Answer:
x = 8
Step-by-step explanation:
Taking the antilog, you have ...
3x +8 = 2^5 = 32
3x = 24 . . . . subtract 8
x = 8 . . . . . . .divide by 3
___
You can have a graphing calculator show you the answer. Subtracting 5 from both sides gives ...
log2(3x +8) -5 = 0
The calculator can plot the left-side function and show you the value of x that makes it zero. That value is x=8.
To calculate the average rate of change, just plug your points into the basic slope formula
![m= \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20)
. This gives you
![m= \frac{6-0}{0-(-2)} = \frac{6}{2} =3](https://tex.z-dn.net/?f=m%3D%20%5Cfrac%7B6-0%7D%7B0-%28-2%29%7D%20%3D%20%5Cfrac%7B6%7D%7B2%7D%20%3D3)
. This means your average rate of change is 3.
Complete Question
Kayla is baking cupcakes. She needs 2 3/4cups of white sugar and 1 5/6 cups of brown sugar. How much sugar is in Kayla's cupcakes?
Answer:
4 5/12 Cups of sugar
Step-by-step explanation:
She needs 2 3/4cups of white sugar and 1 5/6 cups of brown sugar.
The amount of sugar is in Kayla's cupcakes is calculated as:
White sugar + Brown Sugar
= 2 3/4 cups + 1 5/6 cups
2+ 1 + [ 3/4 + 5/6]
Lowes Common Denominator = 12
3 + [9 +10/12]
3 + 19/12
3 + 1 5/12
= 4 5/12 Cups of sugar
Therefore, 4 5/12 Cups of sugar is in Kayla's cupcakes.
Answer:
Step-by-step explanation:
Given that an ordinary deck of 52 cards is shuffled and the cards are then turned over one at a time until the first ace appears.
the first ace is the 20th card to appear
This implies that there are still 32 cards with 3 aces in it.
But 2 clubs can be either 1 remaining or nothing remaining
a) ace of spades
3 aces out of 32
Prob = ![\frac{3}{32}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B32%7D)
b) 2 of clubs
P (2 club already gone in first 19 cards) +P(2 club is in the remaining)
= 0+P(first 20 cards not 2 clubs )*P(2 club in 21st draw)
= ![(\frac{51}{52} )(\frac{1}{32}) \\\\= \frac{51}{1664}](https://tex.z-dn.net/?f=%28%5Cfrac%7B51%7D%7B52%7D%20%29%28%5Cfrac%7B1%7D%7B32%7D%29%20%5C%5C%5C%5C%3D%20%5Cfrac%7B51%7D%7B1664%7D)
Percent is simply /100, so the fraction would be 450/100. Divide both top and bottom and you will get 9/2, or 4 1/2