The perimeter of a square is the product of four and the length of a side. Which of the following function rules could be used to find the perimeter of a square, represented by y, given the length of a side, represented by x?

x=y+4
y=x+4
x= 4y
y=4x

1) In the first quantity reasoning, the next logical pattern that should follow if it is repeated is E.

2) In the second quantity reasoning, the next logical pattern is D.

A logical pattern is logical sequence of numbers, words, objects, pictures, etc., that follows a related sequence.

Logical patterns are used on quantitative reasoning to understand and communicate mathematical principles.

We can identify three types of logical pattern as follows:

The arrow pointing down without an enclosed circle follows the arrow point up with an enclosed circle in the bigger circle.

Similarly, for the second question, the inner circle at the angles matches the pattern with Option D.

Thus, for the first question, the next logical pattern is Option E while it is Option D for question two.

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Answer:

165 minutes

Step-by-step explanation:

To solve for the number of minutes that Joaquin played for, we can use this expression:

(let 'a' represent how much time passed from the time Joaquin started playing basketball until the time he arrived at home)

Subtracting 1:10 from each side:

1:10 - 1:10 cancels out to 0, while 3:35 - 1:10 is equal to 2:25.

So, the expression is now:

So, 2 hours and 25 minutes passed.

If we know that 1 hour is equivalent to 60 minutes, we can use this expression to solve for however many minutes are in 2 hours:

Now we need to add on the number of minutes and the time it took him to get home:

Therefore, 165 minutes passed from the time Joaquin started playing basketball until the time he arrived at home.

Answer: We can plot the given points on a coordinate plane where each unit represents 2 miles:

 y

 |    E(1,2)

 |      

 | M(-4,2)

 |      

 |      

 |H(-4,-1)   F(1,-1)

 |___________________

           x

Now we can see that the distance between the football field (F) and the high school (H) is 5 units in the x direction and 1 unit in the y direction, which corresponds to a distance of 5 x 2 = 10 miles in the x direction and 1 x 2 = 2 miles in the y direction. Using the Pythagorean theorem, we can find the distance between the two points:

distance = sqrt((10)^2 + (2)^2)

        = sqrt(104)

So the distance between the football field and the high school is approximately 10.198 miles. Therefore, the statement that is true is:

"The distance between the football field and the high school is approximately 10.198 miles."

Step-by-step explanation:

Answer:

D 40 square feet

Step-by-step explanation:

2×8=16

16÷2=8 is area of one triangle

8+8=16 is area of both triangles

8×3=24 is area of rectangle

24+16=40 square feet

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:

C

Step-by-step explanation:

I think its C because where x is you see those three lines, those mean congruent so in that triangle whatever x is the other two angles are the same thing. If I had to guess what x is, its prob 60.

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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Answer:

(-6, -5)

(Don't forget to give me brainiest)

Step-by-step explanation:

1. Make the two equations equal to each other: -4x - 29 = -x - 11

2. Add "X" on both sides: -4x - 29 = -x - 11

                                              +x             +x

                                       = -3x - 29 = -11

3. Add both sides by "29":      -3x - 29 = -11

                                                  +29          +29

                                                   =    -3x = 18

4. Divide both sides by "-3" to isolate "X":     -3x = 18

                                                                         -3         -3

                                                                            x = -6

5. Plug in "-6" to "X" on first equation:  y = -4(-6)-29

                                                                y = 24 - 29

                                                                y = -5

6. Solution is: (-6, -5)

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 inequality of the set on the number line is x ≤ 7

The set of numbers on a number line that consists of all whole numbers less than 5 can be represented by the inequality:

x < 5

This inequality means that any number x that is less than 5 is included in the set.

The set of numbers on a number line that consists of all whole numbers less than or equal to 7 can be represented by the inequality:

x ≤ 7

This inequality means that any number x that is less than or equal to 7 is included in the set.

So, we have

x < 5 and x ≤ 7

Combine the inequalites

x ≤ 7

Hence, the set are numbers less than or equal to 7

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It takes apprοximately 3.5 years fοr an investment with an annual interest rate οf 20%, cοmpοunded cοntinuοusly, tο dοuble frοm $9,300 tο $18,600.

Cοmpοund interest is a sοrt οf interest that is calculated using bοth the principal—the initial amοunt invested οr bοrrοwed—and the interest that has accrued οver time. In οther wοrds, the interest fοr the fοllοwing periοd is cοmputed οn the new, larger amοunt after the interest generated during each periοd has been added tο the principal.

Cοmpοund interest can be explained as interest οn interest. The principle grοws οver time at a rising rate as the interest generated in each periοd is added tο it. Because οf this, cοmpοund interest is an effective instrument fοr lοng-term investing and saving.

Fοr instance, if yοu put $1,000 intο an accοunt with a cοmpοund interest rate οf 5%, yοu will receive $50 in interest the first year. Yοur tοtal sum at the end οf the first year will be $1,050 (the initial $1,000 plus $50 in interest). Yοu will receive $52.50 in interest since in the secοnd year the interest is cοmputed οn $1,050 rather than $1,000. This will increase yοur οverall balance tο $1,102.50 by the cοnclusiοn οf the secοnd year, and sο οn fοr succeeding years.

In cοnclusiοn, cοmpοund interest can be a pοtent tοοl fοr lοng-term grοwth οf yοur savings οr investments, but it's critical tο cοmprehend hοw it wοrks and pick assets with cοmpetitive interest rates and lοw expenses.

Tο find the time it takes fοr an investment tο dοuble with cοntinuοus cοmpοunding, we can use the fοrmula:

[tex]t = ln(2) / (r \times ln(1 + r))[/tex]

where:

t is the time it takes fοr the investment to double

r is the annual interest rate as a decimal

In this case, the annual interest rate is 20%, or 0.20 in decimal fοrm. So,

we can plug in the values and sοlve for t:

[tex]t = ln(2) / (0.20 \times ln(1 + 0.20))\\t = 3.5 years[/tex]

Therefore, it takes apprοximately 3.5 years for an investment with an annual interest rate of 20%, compounded continuously, to dοuble from $9,300 tο $18,600.

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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

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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Answer would be shifted up

Step-by-step explanation:

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

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

In Mathematics, a set is a group of unique elements. Here, the set M consists of three-digit numbers where the first digit is greater than the second by 4, and the third digit is greater than the first by 2. Examples of such numbers could be 530, 641, 752, etc.

The subject of the question is Mathematics, more specifically, the definition and properties of a set. In Mathematics, a set is a collection of distinct elements. A three-digit number has three digits: the first, second and third digit. In this case we need numbers where the first digit is greater than the second by 4, and the third digit is greater than the first by 2.

For example, let's take 501. Here, 5 is the first digit, 0 is the second and 1 is the third. The first digit is greater than the second by 5, not 4, therefore 501 does not belong to the set. But if we consider 640, here 6 is the first digit, 4 is the second and 0 is the third. The first digit is greater than the second by 2 and the third digit is less than the first by 6. So 640 belongs to the set. Therefore, our set M can include numbers like 530, 641, 752, and so on.

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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]

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:

Answer: 2 over 3

Step-by-step explanation: The GCF of 90 and 135 is 45. So,

divide 90 by 45 = 2

divide 135 by 45 = 3

Answer: 2/3

Answer:

The last one

Step-by-step explanation:

First one is a parabola

Second one is an absolute value

Third one is a cubic

Fourth one is a linear

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.

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:

I'm assuming the question is how many miles in total did mary swim.

if this is the case then we just multiply the number of days by the number of miles per day.

Hence,

3/4 × 8 = 6

so 6 miles in total.

make sure to ask if you need any further help

Step-by-step explanation:

Answer: 18 boxes per hour

Step-by-step explanation:

72 divided by 4 is 18

The 90% confidence interval for the difference between the two sample proportions are -0.078 <p₁ - p₂ < 0.003.

To find the 90% confidence interval for the difference between two sample proportions, use the formula:

CI = (p₁ - p₂) ± z√((p₁(1-p₁)/n₁) + (p₂(1-p₂)/n₂))

where:

p₁ = number of successes in sample 1 / sample size 1

p₂ = number of successes in sample 2 / sample size 2

n₁ = sample size 1

n₂ = sample size 2

z = z-score for the desired confidence level (90% in this case)

Using the given values:

p₁ = 780/820 = 0.9512

p₂ = 795/804 = 0.9888

n₁ = 820

n₂ = 804

z = 1.645 (from standard normal distribution table for 90% confidence level)

Plugging in the values:

CI = (0.9512 - 0.9888) ± 1.645√((0.9512(1-0.9512)/820) + (0.9888(1-0.9888)/804))

= (-0.0376) ± 0.0403

= (-0.078, 0.003)

Therefore, the 90% confidence interval for the difference between the two sample proportions is (-0.078, 0.003).

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Answer: To determine the total dollar amount of Finished Goods Inventory at the end of March, we need to calculate the total cost of the jobs that have been completed during March and have been transferred to the Finished Goods Inventory.

From the information given, we know that the company has no beginning Work in Process or Finished Goods inventories, so all the costs incurred during March are related to the jobs started during the month.

Let's start by calculating the total cost of Job 2, which is finished but not sold by the end of March. We will then use this cost to calculate the total cost of the jobs that have been completed during March and transferred to the Finished Goods Inventory.

Job 2:

Direct materials: Rs. 10,000

Direct labor: Rs. 8,000

Overhead applied: 60% x Rs. 10,000 = Rs. 6,000

Total cost of Job 2: Rs. 24,000

Now, let's calculate the total cost of the jobs that have been completed during March:

Job 1:

Direct materials: Rs. 6,000

Direct labor: Rs. 4,000

Overhead applied: 60% x Rs. 6,000 = Rs. 3,600

Total cost of Job 1: Rs. 13,600

Job 3:

Direct materials: Rs. 8,000

Direct labor: Rs. 5,000

Overhead applied: 60% x Rs. 8,000 = Rs. 4,800

Total cost of Job 3: Rs. 17,800

Total cost of jobs completed during March: Rs. 13,600 + Rs. 17,800 = Rs. 31,400

Since the company has no beginning Finished Goods Inventory, the total cost of the jobs completed during March and transferred to the Finished Goods Inventory is equal to the total cost of the Finished Goods Inventory at the end of March.

Therefore, the total dollar amount of Finished Goods Inventory at the end of March is Rs. 31,400.

Step-by-step explanation:

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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Step-by-step explanation:

speed = distance / time

distance = speed × time

they both have the same speed.

distanceB = distanceA + 4

so,

distanceA = speed × 25 min

distanceB = distanceA + 4 = speed × 35 min

distanceA = speed × 35 - 4

both distanceA expressions must be equal :

speed × 25 = speed × 35 - 4

subtract 25speed from both sides

0 = speed × 10 - 4

add 4 to both sides

4 = speed×10 min

divide both sides by 10 min

4 miles / 10 min = speed

to get the usual miles per hour, we need to multiply numerator and denominator by the same number, so that the denominator is 1 hour = 60 minutes.

as we cab see, we need to multiply by 6/6 :

4/10 × 6/6 = 24/60 = 24 miles per hour.

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.

Answer:

y = (3a + sqrt(11a^2 - 8b + 41)) / 2

y = (3a - sqrt(11a^2 - 8b + 41)) / 2

Step-by-step explanation:

To find the tangent lines that are perpendicular to the given line, we need to find the slope of the given line and then find the negative reciprocal of that slope. The negative reciprocal will be the slope of the tangent lines we are looking for.

The given line is 2x + y = 10, which can be rewritten as y = -2x + 10. Therefore, the slope of the given line is -2.

The center of the circle can be found by completing the square of the x and y terms. We have:

x^2 - 4x + y^2 = 1

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

Therefore, the center of the circle is (2,0), and the radius is sqrt(5).

Now, we can find the equation of the tangent lines. Let (a,b) be the point where the tangent line intersects the circle. Since the tangent line is perpendicular to the given line, its slope is the negative reciprocal of -2, which is 1/2. Therefore, the equation of the tangent line passing through (a,b) is:

y - b = (1/2)(x - a)

To find the points of intersection of this line and the circle, we substitute y = -2x + 10 into the equation of the tangent line and solve for x:

(x - a)^2 + (-2x + 10 - b)^2 = 5

Expanding and simplifying this equation, we get:

5x^2 - 4ax + 4a^2 + 4bx - 40b + 84 = 0

This is a quadratic equation in x, so we can solve for x using the quadratic formula:

x = [4a ± sqrt(16a^2 - 4(5)(4a^2 + 4b - 84))] / 10

Simplifying this expression, we get:

x = [2a ± sqrt(11a^2 - 8b + 41)] / 5

Now we can substitute these values of x into the equation of the tangent line to find the corresponding values of y:

y = -2x + 10

y = -a + b + (1/2)(2a ± sqrt(11a^2 - 8b + 41))

This gives us two equations for the tangent lines passing through (a,b), one for each value of x. We can simplify these equations to get:

y = (3a ± sqrt(11a^2 - 8b + 41)) / 2

Therefore, the equations of the tangent lines that are perpendicular to the given line are:

y = (3a + sqrt(11a^2 - 8b + 41)) / 2

y = (3a - sqrt(11a^2 - 8b + 41)) / 2

where (a,b) is any point on the circle (x - 2)^2 + y^2 = 5.

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

Learn more about difference of two squares on:

brainly.com/question/22256679

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