Solve the inequality 8k−(2k−1)≥7k−21, and write the solution in interval notation.

Answer: The correct statements that explain that the table does not represent a probability distribution are:

The results are all less than 0.

The probability is greater than 1.

The sum of the probabilities is 31/12.

A probability distribution must have probabilities between 0 and 1 (inclusive) and the sum of all probabilities must equal 1.

Step-by-step explanation:

Miranda needs to work 50 hours at her job in order to purchase the computer.

Amount is a term generally used to refer to a numerical value which represents a quantity of something. It can be used to describe the size, magnitude, or total of an object, event, or concept. Amount is often used to refer to money, but it can also be used to refer to other elements such as time, energy, weight, and volume. Amount can also be used to refer to a certain degree or level, such as a certain amount of effort or a certain amount of progress.

To find the amount of hours Miranda needs to work in order to purchase the computer, the following equation can be used:

12 x = Computer Price x 0.6

Where 12 is the hourly wage Miranda earns, x is the amount of hours Miranda needs to work, and 0.6 is the percentage (60%) of Miranda’s earnings that will be used to purchase the computer.

The computer price is not given, so let’s assume it to be $1000. Plugging in the values, the equation becomes:

12 x = 1000 x 0.6

Simplifying the equation, we have:

12 x = 600

Dividing both sides by 12, we get:

x = 600/12

x = 50

Therefore, Miranda needs to work 50 hours at her job in order to purchase the computer.

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The sum οf all pοssible lengths fοr TP is 12

A triangle is a type οf pοlygοn with three sides; the pοint where the twο sides meet is knοwn as the vertex οf the triangle. Between twο sides, an angle is created. One οf geοmetry's key cοmpοnents is this.

Triangle prοperties are necessary fοr sοme fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry. Based οn its angles and sides, a triangle can be classified intο variοus types.

Given that triangle TIP and triangle TOP are isοsceles triangles with sides;

TI = 5, PI = 7, PO = 11

Therefοre, given that triangle TIP is an isοsceles triangle, the length οf segment TP will be equal either the length οf segment TI οr segment PI which give;

TP = TI 5 οr TP = PI = 7

The sum οf all pοssible lengths fοr TP is given by the sum οf the twο unequal sides οf triangle TIP which gives;

The sum οf all pοssible lengths fοr TP = 5 + 7 = 12.

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Answer:

Answer

Step-by-step explanation:

The probability of Meikel wearing khakis and sandals is

3 / 12 which will give us

1/4

A 0.166 probability that they are over 45 years old is discovered using its notion from histogram.

A histogram is a form of graph that is used to show how a dataset is distributed. The horizontal axis shows the range of values in the dataset, while the vertical axis represents the frequency with which those values occur. It is a graphical depiction of a frequency table. Each bar's height corresponds to the number of observations that occur within a given bin, which is created by dividing the data into equal intervals known as bins.

In statistics and data analysis, histograms are frequently used to examine a distribution's form, particularly its central tendency, variability, and skewness. They are especially helpful for locating patterns and trends in the data as well as for spotting outliers, gaps, and clusters. Moreover, histograms can be used to contrast several datasets or look at how a dataset has changed over time.

The number of desired outcomes divided by the total number of outcomes yields a probability.

In this issue:

There are 150 workers overall, according to the histogram.

25 of them are older than 45 years old.

p = 25/150 = 0.166

This idea reveals a 0.166 probability that they are beyond 45 years old.

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The equation y = 2x + 4 is in slope-intercept form with m = 2 and b = 4. This means that the line has a slope of 2 and intersects the y-axis at the point (0, 4).

An equation is a statement that asserts the equality of two expressions or values, typically separated by an equal sign (=). The expressions or values on either side of the equal sign are called the "sides" of the equation.

Equations are used to represent mathematical relationships between variables and to solve problems involving those variables.

To check if an equation is in slope-intercept form, we need to ensure that it has the form:

y = mx + b

The equation y = 2x + 1/3 is also in slope-intercept form with m = 2 and b = 1/3. This means that the line has a slope of 2 and intersects the y-axis at the point (0, 1/3).

The equation y = 3x/2 + 1 is in slope-intercept form with m = 3/2 and b = 1. This means that the line has a slope of 3/2 and intersects the y-axis at the point (0, 1).

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Two potential locations for drilling are under consideration by an oil corporation.

a) The estimated profit is higher at Site A.

b) We can state that Site A has a larger expected profit than Site B by $17 million because the expected profit for Site A is higher than the expected loss for Site B.

To find the expected profit for each site, we need to multiply the profit from finding oil by the probability of finding oil and subtract the loss from not finding oil multiplied by the probability of not finding oil.

For Site A:

Expected profit = (Profit if oil is found x Probability of finding oil) - (Loss if no oil is found x Probability of not finding oil)

Expected profit = ($120 million x 0.2) - ($20 million x 0.8)

Expected profit = $24 million - $16 million

Expected profit = $8 million

For Site B:

Expected profit = (Profit if oil is found x Probability of finding oil) - (Loss if no oil is found x Probability of not finding oil)

Expected profit = ($180 million x 0.1) - ($30 million x 0.9)

Expected profit = $18 million - $27 million

Expected profit = -$9 million

Therefore, Site A has the larger expected profit of $8 million, while Site B has an expected loss of $9 million.

Since the expected profit for Site A is greater than the expected loss for Site B, we can say that Site A has a larger expected profit than Site B by $17 million ($8 million - (-$9 million)), which is the difference between their expected profits.

The complete question is:-

An oil company is considering two sites on which to​ drill, described as​ follows: Site​ A: Profit if oil is​ found: ​$120 million Site​ B: Profit if oil is​ found: ​$180 million Loss if no oil is​ found: ​$20 million Loss if no oil is​ found: ​$30 million Probability of finding​ oil: 0.2 Probability of finding​ oil: 0.1 a.  Which site has the larger expected​ profit? Site A has the larger expected profit. Your answer is correct. Site B has the larger expected profit. The expected profits for both sites are the same. b.  If the expected profit for both sites is not the​ same, by how much is the expected profit​ larger? ​$ nothing million  ​(Round to the nearest tenth as​ needed.) I need answer B and and explanation. Because I can calculate it as bigger, but my anwser doesn't match B.

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The solution to the problems are;

1.  Area = 108 square feet

2. Area = 342 square feet

3. x = $1, 890, x = $1764

4. Cost, x = $151. 2, $117. 6

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that;

From the diagram shown, we have that;

The deck is gray

The garden is white

1. The area of the garden in design A

Area = 9(12) = 108 square feet

2. The area of the deck in design A is;

Area = 18(25) = 450 square feet

The area of the deck without the garden = 450 - 108

Area = 342 square feet

3. If $4. 20 = 1 square feet in design A

Then, x = 450 square feet

x = $1, 890

Area of deck of design B = 21(20) = 420 square feet

cost = $1764

4. If $1. 40 = 1 square feet of garden A

Then, x = 108 square feet

Cost = $151. 2

For garden of design B

Area = 1/2 × (12)(14) = 84 square feet

Then, cost = $117. 6

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The coefficient of determination (R^2) is 3.78%.

To calculate the coefficient of determination (R^2), we need to first find the total sum of squares (SST) and the sum of squares error (SSE) from the given ANOVA table. SST is the variation between the observed values and the mean value of all observations. SSE is the variation between the observed values and the group means.

SST = Between groups + Within groups = 1,493.76 + 37,941.72 = 39,435.48

SSE = Within groups = 37,941.72

R^2 = (SST - SSE) / SST

Plugging in the values, we get:

R^2 = (39,435.48 - 37,941.72) / 39,435.48

R^2 = 0.0378

To convert this to a percentage, we multiply by 100 and round to two decimal places:

R^2 = 3.78% (rounded to 2 decimal places)

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From your 21st to your 51st birthday, if you deposit $500 quarterly into an account that pays 12% compounded quarterly, you will have about $386,711.70 in the account.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

FV = $500 x [(1 + 0.03/4)²²(4*30) - 1] / (0.03/4)

FV = $500 x [(1 + 0.0075)^120 - 1] / 0.0075

FV = $500 x [6.3207 - 1] / 0.0075

FV = $500 x 773.4234

FV = $386,711.70

Hence, From your 21st to your 51st birthday, if you deposit $500 quarterly into an account that pays 12% compounded quarterly, you will have about $386,711.70 in the account.

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Solution defines by [tex]x\geq 5[/tex]

A number line is typically a horizontal line that extends infinitely in both directions. It is used to represent both positive and negative numbers, and each point on the line corresponds to a unique real number.

Numbers to the right of zero are positive and increase as you move further to the right, while numbers to the left of zero are negative and decrease as you move further to the left. Zero is the midpoint of the number line and is neither positive nor negative.

Based on the information you've provided about the number line, it is clear that the solution set can extend beyond 8, as indicated by the arrow. This means that there are numbers greater than 8 that are included in the solution set.

Solution defines by [tex]x\geq 5[/tex]

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For Mrs. Sanchez's problem, the solution set can extend forever. Using the number line x ≥ 5.

A number line is typically a horizontal line that extends infinitely in both directions. It is used to represent both positive and negative numbers, and each point on the line corresponds to a unique real number.

Numbers to the right of zero are positive and increase as you move further to the right, while numbers to the left of zero are negative and decrease as you move further to the left. Zero is the midpoint of the number line and is neither positive nor negative.

Based on the information you've provided about the number line, it is clear that the solution set can extend beyond 8, as indicated by the arrow. This means that there are numbers greater than 8 that are included in the solution set.

Solution defines by x ≥ 5

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Answer:

v = c - 78930 + 57y - 6

Step-by-step explanation:

V = 207 cm^3

Step-by-step explanation:

volume of box A = 12 × 3 × 5 = 180 cm^3

volume of box B = 3 × 3 × 3 = 27 cm^3

total volume of box A and B = 180 + 27 = 207 cm^3

Option B : The range of 45 is the most accurate measure of variability to use to represent the data.

The range is the difference between the highest and lowest values in a dataset. In this case, the highest donation was $55 and the lowest was $10, so the range is:

range = highest value - lowest value = $55 - $10 = $45

Since the range takes into account all the values in the dataset, it is an appropriate measure of variability for this skewed dataset. The IQR (interquartile range) would also be a valid measure of variability, but it is less appropriate for skewed data because it only takes into account the middle 50% of the data and is less affected by extreme values. In this case, the extreme values (the two $55 donations) have a large effect on the distribution of the data, so the range is a more appropriate measure of variability.

Therefore, the charity should use the range of $45 to represent the variability of their donations.

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Answer: Answer is below <3

Step-by-step explanation:

It’s in-between zero and negative one because it’s a half number. (Not fully one yet)

Therefore, -1/2 would be in-between the number 0 and -1.

Answer:

-1/2 is "-0.5" in form of decimal

So,

the answer will come between 0 and -1

Kindly mark the answer brainliest

The estimated volume of the region obtained by rotating y = √(1 + 6x³) about the y-axis using the Midpoint Rule with n = 5 is 0.702 cubic units.

To use the Midpoint Rule to estimate the volume V, we first need to divide the interval [0, 1] into n subintervals of equal width. In this case, n = 5, so we have:

Δx = (1 - 0)/5 = 0.2

Next, we need to find the midpoint of each subinterval. The midpoints are:

x₁ = 0.1

x₂ = 0.3

x₃ = 0.5

x₄ = 0.7

x₅ = 0.9

Now we can evaluate the function y = √(1 + 6x³) at each midpoint to get the heights of the cylinders that will make up the approximate volume V:

y₁ = √(1 + 6(0.1)³) ≈ 1.027

y₂ = √(1 + 6(0.3)³) ≈ 1.247

y₃ = √(1 + 6(0.5)³) ≈ 1.466

y₄ = √(1 + 6(0.7)³) ≈ 1.687

y₅ = √(1 + 6(0.9)³) ≈ 1.908

Finally, we can use these heights to calculate the volumes of the cylinders and add them up to get an estimate of V:

V ≈ π(Δx/2)²(y₁ + y₂ + y₃ + y₄ + y₅)

≈ π(0.1)²(1.027 + 1.247 + 1.466 + 1.687 + 1.908)

≈ 0.702

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Answer:

x=7, y=6

Step-by-step explanation:

One of the ways we can find a value of a variable in a multiple part equation system is via substitution.

What is substitution?

Substitution works by making one equation equal to a variable with no coefficients (that is, a number without any action being done to the variable), then using this said equation and plugging it into the other equation to find the value of one variable. Then, using this value that was found can be plugged again to one of the two equations to find the other variable.

In our situation, one of the equations ([tex]y=-2x+20[/tex] ) is already equal to y; so we can use this equation to plug it in the second equation.

- Given: [tex]y=-2x+20\\6x-5y=12[/tex]

- Insert the first equation: [tex]6x-5(-2x+20)=12[/tex]

- Distribute the -5: [tex]6x+10x+-100=12[/tex]

- Combine like terms: [tex]16x-100=12[/tex]

- Isolate the variable x: [tex]16x-100=12\\~~~~~~+100+100\\16x=112\\\frac{16x}{16} =\frac{112}{16} \\x=7[/tex]

Now that we have the variable x=7, we can use this number to find the value of the variable y.

- Given: [tex]y=-2x+20[/tex]

- Plug in the known variable value: [tex]y=-2(7)+20\\[/tex]

- Solve: [tex]y=-14+20\\y=6[/tex]

Therefore, x=7, and y=6 is your final answer.

Additionally, we can cross reference this on a graphing calculator. Plug both of those formulas in as so, and the intersection between the two lines will be the answer of what x and y are equal to, (x,y).

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x=7 , y=6

_________________________


Substituting y = -2x + 20 =

6x - 5(-2x + 20) = 12

Simplifying =

6x + 10x - 100 = 12

Combining like terms =

16x - 100 = 12

we add 100 =

16x = 12 + 100
16x = 112

Divide both sides by 16 =

x = 112 / 16

x = 7

y = -2(7) + 20

y = -14 + 20

y = 6

x=7 , y=6

Answer: lim

x

→

2

x

2

−

4

x

−

2

=

4

Step-by-step explanation: If we look at the graph of

y

=

x

2

−

4

x

−

2

we can see that it is clear that the limit exists, and is approximately

4

graph{(x^2-4)/(x-2) [-10, 10, -5, 5]}

The numerator is the difference of two squares, and as such we can factorise using it as

A

2

−

B

2

≡

(

A

+

B

)

(

A

−

B

)

Se we can factorise as follows:

lim

x

→

2

x

2

−

4

x

−

2

=

lim

x

→

2

x

2

−

2

2

x

−

2

=

lim

x

→

2

(

x

+

2

)

(

x

−

2

)

x

−

2

=

lim

x

→

2

(

x

+

2

)

x

−

2

x

−

2

=

lim

x

→

2

(

x

+

2

)

=

(

2

+

2

)

=

4

Answer:

30%

Step-by-step explanation:

750-525/750*100%

225/750*100%

0.3*100%

30%

The definition of inverse states that if f(g(x)) = x, then g(x) is the inverse of f(x). We can substitute our functions in to check if this is true, and it is, so g(x) is the inverse of f(x).

Using our new definition of inverse from 3, we can symbolically verify that the function we wrote down in (d) is the inverse of (). To do this, we will substitute the function we wrote down in (d) into the definition of inverse, and we will substitute () into the definition as well. The definition of inverse states that if f(x) and g(x) are functions such that f(g(x)) = x, then g(x) is the inverse of f(x). We can substitute our functions in to check if this is true.If f(x) = 2x + 3 and g(x) = (x - 3) / 2, then f(g(x)) = ( (x - 3) / 2 + 3) = x. This satisfies the definition of inverse, so we can conclude that g(x) is the inverse of f(x).

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Answer:

y = 6x + 2

Step-by-step explanation:

The slope-intercept form is y = mx + b

What is the slope-intercept form of -6x + y = 2?

-6x + y = 2

Add 6x to both sides

y = 6x + 2

So, the answer is y = 6x + 2

Answer:

Kevin's age = 13

Step-by-step explanation:

Now we have to,

→ Find Kevin's age, if his father's age is 44.

Let us assume that,

→ Kevin's age = k

Forming the equation,

→ 3k + 5 = 44

Then the value of k will be,

→ 3k + 5 = 44

→ 3k = 44 - 5

→ 3k = 39

→ k = 39/3

→ [ k = 13 ]

Hence, the value of k is 13.

The age of Kevin is 13 years.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Given that, Kevin's father age is 5 years more than three times Kevin's age.

Let the age of Kevin be k.

Then, the age of Kevin's father is 3k+5

Kevin's father is 44 years old

Thus, 3k+5=44

3k=39

k=13

Therefore, the age of Kevin is 13 years.

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As a result, it would take 5 pretzel makers 22.6 minutes, or around 0.376 hours, to manufacture 88 pretzels.

To answer mathematical issues involving proportional relationships between various quantities, one can utilize the unitary method. Finding the value of one unit of a quantity and using that value to determine the value of another number of units is what it entails. In business and finance, the unitary technique is frequently used to address issues with cost, price, and quantity. The link between several units of measurement is also computed in physics and other fields.

given

To begin, we can apply the formula:

(Workers' Count) x (Efficiency) x (Time) = (amount of work)

To achieve this, multiply the total quantity of pretzels produced by the two pretzel makers by the sum of the labor hours worked by the number of workers:

One pretzel maker's productivity is calculated as follows: (444 pretzels / 2 workers x 6 hours) = 37 pretzels per worker-hour.

The time it would take for five pretzel producers to produce 88 pretzels may therefore be calculated using this efficiency:

37 pretzels were consumed each worker hour multiplied by five workers yields 88 pretzels.

By solving for time, we obtain:

Time is calculated as follows: 88 pretzels / (5 workers x 37 pretzels per worker-hour) = 0.376 hours.

As a result, it would take 5 pretzel makers 22.6 minutes, or around 0.376 hours, to manufacture 88 pretzels.

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The coordinates of the pre-image point A given the transformation is (4, 0)

If the image point of A after a translation right 1 unit and down 3 units is the point B(5,-3), then we can find the pre-image point A by reversing the translation.

This means we need to move B back 1 unit to the left and up 3 units to get to A.

So, the x-coordinate of A is 5 - 1 = 4 (moved 1 unit to the left)

And, the y-coordinate of A is -3 + 3 = 0 (moved 3 units up)

Therefore, the coordinates of the pre-image point A are (4,0).

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The missing denominator is 24.

Option D is the correct answer.

To find the missing denominator, we can use the property of equality that states that if we multiply or divide both sides of an equation by the same number, the equation remains true.

Starting with:

3/4 = 18/d

We can cross-multiply to eliminate the fractions:

3d = 4 x 18

3d = 72

Finally, we can solve for d by dividing both sides by 3:

d = 24

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The complete question is below:

What is the missing denominator?

3/4 = 18/d

A. 6

B. 10

C. 19

D. 24

The perimeter of the shaded shape KLNM is approximately 11.44 cm to 2 decimal places.

What is a circle?

A circle is a closed two-dimensional shape consisting of all the points that are equidistant from a given point called the center. The distance between the center and any point on the circle is called the radius.

We know that the central angle of both circles is 114 degrees, so the angle at the center of each circle is 114 degrees.

The angle formed by lines KL and KM is half of the central angle, which is 57 degrees. Similarly, the angle formed by lines NL and NM is also 57 degrees.

We can use the Law of Cosines to find the length of KL and NM:

KL² = OK² + OL² - 2(OK)(OL)cos(57°)

NM² = ON² + OM² - 2(ON)(OM)cos(57°)

We know that OK = OL = 5 cm and ON = OM = 6 cm. Plugging these values into the equations above, we get:

KL² = 50 - 50cos(57°) ≈ 26.96

NM² = 72 - 72cos(57°) ≈ 39.04

Taking the square root of both sides, we get:

KL ≈ 5.19 cm

NM ≈ 6.25 cm

The perimeter of the shaded shape KLNM is KL + LM + MN + NK. We can find LM and NK by subtracting KL and NM from the diameter of each circle, which is 10 cm:

LM = 10 - 2(OL) = 10 - 10 = 0

NK = 10 - 2(OM) = 10 - 12 = -2

Since NK is negative, we can ignore it for the perimeter calculation. Therefore, the perimeter of the shaded shape is:

KL + LM + MN + NK ≈ 5.19 + 0 + 6.25 + 0 = 11.44 cm

So, the perimeter of the shaded shape KLNM is approximately 11.44 cm to 2 decimal places.

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Answer:

83.62

Step-by-step explanation:

1. work out the circumference (2x pie x radius)

circumference of KOL= 42 pie

circumference of MON= 32 pie

2. Work out arch length ({114÷360} x circumference)

KL= (114÷360) x 42 pie = 133/10 pie

MN= (114÷360) x 32 pie = 152/15 pie

3. Add both lengths ( KL + MN)

= 41.78318229 + 31.83480556 = 73.61798785

4. Add sides (21-16=5, 5x2= 10)

73.61798785+10= 83.61798785

answer= 83.62 (2dp)

The answers for the following questions are mentioned below respectively.

The branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.

a. To compute the summaries of this experiment, we need to calculate the mean and standard deviation of each condition.

Condition 1: Low Noise

Mean = (15 + 19 + 13 + 13) / 4 = 15

Standard deviation = √([(15-15)²+ (19-15)² + (13-15)² + (13-15)²] / (4-1)) = 2.58

Condition 2: Medium Noise

Mean = (13 + 11 + 14 + 10) / 4 = 12

Standard deviation = √([(13-12)²+ (11-12)² + (14-12)² + (10-12)²] / (4-1)) = 1.87

Condition 3: Loud Noise

Mean = 2978

Standard deviation = undefined, as there is only one observation.

b. The appropriate graph for these data is a histogram, with each condition represented by a different color or pattern. The x-axis represents the productivity scores, and the y-axis represents the frequency or percentage of observations in each condition.

c. Assuming that the data are representative, we would envision the populations produced by this experiment as three different normal distributions, each with its own mean and standard deviation. The population distribution for the low noise condition would be centered around a mean of 15, with most scores falling within 2.58 points of this mean. The population distribution for the medium noise condition would be centered around a mean of 12, with most scores falling within 1.87 points of this mean. The population distribution for the loud noise condition is unknown, as we only have one observation.

d. The conclusions that can be drawn from this experiment depend on the research question and hypothesis being tested. However, based on the information given, we can conclude that there is a difference in productivity scores across the three conditions, with the lowest scores occurring in the medium noise condition. However, we cannot draw any conclusions about the effect of noise on productivity without further analysis or experimental manipulation.

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We must determine the means and standard deviation of each circumstance.

Standard deviation = 1.87

Mean = 2978

The area of mathematics concerned with the gathering, examination, interpretation, display, and arrangement of data.

a). We must compute the means and standard deviations of each condition in order to compute the summaries for this exercise.

Condition 1: Low Noise

Mean = (15 + 19 + 13 + 13) / 4

          = 15

Standard deviation = √([(15-15)²+ (19-15)² + (13-15)² + (13-15)²] / (4-1))

                                = 2.58

Condition 2: Medium Noise

Mean = (13 + 11 + 14 + 10) / 4

         = 12

Standard deviation = √([(13-12)²+ (11-12)² + (14-12)² + (10-12)²] / (4-1))

                                = 1.87

Condition 3: Loud Noise

Mean = 2978

Standard deviation = undefined, as there is only one observation.

b). The suitable graph for these data is a histogram, where the x-axis represents productivity scores and the y-axis represents the frequency or percentage of observations in each condition, with each condition represented by a different color or pattern.

c). We would picture the populations generated by this experiment as three distinct normal distributions, each with its own mean and standard deviation, assuming that the data are representative. Most scores would lie within 2.58 points of the mean for the low noise condition, which would have a population distribution centered around a mean of 15. Most scores would lie within 1.87 points of the mean for the medium noise condition, which would have a population distribution centered around a mean of 12. We only have one observation, so we don't know the population distribution for the loud noise situation.

d). The study query and tested hypothesis determine the conclusions that can be drawn from this experiment. However, based on the available data, we can infer that there is a difference in output scores between the three conditions, with the medium noise condition recording the lowest scores. However, without additional investigation or experimental manipulation, we are unable to make any judgments about how noise affects output.

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The measure of the sector angle KLM is equal to 40 degrees which makes the first option correct.

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

Given that the areas of sectors HIJ and KLM are the same, then we have that;

(angle KLM/360°) × 22/7 × 6 × 6 = (90°/360°) × 22/7 × 4 × 4

(angle KLM/360°) × 22/7 × 36 = (1/4) × 22/7 × 16

(angle KLM/10) × 22/7 = 22/7 × 4

(angle KLM/10) × 22/7 = 22/7 × 4

angle KLM = 22/7 × 7/22 × 4 × 10

angle KLM = 40

Therefore, measure of the sector angle KLM is equal to 40 degrees which makes the first option correct.

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The inverse function of g(x) is g⁻¹(x) = x - 4/5

(g⁻¹ * g)(1) = g⁻¹(g(1)) = g⁻¹(9/5) = 1.

h⁻¹(0) = 8.

What is the inverse function?

An inverse function is a function that undoes the action of another function. In other words, if a function f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes the output y and produces the input x.

To find g⁻¹(x), we need to solve for x in terms of g(x).

g(x) = x + 4/5

Let y = g(x), then we have:

y = x + 4/5

Subtracting 4/5 from both sides, we get:

y - 4/5 = x

Therefore, the inverse function of g(x) is:

g⁻¹(x) = x - 4/5

To find (g⁻¹ * g)(1), we need to evaluate g⁻¹(g(1)).

g(1) = 1 + 4/5 = 9/5

g⁻¹(9/5) = 9/5 - 4/5 = 5/5 = 1

Therefore, (g⁻¹ * g)(1) = g⁻¹(g(1)) = g⁻¹(9/5) = 1.

To find h⁻¹(0), we need to find the element in h whose second coordinate is 0, and then take the first coordinate of that element as the output of h⁻¹(0).

From h, we see that the element with second coordinate 0 is (8,0). Therefore,

h⁻¹(0) = 8.

Therefore, the inverse function of g(x) is g⁻¹(x) = x - 4/5

(g⁻¹ * g)(1) = g⁻¹(g(1)) = g⁻¹(9/5) = 1.

h⁻¹(0) = 8.

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