Answers and Explain

Answer:

42

Step-by-step explanation:

1 dozen equals 12 so 12 x 4 would be 42

Answer:

27 cubic meters

Step-by-step explanation:

For square, length and width is same.

3x3 = 9 square meters

3x3x3 = 27 cubic meters

Volume of a cube = length · width · height, or:

Volume of a cube = length³

We know that a cube is made up of 6 squares, so if the area of one of the squares is 9, we can take the square root to find the sides:

√9 = ±3

(and in this case, you can't have negative measurements, so it's positive.)

Now, all we have to do is cube the side length, so:

3³ = 27.

If you have any questions, feel free to ask! :)

Answer:

\(\text{C. }x^2+(y+3)^2=11\)

Step-by-step explanation:

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

\((x-h)^2+(y-k)^2=r^2\).

What we're given:

Substituting given values, we get:

\((x-0)^2+(y-(-3))^2=\sqrt{11}^2,\\\boxed{\text{C. }x^2+(y+3)^2=11}\)

Answer:

Equation for Leandro: y=0.3x+8.95

Equation for Tina: y=0.25x+8.95

The slope is not the same, because in this equation, the coefficient of the x (the number right before the "x") isn't the same. 0.3 does not equal 0.25.

However, the y-intercept is the same, as for both equations it is 8.95.

From this, we can see that there is only one solution, at the y-intercept of  (0,8.95).

Let me know if this helps!

To answer this question, we need to perform a hypothesis test with the following null and alternative hypotheses:

- Null hypothesis: The true population mean teaching salary in the metro Atlanta area is equal to the average teaching salary in Georgia, i.e., μ = $48,553.

- Alternative hypothesis: The true population mean teaching salary in the metro Atlanta area is greater than the average teaching salary in Georgia, i.e., μ > $48,553.

We can use a one-sample t-test since we have a sample mean, sample standard deviation, and a sample size of n = 228. We can use a significance level of α = 0.05.

The test statistic for the t-test can be calculated as:

t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))

t = (49,021 - 48,553) / (3,127 / sqrt(228))

t = 4.65

Using a t-distribution table with 227 degrees of freedom (n-1), we can find the critical value for a one-tailed test with α = 0.05, which is 1.645.

Since the calculated t-value of 4.65 is greater than the critical value of 1.645, we reject the null hypothesis.

This means that we have statistically significant evidence to conclude that the true population mean teaching salary in the metro Atlanta area is greater than the average teaching salary in Georgia.

In other words, the school districts in the metro Atlanta area do pay their teachers more than the state average.

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Answer:

680x + 170

Step-by-step explanation:

calculate the product

4\(x\) x170 +170=

680x+ 170

Answer:

When 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.

Step-by-step explanation:

The Least Common Multiple ( LCM )

The LCM of two integers a,b is the smallest positive integer that is evenly divisible by both a and b.

For example:

LCM(20,8)=40

LCM(35,18)=630

Since Tom, Sam, and Matt are counting drum beats at their own frequency, we must find the least common multiple of all their beats frequency.

Find the LCM of 4,10,12. Follow this procedure:

List prime factorization of all the numbers:

4 = 2*2

10 = 2*5

12 = 2*2*3

Multiply all the factors the greatest times they occur:

LCM=2*2*3*5=60

Thus, when 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.

Answer:

Nearest Whole Number: 9

Step-by-step explanation:

Answer:

im guessing it would just be 9

Step-by-step explanation:

because its 1 out of three so that leaves two so its closest to 9

Answer:

Step-by-step explanation:

He has $500 to start with, and he takes $25 out of the account each week. But he wants more than 200 in his account by the end of summer. 25 goes into 500 20 times. But if he wanted more than 200 left, like 300-400, he could spend 4 week's worth of money to have 400 left, or 8 weeks to have 300 left. This is the best-case scenario.

The compound inequality given is "and" inequality.

Compound inequalities are inequalities which consist of more than two expressions connected with two or more inequality signs.

Compound inequality can be divided into two or more simple inequalities.

"And" inequalities are those compound inequalities where both the inequalities need to be true for the statement to be true.

"Or" inequality needs only any one of them true.

Given inequality is,

6 > x + 1 > 3

Subtracting 1 throughout,

5 > x > 2

Here x lies between 2 and 5 where x > 2 and x < 5.

Hence this inequality is "and" inequality.

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Answer:

a is the right answer Congress passed the fair labor standards act to protect young workers

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Available-for-sale debt securities are financial instruments that a company holds for investment purposes but not necessarily for immediate resale.  On December 31, Carperk made a journal entry to record the fair value adjustment for their newly acquired portfolio of available-for-sale debt securities.

Available-for-sale debt securities are financial instruments that a company holds for investment purposes but not necessarily for immediate resale. Their fair value, which represents the market value of the securities, needs to be adjusted at the end of each reporting period. In this case, Carperk did not have any available-for-sale debt securities prior to this year, indicating that they acquired these securities during the current year.

To record the fair value adjustment for the portfolio of available-for-sale debt securities on December 31, Carperk would make the following journal entry:

Debit: Fair Value Adjustment (Income Statement)

Credit: Available-for-Sale Debt Securities (Balance Sheet)

The debit to the Fair Value Adjustment account represents the increase in fair value of the debt securities. This adjustment is reported in the income statement as a component of comprehensive income. On the other hand, the credit to the Available-for-Sale Debt Securities account reduces the carrying value of the securities on the balance sheet to reflect their new fair value. The difference between the previous carrying value and the adjusted fair value is recorded as a unrealized gain or loss in the comprehensive income section of the financial statements.

It is important to note that the specific amounts and accounts used in the journal entry would depend on the information provided, such as the fair value adjustment amount and the specific accounts used by Carperk for their available-for-sale debt securities.

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wanna see my archanine pokemon card

Answer: 3/6

Step-by-step explanation:

Calculation steps:

2

3

+

3

6

=  

2 × 2

3 × 2

+

3

6

=  

4

6

+

3

6

=  

4 + 3

6

=  

7

6

=  

1 1

6

To find the ut when u = xe−5t sin θ the value of ut = du/dt = -5xe^(-5t)sinθ

To find ut, we need to differentiate u with respect to t. Using the product rule of differentiation, we have:

u = x e^(-5t) sin θ

∂u/∂t = x (-5) e^(-5t) sin θ + x e^(-5t) cos θ ∂θ/∂t

     = -5x e^(-5t) sin θ + x e^(-5t) cos θ θ'

where θ' represents the derivative of θ with respect to t. Since we are not given any information about θ', we cannot evaluate the derivative any further. Therefore, our final answer for ut is:

ut = -5x e^(-5t) sin θ + x e^(-5t) cos θ θ'

Note that this expression depends on the value of θ'. If we had more information about θ', we could use it to evaluate the derivative more precisely.

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Complete Question

Find ut when 1. ut=5xe−5tsinθ u=xe−5tsinθ \

There are seven elements in the set S, which represents the total number of distinct numbers we can form using one or more of the digits.

To find out how many distinct numbers we can form using these digits, we need to consider all possible combinations of digits. We can use one, two, or all three digits to form a number.

If we use only one digit, we can form three distinct numbers: 2, 3, and 5.

If we use two digits, we can form three distinct two-digit numbers: 23, 25, and 35. We cannot form the number 32 because we do not have the digit 2 available twice.

If we use all three digits, we can form only one three-digit number: 235.

Therefore, in total, we can form 7 distinct numbers using one or more of the digits 2, 3, and 5.

Mathematically, we can represent the solution as follows:

Let S be the set of all distinct numbers we can form using one or more of the digits 2, 3, and 5.

Then, S = {2, 3, 5, 23, 25, 35, 235} = 7

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Answer:

I'm pretty sure 1 is verticle and 2 is complimentary

Step-by-step explanation:

a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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Answer:

A

Step-by-step explanation:

r = 5s

or

s = r/5

Answer:

A show proportional relationship

Step-by-step explanation:

hope that helps :))

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

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the expression 9y^5 - 10y^3 is a polynomial. Specifically, it is a polynomial of the fifth degree (or order) since the highest exponent of the variable y is 5.

A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication, but not division or negative exponents.

In the given expression, we have two terms: 9y^5 and -10y^3. Each term is a monomial (a single term) and can be written in the form of coefficient times variable raised to a non-negative integer exponent.

The coefficient of the first term is 9, and the variable is y raised to the power of 5. Similarly, the coefficient of the second term is -10, and the variable is y raised to the power of 3.

Both terms satisfy the criteria of a polynomial, and the expression can be simplified as:

9y^5 - 10y^3

Therefore, the expression 9y^5 - 10y^3 is a polynomial. Specifically, it is a polynomial of the fifth degree (or order) since the highest exponent of the variable y is 5.

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Answer: The answer is D

Answer:

x = -8 + sqrt(10) and x = -8 - sqrt(10)

Step-by-step explanation:

The quadratic equation to be solved is:

2(x + 8)² + 9 = 29

First, we need to simplify the left-hand side of the equation by expanding the squared term:

2(x + 8)(x + 8) + 9 = 29

Simplifying further, we get:

2(x² + 16x + 64) + 9 = 29

Distributing the 2, we get:

2x² + 32x + 128 + 9 = 29

Combining like terms, we get:

2x² + 32x + 137 = 29

Subtracting 29 from both sides, we get:

2x² + 32x + 108 = 0

Dividing both sides by 2, we get:

x² + 16x + 54 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula :

The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).

¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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The derivative of y = \(3ln(8/x)\) with respect to x is \(du/dx = -8/x^2.\)

To find the derivative of y with respect to x, we need to use the chain rule:

\(y = 3 In (8/x)\\y' = 3 * (d/dx) In (8/x)\)

Now we need to use the chain rule on In (8/x):

\((d/dx) In (8/x) = (1/(8/x)) * (-8/x^2)\)

Simplifying:

\((d/dx) In (8/x) = -1/x\)

Substituting back into y':

\(y' = 3 * (-1/x) = -3/x\)

For y=c In u, u is the argument of the natural logarithm in the expression c In u.

In other words,\(u = e^(y/c).\)

To find du/dx, we can use implicit differentiation:

\(u = e^(y/c)\)

Taking the natural logarithm of both sides:

In\(u = (1/c) * y\)

Differentiating both sides with respect to x:

\((d/dx) In u = (1/c) * (dy/dx)\)

Using the chain rule on the left side:

\((1/u) * (du/dx) = (1/c) * (dy/dx)\)

Solving for du/dx:

\(du/dx = (c/u) * dy/dx\)

Substituting u = e^(y/c) and multiplying by c/c:

\(du/dx = (c/e^(y/c)) * dy/dx = (c/u) * dy/dx\)

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