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3 years ago

The proportionality constant (y to x) is

Mathematics

2 answers:

Dvinal [7]3 years ago

6 0

Answer:

Step-by-step explanation:

NeTakaya3 years ago

5 0

Answer:

the constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

Step-by-step explanation:

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What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p? C

charle [14.2K]

Answer:

$(D)E[ X ] =np.$

Step-by-step explanation:

Given a binomial experiment with n trials and probability of success p,

$f(x)=\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}, 0\leq x\leq n$

$E(X)=\sum_{x=0}^{n}xf(x)= \sum_{x=0}^{n}x\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}$

Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:

$E(X)=\sum_{x=1}^{n}x\left(\begin{array}{c}n\\x\end{array}\right)p^x(1-p)^{n-x}$

Now,

$x\left(\begin{array}{c}n\\x\end{array}\right)= \frac{xn!}{x!(n-x)!}=\frac{n!}{(x-)!(n-x)!}=\frac{n(n-1)!}{(x-1)!((n-1)-(x-1))!}=n\left(\begin{array}{c}n-1\\x-1\end{array}\right)$

Substituting,

$E(X)=\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^x(1-p)^{n-x}$

Factoring out the n and one p from the above expression:

$E(X)=np\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^{x-1}(1-p)^{(n-1)-(x-1)}$

Representing k=x-1 in the above gives us:

$E(X)=np\sum_{k=0}^{n}n\left(\begin{array}{c}n-1\\k\end{array}\right)p^{k}(1-p)^{(n-1)-k}$

This can then be written by the Binomial Formula as:

$E[ X ] = (np) (p +(1 - p))^{n -1 }= np.$

5 0

3 years ago

For working 13 hours you earn $58.50 and $121.50 for 27 hours. What is your rate of pay in dollars per hour?

Contact [7]

Y2-y1/x2-x1
121.5-58.5/27-13
63/14
$4.5 an hour.

8 0

3 years ago

Read 2 more answers

Which one of the following functions is an exponential decay function?

stepan [7]

Answer:

Step-by-step explanation:

Its decaying since its being multiplied by by a number less than 1

6 0

2 years ago

Read 2 more answers

3.2 cm on the map correspond to 4 km in the actual distance?

geniusboy [140]

Answer:

Step-by-step explanation:

Here, 3.2 centimeters on the map is equivalent to 4 kilometers. We can use unitary method to find, how many kilometer/kilometers each centimeter corresponds to. Using the unitary method: Therefore, the scale of map represents 1.25 kilometers for each centimeter.

6 0

3 years ago

A company is selling toothpicks. It costs $0.01 to produce each toothpick and a fixed cost of $60 a month for the company. If th

Lapatulllka [165]

Answer:

6,000 toothpicks

Step-by-step explanation:

In this question, we are trying to evaluate the number of toothpicks a company must sell to ensure that the money spent on production is exactly equal to revenue from sales.

What we do is this!

Let’s assign a variable to represent the number of tooth picks sold and produced by the company. Let us call this number x.

First, we evaluate the total amount spent on production of x toothpicks. From the question, we can see that the cost of producing a single toothpick is $0.01, hence, to produce x toothpicks, amount spent asides the fixed cost is $0.01 * x = $0.01x

Now, the total cost on production which includes the fixed cost of the company would be $(0.01x + 60). This is the total amount spent to produce the goods.

Now revenue from sales for x toothpicks at $0.02 each is $0.02x

Since we are looking to Breakeven, we equate the costs to the revenue.

0.01x + 60 = 0.02x

0.02x-0.01x = 60

0.01x = 60

x = 60/0.01 = 6,000 toothpicks

6 0

3 years ago