5.6 Enrichment and Extension
Please answer A, B, D, F, H, l, N, and P

In the fractions prompts given, the correct output are:

A fraction represents a part of a whole. It consists of a numerator and a denominator, with the numerator indicating the number of parts and the denominator indicating the total number of parts.

The calculations are given as follows;

1 )

= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]

= 1/8

2) (1/5) ÷ 2

= (1/5) x (1/2)

= 1/10

3)

(1/3) ÷ 5

= (1/3) x (1/5)

= 1/15

4) (1/4) ÷ 4

= (1/4) x (1/4)

= 1/16

5) One day, Amy baked a cake and wanted to divide it equally among 3 of her friends. She realized she only had half a cake left, so she decided to divide it into equal parts. Each friend received 1/6 of a cake. To check her calculation, she multiplied 1/6 by 3 and got 1/2. Thus, (1/2) ÷ 3 = 1/6, since dividing by 3 is the same as multiplying by 1/3.

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Answer:

a. f(10)= 20*10+14

f(10)=200+14

f(10)= 214

214

The area of the quadrilateral ABCD for this case is of 4 square units.

The quadrilateral ABCD in the context of this problem represents a diamond, hence it's area is given by half the product of the diagonal lengths of the diamond.

The lengths for each diagonal of the diamond are given as follows:

The product of the diagonal lengths is given as follows:

AC x BD = 2 x 4 = 8 square units.

Hence half the product of these diagonal lengths, representing the area of the quadrilateral, is given as follows:

0.5 x 8 square units = 4 square units.

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Answer: A

Step-by-step explanation: i thing its wrigth

Answer:

53 miles per hour

Step-by-step explanation:

To calculate Jennifer's average rate of speed in miles per hour, we can use the formula:

average speed = total distance / total time

In this case, Jennifer drove a total distance of 265 miles and it took her a total time of 5 hours, so:

average speed = 265 miles / 5 hours

Simplifying the expression, we get:

average speed = 53 miles per hour

Therefore, Jennifer's average rate of speed in miles per hour is 53 miles per hour.

Answer: 53 miles per hour

Step-by-step explanation:

To find Jennifer's average rate of speed in miles per hour, we divide the distance she traveled by the time it took her:

Average speed = distance ÷ time

Average speed = 265 miles ÷ 5 hours

Average speed = 53 miles per hour

Therefore, Jennifer's average rate of speed was 53 miles per hour.

The probability that the sample proportion will be at least k is 0.7580.

Let P be the probability that any one person in the population will cooperate and respond to the questions. We are looking for the probability that at least k people out of n in the sample will cooperate and respond to the questions. Let X be the number of people who cooperate and respond to the questions in the sample. X follows the binomial distribution with parameters n and P.To calculate this, use the following formula:

Z = (X - μ) / σ

Here, X = number of people who cooperate and respond to the questions in the sample

μ = E(X) = np,  σ = sqrt(npq)

q = 1 - P

Now, to calculate the probability, first calculate μ = np =

σ = sqrt(npq)

Then, find the z-score using z = (k - μ) / σ.

Now, use the z-table to find the probability corresponding to the z-score obtained in the previous step. The probability obtained from the z-table is the probability that the sample proportion will be at least k.

The probability that the sample proportion will be at least k is 0.7580.

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The point that partitions segment AB in a 1:4 ratio would be (-3/5, -1/5).

To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.

We can use the formula for finding the coordinates of a point that partitions a line segment in a given ratio. The formula is:

C = ((1 - r) * A + r * B) / 4

where, r is the ratio (in this case, 1:4, so r = 1/5).

Substituting the values for A, B, and r, we get,

C = ((1 - 1/5) * (-3, 2) + (1/5) * (7, -10)) / 4

Simplifying,

C = (4/5 * (-3, 2) + 1/5 * (7, -10)) / 4

C = (-12/5, 8/5 - 2) / 4

C = (-12/20, 8/20 - 10/20)

C = (-3/5, -1/5)

Therefore, the point that partitions segment AB in a 1:4 ratio is (-3/5, -1/5).

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The average of "a, b, c" in terms of p and q is a) p + q + 2

The question asks us to find out the average of a, b, and c in terms of p and q.

The given data in the question are -a, b, and c are the averages of p, 2q, and 4; 2p, 4q, and 8; and 6p, 3q, and 6, respectively.

We need to find the average of these averages.

Let's solve for a first:a = (p + 2q + 4) / 3

We can solve for b as:

b = (2p + 4q + 8) / 3

And, solving for c,c = (6p + 3q + 6) / 3

Now, let's sum a, b, and c:

a + b + c = [(p + 2q + 4) / 3] + [(2p + 4q + 8) / 3] + [(6p + 3q + 6) / 3]= [p + 2q + 4 + 2p + 4q + 8 + 6p + 3q + 6] / 3= (9p + 9q + 18) / 3= 3(p + q + 2)

Therefore, the answer is option A, p + q + 2.

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Harris ate x - 111 slices of pizza, So the total number of slices in the pizza is n ,where x is the number of slices each of the 44 friends received, and n is the total number of slices in the pizza, which must be a multiple of 44.

Let x be the number of slices each of the 44 friends received, then the total number of slices in the pizza is 44x. Since the pizza is evenly divided, the number of slices must be a multiple of 44.

Let y be the number of slices Harris received. Then, according to the problem, Harris ate 111 fewer slices than he received, so the number of slices he ate is y - 111.

Since the total number of slices in the pizza is 44x, we have:

y + 43x = 44x

Simplifying this equation, we get:

y = x

Therefore, Harris received the same number of slices as each of the other friends. So the number of slices he ate is:

y - 111 = x - 111

Substituting y = x, we get:

x - 111

Therefore, Harris ate x - 111 slices of pizza.

To find the value of x, we need to know the total number of slices in the pizza, which must be a multiple of 44. We can express this as:

44n = 44x

Dividing both sides by 44, we get:

n = x

So the total number of slices in the pizza is n.

Putting everything together, we get: Harris ate x - 111 slices of pizza, where x is the number of slices each of the 44 friends received, and n is the total number of slices in the pizza, which must be a multiple of 44.

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In conclusion, 95.4% of students have GMAT scores between 400 and 800.

Calculate z score need to find the proportion of scores that fall within the range of 400 to 800.

[tex]z=\frac{x- mean}{standard deviation}[/tex]

This formula tells us how many standard deviations away from the mean a given score is.

Given:

Mean= 600

Standard deviation = 100.

For the 400 scores:-

[tex]z=\frac{400-600}{100} \\z= -2[/tex]

For the 800 scores:-

[tex]z=\frac{800-600}{100} \\z=2[/tex]

Now we will use the standard normal distribution table to find the percentage of values between -2 and 2.

According to the standard normal distribution table, the percentage of values between -2 and 2 is approximately 95.45%.

Therefore, approximately 95.45% of students have GMAT scores between 400 and 800.

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Answer:calculate the cube root of a cube's volume.

Step-by-step explanation:

When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.

The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.

Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.

The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.

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There are black, blue, and white marbles in a bag. The probability of choosing a black marble is 0.75.

Let's assume that there are 100 marbles in the bag. If the probability of choosing a black marble is 0.36, there are 36 black marbles in the bag. Therefore, there are 64 marbles of other colors (white and blue) in the bag.

Using the same method, we can say that the probability of choosing a white marble after drawing a black one is [tex]\frac{0.27}{0.36}= 0.75[/tex]  (rounded to the nearest hundredth). It means that there are 75 white marbles for every 100 black marbles in the bag.

Therefore, the probability of the second marble being white if the first marble chosen is black is

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The binary representation is (a) a3 in binary is 10100011(b) 1fc in binary is 11111100(c) 2a0b in binary is 1010100000001011

In hexadecimal, each digit represents four bits, which means that two hexadecimal digits can represent eight bits. As a result, converting from hexadecimal to binary is straightforward. The four bits corresponding to each hexadecimal digit can be written down, resulting in an 8-bit binary value.

To convert hexadecimal to binary, simply convert each hexadecimal digit to binary, then combine them to get the final binary representation. For instance, in a, the hexadecimal digit a has a binary representation of 1010, while the digit 3 has a binary representation of 0011.

Combining these results in a binary representation of 10100011. Similarly, the binary representations of 1f and c are 00011111 and 00001100, respectively.

Combining them results in 11111100. Finally, the binary representation of 2a0b is obtained by converting 2, a, 0, and b to binary, resulting in 0010, 1010, 0000, and 1011, respectively. Combining them results in 1010100000001011.

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Answer:

$10

Step-by-step explanation:

We Know

Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.

Let C be the total cost, and x be the number of minutes she talks; we have the equation.

C = 0.05x + 10

If Terri does not make any calls, what would her bill be?

C = 0.05(0) + 10

C = $10

So, her bill will be $10

Answer:

50

Step-by-step explanation:

Let the number = x.

20% of the number is 20% of x = 0.2x.

Since the number exceeds 20% of itself by 40, then teh number minus 20% of itself is 40.  

x - 0.2x = 40

0.8x = 40

x = 40/0.8

x = 50

Answer:

x = 6

Step-by-step explanation:

Verticle angles are equal to each other...

m∠A = m∠B

Thus...

4x + 6 = 2x + 18

Now, we isolate x:

4x + 6 = 2x + 18

Subtract 6 from both sides

4x = 2x + 12

Subtract 2x from both sides

2x = 12

Divide both sides by 2

x = 6

Answer:

$2.90

Step-by-step explanation:

6 × 0.15 = 0.9

2 + 0.9 = 2.9

R(x) = -30(x - 6)² + 320

This equation for the revenue is a quadratic equation model written in the form of completing the square;

This form appears like so:

f(x) = a(x + b)² + c

It is quite useful, especially for this type of question;

Firstly, if a is positive, the quadratic equation will be a u shaped graph when illustrated, if negative, it will be an n shaped graph;

What this means is if a is positive, the vertex of the graph is the lowest point, i.e. the minimum value of f(x), and if a is negative, the vertex will be the highest point, i.e. the maximum value of f(x);

Secondly, the coordinates of the vertex will be:

(-b, c)

So, with regards to the question:

We have -30 in the position of a, the curve is therefore n shaped and the vertex is the highest point (known as the local maximum);

And in place of b and c, we have -6 and 320, so the coordinates of this local maximum are:

(6, 320)

We interpret this like so:

320 is the highest possible value of R(x), which represents revenue, so $320 is the maximum revenue according to this model, and it is achieved when x = 6, i.e. when the price is increased by $0.90 (= 6 × $0.15);

Finally, to get the new ticket price, we add this to the original price to get $2.90.

Frankie's dad used 2/3 of the carton of eggs for their breakfast. Two equivalent fractions are 16/24 and 24/36.

Frankie's dad used 8 out of 12 eggs from a full carton. To express this as a fraction, we can write it as 8/12. However, this fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which in this case is 4. Thus, we get:

8/12 = (8 ÷ 4)/(12 ÷ 4) = 2/3

Alternatively, we can also express this fraction in different forms. One way to do this is by multiplying both the numerator and denominator by the same number. For example, if we multiply both by 2, we get:

8/12 = (8 × 2)/(12 × 2) = 16/24

Similarly, we can multiply by 3 to get:

8/12 = (8 × 3)/(12 × 3) = 24/36

Both of these fractions are equivalent to 2/3, and we can find infinitely many other equivalent fractions by multiplying both numerator and denominator by different numbers.

In summary, when Frankie's dad made scrambled eggs using 8 eggs from a full carton of 12 eggs, he used 2/3 of the carton. This fraction can be expressed in different forms that are equivalent to 2/3 by dividing both numerator and denominator by their greatest common factor or by multiplying both numerator and denominator by the same number.

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According to the perimeter, the value of x is 7/2.

The problem tells us that the perimeter of a square is 8√2x units. We can use this information to set up an equation. Since all four sides of a square are equal, we can let s represent the length of one side of the square. Then, we know that:

Perimeter of square = 4s = 8√2x

We can simplify this equation by dividing both sides by 4:

s = 2√2x

Now, we can use this expression for s to find the area of the square. The area of a square is simply the length of one side squared. So, we have:

Area of square = s² = (2√2x)² = 8x

The problem tells us that the area of the square is 56 units square, so we can set up another equation:

8x = 56

Solving for x, we get:

x = 7/2

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Answer:

50000

Step-by-step explanation:78473294724829384739284732984739824

Transformation of the graph from parent function f(x) to g(x) is:

That whenever a figure is relocated from one place to another without affecting its dimension, shape, or orientation, a transition known as translation takes place. If we are aware of the direction and magnitude of the figure's movement, we may draw the translation in the coordinate plane.

The x - axis and y values are reversed. 180° rotation about the origin Every x and y value reverses from what it was. Each current value becomes the counterpart of what it was after a 270° rotation of the origin. The two x and y values are reversed.

The given function:

f(x) = 1/x-1 + 1 and g(x)=1/x+2 +4

g(x) is obtained function after transformation:

transformation:

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The city had 20,000 residents. The next year, it went up by 2%. The new population of the city after a 2% increase is 20400.

To find the new population of the city after a 2% increase from 20000, we need to use the following formula:

New population = Old population + (Percentage increase x Old population)

Substituting the given values into the formula, we get:

New population = 20000 + (2/100 x 20000)

New population = 20000 + 400

New population = 20400

It is important to note that this calculation assumes that the increase in population is the only factor affecting the total population. In reality, there may be other factors that affect the population, such as migration, birth rates, and mortality rates.

Additionally, this calculation only gives the estimated population based on the percentage increase, and the actual population may differ due to various factors.

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An expression is a combination of numbers, variables, and operations that can be evaluated to produce a value. Expressions can be simple or complex and can involve arithmetic, logical, or comparison operations.

A) To factor [tex]p^2-x^2+6x-9[/tex] first notice that the expression inside the parentheses is the difference of two squares, so we can use the formula:

[tex]p^2 - x^2 = (p + x)(p - x)[/tex]

Therefore, we can write the expression as:

[tex](p + x + 3)(p - x + 3)[/tex]

To check this, you can use FOIL to expand the expression:

[tex](p + x + 3)(p - x + 3) = p^2 - px + 3p + px - x^2 + 3x + 3p - 3x + 9 = p^2 - x^2 + 6x + 9[/tex]

B) To factor b^2-c^2-10(b-c), notice that the first two terms form a difference of squares, so we can use the formula again:

[tex]b^2 - c^2 = (b + c)(b - c)[/tex]

The expression can then be written as:

[tex](b + c)(b - c) - 10(b - c) = (b - c)(b + c - 10)[/tex]

To check this, we can use FOIL again:

[tex](b - c)(b + c - 10) = b^2 - bc - 10b - cb + 10c = b^2 - c^2 - 10(b - c)[/tex]

Therefore, the factored form of the expression is [tex](b - c)(b + c - 10)[/tex].

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Answer:

aeqtq34t

Step-by-step explanation:

q34t35t134

both containers have the same surface area and neither has a smaller surface area than the other.

Container 1:

Surface area of a single ball = π x (54/2)^2 = 3,092.62 mm^2

Total surface area of 4 balls = 12,370.48 mm^2

Container 2:

Surface area of a single ball = π x (54/2)^2 = 3,092.62 mm^2

Total surface area of 4 balls = 12,370.48 mm^2

Both containers have the same surface area.

To calculate the surface area of the two containers, I first calculated the surface area of one ball by using the formula π x (diameter/2)^2. I then multiplied this by 4 to get the total surface area of 4 balls. I repeated this process for both containers and found that both containers had the same surface area of 12,370.48 mm^2. both containers have the same surface area and neither has a smaller surface area than the other.

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There are 495 ways to assign 8 employees to the day shift and 4 employees to the night shift from a group of 12 employees.

Given that, we need to find the number of ways to assign 8 employees to the day shift and 4 employees to the night shift from a group of 12 employees.

We can use combinations to solve this problem.

The number of ways to choose 8 employees from 12 for the day shift is:

C(12,8)

= 12! / ( 12 - 8 )! × 8!

= 495

Similarly, the number of ways to choose 4 employees from the remaining 4 for the night shift is:

C(4,4) = 1

= 4! / ( 4 - 4 )! × 4!

= 4!/4!

= 1

Therefore, the total number of ways to make the assignment is:

495 × 1 = 495

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Answer:

Step-by-step explanation:

X+125=180    (angles on a straight line add to 180 (supplementary) ).

so x=55°

The solution of system of inequalities solved graphically is (18,6).

A group of two or more linear inequalities are graphed together on a coordinate plane to discover the solution that concurrently satisfies all the inequalities. This is known as a system of linear inequalities. The location where all the half-planes overlap is where the system is solved. Each inequality defines a half-plane on the coordinate plane. Every point in this area, which is referred to as the feasible region, fulfils all of the system's inequalities. To identify the optimum solution for an optimization problem given a set of constraints, systems of linear inequalities are frequently utilised.

Let us suppose the number of dimes = a.

Let us suppose the number of nickels = y.

According to the problem we have the following conditions:

a + y ≤ 28 (at most 28 coins)

0.10a + 0.05y ≥ 2 (worth at least $2)

a ≥ 18 (at least 18 dimes)

y ≤ 6 (no more than 6 nickels)

Using different values of a and y plot the points.

The solution of this system of inequality is any point that lies in the feasible region.

One such point is (18, 6).

Hence, the solution of system of inequalities solved graphically is (18,6).

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