Consider the equation 2/3×(p-q)=1
Which one of these can be the values of p and q

a) The probability that the third hole drilled is the first to yield a productive well is given by the following sequence of events: the first two holes must be unproductive, followed by a productive third hole. The probability of each of these events happening is:

- Probability of an unproductive hole: 0.8

- Probability of two unproductive holes in a row: 0.8

The justifications for 2 and 3 are;

Addition property of equality and

Multiplication property of equality

1. x/2 - 9 = -4 given

Add 9 to both sides

2. x/2 = -13 (Addition property of equality)

cross product

3.x = -26 (Multiplication property of equality)

Therefore, x/2 - 9 = -4 where x Is -26 is justified by addition and multiplication property of equality.

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Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

To find the circumference of the triangle, we need to first find the lengths of its sides. Let the three sides be x, y, and z, such that x:y:z is the given ratio. Without loss of generality, we can assume that x is the shortest side.

Let k be a constant such that y = kx and z = lx, where k and l are constants. Then, we have:

x + kx + lx = 2r

Simplifying this equation, we get:

x(1 + k + l) = 2r

So, we have:

x = (2r)/(1 + k + l)

y = kx = k(2r)/(1 + k + l)

z = lx = l(2r)/(1 + k + l)

The circumference of the triangle is the sum of its three sides:

C = x + y + z

Substituting the expressions for x, y, and z, we get:

C = (2r)/(1 + k + l) + k(2r)/(1 + k + l) + l(2r)/(1 + k + l)

Simplifying this expression, we get:

C = (2r(1 + k + l))/(1 + k + l)

C = 2r

Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

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The area of the triangle is equal to A) 8.64. The Correct option is A) 8.64.

Let the lengths of the triangle be, 3x,4x,5x

Square of largest side = [tex]25x^{2}[/tex]

Sum of square of other sides = [tex]3x^{2} + 4x^{2} = 25x^{2}[/tex]

It is a right-angled triangle because the square of the greatest side equals the sum of the squares of the other sides.

The circumference of a right-angled triangle has a diameter equal to its hypotenuse.

hence, 5x=6 or x= [tex]\frac{6}{5}[/tex]

Now, two perpendicular sides are then,  [tex]\frac{18 }{5} , \frac{24}{5}[/tex]

[tex]Area = \frac{1}{2} \times \frac{18}{5} \times \frac{24}{5} = 8.64[/tex]

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Question

A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to

A. 8.64

B. 12

C. 6

D. 10.5

The probability of getting 2 or fewer women when 11 people are picked is approximately 0.0332

To solve this problem, we can use the binomial distribution formula, which gives us the probability of getting k successes in n independent trials, where the probability of success in each trial is p.

In this case, our "success" is selecting a woman, and our "failure" is selecting a man. Since there are approximately equal numbers of men and women in the pool of applicants, the probability of selecting a woman is p = 0.5, and the probability of selecting a man is q = 1 - p = 0.5.

We want to find the probability of getting 2 or fewer women when 11 people are picked, so we need to calculate the probability of getting 0, 1, or 2 women.

P(0 women) = C(11,0) × (0.5)^0 × (0.5)^11 = 0.00048828125

P(1 woman) = C(11,1) × (0.5)^1 × (0.5)^10 = 0.00537109375

P(2 women) = C(11,2) × (0.5)^2 × (0.5)^9 = 0.02734375

where C(n,k) represents the number of ways to choose k items from a set of n items, which is also known as the binomial coefficient.

Therefore, the probability of getting 2 or fewer women when 11 people are picked is

P(0, 1, or 2 women) = P(0 women) + P(1 woman) + P(2 women)

= 0.00048828125 + 0.00537109375 + 0.02734375

= 0.0332

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The numerical measure of linear association is b. correlation coefficient.

The correlation coefficient is a statistical measure that represents the degree of linear relationship between two variables. It takes values between -1 and 1, where -1 represents a perfect negative linear correlation, 0 represents no linear correlation, and 1 represents a perfect positive linear correlation.

A positive correlation means that when one variable increases, the other variable also tends to increase, while a negative correlation means that when one variable increases, the other variable tends to decrease.

The correlation coefficient is calculated using the formula:

[tex]r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)][/tex]

where r is the correlation coefficient, n is the sample size, Σxy is the sum of the products of the corresponding values of x and y, Σx and Σy are the sums of x and y respectively, and Σx^2 and Σy^2 are the sums of the squares of x and y respectively.

In summary, the correlation coefficient is a measure of the strength and direction of the linear association between two variables.

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G is abelian, then the argument is even simpler.

G is abelian, we have [tex](h_1k_1)(h_2k_2) = h_1h_2k_1k_2 = h_2h_1k_2k_1 = (h_2k_2)(h_1k_1)[/tex],

HK is closed under the group operation.

The statement "if H and K are subgroups of a group G, then HK is a subgroup of G", we need to check if HK satisfies the three criteria for being a subgroup:

Closure under the group operation, the existence of an identity element, and the existence of inverse elements.
First, let's consider the case where G is not necessarily abelian.

HK is closed under the group operation, we need to show that for any [tex]h_1, h_2[/tex] in H and [tex]k_1, k_2[/tex] in K, the element [tex](h_1k_1)(h_2k_2)[/tex] is also in HK.

The fact that H and K are subgroups to write [tex]h_1h_2[/tex]in H and [tex]k_1k_2[/tex] in K, and then use the associativity of the group operation to write[tex](h_1k_1)(h_2k_2) = h_1(h_2k_1)k_2[/tex].

Since H and K are subgroups, [tex]h_2k_1[/tex] is in HK, and therefore [tex](h_1k_1)(h_2k_2)[/tex] is in HK.
Next, we need to show that HK has an identity element.

Since H and K are subgroups, they both contain the identity element of G, which we'll denote by e.

Then, for any h in H and k in K, we have [tex]h k e = h (k e) = h k[/tex], which shows that HK contains the identity element.
HK has an inverse in HK. Let hk be an element of HK.

Since H and K are subgroups, [tex][tex]h^{-1}[/tex][/tex]is in H and [tex]k^{-1}[/tex] is in K.

Then, [tex](hk)^{-1 }= k^{-1}h^{-1}[/tex], which is in HK since H and K are subgroups.
H and K are subgroups of a group G, then HK is a subgroup of G, regardless of whether G is abelian or not. .  

The identity element of HK is still the same as in the non-abelian case, and inverses can be computed as before.
H and K are subgroups of a group G, then HK is always a subgroup of G, regardless of whether G is abelian or not.

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The ball that weighs 30g is ball A.

The degree to which a measured value resembles the true or recognised value is known as accuracy. On the other hand, precision describes how closely two measurements of the same quantity agree. In other words, precision is a measure of consistency, whereas accuracy is a measure of correctness. The values obtained are consistent but not always close to the genuine value when a measurement is precise but not exact. On the other hand, a measurement might be accurate without being exact, which means that the result is close to the correct value but produces erratic or dispersed results when repeated.

From the given weights corresponding to different balls, 30 g corresponds to ball A.

Hence, the ball that weighs 30g is ball A.

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Answer: the piece rate for Pam's work is $27.08 per vase.

Step-by-step explanation: The formula used to determine the piece rate per vase involves the division of the total amount produced by the number of vases manufactured.

The remuneration per vase is calculated as $324.96 divided by a quantity of 12 vases, resulting in a piece rate of $27.08 per vase.

The remuneration assigned for each individual vase production is valued at $27.08.

Answer: I say $27.08.

Step-by-step explanation:

Basically like you just multiply 12 into $324.96. 12 goes into 32, 2 times which is 24 then you subtract 24 from 32 which leaves 8. After that u got to bring down the 9 making it 89 and 12 goes into 89, 7 times. 12 multiplied by 7 is 84 so there's 5 left over. It becomes 56 and 12 goes into 56, 8 times making the answer, $27.08 per vase.

Answer: 12 and sqaure root of 194

Step-by-step explanation:

solution 1: 12 because if 13 is the missing side length of the hypotenuse then you would do 5^2 - 13^2 which is 169-25 = 144. the square root of 144 is 12

solution 2: the other solution is trying to get the hypotenuse. you would do 5^2 + 13^2 which is 25 + 169.. therefore the sum is 194. the answer would be the square root of 194

The estimated regression equation with TV advertising as the independent variable is ycap = 53.586 + 25.957x. The model explains 19.8% of the variation in the sample values of weekly gross revenue.

The estimated regression equation with television advertising as the independent variable is ycap = 53.586 + 25.957x. This suggests that for each additional $100 spent on television advertising, there is an estimated increase of $25,957 in weekly gross revenue.

we have already calculated the regression equation as ycap = 53.586 + 25.957x. Using this equation, we can calculate the predicted values of y for each observation in the sample of total sum of squares (SST),  sum of squares due to regression (SSR) and coefficient of determination (R-squared) as the ratio of SSR to SST

R² = SSR / SST.

To calculate the values of ycap and ybar, we first need to find the mean values of the variables

xbar = (4.9 + 4.2 + 4.5 + 3.6 + 3.5 + 5.0 + 6.8) / 7 = 4.93

ybar = (101.3 + 75.8 + 127.2 + 137.8 + 102.4 + 236.8 + 220.6) / 7 = 143.14

Using the regression equation ycap = 53.586 + 25.957x and the given data, we can calculate the predicted values of y

ycap(Mobile) = 53.586 + 25.957(1.4) = 91.08

ycap(Shreveport) = 53.586 + 25.957(1.5) = 92.04

ycap(Jackson) = 53.586 + 25.957(1.5) = 92.04

ycap(Birmingham) = 53.586 + 25.957(4.3) = 167.16

ycap(Little Rock) = 53.586 + 25.957(4.0) = 158.48

ycap(Biloxi) = 53.586 + 25.957(2.3) = 111.35

ycap(New Orleans) = 53.586 + 25.957(8.4) = 261.32

ycap(Baton Rouge) = 53.586 + 25.957(5.9) = 219.13

Thus, the values of ycap are 91.08, 92.04, 92.04, 167.16, 158.48, 111.35, 261.32, and 219.13.

The sum of squared residuals (SSR) can be calculated as

SSR = Σ(ycap - ybar)² = (91.08 - 143.14)² + (92.04 - 143.14)² + (92.04 - 143.14)² + (167.16 - 143.14)² + (158.48 - 143.14)² + (111.35 - 143.14)² + (261.32 - 143.14)² + (219.13 - 143.14)²

= 214,767.63

The total sum of squares (SST) can be calculated as

SST = Σ(y - ybar)² = (101.3 - 143.14)² + (75.8 - 143.14)² + (127.2 - 143.14)² + (137.8 - 143.14)² + (102.4 - 143.14)² + (236.8 - 143.14)² + (220.6 - 143.14)²

= 1,082,685.88

Finally, the coefficient of determination (R-squared) is the ratio of SSR to SST

R² = SSR / SST = 214,767.63 / 1,082,685.88 = 0.198

Multiplying by 100 to convert to a percentage, we get R² = 19.8%.

The coefficient of determination (R-squared) for the model is 0.198, indicating that approximately 19.8% of the variation in the sample values of weekly gross revenue is explained by the variation in television advertising.

This implies that the model is a reasonably good fit for the data, but there may be other factors that also influence the weekly gross revenue that are not accounted for in this model.

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--The given question is incomplete, the complete question is given

" Data for a sample of eight markets for a recent week follow. Weekly Gross Revenue ($100s) Television Advertising Newspaper Advertising ($100s) ($100s) Market Mobile 101.3 4.9 1.4 52.9 3.1 3.2 Shreveport Jackson 75.8 4.2 1.5 Birmingham 127.2 4.5 4.3 Little Rock 137.8 3.6 4.0 Biloxi 102.4 3.5 2.3 New Orleans 236.8 5.0 8.4 Baton Rouge 220.6 6.8 5.9 (a) Use the data to develop an estimated regression equation with the amount of television advertising as the independent variable. Let x represent the amount of television advertising. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) ycap= ____ . (b) how much of the variation in the sample values of weekly gross revenue does the model in part (a) explain? if required, round your answer to two decimal places."--

Answer:

-3

Step-by-step explanation:

To find the slope (m) of the line that passes through Point A(3, -9) and the origin (0, 0), we can use the formula:m = rise/run = (change in y)/(change in x)We can calculate the change in y and change in x as follows:

Change in y = y2 - y1 = 0 - (-9) = 9

Change in x = x2 - x1 = 0 - 3 = -3

Substituting these values into the formula, we get:

m = rise/run = 9/-3 = -3

Therefore, the slope of the line that passes through Point A(3, -9) and the origin is -3.

Assuming that the marbles are either green or not green and that the probability of picking a green marble is constant on every trial, we can use probability to make a prediction.

Let p be the probability of picking a non-green marble on one trial, then the probability of picking a green marble is 1 - p.

Since we pick marbles with replacement, each trial is independent of the others, and the probability of picking a non-green marble is the same for every trial.

The number of times we pick a non-green marble in 42 trials follows a binomial distribution with parameters n = 42 and p.

The expected value (or mean) of a binomial distribution is given by np, so in this case, the best prediction for the number of times we will pick a non-green marble is:

42 * p

We don't know the value of p, but if we assume that the probability of picking a non-green marble is 1/2 (i.e., the marbles are evenly split between green and non-green), then the best prediction for the number of times we will pick a non-green marble is:

42 * (1/2) = 21

Therefore, the best prediction possible for the number of times you will pick a marble that is not green is 21.

a) The expression for the amount of pure copper sulfate in 3x liters of 25% solution is  0.675x.

b) The percentage of pure copper sulfate in the resulting solution is 39.375%.

Since the solution is 25% copper sulfate, we know that there are 0.25(3x) = 0.75x liters of copper sulfate in the solution.

The amount of pure copper sulfate in the solution is given by 0.9 times the amount of copper sulfate. Therefore, the expression for the amount of pure copper sulfate in 3x liters of 25% copper sulfate solution is:

0.9(0.75x) = 0.675x

The amount of pure copper sulfate added from the 90% copper sulfate solution is 0.9x liters.

The amount of pure copper sulfate in the 25% copper sulfate solution is 0.675x liters.

The total amount of pure copper sulfate in the resulting solution is:

0.9x + 0.675x = 1.575x

The total volume of the resulting solution is:

x + 3x = 4x

To find the percentage of pure copper sulfate in the resulting solution, we divide the amount of pure copper sulfate by the total volume of the solution and multiply by 100:

(1.575x / 4x) * 100 = 39.375%

Therefore, the percentage of pure copper sulfate in the resulting solution is 39.375%.

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The expression of the inequality of John profit as per given details is given by  $80,000 ≤ $x ≤ $250,000.

Let us consider the John profit represented by $x.

As per first statement we have,

At least amount of $80,000 John must make to pay bills.

This implies ,

$80,000 is less than or equal to John’s profit.

⇒ $80,000 ≤ John  profit

⇒ $80,000 ≤ $x __(1)

Now, John’s profit is less than or equal to $250,000.

⇒John profit ≤ $250,000

⇒ $x ≤ $250,000 ___(2)

Combine (1) and (2) we get the inequality ,

$80,000 ≤ $x ≤ $250,000

Therefore, the expression used to represents the inequality of John profit is equal to  $80,000 ≤ $x ≤ $250,000.

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The given question is incomplete, I answer the question in general according to my knowledge:

John must make at least $80,000 to pay bills. That can be rephrased as $80,000 is less than or equal to John’s profit. You also know that John’s profit is less than or equal to $250,000 . Write the expression to represents the inequality.

(−2,4) , (4,−4)

Use the midpoint formula to find the midpoint of the line segment.

(x1+x2 /2 , y1+y2 /2)

Substitute in the values for

(x1,y1) and (x2,y2).

((−2+4)/2, (4−4)/2)

Cancel the common factor of

−2+4 and 2.

Tap for more steps...

(−1+2, (4−4)/2)

Add −1 and 2.

(1,4−4/2)

Cancel the common factor of 4−4  and 2.

Tap for more steps...

(1,2−2)

Subtract 2 from 2.

(1,0)

Answer:

x = 25

Step-by-step explanation:

Angle on a straight line add up to 180

therefore

2x + 10 + 4x + 20 = 180

6x + 30 = 180

6x = 180-30

6x = 150

6x/6 = 150/6

x = 25

Hence the value of x = 25°

Area of the polygon 542.5ft²

A polygon is a two-dimensional geometric shape that is made up of a finite number of line segments that are connected end-to-end to form a closed shape. The line segments of a polygon are called sides, and the points where the sides meet are called vertices.

A polygon can have any number of sides, but must have at least three. Some examples of polygons include triangles, squares, rectangles, pentagons, hexagons, and so on.

First way:

Area of the polygon=Area of small rectangular part+ area of trapezium part

=7×7 + 1/2(23+12)×26

49+455

=504ft²

Second Way

Area of the polygon= area of trapezium part-Area of rectangular par=1/2×26(30+19)-19×7=504ft

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The 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is approximately [-6.62, 22.02].

The critical value that should be used in constructing the confidence interval.

Since we are looking for a 90% confidence interval, we need to find the critical value associated with a 5% level of significance in a two-tailed test.

Using a t-distribution with (n1-1) + (n2-1) degrees of freedom and a significance level of 0.05, we find the critical value to be:

t-critical = 1.717 (using a t-distribution table or a calculator)

Step 2 of 3:

Next, we need to find the standard error of the sampling distribution to be used in constructing the confidence interval.

Since the population variances are not equal, we need to use the Welch-Satterthwaite equation to calculate the standard error:

SE = sqrt[([tex]s1^2[/tex]/n1) + ([tex]s2^2[/tex]/n2)]

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Substituting the given values, we get:

SE = sqrt[([tex]19.25^2[/tex]/17) + ([tex]26.25^2[/tex]/12)]

SE ≈ 8.35

Step 3 of 3:

To construct the 90% confidence interval, we can use the formula:

(mean1 - mean2) ± t-critical * SE

where mean1 and mean2 are the sample means, and t-critical and SE are the values calculated in steps 1 and 2.

Substituting the given values, we get:

= (84.80 - 77.10) ± 1.717 x 8.35

= 7.70 ± 14.32

Therefore,

The 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is (approx) [-6.62, 22.02].

We can be 90% confident that the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases falls within this interval.

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The odds of the employee passing the test are 0.25. Alternatively, we can say that the employee has a 1 in 4 chance of passing the test if the probability is 0.20

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents impossibility (an event that cannot occur) and 1 represents certainty (an event that is certain to occur).

For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 0.5 (or 1/2) because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

The odds of an event happening are defined as the ratio of the probability of the event occurring to the probability of the event not occurring. Mathematically, odds can be expressed as:

odds = P(event happening) / P(event not happening)

In this case, the probability of the employee passing the test is 0.20, so the probability of the employee not passing the test is 0.80 (since the sum of probabilities of all possible outcomes must be 1).

Therefore, the odds of the employee passing the test can be calculated as:

odds = 0.20 / 0.80 = 0.25

So the odds of the employee passing the test are 0.25. Alternatively, we can say that the employee has a 1 in 4 chance of passing the test (since 0.25 can be written as a fraction of 1/4).

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Answer:

in picture

Step-by-step explanation:

please like my answer

Answer: C 70%

Step-by-step explanation:

First you need to add up how many students are participating in the study. 4+6+12+8+4=34. There are 24 people who own more than 5 video games. This means that it is 24/34. This equals about 70%

The number of students who like vanilla, butterscotch, and chocolate flavors are 36, 15, and 9 respectively.

The percentage of students who like vanilla flavor is 60%, which means

Number of students who like vanilla flavor = 60/100 x 60 = 36 students

Similarly, the percentage of students who like butterscotch flavor is 25%, which means

Number of students who like butterscotch flavor = 25 / 100 x 60 = 15 students

The remaining students like chocolate flavor

Number of students who like chocolate flavor = Total number of students - Number of students who like vanilla flavor - Number of students who like butterscotch flavor

= 60 - 36 - 15

= 9 students

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The given question is incomplete, the complete question is:

In a class of 60 students 60% like vanilla flavour ,25% like butterscotch and the remaining like chocolate flavour. Find the number of student who like vanilla, butterscotch and chocolate flavour respectively.

Answer:

No, this triangle is NOT a right angle.

Step-by-step explanation:

The known fact is that the largest number is our hypotenuse. The other two numbers can go on either side.

A square plus B square equal C square is our equation

Let's plug in the numbers: 15^2+5^2=16^2

Now we solve.

Once we solve our squares and add them together, we get 250=256. Since these two number are not equal to each other, this triangle is NOT a right angle

much love to you.

As this is a contradiction, the system cannot be solved. The parallel lines of the two equations do not intersect.

A mathematical expression called and equation demonstrates the parity of two factors or values. It typically includes exponents, parameters, constants, and mathematical like addition, subtraction, multiplication, and division. Finding an unknown variable's value or expressing a correlation between a number of variables is the goal of an equation. To simulate real-world occurrences and address issues, equations are utilised in many mathematical areas, science, and engineering. Systems of equations, linear equations, and quadratic equations are a few types of equations.

given

We can multiply the first equation by two and then add the second equation to the system to find the solution via elimination. This results in:

[tex]2(x - 3y = 7) = 2x - 6y = 14\\2x - 6y = 12[/tex]

To remove x, we may now subtract the second equation from the first equation:

[tex](2x - 6y = 14) - (2x - 6y = 12) = 0[/tex]

That amounts to:

0 = 2

As this is a contradiction, the system cannot be solved. The parallel lines of the two equations do not intersect.

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Below is the correct matching of the questions to the right answers

The statistical measures listed in the previous question are often used to describe and analyze statistical variables.

For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.

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1. Mean average deviation - The average deviation of the data from the mean.

2. Range of a data set - The difference between the highest value and the lowest value in a numerical data set.

3. First quartile - The median in the upper half of the rank-ordered data.

4. Second quartile - The median value in the data set.

5. Third quartile - The median in the lower half of the rank-ordered data.

6. Interquartile range - he distance between the first and third quartiles of the data set.

The statistical measures are often used to describe and analyze statistical variables. For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.

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The IQR is a more appropriate measure of variability is 60 - 10.5 = 49.5.

The interquartile range (IQR) is a measure of variability that represents the range of the middle 50% of a dataset, calculated as the difference between the third and first quartiles.

According to the given information :

The most appropriate measure of variability to use for the given data is the IQR (Interquartile Range) of 13. The IQR is the range of the middle 50% of the data and is calculated as the difference between the third quartile (Q₃) and the first quartile (Q₁). In this case, Q₁ is the median of the lower half of the data, which is (5 + 5 + 6 + 8 + 10 + 15)/2 = 21/2 = 10.5, and Q₃ is the median of the upper half of the data, which is (20 + 20 + 20 + 20 + 20 + 20)/2 = 120/2 = 60. Thus, the IQR is 60 - 10.5 = 49.5.

The reason the IQR is a more appropriate measure of variability than the range is that the range is sensitive to extreme values, which can distort the picture of the typical spread of the data. In this case, there are several values of 20 that are much higher than the other values, and including them in the calculation of the range would make it appear that the data is more spread out than it actually is. The IQR, on the other hand, is less sensitive to extreme values and is a better representation of the typical spread of the data.

Using the IQR of 13, the charity can better understand the typical range of donations they receive and make informed decisions about their fundraising efforts. For example, if they find that the typical range of donations is between $10.50 and $60, they may want to consider targeting donors who can give larger donations to increase the overall amount of donations they receive. Additionally, they could use this information to set fundraising goals and measure their progress towards achieving them.

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The correct expression showing the total area of the five rooms is A. (3 x 14²) + (2 x 17²), which simplifies to 1918 square feet.

An expression is a combination of numbers, symbols, and operators (such as addition, subtraction, multiplication, and division) that represent a mathematical calculation. An expression can be a single number, a variable, or a combination of both, and can be used to represent mathematical formulas, equations, or relationships.

In the given question,

C. (3 × 17²) + (2 × 14²)

To find the total area of the five rooms, we need to add the area of each room. The area of a square is found by squaring the length of one side.

For the three rooms with sides of 14 feet each, the area of each room is:

14^2 = 196 square feet

So the total area of these three rooms is:

3 × 196 = 588 square feet

For the two rooms with sides of 17 feet each, the area of each room is:

17^2 = 289 square feet

So the total area of these two rooms is:

2 × 289 = 578 square feet

Therefore, the total area of all five rooms is:

588 + 578 = 1166 square feet

Option C, (3 × 17²) + (2 × 14²), gives the correct expression for this calculation.

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The value of x assuming the line that appear are tangent is option B. 5.

A straight line that precisely touches a circle at one point, or the point of tangency, is said to be tangent to the circle. At the point of tangency, the tangent line is perpendicular to the circle's radius.

Depending on the location of the point where the tangent is drawn, a circle can have an unlimited number of tangents. There are two tangents that can be traced to the circle if the point is outside the circle. There is one tangent that can be made to the circle if the point is on the circle. Additionally, no tangent may be made from a point that is inside the circle.

The given are considered tangents, and tangents to the circle are equal thus we have:

(x + 3) (x + 3 + 2x + 3) =7(7 + 17)

(x + 3)(3x + 6) = 168

3x² + 6x + 9x + 18 = 168

3x² + 15x - 150 = 0

x² + 5x - 50 = 0

x² + 10x - 5x - 50 = 0

x(x + 10) - 5(x+ 10) = 0

(x - 5) (x + 10)

x = 5 and

x = -10

Hence, the value of x assuming the line that appear are tangent is option B. 5.

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2x + 2y = 4xy is wrong

2x + 2y = 2(x+y) is correct

3x+4= 7x wrong

4x²+5x = 9x² wrong

3x²+3x²+4x = 6x² + 4x = 2x(3x + 2)

sorry I don't understand this one.....

-4(3x-5) = -12x + 20

Answer:

120

12 10

4 2 5 2

2 2