Since there is a multiplier of 7 on the left, and both terms on the right are divisible by 7, I'd start by dividing the equation by 7
|8 - 3x| = 3x - 7
The absolute value function may or may not negate its argument. (The argument is negated if it is negative.) Hence this can resolve to two equations
-(8 -3x) = 3x -7
or
(8 -3x) = 3x -7
_____
Starting with the first of these, we can eliminate parentheses to get
... -8 +3x = 3x -7
Subtracting 3x from both sides gives the FALSE statement
... -8 = -7 . . . . FALSE
Thus, this version of the equation has No Solution.
Looking at the second of the equations above, we can add 3x to get
... 8 = 6x -7
Adding 7 and dividing by 6 gives
... (8 +7)/6 = x = 5/2
The solution is x = 5/2.
Answer:
See proof below
Step-by-step explanation:
In trigonometry identity
tan^2 theta = sin^2 theta /cos^2 theta
cot^2 theta = cos^2 theta/sin^2 theta
csc^2 theta = 1/sin^2 theta
Substitute into the expression
(sin^2 theta /cos^2 theta )+ (cos^2 theta/sin^2 theta)/1/sin^2 theta
= [sin^4theta + cos^4theta/cos^2 theta sin^2 theta]÷(1/sin^2 theta)
= 1/cos^2 theta sin^2 theta÷(1/sin^2 theta)
= 1/cos^2 theta sin^2 theta * sin^2 theta/1
= 1/cos^2theta
= sec^2theta (Proved!)
Answer: He can play 4 rounds of his favorite game
Step-by-step explanation:
Zack has 3/4 hours to play video games. This means that he cannot spend more than 3/4 hours playing video games. it takes him 1/12hours to set up the system before he starts playing. This means that the time left for him to play games would be the time he has to play - the time it takes him to set up the video game. It becomes
3/4 - 1/12 = 8/12
If each round of his favorite game takes 1/6 hours, the number of rounds he can play would be the time he has left to play/time per round of his favorite game. It becomes
8/12 ÷ 1/6
= 8/12 × 6/1
= 4
Answer:
0.82% probability that the average time it takes to complete both homework assignments is greater than 82 minutes
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Math homework:
Arts homework:
What is the probability that the average time it takes to complete both homework assignments is greater than 82 minutes?
Here, we have a sum of normal variables. The mean will be the sum of the means, while the standard deviation is the square root of the sum of the variances. So
This probability is 1 subtracted by the pvalue of Z when X = 82. So
has a pvalue of 0.9918
1 - 0.9918 = 0.0082
0.82% probability that the average time it takes to complete both homework assignments is greater than 82 minutes
p = amount of change in price
p = (final amount) - (starting amount)
p = 10.12 - 8.84
p = 1.28
The stock increased by $1.28
Divide the value of p over the original amount 8.84
(amount of change)/(original amount) = p/8.84 = 1.28/8.84 = 0.144796
Convert 0.1447 to percent form to get 14.4796% which rounds to 14.5%
Unfortunately 14.5% isn't listed. I think your teacher made an typo when s/he made the problem.
