There are 125 people and three door prizes. How many ways can three door prizes of $50 each be distributed? How many ways can door prizes of $5,000, $500 and $50 be distributed?

Answers

Answer 1

Answer:

We have been given that there are 125 people and three door prizes.

In the first part we need to figure out how many ways can three door prizes of $50 each be distributed?

Since there are total 125 people and there are three identical door prices, therefore, we need to use combinations for this part.

Hence, the required number of ways are:

$_(3)^(125)\textrm{C}=(125!)/(122!3!)=(125*124*123)/(1*2*3)=317750$

In the next part, we need to figure out how many ways can door prizes of $5,000, $500 and $50 be distributed?

Since we have total 125 people and there are three prices of different values, therefore, the required number of ways can be figured out by using permutations.

$_(3)^(125)\textrm{P}=(125!)/(122!)=125*124*123=1906500$

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Select the two binomials that are factors of this trinomial x2+10x+16

Answers

So for this trinomial, I will be factoring by grouping. Firstly, what two terms have a product of 16x^2 and a sum of 10x? That would be 8x and 2x. Replace 10x with 2x + 8x:

$x^2+2x+8x+16$

Next, factor x^2 + 2x and 8x + 16 separately. Make sure that they have the same quantity inside the parentheses: $x(x+2)+8(x+2)$

Now you can rewrite this as $(x+8)(x+2)$ , which is your final answer.

Answer: (x+8) and (x+2)

Step-by-step explanation:

Solve the system x+y=54
x-5y=0
A. (-45, -9)
B.(45, 9)
C. (9, 45)
D. (45, 9)

Answers

$\displaystyle \n \begin{cases} x+y = 54 \n x-5y = 0~~~~~| \cdot (-1) \end{cases} \n \n \n \begin{cases} x+y = 54 \n -x+5y = 0 \end{cases} \n \texttt{-------------- gather equations} \n .~~/~~~~~6y = 54 \n \n y = (54)/(6) = \boxed{9} \n \n x = 54 - y = 54 - 9 = \boxed{45} \n \n \texttt{Problem solution: } \boxed{x = 45 ~~ and ~~ y = 9 }$

Two large numbers of the Fibonacci sequence are f50=12,586,269,025 and f51=20,365,011,074. What is the approximate value of the quotient f51/f50

Answers

jsut divide them
12,586,269,025 and 20,365,011,074
f51/f50=20,365,011,074/12,586,269,025= 0.6183398874989

Lucas paid for a pair of shoes with a $50 bill after the clerk added 9% tax to the purchase Lucas received $17.3 in change what was the price of the shoes not including the tax

Answers

answer:

$29.75

If Lukas paid for the shoes with $50, and got $17.30 back, the total price of the shoes with the tax was $32.70. Because we are trying to find the price of the shoes without the 9% tax, we calculate what 91% of 32.70 is, which is $29.757

Alli <3

Can't figure this one out super confused please help!

Answers

i think the answer is C.

You test 8 automobiles of the same make and model and find their mileage ratings to be 27, 27, 28, 29, 32, 33, 34, and 1,000,000 mpg, arranged in order from smallest to largest. If you use inferential statistics (and reject the outlier) to predict what mileage consumers can expect when they buy this type of car, what value would you predict?

Answers

Answer:

it 30 mpg

Step-by-step explanation:

The statement " y varies directly as x ," means that when x increases,y increases by the same factor. In other words, y and x always have the same ratio:

= k

where k is the constant of variation.
We can also express the relationship between x and y as:

y = kx

where k is the constant of variation.

Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x , and y = 6 when x = 2 , the constant of variation is k = = 3 . Thus, the equation describing this direct variation is y = 3x .

Example 1: If y varies directly as x , and x = 12 when y = 9 , what is the equation that describes this direct variation?

k = =
y = x

Example 2: If y varies directly as x , and the constant of variation is k = , what is y when x = 9 ?

y = x = (9) = 15

As previously stated, k is constant for every point; i.e., the ratio between the y -coordinate of a point and the x -coordinate of a point is constant. Thus, given any two points (x 1, y 1) and (x 2, y 2) that satisfy the equation, = k and = k . Consequently, = for any two points that satisfy the equation.

Example 3: If y varies directly as x , and y = 15 when x = 10 , then what is y when x = 6 ?

=
=
6() = y
y = 9

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