Answer:
x =12
Step-by-step explanation:
The two angles are complementary, so the add to 90 degrees
5x+1/2x +24 = 90
Combine like terms
5 1/2 x +24 = 90
Subtract 24 from each side
5 1/2 x = 90-24
Change the mixed number to an improper fraction
11/2 x = 66
Multiply by the reciprocal 2/11 on each side
2/11 *11/2 x = 66*2/11
x = 6*2
x =12
A solid dot on the graph of an inequality indicates that the number is contained within the inequality, so yo should use

or

to represent that situation, whereas a white dot indicates that the number is not contained within the inequality.
Our graph is telling us that

is greater or equal than -1, and also

is less than 3. So our inequality will be:
Answer:
(10/3, 2/3)
Step-by-step explanation:
You may find it easier to write these two equations x+y=4 2x-y=6 in a column:
x+y=4
2x-y=6
Adding these together will eliminate y:
3x = 10. Then x = 10/3.
Substituting 10/3 for x in the first equation results in:
10/3 + y = 4
Clear fractions by multiplying all three terms by 3:
10 + 3y = 12
Then 3y = 2, and y = 2/3.
The solution is (10/3, 2/3)
Answer:
The actual dimensions would be 3.375 feet by 3.5 feet. The area of the room would be 11.8 square feet.
Step-by-step explanation:
Given Information:
Mean SAT score = μ = 1500
Standard deviation of SAT score = σ = 3
00
Required Information:
Minimum score in the top 10% of this test that qualifies for the scholarship = ?
Answer:

Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
We want to find out the minimum score that qualifies for the scholarship by scoring in the top 10% of this test.

The z-score corresponding to the probability of 0.90 is 1.28 (from the z-table)

Therefore, you need to score 1884 in order to qualify for the scholarship.
How to use z-table?
Step 1:
In the z-table, find the probability value of 0.90 and note down the value of the that row which is 1.2
Step 2:
Then look up at the top of z-table and note down the value of the that column which is 0.08
Step 3:
Finally, note down the intersection of step 1 and step 2 which is 1.28