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12 + 3 = 15  (0,15)

12 - 3 = 9     (0,9)

What is the equation of the midline for the function f(x) ?

f(x) = 3 cos (x) −2.5

A total of 180 men women and children participated in a fun friend there were three times as many female runners than male runners and five more children than men find the number of the participants in each of the three categories?

How long are the three parts?

How many cats were at the shelter on Tuesday​?

I have a bag with 5 pennies and 6 nickels. I draw coins out one at a time at random. What is the probability that after 4 draws I have removed no more than 2 pennies from the bag?

So not 3 and not 4 pennies

P(pppn) = 5/11 * 4/10 *  3/9 * 6/8 = \(\frac{5*4*3*6}{11*10*9*8}=\frac{1*1*1*1}{11*2*1}=\frac{1}{22}\)

But the n can be in any of 4 places  so that is   4/22

P(pppp)= \(\frac{5*4*3*2}{11*10*9*8}=\frac{120}{7920}=\frac{1}{66}\)

P(all pennies or 3 pennies) = \(\frac{4}{22}+\frac{1}{66}=\frac{13}{66}\)

P(2 or less pennies) = \(1-\frac{13}{66}=\frac{53}{66}\)

Needs to be checked I could have made a careless mistake.

I think these are meant to be mixed fractions and not multiplication.

\(3\frac{4}{6}+4\frac{5}{6}\)

Let's convert to fractions 

3*6+4/6

4*6+5/6

Thus we have:

\(\frac{22}{6}+\frac{29}{6}\) The same denominator we add the numerator 

\(\frac{22+29}{6}=\frac{51}{6}\) Now the asker may want it presented as a mixed number

We know that 6 can go 

6*8=48 which is closest to 51 

so 

\(8\frac{3}{6}\)

Further, simplify

\(8\frac{1}{2}\)  (This is equal to 17/2 , which is a simplified fraction of 51/6 if you are wondering) 

Four houses in a row are each to be painted with one of the colors red, blue, green, and yellow.

In how many different ways can the houses be painted so that no two adjacent houses are of the same color?

\(\begin{array}{|c|c|c|} \hline \text{House} & \text{selectable colors}& \text{number of selectable colors} \\ \hline A & red,~ blue,~ green,~ yellow & 4 \\ \hline B & not~A & 3 \\ \hline C & not~B & 3 \\ \hline D & not~C & 3 \\ \hline && \text{product}~ 4\times 3 \times 3 \times 3 = 108 \\ \hline \end{array} \)

The houses can be painted in 108 different ways.

The probability is 14/47. 

At an all-you-can-eat barbequefundraiser that you are sponsoring adults pay $6 for a dinner and children pay $4 for a dinner.
212 people attend and you raise $1128.
What is the total number of adults and the total number of children attending?

\(\text{Let number of adults $=a$} \\ \text{Let number of children $=c$}\)

\(\begin{array}{|rcll|} \hline a+c &=& 212 \\ \mathbf{c} &=& \mathbf{212-a} \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline 6a+4c &=& 1128 \\ 6a +4(212-a) &=& 1128 \\ 6a + 4*212-4a &=& 1128 \\ 6a + 848-4a &=& 1128 \\ 2a &=& 1128-848 \\ 2a &=& 280 \quad | \quad : 2 \\ \mathbf{a} &=& \mathbf{140} \\\\ \mathbf{c} &=& \mathbf{212-a} \\ c &=& 212-140 \\ \mathbf{c} &=& \mathbf{72} \\ \hline \end{array}\)

The total number of adults is 140
The total number of children is 72

The common ratio for this series is -2/3     --->     r  =  -2/3

The first term is 120                                   --->     a  =  120

There are 8 terms                                      --->     n  =  8

The formula is                                            --->    Sum  =  a · [ (1 - rⁿ) / (1 - r) ]

Sum  =  120 · [ ( 1 - (-2/3)⁸ ) / ( 1 - (-2/3) ) ]

Now, it's calculator time!

($1 000)¹  =  $1 000

($1 000)²  =  $1 000 000

($1 000)³  =  $1 000 000 000

So, ($1 000)⁵²  will equal the number formed by a '1' and followed by 52 sets of 3 zeros each. 

Let me show you how to do the first one; maybe you can follow the procedure to do the second one.

Problem:             a⁴ + 4

Step 1 - complete the square; add and subtract that value:  (a⁴ + 4a² + 4) - 4a²

Step 2 - write as the difference of two squares:                        (a² + 2)² - (2a)²

Step 3 - factor:                                                               [ (a² + 2) - (2a) ] [  (a² + 2) + (2a) ]

Step 4 - remove the extra parentheses:                               (a² + 2 - 2a) (a² + 2 + 2a)

Step 5 - rewrite the terms (if you wish):                                (a² - 2a + 2) (a² + 2a + 2)  

Can you do the second problem?

A sector of a circle has a central angle of 100 degrees. If the area of the sector is 250pi, what is the radius of the circle?

Sector area:      A = 250pi                  100° : 250pi = 360° : X         X = 900pi

Sector angle:    q = 100°

Circle radius:     r = ?                            r = sqrt (900)       r = 30  

                                                            ( A = r²pi        A = 30²pi = 900pi )  

In order to find the original amount of water, we divide the amount given by its corresponding percentage, in this case 15% (because if 85% of water is gone then 15% remains).

If x represents the original amount of water, then:

120 = (0.15)x

x = 800

There was originally 800 liters of water

Can you see that the y value is always 3 so the answer is y=3  

--------------------

How about this one ...   what is the equation?

Lets go further back.

My questions may seem off topic to you but they are not. 

Most likely you will understand easily if you get some basics first.

What is the equation of this line.

The formula for the volume of a cone is   (1/3) • pi • (radius of base)² • height  =  V            

Substitute the numbers you have             (1/3) • 3.14 • (1.5)² • h  = 12      

Do the preliminary arithmetic                    (1/3) • 3.14 • 2.25 • h  =  12              

                                                                                      2.36 • h  =  12               

Divide both sides by 2.36                                                         h  =  5.09              

Round to nearest whole inch                                           height  =  5 inches             

_.

ok thanks for answering.

y=cos x

The midline is the x axis.  Can you see that .. it is the middle of the graph?

The x axis is a line and it has an equation.

Can you see that  (0,0),   (pi,0),   (7pi/4, 0)   etc are all on this x axis?  What do all these points have in common?

Hint: What is the y value?

I apologize, I struggle with even the very basics of what some of these questions ask.

I'm not very confident in mathematics, which I doubt helps my struggles. 

I assume the midline is (0, 1), and I assume the amplitude is (pi, -1).

I'm not really sure how to to determine frequency? Is it (2pi, 1)?

I can try and help you but you will have to cooperate.

First you must know that 360 degrees is the same as   2pi  radians.

This type of trig is nearly always done in radians.

Ok here is the 'parent' function.

y= cos x

For this parent funtion please tell me what tthese are

a) The midline

b) the frequency (how far does it go before the patern repeats)

c) The amplitde  (How far above the middle is the top)

To be entirely honest, I'm not sure how these concepts work. The material my teacher gives me seems to go straight over my head, and with a general lack of enthusiasm for mathematics, I struggle to make sense of how it works on my own.

f(x) = 1/4 cos (2x) + 5

Only one of these numbers will affect frequency.  Which one is it?

Answer this question and then I, or someone else will continue

This is a teaching answer, please no one else answer over me.

Hint, here is the graph.

The answer is C(10,2)^2 = 2025.  

The probability of pulling one of the dice at random = 1 / 3

If its the 6-sided die, then the probability of of rolling a 4 = 1/6

Therefore, the probability that rolling a 4  comes from a 6-sided die = 1 / 3  x  1 / 6 = 1 / 18 =~5.55 %