David deposits $4,300 in an account that pays 5% annual simple interest for 7 years. How much interest is earned?

The maximum possible error that will be associated with the estimate when the analyst uses a sample size of 400 observations is 3.78 percent and the sample size that the analyst would need in order to have the maximum error be no more than ±5 percent is 297 observations.

The maximum possible error that will be associated with the estimate when the analyst uses a sample size of 400 observations is 3.78 percent.

Error formula for proportion:

Maximum possible error = z * √(p^ * (1-p^)/n)

Where z = 1.65 for 90 percent confidencep^

              = 0.3n

              = 400

Substitute the given values into the formula:

Maximum possible error = 1.65 * √(0.3 * (1-0.3)/400)

Maximum possible error = 1.65 * √(0.3 * 0.7/400)

Maximum possible error = 1.65 * √0.0021

Maximum possible error = 1.65 * 0.0458

Maximum possible error = 0.0756 or 7.56% (rounded to two decimal places)

b. The sample size that the analyst would need in order to have the maximum error be no more than ±5 percent can be calculated as follows:

Error formula for proportion:

Maximum possible error = z * √(p^ * (1-p^)/n)

Where z = 1.65 for 90 percent confidencep^ = 0.3n = ?

Maximum possible error = 0.05

Substitute the given values into the formula:

0.05 = 1.65 * √(0.3 * (1-0.3)/n)0.05/1.65

        = √(0.3 * (1-0.3)/n)0.0303

        = 0.3 * (1-0.3)/nn

        = 0.3 * (1-0.3)/(0.0303)n

        = 296.95 or 297 (rounded up to the nearest whole number)

Therefore, the sample size that the analyst would need in order to have the maximum error be no more than ±5 percent is 297 observations.

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It is claimed that the sample of participants is generalizable since it reflects the characteristics of the population.

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i)  The firm's Total Cost function is TC =\(2Q^3 - 5Q^2 + 12Q + C\), where C is the constant of integration representing fixed costs.

ii) The profit-maximizing level of output, when the firm's fixed costs are zero, is approximately 4.41 units.

i) To find the firm's Total Revenue (TR) function, we need to multiply the quantity (Q) by the price. In this case, the price is given by the marginal revenue function (MR).

Given that MR = 100 - 2Q, the total revenue can be calculated as:

TR = Q * MR

  = Q * (100 - 2Q)

  = 100Q - \(2Q^2\)

So, the firm's Total Revenue function is TR = 100Q - 2Q^2.

To find the firm's Total Cost (TC) function, we need to integrate the marginal cost function (MC) with respect to Q.

Given that MC = \(6Q^2 - 10Q + 12,\) the total cost can be calculated as:

TC = ∫(MC) dQ

 \(= ∫(6Q^2 - 10Q + 12) dQ\)

  \(= 2Q^3 - 5Q^2 + 12Q + C\)

So, the firm's Total Cost function is TC =\(2Q^3 - 5Q^2 + 12Q + C\), where C is the constant of integration representing fixed costs.

ii) To find the profit-maximizing level of output, we need to determine the quantity (Q) at which marginal cost (MC) equals marginal revenue (MR). In this case, MR is given by 100 - 2Q.

Setting MC equal to MR, we have:

MC = MR

\(6Q^2 - 10Q + 12 = 100 - 2Q\)

Simplifying the equation, we get:

\(6Q^2 + 8Q - 88 = 0\)

To solve this quadratic equation, we can use the quadratic formula:

\(Q = (-b ± √(b^2 - 4ac)) / (2a)\)

Applying the values a = 6, b = 8, and c = -88, we get:

\(Q = (-8 ± √(8^2 - 4*6*(-88))) / (2*6)\)

Q = (-8 ± √(64 + 2112)) / 12

Q = (-8 ± √2176) / 12

Since we are looking for a positive quantity, we take the positive square root:

Q = (-8 + √2176) / 12

Calculating this value, we find:

Q ≈ 4.41

Therefore, the profit-maximizing level of output, when the firm's fixed costs are zero, is approximately 4.41 units.

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If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

Given,

The total amount you had = $150

The amount you spend in each day = $2

Consider the number of days = x

Then the algebraic expression for this situation is 150-2x

Hence, If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

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Answer:

  106°

Step-by-step explanation:

The intercepted arc is double the measure of the inscribed angle intercepting it. Each of the angles V and Y is 53°, so arc WX is 2×53° = 106°.

Answer:

140.4

Step-by-step explanation:

you have to do 2528 divided by 18 to get the number of pages.

Answer:

0

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

-4-(-4)/-12-(-6)

0/-6

Since the numerator is 0, the slope is 0.

Best of Luck!

Answer:

58

Step-by-step explanation:

Answer: yes,no,no,no

Step-by-step explanation:

34+12=46. Yes

34+7=41.  No

34+10=40.  No

34+4=38.  No

Answer:

12= yes

7= no

10= yes

4= no

Step-by-step explanation:

34 + 12= 46 is greater than 42

34 + 7= 41 is less that 42

34 + 10= 44 is greater than 42

34 + 4= 38 is less than 42

Answer:

The expression equivalent to 3( x - 9) Is

3(x) - 3(9)

3x-27

3(x)-3(9)= 3x-27

Answer:

just take the 96 and 66 and middle it then take y multiply that=answer

Step-by-step explanation:

Answer: 48

Step-by-step explanation: 96/2

Within-groups design compares the same subjects across time. In this design, participants are measured or observed on multiple occasions, such as before and after an intervention or at different time points.

The purpose of the within-groups design is to examine changes within individuals over time, allowing researchers to assess the impact of an intervention or the natural progression of a phenomenon within the same group of subjects.

By comparing the same subjects across time, within-groups designs help to control for individual differences and increase the internal validity of the study.

This design allows researchers to evaluate the effectiveness of an intervention by assessing changes within individuals and determining if those changes are statistically significant.

It also allows for a more precise assessment of the impact of an intervention or the stability of a phenomenon over time.

Within-groups designs are commonly used in fields such as psychology, education, and medicine to study changes in behavior, cognition, or health outcomes.

They provide valuable insights into individual responses to interventions or the natural course of development or disease progression within a specific group of subjects.

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The simplified trigonometric expression is -cot²θ.

To simplify the trigonometric expression 1 - csc²θ, we can use the identity csc²θ = 1 + cot²θ.

So, substituting this identity into the expression, we get:
1 - (1 + cot²θ)

Simplifying further, we have:
1 - 1 - cot²θ

This simplifies to:
-cot²θ

Therefore, the simplified trigonometric expression is -cot²θ.

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Therefore, in response to the given query, we can state that As a result, equation the ultimate solution is t = 40, indicating that Natalie has 40 more minutes to finish the test.

A mathematical equation connects two statements and employs the equals sign (=) to indicate equality. In mathematics, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal symbol separates the numbers by a space. A mathematical formula can be used to determine how the two lines on either side of a letter relate to one another. The emblem and the particular piece of software are frequently identical. like, for instance, 2x - 4 = 2.

We must deduct the time Natalie has already used from the overall time allotted to her in order to determine how many more minutes she has to finish the exam:

Given time: 2 hours divided by 60 minutes per hour equals 120 minutes.

20 minutes were devoted on section A.

Section B took up 60 minutes of your time.

Time remaining = Time allotted Time on section A minus Time on section B t = 120 minus 20 minus 60 minus 40

As a result, Natalie has 40 more minutes to finish the test.

The following algorithm can be used to find t:

t = 120 - 20 - 60

t = 40

As a result, the ultimate solution is t = 40, indicating that Natalie has 40 more minutes to finish the test.

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Answer:

Mean - 119.16

Median - 14

Mode - 13

Step-by-step explanation:

calculator

The linear equation that represents the line that passes through the points (4,5) and (0,-3) is given by:

B. y = 2x - 3

A linear function is modeled by:

y = mx + b

In which:

The line passes through (0,-3), that is, when x = 0, y = -3, hence the y-intercept is of b = -3.

The slope is given by the change in y divided by the change in x, hence:

m = (5 - (-3))/(4 - 0) = 2

Hence the equation is:

y = 2x - 3.

Which means that option B is correct.

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\({ \bf{ \underbrace{Given}}}\):

Diameter of the circle "\(d\)" = \(36\)

Value of \(π\) = \(3\)

\({ \bf{ \underbrace{To\:find}}}\):

The circumference "\(C\)" of the circle.

\({ \bf{ \underbrace{Solution }}}\):

\(\sf\pink{The\:circumference \:"C"\:of\:the\:circle\:is\:108.}\)

\(\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}\)

We know that,

\(\sf\purple{Circumference\:of\:a\:circle \:=\:πd }\)

\( = 3 \times 36\)

\( = 108\)

Therefore, the circumference of the circle is \(108\).

\(\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}\)

Answer:

\(\Longrightarrow: \boxed{\sf{108}}\)

Step-by-step explanation:

Apply the formula for the circle's circumference.

\(\text{Circumference circle formula:}\)

\(\Longrightarrow: \sf{C=\pi d}\)

\(\Longrightarrow:\sf{C=?}\\\\\Longrightarrow:\sf{\pi =3}\\\\\Longrightarrow:\sf{d=36}\)

Multiply.

\(\sf{3*36=\boxed{\sf{108}}\)

I hope this helps! Let me know if you have any questions.

Answer:

0.31x + 2.4 + 3.4p

Step-by-step explanation:

combine like terms

Answer: D.) b=7

Step-by-step explanation:

Take your equation that is given

28=4b

Now divide by 4 on each side to cancel the 4 out

4=b

now just flip them

b=4

Answer:

your answer is 7

Step-by-step explanation:

source: trust me bro

To find directional derivative of the function g(x, y, z), at point P(3, 9, 0) in the direction of the vector PO, where O is the origin (0, 0, 0), we haveto find derivative , The directional derivative of the function g(x, y, z) = \(xye^(3z)\) at point P(3, 9, 0) in the direction of the vector PO is 3√10.

To calculate the gradient of the function: \(∇g = (∂g/∂x, ∂g/∂y, ∂g/∂z) = (ye^(3z), xe^(3z), 3xze^(3z)\)) the gradient at point \(P:∇g(P) = (9e^(3*0), 3e^(3*0), 3*3*0e^(3*0)) = (9, 3, 0).\)

The unit vector in the direction of PO: OP = P - O = (3, 9, 0) Magnitude of OP = |OP| = \(√(3² + 9² + 0²) = √90\), Unit vector, \(u = OP / |OP| = (1/√90)(3, 9, 0) = (1/3√10, 3/√10, 0)\)

Compute the directional derivative of g at P in the direction of \(u: D_ug(P) = ∇g(P) · u = (9, 3, 0) · (1/3√10, 3/√10, 0) = (9(1/3√10)) + (3(3/√10)) + (0*0) = 3√10\)

The gradient of a function is a vector that points in the direction of the steepest increase in the function and its magnitude represents the rate of change of the function at that point.

The directional derivative of the function g(x, y, z) = \(xye^(3z)\) in the direction of the vector PO is 3√10.

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Answer:

X is 9

Step-by-step explanation:

9 + 3 = 12

Let 185lb equate to 100%

20lb of fat will be ?

= 10.81%

Dave has 10.81% of body fat and it falls at the athlete category.

Answer:

113.04

Step-by-step explanation:

Enter the area of the circle, in square centimeters. Round your answer to the nearest hundredth. 1.

To formulate and solve a linear programming model for the resource-allocation problem in Excel, you will need to use the appropriate formulas in each cell. Additionally, you can utilize Solver to optimize the solution.

In Excel, you can use the SUMPRODUCT formula to calculate the contribution per unit by multiplying the profit per unit of each activity by the corresponding allocation. For example, if the profit per unit of activity A is in cell B2 and the allocation for activity A is in cell C2, you can use the formula "=B2*C2" to calculate the contribution per unit for activity A.

To formulate the linear programming model, you will need to define the objective function and the constraints. The objective function represents the goal you want to maximize or minimize, while the constraints specify the limitations on the resources or activities.

To set up Solver, go to the Data tab in Excel and click on Solver. In the Solver Parameters dialog box, you need to specify the objective cell (the cell containing the formula for the total contribution), select the optimization type (maximize or minimize), and add the constraints. The constraints can be added by clicking on the Add button and specifying the cell references for the constraints.

Once Solver is set up, you can click Solve to find the optimal solution that maximizes or minimizes the objective function while satisfying the constraints.

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Answer:

⅔h – 5 = 11

Step-by-step explanation:

         h = babysitting hours last week

     ⅔h = two-thirds of those hours

⅔h - 5 = five hours fewer than two-thirds of those hours

⅔h – 5 = 11

The equation is ⅔h – 5 = 11.

Answer:

Variable B is the area of triangular base.

B = 38.5 \(in^{2}\).

Variable h is the height of pyramid.

In the given prism, h is 9 inches.

The volume of prism is 346.5 \(in^{3}\).

Step-by-step explanation:

Please refer to the attached image for the detailed labeling of all the sides.

\(\triangle ABC\) is the triangular base of the prism.

BC is the base of triangular base of the prism.

AP is the height of triangular base.

Area of triangular base is represented by B and is calculated by following formula of area of a triangle.

\(Area = \dfrac{1}{2} \times \text{Base}\times \text{Height}\)

\(\Rightarrow \dfrac{1}{2} \times 11 \times 7\\\Rightarrow 38.5\ in^{2}\)

Hence, B = 38.5 \(in^{2}\).

Height of prism, h = 9 in

h is represented as side BE in the attached image.

It is know that volume of prism is given as :

V = Bh

Putting values of B and h:

\(V = 38.5 \times 9\\\Rightarrow V = 346.5\ in^{3}\)

Answer:

The formula for volume of a prism is V = Bh.

The variable B stands for the ✔ area of the base.

In this prism, B equals ✔ 38.5  in.².

The variable h stands for ✔ height.

In this prism, h is ✔ 9 in.

The volume of the prism is ✔ 346.5  in.³.

Explanation:

The answer above mine is correct. I hope this helps!