a) A fair dice is tossed 5 times. i) Use counting methods to find the probability of getting 5 consecutive sixes 66666. II) Use counting methods to find the probability of getting the exact sequence 6

Answer:

30 J

Step-by-step explanation:

W = mg = 3 N

h = 10 m

Potential Energy = mgh = 3*10 = 30 J

The potential energy is 30 joules for the given flower pot.

The potential energy of an object is equal to its mass multiplied by the acceleration due to gravity and its height above a reference point.

As per the question, the flower pot has a mass of 3 newtons and it is 10 meters above the reference point (the ground). The acceleration due to gravity is approximately 9.8 meters per second squared.

Given:

mass, m= 0.3 kg

g = 10 or 9.8 m/s²

h= 10 m

So, Potential Energy = m × g × h

= 0.3 × 10 × 10

Apply the multiplication, and we get

= 30 joules

Hence, the potential energy is 30 joules.

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Answer:

The answer is 450 pi  square feet

Step-by-step explanation:

The area of the surface of the silo is 450π square feet.

Surface area is the amount of space covering the outside of a three-dimensional shape.

Given that a silo is constructed using a cylinder with a hemisphere on top.

Both are having equal circumference.

The diameter of the circular base of the cylinder is 10 feet. The cylinder is 40 feet tall.

The surface that will be exposed to the rain is the lateral surface of the cylinder and the hemisphere.

The lateral area of the cylinder is a rectangle with height equal to the height of the cylinder and width equal to the circumference of the base of the cylinder.

Circumference of the base = 2πr = 10π ft

The lateral area = 400π ft²

The surface area of a hemisphere is = 2πr² = 50π ft²

Total surface area = 450π ft²

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Answer: 98268

Step-by-step explanation:

Given: In an international company,

Employees in one country = 22,700

If this is 23.1% of the total number of company's employees,

[\(1\%=\dfrac1{100}\) , replace 'of' by '×']

i.e. 23.1% of (total employees) = 22700

\(\Rightarrow\ \dfrac{23.1}{100}\times\text{(total employees)}=22700\\\\\Rightarrow\ \text{Total employees}=\dfrac{22700\times100}{23.1}\\\\\Rightarrow\ \text{Total employees}=98268.4\approx98268\)

Hence, there are 98268 employees in total.

The shape of the graph changes qualitatively at k = ± 2 and

\(k=\sqrt{(2)\).

The given function is f(x,y) = y-x²+y²+kxy.

The critical points of the function are found by taking the partial derivatives and equating them to zero:

∂f/∂x = -2x + ky = 0

y = 2x/k

∂f/∂y = 2y + kx = 0

y = -kx/2

Substituting y from the first equation into the second equation gives

x = k²x/4, so k² = 4 and k = ± 2.

Therefore, the critical points are (0,0), (2,4), and (-2,4)

We will now examine the critical points to see when the shape of the graph changes qualitatively.

There are two cases to consider:

Case 1: (0,0)At (0,0), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2 0;0 2].

The determinant of the Hessian matrix is -4, which is negative.

Therefore, (0,0) is a saddle point and the graph changes qualitatively as k increases for all values of k.

Case 2: (±2,4)At (2,4) and (-2,4), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2k 2k;2k 2].

The determinant of the Hessian matrix is 4k²+8, which is positive when k is greater than √(2).

Therefore, the critical points (2,4) and (-2,4) are local minima when

k > √(2).

Thus, the shape of the graph changes qualitatively at k = ± 2 and

k = √(2).

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Answer: C) Multiply the number of solid and clear beads by 2.

D) Divide the number of solid and clear beads by 4.

E) Multiply the number of solid and clear beads by 18.

Step-by-step explanation:

Multiplication and Division are the two arithmetic operations that are used to get an equivalent ratio or fraction.

So, the operations that will give an equivalent ratio are Multiplication and Division.

So that correct options are

C) Multiply the number of solid and clear beads by 2.

D) Divide the number of solid and clear beads by 4.

E) Multiply the number of solid and clear beads by 18.

Answer:

9.66 x 10⁴ minutes

Step-by-step explanation:

To convert seconds into minutes, simply divide by 60.

=> 5.8 x 10⁶ / 60

=> 580 x 10⁴ / 60

=> 29 x 10⁴ / 3

=> 9.66 x 10⁴ minutes

Answer:

9.6×10^4

Step-by-step explanation:

1 min=60sec

5.8＊10^6 / 60= 9.6×10^4

Answer:

FG = 51

Step-by-step explanation:

2/5 of 85 = 34

The value of EF is 34

So the value of FG would be the value of EG - EF

85 - 34 = 51

The function f(x) is f(x) = (e - 1)x.

To find the function f(x) given that f(0) = 0 and the tangent line to f(x) at the point (x, f(x)) has slope e - 1, we need to integrate the given slope to obtain the function.

The slope of the tangent line is equal to the derivative of the function at that point. Since the slope is e - 1, we have:

f'(x) = e - 1

To find f(x), we integrate the above equation with respect to x:

∫ f'(x) dx = ∫ (e - 1) dx

Integrating, we get:

f(x) = (e - 1)x + C

where C is the constant of integration.

Since f(0) = 0, we can substitute x = 0 and f(x) = 0 into the equation to find the value of C:

0 = (e - 1)(0) + C

0 = C

Therefore, the function f(x) is given by:

f(x) = (e - 1)x

So, f(x) = (e - 1)x.

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Answer:

it is b for sure sokays uduhdhd

f(x) = x is a simple linear function with a slope of 1, f(x) = 3 5 6 is a constant function, f(x) = 3-x is a linear function with a negative slope of -1,  f(x) = 1 is a constant function, f(x) = 2 is a constant function

A constant function is a mathematical function whose output value is the same for every input value

From the given parameters, f(x) = x is a simple linear function with a slope of 1, this implies  that for every unit increase in x, the value of y increases by 1.

Also,  f(x) = 3 5 6 is a constant function, where the value of y is always 3 5 6, regardless of the value of x.

In the same way,  f(x) = 3-x is a linear function with a negative slope of -1, which means that for every unit increase in x, the value of y decreases by 1. The fourth function f(x) = 1 is a constant function, where the value of y is always 1, regardless of the value of x.

The domain of the fifth function is 3 0, which means that x can take any value between 3 and 0.

The sixth function f(x) = 2 is a constant function, where the value of y is always 2, regardless of the value of x.

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Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

Since they are not the same, they are not the exact same circles.  In other words they are similar.

Since the center point does not affect the size of the circle.

Now, According to the question:

Figures can be proven similar if one, or more, similarity transformations

reflections, translations, rotations, dilations can be found that map one

figure onto another.

To prove all circles are similar, a translation and a scale factor from a

dilation will be found to map one circle onto another

Lets solve the problem

Circle A has center (1 , 1) and radius 4

The standard form of the equation of the circle is:

\((x - h)^2 + (y - k)^2 = r^2\) , where (h , k) are the coordinates the center

and r is the radius

Equation circle A is \((x -1)^2 + (y - 1)^2 = (4)^2\)

Equation circle A is : \((x -1)^2 + (y - 1)^2 = 16\)

\(x^{2} +1-2x+y^2+1-2y=16\\\\x^2 +y^2-2x-2y+2=16\\\\x^2 +y^2-2x-2y-14=0\\\\x^2+y^2= 14+2x+2y\)

Circle B has center (-4 , -2) and radius 3

Equation circle B is \((x - (-4))^2 + (y - (-2))^2 = (3)^2\)

Equation circle B is \((x +4)^2 + (y +2)^2 = 9\)

\(x^2+16+8x+y^2+4+4y=9\\\\x^{2} +y^2+20+8x+4y=9\\\\x^2+y^2+8x+4y+11=0\)

By comparing between the equations of circle A and circle B

As you can see, if we try to equate the \((x^2 + y^2)'s\), the values of them are not the same.  Since they are not the same, they are not the exact same circles.  In other words they are similar.

You can also compare the radii as well, since the center point does not affect the size of the circle.

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Answer:

(13, 5 )

Step-by-step explanation:

The translation

(x, y ) → (x + 3, y - 4)

Means add 3 to the x- coordinate and subtract 4 from the y- coordinate, so

(10, 9 ) → (10 + 3, 9 - 4 ) → (13, 5 )

Answer:

Is y = (x+8) (x+3)

Answer:

1. y=(x+8)(x+3)

Step-by-step explanation:

Problem to solve:

Answer:

in any quadrilateral, the sum of the interior angles is 360 degrees, so angles

a+b+c+d = 360 degrees.

But a = 2b

and b = 2c

and c = 2d so...

b = 4d and

a = 8d so we have:

8d+4d+2d+d = 360

15d = 360 and

d = 24 degrees

c = 2(24) = 48 degrees and

b = 4(24) = 96 degrees and

a = 8(24) = 192 degrees.

Answer:

14 times more than the larger school

Step-by-step explanation: This makes no sense, there is no problem to solve, just a statement

Answer:

Not sure what the answer choices are, but choose the choice that says the new image is either stretched or shrunk. In a dilation, the shape/corresponding sides of the pre-image are preserved in the new image, but the size of the new image is altered.

Step-by-step explanation:

hope this helps!

Answer:

Change 10 (Last number at the end in the Flour (Cups) row) to 20. You need 20 cups of flour.

Step-by-step explanation:

Dr. Gavin will need to examine four main effects in a 2 x 4 independent-groups factorial design. This is because a factorial design involves two or more independent variables, each of which has two or more levels or conditions.

There are two independent variables in this situation, each having four levels. Dr. Gavin will need to look at the primary effects of each independent variable in order to determine its consequences.

Regardless of the levels of the other independent variables, the major effects are the total impacts of each independent variable on the dependent variable.

In other words, Dr. Gavin must look at each independent variable's effects independently, without taking into account the impact of the other independent variable. He must therefore consider a total of four key consequences.

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Siegmeyer Corp. should accept Project A because its NPV is greater than zero, indicating positive profitability.

Siegmeyer Corp. is evaluating the financial feasibility of Project A, a new inventory system that requires an initial investment of $800,000. The company's required rate of return is 12%. To determine whether the project should be accepted or rejected, the net present value (NPV) needs to be calculated.

The NPV of a project represents the difference between the present value of its cash inflows and the present value of its cash outflows. By discounting future cash flows at the required rate of return, we can assess the profitability of the project. In this case, the expected cash flows over the next four years are $350,000, $325,000, $400,000, and $200,000.

To calculate the NPV, we discount each cash flow back to its present value and subtract the initial investment:

NPV = (Cash flow in year one / (1 + required rate of return))¹

     + (Cash flow in year two / (1 + required rate of return))²

     + (Cash flow in year three / (1 + required rate of return))³

     + (Cash flow in year four / (1 + required rate of return))⁴

     - Initial investment

By performing the calculations, the NPV of Project A can be determined. If the NPV is greater than zero, it indicates that the project is expected to generate positive returns and should be accepted.

In this case, the NPV should be compared to zero, and if it is greater, Siegmeyer Corp. should accept Project A.

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Answer:

This problem shows an expression, not an equation.

It cannot be solved.

An equation needs an equal sign.

The correct answer is E) Two of the responses above are correct:

The measurement(s) that would help determine absolute dates by radiometric means are the accumulation of the daughter isotope and the loss of parent isotopes. These two measurements are crucial in radiometric dating methods, which rely on the decay of radioactive isotopes in rocks and minerals over time.

In radiometric dating, scientists measure the ratio of parent isotopes to daughter isotopes in a sample. The parent isotopes decay at a known rate, converting into daughter isotopes. By determining the amount of parent isotope that has decayed and the accumulation of daughter isotope, scientists can calculate the age of the sample.

For example, if a rock sample contains a radioactive isotope with a half-life of 1 million years, and 75% of the parent isotope has decayed into the daughter isotope, it can be inferred that the rock is approximately 2 million years old (since two half-lives have passed).

Therefore, the correct answer is E) Two of the responses above are correct: the accumulation of the daughter isotope and the loss of parent isotopes are measurements that help determine absolute dates by radiometric means.

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Answer: 28.87 seconds

Step-by-step explanation:

Check attached image for explaination

The correct option is B, The null hypothesis to test if the population variances differ is population variance 1 differs from population variance 2.

Variance is calculated as the average of the squared differences of each data point from the mean. In other words, variance measures how far the data points are from their average value. A high variance indicates that the data points are spread out over a wider range, while a low variance indicates that the data points are clustered more tightly around the mean.

Variance is an important concept in statistical analysis because it helps to assess the reliability of data and to make inferences about the population from a sample. It is also used in many areas of research, such as finance, economics, and engineering, to measure the risk or uncertainty associated with a set of data. Variance is closely related to other statistical measures such as standard deviation, covariance, and correlation, and is often used in conjunction with these measures to gain a deeper understanding of the data.

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Complete Question:-

Before comparing means, we need to test the relationship of the population variances. what null hypothesis would you use to determine if the population variances differ?

a. population variance 1 equals population variance 2

b. population variance 1 differs from population variance 2

c. population variance 1 is less than population variance 2

d. population variance 1 exceeds population variance 2

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

The largest number that divides 245 and 1029 leaving a remainder 5 in each case is 16.

We have to subtract 5 from each number & then find the H.C.F

245 - 5 = 240  & 1029 - 5 = 1024

HC.F of 240 & 1024 by Euclid division lemma.

Euclid's division lemma states that given two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. This means that any positive integer a can be divided by another positive integer b, with a unique quotient q and remainder r.

a = 1024  & b = 240

a = bq + r

1024 = 240*4 + 64

240= 64*3 + 48

64= 48*1 + 16

48 = 16*3 + 0

H.C.F is 16.

Hence, the required number is 16.

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The acceleration due to gravity of a falling object is +9.8 m/s²

The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. m/s² is its SI unit. Its nature which includes both magnitude and direction—makes it a vector quantity.

Given:

A linear expression we have

y= k x,

Here, Variation's constant is constant, or k.

The acceleration caused by gravity is stated to be the variational constant in the statement.

So, the linear expression becomes

y = g x, where g is a proportionality constant.

Now, Work is not done against gravity since an object falling downwards accelerates due to gravity at a rate of +9.8 m/s².

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Answer: B.Asha, because she has simplified the numbers involved in the equation

Step-by-step explanation:

Your answer should be -18?

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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