Ralph wants to move a 60.0 kg sofa He applies a force of 480 N. Under these conditions, the sofa initially moves with an acceleration of 3.20 m/s^2

Calculate the friction force on the sofa.
Round your answer to the nearest integer.

The cross-section from any side in a square prism is always square.

A cross-section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections.

Cross-section of a square prism :-

The cross-section of a square prism is a square. Since a square prism has its faces shaped in square and all the edges of the square prism are equal in length.

Therefore, when we cut the cube by a plane, we get a square shape.

Hence, the cross-section from any side in a square prism is always square.

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The isosceles triangle of the maximum area is also an equilateral triangle.

Given, an isosceles triangle ABC is inscribed in a circle with center D and radius r.

We can obtain the side a in function of r and α by applying Law of Sines to triangle BCD,

a/sin(2α) = r/sin β

Since, 2α + β + β = 180°

2α + 2β = 180°

α + β = 90°

β = 90° - α

a = r(sin 2α/sin(90°-α))

a = r(2 sinα cosα)/cosα

a = 2r sinα

a = 4r sin(α/2) cos(α/2)

We can obtain the height h in function of r and α,

tan(α/2) = (a/2)/h

h = a/2tan(α/2)

Replacing with the value of a,

h = [4r sin(α/2) cos(α/2)/2][cos(α/2)/sin(α/2)]

h = 2r cos2(α/2)

Now, find the area of the triangle in function of a and r,

Area, A = (base)(height)/2

A = [4r sin(α/2) cos(α/2)][2r cos2(α/2)]/2

A = 4r2sin(α/2) cos3(α/2)

Now, take the derivative to find the maximum or minimum of the area of the triangle.

dA/dα = [4r2cos(α/2)(1/2)cos3(α/2)] + [4r2sin(α/2) 3cos2(α/2)(-sin(α/2))(1/2)]

On simplification,

= [2r2cos4(α/2)] - 6r2sin2(α/2) cos2(α/2)

Taking out common terms,

= 2r2cos2(α/2)[cos2(α/2) - 3sin2(α/2)]

Equating the derivative to zero, we get

2r2cos2(α/2)[cos2(α/2) - 3sin2(α/2)] = 0

2r2cos2(α/2) = 0

cos2(α/2) = 0

Thus, α/2 = 90°

α = 180°

Also, cos2(α/2) - 3sin2(α/2) = 0

cos2(α/2) = 3sin2(α/2)

[sin2(α/2)/cos2(α/2)] = 1/3

tan2(α/2) = 1/3

tan(α/2) = 1/√3

So, α/2 = 30°

α = 60°

This implies that ∠B = ∠C = 60°

Thus, the isosceles triangle of the maximum area that can be inscribed in a circle of radius r. is also an equilateral triangle.

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Answer:

  (b)  $740.95

Step-by-step explanation:

You want the value of $350 after 3 years when interest is 25% per year compounded continuously.

The formula for the balance resulting from continuous compounding is ...

  A = Pe^(rt)

where P is the amount borrowed, r is the annual rate, and t is the number of years.

For r=0.25 and t=3, the $350 grows to ...

  A = $350·e^(0.25·3) = $350·e^0.75 ≈ $740.95

The amount due after 3 years is $740.95.

Given the information:

Overall average (μ) = 55.0 units

Process population standard deviation (σ) = 1.84

Sample size (n) = 16

To determine the 3-sigma UCL (Upper Control Limit) and LCL (Lower Control Limit) for a 2-sigma X chart, we can use the following formulas:

UCL = μ + 3 * (σ / √n)

LCL = μ - 3 * (σ / √n)

Plugging in the values:

UCL = 55.0 + 3 * (1.84 / √16)

LCL = 55.0 - 3 * (1.84 / √16)

Calculating the values:

UCL = 55.0 + 3 * (1.84 / 4)

LCL = 55.0 - 3 * (1.84 / 4)

UCL = 55.46

LCL = 54.54

Therefore, the 3-sigma UCL for the 2-sigma X chart is 55.46 units, and the LCL is 54.54 units.

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The conditional PMF of Y=i given X=1 is 1 if i=1 and 0 otherwise and  X and Y are not independent because the value of X affects the possible range of values for Y.



a. To compute the conditional probability mass function (PMF) of Y=i given X=1, we need to find the probability of Y=i when X=1. Since X=1, the only possible outcome is (1,1), and Y can only be 1. Hence, the conditional PMF of Y=i given X=1 is:

P(Y=i | X=1) = 1, if i=1; 0, otherwise.

b. X and Y are not independent. If they were independent, the outcome of one die roll would not provide any information about the other die roll. However, given that X is the largest value and Y is the smallest value, we can see that X directly affects the possible range of values for Y. If X is 6, then Y cannot be greater than 6. Therefore, the values of X and Y are dependent on each other, and they are not independent.



Therefore, The conditional PMF of Y=i given X=1 is 1 if i=1 and 0 otherwise and  X and Y are not independent because the value of X affects the possible range of values for Y.

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By evaluating both equations in x = 8 we will see that the hawk will be closer to the ground.

We know that the height of the hawk is modeled by:

y=−20x+350

And the height of the eagle is modeled by:

y=−10x+400

Now we need to evaluate both equations in x = 8.

hawk:

y = -20*8 + 350 = 190

For the Eagle:

y = -10*8 + 400 = 320

We can see that the hawk is closer to the ground.

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The volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant is π units cubed. The curve is not provided here. Therefore, it is impossible to solve this question. We are unable to determine the function whose graph is being revolved around the y-axis based solely on the information given.If the curve had been given, we would have used the disk method, which states that the volume of a solid of revolution generated by rotating a plane figure about a line is equal to the sum of the volumes of an infinite number of infinitesimally thin disks perpendicular to that line. If f(x) is a non-negative function defined on [a, b], then the volume V of the solid generated by revolving the region between the curve y = f(x), the x-axis, x = a, and x = b about the y-axis is given by:V = π∫ab[f(x)]2 dxWhere π is the constant π = 3.14159..., a and b are the limits of integration, and f(x) is the function whose graph is being revolved.

It is also important to avoid ignoring any typos or irrelevant parts of the question and to not repeat the question in the answer unless necessary. Finally, when using math terminology or solving math problems, it is important to show all work and use proper notation.

For example, when solving a problem such as "find the volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant. if the answer does not exist, enter dne. otherwise, round to four decimal places," one might use the formula for finding the volume of a solid of revolution:V=π∫abf(x)2dxwhere f(x) is the function defining the curve, and a and b are the limits of integration. The limits a and b can be found by setting the equation defining the curve equal to zero and solving for x.

Once the limits are found, the function can be integrated and the result can be multiplied by π to find the volume of the solid. The answer should then be rounded to four decimal places and, if the answer does not exist, the answer should be entered as dne.

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The appropriate test statistic to test the hypotheses is 2.71. Hence, the correct option is D.

The appropriate test statistic to test the hypotheses is the z value. The z value is calculated using the formula:

z = (x - μ) / (σ / √n)

Where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, x = 6.65, μ = 6, σ = 1.5, and n = 39.

Plugging these values into the formula gives:

z = (6.65 - 6) / (1.5 / √39)
z = 0.65 / (1.5 / 6.24)
z = 0.65 / 0.24
z = 2.71

Therefore, the appropriate test statistic to test the hypotheses is 2.71, which corresponds to option D.

Note: The question is incomplete. The complete question probably is: A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 39 orders was selected, the average number of days was 6.65 with a population standard deviation of 1.5 days. calculate the appropriate test statistic to test the hypotheses. (z value). A) 4.54 B) 4.87 C) 1.76 D) 2.71.

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Answer:

y = -0.916 * (1 - 0.140)^t

Step-by-step explanation:

f(t) = 0.4 * (1.16)^(t - 1)

To rewrite the equation in the form y = a(1 + r)^prime or y = a(1 - r)^prime, we can take the natural logarithm of both sides:

ln(f(t)) = ln(0.4) + (t - 1)ln(1.16)

ln(f(t)) = ln(0.4) + tln(1.16) - ln(1.16)

So,

y = ln(0.4) + tln(1.16)

Now we can rewrite this in the desired form by letting a = ln(0.4) and r = ln(1.16):

y = a + t * r

a = ln(0.4) = -0.916

r = ln(1.16) = 0.140

So,

y = -0.916 + 0.140 * t

y = -0.916 * (1 - 0.140)^t

This form of the equation shows that the function f(t) represents exponential decay. The value of "a" represents the initial value of f(t) and "r" represents the decay rate. Since r is negative, the function decreases over time, which means that the function represents exponential decay.

7(k+1) gives the equivalent expression

Linear expressions are expressions that has a leading degree of 1. For instance y = mx + b is a linear equation.

Given the expression below
-k-(-8k+7)

Expand to have:

-k-(-8k+7) = -k + 8k - 7

-k-(-8k+7) = 7k + 7

Factor out the value of 7 from the expression

7k + 7 = 7(k+1)

Hence the factored form of the expression is 7(k+1)

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Answer:

-9

Step-by-step explanation:

-2(2x2+2(2)-1)

-2 x 4= -8

since the sign outside the bracket is negative, the positive sign will change to negative.

So we have -8-2(2)-1

-8-3

=-9

Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

Answer: y =\(\frac{ax - 2}{9x}\)

Step-by-step explanation: look for the lcm

a=\(\frac{9xy + 2}{x}\)

cross multiply

ax =9xy + 2

ax - 2 = 9xy

divide both sides by 9x

\(\frac{ax - 2}{9x} = \frac{9xy}{9x}\)

y=\(\frac{ax - 2}{9x}\)

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

In mathematical modeling, some values are considered fixed and cannot vary without consequence. These values are often referred to as constants or parameters, and they represent physical or environmental properties that are assumed to be constant throughout the problem.

For example, in a mathematical model of the motion of a pendulum, the length of the pendulum, the mass of the weight, and the force of gravity are typically considered constants that cannot vary without consequence. If any of these values were to change, the motion of the pendulum would be affected, and the solution to the problem would be different.

Similarly, in a mathematical model of heat transfer, the thermal conductivity of the material, the heat source or sink, and the boundary conditions are typically considered constants that cannot vary without consequence. If any of these values were to change, the temperature distribution and heat transfer rate within the system would be affected, and the solution to the problem would be different.

The choice of which values to consider as constants or parameters depends on the specific problem being modeled and the assumptions made.

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Answer:

(0,8)

Step-by-step explanation:

Answer:the slope of a line it the angle/slope that that line is at

Step-by-step explanation: slope times width

Answer:

t = 2

Step-by-step explanation:

We know that both triangles are the same and have the same value so we know that 4 is the base and we want to find the value of t:

We know that:

\(4 = 2t\)

So let’s solve for t:

\(t = 2\)

We can conclude that t = 2 because ΔABC≅ΔKLM

The graph is a linear function on a coordinate plane that passes through (-5, 4), (0, 2), and (5, 0) and the solution is below the graph. The correct option is D

From the question, we are to determine the graph that best models the given inequality

The given inequality is y ≤ -2/5x + 2

First, we will graph the line of y = -2/5x + 2 by determining the x-intercepts and y-intercepts

Determining the x-intercepts

y = -2/5x + 2

Set y = 0

0 = -2/5x + 2

2/5x = 2

2x = 10

x = 10/2

x = 5

(5, 0)

The line passes through the points (5, 0)

Determining the y-intercepts

y = -2/5x + 2

Set x = 0

y = -2/5(0) + 2

y = 2

(0, 2)

The line passes through the point (0, 2)

Using the x-intercepts and y-intercepts, the graph of the line is shown below

Since the inequality sign is less than or equal to, ≤, the line is a solid line and the solution is below the graph

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As a result, the geometric sequence's sixth term, which has a ratio of 2/3 and a first term of 2, is 32/243.

A mathematical series known as a geometric sequence is one in which each term following the first is obtained by multiplying the previous term by a constant, non-zero quantity known as the common ratio2. To put it another way, it is a sequence in which each term (aside from the initial term) is multiplied by a fixed amount to obtain the subsequent term1.

For instance, the geometric sequence 1, 2, 4, 8, 16,... has a common ratio of 2, since each item after the first is derived by multiplying the previous term by 2.

Aₙ = a₁× r(n-1) is the formula for the nth term of a geometric series, where a1 is the first term and r is the common ratio.

The common ratio in this instance is 2/3, and the first term is 2.

As a result, the sequence's nth term is represented by the formula

a = 2 × (2/3)(n-1).

We change n = 6 in the formula to get the sixth term in the sequence.

A₆ = 2× (2/3)⁵

= 2 × (2/3)⁵ = 32/243 as a result.

As a result, the geometric sequence's sixth term, which has a ratio of 2/3 and a first term of 2, is 32/243.

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Answer:

Cost price (CP) = Rs20

% Profit = 10%

Selling price (SP) = y

By formula:

% Profit = (Profit/CP) x 100%

But Profit= SP - CP

Therefore;

% Profit = [(SP-CP)/C.P)] x 100%

Substituting, we have:

10% = [(y-20)/20] x 100%

10/100 = (y-20)/20

1/10 = (y-20)/20

1 = (y-20)/2

Cross multiply

y - 20 = 2

y = 2 + 20

y = 22

Therefore, the Sale price is Rs 22

The sampling distributions reach a normal distribution as sample sizes increase.

For the given statement in the question-

As sample sizes grow larger, sampling distributions reach a normal distribution.

The mean of the sampling distribution equals the population mean (µ) (with "infinite" numbers of the successive random samples).

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The coordinates of Q will be (-2,-2/5)

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

Scale factor = new dimension /old dimension

The trapezoid will under go a dilation about a scale factor of 2/5.

The original cordinate of Q is (-5,-1). With the dilation;

x cordinate of Q =

2/5 = x/-5

-10 = 5x

x = -2

y cordinate will be

2/5 = y/-1

-2 = 5y

y = -2/5

therefore the new cordinate of Q is ( -2,-2/5)

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Given:

The function f represents the diver's distance from sea level over time, in seconds.

\(f(x)=\begin{cases}3x+1 & \text{ if } -9<x\leq -2 \\ -5 & \text{ if } -2<x\leq 1 \\ x-6 & \text{ if } 1<x<7 \end{cases}\)

To find:

The correct statement for the domain.

Solution:

Domain is the set of input values for which the function is defined.

Here, x values are the input values and they represent time intervals on which the function is defined

Here, the possible intervals for x are \(-9<x\leq -2,-2<x\leq 1,1<x<7\).

\(Domain=(-9,-2]\cup (-2,1]\cup (1,7)\)

\(Domain=(-9,7)\)

Therefore, the domain is the time interval (−9, 7). Hence the correct option is A.

If R is a normal randomly distributed variable with mean 10% and standard deviation 10%, the return on a certain stock can be represented as R - N(10,10²), then the probability of losing money is 0.1587.

To find the probability of losing money, follow these steps:

Hence, the probability of losing money is 0.1587.

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Given data are: Payment of $150 at the end of each of the next 3 years,Payment of $250 at the end of Year 4,Payment of $400 at the end of Year 5,Payment of $500 at the end of Year 6,Rate of interest = 8% annually

Hence, the Present Value of the investment is $382.20

Present value and future value of investment Formula used: PV = Pmt/(1+r)^n,

FV = Pmt((1+r)^n-1)/r

Let's find the Present Value of the Investment: Given, n = 3 years

Pmt = $150

Rate = 8% annually

PV = 150/(1+8%)³

PV = $382.20

Let's find the Future Value of the Investment: Given, n1 = 3 years

Pmt1 = $150

Rate = 8% annually

n2 = 1 year

Pmt2 = $250

n3 = 1 year

Pmt3 = $400

n4 = 1 year

Pmt4 = $500

FV = (150((1+8%)³-1)/8%)+((250+400+500)(1+8%)³)

FV = $1579.51

Hence, the Future Value of the investment is $1579.51.

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The transformation rule used are the reflection over the y-axis, dilation and vertical and horizontal shift.

The translation rule for reflection of the coordinate point (x, y) across the y-axis is (-x, y)

The rule (x, y) → (0.5x, 0.5y) shows a dilation of the coordinate (x, y) by a factor of 0.5. It will reduce the size of the resulting figure since the factor is less than 1.

The rule  (x, y) → (x - 2, y + 2) shows that the figure then shifted horizontally by 2units to the right and up by 2units.

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Answer:

C: Radicals in the denominators of fractions are considered unsimplified. You need to multiply a fraction by a value that removes radicals or imaginary numbers in the denominator, which is the complex conjugate of the denominator.

Step-by-step explanation: