Answer:
The actual measure of ∠1 = 40°
Step-by-step explanation:
We are given: ∠1 = 2x+6 and ∠2 = 8x+4
and both angles are supplementary. we need to find the actual measure of ∠1
Supplementary angles: If the angles are supplementary their sum is equal to 180°
In our case ∠1 +∠2 = 180°
2x+6+8x+4=180
Solving the equation to find x, then we can find the actual measure of ∠1

So, value of x = 17
Now, finding actual measure of ∠1 by putting x=17 in equation 2x+6

So, the actual measure of ∠1 = 40°
The empirical rule states that in a normal distribution,
68% of data is within 1 std deviation of the mean
95% of data is within 2 std deviation of the mean
99.7% of data is within 3 std deviation of the mean
In this case 95% of the cases would be within two std deviations of the mean
mean - 8 and mean + 8
72 - 8 = 64 and 72 + 8 = 80
then 95% of the scores are between 64% and 80% on the test.
Answer:
Step-by-step explanation:
No of ways in which 5 cards are chosen is 
No of ways in which at most 4 cards are spades
Total ways-5 spades

Probability that at most 4 cards are spade 



Answer:
x=6
Step-by-step explanation:
Step 1:
Subtract 3x from both sides:
4x + 8 - 3x = 3x + 14 - 3x
x + 8 = 14
Step 2:
Subtract 8 from both sides:
x + 8 - 8 = 14 - 8
x = 6
Answer:
(1, 1 )
Step-by-step explanation:
Given the 2 equations
y = - 5x + 6 → (1)
y = 3x - 2 → (2)
Since both equations express y in terms of x, equate the right sides
3x - 2 = - 5x + 6 ( add 5x to both sides )
8x - 2 = 6 ( add 2 to both sides )
8x = 8 ( divide both sides by 8 )
x = 1
Substitute x = 1 into either of the 2 equations for corresponding value of y
Substituting x = 1 in (2)
y = 3(1) - 2 = 3 - 2 = 1
Solution is (1, 1 )