Step-by-step explanation:
We can prove the statement is false by proof of contradiction:
We know that cos0° = 1 and cos90° = 0.
Let A = 0° and B = 90°.
Left-Hand Side:
cos(A + B) = cos(0° + 90°) = cos90° = 0.
Right-Hand Side:
cos(A) + cos(B) = cos(0°) + cos(90°)
= 1 + 0 = 1.
Since LHS =/= RHS, by proof of contradiction,
the statement is false.
Complete Question
In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of your total grade, each major test is worth 22:5%, and the final exam is worth 30%. Compute the weighted average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test, and 85 on the final exam. (Enter your answer to one decimal place)
Answer:
The weighted average is
Step-by-step explanation:
From the question we are told that
The worth of the lab score is 25% of total grade
The worth of each major test is 22.5% of total grade
The worth of final exam is 30% of total grade
The score on lab is 92
The score on first major test 81
The score on second major test 93
The score on final exam is 85
Generally the weighted score is mathematically represented as

=> 
=>
Answer:
C. Mrs. Alvarez's scores were less spread out than Mr. Crawford's scores.
Step-by-step explanation:
Mean Absolute Deviation is one of the Statistical measures which we can you to determine the variation that exist amongst a given set of data
Mean Absolute Deviation can be defined as how far or the distance between one set of data to another set of data.
The smaller the Mean Standard Deviation, the lower the degree of variation in the set of data. The data is less spread out
The larger the Mean Standard Deviation, the higher the degree of variation in the set of data. The data is Largely spread out
We are told in the question that:
Mrs. Alvarez's scores had a lower mean absolute deviation than Mr. Crawford's scores. Our conclusion would be that Mrs. Alvarez's scores were less spread out than Mr. Crawford's scores.
Option 2 is correct.
Answer:
need to spend $18 more in addition to $12
Step-by-step explanation:
Given: According to online music store, if you spend $30 or more, you receive 3 songs for free
To find: How much more money need to be spend in addition to $12 to receive three free songs
Solution:
Let x denotes amount to be spend in addition to $12 to receive three free songs
According to question,
