A class of 25 students took a math test. Ten students had an average of 88. The other students had an average of 76. What is the average of the whole class?A) 78.2
B) 80.8
C) 81.7
D) 82.5

Answers

Answer 1

Answer:

Answer:

The average of the whole class is 80.8.

The correct answer is B)

Step-by-step explanation:

To solve this problem, it is very important to understand the phrase: "Ten students had an average of 88". Let's see an example.

Imagine that three students in the class took a test and their scores were: 80, 89 and 95. To calculate the average of they three we must divide the sum of the scores by the total number of scores.

$average=(80+89+95)/(3)=(264)/(3)=88$

The previous value is the average of the three students. Now, if we say that each student got 88, the average would be 88.

$average=(88+88+88)/(3)=(264)/(3)=88$

The previous expression could be simplified as:

$average=(88* 3)/(3)$

Where, the number 3 means the number of students.

With that in mind, the phrase "Ten students had an average of 88" could be written as:

$average_(10\, \, students)=(88+88+88+88+88+88+88+88+88+88)/(10)$

$average_(10\, \, students)=(88* 10)/(10)=88$

On the other hand, the phrase "The other students had an average of 76" means that from the 25 students, 15 students got 76 (25 - 10 = 15), and could be written as:

$average_(15\, \, students)=(76+76+76+76+76+76+76+76+76+76+76+76+76+76+76)/(15)$

$average_(15\, \, students)=(76* 15)/(15)=76$

Finally, to calculate the total average of the 25 students we must divide the sum of the scores of all students by the total number of scores. The sum would be: 88+88+88+88+88+88+88+88+88+88+76+76+76+76+76+76+76+76+76+76+76+76+76+76+76, which equals $88* 10+76* 15$ . The total number of scores would be: 25.

$average_(total)=(88* 10 + 76* 15)/(25)$

$average_(total)=(880 + 1140)/(25)$

$average_(total)=(2020)/(25)$

$average_(total)=80.8$

Thus, the average of the whole class is 80.8. The correct answer is B)

Answer 2

Answer:

The answer is B. 80.8

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An underwater canyon begins at 40 feetbelow sea level and is 105 feet deep.
What is the elevation of the bottom of
the canyon?

Answers

Answer:

145 feet.

Step-by-step explanation:

Given that:

An underwater canyon begins at depth = 40 ft

Depth of canyon = 105 ft

To find:

The elevation of the bottom of the canyon = ?

Solution:

Kindly refer to the image attached for the given dimensions.

A is the sea level.

B is the point at which the canyon starts and

C is the bottom of the canyon.

As per question statement, we are given that:

AB = 40 feet

BC = 105 feet

And we have to find the distance AC = ?

It is clearly observable that:

$AC = AB + BC\n\Rightarrow AC = 40 + 105\n\Rightarrow \bold{AC = 145 ft}$

So, the elevation of the bottom of the canyon is 145 ft.

F (a)=2a^2-16a+32
For which 'a' is this equation 0?

Answers

if xy=0 assume that at leas 1 is zero
set it to zero

0=2a^2-16a+32
undistribute 2
0=2(a^2-8a+16)
2*0=0 so assume
a^2-8a+16=0
factor
(a-4)(a-4)=0
set to zero
a-4=0
a=4

when a=4, equation equals zero

Find the volume and surface area. Round to the nearest hundredth when necessary.