All Answers 353101 Answers

The expected value is 4 and 2/3

See the following ACG :

Since the sphere is tangent to  both the top and bottom bases, the height of the frustum must be   = 6  = BE

And the slant height   = 10  = BD

Notice that  since  AB   and BC  are tangents drawn from  the same point, they are equal

And AB  = 1/2 ot the top  base  of the frustum.....so BC  equals the same.... and  call this, m

But  CD  and  DF are also  tangents drawn from the same point.....so CD  = DF

And because  of the Pythagorean Theorem,  DE  = √ [BD^2  - BE^2=  = √[10^2 - 6^2 ]  =   8  =   r  - m

So.....we have the following eqautions

r + m  = 10

r - m  =   8      add these

2r  = 18

r  = 9   =  bottom radius

So...  9 + m  = 10  ⇒ m  = 1   = top radius

So....the  volume of the frustum  is

(1/3)  pi  *  height  * ( top radius^2  + product of the radii + radius ^2 )  =

(1/3) pi  *  6  * ( 1^2  +  1*9   +  9^2 )  =

(1/3) pi * 6 * ( 1 + 9  + 81)  =

(1/3) pi * 6 ( 81)  =

182 pi  units^3

Edited to correct an error  !!!

Hey GAMEMASTERX40!

In a quadratic equation, there is sometimes two roots, or solutions. 

This happens when the discriminant, b^2-4ac is greater than zero. 

When it is equal to zero, the quadratic will have two identical roots. 

When it is less than zero, the quadratic will have no real solutions. 
 

Therefore, the larger root means the root with the larger value of the two. 

I hope this helped,

Gavin

Express the infinite series

\(\frac{3}{206}+\frac{9}{2\cdot103^2}+\frac{27}{2\cdot103^3}+\cdots\)

as a terminating decimal.

This is a ordinary GP

\(S_\infty=\frac{a}{1-r}\)

If you have done GPs this will be easy. If not then you better say so.

The sum of two numbers is 25. What are the numbers?

a. Create an equation using two variables to represent this situation. Be sure to explain the meaning of each variable.

Let x and y be real numbers such that

x+y=25

b. List at least 3 solutions to the equation you created in part (a).

x=12, y=13

x=-2, y=27

you can do the last one yourself

c. Create a graph that represents the solution set to the equation.

You can graph the points on a number plane and see what shape you get.

Join them all up and you have your graph. :)

lil n****r

How many 2-letter "words" consist of two different letters arranged in alphabetical order?

the guest that you were so eager to criticize was right.

                                Alternate Interior Angle Theorem

∠ ADB    =  ∠CDF

                                  Angle Angle Similarity Postulate

                  Corresponding Angles Postulate

                  Transitive Property

                  Triangle Proportionality  Theorem

                                 Corresponding Angles Postulate

ΔACE  ~ ΔBCD

                                 Segment Addition Postulate

1.

$9.15 - $8.60 =$0.55 inrease per share price in 1 year.

1,000 shares x $0.55 = $550 gross profit on 1,000 shares in 1 year.

$550 - $28.00(broker's fees) = $522.00 net profit on 1,000 shares after 1 year.

2.

$2,500 x [7% / 2] = $87.50 interest on the bond every 6 months.

$87.50 x [10 years x 2] =$1,750 total interest on the bond for 10 years.

3.

FV = PV x [1 + R]^N

10,000 =5,000 x [1 + 0.035]^N         divide both sides by 5,000

2 = 1.035^N                                      take the log of both sides

N =Log(2) / Log(1.035)

N = 20.15 years when $5,000 investment will become $10,000

4.

$51,350 / 26(bi-weekly payments) = $1,975.00 Erin's bi-weekly pay.

$1,975.00 x 5% =$98.75 deducted from his paycheck for 403(b) plan.

$1,975.00 x 4% =$79.00 His employer's contribution to 403(b) plan[If I understand your question]

$98.75 + $79.00 = $177.75 total contribution to 403(b) plan.

The area is 

pi * (diameter / 2)^2  =

pi *  (3 /2)^2  =

pi *  (9/4)  =

(9 / 4) pi   m^2

Present population =PP

Future population =FP

FP = PP x [1 - 0.045]^t

7,000 = 8,500 x [0.955]^t        divide both sides by 8,500

0.823529... = 0.955^t              take the log of both sides

t =Log(0.823529) / Log(0.955)

t = 4.22 = ~ 4.25 years after 2010 when the population of the town will be about 7,000.

1.

$125,340 x 15% = $18,801 - down payment that Leah paid on the house.

$125,340 - $18,801 = $106,539 - mortgage amount that Leah must borrow.

2.

That depends on many factors including Leah other living expenses, such as taxes, food, car payments, health and other insurance payments, education, entertainment....etc. Look at the criteria, in your textbook, that will determine whether Leah can afford to buy the house or not.

3.

Leah's monthly mortgage payment will be: $106,539 / 1,000 x 5.929[from your table under 3.75%] = $631.67.

4.

Leah total payments will be: $631.67 x 240 months(20 years) + $18,801(down payment) = $170,401.80.

5.

Total amount of interest that Leah will pay = $631.67 x 240 - $106,539 = $45,061.80.

(a) 8,500-4.5%(t)

(b) 2010: 8,500

2011: 8117

2012: 7752

2013: 7403

2014: 7069

2015: 6751

Thus, it'll be \(\boxed{2015}\) , when the population will equal 7000.

Once again, this is a basic trigonometry relationship problem. 

In this case, we can use tangent or cotangent. 

Tangent is opposite over adjacent

Cotangent is adjacent over opposite.

Let’s just say we use tangent.

\(\tan{x}=\frac{26}{53}\)

I hope this helped,

Gavin

Just to clear up any confusion, hecticar, \(x\neq -1\). Any time a division-by-zero error arises, the entire expression is immediately deemed as undefined--no matter where. 

We have reached a problem. Do not go any further! Here is another way to think about, I guess.

Any result in the format \(\frac{x}{0}\) is given the name "undefined" because it literally does not have a meaning; it is pure nonsense; it means nothing at all. By taking the reciprocal, you are attempting to attach meaning to nonsense, which you should never do.

for the second one, problem 3, 

the ladder is the hypotenuse forming a right triangle with the wall and ground.

so for part a, sin is used.

sin angle = 9.2/10 

use a calculator to solve that with arcsin or sin^-1

for part b, cos is used.

cos 75 = x/10

x= 10 cos 75

x being the ground distance

|-2| > -2

cause |-2| = 2 and 2 is bigger

| | is called absolute value, it means make what ever is inside a positive value