George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.

a. What is the area of the pool cover?
b. What is the length of the rope?


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The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.

Here,

When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).

Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.

As a result, 186 outcomes or triplets are possible and satisfy this property.

Hence, the required probability is 186/216=31/36.

The required probability is 31/36 for three dice rolls to produce triangle sides.

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Answer:

x=1 is the correct answer

Answer:

Step-by-step explanation:Yes, the points B, C, M, and N are concyclic.

In a triangle ABC, if perpendiculars BM and CN are drawn from the vertices B and C to the sides AC and AB respectively, then the quadrilateral BCNM is a cyclic quadrilateral. This means that the points B, C, M, and N lie on a common circle.

To see why this is true, consider the angles formed by the sides of the quadrilateral BCNM. Since BM is perpendicular to AC, angle BMC is a right angle. Similarly, CN being perpendicular to AB makes angle CNC a right angle as well.

Now, angle BNC is the sum of angles BMC and CNC, which means it is also a right angle. Similarly, angle BMC is the sum of angles BNC and CNB, so it is a right angle too.

Since all angles of the quadrilateral BCNM are right angles, the quadrilateral can be inscribed in a circle where the diameter is the line segment BC. Therefore, the points B, C, M, and N are concyclic.

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Answer:

7

Step-by-step explanation:

5, 5, 6, 7, 7, 7

7 appears the most

Answer:

The mode is 7

Step-by-step explanation:

Add all of these numbers and divide it by 8 to get 7

No, based on the sample data, it does not appear that the number of weekly customer complaints has changed this year. To determine if there is a significant change, we can perform a hypothesis test.

Assuming the population has a normal distribution, we use a one-sample t-test.  The null hypothesis (H0) is that the mean number of complaints is 26.6, and the alternative hypothesis (Ha) is that it is different. With a sample mean of 29.5, sample standard deviation of 5.4, and sample size of 15, we calculate the t-value: (29.5 - 26.6) / (5.4 / sqrt(15)) = 2.136. The degrees of freedom are 15 - 1 = 14. Using a significance level of 0.05, the critical t-value is approximately 2.145. Since the calculated t-value of 2.136 is less than the critical t-value, we fail to reject the null hypothesis.

Thus, there is no sufficient evidence to conclude that the number of weekly complaints has changed this year. Based on the statistical analysis, it can be concluded that the number of weekly customer complaints has not changed significantly this year.

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Answer:

6 in

Step-by-step explanation:

The angle bisector divides the opposite side into segments that are proportional to the other 2 sides.

let the third side of the triangle be x , then

\(\frac{9}{x}\) = \(\frac{6}{4}\) ( cross- multiply )

6x = 36 ( divide both sides by 6 )

x = 6

The third side of the triangle is 6 in

The equation of the circle with a radius of 111 and a center at (9, 5) is:

To determine the equation of a circle, we use the standard form equation:

\((x - h)^2 + (y - k)^2 = r^2\)

Where (h, k) represents the center coordinates of the circle, and r represents the radius.

In this case, the center of the circle is (9, 5), and the radius is 111. Plugging these values into the equation, we have:

(x - 9)^2 + (y - 5)^2 = 111^2

Expanding and simplifying further:

\((x - 9)^2 + (y - 5)^2 = 12321\)

Therefore, the equation of the circle with a radius of 111 and a center at (9, 5) is:

(x - 9)^2 + (y - 5)^2 = 12321

This equation represents all the points (x, y) that are equidistant from the center (9, 5) by a distance of 111 units, forming a circle shape.

To graphically represent the circle, plot the center point (9, 5) on a coordinate plane and then draw the circle with a radius of 111 units around it. Any point on the graph that satisfies the equation will lie on the circle, while points outside the circle will not satisfy the equation.

It's important to note that the equation of a circle can also be expressed in other forms, such as the general form or parametric form. However, the standard form equation provided above is commonly used for representing circles.

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The labor efficiency variance for the month can be calculated by comparing the standard labor hours allowed for the actual output to the actual labor hours worked. The labor efficiency variance for the month is 1,780 hours.

The labor efficiency variance is a measure of the efficiency of labor utilization in the production process. It reflects the difference between the standard labor hours allowed for the actual output and the actual labor hours worked. To calculate the labor efficiency variance, we need to determine the standard labor hours allowed for the actual output and subtract the actual labor hours worked.

In this case, the standard labor hours per unit of output is given as 8.4 hours, and the actual output for the month is 950 units. Therefore, the standard labor hours allowed for the actual output would be 8.4 hours/unit * 950 units = 7,980 hours.

The actual labor hours worked are given as 6,200 hours. To calculate the labor efficiency variance, we subtract the actual labor hours worked from the standard labor hours allowed for the actual output:

Labor Efficiency Variance = Standard labor hours allowed - Actual labor hours worked

= 7,980 hours - 6,200 hours

= 1,780 hours

The labor efficiency variance for the month is 1,780 hours. This indicates that the actual labor hours used were less than the standard labor hours allowed for the actual output, suggesting an efficiency gain in labor utilization.

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Answer:

ahhhhhhhhhhhhhhh im not the person in the pic

Step-by-step explanation:

Answer:

<

Step-by-step explanation:

-7.5 is less than -7 because, as numbers decrease from zero, the larger a negative value is makes the value is worth less because it is furthur away from zero.

Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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Answer:

240

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

the number of ways of choosing 6 cds from 20 to bring on vacation is 27907200

permutation are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

To calculate permutation , we will use the formula nCr = n! / (n - r)!,

where n represents the total number of items, and r represents the number of items being chosen at a time.

20C6 = 20! / 14!

        = 20*19*18*17*16*15

       = 27907200

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Remember that

The volume of a sphere is equal to

we have that

the diameter is reduced to half its original size

D=D/2

so

the new radius is

r=r/2

substitute in the formula of volume

Answer:

6.4 x 1.2=7.68

Step-by-step explanation:

6.4

1.2

----

028

740

add

7.68

3.5 x 4.9=15.435

If Neil uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend , then the number of 41 cent stamp used is 3  and number of 6 cent stamps used is 12 .

Let number of 41 cents stamps used be = x ;

and let number of 6 cents stamps used be = y ;

converting amount 41-cents in dollars is = $0.41  ;

and converting amount 6-cents in dollars is = $0.06  ;

the amount for which Neil used 41-cent stamps , 6-cent stamps is = $1.95 ;

this situation in equation form is written as ⇒ 0.41x + 0.06y = 1.95

Multiplying on both sides by 100 , we get

⇒ 41x + 6y = 195  ;

⇒ y = (195 - 41x)/6 ;

We will test this equations for values of x and y , the number of stamps must be whole numbers .

If x = 1 , then value of y is = 25.66

If x = 2 , then value of y is = 18.833

If x = 3 , then value of y is = 12

If x = 4 , then value of y is = 5.166 .

the only value of x and y which shows a whole number as an output is : If x = 3 , then y = 12 .

Therefore , Neil used "3" 41-cents stamps and "12" 6-cent stamps .

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Answer:

\(\frac{382}{1000}\)

Step-by-step explanation:

Answer:

191/500

Step-by-step explanation:

We have

0.382

0.382 = 382/1,000

Simply 191/500 therefore answer is 191/500. How I got that was I divided .382/1,000 by 2 numerator and denominator.

Hope this helps

Answer:

6ft

Step-by-step explanation:

This requires a little use of the Pythagorean Theorem.

The length of the leaning ladder is the hypothenuse of the right triangle formed by the wall and the ladder.

Hyp. = 10 ft Say this is C

The ladder height up the wall = 8 ft. Say this A.

We need to find the other leg, say B ,of the right triangle.

C^2 = A^2 + B^2

10^2 = 8^2 + B^2

100 = 64 + B^2 => B^2 = 100 - 64 = 36

B^2 = 36 so, B = 6 The positive square root since length is positive.

B = 6 ft This is how far the ladder bottom is from the wall.

Double Check: 10^2 = 8^2 + 6^2 or 100 = 64 + 36 Ok. As, it should. This check could be done mentally.

In addition, this is a Pythagorean Triple. (6, 8, 10).

Answer: 6 ft.

COPIED:)

Answer:

4 17/25

Step-by-step explanation:

Hope this helps!

If not I am sorry.

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is  52!/(47! * 5!).

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52 choose 5, which is equal to 52!/(47! * 5!), where the exclamation point indicates the factorial function. This is known as the binomial coefficient, and it represents the number of ways to choose a certain number of items from a larger set. In this case, the binomial coefficient is used to find the number of ways to choose 5 cards from a deck of 52 cards.

The order of the cards is irrelevant in card games like poker. A five-card draw of 1,2,7,9, K is equivalent to a draw of K,7,9,1,2. What counts is the fundamental overall group.

Order is irrelevant, therefore we utilize a combination (instead of a permutation)

We will substitute n = 52 and r = 5 into the nCr combination formula, which is n C r = (n!)/(r!*(n-r)!)

so we obtain:

n C r = r!*(n-r)!/(n!)

52 C 5 = (52!)/(5!*(52-5)!)

52 C 5 = (52!)/((52-5)!*5!)

The complete question is:-

Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?

a) (52-5)! / 52!5!

b) 52! / (52-5)!

c) 52! / (52-5)!5!

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Based on the given information, it seems that the number of left-handed desks in each classroom is adequate.

Based on the given information, we can calculate the expected number of left-handed students in a classroom:

Expected number of left-handed students = (total number of students in a classroom) x (proportion of left-handed students in the population)

Expected number of left-handed students = 30 x 0.11

Expected number of left-handed students = 3.3

Since each classroom contains four left-handed desks, it seems that the number of left-handed desks is more than enough to accommodate the expected number of left-handed students. In fact, there may even be some unused left-handed desks in each classroom.

Therefore, based on the given information, it seems that the number of left-handed desks in each classroom is adequate.

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Answer:

The arithmetic sequence formula to find the sum of n terms is given as follows: Sn = n/2 (a1 + an) Where Sn is the sum of n terms of an arithmetic sequence.

The integer that represents the exact opposite of the real-world situation; "a credit of $38" is; -$38 which represents a debit for the same amount.

As evident in the task content; the integer which correctly represents the opposite of the given real world problem is required to be determined.

Since the given real-world problem is; $38 which represents a credit.

The exact opposite of that which represents a debit for the same amount is; -$38.

On this note, the number line representation of both integers is as represented in the attached image.

The number, zero represents a point of neither credit nor debit in this situation.

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The independent variable of interest in an ANOVA procedure is called a factor. Hence (d).

The independent variable of interest in an ANOVA procedure is referred to as the factor. The factor represents the different categories or levels being compared to assess their impact on a dependent variable. It is the variable that is manipulated or controlled by the researcher to determine its effect on the outcome. In the context of ANOVA, the factor is typically a categorical variable that divides the data into distinct groups or treatments. These groups are compared to evaluate if there are statistically significant differences in the means of the dependent variable across the different levels of the factor. Therefore, the correct answer is factor(d).

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Answer:

well just add 128 and 0.4 miles and that's your answer

hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: \(y=4x-9\)

The dual for the given linear programming problems are as follows:

(i) Minimize Z' = 10a + 12b Subject to: a + 7b ≥ 3 2a + 3b ≥ 4 a + 9b ≥ 5 a, b ≥ 0.

(ii) Maximize Z' = 5a + 6b + 2c Subject to: 3a + 2b + c ≤ 1 4a + 6b + c ≤ 2 a + b ≤ 0 a, b, c ≥ 0.

In the first problem, we have a maximization problem with three variables (x, y, z) and two constraints. The dual formulation involves minimizing a new objective function with two variables (a, b) and four constraints. The coefficients of the variables and the constraints are transformed according to the rules of duality.

The primal problem is:

Maximize Z = 3x + 4y + 5z

Subject to:

x + 2y + z ≤ 10

7x + 3y + 9z ≤ 12

x, y, z ≥ 0

To find the dual, we introduce the dual variables a and b for the constraints:

Minimize Z' = 10a + 12b

Subject to:

a + 7b ≥ 3

2a + 3b ≥ 4

a + 9b ≥ 5

a, b ≥ 0

In the second problem, we have a minimization problem with two variables (y1, y2) and three constraints. The dual formulation requires maximizing a new objective function with three variables (a, b, c) and four constraints. Again, the coefficients and constraints are transformed accordingly.

The primal problem is:

Minimize Z = y1 + 2y2

Subject to:

3y1 + 4y2 > 5

2y1 + 6y2 ≥ 6

y1 + y2 ≥ 2

To find the dual, we introduce the dual variables a, b, and c for the constraints:

Maximize Z' = 5a + 6b + 2c

Subject to:

3a + 2b + c ≤ 1

4a + 6b + c ≤ 2

a + b ≤ 0

a, b, c ≥ 0

The duality principle in linear programming allows us to find a lower bound (for maximization) or an upper bound (for minimization) on the optimal objective value by solving the dual problem. It provides useful insights into the relationships between the primal and dual variables, as well as the economic interpretation of the problem.

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