The maximum length of the poster that can be put in the box is [tex]28in[/tex].
CuboidIn a cuboid, the longest dimension is the diagonal of the cuboid.
Diagonal = [tex]\sqrt{(length)^{2}+(width)^{2}+(height)^{2} }[/tex]
How to calculate the diagonal of a cuboid?Let, [tex]l=[/tex] the length of the cuboid
[tex]b=[/tex] the width of the cuboid
[tex]h=[/tex] the height of the cuboid
And [tex]d=[/tex] the diagonal of the cuboid
So, as per the formulae [tex]d=\sqrt{l^{2}+b^{2}+h^{2} }[/tex]
Assigning the given values,
[tex]l=24[/tex]
[tex]b=8[/tex]
[tex]h=12[/tex]
Now, calculate [tex]d[/tex] using the formulae,
[tex]d=\sqrt{24^{2}+8^{2}+12^{2}}=\sqrt{576+64+144}=\sqrt{784}=28[/tex]
Hence, the maximum length of the poster that can be put in the box is [tex]28in[/tex].
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The longest poster that fits in the box is 28 inches, matching the diagonal length. Multiple 26-inch posters fit due to the box's length of 24 inches.
To determine the longest poster that can fit inside the box, we need to find the length of the diagonal of the box, as this represents the maximum length a poster can have and still fit within the box.
Given dimensions of the box:
- Height (h) = 12 inches
- Length (l) = 24 inches
- Width (w) = 8 inches
We will use the formula for the diagonal ( d ) of a rectangular box:
[tex]\[ d = \sqrt{h^2 + l^2 + w^2} \][/tex]
Substitute the given values:
[tex]\[ d = \sqrt{12^2 + 24^2 + 8^2} \][/tex]
[tex]\[ d = \sqrt{144 + 576 + 64} \][/tex]
[tex]\[ d = \sqrt{784} \][/tex]
[tex]\[ d = 28 \text{ inches} \][/tex]
Therefore, the diagonal ( d ) of the box is 28 inches.
Now, the longest poster that can fit inside the box cannot exceed this diagonal length of 28 inches. Hence, the longest poster that can fit in the box is 28 inches in length.
Regarding why you can fit multiple 26-inch posters but only one 28-inch poster:
- The box is 24 inches long, so a 26-inch poster can fit along the length of the box without exceeding it.
- However, a 28-inch poster matches the diagonal length exactly, meaning it stretches from one corner of the box to the opposite corner, utilizing the maximum space available inside the box. Trying to fit more than one 28-inch poster would require overlapping or exceeding the box's dimensions, which is not possible.
In conclusion:
- The longest poster that can fit in the box is **28 inches** in length, corresponding to the length of the diagonal of the box.
- You can fit multiple 26-inch posters in the box because each poster fits within the length of the box without overlapping or exceeding the dimensions.
3x-61=2x-50
I need the answer
Answer: [tex]x = 11[/tex]
Solving for variable x
Move all terms containing x to the left, all other terms to the right
Add -2x to each side of the equation
[tex]-61 + 3x + -2x = -50 + 2x + -2x[/tex]
Combine like terms: 3x + -2x = 1x
[tex]-61 + 1x = -50 + 2x + -2x[/tex]
Combine like terms: 2x + -2x = 0
[tex]-61 + 1x = -50 + 0\\-61 + 1x = -50[/tex]
Add 61 to each side of the equation.
[tex]-61 + 61 + 1x = -50 + 61[/tex]
Combine like terms: -61 + 61 = 0
[tex]0 + 1x = -50 + 61\\1x = -50 + 61[/tex]
Combine like terms: -50 + 61 = 11
[tex]1x = 11[/tex]
Divide each side by 1
[tex]1x/1=11/1\\x=11[/tex]
Help me please!! Geometry is my worse subject
Answer:
72 meters squared
Step-by-step explanation:
ABC or FED
(4 x 6)/2
18
FED + ACDF + ABC
18 + 36 + 18
A = 72
Gabriella asked 555 of her hundreds of coworkers how much storage space they were currently using on their computer. Here are their responses (in gigabytes): 4, 8, 8, 9, 114,8,8,9,114, comma, 8, comma, 8, comma, 9, comma, 11 The mean of these amounts is \bar x=8 x ˉ =8x, with, \bar, on top, equals, 8 gigabytes. What is the standard deviation? Round your answer to two decimal places. s_x\approxs x ≈s, start subscript, x, end subscript, approximately equals gigabytes
Answer:
The standard deviation of the sample is 2.55 gigabytes
Step-by-step explanation:
Here we have the responses as follows;
Storage space usage on their computer [tex]x_i[/tex]
The number of respondents or sample size, n = 5
[tex]x_i[/tex] [tex](x_i - \bar x)[/tex] [tex](x_i - \bar x)^{2}[/tex]
4 -4 16
8 0 0
8 0 0
9 1 1
11 3 9
∑ 40 26
The sum = ∑X = 4 + 8 + 8 + 9 + 11 = 40
The mean = (The sum)/(The count) = 40/5 = 8
Formula for population standard deviation is;
[tex]\sigma = \sqrt{\frac{\Sigma (x_i - \mu)^2}{n } }[/tex]
Where:
σ = Population standard deviation
μ = Population mean
Since we are dealing with only 5 out of her hundreds of coworkers we are dealing with a sample therefore;
The formula for sample standard deviation is;
[tex]s = \sqrt{\frac{\Sigma (x_i - \bar x)^2}{n - 1} }[/tex]
Where:
s = Sample standard deviation
n = Sample size
[tex]x_i[/tex] = Each value of the sample
[tex]\bar x[/tex] = Sample mean
We find each value of [tex](x_i - \bar x)[/tex] by subtracting the x values from the mean, 8, as in the table above, next we find [tex](x_i - \bar x)^{2}[/tex] by squaring the [tex](x_i - \bar x)[/tex].
Next, we find the sum of the differences from the mean square values from the table after which we divide by n - 1, to get [tex]{\frac{\Sigma (x_i - \bar x)^2}{n - 1} } = \frac{26}{5 - 1} = \frac{26}{4} = 6.5[/tex]
We find the root of the result which gives us the standard deviation hence
√6.5 = 2.5495.
Standard deviation, s = 2.5495 ≈ 2.55 to two significant places of decimal.
After making a table for summation the standard deviation of the sample is 2.55 gigabytes.
Use the formula for population standard deviation is:
[tex]\sqrt{\dfrac{\sum{(x_i - \mu)^2}}{n}[/tex]
Where:
σ = Population standard deviation
μ = Population mean
The formula for sample standard deviation is;
[tex]\sqrt{\dfrac{\sum{(x_i - X)^2}}{n-1}[/tex]
Where:
s = Sample standard deviation
n = Sample size
[tex]x_i[/tex] = Each value of the sample
X = Sample mean
Since we are dealing with only 5 out of her hundreds of coworkers we are dealing with a sample, therefore;
The storage used is represented by [tex]x_i[/tex]
The number of respondents or sample size represented by n
Then n = 5
The table for summation is attached below.
Find the sum of the differences from the mean square values from the table after which we divide by n - 1,
[tex]\dfrac{\sum{(x_i - X)^2}}{n-1} = \dfrac{26}{5-1}\\\\\dfrac{\sum{(x_i - X)^2}}{n-1} =6.5[/tex]
Find the root of the result which gives us the standard deviation hence
√6.5 = 2.5495.
Hence,
Standard deviation,
s ≈ 2.55 about two significant places of decimal.
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What is the product? 12x/2y • 3y^2/24x^3
Answer: [tex]\frac{3}{4} x^4y^3[/tex]
According to a disease control center, 26% of people in a certain country have high blood pressure. If a person in this country is selected at random, determine the odds in favor of this person having high blood pressure.
Answer:
25
Step-by-step explanation:
Lets choose america and lets say there are 100 people in america then 25 I think tell me if it helped
What is the slope for the line PERPENDICULAR to the line shown in the graph?
A) -3
B) -1/3
C) 3
D) 1/3
"If x = y, then x + 4 = y + 4" represents the ________ property of equality.
Question 9 options:
A)
subtraction
B)
addition
C)
transitive
D)
substitution
Answer:
B
Step-by-step explanation:
My three friends and I have dinner together every weekend. Each weekend, two of us cook and the other two clean up afterwards. How many different ways are there for us to choose who cooks and who cleans?
Final answer:
To find the number of different ways for the four friends to choose who cooks and who cleans, one can use combinators to calculate that there are 6 different combinations.
Explanation:
The student asked, "My three friends and I have dinner together every weekend. Each weekend, two of us cook and the other two clean up afterwards. How many different ways are there for us to choose who cooks and who cleans?" To solve this, we can use combinatorics, which is a branch of mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints.
There are four friends, so we want to know in how many ways we can select two of them to cook. The number of ways to choose the two people who will cook can be calculated using the formula for combinations, which is C(n, k) = n! / (k! * (n-k)!), where n is the total number of items, and k is the number of items to choose.
Here, n would be 4 (since there are four friends), and we want to choose 2 (the number of friends who will cook), so we get C(4, 2) = 4! / (2! * (4-2)!) = (4 * 3) / (2 * 1) = 6 ways to choose cooks. The other two automatically become the cleaners. So, there are 6 different ways for the four friends to choose who cooks and who cleans.
g(x) = 4x+1
What is g(3)?
Answer
13
Step-by-step explanation:
4(3)+1
12+1=13
Type A is 10 feet tall and grows at a rate of 9 inches per year. Type B is 7 feet tall and grows at a rate of 21 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
3 years
Step-by-step explanation:
Suppose you want to simulate surveying 100 people to find the date of the month (1st, 2nd, 3rd, . . .) each was born. You decide to simulate the survey by having your computer randomly list values 1 through 31. Would the simulation provide a fair representation of an actual survey of 100 people? Why or why not?
Yes, because all possible dates of the month would be represented.
No, because for the 12 months in the year not all of the dates are represented. No, because for the 12 months in the year each date is not equally likely.
Yes, because it is possible to get 100 random values in a simulation.
Answer:
No, because for the 12 months in the year each date is not equally likely.
Step-by-step explanation:
Not all months have 31 days, meaning that numbers as high as 31 will not be as common.
The proposed simulation overlooking the fact that not all months have 31 days, results in a bias for the dates 29th, 30th, and 31st. Therefore, it wouldn't represent the actual survey accurately.
Explanation:The simulation proposed would not provide a fair representation of an actual survey of 100 people for their birth dates. This is rooted in the fact that not all months have 31 days. The assumption of the simulation means that the dates from 1 through 31 have an equal likelihood of being selected, ignoring the fact that in reality, dates like the 30th and 31st may not be possible for all months. An accurate simulation would require consideration for these variations, meaning dates 1 through 28 should be uniformly represented, with the 29th, 30th, and 31st having conditional probabilities based on the month.
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A crew is made up of 8 men; the rest are women. If 32 % of the crew are men, how many people are in the crew?
Answer:
12
Step-by-step explanation:
(66 2/3)
---------- (x) = 8
100
Solve for x
(66 2/3)x = 800
x = 800/(66 2/3)
x = 800/(200/3)
x = 800(3/200)
x = 4(3)
x = 12
Two friends shop for fresh fruit. Jackson buys a watermelon for $8.85 and 3 pounds of cherries. Tim buys a pineapple for $3.35 and 2 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more Jackson spent.
Answer + Step-by-step explanation:
Jackson spent $8.85 on watermelon and p*3 dollars on cherries, which simplifies to 8.85 + 3p dollars.
Tim spent $3.35 on pineapple and p*2 dollars on cherries, which simplifies to 3.35 + 2p dollars.
To find how much more Jackson spent than Tim, we can subtract Tim's total cost from Jackson's total cost, giving:
(8.85 + 3p) - (3.35 + 2p) = 5.50 + p
So Jackson spent $5.50 + p more than Tim.
3b + 1 = -17
Show work please
Look at the attached picture
Hope it will be helpful to you
What can be concluded about the volume of the
composite figure? Check all that apply.
It is the difference of the shape's volumes.
It is the product of the shape's volumes.
It is the sum of the shape's volumes.
O
The volume in terms of pi is the exact volume.
Using the calculator to multiply by pi provides the
approximate volume.
The composite figure's volume is
tcm?
AnsweR: I did the hw and got the answers right here,
It is the sum of the shape’s volumes.
The volume in terms of pi is the exact volume.
Using the calculator to multiply by pi provides the approximate volume.
Step-by-step explanation:
The correct answer is :
It is the sum of the shape’s volumes.The volume in terms of pi is the exact volume.Using the calculator to multiply by pi provides the approximate volume.What is a volume of composite shapes?The volume of the composite solid is simply the sum of the volumes of its parts. For composite prisms, where the bases are a composite shape, the area of the bases is the sum of the areas of the parts it is made of.
How do you find the volume of a figure?Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height. How you refer to the different dimensions does not change the calculation: you may, for example, use 'depth' instead of 'height'.
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Plz help i will give brainliest
Answer:
I 7AM I you have the same problem as the one that was the same as a good friend and a friend
A polar bear migrates north during winter to hunt for its food on sea ice. The daily
average temperature decreases 3°C for every 100 km traveled. At the start of the bear's
journey, the temperature is 2°C. What is the temperature after 200 km of its journey?
Answer:
-4 degrees
Step-by-step explanation:
Starting at 2 degrees, you need to subract 6 since 200 km= 6 degrees and it decreases.
The temperature after 200 km of the polar bear's journey is -4° C.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
The daily average temperature decreases 3°C for every 100 km traveled
At the start of the bear's journey, the temperature is 2°C
The total distance traveled by the polar bear = 200 km
For 200 km, [tex](3+3)[/tex] totally 6° C should get decreased.
⇒ [tex](2-6)[/tex]
⇒ [tex]-4[/tex]
Hence we can conclude that the temperature after 200 km of the polar bear's journey is -4° C.
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The repeating decimal number 8.2151515... written as a fraction is
(Simplify your answer. Type a fraction.)
I really need someone to help me with this question ASAP.
Answer:
a=2, b=-20
Step-by-step explanation:
4(2xsquared -5x+3)= 8xsquared -20x +12
How many different triangles can be constructed with angle measurements 90°,45°,50° ?
Answer:
Infinite
Step-by-step explanation:
There can be infinite triangles with those angle measurements as long as they are similar triangles. This means that the sides are proportional.
What is the volume of a rectangular prism?
Answer:
multiply: Length x Width x Height
Step-by-step explanation:
help!! answer needed fast plz!
Answer:
umm whats the question?
Step-by-step explanation:
A line has a slope of 9 and a y-intercept of 5.What is its equation in slope-intercept form
Answer:
y=9x+5
Step-by-step explanation:
y=mx+b is the slope-intercept form where m is the slope and b is the y-intercept.
Given that m (the slope) = 9 and b (the y-intercept) = 5, we can substitute directly into the equation and get this answer:
y=9x+5
Answer the question simplify no work needed
1st page : 16 , 32 , 7
2nd page : (Going down) 8 , 4 , 2 , 15 , 3 , 35 , 12 , 1 , 105 , 25 , 21 , 90
Plz correct me if I'm wrong
The current year’s depreciation expense using the straight-line method and assuming only one depreciable property, is P20,000. What is the machine’s useful life when it was purchased for P200,000 with a salvage value of P20,000?
Answer:
Machine's useful number of years = 9 years
Step-by-step explanation:
Using the straight line method, depreciation is calculated as the difference between the cost of the equipment minus the salvage value, all divided by the number of useful years.
Yearly Depreciation
= (Cost - Salvage value) ÷ (Number of useful years)
Yearly depreciation = P20,000
Cost = P200,000
Salvage Value = P20,000
Number of useful years = n
20000 = (200000 - 20000) ÷ n
20000 = (180000/n)
n = (180000/20000) = 9 years
Hope this Helps!!!
Which of the following is the measure of XBA if ray BA bisects XBY which measures 70 degrees
Answer: The correct answer is C.35.
Step-by-step explanation:
70÷2=35
The value of the measure of XBA is,
⇒ 35 degree
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
We have to given that;
Here, ray BA bisects XBY which measures 70 degrees
Hence, The value of the measure of XBA is half of the measure of XBY.
So, We get;
the measure of XBA is,
⇒ 70 / 2
⇒ 35 degree
Thus, The value of the measure of XBA is,
⇒ 35 degree
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what is the maximum height
Answer:
the highest height would be 144
NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!
Answer:i think a or c
Step-by-step explanation:
Which graph shows a non-proportional linear relationship between x and y?
Answer: It is B
Step-by-step explanation: this is it because a linear line has a point 0,0 and B is the only one who does have that point.
What is the value of x
Answer:
x = 3
Step-by-step explanation:
[tex] \frac{24}{32} = \frac{9x - 9}{6x + 6} \\ \frac{3}{4} = \frac{3(3x - 3)}{3(2x + 2)} \\ \frac{3}{4} = \frac{(3x - 3)}{(2x + 2)} \\ 4(3x - 3) = 3(2x + 2) \\ 12x - 12 = 6x + 6 \\ 12x - 6x = 6 + 12 \\ 6x = 18 \\ x = \frac{18}{6} \\ x = 3[/tex]