I have a square piece of card. I cut a triangle from each corner so that the remaining card is in the shape of a regular octagon. The perimeter of the regular octagon is 32cm. Work out length y

The dimensions of a rectangular prism are 6 cm long, 3 cm wide, and 4 ½ cm tall. 648 cubes are required to completely fill the rectangular prism.

The formula for calculating the rectangular prism's volume is:

Volume = Length x Width x Height

Substituting the given values, we get:

Volume = 6 cm x 3 cm x 4 ½ cm

Volume = 81 cm³

Since the cubes have an edge length of ½ cm, their volume is:

Volume of one cube = (1/2 cm)³ = 1/8 cm³

To find the number of cubes needed to fill the rectangular prism, we can divide the volume of the prism by the volume of one cube:

Number of cubes = Volume of prism / Volume of one cube

Substituting the values, we get:

Number of cubes = 81 cm³ / (1/8 cm³)

Number of cubes = 81 cm³ x 8

Number of cubes = 648

Therefore, 648 cubes are needed to fill the rectangular prism.

The complete Question is:-

A rectangular prism has a length of 6 cm, a width of 3 cm, and a height of 4 1/2cm. the prism is filled with cubes that have edge lengths of ½ cm. how many cubes are needed to fill the rectangular prism?

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Answer:

In a right triangle, one of the angles measures 90 degrees, and the other two angles are acute angles that add up to 90 degrees. Let's call the measures of the two acute angles x and y.

We know that x and y differ by 22 degrees. So we can set up an equation:

x - y = 22

We also know that x + y = 90, since the two acute angles add up to 90 degrees.

Now we can solve this system of equations for x and y. One way to do this is to add the two equations together, which eliminates y:

x - y + x + y = 22 + 90

2x = 112

x = 56

Now we can substitute x = 56 into one of the equations to find y:

x + y = 90

56 + y = 90

y = 34

Therefore, the measures of the two acute angles of the right triangle are 56 degrees and 34 degrees.

Answer:

4cm

Step-by-step explanation:

Area of a triangle=[tex]\frac{1}{2}[/tex]×b×h

[tex]\frac{1}{2}[/tex]×3cm×h=[tex]24cm^{2}[/tex]

L.C.M=2

6cmh=[tex]24cm^{2}[/tex]

h=[tex]24cm^{2}[/tex]÷6cm

h=4cm

Answer:

Step-by-step explanation:

area = [tex]\frac{1}{2} base[/tex]×height

  24 = [tex]\frac{1}{2}[/tex](3)×height

  24 = 1.5×height

  [tex]\frac{24}{1.5}[/tex] = [tex]\frac{1,5}{1,5}[/tex]height

  16 = height

The value of x is approximately 8.15.

To find the value of x, we need to use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the

radius of the base and h is the height of the cone. We know that the volume of the cone below is 392π, so we can set

up the equation:

[tex]392π = (1/3)πx^2h[/tex]

Simplifying, we can divide both sides by π and multiply by 3 to get:

[tex]1176 = x^2h[/tex]

Using the Pythagorean theorem, we can relate the height, radius, and slant height of the cone:

[tex]h^2 + r^2 = x^2[/tex]

Since the cone is a right cone, we know that the radius is half of the diameter, which is equal to x/2. Substituting this in,

we get:

[tex]h^2 + (x/2)^2 = x^2[/tex]

Simplifying:

[tex]h^2 = x^2 - (x/2)^2

h^2 = 3x^2/4[/tex]

Now we can substitute this expression for [tex]h^2[/tex] into our equation for the volume:

[tex]1176 = x^2(3x^2/4)[/tex]

Simplifying again:

[tex]1176 = 3x^4/4[/tex]

[tex]1568 = 3x^4[/tex]

[tex]x^4 = 1568/3[/tex]

Taking the fourth root of both sides:

[tex]x = (1568/3)^(1/4)[/tex]

x ≈ 8.15

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Answer: 14

Step-by-step explanation:

The constant of proportionality is equal to 12.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the variables representing the earnings and time must have the same constant of proportionality:

Constant of proportionality, k = y/x

Constant of proportionality, k = 36/3 = 60/5 = 72/6 = 84/7

Constant of proportionality, k = 12.

Therefore, the required equation is given by:

y = kx

y = 12x

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When comparing two group means, the degree of freedom refers to the number of scores free to vary once the means are known. Correct option is D.

The degree of freedom (df) is the number of independent pieces of information available in a study that may be used to estimate the value of the population parameter in question.

In layman's terms, the degree of freedom is the number of independent pieces of information that can be used to calculate a population parameter estimate in a statistical study. The degree of freedom (df) refers to the number of scores free to vary once the means are known.

This implies that there are a certain number of scores (or values) in the study that can be changed freely without affecting the mean of the study's scores. For instance, if the study's mean score is 75, the degree of freedom is the number of scores that may be adjusted without altering the mean score of 75.

As a result, the degree of freedom represents the number of values that can be varied to get a given statistic, such as the mean.

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After answering the presented question, we can conclude that With an IQR of  [tex]2.5[/tex] , Player B is the most consistent. Thus, option D is correct.

The IQR is a more robust measure of variability that is less vulnerable to outliers or extreme results. It is the difference between the dataset's 75th percentile (Q3) and 25th percentile (Q1). Player A has an IQR of [tex]5-2.5 = 2.5[/tex] , while Player B has an IQR of [tex]3-1.5 = 1.5[/tex]  .

Based on these calculations, we can see that Player A has a wider range, suggesting more variability in the data, but Player B has a narrower range and IQR, indicating less variability and higher consistency in the data. As a result, the right answer is:

Therefore, With an IQR of [tex]2.5[/tex]  , Player B is the most consistent.

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The two consecutive positive integers are 5 and 6.

Let the two consecutive positive integers be x and x + 1. We are given that the product of these integers is 3 less than three times their sum. This can be expressed as:
[tex]x(x + 1) = 3(x + x + 1) - 3[/tex]
Now we can solve for x:
[tex]x^2 + x = 6x + 3 - 3[/tex]
[tex]x^2 + x = 6x[/tex]
[tex]x^2 - 5x = 0[/tex]
Factoring the left side of the equation, we get:
[tex]x(x - 5) = 0[/tex]
From this equation, x can be 0 or 5.

However, since the question asks for positive integers, we can't use x = 0. Therefore, x = 5.

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Quinn is currently 38 years old.

Let's start by using variables to represent their ages.

Let Q be Quinn's current age and B be Banu's current age.

We know that Quinn is 7 years older than Banu, so we can write:

Q = B + 7

In 3 years, their ages will increase by 3, so we can write:

(Q + 3) + (B + 3) = 75

Now we can substitute Q = B + 7 into the second equation:

(B + 7 + 3) + (B + 3) = 75

Simplifying the left side:

2B + 13 = 75

Subtracting 13 from both sides:

2B = 62

Dividing both sides by 2:

B = 31

So Banu is currently 31 years old. Using Q = B + 7, we can find Quinn's age:

Q = 31 + 7 = 38

Therefore, Quinn is currently 38 years old.

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Answer:

1+2=90° .so complementary angle

In other words, we can expect that 95% of the time, the number of applicants who meet the 80-point requirement for the Peace Corps in a randomly selected group of 300 will fall within a range of 67 and 93.

Based on the information provided, it is likely that 0.6% of applicants will meet the 80-point requirement for the Peace Corps. Using the Empirical Rule, we can estimate that 95% of measurements will fall within two standard deviations of the mean. For the random variable x, which is the number of applicants out of 300 who meet the 80-point requirement, this would be approximately[tex]80 +/- 2(6.47),[/tex] or between 67.06 and 92.94.

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Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.

Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.

First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]

Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).

To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:

Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]

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Matthew can travel up to 150 miles for $50, assuming the cost of the limo ride remains constant at a $20 fixed cost plus $0.20 per mile. Let's say Matthew has $50 to spend on the limo ride.

We know that the cost per mile is $0.20, so we can set up an equation:

Cost = $20 + $0.20 x Distance

We can substitute $50 for Cost and solve for Distance:

$50 = $20 + $0.20 x Distance

$30 = $0.20 x Distance

Distance = $30 / $0.20

Distance = 150 miles

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Answer:

546.7

Step-by-step explanation:

According to combinations formula there are 495 possible committees that can be selected from a group of 12 people.

To calculate this, you can use the formula for combinations

nCr = n!/(r!(n-r)!)

where n is the total number of people (12) and r is the number of people on the committee.
Therefore, the possible number of committees that can be selected is;

= {12!}/{4!8!}
= 12*11*10*9/4*3*2*1

= 11880/24
= 495
Therefore, 495 possible committees can be selected from a group of 12 people if a committee of 4 is to be selected.

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The procedure of comparing different instrumental variables estimates of the same parameter is an example of testing over identifying restrictions

Testing the over identifying restrictions is the procedure of comparing different instrumental variables estimates of the same parameter. It is a method used to assess the validity of a set of instruments in a two-stage least squares (2SLS) regression model. In this method, the same parameter is estimated in two different ways using different sets of instruments. The difference between these two estimates is then tested to see if they are statistically different. If they are statistically different, then this indicates that the instruments are not valid and need to be revised.

The over identifying restrictions test is typically used in cases where there is a large number of instruments and the researcher wants to be sure that the instruments are appropriate for the regression model.

This test is also useful for assessing homogeneity, which is when the independent variable is correlated with the error term in the regression model. Heteroscedasticity is another potential issue in regression models, where the variance of the error term is not constant across all observations. The over identifying restrictions test can be used to detect this issue as well.

In summary, the procedure of comparing different instrumental variables estimates of the same parameter is an example of testing over identifying restrictions. It is a method used to assess the validity of a set of instruments in a 2SLS regression model, and can also be used to detect issues such as homogeneity and heteroscedasticity.

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Answer:

100%

Step-by-step explanation:

If 35 specials were served and 35 of them were salmon, then salmon was 100% of the special served.

The algebraic expressions for each statement is given below:

Here are the algebraic expressions for the given statements:

One-third a decreased by 2: (1/3)a - 2

Six times a number divided by 3: (6b)/3 = 2b

Eight more than a number n squared: n^2 + 8

Twice the difference of 8 and a number: 2(8 - c) = 16 - 2c

9 more than the quotient of 14 and a number n: (14/n) + 9

The sum of 15 and twice m: 15 + 2m

Four more than twice a number y is 72: 2y + 4 = 72

One-half a number x is 6 less than the number: (1/2)x = x - 6

4 times the sum of a number n and 7 is 16: 4(n + 7) = 16

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The weight of the cylinder when it is full, in grams, given the volume and radius, can be found to be d. 240, 000, 000πg.

To find the weight of the cylinder when it's full, we need to first find the volume of the cylinder and then multiply it by the density of the fluid.

The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.

V = π(400 cm)²(1000 cm)

V = π(160000 cm²)(1000 cm)

V = 160000000π cm³

Then, find the mass of the fluid inside the cylinder:

Mass = Density × Volume

Mass = 1.5 g/cm³ × 160000000π cm³

Mass = 240,000,000π g

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The probability of Kim getting a 2 and a head is 1/12.

A subfield of mathematics known as probability studies random occurrences and the possibility that they will occur. It is a technique of putting a number on the degree of ambiguity surrounding a situation or result. A number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to express probability. The probability of an occurrence is determined by dividing the number of possible outcomes by the number of ways the event may occur. Several disciplines, including science, engineering, economics, and statistics, employ probability.

For a fair dice, the probability of getting a 2 on the dice is 1/6.

The probability of getting a head on the coin is 1/2.

Thus,

P(getting a 2 and a head) = P(getting a 2) × P(getting a head)

= (1/6) × (1/2)

= 1/12

Hence, the probability of Kim getting a 2 and a head is 1/12.

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Extending to Three Dimensions depend on the specific questions asked and can be calculated using the formula for the volume of a three-dimensional object.

The answers to Edmentum's Unit 3 Post Test: Extending to Three Dimensions depend on the specific questions asked. Generally, the test covers topics such as the definition of three-dimensional objects, the properties of three-dimensional space, and the relationships between three-dimensional figures. For example, a question might ask how to calculate the volume of a rectangular prism. To answer this, one would need to calculate the area of each of the rectangles that make up the prism and then multiply them together to get the volume. For example, if the length of the prism is 4, the width is 3, and the height is 2, the volume of the prism would be 24 (4 * 3 * 2 = 24).

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Answer:No

Step-by-step explanation:

To find the mean, we add up all the numbers in the list and divide by the total number of numbers:Mean = (35 + 16 + 28 + 4 + 62 + 15 + 48 + 22 + 16 + 28) / 10 = 27.4To find the median, we first need to put the numbers in order:4, 15, 16, 16, 22, 28, 28, 35, 48, 62The median is the middle number. In this case, there are 10 numbers, so the middle two are 22 and 28. The median is the average of these two numbers:Median = (22 + 28) / 2 = 25To find the mode, we look for the number that appears most often. In this case, both 16 and 28 appear twice, while all the other numbers appear only once. So the mode is 16 and 28.Mode = 16, 28To find the range, we subtract the smallest number from the largest number:Range = 62 - 4 = 58Therefore, the mean is 27.4, the median is 25, the mode is 16 and 28, and the range is 58.

Answer: the mean is 25.4, the median is 25, the mode is 16 and 28, and the range is 58.

Step-by-step explanation:

To find the mean, we add up all the values and divide by the total number of values:

Mean = (35 + 16 + 28 + 4 + 62 + 15 + 48 + 22 + 16 + 28) / 10

Mean = 254 / 10

Mean = 25.4

So the mean is 25.4.

To find the median, we need to first put the list in numerical order:

4, 15, 16, 16, 22, 28, 28, 35, 48, 62

The median is the middle number in the list, so in this case it is 25, which is between the 5th and 6th numbers in the list.

So the median is 25.

To find the mode, we need to find the number that appears most frequently in the list. In this case, the numbers 16 and 28 each appear twice, which is more than any other number, so both 16 and 28 are modes of the list.

So the mode is 16 and 28.

To find the range, we subtract the smallest value from the largest value:

Range = 62 - 4

Range = 58

So the range is 58.

Therefore, the mean is 25.4, the median is 25, the mode is 16 and 28, and the range is 58.

After a time period of 9 years Mr. Lucas' investment will be 17940 x 10^5

What does investment mean in everyday language?

A purchase made with the intention of earning money or gaining notoriety is referred to as an investment. The acquisition of things that are not used right away but will be utilized to create wealth down the road is known as an investment in an economic perspective. There are numerous investment options available.

Rate in percentage (R) = 5.5%

Principal Amount (P) = 5 200

Total time period (t) = 9 years

Number of times interest is compounded per t (n) = 1

r = R/100

r = 5.5/100

r =  0.055 rate per year,

Then solve the equation for A

A = P(1 + r/n)^(nt)

A = 5200(1 + 0.055/1)⁽¹⁾⁽⁹⁾

A = 5200(1 + 0.055)⁹

A = 5200(1.055)⁹

A =  5200 * 3.45 x 10^5

   = 17940 x 10^5

Hence, after a time period of 9 years Mr. Lucas' investment will be 17940 x 10^5

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The answer to this question is 289 miles. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.

Sum is the total of two or more numbers added together. It is a mathematical operation used to find the aggregate of two or more numbers or amounts. Sum is calculated by adding the numbers together to get the total.

This is because Julie will be driving a total of 89 miles from York to Derby, then 73 miles from Derby to Corby, for a total of 162 miles. She will then have to drive 127 miles from Derby back to York, giving a total of 289 miles.

Once these distances are determined, the total number of miles is simply the sum of the three distances. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.

To further illustrate this answer, it can be thought of as a triangle, where each location is a vertex and the lines connecting them are the distances between the locations.

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Answer:

the answer is the last one

Probability is a branch of mathematics that deals with the measurement of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.

The events A and B are not independent.

To see this, note that the probability of A is given by:

[tex]P(A) = 1/2[/tex] , since there are 6 ways to get an odd sum[tex](1+2, 2+1, 3+4[/tex] ,   [tex]4+3, 5+6, 6+5)[/tex] out of a total of 12 possible outcomes when rolling two dice.

The probability of B is also 1/2, since there are 3 odd numbers on a standard die and 6 possible outcomes for the second die.

Now, to calculate P(A ∩ B), we need to find the probability that both events A and B occur simultaneously.

This happens when we roll an odd sum (which has a 1/2 probability) and then get an odd number on the second die (which has a 1/2 probability). Multiplying these probabilities together, we get:

[tex]P(A ∩ B) = (1/2) * (1/2) = 1/4[/tex]

Finally, we can check whether the events A and B are independent by comparing P(A ∩ B) to P(A)P(B):

[tex]P(A)P(B) = (1/2) * (1/2) = 1/4[/tex]

Therefore, Since [tex]P(A ∩ B) ≠ P(A)P(B)[/tex]  , we can conclude that the events A and B are not independent.

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Events A and B are not independent. Let A = {the sum of the dice is odd}, and let B = {the second die shows an odd number}.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The probability of two events A and B being independent is determined by whether the occurrence of one event affects the occurrence of the other. In the given problem, event A is the sum of two dice being odd, and event B is the second die showing an odd number.

The probability of A and B occurring separately can be calculated, as can the probability of A and B occurring together. While P(A ∩ B) = P(A) * P(B), the events are not independent since knowing that one event has occurred affects the probability of the other event.

If A occurs, the probability of B changes, and if B occurs, the probability of A changes.

No, because P(A∩B) = P({1,3,5})∩P({1,3,5}) = P({1,3,5}) = 1/2, and P(A)P(B) = (1/2) * (1/2) = 1/4, which are not equal.

Therefore, events A and B are not independent.

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