Answer:
The first term is 3. The common difference is 2.
Step-by-step explanation:
The first term is x.
The common difference is d.
The second term is x + d.
3rd term: x + 2d
4th term: x + 3d
7th term: x + 6d
"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"
x + 3d = 3 * x Eq. 1
"the seventh term exceeds twice the third term by 1"
x + 6d = 2(x + 2d) + 1 Eq. 2
Simplify Eq. 1:
2x = 3d
Simplify Eq. 2:
x + 6d = 2x + 4d + 1
x = 2d - 1
Multiply both sides of the last equation by 2.
2x = 4d - 2
2x = 3d (simplified Eq. 1)
Since 2x = 2x, then the right sides are equal.
3d = 4d - 2
d = 2
2x = 3d
2x = 3(2)
2x = 6
x = 3
Answer: The first term is 3. The common difference is 2.
Answer:
0.9606 = 96.06% probability that the system will function tomorrow
Step-by-step explanation:
For each component, there are only two possible outcomes. Either it works, or it does not. Components are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Probability of a component working:
0.7 of 0.2(rain)
0.9 of 1 - 0.2 = 0.8(no rain). So
0.86 - 86% probability that the system will function tomorrow
6 components:
This means that 
What is the probability that the system will function tomorrow
This is
In which
0.9606 = 96.06% probability that the system will function tomorrow
Answer:
WX = 31
Step-by-step explanation:
(65 + WX) = 2 (48)
(65 + WX) = 96
WX = 96 - 65
WX = 31
Answer:
a. The measure of angle 2 is 63 and the measure of angle 3 is 117
b. The measure of angle 4 would be approximately 30.66...
c. The measure of angle 2 would be 17
Step-by-step explanation:
a. Angles 1 and 2 are alternate interior angles which means they are equal to each other. That means that both angles 1 and 2 and 63 degrees. Angles 2 and 3 are supplementary angles which means they add up to 180 degrees.
180-63=117 degrees
b. Angles 1 and 4 are alternate exterior angles and are also equal to each other. You would set up an equation that looks like...
74=3x-18
Add 18 to both sides
92=3x
Divide by 3 on both sides
92/3 which is approximately 30.67
c. Angle 1 and 2 are alternate interior angles. You would set the two given equations equal to each other.
3x-9=x+25
Subtract x from both sides.
2x-9=25
Add 9 to both sides.
2x=34
Divide both sides by 2.
x=17
