Determine whether the pair of functions are inverses functions

The value of x for the given rectangle in which the perimeter of both the rectangle are equal is x = 15.

What about rectangle?

A rectangle is a four-sided plane figure with four right angles (90-degree angles) and opposite sides that are parallel and equal in length. In other words, it is a parallelogram with all angles being right angles. The two pairs of parallel sides of a rectangle are called the length and width (or height) respectively. The area of a rectangle is found by multiplying its length by its width, while its perimeter is found by adding up the lengths of all four sides. Rectangles are commonly used in mathematics, geometry, engineering, and architecture, among other fields.

Define perimeter of rectangle:

The perimeter of a rectangle is the total distance around the outside of the rectangle. It is the sum of the lengths of all four sides of the rectangle. If the length of the rectangle is denoted by "l" and the width (or height) is denoted by "w", then the formula for the perimeter of a rectangle is:

⇒ Perimeter = 2(l + w)

According to the given information:

As, we know that the perimeter of the rectangle is sum of all side of the rectangle in which,

The perimeter of first rectangle is =   [tex]2(1.4x + 5x + 5.25)[/tex]

The perimeter of second rectangle is = [tex]2(4.25x + 3x - 7.5)[/tex]

It is given that perimeter of both the rectangle are equal so,

2(1.4x + 5x + 5.25) = 2(4.25x + 3x - 7.5)

2.8x + 10x + 10.5  = 8.5x + 6x - 15

2.8x + 10x - 8.5x -6x = -15 - 10.5

-1.7x = -25.5

x = 15.

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The total number of students Surveyed was 160, with 56 studying French and 104 studying Language X.

Assuming that there are only two foreign languages in the survey, French and another language (let's call it Language X), we can proceed with the given data.

French: 16, 12, 28
Totals: 40, 40, 80

Step 1: Analyze the given data.

The given data shows that there are three groups of students who are studying French:
- Group 1: 16 students
- Group 2: 12 students
- Group 3: 28 students

The total number of students in each group is:
- Group 1: 40 students
- Group 2: 40 students
- Group 3: 80 students

Step 2: Calculate the number of students studying Language X.

To determine the number of students studying Language X in each group, subtract the number of students studying French from the total number of students in each group:
- Group 1: 40 - 16 = 24 students
- Group 2: 40 - 12 = 28 students
- Group 3: 80 - 28 = 52 students

Step 3: Summarize the results.

In summary, the survey conducted by Christy found the following results:
- French: 16 students in Group 1, 12 students in Group 2, and 28 students in Group 3
- Language X: 24 students in Group 1, 28 students in Group 2, and 52 students in Group 3

The total number of students surveyed was 160, with 56 studying French and 104 studying Language X.

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The given quadrilateral can be named as ABCD, where A(0,-1), B(1,4), C(4,3), and D(3,-2). The area of the given quadrilateral ABCD is 17 square units.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

To find the area of this quadrilateral, we can use the formula:

Area = 1/2 * |(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) - (y₁x₂ + y₂x₃ + y₃x₄ + y₄x₁)|

where (x₁,y₁), (x₂,y₂), (x₃,y₃), and (x₄,y₄) are the coordinates of the vertices of the quadrilateral in order.

Substituting the values, we get:

Area = 1/2 * |(04 + 13 + 4*(-2) + 3*(-1)) - (-11 - 44 - 3*3 - (-2)*0)|

Area = 1/2 * |(-8 - 26)|

Area = 1/2 * |-34|

Area = 17 square units

Therefore, the area of the given quadrilateral ABCD is 17 square units.

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Answer:

2%

Step-by-step explanation:

(sales tax/ cost before tax) x 100%

(6.20 ÷ 310) x 100

0.02 x 100%

= 2

so the answer is 2%

The boat is 1189 feet away from the lighthouse at position A, and the angle between the boat and the beacon light is 10°. The distance between point A and point B is 2811.4 feet.

The boat is 1189 feet away from the lighthouse at position A, and the angle between the boat and the beacon light is 10°.

As a result, if h is the lighthouse's height, we have:

tan 10 = h/1189

h = 1189.tan 10

h = 209.7 feet

The elevation angle at position B is 3°. The following equation provides the distance (d) from the lighthouse:

tan 3 = h/d

d = h/tan 3 = 4000.4 feet

Therefore, the distance between points A and B is 400.4 - 1189

= 2811.4 feet

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Answer: I can help you!

Step-by-step explanation:

Answer and explanations

Answer:

Sure! To find the distance between two points, we can use the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) Using the points (0, -7) and (-9, 5), we can plug in the values: d = sqrt((-9 - 0)^2 + (5 - (-7))^2) d = sqrt((-9)^2 + (12)^2) d = sqrt(81 + 144) d = sqrt(225) So the distance between the two points is 15 units.

Answer:

The distance between the two points is 15 units.

Step-by-step explanation:

The length of the arc AD is approximately 5.24 cm.

What is the length of an arc in circle?

Length of arc = (angle of arc / 360°) x (circumference of circle)

Here, the angle of arc is given as 60° and the radius of the circle is given as 5 cm.

So, the circumference of the circle can be found as:

circumference of circle

[tex]= 2 \times π \times radius \\ = 2 \times π \times 5 \\ = 10π cm[/tex]

Using the formula for length of arc, we can find the length of AD as

length of AD = (angle of arc / 360°) x (circumference of circle)

= (60° / 360°) x (10π cm)

= (1/6) x (10π cm)

= (5/3)π cm

≈ 5.24 cm

Therefore, the length of the arc AD is approximately 5.24 cm.

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Correct question is "There is a circle with centre O and AD is an arc. Now radius of the circle is 5 cm and angle of arc is 60° then what is the length of the arc AD ?"

Answer: Two other positive angles of rotation that take A to B are:

- 13π/6 radians counterclockwise

- 25π/6 radians clockwise

Step-by-step explanation:

Generally, insurance helps the policyholder to transfer the A. Risk from their bank account to the insurance company.

Insurance risk refers to the exposure of a policyholder to financial loss and consequent inability to meet their liabilities.

Insurance risks are transferable to insurance companies who pool resources together from many policyholders to meet and spread the risks.

Insurance does not transfer money, insurance, or health to the insurance company, but it transfers risk.

Thus, the correct option is Option A.

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The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

What is  Graph?

In mathematics, a graph is a visual representation of a set of objects, called vertices or nodes, that are connected by lines or arcs, called edges or links. Graphs are commonly used to represent and analyze relationships between different entities, such as people, places, or things.

here, we have,

The vertices in a graph can represent anything, such as cities on a map, people in a social network, or molecules in a chemical reaction. The edges between vertices represent the connections or relationships between them. For example, in a social network graph, the edges might represent friendships between people, while in a transportation network, the edges might represent roads or train tracks connecting different cities.

Graphs are used in many areas of mathematics and science, including computer science, physics, biology, and social science. They are a powerful tool for analyzing and visualizing complex systems and relationships, and have many practical applications, such as in route planning, network analysis, and social network analysis.

The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

Answer:

y=(11-8p)xz

Step-by-step explanation:

xyz+8p=11

xyz=11-8p

y=(11-8p)xz

Answer:

The student made a mistake when squaring -4.

-4 * -4 = 16.  Had the expressions said -x^2, then the answer would indeed be -16 since -1 *(-4*-4) = -16

Furthermore, since the answer is 16, you'd do (16 - 7) ^3, which equals (9)^3, which is 729 and not -12,167

Step-by-step explanation:

y= -3/3 is equivalent to -1

so y = -1

it located on the negative y-axis

where y= -1

The Julia needs to sell at least 1,819 subs to break even each month with the new upscale repositioning of her sub shop.

1- To break even, Julia needs to cover all her costs which include labor costs, insurance, rent, and utilities along with the cost of ingredients and packaging.
Total fixed costs = Labor costs + Insurance + Rent + Utilities = $7,000 + $900 + $800 + $300 = $8,000
Total variable cost per sub = Average cost of ingredients/packaging = $1.15

To break even, Julia needs to sell enough subs to cover her fixed costs and variable costs.

Breakeven point = Fixed costs / (Price per sub - Variable cost per sub)
Breakeven point = $8,000 / ($6 - $1.15) = 1,778.26

Therefore, Julia needs to sell at least 1,779 subs to break even each month.

2- If Julia is able to lower the average cost of ingredients and packaging per sub to $0.95, then the new variable cost per sub becomes $0.95. All other costs remain the same.

Breakeven point = Fixed costs / (Price per sub - Variable cost per sub)
Breakeven point = $8,000 / ($6 - $0.95) = 1,723.68

Therefore, Julia needs to sell at least 1,724 subs to break even each month with the new lower cost of ingredients and packaging.

3- If Julia raises the price per sub to $10 and the variable cost per sub rises to $4.22, the new breakeven point becomes:

Breakeven point = Fixed costs / (Price per sub - Variable cost per sub)
Breakeven point = $8,000 / ($10 - $4.22) = 1,818.18

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Answer:

y > 3x - 1

set y = 0

0 > 3x - 1

x > 1/3

points are [ 1/3,0]

set x = 0

y > 3(0) - 1

y > - 1

points are [0,-1]

second question

x + y ≤ - 2

set x = 0

y ≤ - 2

points are [0,-2]

set y = 0

x ≤ - 2

points are [-2,0]

So therefore A should be shaded.

Answer:

rational function is:

f(x) = (x² - 4x - 5) / (x - 9)

To find f(5), we substitute x = 5:

f(5) = (5² - 4(5) - 5) / (5 - 9) = (-10) / (-4) = 5/2

To find f(9), we substitute x = 9:

f(9) = (9² - 4(9) - 5) / (9 - 9) = undefined

The function value f(9) is undefined because the denominator becomes zero, which makes the expression undefined.

To find f(7), we substitute x = 7:

f(7) = (7² - 4(7) - 5) / (7 - 9) = (-10) / (-2) = 5

Therefore, the function values are:

f(5) = 5/2

f(9) = undefined

f(7) = 5

The formula to find the interquartile range (IQR) is:

IQR = Q3 - Q1

where Q1 and Q3 are the first and third quartiles, respectively. Since the distribution of weights of pumpkins is approximately normal, we can use the formula for the standard error of the mean to find the standard deviation of the sampling distribution of the mean:

SEM = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size, and sqrt represents the square root function.

Plugging in the given values, we get:

SEM = 1.68 / sqrt(15)

≈ 0.4334

To find the first and third quartiles, we need to find the z-scores corresponding to the 25th and 75th percentiles of the standard normal distribution, respectively. These z-scores can be found using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we find that:

Therefore, the first and third quartiles are:

Q1 = μ + z1 * SEM

= 8.3 - 0.6745 * 0.4334

≈ 7.998

Q3 = μ + z3 * SEM

= 8.3 + 0.6745 * 0.4334

≈ 8.602

Finally, we can calculate the interquartile range (IQR) as:

IQR = Q3 - Q1

≈ 8.602 - 7.998

≈ 0.604

Rounding to the nearest thousandth, we get:

IQR ≈ 0.604

Therefore, the value of the interquartile range (IQR) for the mean weight of 15 pumpkins is 0.604 pounds.

Answer:407.7669

Step-by-step explanation:

The total number of seats available for the baseball game can be calculated by adding the number of box and club seats available whch is found to be 25,200.

The game of baseball can be used to teach various mathematical concepts, such as probability, statistics, graphing, estimation, and basic arithmetic. The game can also be used to introduce concepts such as geometry and trigonometry, as well as to build problem-solving skills.

The total number of seats available can be calculated by adding the number of box and club seats available, which is

12,600 + 5400 = 18,000.

This total can then be multiplied by the respective percentages of the other two categories to get the total number of seats available.

For instance, the total number of bleacher seats available can be calculated by multiplying 12,000 by 18%.

12,000 x 0.18 = 2,160

Similarly, the total number of grandstand seats available can be calculated by multiplying 12,000 by 42%.

12,000 x 0.42 = 5,040

Hence, the total number of seats available for the baseball game is

18,000 + 2,160 + 5,040 = 25,200.

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The absοlute fοrm οf the given inequality is |x+1|>6.

In mathematics, inequality is  a statement οf an οrder relatiοnship that is a relatiοnship between twο values that are nοt equal,—greater than, greater than οr equal tο, less than, οr less than οr equal tο—between twο numbers οr algebraic expressiοns. Such as 7<9 οr 5>3 etc.

Given inequality is

x<−7 οr x>5

The distance between -7 and 5 is

5- (-7) = 5+7= 12

Dividing that by 2 we get,

12/2 =6

It is the c value

We use the greater than since we have an οr

|x−b|>6 ----------------- (1)

Substituting  a value  x=5 in equatiοn (1) with an equals sign tο determine b we get

5-b =6

b= -1

The absοlute fοrm οf the given inequality is |x+1|>6

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The value of t for a t-distribution with 10 degrees of freedom such that the area between -t and t equals 90% is 1.812.

To find the value of t for a t-distribution with 10 degrees of freedom such that the area between -t and t equals 90%, we can use a t-table.

Using a t-table, we can find the t-value that corresponds to a 5% area in the upper tail of the distribution, since the area between -t and t is 90% (leaving 10% in the tails).

For a t-distribution with 10 degrees of freedom, the critical value for a 5% area in the upper tail is 1.812. Check the attached image.

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Answer:

0; п; 1,5п; 2п.

Step-by-step explanation:

all the details are provided in the attachment.

The missing number in the pattern is 64.

To find the missing number in the pattern, we need to identify the rule that relates the given numbers.

If we look at the pattern, we can see that each number is obtained by subtracting a certain value from the previous number.

Starting from 106, we subtract 16 to get 90. Then we subtract 14 to get 76. To get the next number, we need to subtract 12 from 76:

76 - 12 = 64

Therefore, the missing number in the pattern is 64.

After 64, we continue the pattern by subtracting 8 from 64 to get 56, and then subtracting 10 from 56 to get 46.

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We can estimate that apprοximately 41 teachers vοlunteer at an animal shelter.

The given infοrmatiοn tells us that 40% οf the teachers vοlunteer as hοmewοrk tutοrs. We dο nοt knοw hοw many teachers there are in tοtal, sο we cannοt directly determine the number οf teachers whο vοlunteer at an animal shelter.

Hοwever, we can use the infοrmatiοn abοut the percentage οf teachers whο vοlunteer at a seniοr center, spοrts cοach, and animal shelter tο estimate the number οf teachers whο vοlunteer at an animal shelter.

If 15% οf the teachers vοlunteer at a seniοr centre, 25% οf the teachers vοlunteer as spοrts cοaches, and 20% οf the teachers vοlunteer at an animal shelter, then the tοtal percentage οf teachers whο vοlunteer is:

15% + 25% + 20% + 40% = 100%

This means that all οf the teachers at the Blue Pacific Schοοl District vοlunteer in οne οr mοre οf these categοries.

Tο estimate the number οf teachers whο vοlunteer at an animal shelter, we can assume that the percentage οf teachers whο vοlunteer in each categοry is prοpοrtiοnal tο the number οf teachers whο vοlunteer in that categοry. If we let x be the tοtal number οf teachers at the schοοl district, then we can write:

0.15x = number οf teachers whο vοlunteer at a seniοr center

0.25x = number οf teachers whο vοlunteer as spοrts cοaches

0.20x = number οf teachers whο vοlunteer at an animal shelter

0.40x = number οf teachers whο vοlunteer as hοmewοrk tutοrs

Since we knοw that 82 teachers vοlunteer as hοmewοrk tutοrs, we can sοlve fοr x:

0.40x = 82

x = 205

Therefοre, there are 205 teachers in the Blue Pacific Schοοl District. Tο estimate the number οf teachers whο vοlunteer at an animal shelter, we can plug in x and 0.20x intο the equatiοn fοr the number οf teachers whο vοlunteer at an animal shelter:

0.20x = 0.20(205) = 41

Sο we can estimate that apprοximately 41 teachers vοlunteer at an animal shelter.

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Answer:

y = 16000(0.86)^t

Step-by-step explanation:

y = 16000(0.86)^t

Answer:

  a) 7 m

  b) 22 cm

Step-by-step explanation:

Given plans at a scale of 1 : 50, you want (a) the actual length corresponding to a plan length of 14 cm, and (b) the plan length corresponding to an actual length of 11 m.

The actual lengths are wanted in meters, so we can rewrite the scale to translate between plan cm and actual m.

  plan : actual = 1 cm : 50 cm

  = 1 cm : 0.5 m

  = 2 cm : 1 m

Multiplying the scale by 7, we have ...

  2 cm : 1 m = 14 cm : 7 m

The actual length is 7 meters.

Multiplying the scale by 11, we have ...

  2 cm : 1 m = 22 cm : 11 m

The plan length is 22 cm.

Answer: This type of sample is called a stratified random sample. The population (city) is divided into various zones, and then a random sample of households (5 from each zone) is taken from each stratum (zone). This helps ensure that the sample is representative of the population as a whole and includes a proportional number of households from each zone.

Step-by-step explanation:

stratified random sampling is a powerful tool for researchers to ensure that their sample accurately reflects the population of interest, and can help increase the validity and reliability of research findings.

How to study sample?

This sampling method is an example of stratified random sampling, where the population is divided into different subgroups or strata, and a random sample is drawn from each stratum. In this case, the strata are the various zones of the city, and the researcher randomly selects five households from each zone.

Stratified random sampling is a commonly used sampling method in research because it can increase the representativeness of the sample and reduce sampling error. By dividing the population into different strata based on relevant characteristics, such as geographic location, age, gender, or income level, the researcher can ensure that each stratum is adequately represented in the sample.

In this example, the researcher is interested in studying public transportation usage in different zones of the city. By stratifying the population by zone and selecting a random sample of households from each zone, the researcher can obtain a representative sample of the population and draw conclusions about public transportation usage in each zone.

Overall, stratified random sampling is a powerful tool for researchers to ensure that their sample accurately reflects the population of interest, and can help increase the validity and reliability of research findings.

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Your complete question is :-A city collects data about public transportation. The researcher divides the city into various zones, and randomly chooses 5 households from each zone to survey. Which type of sample does this represent?

Step-by-step explanation:

use the formula for completing the square