The quotient of ten to the seventh power and ten cubed?

Answers

Answer 1

Answer: $Use:\ a^n:a^m=a^(n-m)\n\n10^7:10^3=10^(7-3)=10^4\n\n10^4=10*10*10*10=10,000$

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Delaney would like to make a 5lb mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture,and let m represent the number of pounds of the 80% almond-20% peanut mixture.(a) What is the system that models this situation?
(b) How many pounds of peanuts and how many pounds of the 80% almond-20% peanut mixture will she need?

Answers

This is a mixture problem. Let's call the mixture of

20%peanuts - 80% almonds as mixture A

Let's call the

100% peanuts as mixture B

and the

60% peanuts - 40% almonds as mixture C

Since we get mixture C by adding mixture A and B together, we know that the amount in pounds of mixture A and mixture B is 5 pounds.

Hence we

let m be the amount in pounds of 20%peanuts-80% almonds mixture, or mixture A

and

50-m be the amount in pounds of mixture B

So, the system of equations that models this situation is:

0.20m + 1(50-m) = 0.60(5)
0.80m + 0(50-m) = 0.40(5)

Solving for m using equation 2 gives us

m = 2.5 lb.

That means it will take 2.5 lb of mixture A (20%peanuts-80%almonds) and 2.5 lb of mixture B (100%peanuts) to form 5 lb of mixture C (60%peanuts-40%almonds).

SungHee empties her piggy bank and finds that she has 200 quaters,150 dimes,and 300 pennies.How much money does she have?Explain

Answers

So first find out how much each is worth.
Quarter= 25 cents
Dime= 10 cents
Pennies= 1 cent

Then multiply each by how much each is worth.

200 150 300
x x x 1
25 10 --------
------ --------    300
1000 1500
+
4000
------
5000

Then count 2 from the back and add a period.

$50.00
$15.00
$3.00

And then add them

  $50.00
+
$15.00
+
  $3.00
--------------
$68.00

So SungHee has $68.00

X+3y=-14
-4x- 3y=2 this is elimination

Answers

X+3y= -14
-4x- 3y= 2
-----------------
-3x = -12
-3x/-3 = -12/-3
x = 4

X+3y=-14
4+3y=-14
4-4 +3y = 14-4
3y = -18
3y/3 = -18/3
y = -6

Check
-4x- 3y=2

-4(4)- 3(-6) = 2
-16+18 = 2
2=2

Nan rode the Roller coaster 8 timea, which was twice as many as she rode the farriers wheel

Answers

8=2x
x=4
Nan rode farriers wheel 4 times

So the trick is when you hear times two that means that you have times two to in this sample eight. So 8*2=16

Given the equation 1/4(2)^x find the average rate of change between f(2) and f(5)

Answers

Given the function

$f(x)=(1)/(4)\,2^(x)$

The average rate between $f(2)$ and $f(5)$ is

$\left.(\Delta f)/(\Delta x)\right|_(x=2\to 5)=(f(5)-f(2))/(5-2)\n \n \n =((1)/(4)\cdot 2^(5)-(1)/(4)\cdot 2^(2))/(5-2)\n \n \n =((1)/(4)\cdot (2^(5)-2^(2)))/(3)\n \n \n =((1)/(4)\cdot (32-4))/(3)\n \n \n =((1)/(4)\cdot (28))/(3)\n \n \n =(7)/(3)$

A truck driver drove 300 miles in 6 3/4 hours. How many miles per hour did the driver drive?

Answers

44.4 miles per hour. You just divide 300 and 6.75 (Think as the 3/4 as quarters each 1 is .25) then you will get 44.4. To check your answer you would multiply 44.4 and 6.75 and get 299.7. This is not 300 but when you round that .7 to the nearest 10 you will get 300. Hope this helped.

Answer:

44.44 miles per hour.

Step-by-step explanation:

A truck driver drove 300 miles in $6(3)/(4)$ hours.