Answer:
y= 4/3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−2=3(y−2)
−2=(3)(y)+(3)(−2)(Distribute)
−2=3y+−6
−2=3y−6
Step 2: Flip the equation.
3y−6=−2
Step 3: Add 6 to both sides.
3y−6+6=−2+6
3y=4
Step 4: Divide both sides by 3.
3y
/3
=
4
/3
y=
4/3
Answer:
y=
4/3
Answer:
#1: inequality form: x ≤ –1 or x ≥ 2
interval notion: ( -∞,-1] U [2,∞)
#2: false/no solution
#3: A) point form: (3,9)(-1,1)
equation form: x= 3,y=9 and x= -1,y=1
B)point form: (1,7)(7,1)
equation form: x=1,y=7 and x=7,y=1
Step-by-step explanation:
#1: solve for x by simplifying both sides of the inequality, then isolating the variable.
#2: N/A
#3: solve for the first variable in one of the equations, then substitute the results into the other question.
To solve this problem, let us recall that the formula for
probability is:
Probability = total number of successful events / total
events
Where in this case, an event is considered to be successful
if the sum is 3 on the pair of six sided dice.
First, let us calculate for the total number of events. There
are 6 numbers per dice, therefore the total number of combinations is:
total events = 6 * 6 = 36
Next, we calculate for the total number of combinations
that result in a sum of 3. We can identify that there are only two cases that
result in sum of 3. That is:
1st case: first dice rolls 1, second dice
rolls 2
2nd case: first dice rolls 2, second dice
rolls 1
Hence, total number of successful events = 2. Therefore the
probability is:
Probability = 2 / 36 = 1 / 18 = 0.0556 = 5.56%
Answer:
95% Confidence interval for the variance:
95% Confidence interval for the standard deviation:
Step-by-step explanation:
We have to calculate a 95% confidence interval for the standard deviation σ and the variance σ².
The sample, of size n=8, has a standard deviation of s=2.89 miles.
Then, the variance of the sample is
The confidence interval for the variance is:
The critical values for the Chi-square distribution for a 95% confidence (α=0.05) interval are:
Then, the confidence interval can be calculated as:
If we calculate the square root for each bound we will have the confidence interval for the standard deviation:
