Twice the difference of a number and 4 is 7

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 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

Answer:

Answer

Step-by-step explanation:

The probability of Meikel wearing khakis and sandals is

3 / 12 which will give us

1/4

Therefore , the solution of the given problem of equation comes out to be company can be difficult, but with dedication and persistence, you can make your hobby a lucrative endeavor.

The task may be completed using this generally accepted ease, preexisting variables, as well as any essential components from the original Diocesan customizable query. As a result, you might get another opportunity to use the object. If not, significant effects on algorithmic data will disappear.  

Here,

Here are some actions you might consider to launch a business with a $150 budget:

Pick a venture that appeals to your passions and complements your education and experience. Starting a small online business or providing freelance services in your field of expertise are both examples of this.

Describe your objectives, target market, pricing strategy, and marketing strategy in a company plan. This will assist you in maintaining organization and focus as you launch your company.

Spend your money sensibly by making purchases of the startup necessities. For instance, you might need to invest in website storage and a domain name if you're opening an online store. Or,

If you're a freelancer, you might need to spend money on promotional items or a website to display your work.

Maintain organization and keep close tabs on your money. Be sure to remain within your budget by keeping track of all your income and expenses. This will support you in making wise choices as your company expands.

Keep in mind that starting a company can be difficult, but with dedication and persistence, you can make your hobby a lucrative endeavor.

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Hence the Travon account balance reach 9974.42  in 10 years.

The interest charged on a loan or deposit is known as compound interest. That is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this.

If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even while the principal remains the same, the interest changes annually. We can observe that interest rises over time. As a result, we can infer that the interest the bank charges is compound interest, or CI, rather than simple interest.

Traven invest $7246 in a saving account with a fixed annual interest rate of 3.20 compounded monthly, find the time for the account balance to reach $9974.42,

We know that the formula for compounded interest is-

[tex]A=p(1-\frac{r}{100})^n[/tex],

A=9974.42

p=7246

r=3.2

put all the values in the formula,

[tex]9974.42=7246(1-0.032)^n\\\\1.3765=(0.968)^n\\[/tex]

n=10 year

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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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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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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 drip rate for the gravity infusion of 1000 mg of vancomycin diluted in 250 ml D5W over 2 hours with a Macro tubing of 15 gtt/ml is approximately 26 gtt/min.

Drip rate, also known as infusion rate or flow rate, is the speed at which a solution is infused or delivered to a patient over a certain period of time. Drip rate is typically measured in drops per minute (gtt/min) for gravity infusions or milliliters per hour (ml/hr) for infusion pumps.

In a gravity infusion, the drip rate is calculated by dividing the volume of the solution to be infused by the time of the infusion, and then multiplying by the drop factor of the IV administration set. The resulting number is the number of drops that need to be delivered per minute to the patient.

To calculate the drip rate for a gravity infusion, we can use the formula:

Drip rate = (Volume to be infused × Drop factor) ÷ Time of infusion

where:

Volume to be infused = 250 ml (given)

Drop factor = 15 gtt/ml (given)

Time of infusion = 2 hours = 120 minutes (since the infusion is to be given over 2 hours)

To use this formula, we need to first convert the volume of vancomycin from milligrams (mg) to milliliters (ml), since the volume to be infused is given in ml. The concentration of the vancomycin solution is 1000 mg/250 ml = 4 mg/ml. Therefore, the volume of vancomycin to be infused is:

Volume of vancomycin = 1000 mg ÷ 4 mg/ml = 250 ml

Now we can replace in the values into the formula:

Drip rate = (250 ml × 15 gtt/ml) ÷ 120 minutes

Drip rate = 3125 gtt ÷ 120 minutes

Drip rate ≈ 26 gtt/min

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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: 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

Answer:

v = c - 78930 + 57y - 6

Step-by-step explanation:

Answer:

Arithmetic operationsvteAddition (+)Subtraction (−)Multiplication (×)Division (÷)Exponentiation (^)nth root (√)Logarithm (log)vteDivision is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another. 7  This number of times need not be an integer. For example, if 20 apples are divided evenly between 4 people, everyone receives 5 apples .

Step-by-step explanation:

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

→

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(

x

+

2

)

(

x

−

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)

x

−

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=

lim

x

→

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(

x

+

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)

x

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In Bridget's bathroom, the scale indicated the muffin weighed 8 pounds. The more accurate scale at the veterinarian's office indicated that the muffins weighed 8.2 pounds. The bathroom scales' measurement error is 2.4% percent.

To find the percent error, we need to compare the difference between the two measurements (the actual weight and the weight measured by the bathroom scale) with the actual weight, and express it as a percentage.

The actual weight of muffin is 8.2 pounds. The weight measured by the bathroom scale is 8 pounds.

The difference between the two measurements is:

8.2 - 8 = 0.2 pounds

To calculate the percent error, we divide the difference by the actual weight, and multiply by 100:

percent error = (difference / actual weight) x 100

percent error = (0.2 / 8.2) x 100

percent error = 0.0244 x 100

percent error = 2.44

To the nearest tenth of a percent, we round and obtain:

percent error ≈ 2.4%

Therefore,  the percent error for the bathroom scale's measurement is approximately 2.4%.

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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)

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 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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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:

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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In the above word problem,

Let's denote the number of $50 notes that Malcolm and Peiling have as M50 and P50 respectively. Similarly, we'll denote the number of $10 notes as M10 and P10 and the number of $2 notes as M2 and P2.

From the problem statement we have the following information:

1. The total number of notes they have is the same: M50 + M10 + M2 = P50 + P10 + P2

2. The number of $2-notes Peiling has is 1/4 of the number of $2-notes Malcolm has: P2 = (1/4)M2

3. The number of $10-notes Peiling has is twice the number of $10-notes Malcolm has: P10 = 2M10

4. Peiling has 8 more $50-notes than Malcolm: P50 = M50 + 8

5. The total number of $2 and $10-notes they have is 42: M10 + M2 + P10 + P2 = 42

Substituting equations (2), (3) and (4) into equation (1) we get:

M50 + M10 + M2 = (M50+8) + 2M10 +(1/4)M2

Solving for M50 we get:

M50 = 8 + 2M10 - (3/4)M2

Substituting equations (2), (3), and (4) into equation (5) we get:

M10 + M2 + 2M10 + (1/4)M2 = 42

Solving for M10 we get:

M10 = 14 - (1/12)M2

Substituting this value of M10 into the equation for M50 we get:

M50 = 8 + 28 - M2/6 - (3/4)M2

Solving for M50 we get:

M50 = 36 - (11/6)M2

Since the number of notes must be a positive integer, the smallest possible value for M50 is when M2=6. This gives us a value of M50=35.

Substituting these values back into the equations for P50, P10 and P2 we find that Peiling has P50=43 $50 notes, P10=28 $10 notes and P2=1.5 $2 notes. However, since the number of notes must be a positive integer, this solution is not valid.

The next smallest possible value for M50 is when M2=12. This gives us a value of M50=34. Substituting these values back into the equations for P50, P10 and P2 we find that Peiling has P50=42 $50 notes, P10=28 $10 notes and P2=3 $2 notes.

Now we can calculate the total amount of money each person has:

Malcolm: 34 * 50 + 14 * 10 + 12 * 2 = $1,864

Peiling: 42 * 50 + 28 * 10 + 3 * 2 = $2,386

So to answer part (a) of the question: Peiling has more money than Malcolm.

To answer part (b) of the question: They have a total of M2 + P2 = 12 + 3 = 15 $2-notes altogether.


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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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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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a. The proportion or percentage of children with an MDI score of at least 120 is 10.56%.

b. The proportion or percentage of children with an MDI score of at least 80 is also 10.56%.

c. The MDI score that corresponds to the 99th percentile is approximately 137.

d. The MDI score such that only 1% of the population has an MDI score below it is approximately 63.

e. The lower quartile (Q1) of MDI scores is 89.28, and the upper quartile (Q3) is 110.72. These scores represent the range below which 25% of the population falls and the range above which 25% of the population falls, respectively.

f. The interquartile range (IQR) is 21.44.

g. The upper limit for potential outliers is 142.88, and the lower limit is 57.12. Any MDI scores outside this range would be considered potential outliers.

a. To find the proportion of children with an MDI score of at least 120, we need to calculate the z-score and use the standard normal distribution table. The z-score for an MDI score of 120 is (120-100)/16 = 1.25. Using the standard normal distribution table, the proportion of children with an MDI score of at least 120 is 0.1056 or 10.56%.

b. Similarly, to find the proportion of children with an MDI score of at least 80, we need to calculate the z-score for an MDI score of 80, which is (80-100)/16 = -1.25. Using the standard normal distribution table, the proportion of children with an MDI score of at least 80 is 0.1056 or 10.56%.

c. To find the MDI score that corresponds to the 99th percentile, we need to find the z-score that corresponds to the 99th percentile using the standard normal distribution table. The z-score is approximately 2.33. Using the formula z = (x - μ)/σ, we can solve for x to find the MDI score that corresponds to the 99th percentile: x = zσ + μ = 2.33 * 16 + 100 = 136.88. Therefore, the MDI score that corresponds to the 99th percentile is approximately 137.

d. To find the MDI score such that only 1% of the population has an MDI score below it, we need to find the z-score that corresponds to the 1st percentile using the standard normal distribution table. The z-score is approximately -2.33. Using the formula z = (x - μ)/σ, we can solve for x to find the MDI score that corresponds to the 1st percentile: x = zσ + μ = -2.33 * 16 + 100 = 63.12.

Therefore, the MDI score such that only 1% of the population has an MDI score below it is approximately 63.

e. The lower quartile (Q1) represents the 25th percentile, and the upper quartile (Q3) represents the 75th percentile. Using the standard normal distribution table, the z-score for the 25th percentile is approximately -0.67, and the z-score for the 75th percentile is approximately 0.67. Using the formula z = (x - μ)/σ, we can solve for x to find the MDI scores that correspond to Q1 and Q3: Q1 = -0.67 * 16 + 100 = 89.28, and Q3 = 0.67 * 16 + 100 = 110.72.

Therefore, the lower quartile of the MDI scores represents the scores below which 25% of the population falls, and the upper quartile represents the scores above which 25% of the population falls.

f. The interquartile range (IQR) is the difference between Q3 and Q1. Therefore, IQR = Q3 - Q1 = 110.72 - 89.28 = 21.44.

g. To find the upper and lower limits for potential outliers, we need to use the formula:

Upper limit = Q3 + 1.5IQR

Lower limit = Q1 - 1.5IQR

Substituting the values we have found, we get:

Upper limit = 110.72 + 1.521.44 = 142.88

Lower limit = 89.28 - 1.521.

The upper limit for potential outliers is 142.88, and the lower limit is 57.12. Any MDI scores outside this range would be considered potential outliers.

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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

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 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 correct option is (a) i.e. the inverse of the given function is [tex]F^{-1}(x) = \sqrt{x-5} + 19, x \geq 19[/tex]

What is inverse function ?

An inverse function  undoes the effect of another function. Given a function f(x), an inverse function g(x) will return the original input value x when the output of f(x) is given as input to g(x). In other words, if y = f(x), then x = g(y)

To find the inverse of the function F(x), we first replace F(x) with y, and then interchange x and y to obtain an expression for x in terms of y. That is:

[tex]y = (x - 19)^{2} + 5[/tex]

Interchanging x and y gives:

[tex]x = (y - 19)^{2} + 5[/tex]

Now, we solve for y in terms of x:

[tex]x = (y - 19)^{2} + 5[/tex]

[tex]x - 5 = (y - 19)^{2}[/tex]

±[tex]\sqrt{x-5} = y - 19[/tex]

y = ±[tex]\sqrt{x-5} +19[/tex]

However, since the original function is defined only for x ≥ 19, we must consider only the positive square root, and obtain:

[tex]y=\sqrt{x-5} +19, x\geq 19[/tex]

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

[tex]F^{-1}(x) = \sqrt{x-5} + 19, x \geq 19[/tex]

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