2+10+200+56=270

Solve this problem using the proper formula

A gardener is installing a circular garden. The circumference of the circle 132 feet. What radius should he use to layout the circle if he uses p=22/7?

The radius is feet.

Answers

C = 2πr
132 ft = 2(22/7)r
r = (132 ft)*7/44 = 21 ft

The radius is 21 feet.

Given that the garden should be in a circular shape.

And the circumference of the circle would be, C = 132 feet.

It says to find the radius of the circular garden, r = ?

We know the formula for Circumference of the circle is given as follows :-

Circumference of circle = 2π x radius

C = 2·π·r

Hint:- It says to use pi = 22/7.

[tex] 132=2*\frac{22}{7}*r \\\\
132=\frac{44}{7}*r \\\\
r=132*\frac{7}{44} \\\\
r= \frac{924}{44} \\\\
r= 21 \;feet [/tex]

Hence, Radius would be r = 21 feet.

tickets to a play cost $11 each. There is also a service charge of $4 per order. Write ab equation for the relationship that gives the total cost y in dollars for an order of x tickets.

Answers

y=11x+4. formula: y=mx+b. insert the number of tickets where x is times 11 then add 4 to your total

Final answer:

The equation representing the total cost of an order of tickets is y = 11x + 4, where y is the total cost and x is the number of tickets.

Explanation:

The problem involves a constant service charge and a variable cost that depends on the number of tickets bought. In this case, the constant cost is the $4 service fee and the variable cost is the $11 per ticket. We express this relationship with the equation y = 11x + 4, where y is the total cost and x is the number of tickets purchased.

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solve the inequality -×/2 <4

Answers

Multiply by -2.
x > -8

_____
Multiplying or dividing by a negative number causes the direction of the relationship to change.

solve for y
11x+7y=-35

Answers

Solve for y:
11 x + 7 y = -35

Subtract 11 x from both sides:
7 y = -11 x - 35

Divide both sides by 7:

Answer: y = -(11 x)/7 - 5

help!
Twenty seventh grade students are polled about which of three ice cream flavors they prefer. If one student is picked at random, which of the following tables represents vanilla as an event that is likely?

Answers

Hi there!

B would be the answer, because, as you can see, B's rate in vanilla is much higher than any of the other charts, and the difference between each number on the chart is greater as well.

Hope this helps!

20 POINTS!!! Of 35 jewelers in her town, Naomi polled the 5 biggest to learn about the latest jewelery trends. Her sample is (biased; Not biased).The sample is (representative; not representative) PLZ ANSWER IN THAT ORDER!! I NEED THIS ASAP

Answers

Answer:

Biased / Not Representative

Step-by-step explanation:

The answer is biased because she is asking only the 5 biggest jewelers in her whole town, not the whole 35. It is also not representative because it is not representing allts of of the though every jeweler. Hope this helps <3

PS. Brainliest is wrong.

Answer:

I hope this helps

Step-by-step explanation:

If a number is located farther right on the number line than another, then it is larger. True False

Answers

True. When you go right, the number value increases so yes, it is larger

Answer:

it is TRUE my homei

Step-by-step explanation:

Find the product identify the two whole numbers between which the product lies 7x 8/10?

Answers

Hey there!

Let's first simplify this product to see which two whole numbers it lies between. Remember, when we multiply fractions, we just multiply straight across. We have:

7/1 * 8/10 = 56/10

Now, we have to make it an improper fraction. 56 divided by 10 is 5 remainder 6, so we have:

5 6/10 = 5 3/5

Therefore, since it's after 5 but not 6, it's between 5 and 6. Hope this helps!

plz help ill give you brainlist plz help

Answers

The equation for the Area of a rectangle is
A = l * w
in this case A = 108 and w = 9

108 = 9l
l = 12 ft

Find the odds in favor of rolling a two of a kind when rolling a pair of dice

5 to 1
3 to 1
1 to 5
1 to 3

Answers

I think the answer to this question is 5 to 1 and 3 to 1 .I think these are the odds. .

Alex is decorating a large box with pieces of ribbon. He needs 7 sections of ribbon with a length of (3/4) yard. He is going to cut the 7 pieces from a roll of ribbon that is 30.2 yards long

Answers

I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
SEE ATTACHED IMAGE.
For this case what you need to know is how much tape Alex needs.
We have then:
"He needs 7 sections of ribbon with a length of 3/4 yard"
In other words:
(7) * (3/4) = 5.25 yards.
Therefore, the amount of tape that will be left over will be:
30.2-5.25 = 24.95 yards.
Answer:
after Alex cuts the 7 pieces will remain 24.95 yards of ribbon

A rectangular prism with a volume of 6 cubic units is filled with cubes with side lengths of 1/2 units.

How many 1/2 unit cubes does it take to fill the prism?

Answers

48. If the side length is 1/2, cube it to find the volume of the cube. Then divide 6 by 1/8. Remember that if you are dividing a fraction, you multiply by the reciprocal, in this case 8. 6 times 8 is 48.

Answer:

Step-by-step explanation:

Jim Abbott purchased a $60,000 recreational vehicle (RV) with a 40 percent markup on selling price. a. What was the amount of the dealer’s markup? Markup amount $ b. What was the dealer’s original cost? Original cost $

Answers

$42,857.14

Hope this helped!

Answer:

24,000 dealer paid

mark up : 36,000

Step-by-step explanation:

60,000 * 0.40= 24,000

60,000-24,000= 36000

At 7:45 a.m. Mike began walking to school. He arrived at his school at 8:20 a.m. How long did it take him to walk to school?
A. 15 minutes
B. 25 minutes
C. 35 minutes
D. 40 minutes
E. 65 minutes

Answers

c, 35. if you add 15 to 7:45 that’ll get you to 8, then you just add 20.

Hello there!

7:45+15=8:00 = 15:00 minutes so far.

8:00+20= 8:20= 20+15= 35.

Your correct answer would be (option c).

35 is your answer!

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