A shipping company must design a closed rectangular shipping crate with a square base. The volume is 12288ft3. The material for the top and sides costs $2 per square foot and the material for the bottom costs $10 per square foot. Find the dimensions of the crate that will minimize the total cost of material.

The probability of getting an even number or a number less than 8 is:

P = 0.83

The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.

The numbers that are even or less than 8 are:

{1, 2, 3, 4, 5, 6, 7, 8, 10, 12}

So 10 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:

P = 10/12 = 0.83

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Let's assume that the number of shirts that must be sold to cover the costs is x.

The revenue from selling x shirts is 12x dollars, and the total cost is the sum of the setup fee and the cost per shirt multiplied by the number of shirts, which is 65 + 7x dollars.

To break even, the revenue must be equal to the cost:

12x = 65 + 7x

Subtracting 7x from both sides:

5x = 65

Dividing both sides by 5:

x = 13

Therefore, the student council must sell 13 shirts to break even.

To find the total costs, we can substitute x = 13 into the expression for the total cost:

65 + 7x = 65 + 7(13) = 156

So the total costs will be $156.

Answer:

The student council's costs will be $146 and they need to sell 13 shirts to cover their costs.

Step-by-step explanation:

Let's call the number of shirts sold "x".

The revenue from selling x shirts at $12 each is:

The total cost of making x shirts is:

In order to break even (i.e. cover their costs), the revenue must equal the total cost:

[tex]\sf:\implies 12x = 7x + 65[/tex]

Solving for x:

[tex]\sf:\implies 5x = 65[/tex]

[tex]\sf:\implies \boxed{\bold{\:\:x = 13\:\:}}\:\:\:\green{\checkmark} [/tex]

Therefore, the student council must sell 13 shirts to break even.

To find the total costs, we can substitute x = 13 into the total cost equation:

[tex]\sf:\implies Total\: Cost = 7(13) + 65 = \boxed{\bold{\:\:\$146\:\:}}\:\:\:\green{\checkmark} [/tex]

So the student council's costs will be $146 and they need to sell 13 shirts to cover their costs.

The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

The given table shows the prices for various amounts and kinds of bouquets sold by a florist. The prices depend on the number and type of flowers in the bouquet. The table shows prices for bouquets of 2 flowers with daisies, tulips, and roses.

The expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is $18.45 more expensive than a bouquet of tulips. This is because the cost of a 2-flower bouquet of daisies is $23.90 and the cost of a 2-flower bouquet of tulips is $60.80, so the difference between them is $36.90.

However, we subtract 2 from each price to get the price of the actual flowers in the bouquet, which are the same for both daisies and tulips. Therefore, we get the difference of $18.45.

Similarly, the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is $18.45 more expensive than a bouquet of daisies. Here, we subtract the price of a 2-flower bouquet of daisies plus the cost of 2 flowers from the price of a 2-flower bouquet of tulips.

Again, the actual cost of flowers in both bouquets is the same, so we get the difference of $18.45.

The expressions 23.90 - 60.80 and 60.80 - 23.90 represent the price difference between bouquets of daisies and tulips, respectively. The former expression gives a negative result of $36.90, which means that a bouquet of tulips is $36.90 more expensive than a bouquet of daisies.

The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

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They may choose to bring 4 chaperones or even more depending on their preferences and logistical constraints.

For the camping trip with 15 scouts, they will need at least 15/5 = 3 chaperones.

However, it's possible that they may want to have more than the minimum number of chaperones for additional supervision and safety. The number of chaperones they choose to bring may also depend on the ratio of chaperones to scouts that they want to maintain.

So, they may choose to bring 4 chaperones (1 chaperone for every 3.75 scouts), 5 chaperones (1 chaperone for every 3 scouts), or even more depending on their preferences and logistical constraints.

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Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's call the distance from the base of the plateau to our position "x". We can then use the tangent function to find x:

tan(20°) = opposite / adjacent

In this case, the opposite side is the height of the plateau (50 m) and the adjacent side is x. So we can write:

tan(20°) = 50 / x

To solve for x, we can rearrange this equation:

x = 50 / tan(20°)

Using a calculator, we get:

x = 143.45 meters (rounded to two decimal places)

Therefore, if the angle of elevation to the top of the plateau is 20 degrees, and the plateau is 50 meters high, we are approximately 143.45 meters away from the base of the plateau.

Answer:

The distance is 137.3739 feet.

Step-by-step explanation:

I hope this answer is right.

The number of customers surveyed were 15 customers.

The  greatest number of items purchased by a customer was 11 items.

The customers purchased 9 items is 2 customers.

The customers purchased at least 5 items was 7 customers.

The median number of items purchased was 3.

How many customers were surveyed?

1 (0 items) + 1 (1 item) + 2 (2 items) + 4 (3 items) + 0 (4 items) + 2 (5 items) + 0 (6 items) + 2 (7 items) + 0 (8 items) + 2 (9 items) + 0 (10 items) + 1 (11 items) = 15 customers

The greatest number of items purchased by a customer is 11 items. 2 customers purchased 9 items.

How many customers purchased at least 5 items?

2 (5 items) + 0 (6 items) + 2 (7 items) + 0 (8 items) + 2 (9 items) + 0 (10 items) + 1 (11 items) = 7 customers

To find the median, we need to find the middle value of the data. Since there are 15 customers, the median will be the 8th value when the data is ordered.

0, 1, 2, 2, 3, 3, 3, 3, 5, 5, 7, 7, 9, 9, 11

The median number of items purchased is 3.

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The probability of selecting a brown M&M from this bag is 0.

Since there are no brown M&Ms mentioned in your bag, the probability of selecting a brown M&M is 0. In probability terms, we can express this as:

Probability of selecting a brown M&M = Number of brown M&Ms / Total number of M&Ms

There are 0 brown M&Ms, and there are a total of 4 green + 6 yellow + 7 purple + 3 red = 20 M&Ms in the bag. So the probability is:

Probability = 0 / 20 = 0

Thus, the probability of selecting a brown M&M from this bag is 0, meaning it's impossible with the given information.

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Answer:

The answer to 1+1 is 2.

Answer:

2

Step-by-step explanation:

Therefore, the volume of the composite figure is approximately 419.05 cubic cm.

Volume is the amount of space occupied by a three-dimensional object or shape. It is measured in cubic units such as cubic centimeters, cubic inches, or cubic meters. The volume of an object can be calculated by multiplying the area of its base by its height, or by using specific formulas depending on the shape of the object. The volume of an object is an important parameter in many areas of science and engineering, such as physics, chemistry, fluid mechanics, and material science, as it allows us to determine how much space an object will occupy or how much material is needed to fill a container or build a structure.

Here,

The composite figure consists of a cylinder and two cones, so we need to find the volume of each of these shapes and add them together.

Volume of cylinder = πr²h

= π(4²)(5)

= 80π cubic cm

Volume of one cone = (1/3)πr²h

= (1/3)π(4²)(5)

= (1/3)(80π)

= 26.67π cubic cm

Volume of both cones = 2(26.67π)

= 53.34π cubic cm

Total volume of composite figure = Volume of cylinder + Volume of both cones

= 80π + 53.34π

= 133.34π

= 419.05 cubic cm (rounded to two decimal places)

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The artist used a total of $0.33 worth of paint for the project.

The artist purchased 2 liters of paint, which is equivalent to 2,000 milliliters of paint. This amount of paint was used to complete a project, and after the project was finished, there were 350 milliliters of paint left over.

To determine how much paint was used for the project, we subtract the amount of leftover paint from the total amount of paint purchased, which gives us 2,000 - 350 = 1,650 milliliters of paint used for the project.

The cost of the paint is 2 cents per milliliter, which is equivalent to $0.02/100 milliliters or $0.0002 per milliliter. To determine the cost of the paint used for the project, we multiply the amount of paint used by the cost per milliliter.

Therefore, the cost of 1,650 milliliters of paint used for the project can be calculated by multiplying 1,650 milliliters by $0.0002 per milliliter, which gives us $0.33.

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a) The mean is the midpoint of the distribution, the percentage of homes with a price greater than the mean is 19.7%.

b) The percentage of homes on the market for more than the mean number of days is 72.1%.

a) Firstly, the mean selling price of homes is $357.0 thousand, with a standard deviation of $160.7 thousand. To estimate the percentage of homes selling for more than $500.0 thousand, we can use the normal distribution. This assumes that the distribution of home prices is approximately normal. Using the standard normal distribution table, we can find the z-score for a price of $500.0 thousand.

z = (500.0 - 357.0) / 160.7 = 0.88

Using the z-score, we find that the percentage of homes selling for more than $500.0 thousand is approximately 19.7%.

b) Moving on to the days a home spends on the market, the mean is 30 days and the standard deviation is 10 days. To estimate the number of homes on the market for more than 24 days, we can again use the normal distribution. Assuming that the distribution of days on the market is approximately normal, we can find the z-score for 24 days as:

z = (24 - 30) / 10 = -0.6

Using the z-score, we find that the percentage of homes on the market for more than 24 days is approximately 72.1%.

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The area of the composite figure is equal to 104 square feet.

In this question we have a composite figure formed by a part of a rectangle and an entire triangle. The area formulas for a rectangle and a triangle are introduced below:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the area of the mural:

A = (10 ft) · (8 ft) - 0.5 · (10 ft) · (5 ft) + 0.5 · (14 ft) · (7 ft)

A = 104 ft²

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The greatest whole number that rounds to 500 when rounding to the nearest hundred is 550.

When rounding a number to the nearest hundred, you need to look at the digit in the tens place. If that digit is 5 or greater, you round up the hundreds digit; if it is less than 5, you round down the hundreds digit.

For example, let's say we have the number 2,548. The digit in the tens place is 4, which is less than 5, so we round down the hundreds digit (2) to get 2,500.

Now, if we are looking for the greatest whole number that rounds to 500 when rounded to the nearest hundred, we need to find the largest number that has 5 in the tens place and 0 in the ones place. That number is 550. When we round 550 to the nearest hundred, we get 500.

Therefore, the greatest whole number that rounds to 500 when rounded to the nearest hundred is 550.

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Answer:it would still be a 50/50 chance of it be tails

Step-by-step explanation:

a coin has 2 sides. The probability would be 1/2. That means if you flip it a even amount, there would be a 50/tip chance. Let me know if I’m correct.

A student would expect to pay approximately $7,096.47 for room and board in 2017. Rounded to the nearest hundredth, this is $7,096.47 rounded to $7,096.50.

What is Function ?

In mathematics, a function is a rule that assigns each element in a set (the domain) to a unique element in another set (the range). The domain and range can be any sets, but they are typically sets of real numbers.

The cost of room and board after t years since 2000 can be modeled by the equation:

C(t) = 4291[tex](1 + 0.031)^{t}[/tex]

where C(t) is the cost after t years.

To find out how much a student would expect to pay in 2017, we need to plug in t = 17 (since 2017 is 17 years after 2000) into the equation:

C(17) = 4291[tex](1 + 0.031)^{17}[/tex]

≈ 7,096.47

Therefore, a student would expect to pay approximately $7,096.47 for room and board in 2017. Rounded to the nearest hundredth, this is $7,096.47 rounded to $7,096.50.

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Evaluation of S12(x3 – 2x)dx is- 92.875

We can use the definition of the Riemann Sum to evaluate S12(x3 – 2x)dx as follows:

First, we need to choose the width of our intervals.

Let's choose Δx = 1/2, which means we will have 24 subintervals.
Now, we can use the formula for the Riemann Sum to calculate the sum of the areas of the rectangles.
S12(x3 – 2x)dx ≈ ∑[f(xi)Δx] from i=1 to i=24
where xi is the right endpoint of the ith subinterval,

f(xi) = x[tex]i^3[/tex] – 2xi is the height of the rectangle, and Δx = 1/2 is the width of the rectangle.
Evaluating this sum using the given formula, we get:
S12(x3 – 2x)dx ≈ [f(1/2) + f(1) + f(3/2) + ... + f(11)](1/2)
≈ [[tex](1/2)^3[/tex] – 2(1/2) + (1)^3 – 2(1) + (3/2[tex])^3[/tex] – 2(3/2) + ... + (11[tex])^3[/tex] – 2(11)](1/2)
≈ [- 2361/16](1/2)
≈ - 92.875
4) we can simply evaluate the given integral:
S2x2+x=2 = ∫(2[tex]x^2[/tex] + x)dx from 0 to 2
= [[tex]2/3 x^3 + 1/2 x^2[/tex]] from 0 to 2
= [[tex]2/3 (2)^3 + 1/2 (2)^2[/tex]] - [[tex]2/3 (0)^3 + 1/2 (0)^2[/tex]]
= 16/3
5), we can use the following formulas

to find the displacement and distance traveled by the particle over the given time interval:
Displacement = ∫v(t)dt from 1 to 5
Distance traveled = ∫|v(t)|dt from 1 to 5
where v(t) is the velocity function.
a) To find the displacement, we evaluate the integral:
∫v(t)dt = ∫(8 – 2t)dt from 1 to 5
= [8t – t^2] from 1 to 5
= [[tex]8(5) – (5)^2[/tex]] - [8(1) – [tex](1)^2[/tex]]
= 18 meters
b) To find the distance traveled, we evaluate the integral:
∫|v(t)|dt = ∫|8 – 2t|dt from 1 to 5
= ∫(8 – 2t)dt from 1 to 4 + ∫(2t – 8)dt from 4 to 5
= [8t – [tex]t^2[/tex]] from 1 to 4 + [-t^2 + 8t -16] from 4 to 5
= [8(4) – [tex](4)^2[/tex]] - [8(1) – [tex](1)^2[/tex]] + [[tex]-(5)^2[/tex] + 8(5) -16 -(-[tex](4)^2[/tex] + 8(4) -16)]
= 26 meters

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Lana would pick a non-striped marble about 294 times.

The probability of picking a marble that is not striped is 100% - 8% = 92% = 0.92. This means that for each pick, the probability of getting a non-striped marble is 0.92.

If Lana picks a marble and replaces it 320 times, the number of times she would pick a non-striped marble can be predicted by multiplying the probability of getting a non-striped marble by the number of picks.

So, the number of times she would pick a non-striped marble is:

0.92 x 320 = 294.4

Rounding to the nearest whole number = 294.

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5.58g of catalyst is required for 900g of reactants.

If 500g of reactants require 3.1g of catalyst, then for 900g of reactants, we can use the following proportion:

500g reactants / 3.1g catalyst = 900g reactants / x

Where x is the amount of catalyst required for 900g of reactants.

To solve for x, we can cross-multiply:

500g reactants * x = 3.1g catalyst * 900g reactants

Then, we can divide both sides by 500g reactants to isolate x:

x = (3.1g catalyst * 900g reactants) / 500g reactants

Simplifying this expression gives:

x = 5.58g catalyst

Therefore, 5.58g of catalyst is required for 900g of reactants.

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Answer:

The third graph from the top could be the graph of f(x) = (2/5)^x. As x approaches infinity, f(x) approaches 0.

The probability of the captain hitting a home run in his next two at-bats is 1/36, and the best simulations to model the situation are using a six-sided number cube or a random number generator between 1 and 60.

Determine the probability that the captain will hit a home run in his next two at-bats and find the best simulation to model the situation.
The probability of the captain hitting a home run in one at-bat is 1/6. To find the probability of hitting a home run in two consecutive at-bats, you can multiply the individual probabilities:

Probability = (1/6) * (1/6) = 1/36

Now let's evaluate the provided simulations:

1. Using a six-sided number cube: Yes, this can be used to model the situation because the probability of hitting a home run (1/6) and not hitting a home run (5/6) can be represented accurately by the numbers 1 and 2-6, respectively.
2. Using a three-sided number cube: No, this cannot be used to model the situation because the probability distribution is not accurately represented with only three sides.
3. Using a coin flip: No, this cannot be used to model the situation because the probability distribution is not accurately represented with only two outcomes (heads and tails).
4. Using a random number generator between 1 and 60: Yes, this can be used to model the situation because the probability of hitting a home run (1/6) and not hitting a home run (5/6) can be represented accurately by the numbers 1-10 and 11-60, respectively.

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No, 2352 is not a perfect square.

To find the smallest number by which 2352 must be multiplied so that the product is a perfect square, we need to factorize 2352 into its prime factors.

2352 = 2^4 x 3 x 7^2

To make it a perfect square, we need to multiply it by 2^2 and 7, which gives us:

2352 x 2^2 x 7 = 9408

Now, we can take the square root of 9408:

√9408 = √(2^8 x 3 x 7) = 2^4 x √(3 x 7) = 16√21

Therefore, the smallest number by which 2352 must be multiplied so that the product is a perfect square is 2^2 x 7, which gives us the square root of 9408 as 16√21.

Answer:

The smallest number by which 2352 must be multiplied so that the product is a perfect  square = 3

The square root of the new number = 84

Step-by-step explanation:

√2352 ≈ 48.5 so not a perfect square

Prime factorization of 2352 yields

2352 = 2 x 2 x 2 x 2 x 7 x 7 x 3

In exponential form this is
2⁴ x  7² x 3¹

So
[tex]\sqrt{2352} = \sqrt{2^4 \cdot 7^2 \cdot 3}\\\\= \sqrt{2^4} \cdot \sqrt{7^2} \cdot \sqrt{3}\\\\= 2^2 \cdot 7 \cdot \sqrt{3}\\\\= 28 \sqrt{3}[/tex]

To get rid of the radical in the square root and get a whole number, all you have to do is multiply [tex]\sqrt{2352}[/tex]  by √3

[tex]28 \sqrt{3} \cdot \sqrt{3} = 28\cdot 3 = 84\\\\84^2 = 7056 = 2352 \cdot 3\\[/tex]

This means that if you multiply 2352 by 3 it will become a perfect square

Check:
[tex]2352 \cdot 3 = 7056\\\\\sqrt{7056} = 84[/tex]

The correct number of beads is; 4 black, 8 red, and 4 blue. Option A

A molecular model is a depiction of molecules or chemical compounds made physically, visually, or mathematically in order to comprehend their behavior and characteristics. These models can range from real models made of plastic or metal to computer-generated graphics or mathematical formulae, and they can be straightforward or sophisticated.

There are four carbon atoms, eight hydrogen atoms and four oxygen atoms.

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Answer:5

Step-by-step explanation: The median of the lower quartile is 23 and the median of the upper quartile is 28. 28-23=5. The IQR is 5.

The number written as a percentage is:

772.5666118%

To do this, just multiply the number by 100%.

For example, for any number A, the percentage form of A is:

p = A*100%

Here the number is  7.725666118, then the percentage form of this number will be:

N =  7.725666118*100% = 772.5666118%

That is the number as a percentage.

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The new volume of the inflatable ball after the radius becomes half of the original one is 16π.

The original volume of the ball is given as 96π

The radius then becomes half of its original size which means if the radius of the ball is 'r' then the new radius becomes 'r/2'.

The formula for the volume of the ball is equal to, where 'r' is the radius of the ball. (4/3)π X r³

With this the original volume of the ball is

(4/3)π X r³

and the new volume of the ball after it's halved is

V₂ = (4/3)π X (r/2)³

After simplification

V₂ = (4/3)π X (r³/8)

The new volume of the ball is:

V₂ = (1/6) X πr³

So the new volume is (1/6) of the original volume. We can calculate this as

V₂ = (1/6) X 96π

= 16π

Therefore, the new volume of the inflatable ball is 16π.

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This will show that each family gets 5/16 of a pizza.

Sure, I'd be happy to help you with your question!

So, Savannah and Josiah read the following problem in their math class: Five rectangular pizzas were shared equally by 4 families. How much pizza did each family receive?

Savannah and Josiah solve the problem differently. Savannah gives each family 1 whole pizza and then divides the remaining pizza among the 4 families. Josiah divides all of the pizzas into fourths and then shares the fourths equally among the 4 families.

To illustrate both students' solutions, we can use Scratchpad. For Savannah's solution, we can draw 5 rectangular pizzas and then divide them into 4 equal parts each. Then, we can shade in 1 whole pizza and divide the remaining pizza equally among the 4 families. This will show that each family gets 1 whole pizza and a quarter of a pizza.

For Josiah's solution, we can draw 5 rectangular pizzas and then divide each pizza into fourths. Then, we can divide the fourths equally among the 4 families.

This will show that each family gets 5/16 of a pizza.

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The two digit Combinations that never appear in any of the passcodes are 5 and 6.

There are 49 different passcodes that can be used. The sum of the six digits of the current passcode is 81, which is a square number. Therefore, the current passcode is made up of three different two-digit square numbers with the sum of their digits equal to 9.

The possible combinations are

(16, 25, 40),

(16, 49, 16),

(25, 36, 20),

(36, 49, 4),

(49, 64, 9),

(64, 81, 16), and

(81, 16, 64).

The only combination that has the same first and sixth digits is (16, 25, 40), so the current passcode is 162540.

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Here is a two way table that shows the type of music a person likes compared to their gender:

|               | Males | Females | Total |
|---------------|-------|---------|-------|
| Jazz          | 13    | 0       | 13    |
| Rock          | 54    | 27      | 81    |
| Country       | 0     | 66      | 66    |
| Total         | 67    | 93      | 200   |

In this table, we can see that out of the 94 males surveyed, 13 of them liked jazz. Out of the 106 females surveyed, 27 of them liked rock and 66 of them liked country. Overall, out of the 200 people surveyed, 81 of them liked rock, 13 of them liked jazz, and 66 of them liked country.

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Answer:Go to the 6 number on the bottom line.Then go up until you reach 2

Step-by-step explanation:
|      
|
|
|
|        .  
|______

Should look like that-ish

Answer:

Step-by-step explanation:

Put the point to the right 6 times and up two times

Answer:

(x + 5)^2 + (y + 5)^2 = 16.

Step-by-step explanation:

(x - a)^2 + (y - b)^2 = r^2    where (a, b) is the centre and r =- the radius.

Here (a, b) = (-5, -5) and r = 4, so:

(x - (-5))^2 + (y - (-5))^2 = 4^2

(x + 5)^2 + (y + 5)^2 = 16