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kent invested $5000 in a retirement plan. he allocated x dollars off the money to a bond that earns 4% interest per year and the rest into a traditional account that earns 5% interest per year. 

$x into a bond at 4% pa

a. write an expression that represents the amount of money invested in the traditional account

$(5000-x) in the back at 5%pa

b. write a polynomial model in simplest form for the total amount of money T Kent has invested after one year (hint: each account has A + iA dollars, where A is the original amount in the account and i is the interest rate)

After one year the bond will grow to   x + 0.04x

= x(1+0.04)

= 1.04x

After one year the traditional account  will grow to  

(5000-x)    + 0.05(5000-x) 

=5000-x    + 0.05*5000  -  0.05x

=5000  -  x    + 250  -  0.05x

=5250  -  1.05x

So altogether

T = 1.04x + 5250  -  1.05x

T =  5250  -  0.01x

c. if kent put $500 in the bond account, how much money does he have in his retirement plan after one year?

x=500

T= 5250  - 0.01*500

T= 5250 - 5

T= $5245

A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 60 miles and a standard deviation of 7 miles. Find the probability of the following events: A. The car travels more than 64 miles per gallon.

That means that the consumption is  4/7  standard deviations above the mean.

I'll go look for a statistics calc to help me.

Z=+4/7

Here is a great site - it does it all for you

108

a window

3.14159265359...

🤗

Solve for x:
x^2-20 x = -125

Add 100 to both sides:
x^2-20 x+100 = -25

Write the left hand side as a square:
(x-10)^2 = -25

Take the square root of both sides:
x-10 = 5 i or x-10 = -5 i

Add 10 to both sides:
x = 10+5 i or x-10 = -5 i

Add 10 to both sides:
Answer: |x = 10+5 i               or              x = 10-5 i

1 mile = 5,280 feet.

Let x represent the cost of one of Tanya's items.

Then the cost of one of Tony's items =x - 2.25. But we have:

3x =4(x - 2.25)

3x =4x - 9 subtract 3x from both sides

0 =x - 9 add 9 to both sides

x=$9 The cost of one of Tanya's items

$9 x 3 =$27 Total cost of Tanya's 3 items

$9 - $2.25 =$6.75 cost of one of Tony's items.

$6.75 x 4 =$27 Total cost of Tony's 4 items.

3 x $9 =4 x $6.75 =$27. This shows that both Tony and Tanya spent the same amount of money.

1+1=11

It is 188282

2+2=

4

There are 5x2=10 waus to seat the gils.

For each of those there is 4!=24 ways to seat the others.

So that is 10x24=240 favourable ways.

There are 6! Ways to sit 6 people in a row so the prob of the girls being together is 240 / 6!

because the square root of 196 is 14 and the square root of -1 is an imaginary number, represented by i.

A number in which used for forumlas to determine the circumfirence of a circle and other stuff

Use the   'e' button        then the  x^y button underneath the 'e' button   then    2.95    then 

the  + - button ....then  =

- 1/3

One.

Possibly:    19 elephants      =     95  dollars

                    80 sheep          =        4

                       1  horse         =        1

                    100 animals               100 dollars

https://www.khanacademy.org/math/pre-algebra/pre-algebra-decimals/pre-algebra-decimals-to-fractions/v/converting-decimals-to-fractions-1-ex-1

You have to use the standard model equation to solve that.

1 1/3 times 3 equals 4.

1 1/3 times 3 equals 4.

Leave the number on your calc display and divide by the other number ....then press the  1/x button.