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Thank you so much CPhill!!!! I really appreciate it! 

4. Height of 10th grade boys is normally distributed with a mean of 66.9 in. and a standard deviation
of 2.5 in.
The area greater than the z-score is the probability that a randomly selected 15-year-old boy
exceeds 71 in.
What is the probability that a randomly selected 10th grade boy exceeds 71 in.?
Use your standard normal table.

[ 71  -  66.9  ] / 2.5  =  1.8  = z score

Table  vaue for this  z score  =  .8810

Probability  =  1  - .8810   =  .119  =   11.9%

3. An experiment compares weight of fish for two different brands fish food. Nacho Average Minos
fish food has a mean fish weight 12 lbs., and a standard deviation of 1.4 lbs. Impossible Minos fish
food has a mean fish weight of 14 lbs. and a standard deviation of 1.2 lb. A fish is measured to be
13.1 lbs. Which brand of fish food, Nacho Average Minos, or Impossible Minos, is more likely to have
been used to feed this fish?

 Nacho Average Minos  =  [ 13.1  - 12 ] / 1.4 =  .785

Impossible Minos   =  [ 13.1  - 14 ]  /  1.2 =  - .75

Impossible Minos , because  the fish measured   falls closer to  the  average

2. Body mass index, or BMI, of 18-year-old females are normally distributed with a mean of 24.6 and
a standard deviation of 2.4. Eighteen-year-old Sasha BMI has a z-score of 1.22.
What is Sasha’s BMI?

[  Sash's BMI   -  24.6 ] /  2.4 =    1.22

Sasha's BMI  -24.6  =   1.22 ( 2.4)

Sasha's BMI =   1.22 (2.4)  + 24.6  ≈  27.53

1. Suppose that the weights of 3500 registered female Great Danes in the United States aredistributed normally with a mean of 125 lb. and a standard deviation of 5.2 lb.
Approximately how many of the Great Danes weigh more than 130.2 lbs.?

(130 - 125)  /   5.2  =   z score  of .96  =   table value of .8315

So

3500  ( 1 -.8315)  ≈  135  weigh more

I need help with this too, where are you CPhill 

56.52

Angles SAP  and SOP  are equal  because they are inscribed angles intercepting the same arc SP

So

SAP  =    SOP

3 *SOP  - 104  =  SOP

3 SOP   -  SOP   =   104

2 SOP  = 104

SOP  = 104 / 2    =   52°

A , H , M , T

Taken one at a time =   4 words

Taken two at a time =  3 + 2 + 1  =  6 words

Taken three at a time  =  2 + 1  = 3  words

Taken four at a time  = 1  word

So   4 + 6 + 3 + 1 =   14  words

Note that the sum of  arc CE + arc DB    =   360  - 107 -144  =  109°

So  CE + DB  = 109     (1)

And   we  have  that, by a geometry theorem

measure of  angle CAE   =   (1/2) (arc CE   - arc DB) )

21  =  (1/2) (CE  - DB)

42 =   CE - DB      (2)

Add  (1)  and (2)

2CE  =  151

CE =   151  / 2    =    75.5°

Remember  that    Distance  / Rate =   Tme

Let the plane speed in still air =  P   

Time  to  fly to tthe meeting  with the wind =  2000 / (P + 50)

Time to return =   2000  / ( P  - 50)

So

     simplify

2000 / (P + 50)   +  2000 / (P -50)  =   7

2000 (P- 50)  + (2000)(P+50)  =   7  (P + 50)(P -50)

4000P   = 7 (P^2   - 2500)

7P^2  -  4000P  - 17500  =  0

Using the Quadratic Formula

4000 ±  sqrt  [ 4000^2  - 4 * 7 * (-17500)  ]                     4000 + 4060.79

_________________________________        =         ________________   =  P   ≈   576 mph    

                   2 (7)                                                                      14   

Here:

https://web2.0calc.com/questions/geometry_74040

That first answer is not correct.

Have you drawn the pic?

In any triangle the sum of any 2 sides must be bigger than the third side.

This is what you must use to figure it out.

A 288 degree circular sector with radius 18 is rolled to form a cone. Find the height of the cone.

the slant height will be 18

The circumference at the base will be     \(\frac{288}{360}*2\pi*18\)

\(C=2\pi r\\ \frac{288}{360}*2\pi*18=2\pi r\\ \frac{288}{360}*18= r\\ r=14.4\;units\\~\\ \)

Check my working then use pythagoras's Theorem to find the height

Could you please explain your answer a bit more? Thanks!

Two cards are chosen at random from a standard 52-card deck. What is the probability that they are either both hearts or both diamonds or both Aces?

\(2*\frac{13C2}{52C2}+\frac{4C2}{52C2}\)

Compute the number of ordered pairs of positive integers (a,b) that satisfy (a^2)(b^3)=(20)^18.

\( 20^{18}=2^{36}*5^{18}\)

\(5^0*5^{18}\\ 5^6*5^{12}\\ \\~\\ 2^0*2^{36}\\ 2^6*2^{30}\\ 2^{12}*2^{24}\\ 2^{18}*2^{18}\\ \)

5^0 can be paired with 7 of them  (I mean different powers of 2)

5^6 can be paired with 7 of them

So I just get 14  but order counts, and a and b are all interchangeable so  that is 28

Here they are

If you can spot any that I have missed then please let me know.

(I am not guarenteeing that this answer is right)

Try this:

We know that \(EF = 9\)

Using the Pythagorean Theorem, \(BF = \sqrt{45}\)

Let \(DF = BC = x\)

We can derive the following equation using the Pythagorean Theorem: \(x^2=225+(x-\sqrt{45})^2\)

Solving, we find that \(\color{brown}\boxed{BC = 3 \sqrt{45}}\)

idk honestly

Rewrite this equation as: \(x^2-14x+y^2-40y=0\)

Completing the square, we have: \((x-7)^2+(y-20)^2=449\)

The minimum value for x is the center (7) - the radius.

The radius is the square root of the number on the right-hand side. 

You should be able to take it from here!

The real value of t = 16/3 produces the smallest value.

x = 13/38.

The answer is 3/110.

The possible values of AC are 3, 4, 5, 6, 7, 8, and 9.