What is the longest line segment that can be drawn in a right rectangular prism that is 13 cm long, 8 cm wide and 7 cm tall?

Answers

Answer 1
Final answer:

The longest line that can be drawn in a right rectangular prism (a box) is the diagonal from one corner to the opposite corner. This is called the space diagonal. It can be calculated using the Pythagorean theorem in three dimensions. In this case, the longest line is 16.8 cm.

Explanation:

The longest line that can be drawn in a right rectangular prism, also known as a box, is the diagonal drawn from one corner of the box to the opposite corner. This longest line is also known as the space diagonal of the box. To find the length of the space diagonal, we use the Pythagorean theorem in three dimensions, which is given by the formula d = √(l² + w² + h²), where l, w, and h are the length, width, and height of the box respectively.

In this case, the length l is 13 cm, the width w is 8 cm, and the height h is 7 cm. Thus, the length of the space diagonal is d = √((13 cm)² + (8 cm)² + (7 cm)²) = √(169 cm² + 64 cm² + 49 cm²) = √282 cm² = 16.8 cm. Therefore, the longest line segment that can be drawn in the box is 16.8 cm long.

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Answer 2

The longest line segment that can be drawn in the prism is approximately 16.79 cm long.

 First, we calculate the diagonal of the base of the prism, which is the rectangle with dimensions 13 cm by 8 cm.

The diagonal of this rectangle can be found using the Pythagorean theorem in two dimensions:

[tex]\[ d_{\text{base}} = \sqrt{l^2 + w^2} \][/tex]

[tex]\[ d_{\text{base}} = \sqrt{13^2 + 8^2} \][/tex]

[tex]\[ d_{\text{base}} = \sqrt{233} \][/tex]

 Next, we find the diagonal of the entire prism by considering the diagonal of the base and the height of the prism:

[tex]\[ d_{\text{prism}} = \sqrt{d_{\text{base}}^2 + h^2} \][/tex]

[tex]\[ d_{\text{prism}} = \sqrt{(\sqrt{233})^2 + 7^2} \][/tex]

[tex]\[ d_{\text{prism}} = \sqrt{282} \][/tex]

 Therefore, the longest line segment that can be drawn in the prism is the space diagonal, which is approximately:

[tex]\[ d_{\text{prism}} \approx \sqrt{282} \][/tex]

[tex]\[ d_{\text{prism}} \approx 16.79 \text{ cm} \][/tex]

 So, the longest line segment that can be drawn in the prism is approximately 16.79 cm long.


Related Questions

A baby weighs 132 ounces when born.The baby gained 60 ounces. How many pounds is the baby now?
pLeAsE I NeEd HeLp

Answers

Answer:

12 pounds

Step-by-step explanation:

New Weigh = 132 + 60 =192 ounces

(New Weigh = Old Weigh + Weigh gained)

Since 1 pound = 16 ounces

New Weigh = 192 ÷ 16 = 12 pounds

therefore New

Answer: 12 pounds!

Step-by-step explanation:

I hope it helps!

Good luck!

Ben and Roberto each own stores that sell video games. A) Ben’s Game World is having a sale on video games. The store is offering a sale pack of 4 video games for $43.80. What is the unit price of a video game in the sale pack? What would 7 games cost at Ben's Game World? B) Roberto’s Electronics is also having a sale on video games. The unit price of any video game at Roberto’s Electronics is 3/5 of the unit price of a video game in the sale pack at Ben’s Game World. How much would it cost a customer for 7 video games at Roberto’s Electronics?

Answers

Ben- unit price is 10.95

7 games= 76.65

Roberto- unit price is 6.57

7 games=  45.99

Final answer:

The unit price of a video game at Ben's Game World is $10.95, and 7 games would cost $76.65. Video games at Roberto's Electronics would cost $6.57 per game after applying the discount, with 7 games totaling $45.99.

Explanation:

The student has asked for help with finding the unit price of video games in a sale at Ben's Game World and comparing this to the cost of video games at Roberto's Electronics. We are given that Ben is selling a pack of 4 video games for $43.80. To find the unit price, we divide the total cost by the number of games.

Calculate the unit price of a video game at Ben's Game World by dividing the total pack price by the number of games in the pack: $43.80 / 4 games = $10.95 per game.To find the cost for 7 games at Ben's game store, multiply the unit price by 7: $10.95 * 7 games = $76.65.Roberto's Electronics sells video games at 3/5 the price of Ben's unit price. First, calculate this discounted unit price: $10.95 * (3/5) = $6.57.To find the cost for 7 games at Roberto's store, multiply this discounted unit price by 7: $6.57 * 7 games = $45.99.

The circumference of a circle is 3.14 inches. Find the radius of the circle in inches. Round to the nearest whole number. Justify your answer. Please help me all my stuff is due Friday!

Answers

Answer:

0.5

Step-by-step explanation:

The formula for circumference is:

pi * d

3.14 = 3.14*d

1 = d

Since the radius is 1/2 of diameter, r = 0.5

HELP HEL HELP HELP HELP HELP HELP HELP PLEASE

Answers

Answer:

(2,4) and (5,1) --> negative slope

(6,-3) and (-6, -3) --> zero slope

(3,5) and (-1,2) --> positive slope

(-7,8) and (-7,0) --> undefined slope

Step-by-step explanation:

To find the slope of a function, we use the formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{rise}{run}[/tex] (rise/run)

1. [tex]m=\frac{1-4}{5-2} =-1[/tex] (negative slope)

2. [tex]m = \frac{-3--3}{-4-6} =0[/tex] (zero slope)

3. [tex]m = \frac{2-5}{-1-3} =\frac{3}{4} =0.75[/tex] (positive slope)

4. [tex]m=\frac{-7-8}{-7--7} =\frac{-15}{0} = ?[/tex] (undefined slope)

What Is the slope of the line on the graph?

Answers

Answer:

1/2 or 0.5 either way they're both right

Step-by-step explanation:

The slope of the line is 1/2

The formula for calculating the slope of the line is expressed as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

From the graph, using the coordinate points (0, 2) and (-4, 0)

Get the slope using the coordinate;

[tex]m=\frac{0-2}{-4-0}\\m=\frac{-2}{-4}\\m=\frac{1}{2}[/tex]

Hence the slope of the line is 1/2

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what is ( ⅚ -(⅓ )²)x ½
in a fraction please

Answers

Answer: 7/9

I hope that helps. That’s the answer I got.

Answer:

Step-by-step explanation:

[tex][ \frac{5}{6}-(\frac{1}{3})^{2}]*\frac{1}{2}=[\frac{5}{6}-\frac{1}{9}]*\frac{1}{2}\\\\=[\frac{5*3}{6*3}-\frac{1*2}{9*2}]*\frac{1}{2}\\\\=[\frac{15}{18}-\frac{2}{18}]*\frac{1}{2}\\\\=[\frac{15-2}{18}]*\frac{1}{2}\\\\=\frac{13}{18}*\frac{1}{2}\\\\=\frac{13}{36}[/tex]

[ 5,-8,2,y] - [x,7,11,4]=[-2,z,13,13] solve for x y and z​

Answers

Answer:

  [x, y, z] = [7, 17, -15]

Step-by-step explanation:

The list equation resolves to four equations involving corresponding list elements:

  5 -x = -2   ⇒   x = 7

  -8 -7 = z   ⇒   z = -15

  2 -11 = 13   ⇒   looks like a wrong sign somewhere; this is FALSE

  y -4 = 13   ⇒   y = 17

_____

Comment on the question

Since one of the equations turns out to be false, it makes us suspect there may be typos in the others as well. YMMV

I need help like now
Please and thank you

Answers

Answer:

$340.54 flooring

$116.21 paint

$107.73 trim

=$564.48

Step-by-step explanation:

the living room is 2418ft^3

area is 201.5ft^2

perimeter is 57ft

Minimum of the data is ?, The first quartile is ?,
The median of the data is ?,
Third quartile is ?,
The Maximum of the data is ?

Answers

Answer:

Step-by-step explanation:

min= 40

q1=43

med=61

Q3=65

max=97

you just need to put data into the table and do 1-var stats for this problem

The minimum data value is: 40

The first quartile is: 43

The median data value is: 61

The third quartile is: 65

The maximum data value is: 97

The data is presented in a stem and leaf plot.

What is stem and leaf plot?

A stem and leaf plot is a defined as table where values of data are split into a stem and leaf. The first digit or digits will be written in stem and the last digit will be written in leaf

According to the 1st row: 4 | 0 1 3

The weights are: 40, 41, 43

According to the 2nd row: 5 | 0 8

The weights are: 50, 58

According to the 3rd row: 6 | 1 2 3 5

The weights are: 61, 62, 63, 65

According to the 4th row: 7 | 8

The weight is: 78

According to the 6th row: 9 | 7

The weight is: 97

So, all the data for the weights are:

40, 41, 43, 50, 58, 61, 62, 63, 65, 78, 97

We can now determine the five-number summary as follows:

The minimum data value is: 40

(40), 41, 43, 50, 58, 61, 62, 63, 65, 78, 97

The first quartile is: 43

40, 41, (43), 50, 58, 61, 62, 63, 65, 78, 97

The median data value is: 61

40, 41, 43, 50, 58, (61), 62, 63, 65, 78, 97

The third quartile is: 65

40, 41, 43, 50, 58, 61, 62, 63, (65), 78, 97

The maximum data value is: 97

40, 41, 43, 50, 58, 61, 62, 63, 65, 78, (97)

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A recipe for bread calls for 4 1/4 cups of flour. Which expression gives the number of cups of flour needed if you want to make 3 1/2 batches of this recipe?

Answers

Answer:

3 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 1/4. 3.5

1.1

Scientific notation is the product of a coefficient that is greater than or equal to one but less than 10, and a power of 10.

Answers

Answer:

Sample Response: Scientific notation is used to represent very large and very small numbers. Scientific notation is the product of a coefficient that is greater than or equal to one but less than 10, and a power of 10.

im sorry that other person answered, well wierd but thats what im here for.

:)

Can someone help me with this it's making no sense to me

Answers

Answer:

The most reasonable is 2 h

Step-by-step explanation:

If you see the graph is decreasing in hours while is increasing in years. When a person is 45 years the amount of daily physical activity is 3 hours, so a person that is 50 years needs to do less than 3 hours a day and the only option less than 3 hours is 2 hours.

evaluate (tan 60)(cos 45)

Answers

Answer: the tan. Of 60 is .3200

The cos. Of 45 is .5253

Hope this helps :)

Step-by-step explanation:

Answer:

[tex] \sqrt{ \frac{3}{2} } [/tex]

Step-by-step explanation:

[tex] \tan(60) \cos(45) = \sqrt{3} \times \frac{1}{ \sqrt{2} } [/tex]

[tex] = \sqrt{ \frac{3}{2} } \: [/tex]

Complete the sentence below with less than,

greater than or equal to.

The sum of the first 100 even natural numbers is

the sum of the first 101 odd

natural numbers.

Answers

Answer: The Answer is "less than"

Step-by-step explanation:

To find the sum of a series, you find the difference between the first and last term, multiply that by the number of terms, then divide by 2.

For the even numbers, 2 is the first term and 200 is the 100th term (because 2+(100-1)2 is equal to 200). So, (100(2+202)/2 = 10100.

For the odd numbers, 1 is the first term and 201 is the 101th term (because 1+(101-1)2 is equal to 201). So, (101(1+202))/2 = 10251.5.

10100<10251.5 so the sum of the first 100 even numbers is less than the sum of the first odd 101 numbers.

The sum of the first 100 even natural numbers is smaller than the sum of the first 101 odd natural numbers.

What is an even number?

A number that is divisible by two into two equal whole numbers is called an even number. Even numbers are those that end in 0, 2, 4, 6, and 8.

The problem can be solved using the arithmetic sequence. The sum of the first 100 even numbers will be,

[tex]\text{Sum of first 100 even numbers} = \dfrac{100}{2} \times [2(2) +(100-1)2]=10,100[/tex]

The sum of the first 101 odd numbers will be,

[tex]\text{Sum of first 101 odd numbers} = \dfrac{101}{2} \times [2(1) +(101-1)2]=10,201[/tex]

Hence, the sum of the first 100 even natural numbers is smaller than the sum of the first 101 odd natural numbers.

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Use the X method to find the solutions of
6.x2 + 2x - 20 = 0.
X =
X=

Answers

x = -5/3 = -1.667
x = 2

Which statement is true about the relative areas of triangle ABC and triangle XYZ is true

Answers

Answer:

The answer is A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

What is three and fourteen hundredths as a decimal number.

Answers

Answer:

3.14

Step-by-step explanation:

A manufacturer makes conical funnels for professional painters. The
funnels are formed from plastic with an 8-inch diameter base and height
of 9 inches. After the cones cool, a machine cuts off 1 inch of the tip to
leave a 1-inch diameter hole in the end. What is the volume of the funnel?
Round your answer to the nearest tenth and do NOT include units.

Answers

Answer: 151

Step-by-step explanation:

In this situation we have two cones, the big cone with volume [tex]V_{big}[/tex] and the small cone with volume [tex]V_{small}[/tex].

Now, if we want to know the total volume [tex]V_{T}[/tex] we have to substract [tex]V_{small}[/tex] from  [tex]V_{big}[/tex], but first we have to calculate each volume:  

For the big cone:

[tex]V_{big}=\frac{\pi R^{2} H}{3}[/tex]

Where:

[tex]R=\frac{Diameter}{2}=\frac{8 in}{2}=4 in[/tex]

[tex]H=9 in[/tex]

Then:

[tex]V_{big}=\frac{\pi (4 in)^{2} 9 in}{3}[/tex]

[tex]V_{big}=150.79 in^{3}[/tex] Volume of big cone

For the small cone:

[tex]V_{small}=\frac{\pi r^{2} h}{3}[/tex]

Where:

[tex]r=\frac{diameter}{2}=\frac{1 in}{2}=0.5 in[/tex]

[tex]h=1 in[/tex]

Then:

[tex]V_{small}=\frac{\pi (0.5 in)^{2} 1 in}{3}[/tex]

[tex]V_{small}=0.261 in^{3}[/tex] Volume of small cone

Calculating the total volume:

[tex]V_{T}=V_{big}-V_{small}[/tex]

[tex]V_{T}=150.79 in^{3}-0.261 in^{3}[/tex]

Finally:

[tex]V_{T}=150.52 in^{3} \approx 151 in^{3}[/tex]

Answer:

151 in^3

Step-by-step explanation:

Find the volume of the cones the subtract them to get your final answer

Pls help!!!!!!!!!!!!!!!!

Answers

Answer:

23 degrees

Step-by-step explanation:

62+95=157

180-157=23

Answer: The answer is 23 degrees. (Friend me and vote me brainliest)

Step-by-step explanation: A triangle is always equal to 180 degrees. So when they gave you both sides of the triangle, you add them up and subtract your sum from 180.

Find the values of variables in DEFG


Please help show me how to solve this

Answers

Answer:

dav d

Step-by-step explanation:

Of 80 people attending a dance 28 dance with their hands touching the floor. If four people at the dance are selected at random, determine the probability that each of the 4 dance with their hands touching the floor.

`PLEASE HURRY ITS A QUIZ

Answers

Answer: The probability is 0.013

Step-by-step explanation:

Out of 80 people, 28 of them dance with the hands touching the ground.

Then, the probability of selecting at random someone that dances with the hands touching the floor is equal to the number of persons that dance in that way, divided by the total number of persons.

For the first selection, this is p1 = 28/80

now, the probability in the second selection will be 27/79, because we have selected 1 out of the 28 (and also 1 out of the 80)

for the third and the fourth we have:

p3 = 26/78

p4 = 25/77

Then the probability of the fourth events is equal to the product of the four probabilities:

P = (28/80)*(27/79)/(26/78)/(25/77) = 0.013

Answer:

The probability that each of the 4 dance with their hands touching the floor is 0.0129.

Step-by-step explanation:

There are a total of 80 people and out of them, 28 dance with their hands touching the floor. The probability of selecting a person who has their hands touching the floor while dancing can be computed as 28/80.

We are asked to computed the probability that four people are selected at random and all four of them dance with their hands touching the floor. The probability for selecting the first person is 28/80. For the second person, the total no. of people are now 79 and the people who can dance with their hands touching the floor are 27. So, the probability is 27/79. Similarly, for the third person, the probability is 26/78 and for the fourth person, the probability is 25/77.

So, the probability that all four people selected dance with their hands touching the floor is:

28/80 * 27/79 * 26/78 * 25/77 = 0.0129


The table shows the results of rolling a die 100 times. What was the average value per roll?

Answers

where is the table ??

If the chance of rain is 80%, what is the likelihood of it raining?

Answers

Answer:

More likely

Step-by-step explanation: It wouldn't be likely because that is 100% of that happening

Answer:

It would be raining but not raining cats and dog and then goes away like 15-20 minutes. But the weather can change how much it is going to rain like if its hot and sunny at a high number it is 50 chance to not rain but if its like a low weather then its likely to rain.

I really hope this helps! But if it doesn't I'm sorry. (OwO)

The measure of angle M is_degrees.

Answers

Answer:

m=37

Step-by-step explanation:

The 2 angles are complementary, or add to 90 degrees. Wee know this because of the little square in the corner that indicates a right angle, which is equal to 90 degrees.

m+53=90

Solve for m by getting m by itself. To do this, subtract 53 from both sides to "reverse" the addition being done to m.

m+53-53=90-53

The 53s on the left cancel, and we are left with:

m=37

Answer:

M = 37°

Step-by-step explanation:

M + 53° = 90°

M = 90° - 53°

M = 37°

Which choice could be used in proving that the given triangles are similar?

Answers

If at least 2 of the angles are the same
If at least 2 of the angles are the exact same as each other. Hope I helped

A cereal box is 6 1/2 inches long ,3 1/2 inches wide , and 12 inches high .What is the volume of the box?

Answers

Answer:

273

Step-by-step explanation:

base (l times w) times height

Answer:

273 inch³

Step-by-step explanation:

v = l*h*w

v= 6 1/2 * 3 1/2 * 12

v= 13/2 * 7/2 * 12

v= 273

I really need help with 15 and 16 please

Answers

Answer:

  15. 50 kg

  16a. 5 kg

  16b. 3.75 kg

Step-by-step explanation:

The formula relating force, mass, and acceleration can be solved for mass. This formula will apply to both problems. We'll use m for both "mass" and "meters". We presume you can avoid getting mixed up by understanding that meters is used in the context of acceleration: m/s².

  F = ma

  m = F/a . . . . . divide by a

__

15. m = (250 N)/(5 m/s²) = 50 kg

__

16a. m = (15 N)/(3 m/s²) = 5 kg

16b. m = (15 N)/(4 m/s²) = 3.75 kg

_____

Comment on units

Especially for physics problems, I like to keep the units with the numbers. It is helpful to remember that Newtons are equivalent to kg·m/s². So, dividing Newtons by acceleration in m/s² will give mass in kg. Since you're familiar with F=ma, it's not too hard to remember that the units of force (N) are the product of the units of mass (kg) and acceleration (m/s²).

The nth term of a sequence is n-4
a) Work out the first three terms of the sequence.
b) Work out the tenth term of the sequence.

Answers

Answer:

Step-by-step explanation:

nth term = n - 4

A) 1st term = 1 - 4 = -3

2nd term = 2 - 4 = -2

3rd term = 3 - 4 = -1

First three terms are:  -3, -2, -1

b) tenth term = 10 - 4 = 6

a) The first three terms of the sequence are -3, -2, and -1.

b) The tenth term of the sequence is 6.

a) To find the first three terms of the sequence with the nth term given as n - 4, we can substitute the values of n from 1 to 3 into the formula:For n = 1:nth term = n - 4 = 1 - 4 = -3For n = 2:nth term = n - 4 = 2 - 4 = -2For n = 3:nth term = n - 4 = 3 - 4 = -1So, the first three terms of the sequence are: -3, -2, -1.b) To find the tenth term of the sequence, we can again use the formula with n = 10:nth term = n - 4 = 10 - 4 = 6So, the tenth term of the sequence is 6.

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20 POINTS! WILL MARK BRAINIEST FOR FIRST CORRECT ANSWER!



The figures in (a) and (b) below are made up of semicircles and quarter circles; The figure in (c) shows a quarter of a circle in a square. Find the area and the perimeter of each figure in terms of π.





Answers

Answer:

https://brainly.com/question/8182874

Step-by-step explanation:

Answer:

Area: 5π/2 in²

Perimeter: (3π+2) in

step-by-step explanation:

Area =

larger semicircle + small semicircle

= ½(pi × r1²) + ½(pi × r2²)

r1 = 2 in

r2 = 2/2 = 1 in

Area:

½(pi × 2²) + ½(pi × 1²)

= 2pi + ½pi

= 5pi/2 in²

Perimeter:

½(2pi × r1) + ½(2pi × r2) + r1

½(2pi × 2) + ½(2pi × 1) + 2

2pi + pi + 2

3pi + 2

When you square six times a number, you get two more than the number.

Answers

Answer:the answer is 6

Step-by-step explanation:

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