What is the result of adding these two equations?<br> - 50 - 9y = 3<br> 5x

Passes through (1,12) and has a vertex (10,-4)

agasfer [191]

Answer: 16/81 (x-10)^2 -4

Step-by-step explanation:

To write a vertex equation with just a point and the vertex, you have to figure out the variables.

In vertex form, the equation is y = a (x-h)^2 + k

Your y is 12, x = 1, h = 10, and k = -4

Plug everything into equation

12 = a (1 - 10)^2 -4

12 = a (-9)^2 - 4

12 = 81a - 4

16 = 81a

16/81 = a

Now you know what the 'a' value is.

If you graph 16/81 (x-10)^2 -4 , you will get a point at (1,12) and a vertex of (10,-4)!

I hope this helps!

3 0

3 years ago

A construction company is considering submitting bids for contracts of three different projects. The company estimates that it h

julsineya [31]

Answer:

a. $P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

b. $E(x) = 0.3$

c. $S(x)=0.5196$

d. $E=5,000$

Step-by-step explanation:

The probability that the company won x bids follows a binomial distribution because we have n identical and independent experiments with a probability p of success and (1-p) of fail.

So, the PMF of X is equal to:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

Where p is 0.1 and it is the chance of winning. Additionally, n is 3 and it is the number of bids. So the PMF of X is:

$P(x)=\frac{3!}{x!(3-x)!}*0.1^{x}*(1-0.1)^{n-x}\\$

For binomial distribution:

$E(x)=np\\S(x)=\sqrt{np(1-p)}$

Therefore, the company can expect to win 0.3 bids and it is calculated as:

$E(x) = np = 3*0.1 = 0.3$

Additionally, the standard deviation of the number of bids won is:

$S(x)=\sqrt{np(1-p)}=\sqrt{3(0.1)(1-0.1)}=0.5196$

Finally, the probability to won 1, 2 or 3 bids is equal to:

$P(1)=\frac{3!}{1!(3-1)!}*0.1^{1}*(1-0.1)^{3-1}=0.243\\P(2)=\frac{3!}{2!(3-2)!}*0.1^{2}*(1-0.1)^{3-2}=0.027\\P(3)=\frac{3!}{3!(3-3)!}*0.1^{3}*(1-0.1)^{3-3}=0.001$

So, the expected profit for the company is equal to:

$E=-10,000+50,000(0.243)+100,000(0.027)+150,000(0.001)\\E=5,000$

Because there is a probability of 0.243 to win one bid and it will produce 50,000 of income, there is a probability of 0.027 to win 2 bids and it will produce 100,000 of income and there is a probability of 0.001 to win 3 bids and it will produce 150,000 of income.

5 0

3 years ago

1/8 + 1/4 ?? Why do I need 20 characters to summit this

abruzzese [7]

Answer:

0.375

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Points X and Z are on a number line, and point Y partitions

abruzzese [7]