The gravitational force between two marbles that are 50 cm apart is 2.67×|
10-14 N. What is the mass of each marble?

Answer:

-75

Step-by-step explanation:

-123 + 48

-*+ = -

123-48

75

But as the bigger number i.e 123 has a negative sign before so the answer will be in negative

i.e -75

Within sample variance occurs within a single sample or group.

Within sample variance refers to the variation or dispersion of values within a single sample or group. It measures how much the individual data points deviate from the mean or central tendency within that specific sample. This variance is calculated by taking the average of the squared differences between each data point and the sample mean.

For example, let's say we have a sample of test scores for a group of students. Within sample variance would help us understand how much the individual test scores vary within that particular group. If the test scores are tightly clustered around the mean, the within sample variance would be low, indicating a high level of similarity among the scores. Conversely, if the test scores are widely spread out, the within sample variance would be high, suggesting a greater diversity or variability among the scores.

In summary, within sample variance occurs within a single sample or group and quantifies the dispersion of values around the mean within that sample. It helps assess the level of variation or homogeneity within the data set.

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Answer:

A

Step-by-step explanation:

because

Answer:

3

Step-by-step explanation:

Express the numbers as a product of their primes.

42 = 2 × 3 + 7

30 = 2 × 3 × 5

45 = 3 × 3 × 5

Identify the prime factors common to all 3 numbers.

common prime factor = 3 , thus

GCF = 3

Answer: 3

Step-by-step explanation: The factors of 30 are 1. 2. 3. 5. 6. 10, 15, 30

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The factors of 45 are 1, 3, 5, 9, 15, 45

As you can see they all share the factors of 1 and 3. Since 3 is the greatest number of the factors all of them share it is the greatest common factor.

Answer:

553

Step-by-step explanation:

A quotient is a quantity that is obtained by dividing two integers. The quotient of the division \(\dfrac{2}{\sqrt{13}+\sqrt{11}}\) is (√13-√11).

A quotient is a quantity that is obtained by dividing two integers. The quotient is a term that is widely used in mathematics to refer to the integer component of a division, as well as a fraction or a ratio.

In order to find the quotient of the fraction, we need to take the rationalise of the fraction.

\(\dfrac{2}{\sqrt{13}+\sqrt{11}} \\\\\\ =\dfrac{2}{\sqrt{13}+\sqrt{11}} \times \dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\\\\\= \dfrac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\\\\\= \dfrac{2(\sqrt{13}-\sqrt{11})}{2}\\\\=(\sqrt{13}-\sqrt{11})\)

Hence, the quotient of the division \(\dfrac{2}{\sqrt{13}+\sqrt{11}}\) is (√13-√11).

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Answer:

D.) StartRoot 13 EndRoot minus StartRoot 11 EndRoot

Step-by-step explanation:

on edge took the test .

Answer:

1

Step-by-step explanation:

The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.

A) The rate of change in the direction of motion is approximately 2.94.

B) The direction in which the bug should move from P for the temperature to increase the fastest is in the direction of <-0.649, -0.761>.

C) The magnitude of the rate of change of temperature in that direction is given by ||∇T(2,3) · v|| = ||∇T(2,3)|| ||v|| cosθ

We can use the gradient of the temperature function to find the direction of maximum increase and the rate of change in that direction.

The gradient of T(x,y) is given by:

∇T(x,y) = <-2x/5, -y>

At point P=(2,3), the gradient is:

∇T(2,3) = <-4/5, -3>

The direction of maximum increase is given by the unit vector in the direction of the gradient. We can find this by normalizing the gradient:

u = ∇T(2,3) / ||∇T(2,3)||

Where ||∇T(2,3)|| is the magnitude of the gradient at point P:

||∇T(2,3)|| = √((-4/5)² + (-3)²) = √(16/25 + 9) = √(41/5)

Therefore,

u = <-4/5, -3> / √(41/5) = <-0.649, -0.761>

So the direction in which the bug should move from P for the temperature to increase the fastest is in the direction of <-0.649, -0.761>.

To find the rate of change in the direction of motion, we need to project the gradient onto the unit vector connecting P and Q. Let R be the position vector of the point on the line connecting P and Q that is closest to P. Then the direction of motion is given by the unit vector:

v = (Q - P) / ||Q - P||

Where ||Q - P|| is the distance between P and Q:

||Q - P|| = √((3 - 2)² + (-2 - 3)²) = √26

Therefore,

v = <1/√26, -5/√26>

The rate of change in the direction of motion is given by the dot product of the gradient and the unit vector v:

∇T(2,3) · v = (-4/5)(1/√26) + (-3)(-5/√26) = 15/√26 ≈ 2.94

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Answer:

b is correct

Step-by-step explanation:

Answer:

a), b) and c) are correct.

d) 12g^4h^5

Step-by-step explanation:

Answer:

• Binomial

• Degree = 0

• Coefficient = 8

• Constant = 8

Step-by-step explanation:

It is Binomial because Bi means 2. So there are 2 terms which in this case are 8 and 4r.

The Degree is 0 because neither one have an exponent.

The Coefficient is which number has the highest value which in this case is 8.

The Constant is 8 because it doesn't have a variable nor a exponent.

Hope this Helps!!

:D

Answer:

A. h = h₀ + u·t - 1/2·g·t²

B. 30.9 m

C. 4.73 seconds

2. A. h = h₀ + u·t - 1/2·a·t²

B. 67.8 m

C. Approximately 25.73 seconds

3. A. h = h₀ + u·t - 1/2·g·t²

B. 31.38 m

C. Approximately 5.142 seconds

D. Approximately 32.9 m

Step-by-step explanation:

The given parameters are;

The initial height of the ball, h₀ = 15 m

The upward velocity with which the ball is thrown, u = 20 m/sec.

The acceleration due to gravity, g = 9.8 m/s²

A. The relation between the height, h, and the time, t, after the ball is released is given as follows;

h = h₀ + u·t - 1/2·g·t²

B. The height of the ball after 3 seconds is given by substitution as follows;

At t = 3 seconds, h = 15 + 20 × 3 - 1/2 × 9.8 × 3² = 30.9

The height of the ball, h, after 3 seconds is h = 30.9 m

C. The time the ball takes to hit the ground = 2 × The time it takes to maximum height + The time it takes the ball to fall with an initial velocity of 20 m/sec for 15 m height

The time it takes to maximum height, \(t_{max}\), is given as follows;

v = u - g·\(t_{max}\)

Where;

v = The final velocity = 0 at maximum height

Therefore, we have;

0 = 20 - 9.8 × \(t_{max}\)

∴ \(t_{max}\) = 20/9.8 ≈ 2.0408

The time it takes to maximum height, \(t_{max}\) ≈ 2.0408 seconds

The time it takes the ball to fall with an initial velocity of 20 m/sec for 15 m height, \(t_{15}\) is  given as follows;

v₂² = u₂² + 2·g·h₀

v₂² = 20² + 2×9.8×15 = 694

v₂ = √694 ≈ 26.344 m/s

v₂ ≈ 26.344 m/s

From, v₂ = u₂ + g·\(t_{15}\), we have;

26.344 = 20 + 9.8×t

9.8·\(t_{15}\) = 26.344 - 20 = 6.344

∴ \(t_{15}\) = 6.344/9.8 ≈ 0.647

The ball will hit the ground after 2 × \(t_{max}\)  + \(t_{15}\) ≈ 2 × 2.0408 + 0.647 ≈ 4.7286

The ball will hit the ground after approximately 4.7286 ≈ 4.73 seconds

2. When the ball is thrown upward from the Moon, we have;

The acceleration due to gravity on the moon, a = 1.6 m/s², therefore, we have;

A. The relation between the height, h, and the time, t, after the ball is released is given as follows;

h = h₀ + u·t - 1/2·a·t²

B. The height of the ball after 3 seconds is given by substitution as follows;

At t = 3 seconds, h = 15 + 20 × 3 - 1/2 × 1.6 × 3² = 67.8

The height of the ball, h,  thrown on the Moon, after 3 seconds is h = 67.8 m

C. The time the ball takes to hit the ground = 2 × The time it takes to maximum height + The time it takes the ball to fall with an initial velocity of 20 m/sec for 15 m height

The time it takes to maximum height, \(t_{max}\), is given as follows;

v = u - a·\(t_{max}\)

Where;

v = The final velocity = 0 at maximum height

Therefore, we have;

0 = 20 - 1.6 × \(t_{max}\)

∴ \(t_{max}\) = 20/1.6 = 12.5

The time it takes to maximum height, \(t_{max}\) = 12.5 seconds

The time it takes the ball to fall with an initial velocity of 20 m/sec for 15 m height, \(t_{15}\) is  given as follows;

v₂² = u₂² + 2·a·h₀

v₂² = 20² + 2×1.6×15 = 448

v₂ = √448 ≈ 21.166 m/s

v₂ ≈ 21.166 m/s

From, v₂ = u₂ + a·\(t_{15}\), we have;

21.166 = 20 + 9.8×t

1.6·\(t_{15}\) = 21.166 - 20 = 1.166

∴ \(t_{15}\) = 1.166/1.6 ≈ 0.72785

The ball will hit the ground after 2 × \(t_{max}\)  + \(t_{15}\) ≈ 2 × 12.5 + 0.72875 = 25.72875 ≈ 27.73

The ball will hit the ground after approximately 25.73 seconds

3. The height from which the ball is kicked, h₀ = 1 m

The initial velocity of the ball, u = 25 m/sec

The acceleration due to gravity, g = 9.8 m/s²

The relationship between the height, h and the time, t after the ball is released, is given as follows;

h = h₀ + u·t - 1/2·g·t²

B. The height of the ball after 2 seconds is given as follows;

At t = 2, h = 1 + 25 × 2 - 1/2 × 9.81 × 2² = 31.38

The height of the ball, after 2 seconds, h = 31.38 m

C. The time it takes the ball to hit the ground is given by the following kinematic equation, as follows;

h = h₀ + u·t - 1/2·g·t²

At the ground level, h = 0, therefore, we have;

0 = 1 + 25·t - 4.9·t²

Therefore, by the quadratic formula, we have;

t =  (-25  ± √(25² - 4×(-4.9)×1))/(2 × -4.9)

Therefore, t ≈ 5.142, or t ≈ -0.03969

Given that the time is a natural number, we have, t ≈ 5.142 seconds

D. The maximum height, \(h_{max}\) the ball reaches is given as follows;

From the kinematic equation, v² = u² - 2·g·h,

Where;

v = 0 at maximum height

h = The height the ball reaches above the initial height, we have;

0² = u² - 2·g·h

u² = 2·g·h

h = u²/(2·g) = 25²/(2 × 9.8) ≈ 31.888

\(h_{max}\) = h₀ + h = 1 + 31.888 ≈ 32.9

The maximum height the ball reaches, \(h_{max}\) ≈ 32.9 m

The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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Answer: 18.5

Step-by-step explanation:

First, I did 2x2 witch is 4. Then I added 4 to 33, to get 37, lastly I divided 37 by 2 to get 18.5 as my product.

Answer:

- 190

Step-by-step explanation:

-10x (4x - 12 - 3)

-40x - 120x - 30x

- 190

Answer:

-20x³ + 30x^4 + 15x²

Step-by-step explanation:

−5x²(4x − 6x² − 3)

-20x³ + 30x^4 + 15x²

The total surface area of the pyramid is 100 + 4 x 50 = 100 + 200 = 300 square inches.

A square pyramid's surface area is calculated by summing the areas of its four lateral sides and base.

Since each side of the base of the pyramid measures 10 inches, the base has an area of 10 x 10 = 100 square inches.

Due to the fact that each lateral face is a triangle with a base of 10 inches and a height of 10 inches each, they each have an area of (1/2) x 10 x 10 = 50 square inches.

Therefore, the total surface area of the pyramid is 100 + 4 x 50 = 100 + 200 = 300 square inches.

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\(\frac{6}{8}\) is a fraction that is equivalent to three fourth, or \(\frac{3}{4}\). The numerator and denominator are changed by multiplying and dividing the original fraction by the same natural number as 2.

According to equivalent fractions, two or more fractions are considered to be equal if both provide the same fraction followed by simplification. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions. An equivalent fraction can be obtained by multiplying and dividing the same natural number with the given fraction. As of the query, \(\frac{3}{4}\) is an improper fraction, whose equivalent fractions can be obtained as follows:

Multiplying natural numbers lie 2, 3, 4... with the given fraction:

\(\frac{3}{4}\) × \(\frac{2}{2}\) = \(\frac{6}{8}\)

Hence, 6/8 is an equivalent fraction of 3/4. Other than this, we can also obtain more equivalent fractions in the same manner.

\(\frac{3}{4}\) × \(\frac{3}{3}\) = \(\frac{9}{12}\)

Hence, 9/12 is also equivalent to 3/4 when reduced to lowest terms. Similarly, we can find that 12/16, 15/20, and 18/24 are also equivalent fractions of 3/4.

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Answer: Ayshab's average speed for the whole journey =  \(3\dfrac{3}{11}\text{ mph}\)

Step-by-step explanation:

Formula: Speed = \(\dfrac{Distance}{Time}\)

i.e. Time = \(\dfrac{Distance}{Speed}\)

If Ayshab walked x miles at 4 mph, then time taken by him = \(\dfrac{x}{4}\) hours

If she then walked 2x miles at 3 mph, then time for this period = \(\dfrac{2x}{3}\) hours

Average speed = \(\dfrac{Total \ distance}{Total\ time}\)

\(=\dfrac{x+2x}{\dfrac{x}{4}+\dfrac{2x}{3}}\\\\\\=\dfrac{3x}{x(\dfrac{1}{4}+\dfrac{2}{3})}\\\\\\=\dfrac{3}{\dfrac{3+8}{12}}\\\\\\=\dfrac{3\times12}{11}\\\\=\dfrac{36}{11}\\\\=3\dfrac{3}{11}\text{ mph}\)

Hence, Ayshab's average speed for the whole journey =  \(3\dfrac{3}{11}\text{ mph}\)

Ayshab's average speed for the whole journey is 36/11 mph and this can be determined by using the formula of average speed.

Given :

The formula of speed is given by:

\(\rm Speed = \dfrac{Distance }{Time}\)

\(\rm Time = \dfrac{ Distance}{Speed}\)

Now, the time taken by Ayshab to walk x miles at 4 mph is :

\(\rm t_1 = \dfrac{x}{4}\)

Now, the time taken by Ayshab to walk 2x miles at 3 mph is:

\(\rm t_2 = \dfrac{2x}{3}\)

Now, the average speed is given by the formula:

\(\rm Avg. \; Speed = \dfrac{Total \;Distance}{Total \; Time}\)

                  \(=\dfrac{x+2x}{\dfrac{x}{4}+\dfrac{2x}{3}}\)

                  \(= \dfrac{36}{11}\)

Ayshab's average speed for the whole journey is 36/11 mph.

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Answer:

25 questions

Step-by-step explanation:

20 questions = 80%  If she got 80%, that means she got 20 questions correct.

5 questions = 20%  Here, we simply just divide by 4 to give us 20%.

25 questions = 100%  The total of the test would of course equal 100%, so we just multiply by 5 to give the total questions.

I hope this helps you!! ^-^

Answer:

25.

Step-by-step explanation:

By proportion it is

(100/80) * 20

= 1.25 * 20

= 25.

Answer:

3

Step-by-step explanation:

7 7/8÷51/4

3/2÷1/2

3

A=bh1/2

A=5 1/4×3×1/2

A=15 3/4×1/2

A= 7 7/8

(Mark as brainliest please)

Answer:

 (b+3)+b=51

"b" is a smaller number, that is 24.

So a larger numer is 27

Step-by-step explanation:

L = b +3

L+b = 51

(b+3) + = 51

2b + 3 = 51 >> subtract 3 to both sides

2b = 48 >> divide by 2 to both sides

b = 24

Larger = b + 3= 24 + 3= 27

This exercise is about creating two-dimensional shapes. The resulting shape is a quadrilateral - Square. See the attached for the lines drawn.

What was noticed about the two lines drawn?

When two lines intersect with one another such that they create a right angle, perpendicularity has occurred and both lines are said to be perpendicular to one another.

Hence:

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Answer:

94.3% is the answer, based on the data.

Answer:

I think live interviews

Pounds of apples sold y = 11.04

Pounds of raspberries sold = 33.12  

A farm, often referred to as an agricultural holding, is a piece of land that is predominantly used for agricultural pursuits with the goal of producing food and other crops; it is the key component in the production of food.

The phrase is used to describe specialized businesses such arable farms, vegetable farms, fruit farms, dairy farms, pig farms, and poultry farms as well as land used to generate natural fiber, bio-fuel, and other goods.

Along with the farmhouse and other agricultural buildings, this category also includes ranches, feedlots, orchards, plantations and estates, smallholdings, and hobby farms.

Modern usage of the phrase has expanded it to include both on land and in the water operations like wind farms and fish farms.

each pound of raspberries sells for $3.25

and each pound of apples sells for $2.75.

3.25x + 2.75y = $138 equⁿ 1

3 times as many pounds of apples as pounds of raspberries,

x = 3y  

where, x = pounds of raspberries  sold

y = pounds of apples sold

on putting x = 3y  in  equⁿ 1, we get

3.25 * 3x + 2.75y = 138

y = 138 /12.50

y = 11.04

x = 33.12

hence,  pounds of apples sold y = 11.04

pounds of  raspberries sold = 33.12

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Answer:

24/9

Step-by-step explanation:

-20-4=-24

-8-1=-9

(i) The dual of the given LP problem can be found by following these steps:

1. For each constraint in the primal problem, create a dual variable. In this case, we have three constraints, so we'll have three dual variables: y1, y2, and y3.
2. The objective function of the dual problem will be the sum of the products of the primal variables and their corresponding dual variables. So, the dual objective function is:
  Maximize w = 3y1 + 2y2 + y3.
3. For each primal variable x, create a constraint in the dual problem with the coefficient of the corresponding dual variable equal to the coefficient of x in the primal objective function. So, the dual constraints are:
  y1 + 2y2 - y3 ≤ -2
  y1 + y2 + y3 ≤ -1
  y1, y2, y3 ≥ 0.

(ii) To find the optimal solution to the dual problem, we need to solve the optimal tableau of the dual problem. From the given information, we know that Row 0 of the optimal tableau is:
  w = 4x1 + e2 + (M-1)a2 + (M+2)a3 = 0.
 
  However, the given information does not provide any details about the values of x1, e2, a2, or a3. Therefore, without this information, we cannot determine the specific optimal solution to the dual problem.

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Answer:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set

Step-by-step explanation: