Word problem involving permutations
There are 3 cyclists in a race. There will be a first-place and a second-place prize awarded. In how many different ways can the 2 prizes be awarded?

The value of the angle θ required in the water main for the turn from north to east is 87.40°.

According to the statement

We have to find that the value of the angle.

So, For this purpose, we know that the

An angle is created when two straight lines or rays meet at a standard endpoint.

From the given information:

a main is to be constructed with a 20% grade within the north direction and a tenth grade within the east direction.

Then

Let n = North

and e = east

Then

using vectors,

n =  j + 0.20 k

e = i + 0.25 k

And the

n · e = 1x0 + 0x1 + 0.20×0.25 = 0.05

Now take magnitude then

|n|·|e| = i(1² + 0.20²)·i(1²+0.25²) = 1.105

Now,

E° = arccos((n · e)/|n|·|e|)

E° = arccos(0.05/1.105)

E° = arccos (0.0452)

E° = 87.40°

So, The value of the angle θ required in the water main for the turn from north to east is 87.40°.

Learn more about angle here

https://brainly.com/question/24368895

#SPJ4

The Expression for the Area a of the rectangle as a function of length L is given by A(L) = 12L - L^2 .

Let,

length, L, and the width, W, are components that help determine the area, A, and the perimeter, P of the rectangle. These are given by the following equations

 A=LW

 P=2L+2W

Given,

Perimeter of the Rectangle = 24m.

We are asked to express the perimeter of the rectangle as a function of the length, L, of one of its sides.

We will first set up the equation of the Perimeter of the rectangle. We can let the width of the rectangle be W.

P = 2L+2W

24 = 2L+2W

12 = L+W

W = 12-L

Since we want to express the Area as a function of L, we have to find the value of W in terms of L. This is so we can eliminate the width in the equation for the Area. The Area as a function of L is as follows.

A(L, W) = LW

A(L) = L(12-L)

A(L) = 12L-L^2

Therefore, the Area as a function of L is given by A(L) = 12L-L^2.

To know more about "Area"

Refer this link:

https://brainly.in/question/35108030?referrer=searchResults

#SPJ4

Answer:  L isn't the midpoint of segment MN.

Step-by-step explanation:

NL+LM=NM

6x-5+2x+3=4x+9

8x-2=4x+9

8x-2+2=4x+9+2

8x=4x+11

8x-4x=4x+11-4x

4x=11

Divide both parts of the equation by 2:

2x=5.5

NL=6x-5

NL=(2x)(3)-5

NL=(5,5)(3)-5

NL=16.5-5

NL=11.5

LM=2x+3

LM=5.5+3

LM=8.5

NL≠LM

Hence, L isn't the midpoint of segment MN.

In summary, based on the given lengths and mathematical reasoning, we have determined that point L is the midpoint of segment MN because the lengths of NL and LM are equal when x = 2.

We must compare the lengths of the two segments NL and LM and see if they are identical in order to establish whether point L is the midpoint of segment MN.

NL = 6x - 5

LM = 2x + 3

The lengths of NL and LM ought to be equal if L is the middle of segment MN. To put it another way, NL and LM ought to be equal.

Constructing the equation

6x - 5 = 2x + 3

Now, solve for x:

6x - 2x = 3 + 5

4x = 8

x = 2

As soon as we know the value of x, we can put it back into the NL and LM formulas to get their lengths at x = 2:

NL = 6x - 5 = 6 * 2 - 5 = 12 - 5 = 7

LM = 2x + 3 = 2 * 2 + 3 = 4 + 3 = 7

The lengths of NL and LM are both 7 units.

Point L is in fact the middle of segment MN because both segments NL and LM have similar lengths.

To learn more about reasoning link is here

brainly.com/question/33269159

#SPJ3

In the survey study, the explanatory variable is: number of complaints .

An explanatory variable can be described as a type of independent variable that is manipulated by the researcher which explains the or predict the differences that occurs in a response variable.

For example, number of complaints is the independent variable that the dependent variable, "accidents that occurs in an area" depends on. That is, it explains or predicts the accidents that occurs in an area.

Therefore, we can conclude that, in the survey study, the explanatory variable is: number of complaints .

Learn more about the explanatory variable on:

https://brainly.com/question/22046153

#SPJ1

The number if miles per gallon is 35 miles.

How to solve the box plot.

From the information, it was stated that the box plot shows a gas mileage for twenty cars.

Therefore, based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least 35 miles per gallon.

Learn more about box plots on: brainly.com/question/1523909

20796

1140 is the final price.

Step-by-step explanation: 20% of 950 is 190, so add that to 950 and you get 1140

Basically, this is a domain. Well, a condition.

It's saying that any value that you subsitute in x , which is then multiplied by 4 and added 6, must ALWAYS be greater than -14, but lesser than 18.

Literal equations are equations containing two or more variables. Our goal is to solve for just one variable with respect to others. If it is known to us that  how to solve regular equations, then literal equations are very easy to solve.

Literal equation is also termed as simultaneous equation ,

where more than 1 variable is present and can be solved by inputting value entirely into 1 variable form

For example,

x+ y=6

x-y=2

now putting x=y+2 from  the second equation,

y+2+y=6

2y+2=6

y+1=3

y=2

x=y+2=2+2=4

To solve a literal equation means to express one variable with respect to the other variables in the equation.

For further reference:

https://brainly.com/question/28437973?referrer=searchResults

#SPJ9

Equations that have two or more variables are considered literal equations. Our aim is to solve for a single variable in relation to other variables. Literal equations are fairly simple to solve if we know how to solve regular equations.

Simultaneous equation is another name for a literal equation.

where a problem with more than one variable can be handled by entering all of the values into a single variable form.

For Example :

                          x + y = 6

                          x - y = 2

Now putting x = y + 2 from the equation

                              y + 2 +y = 6

                                  2y + 2 = 6

                                  2y = 6-2

                                   2y = 4

                                    y = 2

  Hence,

                        x = y + 2 = 2 + 2 = 4

To express one variable in relation to the other variables in an equation is to solve it literally.

Learn more about event correlation here: brainly.com/question/24455262

#SPJ9

Answer:

no solution

Step-by-step explanation:

4x + 9y = - 72 → (1)

4x + 9y = 54 → (2)

multiply (1) by - 1

- 4x - 9y = 72 → (3)

add (2) and (3) term by term

0 + 0 = 126 , that is

0 = 126 ← not possible

This indicates the system has no solution

Amount of sugar eaten in the US in 2010 = 4.95 x 10¹⁰ lb

Approximate number of people in the United States of America in 2010 = 3.3 x 10⁸

Amount of sugar ate by an average person in US = 1.5 x 10² lb

We have to find an approximate amount of sugar eaten in US in 2010.

It will be the product of the number of people in US and the sugar ate by a person in US.

So, Amount of sugar eaten in the US in 2010 approximately = 3.3 x 10⁸ x1.5 x 10²

                                                                           = 4.95 x 10¹⁰ lb

Learn more about approximation problems at https://brainly.com/question/25896797

#SPJ4

The equation of the line y = -4.2x + 7.9 expressed in standard form is 42x + 10y = 79.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is written as axe + by = c, where a and b are the coefficients of the variables x and y, respectively, and c is a constant. On the other hand, we can write the equation in point-slope form, (y - y1) = m, if we know the slope m and a point on the line (x, y).

Given the equation of a line, multiply both sides by 10 to turn the decimals into integers.

y = -4.2x + 7.9

10y = 10(-4.2x + 7.9)

10y = -42x + 79

Rewriting it in standard form ax + by = c,

10y = -42x + 79

42x + 10y = 79

Learn more about standard form of a line here:

https://brainly.com/question/28584841

#SPJ1

1264₈ = 1•8³ + 2•8² + 6•8¹ + 4•8⁰

1264₈ = (2³)³ + 2•(2³)² + 3•2•2³ + 2²

1264₈ = 2⁹ + 2⁷ + 3•2⁴ + 2²

1264₈ = 512 + 128 + 3•16 + 4

1264₈ = 692

After converting the base, 1264 base 8 is equal to 692 base 10.

To convert a number from base 8 (octal) to base 10 (decimal), we need to evaluate the value of each digit in the base 8 number and then calculate the equivalent decimal value.

Given the number 1264 in base 8, we can break it down into its digits:

1 * 8³ + 2 * 8² + 6 * 8 + 4 * 1

Simplifying this expression:

1 * 512 + 2 * 64 + 6 * 8 + 4 * 1

Evaluating the multiplication:

512 + 128 + 48 + 4

Adding the products together:

692

In summary, to convert a number from base 8 to base 10, we evaluate the value of each digit by multiplying it with the corresponding power of 8, and then sum up the results. This gives us the equivalent decimal value of the number.

To learn more about conversion click on,

https://brainly.com/question/33187951

#SPJ2

Answer:

12

Step-by-step explanation:

-4 X 3 =-12

=-(-12)

=12

Answer:

$675.75

Step-by-step explanation:

To find the sale price of the recliner, we can multiply 15% by the regular price.

15% = 0.15

(0.15)(795.00) = $119.25

This gives us the amount that the sale takes off from the regular price. We can subtract that from the regular price to find the sale price.

795.00 - 119.25 = $675.75

A bonus shortcut way to get our answer would be to subtract 15% from 100%.

100% = 1.00

1.00 - 0.15 = 0.85

This tells us that the sale price is 85% of the regular price. Using this information, we can multiply 85% by the regular price to also get our sale price.

85% = 0.85

(0.85)(795.00) = $675.75

The number of times that the value of the digit 1 in the population of Cleveland in this value is 10.

Based on the information, it should be noted 7 is in ten thousand place for Memphis. This means that it represents 70000.

It should be noted the 1 in Denver is in the same place. It represents 10000. On Cleveland, this is 1000.

Therefore, the number of times will be:

= 10000 / 1000

= 10

Therefore, the correct option is 10.

Learn more about population on:

brainly.com/question/25896797

#SPJ1

Cleveland population 431,369 Denver population 610,345

Memphis population 676,640 What is the value of the digit 7 in the population of Memphis? What is the value of the digit 1 in the population of Denve?How many times as great the value of the digit 1 in the population of Cleveland is this value?

Answer: x=3

Step-by-step explanation:

1. Hans needs to rent a moving truck. Suppose Company A charges $40.00 per day and Company B charges a $60.00 fee plus $20.00 per day, for what number of days is the cost the same?

Let x = # of days, since Company A charges $40/day then cost after x days = 40x

Let x = # of days, since Company B charges $20/day plus $60 fee, then cost after x days = 20x + 60

a. For what # of days is the cost the same?

   When the cost is the same => 40x = 20x + 60

                                                    40x - 20x = 60

                                                             20x = 60

                                                                 x = 60/20

                                                                 x = 3

 The cost is the same after 3 days.

 Checking:

$40(3)  = $20(3) + $60

$120    = $60 + $60

$120    = $120

y = -3/2x - 20.5 is the line crossing through (-7,10) perpendicular to 2x - 3y= -3

In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that  2x - 3y= -3

can also be written as

y = 2/3x + 1

Here 2/3 is the slope and 1 is the y-intercept

To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = -3/2,  x₁ = -7 and y₁ = 10

y - 10 = -3/2(x - (-7))

y - 10 = -3/2(x + 7)

y - 10 = -3/2x - 21/2

y = -3/2x - 21/2 + 10

y = -3/2x - 20.5

Learn more about point-slope formula

https://brainly.com/question/24907633

#SPJ9

Answer:

86

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

3^-4 x 3^5

3 - 2

=1

The statement is true that the domain of f(x)/g(x) consists of numbers "x" that are in the domains of both f(x) and g(x) for which g(x) is not equal to 0.

To learn more about functions, visit :

https://brainly.com/question/12431044

#SPJ4

========================================================

Explanation:

She read 40 books over 5 months. This means her unit rate is 8 books per month (since 40/5 = 8)

x = number of months

(unit rate)*(number of months) = total books read

8x = 72

x = 72/8

x = 9

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

Another way to solve

(40 books)/(5 months) = (72 books)/(x months)

40/5 = 72/x

40x = 5*72 ... cross multiplying

40x = 360

x = 360/40

x = 9

The probability the bus is late on each of those days will be 0.0625.

It should be noted that the probability that a bus is on time is 0.75. The probability that it's late will be:

= 1 - 0.75

= 0.25

Therefore, the probability the bus is late on each of those days will be:

= 0.25 × 0.25

= 0.0625

Therefore, the probability is 0.25.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:  Food is Food

Step-by-step explanation:

Answer:4x + 8 y -12

Step-by-step explanation:

The answer to this question is 14