Ms. Lund placed a 7 foot ladder against a wall with the base of the ladder 4 feet away from the wall . she decided that a different , 10 foot ladder needed to be used . for if Ms. Lund wants the longer ladder to rest against the wall at the same angle as the shorter ladder , about how far away from the wall should she place its base ?

Answer: Option D

Step-by-step explanation:

If we have a main function [tex]f (x) = x ^ 4[/tex]

And we perform the transformation:

[tex]g (x) = f (x + h) = (x + h) ^ 4[/tex]

Then it is fulfilled that:

If [tex]h> 0[/tex] the graph of [tex]f(x)[/tex] moves horizontally h units to the left

If [tex]h <0[/tex] the graph of [tex]f(x)[/tex] moves horizontally h units to the right

If we have a main function [tex]f (x) = x ^ 4[/tex]

And we perform the transformation:

[tex]g (x) = -f(x) = -x ^ 4[/tex]

Then it is fulfilled that:

The graph of [tex]g(x)[/tex] is equal to the graph of [tex]f(x)[/tex] reflected on the x axis

In this case we have to:

[tex]g(x) = -(x + 3)^4[/tex] and [tex]f(x) = x^4[/tex]

Therefore [tex]h=3>0[/tex] and [tex]g(x) = -f(x)[/tex]

This mean that: g(x) is shifted 3 units to the left and reflected over the x-axis.

Answer:

-1 9/18 and then -32/40 and then 1 8/20

Step-by-step explanation:

The largest negatives is the least , then the second to least and then non-negative should be the greatest or the last

Answer:

13.69%.

Step-by-step explanation:

The probability he scores in 1 shot = 1 - 0.63 = 0.37.

The probability that he scores twice in 2 shots = 0.37 * 0.37

= 0.1369

= 13.69%.

The probabilities are multiplied because the 2 events are independent.

Answer:

For plato user the answer is 13.69 %.

Step-by-step explanation:

If this player shoots twice, the probability that he scores a goal both times is  

13.69 %.

Answer:

Step-by-step explanation:

A better way to write the first function would be:

c(n) = 4*c(n-1), meaning that the number of likes is equal to four times the number of likes from the previous day. 

On the first day, c(n)=c(0) = 100

Therefore:

C(n) = 100 * 4^n 

Let's plug in a view values to test our function: 

When n= 0 (first day)

C(0) = 100 * 4 ^0 = 100*1 = 100 likes

C(1) = 100 * 4^1 = 100 * 4 = 400 likes, four times the previous day

C(2) = 100 * 4^2 = 100 * 16 = 1600 likes, four times the previous day

And so on. Our function is an accurate descriptor of the model. 

Answer:

Equation:

[tex]{x}^{2} + {y}^{2} + 2x - 2y - 35= 0[/tex]

The point (0,-5), (0,7), (5,0) and (-7,0)also lie on this circle.

Step-by-step explanation:

We want to find the equation of a circle with a diamterhat hs endpoints at (-3, 4) and (5, -2).

The center of this circle is the midpoint of (-3, 4) and (5, -2).

We use the midpoint formula:

[tex]( \frac{x_1+x_2}{2}, \frac{y_1+y_2,}{2} )[/tex]

Plug in the points to get:

[tex]( \frac{ - 3+5}{2}, \frac{ - 2+4}{2} )[/tex]

[tex]( \frac{ -2}{2}, \frac{ 2}{2} )[/tex]

[tex]( - 1, 1)[/tex]

We find the radius of the circle using the center (-1,1) and the point (5,-2) on the circle using the distance formula:

[tex]r = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]

[tex]r = \sqrt{ {(5 - - 1)}^{2} + {( - 2- - 1)}^{2} } [/tex]

[tex]r = \sqrt{ {(6)}^{2} + {( - 1)}^{2} } [/tex]

[tex]r = \sqrt{ 36+ 1 } = \sqrt{37} [/tex]

The equation of the circle is given by:

[tex](x-h)^2 + (y-k)^2 = {r}^{2} [/tex]

Where (h,k)=(-1,1) and r=√37 is the radius

We plug in the values to get:

[tex](x- - 1)^2 + (y-1)^2 = {( \sqrt{37}) }^{2} [/tex]

[tex](x + 1)^2 + (y - 1)^2 = 37[/tex]

We expand to get:

[tex] {x}^{2} + 2x + 1 + {y}^{2} - 2y + 1 = 37[/tex]

[tex]{x}^{2} + {y}^{2} + 2x - 2y +2 - 37= 0[/tex]

[tex]{x}^{2} + {y}^{2} + 2x - 2y - 35= 0[/tex]

We want to find at least four points on this circle.

We can choose any point for x and solve for y or vice-versa

When y=0,

[tex]{x}^{2} + {0}^{2} + 2x - 2(0) - 35= 0[/tex]

[tex]{x}^{2} +2x - 35= 0[/tex]

[tex](x - 5)(x + 7) = 0[/tex]

[tex]x = 5 \: or \: x = - 7[/tex]

The point (5,0) and (-7,0) lies on the circle.

When x=0

[tex]{0}^{2} + {y}^{2} + 2(0) - 2y - 35= 0[/tex]

[tex] {y}^{2} - 2y - 35= 0[/tex]

[tex](y - 7)(y + 5) = 0[/tex]

[tex]y = 7 \: or \: y = - 5[/tex]

The point (0,-5) and (0,7) lie on this circle.

Answer:

Perimeter= 36mm

Area= 81mm

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Let his current age = x

Now if you add 46 to that, you will get x + 46.

x + 46

At which point he will be 3 times as old as he is now

x + 46 = 3x            Subtract x from both sides.

x-x + 46 = 3x-x      Combine

46 = 2x                  Divide by 2

46/2=2x/2             Do the division

23 = x

He is 23 right now

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

It might be a little easier to see if you represent the situation a little more literally.

3x - 46 = x            The answer comes to the same thing. You might think about which way you want to do it.

48 more miles

Coyote= 43h

Rabbit= 35h

Coyote= 43(6)= 258

Rabbit= 35(6)= 210

Now subtract 258 by 210

258-210= 48

Answer:

The correct ordered pair is (7,1)

Step-by-step explanation:

The given system has equations:

[tex]2x - 6y = 8....(1)[/tex]

[tex]5x- 4y = 31....(2)[/tex]

We make x the subject in the first equation to get:

[tex]x = 4 + 3y...(3)[/tex]

Put equation 3 into equation 2 to get:

[tex]5(4 + 3y) - 4y = 31[/tex]

Expand:

[tex]20 + 15y - 4y = 31[/tex]

[tex]15y - 4y = 31 - 20[/tex]

[tex]11y = 11[/tex]

[tex]y = 1[/tex]

Put y=1 into equation 3 and solve for x.

[tex]x = 4 + 3( 1) = 7[/tex]

The correct ordered pair is (7,1)

Answer:

A.

[tex]a_n=9+(n-1)\cdot 5[/tex].

Step-by-step explanation:

The common difference is 5. The y values are going up by 5. So this is an arithmetic sequence since we have a common difference.

The explicit form for arithmetic sequence is:

[tex]a_n=a_1+(n-1) \cdot d[/tex] where d represents the commom difference and [tex]a_1[/tex] is the first term.

Here the first term is [tex]a_1=9[/tex] and we already determined the value for d which is 5.

Inputing these values for first term and common difference give:

[tex]a_n=9+(n-1)\cdot 5[/tex].

Answer:

the answer is A

Step-by-step explanation:

Answer: 8

Step-by-step explanation: 8 divided by 1 is 8

8 is the whole number equal to fraction 8/1.

A number system is defined as a system of writing to express numbers.

The given fraction is 8/1

Eight divided by one.

A fraction represents a part of a whole or, more generally, any number of equal parts.

8 is the numerator and 1 is the denominator.

The complete set of natural numbers along with '0' are called whole numbers.

If a number is divided by another number then the result will be the numerator which is whole number.

8/1=8

Hence, 8 is the  whole number equal to fraction 8/1.

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Answer:(a+b)^2+(ab+a+b)2

Step-by-step explanation:

You break it up into two part, based on the exponents.

(a^2+b^2)+(2ab+2a+2b)

Now you can factor out from each...

(a+b)^2+(ab+a+b)2

Answer: (x+y+2)(x+y)

Step-by-step explanation:

Using square roots and factorising

Answer:

111

Step-by-step explanation:

because the lines are parallel and they are on opposite sides its like having two angles on the same line but on different sides so they are supplementary meaning they add up to 180 and 180-69 = 111

please mark brainliest :)

Answer:

(x-4)^2 + (y-1)^2 = 6^2

or

(x-4)^2 + (y-1)^2 = 36

Step-by-step explanation:

The equation for a circle is given by

(x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-4)^2 + (y-1)^2 = 6^2

or

(x-4)^2 + (y-1)^2 = 36

Answer:

(x - 4)^2 + (y - 1)^2 = 6^2

Step-by-step explanation:

Adapt the standard equation of a circle with center at (h, k) and radius r:

(x-h)^2 + (y-k)^2 = r^2

Here we have:

(x - 4)^2 + (y - 1)^2 = 6^2

Step-by-step explanation:

[tex]\dfrac{a}{b}\cdot(-1)=-\dfrac{a}{b}[/tex]

On the number line, fractions a/b and -a/b lie on the opposite sides of the number 0, at the same distance (look at the picture).

It would be C. they are skew on ED :)

Answer: C

Step-by-step explanation: your welcome

Answer:

Step-by-step explanation:

Look at the picture.

Use the long division.

The full length of one line times the length of the line outside the circle is equal the the other line.

(x-1) +5 x 5 = (2+x)+4 x 4

Simplify:

(x+4) x 5 = (x +6) x 4

5x +20 = 4x +24

Subtract 20 from each side:

5x = 4x +4

Subtract 4x from each side:

x = 4

The answer is B. 4

Subtract 121 from both sides:

[tex]25x^2=-121[/tex]

Divide both sides by 25:

[tex]x^2 = -\dfrac{121}{25}[/tex]

The solutions would be

[tex]x = \pm\sqrt{-\dfrac{121}{25}}[/tex]

This expression cannot be evaluated using real numbers, because the square root of negative numbers are not allowed. If we're using complex numbers, the solutions are

[tex]x = \pm\sqrt{-\dfrac{121}{25}} = \pm\dfrac{11i}{5}[/tex]

Answer:

B. y + 2 = ½(x + 3)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, which is the reason why you see two "+" in the equation. The ordered pair of [-3, -2] has two negative numbers, therefore you need to make them both positive in the equation [see above answer].

I am joyous to assist you anytime.

Answer:

The answer is B. 2374

Answer:

B. 2374

Step-by-step explanation:

Division by 5: If a number ends in 0 or 5 it is divisible by 5.

A. 5000 is divisible by 5.

D. 2505 is divisible by 5.

Division by 3: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

B. 2374

Add the digits of 2374: 2 + 3 + 7 + 4 = 16. 16 is not divisible by 3, so 2374 is not divisible by 3. It is also not divisible by 5 since it does not end in 0 or 5.

C. 1203

Add the digits of 1203: 1 + 2 + 0 + 3 = 6. Since 6 is divisible by 3, 1203 is divisible by 3.

Answer: B. 2374

Answer:

9. 75°

10. 60°

Step-by-step explanation:

Note the angle-intercept theorem. If you create an angle in the opposite side of a circle from 2 points on other side, the arc will have a measure TWICE that of the intercepted angle created on other side.

Question 9

Arc WX has a measure 76, thus the angle created is Angle V, which should be HALF of that. So angle V is  76/2 = 38

Now looking at the triangle inside the circle, we know three angles of a triangle add up to 180, thus we can write and solve for "?" angle:

X + W + V = 180

? + 67 + 38 = 180

? + 105 = 180

? = 180 - 105 = 75°

Question 10

Using the theorem we can say that Angle B is HALF of ARC XYZ.

So,

2*Angle B = Arc XY + Arc YZ

2*102 = Arc XY + 124

204 = Arc XY + 124

Arc XY = 204 - 124 = 80°

Also, Arc BX + Arc XY is twice that of Angle Z (which is 70), thus

Arc BX + Arc XY = 70 *2

Arc BX + Arc XY = 140

Arc BX + 80 = 140

Arc BX = 140 - 80 = 60°

Answer:

[tex](x-6i)(x+6i)(x-3)(x+3)[/tex]

Step-by-step explanation:

If 6i is a zero then -6i is a zero.

In general, if a+bi is a zero then a-bi is a zero (if the polynomial has real coefficients which this one does: 1,27,-324).

Let's test it to see:

Check [tex]x=6i[/tex]

[tex]P(6i)=(6i)^4+27(6i)^2-324\\

P(6i)=6^4(i^4)+27(6)^2(i^2)-324\\

P(6i)=1296(1)+27(6^2)(-1)-324\\

P(6i)=1296-27(36)-324\\

P(6i)=1296-972-324\\

P(6i)=1296-1296\\

P(6i)=0\\[/tex]

Check [tex]x=-6i[/tex]

[tex]P(-6i)=(-6i)^4+27(-6i)^2-324\\

P(-6i)=(6i)^4+27(6i)^2-324\\

P(-6i)=P(6i)\\

P(-6i)=0\\[/tex]

So yep they both give us 0 when we plug it in.

If x=6i is a zero then x-6i is a factor by factor theorem.

If x=-6i is a zero then x+6i is a factor by factor theorem.

What is (x-6i)(x+6i)?

Let's use the multiply conjugates formula: [tex](u-v)(u+v)=u^2-v^2[/tex].

[tex](x-6i)(x+6i)=x^2-36i^2=x^2-36(-1)=x^2+36[/tex]

Now we know [tex](x^2+36)[/tex] is a factor of [tex]x^4+27x^2-324[/tex].

We can use long division or we could try to find two numbers that multiply to be -324 and add up to be 27 since this is a quadratic in terms of [tex]x^2[/tex] with leading coefficient of 1.

Well we already know we are looking for number times 36 that would give us -324.

So -324=-9(36) and 27=-9+36

So the factored form in terms of real numbers is:

[tex](x^2+36)(x^2-9)[/tex]

We already know the first factor can be factored as (x+6i)(x-6i).

The other can factored as (x-3)(x+3) since (-3)(3)=-9 and -3+3=0.

So the complete factored form is

[tex](x-6i)(x+6i)(x-3)(x+3)[/tex].

To find the remaining zeros of the polynomial, we use synthetic division and find a quadratic factor. The remaining zeros are the solutions to the quadratic equation x^2 + 9 = 0, which are 3i and -3i.

To find the remaining zeros of the polynomial, we can use polynomial long division or synthetic division. Let's use synthetic division:

Since 6i is a zero of P(x), the conjugate -6i is also a zero. We can divide P(x) by (x - 6i)(x + 6i) to find the remaining quadratic factor.

Performing the synthetic division, we get a quadratic factor of x^2 + 9. Therefore, the remaining zeros of the polynomial are the solutions to the equation x^2 + 9 = 0.

Solving the quadratic equation x^2 + 9 = 0, we find that the remaining zeros are x = 3i and x = -3i.

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Answer:

12

Step-by-step explanation:

The general formula for this is

Formula

1/t1 + 1/t2 = 1/t_tot

givens

t1 = 6 hours

t2 = x

t_tot = 4 hours

Solution

1/6 + 1/x = 1/4                 Subtract 1/6 from both sides.

1/6-1/6 + 1/x = 1/4 - 1/6   Change to 12 as your common denominator

1/x = 3/12 - 2/12              subtract

1/x = 1/12                         Cross multiply

x = 12

Tom would need 12 hours to do the job alone.

Answer:

Option D. 12 hours

Step-by-step explanation:

Let the work done by Tom to do the job alone = x hours

So per hour work done by Tom = [tex]\frac{1}{x}[/tex]

Jerry can do the job alone in the time = 6 hours

Per hour work done by Jerry = [tex]\frac{1}{6}[/tex]

Similarly job done by both together in the time = 4 hours

Per hour work done by both together = [tex]\frac{1}{4}[/tex]

Now we know,

Per hour work done by both together = per hour work done by Tom + Per hour work don by Jerry

[tex]\frac{1}{4}=\frac{1}{x}+\frac{1}{6}[/tex]

[tex]\frac{1}{x}=\frac{1}{4}-\frac{1}{6}[/tex]

[tex]\frac{1}{x}=\frac{3-2}{12}[/tex]

[tex]\frac{1}{x}=\frac{1}{12}[/tex]

x = 12 hours

Option D. will be the answer.

Answer:

y = 3x - 11

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (2, - 5) into the partial equation

- 5 = 6 + c ⇒ c = - 5 - 6 = - 11

y = 3x - 11 ← equation of parallel line

the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:

To find the equation of a line that is parallel to a given line and passes through a certain point, we need to use the concept that parallel lines have the same slope. The slope-intercept form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. Given that the line is parallel to y = 3x - 4, it will have the same slope, which is 3. Thus the slope of our new line is also 3.

We want our line to pass through the point (2, -5). Plugging these values into the slope-intercept form, we get:

which simplifies to:

Thus, the y-intercept b of our new line is:

Therefore, the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:

Answer:

21

Step-by-step explanation:

you can arrange 7×3 ways

Answer with explanation:

Number of trophies possessed by me= 7

Number of trophies that is to be selected from 7 trophies =3

⇒⇒So, Chosing 3 out of 7 trophies and arranging them on a shelf requires Concept of Permutation, as order of arrangement is also taken into consideration

    [tex]=_{3}^{7}\textrm{P}\\\\=\frac{7!}{(7-3)!}\\\\=\frac{7!}{4!}\\\\=\frac{4!*5*6*7}{4!}\\\\=5*6*7\\\\=210\text{Ways}[/tex]

Or

⇒First place can be filled in 7 ways,second place can be filled in 6 ways and third place can be filled in 5 ways.

So total number of ways of selecting 3 trophies from 7 trophies

                             =7 *6 *5

                             =210 ways

⇒Now, 3 trophies can be arranged in a shelf in 3! =3 *2*1=6 ways.

Answer:

Option 3 [tex]\frac{67}{441}[/tex]

Step-by-step explanation:

step 1

Find the roots of the quadratic equation

we have

[tex]3x^{2}+5x-7=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]3x^{2}+5x-7=0[/tex]

so

[tex]a=3\\b=5\\c=-7[/tex]

substitute in the formula

[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(3)(-7)}} {2(3)}[/tex]

[tex]x=\frac{-5(+/-)\sqrt{109}} {6}[/tex]

[tex]x=\frac{-5+\sqrt{109}} {6}[/tex]

[tex]x=\frac{-5-\sqrt{109}} {6}[/tex]

step 2

Let

[tex]\alpha=\frac{-5+\sqrt{109}} {6}[/tex]

[tex]\beta=\frac{-5-\sqrt{109}} {6}[/tex]

we need to calculate

[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]

step 3

Calculate   [tex](3\alpha+5)^{2}[/tex]

[tex](3\alpha+5)^{2}=[3(\frac{-5+\sqrt{109}} {6})+5]^{2}[/tex]

[tex]=[(\frac{-5+\sqrt{109}} {2})+5]^{2}[/tex]

[tex]=[(\frac{-5+\sqrt{109}+10} {2})]^{2}[/tex]

[tex]=[(\frac{5+\sqrt{109}} {2})]^{2}[/tex]

[tex]=[(\frac{25+10\sqrt{109}+109} {4})][/tex]

[tex]=[(\frac{134+10\sqrt{109}} {4})][/tex]

[tex]=[(\frac{67+5\sqrt{109}} {2})][/tex]

step 4

Calculate   [tex](3\beta+5)^{2}[/tex]

[tex](3\beta+5)^{2}=[3(\frac{-5-\sqrt{109}} {6})+5]^{2}[/tex]

[tex]=[(\frac{-5-\sqrt{109}} {2})+5]^{2}[/tex]

[tex]=[(\frac{-5-\sqrt{109}+10} {2})]^{2}[/tex]

[tex]=[(\frac{5-\sqrt{109}} {2})]^{2}[/tex]

[tex]=[(\frac{25-10\sqrt{109}+109} {4})][/tex]

[tex]=[(\frac{134-10\sqrt{109}} {4})][/tex]

[tex]=[(\frac{67-5\sqrt{109}} {2})][/tex]

step 5

substitute

[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]

[tex]\frac{1}{[(\frac{67+5\sqrt{109}} {2})]}+ \frac{1}{[(\frac{67-5\sqrt{109}} {2})]}[/tex]

[tex]\frac{2}{67+5\sqrt{109}} +\frac{2}{67-5\sqrt{109}}\\ \\\frac{2(67-5\sqrt{109})+2(67+5\sqrt{109})}{(67+5\sqrt{109})(67-5\sqrt{109})} \\ \\\frac{268}{1764}[/tex]

Simplify

Divide by 4 both numerator and denominator

[tex]\frac{268}{1764}=\frac{67}{441}[/tex]

Answer:

  3)  67/441

Step-by-step explanation:

Comparing the given equation to the expressions you need to evaluate, you find there might be a simplification.

  3x² +5x -7 = 0 . . . . . given equation

  3x² +5x = 7 . . . . . . . add 7

  x(3x +5) = 7 . . . . . . . factor

  3x +5 = 7/x . . . . . . . . divide by x

Now, we can substitute into the expression you are evaluating to get ...

  1/(3α +5)² +1/(3β +5)² = 1/(7/α)² +1/(7/β)² = (α² +β²)/49

__

We know that when we divide the original quadratic by 3, we get

  x² +(5/3)x -7/3 = 0

and that (α+β) = -5/3, the opposite of the x coefficient, and that α·β = -7/3, the constant term. The sum of squares is ...

  α² +β² = (α+β)² -2αβ = (-5/3)² -2(-7/3) = 25/9 +14/3 = 67/9

Then the value of the desired expression is ...

  (67/9)/49 = 67/441

Answer:

26 m

Step-by-step explanation:

Perimeter = 92 m

Length = 8 m more than width

Width: 20 m

Therefore,

The width of the rectangular lot is 19 m and the length is 27 m.

The subject of this question is the calculation of the length of a rectangular lot. The perimeter of a rectangle is the sum of all its sides, given by the formula 2*(length + width). From the question, we know that the perimeter is 92 m, and the length is 8 m more than the width. Suppose 'w' is the width. Thus the length is 'w + 8' m.

So, we can set up the equation 2*(w + w + 8) = 92. Solving this equation will give us the value for the width (w) and consequently, the length by adding 8 to it.

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Answer:

D.

Step-by-step explanation:

First, put your original equation in slope-intercept form to find your slope.

[tex]y=mx+b\\2x+4y=-5\\4y=-2x-5\\y=-\frac{1}{2} x-\frac{5}{4}[/tex]

Now that you have your slope ([tex]-\frac{1}{2}[/tex]) and a point, you can use point-slope form to find your y-intercept.

[tex]y-y1=m(x-x1)\\y-(-8)=-\frac{1}{2} (x-(-4))\\y+8=-\frac{1}{2} (x+4)\\y+8=-\frac{1}{2} x-2\\y=-\frac{1}{2} x-10[/tex]

Your answer choices are all in [tex]Ax+By=C[/tex] form, so lets convert our equation into that form.

[tex]y=-\frac{1}{2} x-10\\1/2x+y=-10\\x+2y=-20[/tex]

If we multiply all of our terms by 2, we can get answer choice D.

Answer:

Explanation:

The formula for permuations is nPk:

Where n is the total number of elements from which you must choose combinations of k number of elements, and where the order of selection is relevant.

In this case n = 22 (the number of participants), k = 5 (the number of top participants). Since, the order in which the participants finish is relevant, then you have to use the formula of permutations, such as the question states.

Calculations: