There are 5 participants in a potato sack race. find the number of orders in which the participants can finish

Answers

Answer 1

5 x 4 x 3 x 2 x 1 = 120

120 different ways


Related Questions

You have just won the lottery and will receive $1,000,000 in one year. you will receive payments for 30 years, and the payments will increase 3 percent per year. if the appropriate discount rate is 7 percent, what is the present value of your winnings?

Answers

Final answer:

The student's question involves determining the present value of annuity payments from a lottery winning, which increase over time and are discounted by a particular rate. The present value is calculated using a formula for a growing annuity, taking into account factors like the growth rate of the payments, the discount rate, and the number of periods. An example with a simple bond issue is provided to illustrate the process of calculating present value at different discount rates.

Explanation:

The student's question pertains to calculating the present value of annuity payments that increase at a fixed percentage rate over time, using a specified discount rate. This is a common exercise in finance and economics, especially related to determining the value of future cash flows given a particular rate of return (or discount rate). To solve the problem, we use the present value formula for a growing annuity.

For the lottery winnings scenario, we would calculate the present value of each individual payment and then sum them up. The first payment of $1,000,000 is received in one year, and it increases by 3 percent each year for 30 years. The discount rate is 7 percent. To analyze this, we must consider the effects of inflation and the time value of money, which is why the payments are 'discounted' back to their present value at the prevailing discount rate.

The general formula for the present value of a growing annuity is:

PV = P * [(1 - ((1 + g)/(1 + r))^n) / (r - g)]

where PV is the present value, P is the first payment, g is the growth rate of the payments, r is the discount rate, and n is the number of periods.

Using the simple two-year bond example provided, the present value calculations at an 8% discount rate are:

$240/(1+0.08) = $222.22

$3,240/(1+0.08)^2 = $2,777.78

Total present value = $222.22 + $2,777.78 = $3,000

If the discount rate increases to 11%, the new present values would be calculated using the higher rate, resulting in a lower total present value for the bond. The calculations reflect the principle that if the cost of borrowing money increases (higher discount rate), the present value of future payments decreases.

Three orders are placed at a pizza shop. two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas, a liter of soda, and two salads cost $22. how much does each item cost?

Answers

To determine the cost of each item, we need to set up equations. From the problem statement, we have three unknowns so we need three equations. We set up equations as follows:

let x cost of small pizzas
     y cost of soda
     z cost of salad
 
two small pizzas, a liter of soda, and a salad cost $14
2x + y + z = 14

one small pizza, a liter of soda, and three salads cost $15

x + y + 3z = 15

three small pizzas, a liter of soda, and two salads cost $22
3x + y + 2z = 22

Solving for x, y and z, we will have:

x = $ 5
y = $ 1
z = $ 3
Final answer:

We can solve this problem by setting up a system of equations using the given information and using algebraic methods to solve for each variable, which represent the cost of the individual items.

Explanation:

This question can be solved by using the method of linear equations. Let's denote the cost of a small pizza as P, a liter of soda as S, and a salad as A. From the given information, we can create three equations:

2P + S + A = $14 P + S + 3A = $15 3P + S + 2A = $22

By solving these equations, we can determine the prices of the individual items. The details of solving these equations may vary based on your level of comfort with algebra and systems of equations, but the general method involves isolating one variable in one equation and then substituting it into the other equations to eventually solve for each variable.

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If 6 cats can kill 6 rats in 6 minutes, how many cats will it take to kill 100 rats in 50 minutes? previous next

Answers

6 cats-6 rats-6mins = 200 cats-100 rats-50 minutes.

200



Loretta invested $1000 in a simple interest account yielding 5% paid annually. In 2 years, she will have $1100 in her account. From this example, we can conclude that 5% represents the:

Answers

Final answer:

The 5% represents the annual interest rate on Loretta's investment in a simple interest account.

Explanation:

The 5% represents the annual interest rate on Loretta's investment. In simple interest, the interest is calculated as a percentage of the initial investment. So, if Loretta invested $1000, and after 2 years her account has grown to $1100, the interest earned would be $100 (1100 - 1000).

To find the interest rate, we can use the formula:

Interest = Principal * Rate * Time

Using the given information, we can plug in the values and solve for the rate:

100 = 1000 * Rate * 2

Simplifying the equation, we get:

Rate = 100 / (1000 * 2) = 0.05 or 5%

Therefore, the 5% represents the annual interest rate in this scenario.

the base of a pyramid has n sides write an expression for the number of faces of the pyramid

Answers

A pyramid always have a number of slant triangles equal to the number of the sides of the base.

This means that a pyramid always have the number of face which is one more than the number of sides of the base.

Therefore, given that a pyramid has n number of sides of the base, the expression for the number of faces of the pyramid is given by

number of faces = n + 1.

If i multiply the numerator do i have to multiply the denominator

Answers

It depends. If you have a fraction times a whole, only multiply the numerator. If it is fraction times fraction, then multiply 

Which lines must be parallel if angle 10 is supplementary to angle 11?

Answers

lines x and z must be parallel with line c as its transversal for angle 10 and angle 11 to be supplementary

A segment has an endpoint (14,-8) and (4,12) what are the coordinates of its midpoint

Answers

I believe it's (9,2)

The coordinates of the midpoint of the segment that has endpoints as (14,-8) and (4,12) are (9,2).

What are the coordinates of the midpoint of the line segment AB?

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

Suppose we've two endpoints of a line segment:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

x = (p+m) / 2

and

y = (q+n) / 2

Given that a segment has an endpoint (14,-8) and (4,12). Therefore, The coordinates of the midpoint of the segment can be written as,

X- coordinate = (14+ 4)/2

                      = 18/2

                      = 9

Y- coordinate = (-8+12)/2

                      = 4/2

                      = 2

Hence, the coordinate of the midpoint of the segment that has endpoints as (14,-8) and (4,12) is (9,2).

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A diver descends from an elevation of 6 feet below sea level to an elevation
of 98 feet below sea level in 4 equal intervals. What was the diver’s change in
elevation in each interval? Explain how you solved this problem.

Answers

So first, we want to find how much in total did his elevation change. So we want to subtract the him starting from 6 feet below sea from the 98 feet below sea level, to get 92 feet.

Now, since he descended in four equal intervals, we can just divide 92 into four equal parts, or divide by 4, to get 23 feet.

So the diver's change in elevation in each interval was (negative?) 92 feet.

Bethany sells roses and petunias. The expression 3r+2.5p gives the cost (in dollars) of r roses and p petunias.What is the cost of 7 roses and 8 petunias?

Answers

3(7) + 2.5(8)
21 + 20
41

Hope this helps!
3r+2.5p

3(7)+2.5(8)
21+20
41

your answer would be $41

Approximately how many times greater is 9.75 * 10^6 than 1.25 * 10^2?

Answers

9.75 / 1.25 = 7.8

10^6 - 10^2 = 10^4

= 7.8 x 10^4 greater

What is negative three divided by zero fraction form should i just remove the zero?

Answers

For -3/0, anything divided by 0 is undefined, so this answer is undefined. It is undefined due to that we don't know what we have to multiply 0 by to get to 3

Use the chart to multiply the binomial by the trinomial.

What is the product?
A.y3 + 27
B.y3 – 27
C.y3 – 6y2 + 27
D.y3 + 6y2 + 27

Answers

(y + 3)(y^2 - 3y + 9) =
y(y^2 - 3y + 9) + 3(y^2 - 3y + 9) =
y^3 - 3y^2 + 9y + 3y^2 - 9y + 27 =
y^3 + 27 <==

Answer:

option (1) is correct.

the product of the binomial by the trinomial is [tex]y^3+27[/tex].

Step-by-step explanation:

Binomial is the term having two different term and trinomial  having three different terms.

Here, Binomial is [tex]y+3[/tex] and trinomial is [tex]y^2-3y+9[/tex]

We have find the product of the binomial by the trinomial.

[tex](y+3)(y^2-3y+9)[/tex]

Multiply each term of binomial with trinomial,

[tex]\Rightarrow y(y^2-3y+9)+3(y^2-3y+9)[/tex]

[tex]\Rightarrow y^3-3y^2+9y+3y^2-9y+27[/tex]

Combining like term, we get,

[tex]\Rightarrow y^3+(3-3)y^2+(9-9)y+27[/tex]

[tex]\Rightarrow y^3+27[/tex]

Thus, the product of the binomial by the trinomial is [tex]y^3+27[/tex].

Hence, option (1) is correct.


Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each does he have

Answers

Answer:

Dustin has 17 nickels and 32 quarters.

Explanation:

Let's denote the number of nickels as [tex]\(n\)[/tex] and the number of quarters as [tex]\(q\).[/tex]

We can set up a system of equations based on the given information:

1. The total number of coins: [tex]\(n + q = 49\)[/tex]

2. The total value of the coins: [tex]\(0.05n + 0.25q = 8.85\)[/tex]

We can solve this system of equations to find the values of [tex]\(n\) and \(q\).[/tex]

From equation (1), we can express [tex]\(n\)[/tex] in terms of [tex]\(q\):[/tex]

[tex]\[n = 49 - q\][/tex]

Now, substitute this expression for [tex]\(n\)[/tex] into equation (2):

[tex]\[0.05(49 - q) + 0.25q = 8.85\][/tex]

[tex]\[2.45 - 0.05q + 0.25q = 8.85\][/tex]

Combine like terms:

[tex]\[0.20q + 2.45 = 8.85\][/tex]

Subtract 2.45 from both sides:

[tex]\[0.20q = 6.40\][/tex]

Now, divide both sides by 0.20:

[tex]\[q = \frac{6.40}{0.20} = 32\][/tex]

So, Dustin has 32 quarters.

To find the number of nickels, we can substitute the value of \(q\) into the equation [tex]\(n + q = 49\):[/tex]

[tex]\[n + 32 = 49\][/tex]

[tex]\[n = 49 - 32\][/tex]

[tex]\[n = 17\][/tex]

So, Dustin has 17 nickels.

At Susie's school, 5/8 of all students play sports. Of the students who play sports, 2/5 play soccer. What fraction of the students in Susie's school play soccer?

Answers

9/40 because you would convert 2/5 into 16/40 and 5/8 into 25/40. then you just need to subtract

You would multiply 5/8 * 2/5, and the answer is 0.25, which converts to 25/100 or 1/4

Khalid invested $9500 in a savings account with a yearly interest rate of 3% for 8 years. How much simple interest did he earn?

Answers

So simple interest, you don't compound anything, you will always add 3% from $9500 and it will not change. The equation will look like this:

9500*[1+(0.03*8)]
giving us 9500*1.24 = $11,780

Answer:

$2280

Step-by-step explanation:

Which equation represents the line that passes through the points (–3, 7) and (9, –1)?

A) y = - 2/3 x + 5
B) y = - 2/3 x - 7
C) y = 2/3 x - 7
D) y = 2/3 x - 5

Answers

slope = (7 + 1)/(-3 - 9) = 8 / -12 = -2/3

y = mx + b
7 = -2/3(-3) + b
7 = 2 + b
b = 5

equation
y = -2/3x + 5

answer
A) y = - 2/3 x + 5

The equation represents the line that passes through the points (–3, 7) and (9, –1) will be A) y = - 2/3 x + 5.

What is the slope of a line which passes through points ( p,q) and (x,y)?

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

The slope = (7 + 1)/(-3 - 9)

                = 8 / -12

                = -2/3

The equation of a line

[tex]y = mx + b\\7 = -2/3(-3) + b\\7 = 2 + b\\b = 5[/tex]

y = -2/3x + 5

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If a car travels 23 miles on 1.0 gal of gas, how many liters of gasoline are needed for a 135 mile trip?

Answers

Solution can be gained by using "Product of means = Product of extremes" concept. So the information we have is 23 miles on 1 gal and 135 mile on 'x' gal. 23 : 1 :: 135 : x As per Product of means = Product of extremes, 23 multiplied x = 135 multiplied by 1. And x will be 135 divided by 23 which is 5.86 gal Now, we have to convert gal to liters, 1 gal = 3.78 liters, so 5.86 gal = 5.86 multiplied by 3.78, which is 22.15 liters. Hence, 22.15 liters of gasoline are needed for a 135 mile trip

Group A has an elevation of -282 feet. group B has an elevation of 279 feet. which is closer to sea level

Answers

~ 279 feet







--- sea level ---












~ -282 feet
distance of group A = 282 ft
distance of group B = 279 ft

So group B is closer

Solve for y.


d = 5x + 5y

Answers

d = 5x + 5y
5y = d - 5x
  y = (d - 5x) / 5

The solution for y of the given equation is y = (d - 5x)/ 5.

What are Arithmetic operations?

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

The operator that performs the arithmetic operations are called arithmetic operators.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that the equation as

⇒ d = 5x + 5y

Rearrange the terms in the above equation

⇒ 5y = d - 5x

Divided by 5 both sides of the equation

⇒  y = (d - 5x)/ 5

Hence, the solution for y of the given equation is y = (d - 5x)/ 5.

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Which of the following is an odd function? f(x) = x3 + 5x2 + x mc023-1.jpg f(x) = x2 + x f(x) = –x

Answers

Given the functions
(a) f(x) = x³ + 5x² + x
(b) f(x) = x² + x
(c) f(x) = -x

Function (a)
f(-x) = (-x)³ + 5(-x)² + (-x)
       = -x³ + 5x² - x
       = -(x³ - 5x² + x)
The function is neither even nor odd.

Function (b)
f(-x) = (-x)² + (-x)
        = -(-x² + x)
The function is neither even nor odd.

Function (c)
f(-x) = -(-x)
       = x
       = -f(x)
Because f(-x) = -f(x) the function is odd.

Answer: f(x) = -x is an odd function.

By evaluating each function in -x, we will see that the only odd one is:

f(x) = -x

What is an odd function?

We say that a function is odd if:

f(-x) = f(x)

Then we just need to check that for the given functions, let's see what we get:

1) f(-x) = (-x)^3 + 5*(-x)^2 + (-x) = -x^3 + 5x^2 - x ≠ -f(x)

2) f(-x) = (-x)^2 - x= x^2 - x ≠ -f(x)

3) f(-x) = -(-x) = x = -f(x)

So the only odd function is the third one, one useful thing that you may need to know is that usually when you see even exponents, that function will not be odd.

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A puzzle contains a triangular piece with a base of 3 in. and a height of 4 in. A manufacturer wants to make 80 puzzles. Find the amount of wood used if each puzzle contains 20 triangular pieces.

Answers

Since the base is 3 inches and the height is 4 inches, as well as the area of a triangle being base*height/2, we get 3*4/2=6 in. for each triangle. Since we need 20 pieces for each puzzle, we multiply 6 by 20 to get 120. In addition, since 80 puzzles are needed, with 20 pieces for each puzzle, we have 120 inches for each puzzle and 120*80 = 9600 square inches of wood used

Answer:

9600 square inches.

Step-by-step explanation:

We have been given that a puzzle contains a triangular piece with a base of 3 in. and a height of 4 in.

The would used for each triangular piece would be equal to area of triangle.

[tex]\frac{1}{2}\times 3\text{ in}\times 4\text{ in}=3\text{ in}\times 2\text{ in}=6\text{ in}^2[/tex]

Each puzzle contains 20 triangular pieces, so wood used for each piece of puzzle would be 20 times 6 square inches.

[tex]\text{Wood used for each puzzle}=20\times 6\text{ in}^2[/tex]

[tex]\text{Wood used for each puzzle}=120\text{ in}^2[/tex]

[tex]\text{Wood used for 80 puzzles}=80\times 120\text{ in}^2[/tex]

[tex]\text{Wood used for 80 puzzles}=9600\text{ in}^2[/tex]

Therefore, 9600 square inches of wood is needed to make 80 puzzles.

Find all values of thetaθ​, if thetaθ is in the interval ​[0degrees°​, 360degrees°​) and has the given function value cot thetaθ=1

Answers

In the first quadrant, 0-90 degrees, the angle whose cotangent  is is 45 degrees.  The only other quadrant where cot theta is 1 is 3rd quadrant.

The 2 angles are 45 and 180+45  = 225 degrees

Answer 45 , 225 degrees.

Simplify 5x + 50/x+5 · 1/x+10
A. 5/x+5
B. 5x^{2}
C. x-3/x+7
D. x-2

Answers

the answer is A. 5/x+5

What is the length of a rectangle with area 402 ft^2
and width 12 ft?

Answers

So find area, you multiply length times width. In this case, it wants you to find length so you will do the opposite. Divide the area by the width.

402 / 12 = 33.5

So the length is 33.5 feet.

Hope this helps! :)

The length of the rectangle is 33.5 feet.

To find the length of the rectangle, we can use the formula for the area of a rectangle:

Area = length * width

Given:

Area = 402 ft^2

Width = 12 ft

Let's solve for the length:

402 ft^2 = length * 12 ft

To find the length, divide both sides by 12 ft:

length = 402 ft^2 / 12 ft

length = 33.5 ft

So, the length of the rectangle is 33.5 feet.

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define a variable and write an inequality to model each situation. The school auditorium can seat at most 1200 people.

Answers

The picture is the answer

0.90 divided by 0.30 PLEASE SHOW WORK OR EXPLAIN YOUR REASONING!

Answers

How many times does 0.30 fit in 0.90? Well, exactly 3 times since 9 is 3 times more than 3!

Hope this helps!
0.90 divided by 0.30=3
first write it as a fraction =0.9/0.3
then you multiply the numerator and the denominator by 10= 9/3
divide the 9 and the 3 =3
hope this helps

for geometric sequence below, determine the explicit formula. be sure to enter your answer as a formula of the form a_n= a_1(r)^(n-1) with the correct a_1 and r values.

5/8, 25/8, 125/8, 625/8, . . ., a_n

Answers

Hello.

Let's calculate r:

r = a₂ / a₁

r = (25/8) / (5/8)

r = 5.

Since a₁ = 5/8

[tex]\boxed{\mathsf{a_n = \frac{5}{8}\cdot 5 ^{n-1}}}[/tex]

The __________ is the score that occurs most frequently in a distribution.

Answers

The mode occurs most often.

Express the set of real numbers between but not including 2 and 5 as follows.

Answers

2 < x < 5

i think this is the answer
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