Answer:
Step-by-step explanation:
1. regroup terms

2. Rewrite
as
and 343 as 

3. Since both terms are perfect cubes, factor using the sum of cubes formula,
, where
and 


4. Factor
out of 

5. Regroup


6. Factor again


When looking at probabilities, two ideas are always true.
1) Any probability is more than 0.
2) The sum of all the probabilites is 1.
Idea #2 works here. (For example, think of how a die has six things and the probability of each is 1/6. So 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1.) Let G = the probability of grape, C = probability of cherry and O = the probability of orange. From Idea #2, G + C + O = 1. Since we know G and C, then
3/10 + 1/5 + O = 1.
3/10 + 2/10 + O = 1
5/10 + O = 1
O = 5/10
Thus, the probability of an orange jelly bean is 5/10 = 1/2.
Suppose the spinner lands on <em>a</em>. There's a 1/3 chance that it'll land on <em>a</em> the second time.
Suppose the spinner lands on <em>b</em>. There's a 1/3 chance that it'll land on <em>b</em> the second time.
Suppose the spinner lands on <em>c</em>. There's a 1/3 chance that it'll land on <em>c</em> the second time.
We've covered all possibilities for the first spin, and they're all equal, so their average is 1/3.
The probability that it'll land on the same letter twice is 33.3%.
Answer:
Residual = -2
The negative residual value indicates that the data point lies below the regression line.
Step-by-step explanation:
We are given a linear regression model that relates daily high temperature, in degrees Fahrenheit and number of lemonade cups sold.

Where y is the number of cups sold and x is the daily temperature in Fahrenheit.
Residual value:
A residual value basically shows the position of a data point with respect to the regression line.
A residual value of 0 is desired which means that the regression line best fits the data.
The Residual value is calculated by
Residual = Observed value - Predicted value
The predicted value of number of lemonade cups is obtained as

So the predicted value of number of lemonade cups is 23 and the observed value is 21 so the residual value is
Residual = Observed value - Predicted value
Residual = 21 - 23
Residual = -2
The negative residual value indicates that the data point lies below the regression line.
Answer:
6f = 24
f = 4
Step-by-step explanation: