Kurt organized a bike race that was 84 miles long. All 469 riders completed the race. How many miles were biked in all?

The probability that:

Probability refers to the possibility of the occurrence of an event.

P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]

Now,

(a) Total number of books = 5 + 3 + 1 = 9

Probability of getting a dictionary = [tex]\frac{1}{9}[/tex]

(b) Number of ways to select 3 books out of 9 books = [tex]\binom{9}{3}[/tex] =  [tex]\frac{9!}{3!(6!)} = \frac{9\times\ 8 \times 7}{6}[/tex] = 84

Number of ways to select 1 out of 3 books of poems = [tex]\binom{3}{1} = \frac{3!}{2!}[/tex] = 3

Number of ways to select 2 out of 5 novels = [tex]\binom{5}{2} = \frac{5!}{2! 3!} = \frac{5\times 4}{2} = 10[/tex]

Thus, the probability of getting 2 novels and 1 book of poem = [tex]\frac{3\times10}{84} = \frac{10}{28} = \frac{5}{14}[/tex]

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(COMPLETE QUESTION:

If three books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that (a) a dictionary is selected? (b) 2 novels and 1 book of poems are selected?)

Usando la propiedad exponencial, hay que el resultado es: 125/64.

Con el expoente negativo, hay que:

[tex]\left(\frac{a}{b}\right)^{-x} = \left(\frac{b}{a}\right)^{x}[/tex]

Así, la expresion equivalente es dada por:

[tex]\left(\frac{16}{25}\right)^{-\frac{3}{2}} = \left(\frac{25}{16}\right)^{\frac{3}{2}}[/tex]

Hay que 25 = 5² y 16 = 4², así:

[tex]\left(\frac{25}{16}\right)^{\frac{3}{2}} = \left(\frac{5^2}{4^2}\right)^{\frac{3}{2}} = \left(\frac{5}{4}\right)^3 = \frac{125}{64}[/tex]

Así, hay que el resultado es: 125/64.

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First of all, every number in each row is odd, so we can eliminate 392 and 394.

The number of elements in each row forms an arithmetic sequence:

• 1st row : 1 element

• 2nd row : 3 elements - and 3 - 1 = 2

• 3rd row : 5 elements - and 5 - 3 = 2

• 4th row : 7 elements - and 7 - 5 = 2

and so on, so that the [tex]n[/tex]-th row has [tex]1 + 2(n-1) = 2n - 1[/tex] elements.

This means that in [tex]n-1[/tex] complete rows, there is a total of

[tex]\displaystyle \sum_{i=1}^{n-1} (2i-1) = n^2 - 2n + 1[/tex]

elements, so that the first element in the subsequent [tex]n[/tex]-th row is the [tex](n^2-2n+2)[/tex]-th number in the sequence {1, 3, 5, 7, …}, i.e the [tex](n^2-2n+2)[/tex]-th odd positive integer. To compute the sum, I use the following well-known formulas.

[tex]\displaystyle \sum_{i=1}^n 1 = n[/tex]

[tex]\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}2[/tex]

Now, the [tex]n[/tex]-th term of the sequence {1, 3, 5, 7, …} is simply [tex]2n-1[/tex], the [tex]n[/tex]-th odd positive integer. So the first element in the [tex]n[/tex]-th row is

[tex]2(n^2-2n+2) - 1 = 2n^2 - 4n + 3[/tex]

and hence the 1st element of the 15th row is

[tex]2\cdot15^2 - 4\cdot15 + 3 = \boxed{393}[/tex]

The value of the constant of variation is 130

Constant of variation can be defined as the ratio between two variables in  an inverse variation on a direct variation.

From the information given, we have that;

The number of hours is x

The temperature is y

x α 1/ y

x = k/y

k = xy

Substitute the values

k = 2 × 65

k= 130

Thus, the value of the constant of variation is 130

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The complete question:

the number of hours it takes for a block of ice to melt varies inversely as the temperature. If it takes 2 hours for a square inch of ice to melt at 65 degrees find the constant of variation

The data measured on ordinal scale exhibits all the properties of data measured on nominal scale.

A nominal scale  can be described as the scale of measurement  which is been assign events or objects with respect to a discrete categories.

However in relation with nominal scale, Ordinal scale  serves as the  2nd level of measurement  which help to give the reports of  ranking as well as  ordering of the data  however the  degree of variation  is not usually considered, hence data measured on ordinal scale exhibits all the properties of data measured on nominal scale.

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The dimensions of the playing field the width is 54 yards and the length is 210 yards.

Given that the perimeter of the rectangular playing field is 528 yards and the length of the field is 6 yards less than quadruple the width.

Let the width of the rectangular playing field is x yards and it is given that the length of the field is 6 yards less than quadruple the width means the length is 4x-6.

As we know that the perimeter of the rectangle is two times the sum of length and breadth so.

P=2(l+w)

As it is given that the perimeter is 528 yards.

So, we will substitute all the values in the formula, we get

528=2(4x-6+x)

528=2(5x-6)

528=10x-12

528+12=10x-12+12

540=10x

540/10=10x/10

54=x

Now, substitute this values in l=4x-6 to find the length, we get

l=4(54)-6

l=216-6

l=210

Hence, the dimension of the playing field when the perimeter of the rectangular playing field is 528 yards is width is 54 yards and length is 210 yards.

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The value of the numbers given will be:

1. 108

2. 1618

1. The expression given will be calculated as:

= 97.83 - 4.378 + 5.92

= 98 + 4 + 6

= 108

2. 1,342.8+ 85.32 + 173.54 + 16

= 1343 + 85 + 174 + 16

= 1618

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Answer:

-1 yard per play

play 6 - play 3=0

play 2 - play 4=0

play 1 - play 5 = -6

hope it helped

Answer:

B. 6x²-7x-20

Step-by-step explanation:

(2x-5)(3x+4)

2x(3x+4)-5(3x+4)

Use distributive property.

6x²+8x-15x-20

Combine like terms.

6x²-7x-20

Hope this helps!

Please mark as brainliest if correct!

Answer:

AP = 29,37,45,...

d= t2-t1

=37-29

=8

n=59

t59=?

tn=a+(n-1)d

t59=29+(59-1)8

t59=28+58×8

t59=28 + 464

t59=492

Step-by-step explanation:

please mark it brainliest and thank it please  

Step-by-step explanation:

it all starts with having a good definition for a

a = 3x + 6

for the definition of b we need to transform the second equation

x = 1/3 b - 2 = b/3 - 2

3x = b - 6

3x + 6 = b

remember, if a = c and b = c, then it must be a = b.

that is the whole principle here. the symmetric property.

I am not sure what you must do here. so you select on the left the number of the step in the proof ?

if so, then

statement reason : number 1

a = 3x + 6 and 3x = b - 6 division : number 2

a = 3x + 6 and -b = -3x - 6 subtraction : number 3

a = 3x + 6 and b = 3x + 6 division : number 4

a = b = 3x + 6 symmetric : number 5

always remember, every change needed on one side of an equation we need to do on both sides, otherwise the equation is destroyed.

number 2 is "division" as division is a form of multiplication (and multiplication a form of division). we are multiplying by 3.

number 3 subtracts b and also 3x.

number 4 divides by -1.

and number 5 is the fished proof as mentioned above.

The ratio of all flowers in the vase to roses is 9:16. The ratio of all flowers in the vase to daisies is 16:7.

An expression known as a ratio in mathematics shows how many times one number is contained in another. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the proportion of oranges to the overall amount of fruit is 8:14, and that of lemons to oranges is 6:8 (or 3:4). (or 4:7).

A ratio can have any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values. Both numbers are usually limited to positive values in settings.

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Statistics expert daniel yankelovich believes that middle-class values give Americans a certain amount of self-esteem and a fairly clear idea of who they are.

This is the title that is used to refer to the people that have being trained in such a way that they are able  to apply statistical approaches and methods to the real life problems that exists in the environment.

They are known to be able to get the solutions to problems by the use of models of statistics and analyzing them as well.

Hence we can say that Statistics expert daniel yankelovich believes that middle-class values give Americans a certain amount of self-esteem and a fairly clear idea of who they are

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Step-by-step explanation:

⎡02413524−6⎦⎥⎥⎤ and B=⎣⎢⎢⎡−10021030−1⎦⎥⎥⎤

∴4A=⎣⎢⎢⎡081641220816−24⎦⎥⎥⎤ and 6B=⎣⎢⎢⎡−600126080−6⎦⎥⎥⎤ 

⇒4A−6B=⎣⎢⎢⎡0−(−6)8−016−04

Answer:

120

Step-by-step explanation:

I don't think you can solve this, considering the given expression is false. However consult a tutor perhaps and see if they can help you further.

Answer:

8 hours

Step-by-step explanation:

69 = 7t -8

61 = 7t

t = 8.71428571

Answer:

So if you roll the die ten times, that means every time you roll it, it is 10%, with that knowledge, if you rolled 6, four times, that means the experimental probability is 40% to get 6.

Answer: BABABAB

Step-by-step explanation:

BHBAHBABAHBABHABHBAHBABHABHBAbhaBHBA

Answer:

(2/x²y³)    

Step-by-step explanation:

(2(x^-2)y)/(y^4)

x^-2 can also be written as (1/x²)

(2(1/x²)y)/(y^4)

(2/x²)(y)/(y^4)

(2y/x²)/(y^4)

this can also be written as (2y/x²) × (1/y^4)

= 2y/(x² × y^4)

WHEN THE SAME VARIABLE IS DIVIDED THEIR POWERS ARE SUBTRACTED

= (2/x²y³)       (we got y³ by y^1 /y^4  The powers got subtracted)

The triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.

So,

In triangle ABC, ∠A = 120°.

As a result, DE is the exterior angle bisector of ABCD.

Similarly, for the ABC, F is ex-center because AB is the exterior angle bisector and CF is the interior angle bisector.

As a result, DF is the exterior angle bisector.

BC is a straight line.

So, DEF is the right triangle.

As a result, the triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.

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The correct form of the question is given below:
Prove in any ΔABC, if one angle is 120°, the Δ formed by the feet of the angle bisectors is right-angled.

The value of x is -(11/7).

This problem is related to solving an algebraic equation.

In algebra there are many types of equations such as linear equation in one variable and two variable.

Here we have been given two variables and two equations which means we can solve the equation. To solve an equation in algebra it is important that the number of unknowns is equal to the number of equations given.

Given, m/1=2x+3 i.e., m=2x+3

also m/2=3x+7 i.e., m=6x+14

Now equating both the values of m;

  2x+3=6x+14

⇒6x-2x=3-14

⇒4x=-11

∴ x= -(11/4)

Hence, the value of x is -11/4.

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The probability that at least one of them is a boy is 0.9947

The probability = (1 - P) none of these 7 is a boy

= 1 - P (all girls)

1 - 0.473^7

1 - 0.00529697

= 0.9947

Hence in a certain​ country, the true probability of a baby being a girl is 0.473 . among the next seven randomly selected births in the​ country, the probability that at least one of them is a boy is 0.9947

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The probability of getting February, then a number less than 5 is:

P = 1/18

First, we need to find the two individual probabilities:

We have a total of 12 months, and we assume that the probability for each of these is the same one, then the probability of getting February will be:

p = 1/12.

Now, the standard die has 6 sides, the numbers that are less than 5 are:

{1, 2, 3, 4}

So 4 out of the 6 outcomes are less than 5, then the probability here is:

q = 4/6 = 2/3.

Then the joint probability is:

P = p*q = (1/12)*(2/3) = 2/36 = 1/18

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The first-order differential equation is non-separable and non-linear.

[tex]\frac{dx}{dy} +e^{x} y=x^{2} y^{2}[/tex]

[tex]\frac{1}{y^{2} } \frac{dx}{dy} +e^{x} \frac{1}{y} =x^{2}[/tex]

[tex]\frac{dt}{dx} -e^{x} t = -x^{2}[/tex]

Since, x and y terms separated also linear equation

linear and separable both

[tex]\frac{dy}{dx} = cos y = tan x[/tex]

non-linear and non-separable

What distinguishes a linear equation from a non-linear equation?

Something that is linear is related to a line. A line is built using all of the linear equations. A non-linear equation is one that cannot be represented by a straight line.  It has a changeable slope value and resembles a graphed curve.

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Answer: 3 gallons of gas left

Step-by-step explanation: since the car started out with 15 1/5 and then fills up 5 3/5 now there is 20 4/5 in the car then since the car consumed 17 4/5 just subtract the 17 4/5 from 20 4/5 and then you get 3 gallons left since 17 - 20 = 3 and 4/5 - 4/5 = 0/0 or 0 the answer is just 3 gallons left

Answer: it is 3 gallons

Step-by-step explanation:

Answer:

137 ≤ 15x +

Step-by-step explanation:

Answer:

looking at the screenshot! it can be a or b

Step-by-step explanation:

There are 256 different pizzas can you make with anywhere from 0 to 4 toppings.

Combinations:

Combinations defines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given,

Pizza pies with a choice of any of 4 toppings: pepperoni, mushrooms, green peppers, or sausage.

Here we need to find how many different pizzas can you make with anywhere from 0 to 4 toppings.

Here we need to assume that each pizza can have at most 1 serving of each topping.

Here we have four level of toppings like no serving, single serving, double serving and triple serving.

Suppose you had one topping, let's say mushrooms.  How many different possible pizzas would there be?

If you understand the setup right, there would be 4: no topping, single mushrooms, double mushrooms, or triple mushrooms.

Similarly, imagine that there are two toppings, mushrooms and sausage.

Then, there are 4 x 4 = 16 different combinations with two items.

We could continue this for a long time.  

If you have only sausage, mushroom, pepperoni and onion, then for a total of

=> 4 x 4 x 4 x 4 = 256 combinations.

Therefore, there are 256 different pizzas can you make with anywhere from 0 to 4 toppings.

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The angles of the given triangle are 136°,24°, and 20°.

Given that a triangle has angles as  4y°,(y-10)°, and 20° and asked to find out the angles of the given triangle

The sum of the angles of the triangle =180°

⇒4y°+(y-10)° + 20°=180° { adding the given angles and equating it to 180° as the sum of the angles in the triangle is 180°}

⇒5y+10=180°.{added all the given angles and equated it to 180°}

⇒5y=170°

⇒y=34°

⇒4y=136°, (y-10)°=24° and 20°

Therefore the angles of the given triangle are  136°,24°, and 20°.

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