An open box is to be constructed by cutting out
square corners of x-inch sides from a piece of
cardboard 8 inches by 8 inches and then folding
up the sides. Express the volume of the box as a
function of x

Answer:

the greater integer is "y", which is 13.

Step-by-step explanation:

Let's call the odd integer "x", and the next consecutive integer "y". Since "y" is the next consecutive integer after "x", we know that:

y = x + 2

We are told that the sum of "x" and 4 times "y" is 63. We can set up an equation to represent this:

x + 4y = 63

Now we can substitute the expression for "y" in terms of "x" into this equation:

x + 4(x + 2) = 63

Simplifying this equation, we get:

x + 4x + 8 = 63

5x + 8 = 63

Subtracting 8 from both sides, we get:

5x = 55

Dividing both sides by 5, we get:

x = 11

So the odd integer is 11. We can use the expression for "y" in terms of "x" to find the next consecutive integer:

y = x + 2 = 11 + 2 = 13

Therefore, the greater integer is "y", which is 13.

Answer:

13

Step-by-step explanation:

there is an interval of 2 between consecutive odd numbers

let n and n + 2 be the 2 consecutive integers , then

n + 4(n + 2) = 63 , that is

n + 4n + 8 = 63

5n + 8 = 63 ( subtract 8 from both sides )

5n = 55 ( divide both sides by 5 )

n = 11

then larger integer is n + 2 = 11 + 2 = 13

Answer

The shape of sampling distribution of ^p is approximately normal because n < greater than 0.05N and np (1-p) > less than 10.

Step-by-step explanation:

The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.

The distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n is defined by the central limit theorem, where:

As long as these two conditions are respected:

n≤ N

np(1-p) > 10.

Here, we have the parameters

n= 700, p = 0.172, N= 15, 000

So, n/N = 0.0466 < 0.05

and, np(1-p)

= 700 x 0.172 ( 1- 0.172)

= 99.69 >10

Then the shape is approximately normal.

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The types of numbers are: -7: Integer, √2: Irrational, 0: Whole Number, 5: Natural Number, √16: Rational

-7: Integer. An integer is any positive or negative whole number or zero, including negative natural numbers.

√2: Irrational: An irrational number is a number that cannot be expressed as a ratio of two integers, meaning they cannot be written as a fraction.

0: Whole Number: A whole number is any positive integer or zero.

√16: Rational: A rational number is any number that can be expressed as a ratio of two integers, meaning they can be written as a fraction.

5: Natural Number: A natural number is a positive integer, excluding zero.

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Answer:

True

Step-by-step explanation:

To compare the two speeds, we can calculate the speed of each in miles per hour (mph) and then compare them.

22 miles in 20 minutes = (22/20) miles per minute = 1.1 miles per minute

To convert to mph, we can multiply by 60 to get:

1.1 x 60 = 66 mph

38 miles in 30 minutes = (38/30) miles per minute = 1.27 miles per minute

To convert to mph, we can multiply by 60 to get:

1.27 x 60 = 76.2 mph

Therefore, 38 miles in 30 minutes is faster than 22 miles in 20 minutes, as 76.2 mph is greater than 66 mph.

In other words, the statement "22 miles in 20 minutes is less than 38 miles in 30 minutes" is true.

No. 2: Kennedy error is that he mistakenly distributed the negative sign when multiplying -3 and +3. The correct answer is x² - 9.

No. 3: The product (x + 6)(x - 6) is equivalent to the expression x² - 6².

No. 4: The pattern for the squares of binomial are: (a + b)² = a² + 2ab + b²

and (a - b)² = a² - 2ab + b².

Sum and  difference pattern: (a + b)(a - b) =   a² - b²

No. 2

Kennedy made an error in multiplying (x - 3)(x + 3) because the correct result of this multiplication is x² - 9, not x² - 6x - 9.

This error occurred because Kennedy mistakenly distributed the negative sign when multiplying -3 and +3, resulting in an additional -6x term in the final answer.

The correct way to multiply (x - 3)(x + 3) is to use the FOIL method, which stands for First, Outer, Inner, Last. This gives us:

(x - 3)(x + 3) = x² + 3x - 3x - 9 = x² - 9

No. 3

The product (x + 6)(x - 6) is equivalent to the expression x² - 36, which is called the difference of two squares because it represents the difference between two perfect squares: x² and 6².

Specifically, (x + 6)(x - 6) can be written as x² - 6², and using the identity (a + b)(a - b) = a² - b² we can simplify this to x² - 36.

No. 4

The pattern for the squares of binomial are:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

The pattern for the product of a sum and a difference is:

(a + b)(a - b) =   a² - b²

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Answer: (a) Since the time to get the order follows a uniform distribution between 19 to 35 minutes, the probability of getting the order in any interval of time within this range is proportional to the length of that interval. Therefore, the probability of taking at least 23 minutes to get the order is:

P(X ≥ 23) = (35 - 23) / (35 - 19) = 0.4

Rounding to 4 decimal places, the probability is:

P(X ≥ 23) ≈ 0.4000

(b) If you arrive at Tim Horton's at 7:30am and your friends show up at 8:00am, you have 30 minutes to receive your order. Since the time to get the order follows a uniform distribution, the probability of receiving the order before your friends show up is the probability of getting the order in 30 minutes or less, which is:

P(X ≤ 30) = (30 - 19) / (35 - 19) = 0.5789

Rounding to 4 decimal places, the probability is:

P(X ≤ 30) ≈ 0.5789

(c) Let's call the time in minutes to get the order that is longer than 10% of the time as t. Since the distribution is uniform, we know that the probability of taking longer than t minutes is 0.1. Therefore, we can write:

(35 - t) / (35 - 19) = 0.1

Solving for t, we get:

t = 19 + 0.9(35 - 19) = 32.4

Rounding to 2 decimal places, we get:

t ≈ 32.40 minutes

Therefore, 10% of the time it takes longer than 32.40 minutes to get the order.

Step-by-step explanation:

The profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To calculate the profit for selling 300 vetkoek every week, we need to first calculate the total revenue generated and the total cost of producing the vetkoek.

Total revenue = Price per vetkoek x Number of vetkoek sold

Total revenue = 10 x 300 = 3000

Total cost = Cost per vetkoek x Number of vetkoek sold

Total cost = 3.80 x 300 = 1140

Profit = Total revenue - Total cost

Profit = 3000 - 1140 = 1860

Therefore, the profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.

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We can infer that the function y = 2 + log2(x - 1) has the following final behaviour:

A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for every function. A function is typically referred to as f(x), where x is the input. Y = f is a common way to represent a function (x).

A function in mathematics is a certain configuration of the inputs (also known as the domain) and their outputs (also known as the codomain), where each input has precisely one output and the output can be connected to its input.

from the question;

We may look at what happens to the function as x gets closer to positive and negative infinity to figure out the final behaviour of the function

y = 2 + log2(x - 1).

The formulas (x - 1) and log2(x - 1) also approach infinity as x gets closer to positive infinity. As a result, y increases as x moves closer to positive infinity. The following can be written:

lim x→∞ 2 + log2(x - 1) = ∞

Expression (x - 1) moves closer to zero and log2(x - 1) moves closer to negative infinity as x moves towards 1 from the right. So, as x moves closer to 1 from the right, y moves closer to negative infinity. The following can be written:

lim x→1+ 2 + log2(x - 1) = -∞

This leads us to the following conclusion about the final behaviour of the function y = 2 + log2(x - 1):

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Answer would be shifted up

Step-by-step explanation:

hence the +9 you would be going up 9 units :)

An equation that represents this problem "Anthony read 5/6 hour each day for 2 days." is: A. 2 × 5/6 = 10/12.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we can reasonably infer and logically deduce that Anthony's reading rate is 5/6 hour on a daily basis and for a period of 2 days only:

Total number of hours = 2 × 5/6

Total number of hours = 10/12 hours.

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Based on the given information, the graph of the function will shift 6 units up from the parent graph, f(x).

A function is a mathematical rule that relates one input value to one output value. The parent graph of a function is the simplest form of the graph that shows the basic behavior of the function.

In this case, the function is being shifted vertically by 6 units. This means that all points on the graph will be shifted upward by 6 units compared to the parent graph.

The shape of the graph will remain the same, but its position will change. Understanding how functions are transformed is important in mathematics and can be used to model a wide range of real-world phenomena.

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Answer:

To solve this problem, we can use the principle of inclusion-exclusion. We first count the total number of ways to assign rooms to the Italians and Englishmen without any restrictions. Then, we subtract the number of ways that violate the Italian's restriction, and the number of ways that violate the Englishmen's restriction. Finally, we add back the number of ways that violate both restrictions.

Step 1: Total number of ways to assign rooms

There are 8 rooms, so there are 8 choices for the first person, 7 choices for the second person, and so on. Therefore, there are 8 x 7 x 6 x 5 x 4 = 6,720 total ways to assign rooms to the Italians and Englishmen without any restrictions.

Step 2: Number of ways that violate the Italian's restriction

There are 3 blue rooms and 2 yellow rooms, so there are 3 x 2 = 6 ways to assign rooms to the Italians that violate their restriction. For each of these ways, there are 6 x 5 x 4 = 120 ways to assign rooms to the Englishmen. Therefore, there are 6 x 120 = 720 ways that violate the Italian's restriction.

Step 3: Number of ways that violate the Englishmen's restriction

There are 3 green rooms and 2 yellow rooms, so there are 3 x 2 = 6 ways to assign rooms to the Englishmen that violate their restriction. For each of these ways, there are 5 x 4 x 3 x 2 = 120 ways to assign rooms to the Italians. Therefore, there are 6 x 120 = 720 ways that violate the Englishmen's restriction.

Step 4: Number of ways that violate both restrictions

If the Italians are in blue rooms and the Englishmen are in yellow rooms, there is only 1 choice for this assignment. If the Italians are in yellow rooms and the Englishmen are in green rooms, there are also only 1 choice for this assignment. Therefore, there are 2 ways that violate both restrictions.

Step 5: Calculate the final answer

Using the principle of inclusion-exclusion, we can calculate the number of ways that satisfy all the restrictions as follows:

Total number of ways - Number of ways that violate the Italian's restriction - Number of ways that violate the Englishmen's restriction + Number of ways that violate both restrictions

6,720 - 720 - 720 + 2 = 5,282

Therefore, there are 5,282 ways to assign rooms to the two Italians and three Englishmen so that each of them is alone in one room, while satisfying their loyal guest preferences.

Step-by-step explanation:

The value of dz/ dt using Chain Rule is (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex].

The chain rule states that the derivative D of a composite function is given by a product, as D(f(g(x))) = Df(g(x)) ∙ Dg(x).

In other words, the first factor on the right, Df(g(x)), indicates that the derivative of f(x) is first found as usual, and then x, wherever it occurs, is replaced by the function g(x).

Given:

By chain rule we can write z= f(x, y) = f( x(t), y(t))

dz/ dt = df/ dx . dx/ dt + df/ dy. dy/dt

So, df/ dx = [tex]e^y[/tex]

df/dy =   [tex]e^y[/tex] + (x+ y)  [tex]e^y[/tex]

x(t)=5t, while y(t)=1-t², So,

So, dx/dt = 5

and, dy/dt = -2t

Now, dz/ dt = 5 . [tex]e^y[/tex] + -2t ( [tex]e^y[/tex] + (x+ y)  [tex]e^y[/tex])

                   = (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex]

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Answer:

AC = 14.9

BC = 10.5

Step-by-step explanation:

The triangle is a isosceles right triangle with ∠B = 90o, ∠A = ∠C = 45o.

Therefore AB = BC = 10.5

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse, which is AC.

AC^2 = AB^2 + BC^2

AC^2 = 2AB^2

AC^2 = 2(10.5)^2

AC^2 = 220.5

AC = √220.5 = 14.85 or 14.9

Answer:

The probability that a randomly chosen cancer patient who has received chemotherapy has also had elective surgery can be expressed as P(E|C), where "P" represents probability and the vertical bar "|" indicates "given." So, P(E|C) represents the probability of event E given that event C has occurred.

Step-by-step explanation:

In response to the given question, we have that Therefore, on Tuesday, equation the yield was 2.92%, and on Monday, it was 2.96%.

In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14.

Divide the yearly dividend by the share price to determine the yield, then multiply the result by 100 to get the percentage:

Tuesday's yield is calculated as (Annual dividend / Share Price) times 100.

Tuesday's yield is calculated as ($2.10 / $72) times 100, which is 2.92%.

Tuesday's closing price minus Monday's closing price is the difference.

The price on Monday was $72 minus $0.95.

$71.05 was the final price on Monday.

We apply the same procedure as previously to determine the yield as of Monday's close:

Monday's yield is calculated as (annual dividend / share price) x 100.

Yield on Monday is equal to ($2.10 / $71.05) times 100, or 2.96%.

Therefore, on Tuesday, the yield was 2.92%, and on Monday, it was 2.96%.

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By answering the above question, we may state that Thus, the third side function might be anywhere between 22 and 36 kilometer's long.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

The triangle inequality theorem states that the third side of a triangle's length must be bigger than the difference between the other two sides and less than the total of the other two sides.

Hence, the third side's range of potential lengths for a triangle with sides of 7 km and 29 km is:

The third side's length is less than 29 km plus 7 km, which equals 36 km.

The third side is longer than 29 km minus 7 km, which equals 22 km.

Thus, the third side might be anywhere between 22 and 36 kilometer's long.

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The percent of the fluid ounces under 60 is option D. Not here

To calculate the percentage of fluid ounces, you first need to determine the total volume of the container in fluid ounces. Then, you need to determine the volume of the specific substance that you are interested in as a fraction of the total volume. Finally, you can convert this fraction into a percentage by multiplying it by 100.

Here's the formula to calculate the percentage of fluid ounces:

Percentage of fluid ounces = (Volume of substance in fluid ounces ÷ Total volume of container in fluid ounces) x 100%

For example, if you have a 16 fluid ounce container of juice and you want to know what percentage of the container is filled with orange juice, and you measure that there are 4 fluid ounces of orange juice, you can calculate the percentage of orange juice as follows:

Percentage of orange juice = (4 fluid ounces ÷ 16 fluid ounces) x 100% = 25%

Therefore, the orange juice fills 25% of the 16 fluid ounce container. It could then be concluded that the percent of the fluid ounces is not here.

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The answer is 6

but specifically, it can land on green 6.8181%

Step-by-step explanation:

a. The mean is E(X)=np=220(0.2)=44, and the standard deviation is 5.93

b. I think you meant the probability that Cindy will get at least 50 orange Stattles in her next 14 ounce bag, if so the answer is 0.1762= 17.62% probability

If you need more clarification or it's not right, just comment and I'll help you even more.

The required quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.

Arithmetic involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.

Here,
To simplify the given expression, we can start by factoring out the common factor of 2x from the numerator. This gives:

(16x⁻² - 8x⁻² - 2x⁻⁹) / 2x

Next, we can simplify the terms in the numerator by combining the like terms:

= (4x⁻² - x⁻⁹) / x

= 4x⁻²⁻¹ - x⁻⁹⁻¹
= 4x⁻³ - x⁻¹⁰

= 4x⁻³ - x⁻¹⁰

Therefore, the quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.

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Answer:

52 - 13 = 39 so p = 39

Step-by-step explanation:

Answer:

P=25

Step-by-step explanation:

180=52+90+p+30

180=155+P

180-155=p

p=25

Answer:

4. y = 192 * 4^x

5. y=8*2^(-x)

6. y = -2.5x - 37

Step-by-step explanation:

4.

From the given data, we can see that as x increases by 1, y increases by a factor of 4.

Using the second and third data points, we can find a and b as:

When x = -2, y = 12, so we have:

12 = ab^(-2)

When x = -1, y = 48, so we have:

48 = ab^(-1)

Dividing the second equation by the first, we get:

4 = b^1

So b = 4, and substituting this into the first equation, we get:

12 = a(4)^(-2)

Simplifying, we get:

a = 192

So the equation for this exponential relationship is:

y = 192(4)^x

Simplifying further:

y = 192 * 4^x

5.

From the given data, we can see that as x increases by 1, y decreases by a factor of 2.

Using the second and third data points, we can find a and b as:

When x = -2, y = 32, so we have:

32 = ab^(-2)

When x = -1, y = 16, so we have:

16 = ab^(-1)

Dividing the second equation by the first, we get:

16/32=b^(-2+1)

1/2=b^(-1)

b=2

So b = 2, and substituting this into the first equation, we get:

32 = a*2^(-2)

32= 4a

a=32/4

a=8

So the equation for this exponential relationship is:

y = 8(2)^(-x)

Simplifying further:

y=8*2^(-x)

6.

The data suggests that as x increases by 1, y decreases by a constant amount. This suggests that the relationship between x and y is linear.

To find the equation for this relationship, we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

To find the values of m and b, we can use any two data points. Let's use the first and last data points:

When x = -3, y = -29.5, so we have:

-29.5 = m(-3) + b

When x = 3, y = -44.5, so we have:

-44.5 = m(3) + b

We can now solve for m and b. Subtracting the first equation from the second equation, we get:

-15 = 6m

So, m = -2.5.

Substituting this value into the first equation, we get:

-29.5 = (-2.5)(-3) + b

-29.5=7.5+b

b=-29.5-7.5

So, b =-37

Therefore, the equation for this linear relationship is:

y = -2.5x - 37

Answer:

[tex]\textsf{4)} \quad \textsf{Exponential:} \quad y=192 \cdot 4^x[/tex]

[tex]\textsf{5)} \quad \textsf{Exponential:} \quad y=8\cdot \left(\dfrac{1}{2}\right)^x[/tex]

[tex]\textsf{6)} \quad \textsf{Linear:} \quad y=-2.5x-37[/tex]

Step-by-step explanation:

When the x-values increase by a constant amount, the y-values have a constant difference.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Linear Function}\\\\$f(x)=ax+b$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

When the x-values increase by a constant amount, the y-values have a constant ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

From inspection of the given table, as the x-values increase by one, the y-values are 4 times the previous y-value. Therefore, they have a constant ratio of 4. This means that the equation is exponential.

The initial value "a" is the y-intercept, so a = 192.

The y-values have a growth factor of 4, so b = 4.

Substitute these values into the formula to create an equation for the table of values:

[tex]\boxed{y=192 \cdot 4^x}[/tex]

From inspection of the given table, as the x-values increase by one, the y-values are half the previous y-value. Therefore, they have a constant ratio of 1/2. This means that the equation is exponential.

The initial value "a" is the y-intercept, so a = 8.

The y-values have a growth factor of 1/2, so b = 1/2.

Substitute these values into the formula to create an equation for the table of values:

[tex]\boxed{y=8\cdot \left(\dfrac{1}{2}\right)^x}[/tex]

From inspection of the given table, as the x-values increase by one, the y-values decrease by 2.5. Therefore, they have a constant difference of -2.5. This means that the equation is linear.

The slope "a" is the change in y-values divided by the change in x-values. As the y-values decrease by 2.5 for ever increase in one in the x-values, a = -2.5.

The y-intercept is the y-value when x = 0, so b = -37.

Substitute these values into the formula to create an equation for the table of values:

[tex]\boxed{y=-2.5x-37}[/tex]

Answer: Let's use the variables c and a to represent the number of children and adults who used the pool, respectively.

We know that the total number of people who used the pool is 631, so we can write:

c + a = 631 (equation 1)

We also know that the total receipts for admission were $1013.00. The cost for children is $1.25 and the cost for adults is $2.00, so we can write:

1.25c + 2a = 1013 (equation 2)

Now we have two equations with two unknowns. We can solve for c and a by using elimination or substitution.

Let's use elimination. Multiply equation 1 by 1.25 to get:

1.25c + 1.25a = 788.75 (equation 3)

Subtract equation 3 from equation 2 to eliminate c:

0.75a = 224.25

a = 299

Now we can use equation 1 to solve for c:

c + 299 = 631

c = 332

Therefore, there were 332 children and 299 adults who used the pool that day.

Step-by-step explanation:

The volume of the right cone below is 1152π/3 cubic units then the value of x is 24.

The volume of a right circular cone is given by the formula:

V = (1/3)πr²h

where π is pi (approximately equal to 3.14), r is the radius of the circular base, and h is the height of the cone.

In this problem, we are given that the volume of the cone is 1152π/3 cubic units and that the value of x is related to the radius and height of the cone.

Let's first write the formula for the volume of the cone in terms of x:

V = (1/3)π(x/3)²(x/3)

Simplifying this expression, we get:

V = (1/27)πx²

We are given that V = 1152π/3, so we can substitute this into the formula above and solve for x:

1152π/3 = (1/27)πx³

Multiplying both sides by 27/π, we get:

x³ = 1152*27/3

x³ = 27648

Taking the cube root of both sides, we get:

x = 24

Therefore, the value of x is 24.

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The correct options for the frequency table problem is -

D. Categories are descriptions of​ data, such as which grades students received on a test or the heights of trees in a forest. They can describe qualities or represent counts or measurements. The frequency of a category is the number of data values in the category.

What is frequency table?

A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.

D. Categories are descriptions of data, such as which grades students received on a test or the heights of trees in a forest.

They can describe qualities or represent counts or measurements.

The frequency of a category is the number of data values in the category.

A frequency table is a table that displays the categories or groups of a set of data along with their corresponding frequencies.

The categories are typically represented in the left column, and the frequencies are listed in the right column.

The categories represent the possible values or ranges of values that the data can take.

For example, in a frequency table of student grades on a test, the categories might be "A," "B," "C," "D," and "F."

The frequency of a category is the number of times that the data falls within that category.

For example, if there are 20 students in a class and 5 of them received an "A" on a test, then the frequency of the "A" category would be 5.

Relative frequency is the proportion or percentage of observations in a category relative to the total number of observations.

It is calculated by dividing the frequency of a category by the total number of observations.

For example, if there are 20 students in a class and 5 of them received an "A" on a test, then the relative frequency of the "A" category would be 5/20 = 0.25 or 25%.

Cumulative frequency is the running total of frequencies for a set of data.

For example, if the frequency of the "A" category is 5 and the frequency of the "B" category is 10, then the cumulative frequency of the "B" category would be 5 + 10 = 15.

It represents the total number of observations that fall within a category and all previous categories.

Therefore, the correct option is D.

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Answer:

Step-by-step explanation:

Therefore, 12 minutes of play awards 4.5 points.

The constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded and 5 points are awarded for 20 minutes of play.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that for every 4 minutes of play, 1/2 point is awarded.

For every 12 minutes of play, 1 1/2 points are awarded.

We can set up a proportion to find the constant of proportionality:

(1/2 point) / (4 minutes) = (3/2 points) / (12 minutes)

Simplifying the left side, we get:

1/8 = (3/2 points) / (12 minutes)

Multiplying both sides by 12, we get:

1.5 = (3/2)P

P = (1.5) x (2/3) = 1

Therefore, the constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded.

By constant of proportionality, the equation that represents the relationship between the number of points awarded and the amount of time played:

P = (1/4)t

To find the number of points awarded for 20 minutes of play, we can use the equation P = (1/4)t:

P = (1/4)(20)

= 5

Hence, the constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded and 5 points are awarded for 20 minutes of play.

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7 in

[tex] \frac{1}{2} = \frac{x}{84} \\ 84 \times \frac{1}{12} = \frac{x}{84} \times 84 \\ 84 \times \ \frac{1}{12} = x \\ 7 = x[/tex]