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shepuryov [24]
2 years ago
10

A pencil box in the shape of a rectangular prism measures 3 inches by 4 inches by 12 inches. What is the length of the longest p

encil that can fit in the box? Explain your answer.
Mathematics
1 answer:
stepan [7]2 years ago
4 0

Answer:

(square root of 160)in

Step-by-step explanation:

the longest 2 sides are 4 and 12

4^2 + 12^2 = c^2

16+144=c^2

160=c^2

c = square root of 160

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??? Anyone know how to answer this question
True [87]
Answer: 35 additional teachers are needed

-------------------------------------------------
-------------------------------------------------

Explanation:

We have 2470 students and the ratio of students to teachers is 26:1. This means that for every teacher, there are 26 students. Put another way, we can set up this ratio

2470/x = 26/1

where x is the number of teachers. Cross multiply and solve for x

2470/x = 26/1
2470*1 = 26*x
2470 = 26x
26x = 2470
26x/26 = 2470/26
x = 95

So we have 95 teachers currently

-------------

Let y be the new number of teachers needed to bring the ratio down to 19:1

Using a similar idea as done above, we would have this ratio

2470/y = 19/1

Let's solve for y
2470/y = 19/1
2470*1 = 19*y
2470 = 19y
19y = 2470
19y/19 = 2470/19
y = 130

So we'll need 130 teachers to have the ratio be 19:1

The difference of the values is y - x = 130 - 95 = 35, which is the final answer. This is the additional amount of teachers needed.
5 0
3 years ago
We want to factor the following expression:
S_A_V [24]

Answer:

A. (U+V)^2 or (U-V)^2

Step-by-step explanation:

9x^6 + 6x^3y + y^2 \\  \\  =  {(3 {x}^{3} )}^{2}  + 2.(3x^3).y +( y)^2  \\  \\  =  \bigg({3 {x}^{3} } + y \bigg)^{2} \\  \\   = \bigg({3 {x}^{3} } + y \bigg) \bigg({3 {x}^{3} } + y \bigg) \\  \\ \\  \\

4 0
2 years ago
A room has the area of 60 square meters and perimeter of 32 meters .What are the length and width of the room?
ad-work [718]
I am sorry but i don't no
4 0
3 years ago
Fifty percent of students in your school own a bike. Of a sample of students in your school, the ratio of students who own a bik
Svetradugi [14.3K]

Answer:

Yes

Step-by-step explanation:

If 4 is half of 8, and 50% is half of 100%, then 4:8 is an accurate ratio depecting that half the school owns a bike.

8 0
3 years ago
Read 2 more answers
Find the value of x such that the data set has the given mean. 98, 123, 105, 114, 109, x ; mean 113 x = (Type an integer or a de
kotykmax [81]

Answer: 129

Step-by-step explanation:

the mean is the average of the data. including x, there are 6 data points

average = total/6

average = (98 + 123 + 105 +114 +109 + x) / 6

113 = (98 + 123 + 105 +114 +109 + x) / 6

113 = (549+ x) / 6

678 = 549 + x

x = 129

6 0
3 years ago
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