For 0 ≤ t ≤ 6 seconds, a screen saver on a computer screen shows two circles that start as dots and expand outwards. 1) At the instant that the first circle has a radius of 9 centimeters, the radius is increasing at a rate of 3/2 cm/sec. Find the rate at which the area of the circle is changing at that instant. 2)The radius of the first circle is modeled by g(t) = 12 - 12e-0.5t for 0 ≤ t ≤ where g(t) is measured in centimeters and t is measured in seconds. At what time t is the radius of the circle increasing at a rate of 3 cm/sec. 3) A model for the radius of the second circle given b the function f for 0 ≤ t ≤ 6, where f(t) is measured in cm and t is measured in seconds. The rate of change of the radius of the second circle is given by f1(t) = t2-4t+4. Based on this model, by how many cm is the radius of the second circle increasing from time t =0 to t = 3?

The amount of bad debt expense will the company actually record is c)$139500.

So, correct option is c.

We have some details like total account receivable  as $1800000

allowance for doubtful accounts as $40,500

Now, we have also percentage of bad debt expense as 10% of accounts receivable.

So,10% of  of accounts receivable=(10/100)×1800000=$180000

Now, for getting information of bad debt expense we need to subtract allowance for doubtful accounts.

So, bad debt expense=10% of account receivable - allowance for doubtful debts

=>bad debt expense=$180000-$40500=$139,500

Hence, amount of bad debt expense is $139,500

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(Complete question) is:

Sheffield Corp. unadjusted trial balance includes the following balances (assume the normal balances): Accounts receivable as $1800000. Allowance for doubtful accounts as $40500. Bad debts are estimated to be 10% of the outstanding receivables. What amount of bad debt expense will the company actually record?

a)$137370

b)$182500

c)$139500

d)$177130

The required an equation for the perpendicular bisector of the line segment joining (1,2) and (-5,12) is y = 3x/5 + 41/5.

Equation of the lines which are even or lined up with the X-pivot is y = a, where an is the y - direction of the focuses on the line. Essentially, the condition of a straight line which is vertical or lined up with the Y-hub is x = a, where an is the x-direction of the focuses on the line.

Mid point of the line passing through the points (1,2) and (-5,12).

mid point = [tex](\frac{1-5}{2} , \frac{2+12}{2} )[/tex] = (-2, 7)

So, the line perpendicular to given line is passing through  (-2, 7)

Slope of line of points (1,2) and (-5,12).

Slope(m) = [tex]\frac{12-2}{-5-1}=-\frac{5}{3}[/tex]

Then slope of perpendicular bisector of this line is negative and reciprocal of Slope(m).

slope of perpendicular bisector(n)  = 3/5

Now, equation of line is

[tex](y-y_{1})=n(x-x_{1})[/tex]

(y - 7) = 3/5(x + 2)

y = 3x/5 + 41/5

Thus required equation of perpendicular bisector is y = 3x/5 + 41/5

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The slope of this line is given as 1/2

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

Taking two points from the graph;

The slope of the line is calculated as

m = y₂ - y₁ / x₂ - x₁

Substituting the values into the formula above;

m = -3 - (-1) / 1 - 5

m = -2 / - 4

m = 1/2

Slope = 1/2

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A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits.

In the given question we have to explain about 2-digit special number.

A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits.

Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.

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The estimated kilowatt usage when the temperature is 90° outside is 1132.5.

Here we have to find the point estimate kilowatt usage when the temperature is 90° outside.

We have to find the linear regression model:

Creating the table with the following:

∑y; ∑x; ∑xy; ∑x²; ∑y²

Now use these equations to find coefficients a and b:

a = (∑y) (∑x²) - (∑x) ( ∑yx) / n(∑x²) -(∑x²)

b = n( ∑xy) - (∑x ) (∑y) / n( ∑x²) -(∑x²)

Now substitute this in the equation:

y = a + bx

The linear regression equation is:

y = -2004 + 34.85x

Here it is asked for the temperature at 90°

So we take x = 90°

y = -2004 + 34.85× 90

y = 1132.5

Therefore the estimated kilowatt is 1132.5.

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The complete question is:

The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a point estimate Kilowatt usage when the Temperature is 90 degrees outside.

Temperature(x)                       Kilowatts(y)

       73                                         680

       78                                         760

       85                                         910

       98                                         1510

       93                                         1170

       83                                         888

       92                                         923

       81                                          837

       76                                         600

     105                                        1800

The equation in closed form for the sequence {aₙ: n ≥0} that each of the exponential generating functions below represents.

b. x²e³ˣ is aₙ=(3ⁿ.xⁿ⁺²)/n!, n≥0

d. (eˣ)⁴ is aₙ=x⁴ⁿ/n!,  n≥0

Given that,

We have to give an equation in closed form for the sequence {aₙ: n ≥0} that each of the exponential generating functions below represents.

b. x²e³ˣ

d. (eˣ)⁴

We have to find the simplified form.

First take the

b. x²e³ˣ

=x²[1+3x+(3x)²/2!+(3x)³/3!+(3x)⁴/4!....]

=x²+3x³+3².x⁴/2!+3³.x⁵/3!+3⁴/x⁶/4!....]

aₙ=(3ⁿ.xⁿ⁺²)/n!, n≥0

d. (eˣ)⁴

=1+x⁴+(x⁴)²/2!+(x⁴)³/3!+(x⁴)⁴/4!....

aₙ=x⁴ⁿ/n!,  n≥0

Therefore, The equation in closed form for the sequence {aₙ: n ≥0} that each of the exponential generating functions below represents.

b. x²e³ˣ is aₙ=(3ⁿ.xⁿ⁺²)/n!, n≥0

d. (eˣ)⁴ is aₙ=x⁴ⁿ/n!,  n≥0

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From the four possible outcomes for signal detection theory exhibited in the given example is miss.

Signal detection theory refers to an approach of differentiating an individual ability to discriminate the presence and absence of a stimulus (or different stimulus intensities) from the individual’s criterion (physical/psychological state) to responses to those stimuli. It is a measure of the ability to differentiate between information-bearing patterns and random patterns that distract from the information. The four possible outcomes defined by the theory are hit (signal present and observer respond), miss (signal present and observer did not respond), false alarm (signal absent and observer respond), and correct rejection (signal absent and observer did not respond). As the brother is hiding under a pillow but the sister comes into the room and looks at the sofa, but seeing nothing, she leaves, it is a miss outcome.

Note: The question is incomplete. The complete question probably is: A brother and sister are playing hide and seek and the brother has hid under a pillow on the sofa. His sister comes into the room and looks at the sofa, but seeing nothing, she leaves. What signal detection theory potential outcome is shown in the example.

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The total cheese production in 2006 was about 7.7 billion pounds and the total cheese production in 2014 was about  9.7 billion pounds

The function that can be used in our computation is given as

y = 7(1.03)ˣ

Such that

x = Number of years after 2003 and y is the amount of cheese

The value of x can be calculated using

x = year - 2003

Substitute 2006 for year

x = 2006 - 2003

Evaluate

x = 3

Substitute x = 3 in the equation y = 7(1.03)ˣ

y = 7(1.03)³

Evaluate

y = 7.7

In the year 2014, the value of x is calculated as

x = Current year - 2003

So, we have

x = 2014 - 2003

Evaluate

x = 11

Substitute x = 11 in the equation y = 7(1.03)ˣ

y = 7(1.03)¹¹

Evaluate

y = 9.7

Hence, the amount of cheese is 9.7 billion pounds

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A power function with two points can be written by substituting the values of the two points in the given function.

To given an example, let f(x) = aˣ b;

Taking natural logs on both sides:

ln f(x) = ln (aˣb);

ln f(x) = ln (aˣ) + ln (b);

ln f(x) = xln (a) + ln (b);

Taking Exponential both sides

then,  

Let the two points be P (x₁, y₁) and Q (x₂, y₂)

The we get two equations:

(i) ln f(y₁) = x₁ ln (a) + ln (b);

(ii) ln f(y₂) = x₂ ln (a) + ln (b);

Subtracting (ii) from (i)

ln f(y₁) - ln f(y₂) = x₁ ln (a)  - x₂ ln (a) + ln (b) - ln (b);

ln f(y₁)/f(y₂) = ln a( x₁ - x₂)

[ln f(y₁)/f(y₂)]/ [( x₁ - x₂)] = ln a

Taking exponential both side

let f(y₁)/f(y₂) = s

let ( x₁ - x₂)= r

[tex]e^{ \frac{ln s}{r} } = e^{ ln a}[/tex]

[tex]e^{ \frac{ln s}{r}[/tex] = a

On solving both the equations we get two values of b

f(y₁) = aˣ₁ . b

f(y₂) = aˣ₂ . b

ln f(y₁) = ln (aˣ₁) + ln (b); --(1)

ln f(y₂) = ln (aˣ₂) + ln (b); --(2)

subtracting (2) from (1)

ln f(y₁) - ln(y₂) = ln([tex]e^{\frac{ln s}{r}^x1}[/tex]) - ln([tex]e^{\frac{ln s}{r}^x2}[/tex]) + ln(b) - ln(b)

ln f(y₁)/f(y₂) = (ln s/r)ˣ₁ - (ln s/r)ˣ₂

ln f(y₁)/f(y₂) = x₁ ln s/rˣ₁ - x₂ ln s/rˣ₂

rˣ₁rˣ₂ ln f(y₁)/f(y₂) = x₁ rˣ₂ ln s - x₂ rˣ₁  ln s

ln [tex]f(y1)/f(y2)^{r^{x1} r^{x2}}[/tex] = ln [tex]s^{x1 r^{x2}}[/tex] - ln [tex]s^{x2 r^{x1}}[/tex]

ln [tex]f(y1)/f(y2)^{r^{x1} r^{x2}}[/tex] = ln [tex]\frac {s^{x1 r^{x2}}}{s^{x2 r^{x1}}}[/tex]

Taking exponential both sides.

let [tex]f(y1)/f(y2)^{r^{x1} r^{x2}}[/tex] = w

let [tex]\frac {s^{x1 r^{x2}}}{s^{x2 r^{x1}}}[/tex] t

then,

[tex]e^{ln w} } = e^{ ln t}[/tex]

w = t

[tex]f(y1)/f(y2)^{r^{x1} r^{x2}}[/tex] = [tex]\frac {s^{x1 r^{x2}}}{s^{x2 r^{x1}}}[/tex]

Solving this equation we get the value of x by putting the values given

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Answer:

Original = (8,-6) New = (0,1)

Step-by-step explanation:

Arrange the adjustments like this in the parenthesis of the original point

(8 - 8, -6 +7)

Then do the math and get (0,1)

The average of numbers from 8 to 49 will be 21.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The numbers 8 to 49.

Now,

The average of numbers from 8 to 49 is calculated as;

⇒ Average = (n + 1) / 2

Where, n is the numbers in between 8 to 49.

Hence, n = 49 - 8

               = 41

Thus, We get;

⇒ Average = (n + 1) / 2

                  = (41 + 1) / 2

                  = 42/2

                  = 21

Therefore, The average of numbers from 8 to 49 will be 21.

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Step-by-step explanation:

Let's say that the you have to found the mean of 5, 2, and 8

first you would have to add up all of the number 5+2+8 which equals to 15

now you would have divide 15 by the amount of the data points which is 3, so your mean in this problem is 5.

here is an example by only using numbers:

(5+2+8) ÷ 3 = 5

The "correct" statement is that the odds ratio appears statistically significant when the whole 95% confidence interval is much less than 1.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values a predetermined percentage of the time.

Thus, the "correct" statement is that the odds ratio appears statistically significant when the whole 95% confidence interval is much less than 1.

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The surface area of the square pyramid that has the above stated dimensions is: 112 in.².

A square pyramid is a three-dimensional geometric shape that is made up of one square base and four triangular faces that meet at a vertex point.

The diagram attached below shows what a typical square pyramid looks like.

The formula for the surface area of a square pyramid (SA) = A + 1/2Ps, where:

Given the following:

Length of a side of the base (b) = 4 in.

Base area (A) = 4²

A = 16 in.²

Perimeter of the base (P) = 16 in.

Slant height (s) of the square pyramid = 12 in.

Surface area (SA) = 16 + 1/2(16)(12)

SA = 16 + 96

Surface area of the square pyramid = 112 in.²

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Using the Indifference curve , the slope of ambrose indifference curve is -2.

Indifference Curve

A bunch of places of consumption where consumer tastes are indifferent is an indifference curve. Indifference curves are usually convex towards the origin.

Rewriting algebraically the equation of the indifference curve U(t, y)=c in the form y=g(t, c),

where g(t, c) is a decreasing convex function of t for c given .

Indifference curve is given by:

x₂ = C − 4x₁¹/²

Slope of the indifference curve = dx₂/dx₁

Hence, Slope of the Ambrose indifference curve = dx₂/dx₁ = -(1/2)(4/x₁¹/²)

=> Slope of the Ambrose indifference curve = -2/x₁¹/²

At (1,6), Slope of the Ambrose indifference curve = -2/x₁¹/² = -2/1= -2

Hence, Slope of the Ambrose indifference curve = -2

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The feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

With the constraint that x and y are both non-negative, the second constraint has only one point in common with each of the first and third constraints; and those two points are different.

The feasibility region is empty; so nothing can be optimized.

Plots x + 2y = 30 (red),  2x + 2y = 30 (green)  and  2x+y = 30 (blue)

The feasibility area, according to the condition, is the area of the first quadrant

   - above the red line,

   - below the green line,

   - above the blue line.

It can be seen from the plot that this set is empty.

Therefore, the feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

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Disclaimer

The question given by you is incomplete, so the above solution is of a similar question, and the question is

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT

Maximize p = x + y subject to

x + 2y ≥ 30

2x + 2y ≤ 30

2x + y ≥ 30

x ≥ 0, y ≥ 0.

p=

(x, y)=

Option(4) The different decisions in both study 1 & study 2 are possible because the second test was associated with a greater power to detect an effect.

In statistics, power is the probability of rejecting a null hypothesis when, in fact, it is true. An error of Type II is less likely to occur when power is high. In the event of a false null hypothesis, power is the probability of making the correct decision (to reject the null hypothesis).

The power of a test of significance is the likelihood that an effect will be found. In the event of a deviation from the null hypothesis, power is the probability that the test of significance will detect it.

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The journal enetry,

Debit cash is $67,000

Debit discount on payable is $670

Credit bonds payable is $66,330

(Recorded on bonds )

Debit Interest expense is $46,90

Debit discount on bonds payable is $46.9

credit cash is $4643.1..

Bonds payable

Bonds issued when the market price equals the standard rate are issued at face value. In other words, the cash received is face value.

Interest paid on the par Bond includes only the indicated. Interest rate calculated based on the number of annual payments.

We have given that

face amount, F = $67,000

Annually paid interest= $67,000

rate of bond, r = 7%

time bond, n = 10 year

market bond of interest= 7%

Coupon ammount = 7% of 67000 =$ 4690

we have to calculate bond issue and first interest payment .

bond price= C×[1 - (1 + r)⁻ⁿ] /r + F/(1+r)ⁿ

= 4690[ 1 - (8)¹⁰]/7 + 67000/(8)¹⁰

=669.99 + 0.000062 = 669.9901 ~ 670

Interest Expense = Principal * Rate * Time

=> Interest Expense = $67,000×7% ×1

= $46,90

discount or primum on bond payable

= interest expense - $66,330×7% × 1

= $46,90- $4643.1 = $46.9

date General

General journal debit credit

January, cash $67,000 $66,330

2024 Bonds

payable

Discount on

bond $670

payable

December

31, cash $4643.1

2024 interest

expense $46,90

Discount on

bond $46.9

payable

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Complete Question:.Pretzelmania, Inc., issues 7%, 10-year bonds with a face amount of $67,000 for $67,000 on January 1, 2024. The market interest rate for bonds of similarrisk and maturity is 7%. Interest is paid annually on December 31.Record the bond issue and first interest payment on December 31 . (If no entry is required for a transaction/event, select "No journal entry required" in thefirst account

To graph an inequality, consider the < or > sign to be a = sign and graph the equation. If the inequality is < or >, draw a dotted line to represent the equation.

Graph the equation as a solid line if the inequality is ≤ or ≥, This line divides the xy-plane into two regions: one that meets the inequality and one that does not.

When inequalities are graphed on a coordinate plane, the solutions are found in a region of the plane that is shaded. If the points on the line satisfy the inequality, as in the case of and, the boundary line for the inequality is drawn as a solid line.

Linear inequalities are not the same as linear equations, but what you know about equations can help you understand inequalities. Equations and inequalities are both mathematical statements that compare two values. 

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Trigonometric functions, rational functions, hyperbolic functions, and log functions are some examples of having inverse.

The inverse of a function is basically a reverse function or undo of the function.

For example y = f(x) then the inverse will be x = f(y).

It means in the inverse function we need to interchange x and y.

Suppose a function,

y = sinx here x is the angle while y is the real number.

Now, x = sin⁻(y) here sin⁻(y) is a function of x as inverse.

Another example y = 2x

x = 2/y if x is output then it will be inverse.

Hence "Trigonometric functions, rational functions, hyperbolic functions, and log functions are some examples of having inverse".

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The area of grass that the horse has access to is 314 square-foot

From the question, we are to determine how much grass the horse have access to.

From the given information,

"A horse is tied with a 10 -foot-long rope to a pole"

This means the horse has access to a circular area of radius 10 feet.

Now, we will calculate the area of a circle with radius 10 feet.

Using the formula for calculating the area of a circle,

A = πr²

Where A is the area of the circle

and r is the radius of the circle

Substitute r = 10 into the equation,

A = π × 10²

A = 100π

Take π = 3.14

Then,

A = 100 × 3.14

A = 314 square foot

Hence, the area is 314 square foot

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The diameter of the Ferris wheel is equal to 95 ft.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a function that models the height of a seat on a Ferris wheel after [t] minutes.

We have the following function -

f(t) = 95 cos(π/10)t

The diameter of the Ferris wheel would be the maximum height reached by the wheel. We have -

f(t) = 95 cos[(π/10)t]

df/dt = 95 x - sin[(π/10)t] x (π/10)

df/dt = -(95π/10) sin[(π/10)t]

For maximum height -

df/dt = 0

- (95π/10) sin[(π/10)t] = 0

sin[(π/10)t] = 0

sin[(π/10)t] = sin (0)

(π/10)t = 0

t = 0

Put t = 0, in f(t) = 95 cos[(π/10)t], we get -

f(max) = 95 cos(0) = 95 ft

Therefore, the diameter of the Ferris wheel is equal to 95 ft.

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Answer: Option C (190 ft)

Step-by-step explanation:

Hi, your answer is b. (1, 2)

Hope this helps.

This is the binomial probability distribution.

n = 10, p = 0.4965 and q = 0.5035

In a binomial probability distribution, the possible outcomes is two that is either success or failure

Here , we are determine the probability of a male,

so here success is male and failure is female

And in selecting ten texans at random, the outcome of one individual is independent of th eother

so it is an binomial probability.

Therfeore, the given experiment is an binomial probability distribution.

n = 10 (the number of randomly selected Texans)

p = 0.4965 (the probability that randomly selected Texan will be male)

q = 0.5035 (the probability that randomly selected Texan will be female)

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The equation of the line in slope intercept form is y = 4/3x - 10/3.

What is a line in slope-intercept?

The equation of a line with a slope of m and a y-intercept of (0, b) is y = mx + b. To graph a slope-intercept line, do the following: On the coordinate plane, draw the y-intercept. Find another point on the line using the slope.

We have,

the line that passes through (2,6) and (-4,-2).

We know that the formula to find the slope of two points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

m = (-2 - 6) / (-4 - 2)

m = -8/ -6

m = 4/3

Now using the slope and the point (2, 6) the y-intercept is

y = mx + b

6 = 4/3 (2) + b

6 = 8/3 + b

By further calculation,

b = 6 - 8/3

Taking LCM

b = (18 - 8)/3 = 10/3

By writing the equation in slope intercept form

y = mx + b

y = 4/3x - 10/3

Therefore, the equation of the line in slope intercept form is y = 4/3x - 10/3.

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The gravitational force on one sphere due to the three of square is 1042.18 ×10⁻¹¹N

We are given that ,

Mass = m = 7.5 kg

Side = d = 0.6 m

Due to the square's three corner there will be up , right and diagonal three forces acting on the system,

Fup = G(m²/d²)

Fright =  G(m²/d²)

Fdia = G (m²/(√2d)²)cos45°+ G (m²/(√2d)²)sin45°

To calculate the force on the left sphere in the lower left corner. From the symmetry of the problem the net forces in the x and y direction will be the same and θ = 45°

Therefore, the force will be,

Fx =Fright +Fdia

Fx =  G(m²/d²) +G (m²/(√2d)²)(1/√2)

Fx = G(m²/d²)[(1+(1/2√2)]

Thus, Fy = Fx =G(m²/d²)[(1+(1/2√2)]

By the Pythagorean combination of the two component forces , due to symmetry the the net force will be along the diagonal of the square,

F = √Fx +Fy= Fx√2

F = G(m²/d²)[(1+(1/2√2)]√2

F = (6.67 ×10⁻¹¹ Nm²/kg²)(7.5kg)²/(0.6m)²

F = 1042.18 ×10⁻¹¹N

The force at points are the center of the square.

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Yes, angry is considered to be a tone in a paper.

The tone of writing appears an author’s attitude or intent. The tone is the essence of the voice, which is how a writer passes on their thoughts to the peruser. Tone can be found through particular words, expressions, and sentence structure. The tone is broadly depicted as the author’s demeanor toward his or her subject. It can be enthusiastic, far off, irate, and cheerful, among numerous other possibilities. Tragically there are as well numerous possibilities for us to cover, and without knowing your subject, we cannot allow the foremost particular advice possible. The obvious pitfalls incorporate sounding condescending or silly, whereas sounding energetic and eager could be a definite positive. An angry tone is ordinarily utilized when the author needs to communicate a sense of frustration or outrage. It can take diverse forms such as passive-aggressive, protective, or sarcastic.

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Answer:

The answer to that question is 8

Step-by-step explanation:

2/3 times 12 = 8

The perimeter of the rectangle is: 2⅙ yd

The area of the rectangle is: 1/4 yd².

Given the following:

Length of rectangle = 3/4 yd

Width of rectangle = 1/3 yd

The perimeter of rectangle = 2(3/4 + 1/3) = 2(13/12)

Perimeter = 2⅙ yd

The area of the rectangle = (3/4)(1/3)

Area = 3/12

Area = 1/4 yd²

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