if I dig 6 feet in the ground how deep in the hole?

The average total cost can be found by dividing the total cost by the quantity produced. In this case, the total cost function is given as C = 90 + 35Q + 25Q^2 + 10Q^3, and we want to find the average total cost when Q = 2.

To find the average total cost, we need to calculate the total cost when Q = 2. Plugging Q = 2 into the cost function, we get:
C = 90 + 35(2) + 25(2^2) + 10(2^3)
C = 90 + 70 + 100 + 80
C = 340

Next, we divide the total cost by the quantity produced:
Average Total Cost = Total Cost / Quantity
Average Total Cost = 340 / 2
Average Total Cost = 170

Therefore, the value of average total cost when Q = 2 is $170.

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The probability that a student received an A in Statistics given that the student received less than a B grade in Calculus I is denoted as P(S|C'). Here's the explanation for each option:

P(S∣C): This denotes the probability of receiving an A in Statistics given that the student received a B or better grade in Calculus I. However, this is not the probability asked in the question.

P(S'∣C'): This denotes the probability of not receiving an A in Statistics given that the student did not receive a B or better grade in Calculus I. Again, this is not the probability asked in the question.

P(C∣S): This denotes the probability of receiving a B or better grade in Calculus I given that the student received an A in Statistics. This is also not the probability asked in the question.

Therefore, the correct notation for the probability that a student received an A in Statistics given that the student received less than a B grade in Calculus I is P(S|C').

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0 lol this is funny thanks for free points

Answer:

I think its zero but I'm not sure dude

hope this helps :)

Answer: 476 ft³

Step-by-step explanation:

Volume = width x hight x length

        V = 4 ft x 17 ft x 7 ft

        v  = 476 ft³

To prove that A, B, and C are subsets of a universal set U, we showed that every element in A, B, and C is also an element of U. This demonstrates that A, B, and C are subsets of U.

To prove that A, B, and C are subsets of a universal set U, we need to show that every element in A, B, and C is also an element of U.
1. Let's start by considering set A. If A is a subset of U, then every element in A must also be an element of U. In other words, for any element x in A, x must also belong to U.
2. Now let's move on to set B. Similar to A, if B is a subset of U, then every element in B must also be an element of U. For any element y in B, y must also belong to U.
3. Finally, let's consider set C. Again, if C is a subset of U, then every element in C must also be an element of U. For any element z in C, z must also belong to U.
4. Combining the above statements, we can conclude that every element in A, B, and C is also an element of U. Therefore, A, B, and C are subsets of U.
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The area of the circle with a diameter having endpoints at (2,5) and (10,5) on a coordinate plane is 16π square units.

The midpoint of the line segment connecting the endpoints of the diameter is the center of the circle.

The distance from the center of the circle to the endpoints of the diameter is the radius of the circle.

The diameter of the circle in this problem is AB, which has endpoints (2,5) and (10,5).

We know that this diameter is a horizontal line because both endpoints have the same y-coordinate of 5.

The midpoint of AB will also have a y-coordinate of 5 since it lies on the horizontal line containing AB. The x-coordinate of the midpoint is the average of the x-coordinates of A and B.  

It is easy to find the distance between the endpoints of the diameter, so the radius can also be found as follows:

r = AB/2 = 8/2 = 4

Therefore, the area of the circle is 16 π square units.

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Answer:

im sorry I dont know

The p and t represent Principal and time and interest is 517.7

We are given the formula to find the interest. So, the formula is -

I = (PRT) ÷ 100

In this formula, I refers to interest, P refers to Principal, R refers to rate of interest and T refers to time. Time will be in years and division by 100 is done for rate of interest.

Keep the values in formula to calculate the interest -

As per the known fact, 12 months = 1 year

So, 20 months = (1 ÷ 12) × 20

20 months = 1.67 years

Interest = (2500 × 12.4 × 1.67) ÷ 100

Performing multiplication in numerator

Interest = 51,770 ÷ 100

Performing division to find the interest

Interest = 517.7

Hence, p refers to principal and t refers to time. The interest that Gordon will receive will be 517.7.

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The coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

The given parameters are

Number of pen = 2

Unit price = $2

This means that the total amount spent is

Total amount = Number of pen * Unit price

Evaluate the product

Total amount = 2 * 2

Evaluate the product

Total amount = 4

So, the coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

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Answer:

0,-11

Step-by-step explanation:

-p^2 − 11p = 0

Factor out -p

-p( p+11) =0

Using the zero product property

-p =0    p+11 =0

p =0      p = -11

From the figure of the triangle, the length of LK is calculated to be 10

The knowledge used here is that of similar triangles.

In similar triangles the sizes of the triangles are not equal however the ratio of the sizes are equal

The formula for the similar triangle used here is:

JR / JL = SR / LK

from the given figure

JL = 2JR,  SR = 5

plugging the values into the equation gives

JR / 2JR = 5 / LK

1 / 2 = 5 / LK

LK = 10

The length of KL = 10 units

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Explanation

The equation of a circle with center (h,k) and radius r units is given by:

then

Step 1

find the diameter of the cirlce:

to do this, we can use the distance between two points formula:

if

the distance from A to B is

so,let

distance CD=

hence, the diameter of the circle is

Step 2

find the center of the circle:

the center of the circle is the midpoint of CD

so

replace

so, the center of the circle is (-3,-1)

Step 3

finally, replace in the formula to get the equation of the circle

let

replace

therefore, the answer is

I hope this helps you

The equation is y = 2.50x + 10.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: An international data plan charges $10.00 for 4GB of data. Anything over 4GB is priced at $2.50 per GB.

We have to find the equation that can be used to find y, the total cost of the international plan, if x represents the number of GB over 4.

Let the total cost of the international plan = y

x be the cost of the plan for over 4 GB.

Fixed charge for 4 GB = $10

Now y = 2.50x + 10

Hence, the equation is y = 2.50x + 10.

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Answer:

i think probably 20

Step-by-step explanation:

if 200 students, students do not prefer math 10/100 × 200 = 20

Answer:

The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.

Answer:

You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.

Step-by-step explanation:

(a) A system of two equations, x=2 and y=3, is needed to express (2,3) in R2. (b) No, only two equations can express (2,3) in R2. (c) The maximum number of distinct equations that can be added is three. (d) Yes, the general form for the equations is x-2=0, y-3=0, and z=0.

(a) The smallest number of equations you would need is two. The system of linear equations would be:

x + 2y = 6

2x + 4y = 12

(b) Yes, you can add one more equation to the system in (a) so that the new system still has the unique solution (2,3). The equation would be:

3x + 6y = 18

(c) The maximum number of distinct equations you can add to your system in (a) to still maintain the unique solution (2,3) is three. The equations would be:

x + 2y = 6

2x + 4y = 12

3x + 6y = 18

(d) Yes, there is a general form for the equations in (c). The general form is:

ax + by = c, where a, b, and c are constants.

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Answer:

  x=12

Step-by-step explanation:

12+x=-12+3x

-2x=-24

x=12

Answer:

x=12

Step-by-step explanation:

12+x=-3(4-x)

12+x=-12+3x

2x=24

x=12

Answer:

After 6 days, there will be approximately 691.6 files.

Step-by-step explanation:

We can use the given information to solve for the constants a and b in the exponential growth equation. First, we can rearrange the equation to solve for b:

y(t) = aebt

ln(y(t)) = ln(aebt)

ln(y(t)) = ln(a) + ln(ebt)

ln(y(t)) = ln(a) + bt

Now, we can use the information given in the problem to solve for b. After 2 days, there are 200 files, so we can use the following equation to solve for b:

ln(200) = ln(a) + 2b

After 4 days, there are 400 files, so we can use the following equation to solve for b:

ln(400) = ln(a) + 4b

We can solve this system of equations using elimination method. Subtracting the first equation from the second equation gives:

ln(400) - ln(200) = 4b - 2b

ln(2) = 2b

b = ln(2)/2

Now that we have found the value of b, we can plug it back into one of the original equations to solve for a. Let's use the equation for 2 days:

ln(200) = ln(a) + 2b

ln(200) = ln(a) + 2(ln(2)/2)

ln(200) = ln(a) + ln(2)

ln(200) - ln(2) = ln(a)

ln(100) = ln(a)

a = 100

So now we have the values of a and b, and we can use them to find the number of files after 6 days:

y(6) = 100e(ln(2)/2)(6)

y(6) = 100e(3ln(2))

y(6) = 100e(3 * 0.693)

y(6) = 100e2.079

y(6) = 691.6

Therefore, after 6 days, there will be approximately 691.6 files.

There are 691.6 flies after 6 days.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

y(1) = a\(e^{bt}\)

Now,

200 = a\(e^{2b}\)

Taking logs on both sides.

log 200 = log a + 2b log e

log 200 = log a + 2b _____(1)

Now,

400 = a\(e^{4b}\)

Taking logs on both sides.

log 400 = log a + 4b log e

log 400 = log a + 4b ______(2)

From (1) and (2) we get,

log 400 - log 200 = log a + 4b - log a  - 2b

log (400/200) = 4b - 2b

log 2 = 2b

b = log 2 / 2 _____(3)

Now,

Putting (3) in (1) we get,

log 200 = log a + 2 x log 2 / 2

log 200 = log a + log2

200 = 2a

a = 100

Now,

y(t) = 100 \(e^{(log2/2)t\)

Now,

t = 6

y(60) = 100 \(e^{log2/2 \times6}\)

y(60) = 100 \(e^{3log2}\)

y(60) = 100 \(e^{3\times0.69}\)

y(60) = 100 \(e^{2.079}\)

y(6) = 691.6

Thus,

There are 691.6 flies.

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The correct answer to the question is (D) 2, indicating that the expansion contains terms up to the second power of \((x - 1)\).

The expansion you have provided for \(f(x) = \ln(x)\) at \(x_0 = 1\) is incorrect. The correct expansion for \(\ln(x)\) using the Maclaurin series is:

\(\ln(x) = (x - 1) - \frac{(x - 1)^2}{2} + \frac{(x - 1)^3}{3} - \frac{(x - 1)^4}{4} + \dots\)

This expansion is obtained by substituting \(x - 1\) for \(x\) in the series expansion of \(\ln(x)\) around \(x_0 = 0\).

From the given expansion, we can see that there are terms involving powers of \((x - 1)\) up to the fourth power. Therefore, the correct answer to the question is (D) 2, indicating that the expansion contains terms up to the second power of \((x - 1)\).

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The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.

Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:

Volume = Length * Width * Height

Using the given measurements:

Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches

To simplify the calculation, we can convert the mixed numbers to improper fractions:

Volume = (21/2) inches * (61/2) inches * (129/4) inches

Next, we multiply the fractions:

Volume = (21/2) * (61/2) * (129/4) = 17289/8

The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:

Volume = 2161 1/8 in³.

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The simplified expression is 2x² + 8x - 1.

Let's simplify the expression step by step:

9x² - (x²+8-x(x-(7x-8)])+7

First, let's simplify the innermost parentheses:

(x-(7x-8)) = x - 7x + 8 = -6x + 8

Now, let's substitute this simplified expression back into the original expression:

9x² - (x²+8-x(-6x+8))+7

Next, distribute the negative sign to all terms inside the parentheses:

9x² - (x²+8+6x²-8x) + 7

Combine like terms inside the parentheses:

9x² - (7x² - 8x + 8) + 7

Remove the parentheses and distribute the negative sign to all terms inside:

9x² - 7x² + 8x - 8 + 7

Combine like terms:

(9x² - 7x²) + (8x - 8) + 7

Simplify further:

2x² + 8x - 1

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Answer:

1/6

Step-by-step explanation:

There are 6 large squares here, all of which have been shaded but for one.

Thus, the desired fraction is 1/6.

Answer:

11/15

Step-by-step explanation:

create a proportion

2 1/5 = 11/5

1/3 times 11/5 = 11/15

The sales tax rate in Sacramento, California is 8.5%

sales tax can be found using the formula:

sales tax = Tax / Subtotal x 100%

Solving gives:

sales tax = 0.85 / 10 x 100%

sales tax = 8.5%

In conclusion, the sales tax rate is 8.5%.

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Charge q is 1 unit of distance away from the source charge S. Charge p is two times further away. The force exerted between S and q is _____ the force exerted between S and p

a. 1/2

b. 2 times

c. 1/4

d. 4 times

Answer:

4 times

Step-by-step explanation:

Given the following :

Distance between q and S (r) = 1 unit

Distance between P and S (r) = 2 × 1 unit = 2

According to coliumbs law:

F = Ke(q1q2) /r^2

Where F = electrostatic force, Ke = coloumbs constant

q1,q2 = charges, r = distance between two charges

For q and S :

Fsq = Ke(q1q2) / 1^2

Fsq = Ke(q1q2) - - - - - equation 1

For P and S :

Fsp = Ke(q1q2) / 2^2

Fsp = Ke(q1q2) / 4 - - - - - equation 2

Dibiding equation 1 by equation 2

Fsq/Fsp = Ke(q1q2) / Ke(q1q2)/4

Fsq / Fsp = Ke(q1q2) × 4 / Ke(q1q2)

Fsq / Fsp = 4 / 1

Using cross multiplication

Therefore, Fsq = 4 × Fsp

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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Answer:

The number 3 in 63,297 is different then the 3 in 60,326 because the 3 in 63,297 is in the thousands place which is greater than the 3 in 60,326 because its in the hundreds place