Find the roots of the equation
x² − 2(a² + b²)x + (a²-b²)² = 0

Why is it crucial to ensure that each sample has at least 10 successes and failures when building a confidence interval for the difference between two population proportions. This will allow us to select a sample distribution for p1-p2 that is roughly normal.

A distributor is a business that takes part in the value chain's distribution step. Making a good or service available to the consumer or business user who wants it is the process of distribution. This might be done by the producer or service provider directly or through indirect channels like distributors or intermediaries. Distribution is one of the four elements of the marketing mix, along with the other three being the product, pricing, and promotion. The broad strategic goal and objective of a corporation should guide distribution decisions. The main task of strategic planning is to develop a thorough distribution plan. At the strategic level, there are three basic distribution tactics: mass, selective, and exclusive distribution.

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Distributive property is expressed as:

Apply this to the given expression and simplify

Step-by-step explanation:

50

because 50*(30/100)=1500/100

then it gives 15

so the 30 percent of a number is 15 that number is 50.

The requried, 30 percent of 50 is 15, as of the given condition.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

We can use algebra to solve the problem.

Let's call the number we're looking for "x". Then we can translate the problem statement into an equation:

30% of x is 15:

0.3x = 15

To solve for x, we can divide both sides of the equation by 0.3:

x = 15 ÷ 0.3

x = 50

Therefore, 30 percent of 50 is 15.

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There are 12 trapezoids needed to create two hexagons with pattern blocks.

1. To create two hexagons with pattern blocks, you will need 12 trapezoids.

2. Each hexagon consists of six trapezoids.

3. Since you need two hexagons, you will need 12 trapezoids in total.

In order to create two hexagons with pattern blocks, you will need to use 12 trapezoids in total. Each hexagon consists of six trapezoids, so you will need two hexagons to use all twelve trapezoids. The two hexagons can be formed by arranging the trapezoids in a pattern of two triangles, two parallelograms, two rhombuses, and two trapezoids. With these 12 trapezoids, you will be able to create two complete hexagons.

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Answer:

Step-by-step explanation:

how many pattern blocks triangles would create 1 hexagon

Answer:

<A=45°,<B=65°,<C=70°

Step-by-step explanation:

<A=3(x+5)=3x+15

<B=5x+15

<C=7x

sum angles in a triangle is 180°

so,<A+<B+<C=180

(3x+15)+(5x+15)+(7x)=180

C.L.T

3x+5x+7x+15+15=180

15x+30=180

15x=180-30

15x=150

divide both sides by 15

x=10

<A=3(x+5)=3(10+5)=3(15)=45°

<B=5(10)+15=50+15=65°

<C=7(10)=70°

The Correct option Will be  An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem i.e. A.

The likelihood of an event is expressed by probability. The occurrence of a random event is the subject of this mathematical field of study. The value is between zero and one. In mathematics, probability is a tool for calculating the likelihood that certain events will take place.

Probability is the possibility of something happening. The probability distribution also makes use of this central concept in probability theory. We must first ascertain the total number of possibilities before calculating the likelihood that a specific event will occur.

When something unusual happens, it does not happen frequently in terms of sight or sound.

The probability that an event will occur P(E) = the number of positive outcomes divided by the total number of outcomes.

Now,

As an unusual event has low probability because it does not happen often and The same cutoff should not be used to detect unexpected events all of the time. Choosing a cutoff is subjective, and it should consider the repercussions of erroneously labelling an occurrence as rare.

Hence,

            An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem.

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The addition and subtraction of the fractions by finding the LCD gives:

NUMBER 1: (8y-49) /(y²-49)

NUMBER 2: (x+10) /(2x+8)

NUMBER 3: (7a-2)/10b

NUMBER 4: 1

Least Common Denominator (LCD) refers to the smallest multiple that two or more denominators have in common, and is used in operations involving fractions.

NUMBER 1

y/(y²-49) - 7(y+7) = y/[(y+7)(y-7)] - 7(y+7)

LCD of (y+7)(y-7) and (y+7) is (y+7)(y-7):

                          = [y + 7(y-7)] / [(y+7)(y-7)]

                          = [y + 7y-49)] / [(y+7)(y-7)]

                          = (8y-49) / (y+7)(y-7)

                          = (8y-49) /(y²-49)

NUMBER 2

1/2 + 3/(x + 4) = [1(x+4) + 3*2] /[2(x+4)]

                      = [x+4 + 6] /[2(x+4)]

                      = (x+10) /(2x+8)

NUMBER 3

(a+2)/4b + (a-1)/10b + (a-3)/5b = [5(a+2) + 2(a-1) + 4(a-3)]/20b

                                                 = [5a+10 + 2a-2 + 4a-12]/20b

                                                 = (14a-4)/20b

                                                 = 2(7a-2)/20b

                                                 = (7a-2)/10b

NUMBER 4

x/(x+1) - 1/(x-1) + 2x/(x²-1) = [x(x-1) - 1(x+1) + 2x]/(x²-1)

                                         = [x²-x -x-1 + 2x]/(x²-1)

                                         = (x²-1)/(x²-1)

                                         = 1

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Answer:6

Step-by-step explanation:

day one-2 bread

day two-4 bread

10-4=6

6 at the end of the day

The number of loaves of bread remaining at the end of second day = 6 loaves of bread

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let number of loaves of bread remaining at the end of second day be A

The total number of loaves of bread = 10 loaves

The number of loaves of bread sold each day = 2 loaves

Substituting the values in the equation , we get

So , the number of loaves of bread remaining at end of first day = 10 - 2 = 8

Now , the number of loaves of bread remaining at end of second day = 8 -2

The number of loaves of bread remaining at the end of second day = 6

Therefore , the value of A is 6 loaves of bread

Hence , the equation is A = 6 loaves

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The perimeter of the rectangle in the given diagram is: D. 42 units.

In order to determine the perimeter of this rectangle, we would have to find the length of the third side of the right-angled triangle by using Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

9² + b² = 15²

81 + b² = 225

b² = 225 - 81

b = √144

b = 12 units.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

P = 2(9 + 12)

P = 42 units.

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The point estimator for the proportion of registered voters expressed concern about a loosening of restrictions is 0.58. The margin of error for this poll is 3.6%.

The point estimator for the proportion of registered voters expressing concern about a loosening of restrictions is:

58/100 = 0.58 or 58%

To determine the margin of error for this poll assuming a confidence level of 95%, we can use the following formula:

margin of error = zsqrt(p(1-p)/n)

where z is the z-score for the desired confidence level (1.96 for 95%), p is the point estimator for the proportion (0.58), and n is the sample size (900).

So, the margin of error is:

1.96sqrt(0.58(1-0.58)/900) ≈ 0.036 or 3.6%

Therefore, the margin of error for this poll is 3.6%.

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____The given question is incomplete, the complete question is given below:

Read the following news article and then answer the two questions at the end According to an NBC News/Wall Street Journal poll released Sunday, 58 percent of registered voters expressed concern about a loosening of restrictions compared with 32 percent who worried that the restrictions would stay in place for too long 3 percent said they were concerned about both scenarios. A mere 3 percent said the pandemic had no impact on their lives, compared with 77 percent who said it had affected them either in a very major way" or "fairly major way The sample size was 900 registered voters a What is the point estimator for the proportion of registered voters expressed concern about a loosening of restrictions b. Determine the margin of error for this poll assuming a confidence level of 95%.

He earns $184 in commission yesterday on sold 5 watches for $60 each and 4 watches for $40 each.

A sales commission is a sum of money paid to an employee upon completion of a task, usually selling a certain amount of goods or services. Employers sometimes use sales commissions as incentives to increase worker productivity. A commission may be paid in addition to a salary or instead of a salary.

A salesman earns a commission 40%

He sold yesterday 5 watches for $60 each

and, 4 watches for $40 each.

We have to find the how much he earn commission?

Now, According to the question:

Price of 5 watches = 60.00 × 5 = $300

4 watches = $40.00 each

Price of 4 watches = 40.00 × 4 = $160

Total sales made = 300 + 160 = $460

His commission is 40% of the sales = 40% × 460

                                                       = 0.40 × 460 = $184

Hence, He earns $184 in commission.

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The ratio of cups of flour to water for 6 batches is 18:6

18:6 = 3:1

The ratio is maintained.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Two batches:

The ratio of cups of flour to water.

= 6: 2

= 3:1

Now,

For 1 batch.

The ratio of cups of flour to water.

= 3 : 1

Now,

For m batches.

The ratio of cups of flour to water.

= 3m : 1m

So,

For m = 6

The ratio of cups of flour to water.

= 18 : 6

Thus,

The ratio of cups of flour to water for 6 batches is 18:6.

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The complete question.

For two batches the ratio is 6 cups of flour to 2 cups of water,

This means for every 3 cups of flour, you need 1 cup of water.

The ratio 3:1 is maintained.

Find the ratio for 6 batches

The maximum and minimum values are 34.5 and 2

from the question, we have the following parameters that can be used in our computation:

P = 2x + 7y

Subject to:

4x - 2y <= 5

x >= 1

0 <= y <= 4

Next, we plot the constraints on a graph

From the graph, we have the following vertices

(1, 0), (4, 0) and (3.25, 4)

This gives

P = 2(1) + 7(0) = 2

P = 2(4) + 7(0) = 8

P = 2(3.25) + 7(4) = 34.5

Hence, the minimum is 2 and the maximum is 34.5

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As per the discount, the customer will only need to pay P4,950 on May 12.

Discounts are a common practice in business transactions, where the seller offers a reduction in the price of goods or services as an incentive for the buyer to make a purchase.

The terms of the sale are as follows: 2/10, 1/15, n/30. This means that the customer is entitled to a 2% discount if they pay within 10 days, or a 1% discount if they pay within 15 days. Otherwise, the full amount is due within 30 days.

The customer makes a partial payment of P1,000, which means that they still owe P5,000. However, since the discount is only given upon full payment, the customer is not eligible for any discounts at this point.

Assuming that the customer pays the balance on May 12, they will have taken 11 days to make the payment. Since this is within the 15-day discount period, they are entitled to a 1% discount.

The calculation of the discount is as follows: P5,000 x 1% = P50. Therefore, the customer will only need to pay is calculated as,

=> P5,000 - P50 = P4,950

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Complete Question:

On May 1, RVQ Company sold goods for P6,000 on terms of 2/10, 1/15, n/30. Customer made a partial payment of P1,000 discounts are given only upon full payment of an account. The customer pays the balance on May 12, RVQ will receive on May 12 the amount of

Answer:

1/237.12.

Step-by-step explanation:

The probability of winning the minimum award can be calculated by multiplying the probability of picking 4 numbers correctly from 1 to 51 and then multiplying by the probability of picking 1 number correctly from 1 to 42.

The probability of picking 4 numbers correctly from 1 to 51 is given by the formula:

(number of combinations of 4 numbers from 51) / (number of combinations of 5 numbers from 51)

= (51 choose 4) / (51 choose 5)

= 51! / (4! * 47!) / (51! / (5! * 46!))

= (51 * 50 * 49 * 48) / (5 * 4 * 47 * 46)

= 19600 / 10,946

= 1/5.6 approximately

The probability of picking 1 number correctly from 1 to 42 is given by the formula:

1/42

The final probability of winning the minimum award is given by multiplying the above two probabilities:

1/5.6 * 1/42 = 1/237.12

So, the probability of winning the minimum award is approximately 1/237.12.

The following measures of typical value in a data set would be affected by the error:

Mean: The mean is the sum of all the values divided by the number of values. If one value is significantly different from the rest, it can significantly affect the mean. In this case, the mean would be affected because the value of 5 is much lower than the other values in the data set, which would cause the mean to be lower than it should be.

Median: The median is the middle value in a data set. If the error is low enough, it may not affect the median, but if it is low enough to move the value of 5 to the middle of the data set, the median would be affected.

In conclusion, the mean and median of this data set would be affected by the error of recording the value of 75 as 5.

The mode, mean and median of this data set would be affected by the error of recording the value of 75 as 5.

Given that, a data set represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75 suppose that the last value, 75, was mistakenly recorded as 5.

so, here, due to mistake the mode, mean and the median will be affected.

Adding a data point to the set, or taking one away, can affect the mean, median, and mode.

If we add a data point that's above the mean, or take away a data point that's below the mean, then the mean will increase.

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Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.

The 12.4% calculation made by Dr. Raynor is referred to as a confidence interval. A confidence interval is a range of numbers that is likely to contain a population parameter. In this case, the population parameter is the percentage of students in the school with concerning behaviors that impact their performance in the classroom. To calculate the confidence interval, Dr. Raynor first determined the sample proportion, which is 12.4%. Then, she used the following formula to calculate the confidence interval:

Confidence Interval = (Sample Proportion ± Margin of Error)

In this case, the margin of error was 2.2%, which is calculated by multiplying the sample proportion by 1.96 (1.96 being the critical value for a 95% confidence interval). Thus, the confidence interval of 10.2% to 14.6% was determined. This confidence interval means that Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.

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The length is 1 and width is 4 and height is 3.

In geometry, a cuboid is a solid or three-dimensional shape. A convex polyhedron bounded by 6 rectangular faces with 8 vertices and 12 sides is called a cuboid. A cuboid is also called a cuboid. A cuboid with six square faces is called a cube. An example of a real cube is a rectangular box. In mathematics, we can observe other shapes that are exactly the same as the cuboid. They are cuboid, cuboid, right prism, cuboid, cuboid, cuboid. Learn more about cuboids here

has a volume of 12cm^3

volume of cuboid is = length*width*height.

a*b*c  = 12

and the top faces has an area of 4 cm^2

op faces has an area = a*b.

ab = 4

a = length

b = width

ab = 4 = 1x4 = 2x2

and a = 1

b = 4  because the cuboid is longer than it is width

now

abc = 12

ab = 4

c = 12/ab

c = 12/4

c = 3

length = 1 width = 4 height = 3

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The domain of the relation is 0, 2, 3, and 7.

The range of the relation is 1 and 3.

The domain of a function is the set of all possible inputs for the function. The domain of a relation is the independent variable of the relation. The domain of the relation are the x values.

Therefore, the domain of the relation are 0, 2, 3 and 7.

The range of the relation is the set of the second coordinates from the ordered pairs. The range is the output of the relation. The range are the y axis values.

Therefore, the range of the relation are 1 and 3.

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Answer:

C. m4/n2    :))))

Answer: To find out what Kelly's next score must be in order to obtain an average that is more than 88, we first need to find the current average of her scores. To do this, we add up her current scores and divide by the number of scores:

(79 + 89 + 86 + 93) / 4 = 337 / 4 = 84.25

Since the current average is 84.25, which is less than 88, Kelly must score higher than 88 on her next quiz to bring the average up to more than 88. To be specific, Kelly must score at least 89 on her next quiz.

Step-by-step explanation:

Equity is generally defined as the difference between the value of a company’s assets and its liabilities, and is typically expressed as a dollar amount.

The formula for equity is: Equity = Assets - Liabilities To calculate equity, you would first need to calculate the value of all of the company’s assets, such as cash, investments, inventory, property, and equipment. Then, you would need to calculate the value of all of the company’s liabilities, such as accounts payable, short and long-term debt, and any other financial obligations. Once the value of the assets and liabilities have been calculated, the difference between them is the company’s equity. For example, if a company has total assets of $4,000 and total liabilities of $2,500, the equity can be calculated as follows :Equity = Assets - Liabilities Equity = $4,000 - $2,500  Equity = $1,500

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The cups of milk required for the  ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee is given by 2.4 cups.

Here,

( 2 / 5 ) of a gallons is equal to 0.4 gallons.

( 1 / 4 ) of gallons used for coffee that is equal to 0.25 gallons.

Total gallons left after coffee is equal to

= ( 0.4 ) - ( 0.25 )

= ( 0.15 )gallons

Conversion of gallons to cups is given by :

1 gallon = 16 cups

⇒  ( 0.15 )gallons = 0.15 × 16 cups

⇒  ( 0.15 )gallons = 2.4 cups of milk used.

Therefore, the 2.4 cups of milk is used when  ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee.

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Answer:

To solve it, you need to use compound interest. Let me show you how.

Let P be the initial amount that Terry invested. Then after 4 years, the amount in the account is:

P × (1 + 0.037)^4

After withdrawing $2000, the remaining amount is:

P × (1 + 0.037)^4 - 2000

This amount is then moved to another account earning 4.5% p.a. compounded annually. After 3 more years, the amount in the account is:

(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3

We are given that this amount is equal to $5635.66. So we can write an equation:

(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3 = 5635.66

Simplifying the equation, we get:

P × 1.1597 - 2000 = 5635.66 / 1.1406

Adding 2000 to both sides, we get:

P × 1.1597 = 5635.66 / 1.1406 + 2000

Dividing both sides by 1.1597, we get:

P = (5635.66 / 1.1406 + 2000) / 1.1597

Using a calculator, we get:

P ≈ 5000.01

Therefore, Terry initially invested about $5000.01.

Step-by-step explanation:

The system is consistent.

A system of equations is said to be consistent when they have atleast one solution in common.

A system of equations has one line with a positive slope and one line with a negative slope

The system has 1 line with a positive slope, so a line that has a positive slope is going to be rising from left to right.

The second line that has a negative slope. So just a line ,it is decreasing. Now a negative slope means the line, falls from left to right or is downward sloping.

If 1 line has a positive slope and 1 line has a negative slope, then at some point those lines are going to intersect, which will be the solution to the system.

Hence, the system is consistent.

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Answer

Step-by-step explanation:

Answer:

  7 feet

Step-by-step explanation:

You want the height of a 6' by 12' cuboid box that has a total surface area of 396 square feet.

The formula for the surface area of a cuboid is ...

  SA = 2(LW +H(L+W))

For the given box, this is ...

  396 = 2(6·12 +H(6+12))

  198 = 72 +18H . . . . . . . . . . divide by 2

  126 = 18H . . . . . . . . . . . subtract 72

  7 = H . . . . . . . . . . . . divide by 18

The height of the box is 7 feet.

Answer: y = x(x+1)(x-4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,y=x^3-3x^2-4x

taking x commonly

y=x(x^2-3x-4)

y=x(x^2+x-4x-4)

y=x[x(x+1)-4(x+1)]

y=x(x+1)(x-4)

Answer:

74.90d + 0.13m = Total cost of the car rental

Step-by-step explanation:

Hmmm you didn't give enough information but....

let d represent the number of days

let m represent the number of miles driven

74.90d + 0.13m = Total cost of the car rental

For example Tyee rents the car for 2 days and drives 100 miles

149.8 + 13 = Total cost of the car rental.

$162.8 is the Total cost of the car rental.

16 iron spheres each of radius 1.5 cm are required to raise the level of water by 2 cm

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, A cylindrical jar of radius 6 cm contains water.

Therefore, the volume of the cylinder is π(6²)h = 36πh.

Given, The height raises by 2cm therefore, 36π(h + 2).

We know, The volume of a sphere is, (4/3)πr³

=  (4/3)π(1.5)³.

= (4/3)π×3.375.

= (13.5/3)π.

let, We need 'x' number of spheres.

Therefore,  36πh + (13.5/3)πx = 36π(h + 2).

36πh - 36π(h + 2) =  - (13.5/3)πx.

36h - 36(h + 2) =  - (13.5/3)x.

108h - 108(h + 2) = - 13.5x.

108(h - h - 2) = - 13.5x.

108(-2) = - 13.5x.

x = 216/13.5.

x = 16.

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