The product of two integers is ─24. The difference between the two integers is 14. The sum of the two integers is 10. What are the two integers? Name them from least to greatest

The length of radius of the circle having center at (2-i) and point on circle at (8+7i) is 10 units .

To find the length of the radius of a circle with a center at (2-i) and a point on the circle at (8+7i), we can use the distance formula , which is

The formula to find distance between 2 points (x₁, y₁) and (x₂, y₂) is given by:

⇒ d = √[(x₂ - x₁)² + (y₂ - y₁)²] ,

In this case, the center of the circle is (2-i), which means that the x-coordinate of the center is 2 and the y-coordinate is -1.

The point on the circle is (8+7i), which means that the x-coordinate of the point is 8 and the y-coordinate is 7.

By using distance formula, we can find distance between the center and the point on circle ,

⇒ d = √[(8 - 2)² + (7 - (-1))²]

⇒ d = √[6² + 8²]

⇒ d = √[36 + 64]

⇒ d = √100

⇒ d = 10

Therefore, the length of the radius of the circle is 10 units.

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The given question is incomplete , the complete question is

What is the length of the radius of a circle with a center at (2-i) and a point on the circle at (8+7i)?

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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To complete the Material Requirements Planning (MRP) table for product A, we need to calculate the Net Requirements and Planned Order Releases based on the given information. Here's the completed MRP table:

Lot Volume = multiples of 50

Delivery Time = 2 weeks

Starting Inventory: 30

| Period | Gross Need | Scheduled Receipt | Projected Inventory | Net Requirements |

| 1 | 25 | | 30 | 0 |

| 2 | 30 | | | |

| 3 | 56 | | | |

| 4 | 25 | | | |

| 5 | 100 | | | |

| 6 | 40 | | | |

| 7 | 30 | | | |

To calculate the Scheduled Receipt and Projected Inventory, we need to consider the lot volume and delivery time. Assuming a lot volume of 50 and a delivery time of 2 weeks, the calculations are as follows:

Period 1:

Scheduled Receipt = 0 (No orders scheduled to arrive in this period)

Projected Inventory = Starting Inventory + Scheduled Receipt - Gross Need = 30 + 0 - 25 = 5

Period 2:

Scheduled Receipt = 50 (Order placed to fulfill the gross need of 30)

Projected Inventory = Previous Projected Inventory + Scheduled Receipt - Gross Need = 5 + 50 - 30 = 25

Period 3:

Scheduled Receipt = 50 (Order placed to fulfill the gross need of 56)

Projected Inventory = Previous Projected Inventory + Scheduled Receipt - Gross Need = 25 + 50 - 56 = 19

Period 4:

Scheduled Receipt = 0 (No orders scheduled to arrive in this period)

Projected Inventory = Previous Projected Inventory + Scheduled Receipt - Gross Need = 19 + 0 - 25 = -6

Period 5:

Scheduled Receipt = 100 (Order placed to fulfill the gross need of 100)

Projected Inventory = Previous Projected Inventory + Scheduled Receipt - Gross Need = -6 + 100 - 100 = -6

Period 6:

Scheduled Receipt = 50 (Order placed to fulfill the gross need of 40)

Projected Inventory = Previous Projected Inventory + Scheduled Receipt - Gross Need = -6 + 50 - 40 = 4

Period 7:

Scheduled Receipt = 0 (No orders scheduled to arrive in this period)

Projected Inventory = Previous Projected Inventory + Scheduled Receipt - Gross Need = 4 + 0 - 30 = -26

The Net Requirements are calculated as the difference between the Gross Need and the Projected Inventory. If the Net Requirements are positive, it indicates the quantity needed to fulfill the demand. If the Net Requirements are negative, it means there is excess inventory.

Please note that this MRP table assumes no changes in demand, lead time, or lot sizing throughout the periods.

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Answer: False

Step-by-step explanation:

Answer:\(313^{\circ}\)

Step-by-step explanation:

Given

\(\angle {EFG}=133^{\circ }\)

When rotated 180 degree clockwise gives E'F'G' which measures

\(\angle E'F'G'=180^{\circ}+133^{\circ}=313^{\circ}\)

This can be explained by the below-given digram  

Rotation is a rigid transformation.

The measure of angle E'F'G' is 133 degrees

Because rotation is a rigid transformation, it does not change the side lengths and the angle measures.

This means that the measure of angle EFG will remain unchanged after rotation.

i.e.

\(\mathbf{\angle E'F'G' = \angle EFG}\)

Hence, the measure of angle E'F'G' is 133 degrees

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The expressions that are equivalent to 5% of 60 are  5/100 * 60, 0.05 * 60 and 1/20 * 60

The expression is given as:

5% of 60

Express as fraction and decimal

5% of 60 = 5/100 * 60

5% of 60 = 0.05 * 60

This gives

5% of 60 = 1/20 * 60

Hence, the expressions that are equivalent to 5% of 60 are  5/100 * 60, 0.05 * 60 and 1/20 * 60

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Answer:

No

Step-by-step explanation:

you can check with the pythagorean theory

\(8^{2}+9^{2} =12^{2}\)

64 + 81 = 144

145 = 144

this is not true, therefore those side lengths do not make a right triangle.

Answer:

Area required for circular hot tube = 6,218 inch² (Approx.)

Step-by-step explanation:

Given:

Diameter of circular hot tube = 89 inches

Value of π = 3.14

Find:

Area required for circular hot tube

Computation:

Radius of hot tube = Diameter / 2

Radius of hot tube = 89 / 2 inches

Area required for circular hot tube = Area of circle

Area of circle = πr²

Area required for circular hot tube = πr²

Area required for circular hot tube = (3.14)(89/2)²

Area required for circular hot tube = (3.14)(7921 / 4)

Area required for circular hot tube = (3.14)(1,980.25)

Area required for circular hot tube = 6,217.985

Area required for circular hot tube = 6,218 inch² (Approx.)

Average number of books read per month by individuals in a given community.

This question aims to gather data on the reading habits of individuals within a specific community.

By asking at least twenty different people, we can collect a range of numerical answers representing the number of books read per month by each participant.

The responses may vary greatly, as some individuals may read extensively while others may read minimally.

By calculating the average of the collected data, we can determine the estimated average number of books read per month within the community.

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Answer:

h = 16 m

Step-by-step explanation:

Given that,

The area of a trapezium, A = 700 m²

The sum of the length of the parallel sides = 70 m

The area of a trapezium is given by :

\(A=\dfrac{1}{2}\times \text{sum of parallel sides}\times height\\\\h=\dfrac{2A}{Sum}\\\\=\dfrac{2\times 700}{70}\\\\=20\ m\)

So, the height of the flower bed is 20 m.

Answer:

3/14, 3/20, 1.2, 1.875

Step-by-step explanation:

31. 6/7÷4 is 1.5/7 and then 3/14

32. 3/10 is 1.5/10 then 3/20

33. 2/5÷1/3 is equal to 2/5x3/1 or 6/5 then 1.2

34. Write as improper fractions 5/2÷4/3 which is then 5/2x3/4=15/8=1.875

Answer:

$16.80

Step-by-step explanation:

0.30 × 24 = 7.20

24 - 7.20 = $16.80

Hope that helps.

The image showing the locus points equidistant from X, Y, and Z is B. See the attached image.

If the distances between a point and each object in the set are equal, the point is said to be equidistant from the set.

When a point is equidistant from two other points, it is at the same distance from both of them. The distance between two points may be computed using the distance formula and the coordinates of the two points.

In geometry, a locus is a set of points that satisfy a specific condition or circumstance for a form or figure. The locus is pluralized as loci. The region is the location of the locus. The term locus comes from the word location.

Thus, the point that is equidistant from X, Y, and Z is B.

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To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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a. population mean

The mean of all possible sample means is equal to the population mean.

This is known as the sampling distribution of the sample mean. When we take multiple random samples from a population and calculate the mean of each sample, the average of these sample means will converge to the population mean.

This is a fundamental result of statistics known as the Central Limit Theorem. As the sample size increases, the variability of the sample means decreases and they become centered around the population mean.

Therefore, the mean of all possible sample means provides an unbiased estimate of the population mean.

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Answer: 47°

Step-by-step explanation:

Answer:225 degrees

Step-by-step explanation:

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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Correlation measures the degree of association between two variables and outliers can distort the relationship between them.

True. One or two extreme data points, also called outliers, can have a dramatic effect on the size of a correlation. This is because correlation measures the degree of association between two variables and outliers can distort the relationship between them.

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The scenario modeled in the given graph is option A. A ball is dropped and bounces on the ground before stopping.

Any item launched into space with just gravity acting on it is referred to as a projectile. Gravity is the main force affecting a projectile. This doesn't imply that other forces don't affect it; it merely means that their impact is far smaller than that of gravity. A projectile's trajectory is its route after being fired. A projectile is something that is launched or hit, as a baseball.

When a ball is thrown from a certain height it bounces off the ground continuously until it comes to a stop. When the movement of such a ball is traced we obtain the above graph.

Hence, option A is correct.

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The activities are in following order The sun will set tonight, A fair six-sided dice is rolled and lands on a number less than 6, A fair coin is flipped and it lands on tails, Someone you know will win the National Lottery, Someone in this class has the same birthday as you, A pig will fly past the window.

I am confident that the first three activities which are The sun will set tonight, A fair six-sided dice is rolled and lands on a number less than 6, A fair coin is flipped and it lands on tails,  are in the correct order from certain to less certain, as they are all possible events, but their likelihood of occurring decreases in the given order.

It was most difficult to place the activity "A pig will fly past the window" as it is highly unlikely to happen, but still possible in some rare circumstances.

The last activity "Someone in this class has the same birthday as you" is impossible to place with certainty, as it depends on the size of the class and the number of people in it. It could be possible, but it is not a definite event.

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The values of x in the open interval (0, 1.565) is: (B) One.

The instantaneous rate of change of a function is given by the derivative, while the average rate of change is given by the difference quotient.

In this problem, we need to find the values of x in the open interval (0, 1.565) where the derivative of f is equal to the difference quotient of f over the closed interval [0, 1.565].

The derivative of f(x) is f'(x) = 2x - 2, and the difference quotient of f over [0, 1.565] is:

[f(1.565) - f(0)] / (1.565 - 0) = [1.565^2 - 2(1.565)] / 1.565 = -0.624

So we need to find the values of x in (0, 1.565) where f'(x) = -0.624.

Setting f'(x) = -0.624 and solving for x, we get:

So there is only one value of x in (0, 1.565) where the instantaneous rate of change of f is equal to the average rate of change of f over [0, 1.565]. The answer is (B) One.

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Answer:

Large books = 11

Small books = 6

Step-by-step explanation:

7x + 5y = 107

7x = 107 - 5y

x = 107/7 - 5y/7

5x + 7y = 97

5 (107/7 - 5y/7) + 7y = 97

535/7 - 25y/7 + 7y = 97

535/7 + 24y/7 = 97

535 + 24y = 679

24y = 679 - 535

y = 144/24 = 6: So x =

7x + 5(6) = 107

7x = 107-30

x = 77-7 = 11

The torque on the current loop is maximum in position 1 where the plane of the loop is perpendicular to the magnetic field lines. This is because the magnetic field exerts a force on the moving charges in the wire, causing them to experience a torque that is perpendicular to both the magnetic field and the current in the loop. In position 2 and 3 where the plane of the loop is parallel to the field, the torque is zero as there is no perpendicular component to the magnetic field.

The torque on a current loop in a magnetic field depends on its orientation. Here, we have three positions to consider:

1. The plane of the loop is perpendicular to the field lines.
2. The plane of the loop is parallel to the field lines (Position 2).
3. The plane of the loop is parallel to the field lines (Position 3).

The torque on the loop is given by the formula: torque = μ x B, where μ is the magnetic moment of the loop, B is the magnetic field, and x represents the cross product. The maximum torque occurs when the angle between μ and B is 90 degrees.

In Position 1, the plane of the loop is perpendicular to the field lines, which means the angle between μ and B is 90 degrees. Thus, the torque is at its maximum in this position.

In Positions 2 and 3, the plane of the loop is parallel to the field lines, meaning the angle between μ and B is either 0 or 180 degrees. In both these cases, the torque is at its minimum.

Therefore, the torque on the loop is maximum in Position 1, where the plane of the loop is perpendicular to the field lines.

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Answer:

y=2/7x-2

Step-by-step explanation:

The change in temperature is 15°

How to find Change in temperature ?

        t₂ = t₁ + final temperature

We have given,

In morning, when Rae woke up the temperature is (t₁) = -20°

At dinner time, the temperature is = 35°

t₂ = t₁ + 35

t₂ = (-20) + 35

t₂ = 15°

Hence, the change in temperature is 15°

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The interpretation of the graphs are:

The given graphs pass through the origin

So, the slopes of the graphs are

Slope = y/x

Where x and y are ordered pairs on the line of the graph

Graph A

(x, y) = (4, 16)

Slope = 16/4

Slope = 4

This means that Jesse walks 4 miles per hour for 4 hours.

Graph B

(x, y) = (5, 15)

Slope = 15/5

Slope = 3

This means that Mikes walks 3 miles per hour for 5 hours.

Graph C

(x, y) = (4, 18)

Slope = 18/4

Slope = 4.5

This means that Josh walks 4.5 miles per hour for 4 hours.

Graph D

(x, y) = (5, 17.5)

Slope = 17.5/5

Slope = 3.5

This means that Brad walks 3.5 miles per hour for 5 hours.

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