3. Suppose g(t) = [0.5sinc²(0.5 t) cos(2 t)], where the sinc function is defined as (3.17) on p. 100 of the textbook. (a) Apply Parseval's Theorem to determine the 95% energy bandwidth (B) of this signal, where we define the 95% energy bandwidth as:
(b) Gf²df = 0.95Eg. What is the 95% energy bandwidth of g(2t) in terms of the value of B determined in Part a. Please provide full justification for your answer.

The function f(x) is undefined when x = -8 or x = 1. The domain of f(x) is all real numbers except -8 and 1. In interval notation, the domain can be expressed as (-∞, -8) U (-8, 1) U (1, ∞).

To find the domain of the function f(x) = 3/(x+8) + 5/(x-1), we need to identify any values of x that would make the function undefined.

The function f(x) is undefined when the denominator of any fraction becomes zero, as division by zero is not defined.

In this case, the denominators are x+8 and x-1. To find the values of x that make these denominators zero, we set them equal to zero and solve for x:

x+8 = 0 (Denominator 1)

x = -8

x-1 = 0 (Denominator 2)

x = 1

Therefore, the function f(x) is undefined when x = -8 or x = 1.

The domain of f(x) is all real numbers except -8 and 1. In interval notation, the domain can be expressed as (-∞, -8) U (-8, 1) U (1, ∞).

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Answer:

The area of LQM is \(48cm^2\)

Step-by-step explanation:

Given

Area of PNQ = 8

Area of LPQ = 16

See attachment for triangles

The area of PNQ is calculated as:

\(Area = \frac{1}{2} * PQ * PN\)

Substitute 8 for Area

\(8 = \frac{1}{2} * PQ * PN\)

\(PQ * PN = 16\)

The area of LPQ is calculated as:

\(Area = \frac{1}{2} * PQ * LP\)

Substitute 16 for Area

\(16= \frac{1}{2} * PQ * LP\)

From the attachment:

\(PN + LP =LN\)

Make LP the subject

\(LP = LN -PN\)

So:

\(16= \frac{1}{2} * PQ * (LN -PN)\)

We have:

\(16= \frac{1}{2} * PQ * (LN -PN)\) and \(PQ * PN = 16\)

Equate both expressions:

\(\frac{1}{2} * PQ *(LN - PN) = PQ * PN\)

Divide both sides by PQ

\(\frac{1}{2} (LN - PN) = PN\)

Multiply both sides by 2

\(LN - PN = 2PN\)

\(LN= 3PN\)

Since PNQ is similar to LNM, the following equivalent ratios exist:

\(\frac{LM}{PQ} = \frac{LN}{PN}\)

Substitute \(LN= 3PN\)

\(\frac{LM}{PQ} = \frac{3PN}{PN}\)

\(\frac{LM}{PQ} = 3\)

\(LM = 3PQ\)

Area of LQM is:

\(Area = \frac{1}{2} * LM * LP\)

This gives:

\(Area = \frac{1}{2} * 3PQ * LP\)

\(Area = 3 *\frac{1}{2} *PQ * LP\)

Recall that:

\(16= \frac{1}{2} * PQ * LP\)

So:

\(Area = 3 *16\)

\(Area = 48cm^2\)

Step-by-step explanation:

f(x)=-3x+3

f(3)=-9+3=-6

f(0)=0+3=3

f(1)=-3+3=0

the3 0 1 should be used in place of x and f(x) should be founs

Answer:

The functions are defined as:

Step-by-step explanation:

We are given a function:

\(\bullet \ \ \ f(x) = -3x + 3\)

We need to find the values of the function at:

When we replace the x in f(x) with a number, we are saying that "f of 3" or "f of 0" or "f of 1." This means that when we change the x in f(x), we need to also change the rest of the x-variables in the function.

Therefore, to solve f(3), every x must be changed to 3.

\(f(x) = -3x + 3\\\\f(3) = -3(3) + 3\\\\f(3) = -9 + 3\\\\f(3) = -6\)

We can follow the same method for f(0) and f(1).

\(f(x) = -3x + 3\\\\f(0) = -3(0) + 3\\\\f(0) = 0 + 3\\\\f(0) = 3\)

And finally, we can solve for f(1).

\(f(x) = -3x + 3\\\\f(1) = -3(1) + 3\\\\f(1) = -3 + 3\\\\f(1) = 0\)

Therefore, the function is defined at each value as:

The gcd of x and n is 1, and the multiplicative inverse of 52 mod 77 is 40.

As we know the equation x = 52, n = 77. To identify the gcd of x and n, we will use the Euclidean algorithm. The equations for substitution are:

1 = 25 - 122

= 52 - 2.2525

= 77 - 52

Substitute (52 - 2.25) for 2 into the equation 1 = 25 - 12:21 = 25 - 12:(52 - 2.25) = 25-25 - 12:52

Substitute (77 - 52) for 25 into the equation 1 = 25-25 - 12:521 = 25:

(77 - 52) - 12:52 = 25.77 - 37.52

gcd(77, 52) = 1 = 25.77 - 37:52

The coefficient of 52 in the equation above is -37. The multiplicative inverse of 52 mod 77 is (-37 mod 77) = 40.

Check: 52:40 mod 77 = 2080 mod 77 = 1

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Answer: x=16

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    -9/8*x-7-(-25)=0

simplify 9/8

((0 -  (9/8 • x)) -  7) -  -25  = 0

 Subtracting a whole from a fraction

Rewrite the whole as a fraction using  8  as the denominator

7 = 7/1 = 7*8/8

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

  -9x - 56  =   -1 • (9x + 56)

   Adding up the two equivalent fractions

(-9x-56) - (-25 • 8)/8     144 - 9x/8

  144 - 9x  =   -9 • (x - 16)

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, multiply both sides of the equation by the denominator.

Here's how:

 -9•(x-16)/8 • 8 = 0 • 8

Now, on the left hand side, the  8  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  -9  •  (x-16)  = 0

   Solve  :    x-16 = 0  

Add  16  to both sides of the equation :  

                     x = 16

Answer: x=16

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                   -9/8*x-7-(-25)=0

simplify 9/8

((0 -  (9/8 • x)) -  7) -  -25  = 0

Subtracting a whole from a fraction

Rewrite the whole as a fraction using  8  as the denominator

7 = 7/1 = 7*8/8

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

 -9x - 56  =   -1 • (9x + 56)

  Adding up the two equivalent fractions

(-9x-56) - (-25 • 8)/8     144 - 9x/8

 144 - 9x  =   -9 • (x - 16)

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, multiply both sides of the equation by the denominator.

Here's how:

-9•(x-16)/8 • 8 = 0 • 8

Now, on the left hand side, the  8  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

 -9  •  (x-16)  = 0

  Solve  :    x-16 = 0  

Add  16  to both sides of the equation :  

                    x = 16

Answer:

(a) Area is about 285 square feet

(b) Percentage decrease = 36%

Step-by-step explanation:

(a) The formula for area of a sector in degrees is

A = (θ/360º) × πr^2, where

Since we're shown that the measure of the sector is 145º and the radius is 15 feet, we can plug these in for θ and r in the area formula:

A = (145/360) * π(15)^2

A = (29/72) * 225π

A = (725/8)π

A = 284.7068342

A ≈ 285 square feet

Thus, the area of the sector is about 285 square feet.

(b)  

Step 1:  First, we'll need to find the area of the sector if the radius was decreased to 12 feet.  And since we rounded to the nearest whole number for (a), we can do that again at the end:

A = (145/360) * π(12)^2

A = (29/72) * 144π

A = 58π

A = 182.2123739

A ≈ 182 square feet

Thus, the area of the sector if the radius was decreased to 12 feet would be about 182 square feet.

Step 2:  To find the percentage decrease, we can use the formula:

((starting value - ending value) / starting value) * 100.  Our starting value is 285, whereas our ending value is 182:

% decrease = ((285 - 182) / 285) * 100

% decrease = (103 / 285) * 100

% decrease = 36.140

% decrease = 36

Thus, the percentage decrease from changing the radius from 15 feet to 12 feet is 36%

The cricket Player class has been designed to keep track of the different stats.

This class was created with the aim of creating a player, incorporating a match's statistics, and finally displaying the stats.

The object can then be used to call the various member functions of the class.

The stats can be added by calling the appropriate member functions and providing the required data as parameters. Finally, the stats can be displayed by calling the member function that displays the stats.

The cricket Player class has the following member functions:

• setData() - This function is used to set the data members of the cricket Player class. It takes four parameters that represent the player's name, team name, the total number of runs scored, and the number of wickets taken by the player. The function then sets these values to the appropriate data members.

• displayData() - This function is used to display the data members of the cricket Player class. It displays the player's name, team name, the total number of runs scored, and the number of wickets taken by the player.

• addRuns() - This function is used to add runs to the total runs scored by the player. It takes a single parameter that represents the number of runs scored in a particular match. The function then adds this value to the total runs scored by the player.

• addWickets() - This function is used to add wickets to the total number of wickets taken by the player. It takes a single parameter that represents the number of wickets taken in a particular match. The function then adds this value to the total number of wickets taken by the player.

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We are comparing the average gain in test scores for two different groups of girls - those assigned to coeducational chemistry classes and those assigned to single-sex chemistry classes. Since these gains are calculated from the data obtained from these specific groups of girls, they represent statistics rather than parameters.

In the given scenario:

The boldface number "12.2" represents a statistic.

The boldface number "15.1" represents a statistic.

A statistic is a numerical value that summarizes a sample of data, while a parameter is a numerical value that summarizes a population.

In this case, we are comparing the average gain in test scores for two different groups of girls - those assigned to coeducational chemistry classes and those assigned to single-sex chemistry classes. Since these gains are calculated from the data obtained from these specific groups of girls, they represent statistics rather than parameters.

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The upper control limit for the control chart is 12.7433 and the lower control limit is 3.2567.

Assuming that the manufacturer's inspection process is a binomial process, we can use the normal approximation to the binomial distribution to calculate the control limits for their control chart. The mean of the binomial distribution is given by:

μ = np

where n is the sample size (4000 phones per day), and p is the probability of a defective display (0.002). The standard deviation of the binomial distribution is given by:

σ = sqrt(np(1-p))

Using these formulas, we can calculate the mean and standard deviation of the binomial distribution:

μ = 4000 x 0.002 = 8

σ = sqrt(4000 x 0.002 x 0.998) = 1.5811

The upper and lower control limits for the control chart can be calculated using the following formulas:

UCL = μ + 3σ

LCL = μ - 3σ

Substituting the values of μ and σ, we get:

UCL = 8 + 3 x 1.5811 = 12.7433

LCL = 8 - 3 x 1.5811 = 3.2567

Therefore, the upper control limit for the control chart is 12.7433 and the lower control limit is 3.2567. Any sample mean outside this range would be considered statistically significant and would require investigation to identify the cause of the deviation from the historical process average.

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Answer:

the first one is 14

the second one is -14 (NEGATIVE not positive)

the third one is 67

Step-by-step explanation:

IM A F*U*C*K*I*N*G GENIUS

lm.ao

Answer: x=3.2

Ste by Step

We have that for the Question "The figures are similar, and the ratio of the perimeters is 2 : 5. Find x." it can be said that  the perimeters of x is

x=3.2

From the question we are told

The figures are similar, and the ratio of the perimeters is 2 : 5. Find x.

Generally the equation for the the ratio is mathematically given as

2=x

and

5=8

Therefore

x=3.2

Therefore

the perimeters of x is

x=3.2

Answer:

21

Step-by-step explanation:

Step 1: add 2 to 5

=> 2 + 5

=> 7

Step 2: Multiply the result by 3:

=> 7 * 3

=> 21

Therefore the final answer = 21

Hope this helps!

the solution w = -36 is correct

The given equation is w/4 + 16 = 7.The main objective here is to solve for the variable w. Let us see the step-by-step process to solve for w:

Step 1: Simplify the left side of the equation by subtracting 16 from both sides. w/4 + 16 = 7 ⇒ w/4 = -9The justification for subtracting 16 from both sides is the additive inverse property of equality, which states that if a = b, then a - c = b - c for any real number c.

Step 2: Multiply both sides of the equation by 4 to isolate w. w/4 = -9 ⇒ (4)(w/4) = (4)(-9) ⇒ w = -36The justification for multiplying both sides of the equation by 4 is the multiplication property of equality, which states that if a = b, then ac = bc for any real number c.

Step 3: Check the solution. Substitute -36 for w in the original equation to make sure it satisfies the equation. w/4 + 16 = 7 ⇒ (-36)/4 + 16 = 7 ⇒ -9 + 16 = 7 ⇒ 7 = 7Since 7 = 7 is a true statement, . The justification for this step is that it ensures that the solution obtained in the previous step is valid.

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The flowchart symbol for adding number constants X, Y, and Z and assigning them to the variable SUM is the "Process" symbol.

The condition "if x>y" can be expressed in the flowchart symbol "Decision" or "Conditional" symbol.

The statement "print("Please enter a number: ")" can be expressed using the "Output" symbol.

The statement "number = int(input("Number: "))" can be expressed using the "Input" symbol.

For adding number constants X, Y, and Z and assigning them to the variable SUM, we use the "Process" symbol, which is represented by a rectangular shape. Inside the shape, we write the expression "SUM = X + Y + Z".

To express the condition "if x>y", we use the "Decision" or "Conditional" symbol, represented by a diamond shape. Inside the diamond, we write the condition "x>y". The flowchart would have two paths: one for the condition being true and another for the condition being false.

The statement "print("Please enter a number: ")" is an output statement to display a message. It can be represented using the "Output" symbol, which is represented by a parallelogram shape. Inside the symbol, we write the message "Please enter a number: ".

The statement "number = int(input("Number: "))" is used to receive input from the user and assign it to the variable "number". It can be represented using the "Input" symbol, which is represented by a parallelogram shape.

Inside the symbol, we write the prompt message "Number: ", and the value entered by the user is assigned to the variable "number".

To find the sum of all the salaries for the year, we can use an assignment statement inside a loop. Assuming we are iterating through the file and each salary is stored in the variable "salary", the assignment statement to achieve the running total would be "SUM = SUM + salary".

This statement can be represented using the "Process" symbol, where we write the expression "SUM = SUM + salary". This process is commonly known as an accumulation or running total.

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Answer: $60

Step-by-step explanation:

If the glee club keeps 10% of the revenue from ticket sales, it means they will receive 10% of the total revenue.

To calculate the amount the glee club will get, you can multiply the revenue by 10% (or 0.10):

Amount the glee club will get = Revenue * 0.10

In this case, if the revenue is $600, the amount the glee club will get can be calculated as:

Amount the glee club will get = $600 * 0.10 = $60

Therefore, the glee club will get $60 from the $600 revenue.

Answer:

44 units²

Step-by-step explanation:

For triangles: (bases and heights of both triangles are equal)

Base = 4 units, height = 3 units

For trapezoid:

Base 1 = 5 units, base 2 = 3 units, height = 8 units

Area of figure = Area of two triangles + Area of trapezoid

= 2 *1/2 * base * height + 1/2(base 1+ base 2) *height

=4*3 + 1/2(5+3)*8

= 12 + 8*4

= 12 + 32

= 44 units²

The required area of the figure shown in the graph is given as 44 square units.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

here,
The area of the given figure  is given as,
Area = Area of 1 + Area of 2 + Area  3 + Area 4
Area = length × width + [1/2× base × height] + [1/2× base × height] + [1/2× base × height]

Area = 8 × 3 + 1/2 × 4 × 3 + 1/2 × 4 × 3 + 1/2 × 8 × 2
Area = 44 square units.

Thus, the required area of the figure shown in the graph is given as 44 square units.

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Answer:

The last year value of the house will be $230,000.

Step-by-step explanation:

GIVEN: Decrease in house price = 20%

            Current house price = $184,000

TO FIND: Value of the house last year

SOLUTION:

If the value of the house decreased by 20% during last year, this means the value of the house this year is 80% of last year's value.

Let the value of the house last year be 'x'.

If the value of the house today is  $184,000, then:

                           \(80/100 * x = 184,000\\\\0.8x = 184,000\\\\x = 184,000/0.8\\\\x = 230,000\)

Therefore, the last year value of the house will be $230,000.

Answer:

2.94

Step-by-step explanation:

I just found 1%

Which is 0.98

then times that by 3 which is 2.94

hope that helps!

According to the question 1.) False - 3 × 5 matrix columns can be linearly independent. 2.) True , 3.) True , 4.) True , 5.) True , 6.) True - 3 × 2 matrix transformation not one-to-one.

1.) True. If the set of columns of a 3 × 5 matrix is linearly dependent, it means that there exists a nontrivial linear combination of the columns that equals the zero vector.

2.) False. The effect of a linear transformation on the columns of the n × n identity matrix only determines the image of the standard basis vectors. It does not completely determine the entire transformation.

3.) False. If each row of matrix A has a pivot, it means that the rows of A are linearly independent, not linearly dependent.

4.) True. If A has a pivot in each row, it means that the rows of A are linearly independent, and the linear transformation T : Rn → Rm represented by A is one-to-one.

5.) True. Similar to statement 1, if the set of columns of a 5 × 3 matrix is linearly dependent, it means that there exists a nontrivial linear combination of the columns that equals the zero vector.

6.) True. If A is a 3 × 2 matrix, it means that the transformation x → Ax maps from R2 to R3. Since the dimensions of the domain and codomain are different, the transformation cannot be one-to-one.

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Step-by-step explanation:

The formula for Arithmatic Series is

\(a_n=a_1+(n-1)d\)

where a_1 and a_n are the first and n-th term of the series respectively,

d is the common difference of the series.

Now,

The eigth term is given by,

\(a_8=(\frac{d}2)+(8-1)d=\frac{15}{2}d\)

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

The given equation represents the motion of a mass connected to a spring with viscous friction. To plot the displacement, y(t), we need to solve the differential equation. With initial conditions y(0) = 0, we can find the solution using the Laplace transform. After solving the equation, we can plot y(t) for t < 0 and t ≥ 0 separately. For t < 0, the applied force, f(t), is zero, so the mass will not experience any external force and will remain at rest. For t ≥ 0, the applied force is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position.

To solve the given differential equation, we can start by finding the characteristic equation by setting the coefficients of y, its derivative, and its second derivative to zero:

s^2 + 18s + 102 = 0.

Solving this quadratic equation gives us the roots s1 = -3 + 3i and s2 = -3 - 3i. These complex roots indicate that the mass will undergo damped oscillations.

Using the Laplace transform, we can solve the differential equation and obtain the expression for Y(s), the Laplace transform of y(t):

(s^2 + 18s + 102)Y(s) = F(s),

where F(s) is the Laplace transform of f(t). Since f(t) = 10 for t ≥ 0, its Laplace transform is F(s) = 10/s.

Solving for Y(s) gives us:

Y(s) = 10 / [(s^2 + 18s + 102)].

To find y(t), we need to inverse Laplace transform Y(s). Using partial fraction decomposition, we can express Y(s) as:

Y(s) = A / (s - s1) + B / (s - s2),

where A and B are constants to be determined. After finding A and B, we can inverse Laplace transform Y(s) to obtain y(t).

With the given initial condition y(0) = 0, we can solve for A and B by setting up equations using the initial value theorem:

A / (s1 - s1) + B / (s1 - s2) = 0,

A / (s2 - s1) + B / (s2 - s2) = 0.

Solving these equations will give us the values of A and B. Finally, we can substitute these values back into the inverse Laplace transform of Y(s) to obtain y(t).

For t < 0, since the applied force f(t) is zero, the mass will not experience any external force. Therefore, y(t) will remain at its initial position, y(0) = 0.

For t ≥ 0, the applied force f(t) is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position. The displacement, y(t), will depend on the properties of the mass, the spring, and the viscous friction. The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

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Answer:

1

Step-by-step explanation:

remember that \(|a| = a\)if a is positive or zero, and \(|a| = -a\)if a is negative.

\(4-| |14|-11| = 4-|14-11| = 4-|3| = 4-3 = 1\)

Answer:

C. 4/8

Step-by-step explanation:

She bought 4 pounds, and she wants to make 8 sandwiches.

1 and a half would be 1.5 pounds. 1.5 lb each sandwich x 8 sandwiches = 12, which is more than 4. So option A is incorrect.

3/4 is 0.75. 0.75 lbs each sandwich x 8 sandwiches = 6 lbs, which is more than 4. Option B is incorrect

4/8 = 0.5. 0.5 lbs each sandwich x 8 sandwiches = 4 lbs. Option C is correct.

1/4 is 0.25. 0.25 lbs per sandwich x 8 sandwiches = 2 lbs, which is less than 4 lbs. Option D is incorrect.

Also, 4 lbs divided by 8 sandwiches is 0.5 lbs a sandwich

3 hours of soccer to 5 hours of piano

It would be written as 3:5

Answer:

3:5 or 3/5

Step-by-step explanation:

Answer:

The interest earned on a savings account with a balance of $3500 and an interest rate of 1.5% per year compounded yearly would be $52.50 after 12 months.

Step-by-step explanation:

To calculate the interest earned on a savings account, you need to know the interest rate, the length of time the money is deposited, and the starting balance. Based on the information provided, it appears that the interest rate is 1.5% per year, the money is deposited for 12 months, and the starting balance is $3500.

To calculate the interest earned, you would first need to convert the interest rate to a decimal by dividing it by 100. In this case, the interest rate would be 0.015. You would then multiply the interest rate by the starting balance to get the amount of interest earned in a year. In this case, the interest earned would be $3500 * 0.015 = $52.50.

Since the interest is compounded yearly, the total balance after one year would be the starting balance plus the interest earned. In this case, the total balance would be $3500 + $52.50 = $3552.50. Therefore, the interest earned on a savings account with a balance of $3500 and an interest rate of 1.5% per year compounded yearly would be $52.50 after 12 months.

The Output Variable is Total cost represented by c(m).

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

A website charges $3 for each movie you download.

They also charge a one-time sign-up fee of $14.99.

So, the input variable will be m which shows the number of movies.

and, the output variable will be c which shows the total cost.

Then, the equation models the cost c(m), is c(m)=3m+14.99

Now, putting the values for m = 0, 1, 2, ....

c(0)= 4.99, c(1)= 17.99, c(2)= 20.99

Hence, the output variable is total cost.

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a) If the first 2 cards are both spades, the probability of the next 3 cards also being spades can be calculated by using the following formula:P(5 spades) = P(3 spades AND 4 spades AND 5 spades) = P(3 spades) x P(4 spades | 3 spades) x P(5 spades | 3 spades and 4 spades)The probability of picking 3 spades out of 50 cards is:P(3 spades) = (13/52) x (12/51) x (11/50)To calculate the probability of drawing the fourth spade, we know there are 11 spades left in the deck and only 49 cards remaining. Hence,P(4 spades | 3 spades) = (11/49)To calculate the probability of drawing the fifth spade, we know there are 10 spades left in the deck and only 48 cards remaining. Hence,P(5 spades | 3 spades and 4 spades) = (10/48)Therefore, P(5 spades) = (13/52) x (12/51) x (11/50) x (11/49) x (10/48) which is approximately equal to 0.0026. Hence, the probability of the next 3 cards being spades is 0.0026. The answer is rounded to four decimal places.

b) If the first 3 cards are all spades, then the probability of the next 2 cards being spades can be calculated as follows:To calculate the probability of the fourth spade, we know there are 11 spades left in the deck and only 49 cards remaining. Hence, P(4 spades | 3 spades) = (11/49)To calculate the probability of the fifth spade, we know there are 10 spades left in the deck and only 48 cards remaining. Hence, P(5 spades | 3 spades and 4 spades) = (10/48)Therefore, P(2 spades | 3 spades) = P(4 spades | 3 spades) x P(5 spades | 3 spades and 4 spades) = (11/49) x (10/48) which is approximately equal to 0.0045. Hence, the probability of the next 2 cards being spades is 0.0045. The answer is rounded to four decimal places.

We can write the probability of picking 5 spades as the probability of picking 4 spades AND 5 spades. This can be represented as:P(5 spades) = P(4 spades AND 5 spades) = P(4 spades) x P(5 spades | 4 spades).The probability of picking 4 spades out of 49 cards is: P(4 spades) = (10/48) x (9/47). This means that there are 10 spades out of the 48 cards in the deck for the first pick, and 9 spades out of the remaining 47 cards for the second pick.

Hence, the probability of drawing a spade given that the first four cards are spades is:P(5 spades | 4 spades) = (9/47). This is because there are 9 spades left in the deck and only 47 cards remaining.

Therefore, the probability of the next 2 cards being spades is calculated as follows:P(5 spades) = P(4 spades) x P(5 spades | 4 spades) = (10/48) x (9/47) x (9/47) ≈ 0.0030. This means that the probability of the next 2 cards being spades is 0.0030, rounded to four decimal places.

If the first 4 cards are all spades, then the probability of the next card being a spade is given by:P(5 spades) = P(5 spades) / P(4 spades). The probability of picking 5 spades out of 48 cards is:P(5 spades) = (9/46).

Thus, the probability of the next card being a spade is:P(5 spades) / P(4 spades) = (9/46) / (9/47) ≈ 0.9672. This means that the probability of the next card being a spade is 0.9672, rounded to four decimal places.

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Answer:

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