Five students are competing in a race. In how many different
could the five students place in the race?
combinations

Answer:

1.08

Step-by-step explanation:

This is because it grows upon itself so it starts with a multiplier of 1, but it is growing with .08 (8 percent) on itself so you add these two numbers together to get 1.08

The statement is true.

To prove this, we will use a proof by contradiction.

Assume that all of the sets {ai lie i} are finite. Then, for each set ai, there exists a finite number of elements in that set. Therefore, the union of all of these sets will also be finite.

However, we are given that the union of all the sets is countably infinite. This means that there exists a countable list of elements in the union.

Let's construct this list:
- First, list all of the elements in a1.
- Then, list all of the elements in a2 that are not already in the list.
- Continue this process for all of the remaining sets.

Since the union is countably infinite, this process will never terminate and we will always have elements to add to our list.

But this contradicts the fact that each set is finite. If each set has a finite number of elements, then there can only be a finite number of unique elements in the union.

Therefore, our assumption that all of the sets are finite must be false. At least one of the sets must be countably infinite.

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Step-by-step explanation:

remember, a probability is always desired cases over total possible cases.

the class has 10+15 = 25 students.

and 5 of them will be picked as representatives to the school board.

how many total possibilities do we have ?

since picked students can be picked only once, and the sequence of the 5 picked students in the group does not matter, we have a combination without repetition :

C(25, 5) = 25! / (5! × (25-5)!) = 25! / (5! × 20!) =

= 25×24×23×22×21 / (5×4×3×2) =

= 5×1×23×22×21 = 53,130 possible outcomes.

how many desired outcomes ?

that would be how many options we have to pick 2 out of 10 and 3 out of 15 :

C(10,2) × C(15,3) = 10! / (2 × 8!) × 15! / (3! × 12!) =

= 10×9/2 × 15×14×13/(3×2) =

= 5×9 × 5×7×13 = 20,475 desired outcomes

and the probability is

20475 / 53130 = 4095 / 10626 = 1365 / 3542 = 195 / 506

= 0.385375494... ≈ 0.39

Answer:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Step-by-step explanation:

We can find the function f(x) by integrating f'(x) with respect to x:

â«f'(x) dx = â«(2/(x^3) + 4e^x + 5) dx

f(x) = -1/x^2 + 4e^x + 5x + C

To find the constant C, we can use the given initial conditions:

f(-1) = 1 = -1/(-1)^2 + 4e^(-1) - 5 + C

C = 1 + 1/1 - 4e^(-1)

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Therefore, the function f(x) is:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Answer:

Step-by-step explanation:

$18 spent on parking. 100-18=82

$42.50 on admission 80- 42.50= 39.5

20 percent of 100 is 20 so 39.5-20=19.5

12.75 so 19.4-12.75=6.65

1.75x=6.65

x=3.8 so basically henry played 3 games

The composite function aob(x) = 4x².

Functions which are formed by composing two or more functions in a way that one's output is another's input are called composite functions.

They are also called function of functions.

Given:

a(x) = x²

and b(x)= 2x

The composite of the function;

aob= a(b(x))

= a(2x)

= (2x)²

= 4x²

Hence, The composite function aob(x) = 4x².

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Make a story problem about conversion of measurements.

Cairo wants to join the basketball team, so he tried out and filled up a form. But he realized that the form wanted to get his height in "cm or centimeters", the problem is that he only knows his height in "feet" which is 6'5.

Since he didn't know how to convert centimeters to feet, he asked his friend Tyga and Tyga easily converted his height into cm. Cairo then filled up the form again and wrote "195.58 cm" in his official height--the equivalent of 6'5 in centimeter measurement.

The correct hypothesis statement for this golfer to prove his claim would be:

\(H_{0} :u\geq 90\)

\(H_{1} :u < 90\)

The golfer claims that his average score is less than 90.

Therefore, the null hypothesis is the opposite of what he claims

Null hypothesis \(H_{0}\) is average score \(u\) is greater than or equal to 90:

\(u \geq 90\)

\(H_{0} :u\geq 90\)

Alternative hypothesis \(H_{1}\) is then the opposite of null hypothesis.

Hence alternate hypothesis \(H_{1}\) is u< 90

\(H_{1} :u < 90\)

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Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

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Answer:

Yes, they are equivalent

Step-by-step explanation:

Tell whether the rates are equivalent.

Rate formula = Speed(miles)/Time(hour)

1)7 1/2 miles for every 3/4 hour

Hence

Rate = 7 1/2 miles ÷ 3/4 hour

= 15/2 ÷ 3/4

= 15/2 × 4/3

= 5 × 2

= 10 miles per hour

2) 1/2 mile for every 3 minutes

Time = 60 minutes = 1 hour

3 minutes = x

x = 3/60

x = 0.05 hour

Hence

Rate = 1/2 mile ÷ 0.05 hour

= 0.5 mile ÷ 0.05 hour

= 10 mile per hour

Therefore, both rates are equivalent

Using trigonometric identities, it is found that the exact value of the secant of the angle is given by:

c. \(\sec{\theta} = - \sqrt{5}\)

According to the following identity:

\(\sec^2{\theta} = 1 + \tan^2{\theta}\)

The tangent is the inverse of the cotangent, hence in this problem, we have that:

\(\tan{\theta} = -2\)

Then, the secant is given as follows:

\(\sec^2{\theta} = 1 + (-2)^2\)

\(\sec^2{\theta} = 5\)

\(\sec{\theta} = \pm \sqrt{5}\)

The angle is in the second quadrant, where the cosine is negative, hence the secant also is and option c is correct, that is:

c. \(\sec{\theta} = - \sqrt{5}\)

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Answer:

D

Step-by-step explanation:

Answer:

The answer is D, 200

Step-by-step explanation:

Since the formula for the volume of a rectangular prism is V = lwh, we multiple the length, width, and height together. This works for any rectangular prism.

V = lwh = 5 * 4 * 10 = 200

Answer:

200 ft3

Step-by-step explanation:

Carter must go north to get back to City Hall.

First carter needs to travel 5 blocks north and 2 blocks west from his current position.

Let's imagine that Carter's starting point (City Hall) is at the center of a coordinate system, where the positive x-axis points east and the positive y-axis points north. Carter's movements can then be represented as vectors in this coordinate system:

We can add up all of these vectors to find Carter's final position relative to City Hall:

(0, 5) + (5, 0) + (-7, 0) + (0, -5) = (-2, 0)

This means that Carter is now 2 blocks west of City Hall (since the x-coordinate is negative), and he needs to travel 5 blocks north to get back to City Hall.

Therefore, Carter must go north to get back to City Hall.

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The dimension that is shared between the top view and the left side view is the depth. Both views show the object in two different perspectives, but the depth remains the same in both views.

Depth refers to the measurement of how far an object extends from front to back, and it is an important dimension that must be accurately represented in technical drawings and engineering designs. Without a consistent and accurate representation of depth, it can be difficult to create a functional and effective product. The other two terms, normal and inclined, refer to the angle or orientation of an object in relation to a reference plane, and are not necessarily related to the shared dimension between the top view and left side view.

The dimension shared between the top view and the left side view in a technical drawing or orthographic projection is the depth. In a three-view drawing, the top view shows the width and depth, while the left side view shows the height and depth. The depth, therefore, is the common dimension that helps to understand the object's 3D structure more effectively. The terms "normal" and "inclined" refer to different types of lines or surfaces but do not describe the shared dimension between these two views.

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Answer:

x = -7

Step-by-step explanation:

First, we simplify:

-3x = 21

Then, we divide -3 on both sides:

x = -7

Hope this helps ^^

Answer:

B IS THE ANSWER

Step-by-step explanation:

Answer:- D

- Supplementary

- BC

- Addition

Step-by-step explanation:

To solve the differential equations provided, we will use the method of undetermined coefficients.

For the equation (2x + 1)(x + 1)y" + 2xy' - 2y = (2x + 1)², we can first divide through by (2x + 1)(x + 1) to simplify the equation:

y" + [(2x + 1)/(x + 1)]y' - (2y/(x + 1)) = 1

The homogeneous equation associated with this differential equation is:

y"h + [(2x + 1)/(x + 1)]y' - (2y/(x + 1)) = 0

We can assume a particular solution of the form y_p = A(x + 1)², where A is a constant to be determined.

Taking the derivatives and substituting into the original equation, we get:

y_p" + [(2x + 1)/(x + 1)]y_p' - (2y_p/(x + 1)) = 2A - 2A = 0

Therefore, A cancels out and we have a valid particular solution.

The general solution to the homogeneous equation is given by:

y_h = c₁y₁ + c₂y₂

where y₁ and y₂ are linearly independent solutions. Since the equation is of Euler-Cauchy type, we can assume a solution of the form y = x^r.

Substituting into the homogeneous equation, we get:

r(r - 1)x^(r - 2) + [(2x + 1)/(x + 1)]rx^(r - 1) - (2/x + 1) x^r = 0

Expanding and rearranging terms, we obtain:

r(r - 1)x^(r - 2) + 2rx^(r - 1) + rx^(r - 1) - 2x^r = 0

Simplifying, we have:

r(r - 1) + 3r - 2 = 0

r² + 2r - 2 = 0

Solving this quadratic equation, we find two distinct roots:

r₁ = -1 + sqrt(3)

r₂ = -1 - sqrt(3)

Therefore, the general solution to the homogeneous equation is:

y_h = c₁x^(-1 + sqrt(3)) + c₂x^(-1 - sqrt(3))

Combining the particular solution and the homogeneous solutions, the general solution to the original equation is:

y = y_p + y_h = A(x + 1)² + c₁x^(-1 + sqrt(3)) + c₂x^(-1 - sqrt(3))

where A, c₁, and c₂ are constants.

9. For the equation x²y" - 3xy' + 4y = 0, we can rewrite it as:

y" - (3/x)y' + (4/x²)y = 0

The homogeneous equation associated with this differential equation is:

y"h - (3/x)y' + (4/x²)y = 0

Assuming a particular solution of the form y_p = Ax², where A is a constant to be determined.

Taking the derivatives and substituting into the original equation, we get:

2A - (6/x)Ax + (4/x²)Ax² = 0

Simplifying, we have:

2A - 6Ax + 4Ax = 0

2A - 2Ax = 0

Solving for A, we find A = 0

Therefore, the assumed particular solution y_p = Ax² = 0 is not valid.

We need to assume a new particular solution of the form y_p = Ax³, where A is a constant to be determined.

Taking the derivatives and substituting into the original equation, we get:

6A - (9/x)Ax² + (4/x²)Ax³ = 0

Simplifying, we have:

6A - 9Ax + 4Ax = 0

6A - 5Ax = 0

Solving for A, we find A = 0.

Again, the assumed particular solution y_p = Ax³ = 0 is not valid.

Since the homogeneous equation is of Euler-Cauchy type, we can assume a solution of the form y = x^r.

Substituting into the homogeneous equation, we get:

r(r - 1)x^(r - 2) - (3/x)rx^(r - 1) + (4/x²)x^r = 0

Expanding and rearranging terms, we obtain:

r(r - 1)x^(r - 2) - 3rx^(r - 1) + 4x^r = 0

Simplifying, we have:

r(r - 1) - 3r + 4 = 0

r² - 4r + 4 = 0

(r - 2)² = 0

Solving this quadratic equation, we find a repeated root:

r = 2

Therefore, the general solution to the homogeneous equation is:

y_h = c₁x²ln(x) + c₂x²

Combining the particular solution and the homogeneous solution, the general solution to the original equation is:

y = y_p + y_h = c₁x²ln(x) + c₂x²

where c₁ and c₂ are constants.

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Answer:

x ≈ .1138985869

Step-by-step explanation:

\(tangent = \frac{opposite}{adjacent}\)

\(tan(\frac{10}{x} ) = 26\)

\(tan^{-1}[ tan(\frac{10}{x} )] = tan^{-1}(26)\)

\(\frac{10}{x} = tan^{-1}(26)\)

\(10 =x[ tan^{-1}(26)]\)

\(\frac{10}{tan^{-1}(26)} =x\)

x ≈ .1138985869

The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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1: 2.62 2.4 0.268 2.26 2.71 (not answer)

for number 1 (greatest to least)

271% then 2.62 then 2 2/5 then 2.26 then 26.8%

2: least to greatest

.86 .91 .875 .84

84% then 43/50 then 7/8 then 0.91

The coordinates of endpoint B(x, y) on segment AB are ( 3, 12 ).

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point A(-5, -8)

Point B( x,y )

Midpoint( -1, 2 )

Plug the given coordinates into the equation above.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

(-1,2) = ( ( -5 + x )/2, ( -8 + y )/2 )

First, we find the x-coordinate

-1 = ( -5 + x )/2

-2 = -5 + x

x = -2 + 5

x = 3

Next, we find the y-coordinate

2 = ( -8 + y )/2

4 = -8 + y

y = 4 + 8

y = 12

Therefore, the coordinates of endpoint B are ( 3, 12 ).

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Answer:

EFBGCADHI

That one is confusing, I'm not really sure.

Answer:

x = 9

Step-by-step explanation:

square each side first to get:

8x - 8 = 64

8x = 72

x = 9

Answer: x

=

5

±

i

√

23

6

Explanation:

y

=

3

x

2

−

5

x

+

4

=

0

Use the improved quadratic formula.

D

=

d

2

=

b

2

−

4

a

c

=

25

−

48

=

−

23

=

23

i

2

-->

d

=

±

i

√

23

There are no real roots. There are 2 complex roots:

x

=

−

b

2

a

±

d

2

a

=

5

6

±

i

√

23

6

=

5

±

i

√

23

6

Step-by-step explanation:

Answer:

X= (5 ± i√23)/6

Answer:

\(\frac{5}{9}\)

Step-by-step explanation:

\(\mathrm{Given,}\\\mathrm{(x_1,y_1)=(7,8)}\\\mathrm{(x_2,y_2)=(-2,3)}\\\mathrm{Now,}\\\mathrm{Slope = \frac{y_2-y_1}{x_2-x_1}=\frac{3-8}{-2-7}=\frac{-5}{-9}=\frac{5}{9}}\)