9) There are six girls and 12 boys in Ms. Jeffry's environmental club. She wants to divide the students into groups with the same number of boys and the same number of girls in each group. What is the maximum number of groups she can make? *​

Answer:

34 i think

Step-by-step explanation:

if the sum is 180  then

18+28+100+34

sorry if its wrong

Answer:

Answers are below

Step-by-step explanation:

29. 3(4x-5) + 4(2x+6)

Solution: 20 + 9

30. -8(2a - 3b) - 5(6b - 4a)

Solution: 4 − 6

31. 10(5g + 2h - 3) - 4(3g - 4h + 2)

Solution: 38 + 36ℎ − 38

hope this helps :) Let me know if you need any further explanations.

In calculating a one-sample chi-square test with 3 degrees of freedom, the variable has 4 categories.

Step-by-step explanation:
1. The degrees of freedom (df) in a one-sample chi-square test are calculated as df = k - 1, where k is the number of categories.
2. Given that there are 3 degrees of freedom, we can solve for k: 3 = k - 1.
3. Add 1 to both sides of the equation: 3 + 1 = k.
4. Therefore, k = 4, meaning there are 4 categories in the variable.

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1. The probability of event C or event D occurring is 0.6, given their individual probabilities and the probability of their intersection. 2. The probability of event D occurring given that event C has occurred is 0.75. 3. Events C and D are not disjoint because they have a non-zero intersection. 4. Events C and D are not independent since the conditional probability of D given C is not equal to the marginal probability of D.

1. To determine the probability of event C or event D occurring, we can use the addition rule for probability:

P(C ∪ D) = P(C) + P(D) - P(C ∩ D)

Given that P(C) = 0.4, P(D) = 0.5, and P(C ∩ D) = 0.3, we can substitute these values into the formula:

P(C ∪ D) = 0.4 + 0.5 - 0.3 = 0.6

Therefore, the probability of event C or event D occurring (C ∪ D) is 0.6.

2. To determine the probability of event D occurring given that event C has already occurred, we can use the conditional probability formula:

P(D | C) = P(C ∩ D) / P(C)

Given that P(C) = 0.4 and P(C ∩ D) = 0.3, we can substitute these values into the formula:

P(D | C) = 0.3 / 0.4 = 0.75

Therefore, the probability of event D occurring given that event C has occurred (D | C) is 0.75.

3. Events C and D are not disjoint because the probability of their intersection (C ∩ D) is not equal to zero (0.3). Disjoint events have no common outcomes, but in this case, there is an overlap between events C and D.

4. To determine if events C and D are independent, we can compare the conditional probability of event D given event C (P(D | C)) with the marginal probability of event D (P(D)). If these probabilities are equal, events C and D are independent.

Given that P(D | C) = 0.75 and P(D) = 0.5, we can see that they are not equal. Therefore, events C and D are not independent.

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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The complete statements are:

To do this, we evaluate each equation

So, we have

Equation 1

x + c = 0

Make x the subject

x = -c

The above implies that x and c are additive inverses

Hence, as c increases, the value of x decreases

Equation 2

-xc = -c

Divide both sides by -c

So, we have

x = 1

The above implies that c does not have any effect on the value of a

Hence, as c increases, the value of x stay the same

Equation 3

x/c = 1

Make x the subject

x = c

The above implies that x and c have the same value

Hence, as c increases, the value of x increases

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Answer:

a). -23,   b). +250,    c). +8,800  d). -18,  e). -30

Step-by-step explanation:

Words like owe and below usually are negative integers.

Words like earn, altitude (above), are positive integers.

Answer:

d

Step-by-step explanation:

527 / 17 = 31

Answer:

y = -8 5/8; explanation in the attached photo.

Step-by-step explanation:

Answer:

22%

Step-by-step explanation:

Well if the ramp can hold 1000lbs and 6 people all weight 780 in total (they must be really fat lol, but anyway) we can make the following fraction.

780/1000

So now we simplify the fraction to 39/50.

And do 39 / 50 = .78

To make that a percent we move the decimal point 2 times to the right so 78% of the ramp‘s capacity is being used meaning there is stil 22% capacity left.

Answer: C

Step-by-step explanation:

The arithmetic sequence is solved and the nth term is Aₙ = 5 + ( n - 1 )12

Given data ,

Let the terms of the AP be represented as

a₂ = 17, a₄ = 41, and a₇ = 77

So , a + d = 17

Now , a₂ + 2d = 41

On simplifying , we get

2d = 24

Divide by 2 on both sides , we get

d = 12

So , the first term is a = a₂ - 12

a = 5

So , the nth term of AP is Aₙ = 5 + ( n - 1 )12

Hence , the arithmetic progression is solved

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Answer:

x = 12

Side length = \(2\sqrt{3}\) in

Step-by-step explanation:

Area of the given hexagon = 6 × (Area of the triangular section)

Area of the triangular section = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                                 = \(\frac{1}{2}(2)(\sqrt{3})^{\frac{x}{12}}(\sqrt{3})^{\frac{x}{6}}\)

                                                 = \((\sqrt{3})^{\frac{x}{12}}[(\sqrt{3})^2]^{\frac{x}{12}}\)

                                                 = \((\sqrt{3})^{\frac{x}{12}}(3)^{\frac{x}{12}}\)

                                                 = \((3\sqrt{3})^{\frac{x}{12}}\)

Now area of the given hexagon = \(6(3\sqrt{3})^{\frac{x}{12}}\)

Since, area of the hexagon is = \(18\sqrt{3}\) in²

\(6(3\sqrt{3})^{\frac{x}{12}}=18\sqrt{3}\)

\((3\sqrt{3})^{\frac{x}{12}}=(3\sqrt{3})^1\)

\(\frac{x}{12}=1\)

x = 12

Therefore, side length = \(2(\sqrt{3})^{\frac{x}{12}}\)

                                      = \((2\sqrt{3})^{\frac{12}{12}}\)

                                      = \(2\sqrt{3}\) in.

Answer:

x = 20

Step-by-step explanation:

\(\frac{10}{x}\) = \(\frac{x}{40}\)

We cross-multiply and get

400 = \(x^{2}\)

\(\sqrt{400}\) = \(\sqrt{x^{2} }\)

x = 20

So, the answer is x = 20

To solve this problem, we will use the formula for exponential decay as follows: V = P * e^(-rt) where V is the value after t years, P is the initial value, r is the annual interest rate as a decimal, and t is the time in years.

What is Depreciation: Depreciation is dependent on a number of estimates.The method in which companies determine the depreciation value of their assets is different from one another. Some companies may use a straight line method of depreciation and another may count the depreciation according to asset's production value. What is exponential decay: An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time .Given that a brand new Audi R8 is purchased for $148,700 before taxes, and the car depreciates at a rate of 8%, we can find how much it will be worth in 5 years. Using the formula for exponential decay, we have V = P * e^(-rt) where     P = $148,700r = 0.08t = 5. Therefore,V = $148,700 * e^(-0.08 * 5), V = $148,700 * e^(-0.4)V ≈ $82,429.61. Therefore, the car will be worth approximately $82,429.61 in 5 years.

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Answer:

306 square meters

Step-by-step explanation:

The maximum area is when the length and width are the closest together.

70/2=35 we divide because there are 2 lengths and 2 widths in a rectangle

35/2=17.5, find the 2 closest integers, they are 17 and 18

17*18=306

Answer:

36. 22 inches

Step-by-step explanation:

Given that :

Head band fabric :

Total = 877.76 inches

Number of players = 30

Number of coaches = 2

Total number = (30 + 2) = 32

Head band Fabric per person :

877.76 / 32

= 27.43

Wristband fabric:

Total fabric used = 263.70

Number of players = 30

Wristband fabric per player :

263.70 / 30 = 8.79

Amount o fabric used on headband and Wristband for each player :

(27.43 + 8.79) = 36.22 inches of fabric per player

Answer:

The scientific notation for 500000000000 is 5 × 1011

Step-by-step explanation:

The 11 is going to be a superscripts(meaning its going to be placed at the top right corner of the 10)

The numbers in the eighth row of Pascal's Triangle are 1 7 21 35 35 21 7 1.

The numbers in the eighth row of Pascal's Triangle are:

1 7 21 35 35 21 7 1

In Pascal's Triangle, each number is obtained by adding the two numbers directly above it. The first and last numbers in each row are always 1. To generate subsequent rows, we add the adjacent numbers from the previous row to obtain the new numbers.

For example, to generate the eighth row:

Row 7: 1

Row 8: 1  +  7  +  21  +  35  +  35  +  21  +  7  +  1

Therefore, the numbers in the eighth row of Pascal's Triangle are 1 7 21 35 35 21 7 1.

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(i) Pen A would require the most fencing with a perimeter of 28 m.

(ii) Assuming the cost of fencing material is the same per unit length, Pen C would minimize the cost of fencing as it has the smallest perimeter of 20 m.

To determine which pen would require the most fencing and which pen would minimize the cost of fencing, we need to calculate the perimeters of each pen.

The perimeter of a rectangle can be calculated using the formula: Perimeter = 2 * (Length + Breadth).

Let's calculate the perimeters of each pen:

Pen A:

Length = 12 m

Breadth = 2 m

Perimeter of Pen A = 2 * (12 + 2) = 2 * 14 = 28 m

Pen B:

Length = 8 m

Breadth = 3 m

Perimeter of Pen B = 2 * (8 + 3) = 2 * 11 = 22 m

Pen C:

Length = 6 m

Breadth = 4 m

Perimeter of Pen C = 2 * (6 + 4) = 2 * 10 = 20 m

(i) The pen that would require the most fencing is Pen A, with a perimeter of 28 m.

(ii) To minimize the cost of fencing, we need to consider the perimeter in relation to the cost per unit length of the fencing material. Since the cost of fencing is not provided in the question, we cannot make a definitive determination.

However, if the cost of fencing material is the same per unit length for all pens, minimizing the cost would involve selecting the pen with the smallest perimeter. In this case, Pen C would minimize the cost of fencing as it has the smallest perimeter of 20 m.

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Answer:

Step-by-step explanation:

5y or 5x which ever one you see

Answer:

no solution

Step-by-step explanation:

y = 2x - 1 → (1)

y = 2x + 4 → (2)

substitute y = 2x - 1 into (2)

2x - 1 = 2x + 4 ( add 1 to both sides )

2x = 2x + 5 ( subtract 2x from both sides )

0 = 5 ← not possible

This indicates the system has no solution

Answer:

the answer is 20

Henry will need to work more than 44 hours per week to earn more money than Garry.

We first need to convert Garry's annual salary to a weekly salary.

We can do this by dividing $42,500 by 52 (the number of weeks in a year).

$42,500 / 52 = $817.30

Next, we need to calculate how much Henry earns in a week.

$18.50 * hours per week = weekly salary

We'll call the number of hours Henry works per week "x".

$18.50 * x = weekly salary

Now we need to set up an equation to find out how many hours Henry needs to work in a week to earn more than Garry.

$18.50 * x > $817.30

To solve this equation, we'll divide both sides by 18.5.

x > 44

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To maximize efficiency, Country B should specialize in Meat production, and Country A should specialize in Cheese production.

To determine the optimal production allocation between the two products (Meat and Cheese) and the two countries (Country A and Country B), we can use the concept of comparative advantage.

Comparative advantage refers to the ability of a country to produce a particular good or service at a lower opportunity cost compared to another country. The opportunity cost is measured in terms of the number of hours of labor required to produce each unit of a product.

To find the country with a comparative advantage in each product, we compare the opportunity costs between the two countries.

For Meat:

The opportunity cost of producing 1 ton of Meat in Country A is 30 hours of labor.

The opportunity cost of producing 1 ton of Meat in Country B is 10 hours of labor.

Since the opportunity cost of producing Meat is lower in Country B (10 hours) compared to Country A (30 hours), Country B has a comparative advantage in Meat production.

For Cheese:

The opportunity cost of producing 1 ton of Cheese in Country A is 5 hours of labor.

The opportunity cost of producing 1 ton of Cheese in Country B is 5 hours of labor.

Both countries have the same opportunity cost for Cheese production, so neither country has a comparative advantage in Cheese production.

Based on comparative advantage, Country B is better suited for producing Meat, while both countries are equally efficient in producing Cheese.

To maximize efficiency, Country B should specialize in Meat production, and Country A should specialize in Cheese production. This specialization allows each country to focus on producing the product in which they have a comparative advantage, leading to overall lower production costs and increased efficiency.

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Answer:

3(b-2)=24

Step-by-step explanation:

3b - 6 = 24

3b = 30

b= 10

The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

The given statement is

As you can observe, the observe, we made a substitution. However, the exact property used here is the transitive property of equalities, that's the property responsible for the substitution in mathematics.

The example that illustrates the difference between statistical significance and practial significance is

In a survey arranged by school-authority of a district on participation in sports by school-going boys and girls, it is found that 60% of boys and 57% of girls participate in outdoor sports. Thus the survey shows a 3% difference between school-going boy-participants and girl-participants in outdoor sports. Now the point is how much significance this 3% difference has statistically as well as practically. Statistical significance of this 3% depends upon the size of data used in determining the percentage of boys and girls participate in sports. If a sufficiently big sample size is used then the difference is statistically significant, and if a very small sample size is used then the difference is statistically insignificant. Thus bigger the sample size more is the statistical significance of a computed figure.

On the other hand practical significance of this 3% difference arises if decision is made or action is taken or needs to be taken on the basis of this 3% difference. If cost permits, the authority may consider promoting girl students participation in sports in order to bring about more gender parity in outdoor sports. In this case the 3% difference though small, may be practically significant.

Statistical significance is a measure of whether your research findings are meaningful. It is concerned with whether a research result is due to chance or sampling variability. Where, practical significance is concerened with wheteher the result is useful in the real world.

Therefore, the example that illustrates the difference between statistical significance and practial significance is

In a survey arranged by school-authority of a district on participation in sports by school-going boys and girls, it is found that 60% of boys and 57% of girls participate in outdoor sports. Thus the survey shows a 3% difference between school-going boy-participants and girl-participants in outdoor sports. Now the point is how much significance this 3% difference has statistically as well as practically. Statistical significance of this 3% depends upon the size of data used in determining the percentage of boys and girls participate in sports. If a sufficiently big sample size is used then the difference is statistically significant, and if a very small sample size is used then the difference is statistically insignificant. Thus bigger the sample size more is the statistical significance of a computed figure.

On the other hand practical significance of this 3% difference arises if decision is made or action is taken or needs to be taken on the basis of this 3% difference. If cost permits, the authority may consider promoting girl students participation in sports in order to bring about more gender parity in outdoor sports. In this case the 3% difference though small, may be practically significant.

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The sample size required is 182 families should be interviewed.

To calculate the number of families that should be interviewed to obtain the desired precision and degree of confidence, one must first determine the minimum sample size required to achieve the desired degree of confidence. As the standard deviation of the sample was computed to be $400 with the mean of $60,000.

Sample size formula: n = (Z² * s²) / E²

The formula for the degree of confidence: Z = 2.576

Sample size formula: n = (Z² * s²) / E²

Substituting the values, we get n = (2.576² * $400²) / $90²= 181.49 = 182 families. The sample size required is 182 should be interviewed families.

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