Denote the sequence by
with
.
Recursively:
The first number is
, and each successive number is twice the previous one. So
,
,
, ... .
In other words,
and so in general,
Explicitly:
We can arrive at this formula by, in a way, working backwards. If
, that means
, and so
, and so on. We would end up with
(You'll notice a pattern here: the exponent of the 2 and the index of the earlier term in the sequence add up to
. For example,
.)
or simply
Then the 15th term is obtained immediately by evaluating this rule at
. We get
In order to solve this, we first need to know what the ratio of servings of pudding to cups of milk is. We can see that 8 servings of pudding requires 2 cups of milk, so the ratio is 8/2, which can be reduced to 4/1. This means that for every 4 servings of pudding, we will be adding 1 cup of milk. So all we need to do to find out how many cups would be needed for 64 servings of pudding, we simply need to divide by 4.
64 / 4 = 16
So for 64 servings of pudding, we will need 16 cups of milk. But that's not what the question wants to know, it wants to know how many gallons of milk it would need.
In order to find that out, we have to know how many cups there are in one gallon. There are 2 cups in one pint, there are 2 pints in a quart, and there are 4 quarts in a gallon, so we just have to multiply those numbers, and we get 4 * 2 * 2 = 8 * 2 = 16
There are 16 cups in one gallon, therefore, 64 servings of pudding will require 1 gallon of milk.
Hope that helped! =)
Answer:
D
Step-by-step explanation:
a meter is 100 centimeters so the ratio of the real car to the model is 300 centimeters to 3 centimeters, or 100:1 so D
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'-O------O--'
Hi there!
To convert this equation into slope intercept form before graphing it, we need to put it into this form:
y = mx + b
So, first, we should move the 2x to the right side of the equation by subtracting 2x from both sides.
y = -2x + 6
and then, you graph.
Hope this helps!
Answer:
12. a = 2
13.
Step-by-step explanation:
12.
6a(a + 3) = 2a(3a + 5) + 16
First, distribute 6a on the left side, and distribute 2a on the right side.
6a² + 18a = 6a² + 10a + 16
Subtract 6a² from both sides.
18a = 10a + 16
Subtract 10a from both sides.
8a = 16
Divide both sides by 8.
a = 2
13.
The LCD of 2 and 3 is 6. We multiply both sides of the equation by 6 to get rid of all denominators.
Combine like terms on the left side. Distribute the 2 on the right side.
Subtract 2x from both sides.
Divide both sides by 3.