MATHEMATICS HIGH SCHOOL

A shipping company sells a rectangular box with dimensions of 12inches by 12 inches by 18 inches. Find the length of the longest
diagonal in the box.
24.7.
24.8
O 288
0 612

Answers

Answer 1

Answer:

24.7 inches

Step-by-step explanation:

Length = 18 inches

Width = 12 inches

Height = 12 inches

Length of the longest diagonal,d = length^2 + width^2 + height^2

d^2 = 18^2 + 12^2 + 12^2

d^2 = 324 + 144 + 144

d^2 = 612

d = √612

= 24.7 of inches

Length of the longest diagonal in the box = 24.7 inches

Answer 2

Answer:

Final answer:

The length of the longest diagonal in a box with dimensions 12 inches by 12 inches by 18 inches, calculated using the three-dimensional Pythagorean theorem, is approximately 24.7 inches.

Explanation:

The longest diagonal of a rectangular box can be found using the Pythagorean theorem, but in three dimensions. This length is also known as the space diagonal of the box. Specifically, if you have a box with length (l), width (w) and height (h), the equation for the space diagonal (d) is d = √(l2 + w2 + h2).

Substituting the given dimensions into the equation: d = √[(12)2 + (12)2 + (18)2] = √(144 +144 + 324) = √(612) which is approximately 24.7 inches long.

Learn more about Space Diagonal Length here:

brainly.com/question/31304395

#SPJ3

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the functions b(n)= 6n and represents the number of light bulbs B(n) that are needed for n chandeliers how many light bulbs are needed for 15 chandeliers

Answers

b(n) = 6n

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Debbie needs to fill juice cups for her little brother's birthday party. There are 20 juice cups and each juice cup holds 10 fluid ounces. The juice comes in 1-gallon bottles. How many 1-gallon bottles of juice will Debbie need to purchase? (1 quart = 32 fluid ounces, 1 gallon = 4 quarts)

Answers

she would need to buy at least 2 gallons of juice but she would have a little left over

20 juice cups(each juice cup holds 10 fluid ounces)=20*10 ounces so, you need to purchase: 200/128=1.562 gallons= 2 bottles of juice each containing one gallons

Answer: 2 bottles of juice for her little brothers birthday party

A theater has 675 seats. there are three times as many seats in a row as their are rows

Answers

Answer:

Step-by-step explanation:

let the number of rows=x

seats in each row=3x

so number of seats=x(3x)=3x²

3x²=675

x²=225

x=15

number of rows=15

and seats in each row=15×3=45

Answer: 15 rows with 45 seats each

Step-by-step explanation:

Let x = the number of rows, then 3x= the number of seats in a row.

seats × row= total

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PLEASE HELP !!!!!! WILL MARK THE BRAINLIEST

Answers

Answer:

hope its right :)

good luck!

Ethan‘s bank account listed a balance of $328.80. He originally opened the account with a $200 deposit and a simple interest rate of 4.6% If there were no deposit or withdrawals, how long ago was the account opened

Answers

Answer:

Step-by-step explanation:

$Interest=\frac {PRT}{100}$ where P is principal amount, R is rate in percentage and T is time.

Making T the subject of the formula,

$T=\frac {Interest * 100}{PR}$

For Ethan's case, Interest=$328.8-$200=$128.8

Substituting $128.8 for interest, 4.6% for rate and $200 for P we obtain

T=(128*100)/(4.6*$200)=14

Since the rate wasn't specified whether annually or monthly, the time can be 14 years or 14 months

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Answers

Write 24000 as the numerator and 50 as the denominator: 24000/50.

Notice that both the numerator and denominator have a common factor of 50.

Divide both the numerator and denominator by 50 to simplify the fraction:

(24000 / 50) / 50 = (24000 ÷ 50) / (50 ÷ 50) = 480 / 1

So, 24000/50 simplifies to 480/1, which is just 480 as a whole number. Therefore, 24000/50 = 480.

Dividing by 50 is the same as multiplying by 1/50, which is equivalent to 2/100.

The fraction 2/100 means we'll double 24000 to get 48000. Then remove 2 zeros at the end to get 480. The removal of two 0's is due to the division by 100.

Therefore, 24000/50 = 480

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

Dividing by 5 will follow a similar pathway. We can multiply by 1/5 aka 2/10

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Notice the numerator doubled to 48000, and then we remove a zero at the end.

All of this can be done using pure mental math only. Each answer can be confirmed with a calculator.

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