The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone.

Answer:

no A

Step-by-step explanation:

sqrt13 is the ans

hope it helps

Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

9514 1404 393

Answer:

  t ≤ 4.5

Step-by-step explanation:

If we let t represent the time (in minutes) the speech will last, and we assume it is unlikely to be longer than 4 1/2 minutes, we have ...

  t ≤ 4.5                                                                                                                                                    

The cournot theory of oligopoly is based on the assumption that each firm believes that rivals will keep their output constant if it changes its output.

The Cournot theory of oligopoly is an economic model that analyzes the behavior of firms in an oligopolistic market structure. It is named after the French economist Antoine Augustin Cournot.

In the Cournot model, each firm in the market assumes that its rivals will keep their output constant if it changes its own output. This assumption is based on the idea that firms make strategic decisions regarding their production levels, taking into account the likely responses of their competitors.

Under the Cournot model, firms choose their output levels simultaneously, considering the current market conditions and their expectations of how their competitors will react. Each firm acts as a quantity-setter, determining its production quantity based on its own cost structure, market demand, and beliefs about how its rivals will behave.

The assumption that rivals will keep their output constant if one firm changes its output is a simplification used in the Cournot model. It implies that firms do not engage in immediate or aggressive reactions to changes in their competitors' output levels. Instead, they make decisions based on the expectation that their rivals' production decisions will remain unchanged.

By making these assumptions, the Cournot model allows economists to analyze the equilibrium outcomes and market shares that arise in oligopolistic markets. It provides insights into how firms' interdependent behavior affects prices, quantities, and overall market outcomes.

It is important to note that the Cournot model is a simplified representation of real-world oligopoly markets, and the actual behavior of firms may deviate from these assumptions. Nonetheless, the model serves as a useful tool for understanding strategic interactions among firms in oligopolistic industries.

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The interior solution is x₁ = 4 and x₂ = 10. This means that Ambrose would buy 4 units of nuts and 10 units of berries to achieve utility maximization. The corner solutions are x₁ = 0 and x₂ = 12 (buying only berries) and x₁ = 16 and x₂ = 0 (buying only nuts).

Ambrose can achieve utility maximization by choosing any of these combinations based on his preferences and budget constraints.

To find the optimal consumption of nuts and berries for Ambrose, we can set up the LaGrange function and solve the associated equations. The LaGrange function for this utility maximization problem is given by:

L (x₁, x₂, λ) = 4√(x1) + x₂ - λ(1x₁ + 2x2 - 24)

Where λ is the Lagrange multiplier associated with the budget constraint.

Now, let's find the first-order conditions for maximization:

1. ∂L/∂x1 = 2/√(x₁) - λ = 0

2. ∂L/∂x2 = 1 - 2λ = 0

3. ∂L/∂λ = 1x1 + 2x2 - 24 = 0

Solving the first two equations for x₁ and x₂:

1. 2/√(x1) = λ(Equation 1)

2. 1 = 2λ  (Equation 2)

Now, we can find the value of λ from Equation 2:

λ = 1/2

Substitute the value of λ into Equation 1:

2/√(x₁) = 1/2

Now, solve for x1:

√(x1) = 2

x₁ = 4

Now that we have x₁, we can find x₂ using the budget constraint:

1x1 + 2x2 = 24

1(4) + 2x2 = 24

2x2 = 20

x₂ = 10

So, the interior solution is x₁ = 4 and x₂ = 10. This means that Ambrose would buy 4 units of nuts and 10 units of berries to achieve utility maximization.

It seems there is a mistake in your initial calculation. The solution should be x₁ = 4 and x₂ = 10 for the interior solution.

Let's verify the corner solutions to make sure there are no other optimal points:

1. x₁= 0 (buying no nuts) and x₂ = 12 (spending the entire income on berries):

U (0, 12) = 4√ (0) + 12 = 12

Budget constraint: 1(0) + 2(12) = 24 (satisfied)

2. x₁ = 16 (spending the entire income on nuts) and x₂ = 0 (buying no berries):

U (16, 0) = 4√ (16) + 0 = 4 * 4 + 0 = 16

Budget constraint: 1(16) + 2(0) = 16 (satisfied)

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Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario. The formula is given to be:

where f is the number of times the data occurred and n is the total number of observations.

We have the frequency of the individual groups as shown below:

The total number of observations is 19.

Therefore, the relative frequencies are calculated below:

ANSWER

T

Answer:

1. 11

2. 20

3. 34

4. 12.6

5. 18

6. 105

Step-by-step explanation:

We are told that ---> t = 0, x = 1.5, y = 6, and z = 23

1. y + 5

= 6 + 5

= 11

2. z - 2x

= 23 - 2(1.5)

= 23 - 3

= 20

3. 2z - 2y

= 2(23) - 2(6)

= 46 - 12

= 34

4. 2.6y - 2x

= 2.6(6) - 2(1.5)

= 15.6 - 3

= 12.6

5. 4(y - x)

= 4(6 -  1.5)

= 24 - 6

= 18

6. 4(2 + z) + 5

= 4(2 + 23) + 5

= 8 + 92 + 5

= 105

Answer: hi thanks for the five

Step-by-step explanation:

Answer:

Let x = the cost of a movie

Let y = the cost of a game

Using these variables, we can set up equations.

3x + 5y = 42 eq1

9x + 7y = 72 eq2

We have here a system of equations, where we have two or more equations with two or more different variables. We use the elimination method to solve for the variables.

Multiply eq1 by 3. Keep eq2.

9x + 15y = 126 eq1

9x + 7y = 72 eq2

Subtract eq2 from eq1 to eliminate the x terms.

8y = 54

y = 6.75

This rental cost of one video game is $6.7

Substitute the value of y into eq1 to solve for x. This will give you the rental cost of one movie.

Step-by-step explanation:

pa brainly po

The cost of movie is $4.5 and cost of video game is $5.75.

Two or more expressions with an Equal sign is called as Equation.

Let x be the cost of movie and y be the cost of video game

Calvin rents 3 movies and 2 video games and spends a total of $25.

3x+2y=25...(1)

Samantha rents 2 movies and 1 video game and spends a total of $14.75.

2x+y=14.75

y=14.75-2x..(2)

Substitute (2) in equation (1)

3x+2(14.75-2x)=25

3x+29.5 -4x=25

-x+29.5 = 25

Subtract 29.5 from both sides

-x=25-29.5

x=4.5

Now let us plug in x value in equation (2)

y=14.75-2(4.5)

y=5.75

Hence, the cost of movie is $4.5 and cost of video game is $5.75.

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Answer:

bhe ganyan din

akin

Step-by-step explanation:

please help us

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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Answer:

Solve for x

Step-by-step explanation:

Answer:

The distributive property states that you can "distribute" the contents of one parentheses into the other to find an answer.

Let's first break down the larger number in the second parentheses:

400 + 10 + 5.

Then, let's multiply all those numbers by 3.

400 x 3 = 1200. 10 x 3 = 30. 5 x 3 = 15.

Then add up all the numbers and you get 1245.

Answer:

1245

Step-by-step explanation:

400+10+5

400×3=1200. 10×3=30. 5×3=15

Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.

Pentagons is that are two-dimensional polygons having five sides and fifth angles. When we mix the Greek terms "penta" and "gon," which mean "five" and "angles," respectively, we have the word "pentagon."

Here, we know that a pentagonal prism has five rectangular sides in addition to two pentagonal bases at the top and bottom.

Pentagonal prisms are pentagon-shaped if we look at them from the bottom.

When viewed from the side, a pentagonal prism would have a rectangular shape.

If we were to look at the pentagonal prism from the front, it would appear rectangular.

Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.

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On solving the provided question, we can say that In triangle DBC and BDA, So, By SSS, △DBC ≅ △BDA

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

In triangle DBC and BDA

BD = BD ( common base)

AB = CD

AD = BC

So, By SSS,

△DBC ≅ △BDA

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Answer:

64? I'm not sure but because if 1= girls (8 girls) and boys is 8 times more you do 8x8 I think sorry if I'm wrong

Answer:

There are 64 boys

Step-by-step explanation:

If there are 8 girls it would be 8*1

so you would have to multiply 8 by the ratio of boys which is 8*8

which equals 64 boys to 8 girls (8:1)

Your welcome

The area of the region inside the rectangle that surrounds the square is 147 square in.

The side of square is 10 in

Area of square is = side x side

A = 10 x 10

A = 100 square in.

Therefore, Area of square  is 100

The length of rectangle is 19 in and width of rectangle is 13in

area of rectangle  = l x w

A = 19 x 13

A = 247 square in.

Area of rectangle is 247 square in.

To calculate area of the region inside the rectangle that surrounds the square,

= A[rectangle] - A[square]

= 247 - 100

= 147 square in.

Therefore, The area of the region inside the rectangle that surrounds the square is 147 square in.

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Answer: 1.45 is a growth factor.

Step-by-step explanation:

Exponential growth function: \(y=Ab^x\), where A = initial value , b = growth factor (if b>1)

Here, The expression \(6.7\cdot(1.45)^t\) models the number of billions of genetic sequence bases available in the public database of the Whole Genome Shotgun project t years since 2002.

Here, b=1.45 >1

Thus,1.45 is a growth factor.

The probability of winning at least one award is 1 - 0.2373 = 0.7627 or 76.27%.

If the probability of winning an MTV music award after being nominated is 25%, the probability of not winning is 75%. Thus, the probability of not winning any of the five awards is (0.75)^5 = 0.2373.

As for how many awards Ariana Grande should expect to win, we can use the expected value formula: E(x) = n * p, where n is the number of trials (in this case, 5) and p is the probability of success (0.25). Therefore, E(x) = 5 * 0.25 = 1.25. So, Ariana Grande can expect to win about 1 award.

Finally, to calculate the standard deviation associated with this probability, we can use the formula: σ = sqrt(n * p * (1-p)). Plugging in the values, we get σ = sqrt(5 * 0.25 * 0.75) = 0.866. Therefore, the standard deviation associated with this probability is approximately 0.866.

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The probability that all the marbles drawn are red is 1 in 1428, or approximately 0.0007 (rounded to four decimal places).

To calculate the probability of drawing all red marbles from a bag containing 6 red marbles, 6 white marbles, and 6 blue marbles, without replacement, we can use the concept of combinations. The probability is determined by dividing the number of ways to draw 5 red marbles out of the 6 available by the total number of ways to draw 5 marbles out of the 18 total marbles in the bag.

The total number of ways to draw 5 marbles out of 18 without replacement is given by the combination formula C(18, 5) = 18! / (5! * (18-5)!), which equals 8568.

The number of ways to draw 5 red marbles out of the 6 available is given by C(6, 5) = 6! / (5! * (6-5)!), which equals 6.

Therefore, the probability of drawing all red marbles is 6 / 8568, which simplifies to 1 / 1428.

Hence, the probability that all the marbles drawn are red is 1 in 1428, or approximately 0.0007 (rounded to four decimal places).


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The absolute value of the error in the instructor's estimate is 0.644.

To find the absolute value of the error in the instructor's estimate, we need to calculate the difference between the sample mean and the population mean.

Given:

Population mean (μ) = 3.15

Sample mean (\(\bar{X}\)) = (3.89 + 4.00 + 3.85 + 3.77 + 3.81 + 3.43 + 3.28 + 3.27 + 3.56 + 3.92) / 10

= 36.78/10

= 3.678

Absolute value of the error = |\(\bar{X}\) - μ|

|\(\bar{X}\) - μ| = |3.678 - 3.15| = 0.528

Therefore, the absolute value of the error in the instructor's estimate is 0.644.

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The domain of the function f(x, y) = ln(6 − x^2 − 5y^2) is the set of all (x, y) pairs such that 6 − x^2 − 5y^2 is positive.

The natural logarithmic function ln is defined only for positive arguments. Therefore, for f(x, y) = ln(6 − x^2 − 5y^2) to be defined, the argument 6 − x^2 − 5y^2 must be positive.

To find the domain of the function, we solve the inequality:

6 − x^2 − 5y^2 > 0

Rearranging, we get:

x^2 + 5y^2 < 6

This is the equation of an ellipse centered at the origin with semi-axes lengths a = √6 and b = √(6/5). Therefore, the domain of f(x, y) is the interior of this ellipse. That is, the set of all (x, y) pairs such that x^2 + 5y^2 is less than 6. In interval notation, this can be written as:

{(x, y) | x^2 + 5y^2 < 6}

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Answer:

D) L+S=9 ; 6L+3S=9

Step-by-step explanation:

Given this information, we know that the total number of large and small Ubers must be 9, so we can eliminate choices A and C as the first part of the system of equations is L+S=9

Also, since the large Ubers can fit only 6 people per vehicle and the small Ubers can only fit 3 people per vehicle, then we can eliminate choice B as the second part of the system of equations is 6L+3S=39

Therefore, the only correct choice is D

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

In this scenario, "p" represents the proportion of defective circuits in the shipments. To test these hypotheses, the manufacturer collected a random sample of 300 circuits and found 28 defective ones.

Null hypothesis: The proportion of defective circuits is equal to or less than 5%. (H0: p <= 0.05)

Alternative hypothesis: The proportion of defective circuits is greater than 5%. (Ha: p > 0.05)

Calculation of the test statistic: z = (x - np) / sqrt(np(1-p)), where x = 28 (number of defective circuits), n = 300 (sample size), and p = 0.05 (null hypothesis proportion)

Calculation of the p-value: p-value = P(Z > z), where Z is the standard normal distribution

Decision rule: Reject the null hypothesis if the p-value is less than the significance level (alpha), typically 0.05 or 0.01.
Conclusion: Based on the sample of 300 circuits and the calculated test statistic and p-value, we either reject or fail to reject the null hypothesis, and make a conclusion about whether the manufacturer's claim is supported or not.


In this scenario, "p" represents the proportion of defective circuits in the shipments. To test these hypotheses, the manufacturer collected a random sample of 300 circuits and found 28 defective ones.

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According to the liquidity preference hypothesis, the expected forward rate in the third year when ∆ is 1% is 12.18%, and the yield to maturity on a three-year zero-coupon bond is 10.35%.

According to the liquidity preference hypothesis, the interest rate for a long-term investment is expected to be equal to the average short-term interest rate over the investment period. In this case, the expected forward rate for the third year is stated as 4.28%.

To calculate the expected forward rate for the third year, we first need to calculate the prices of zero-coupon bonds for each year. Let's start by calculating the price of a four-year zero-coupon bond, which is determined to be $731.74.

The rate of return on a four-year zero-coupon bond is then calculated as follows:

Rate of return = (1000 - 731.74) / 731.74 = 0.3661 = 36.61%.

Next, we use the yield of the four-year zero-coupon bond to calculate the price of a three-year zero-coupon bond, which is found to be $526.64.

The expected rate in the third year can be calculated using the formula:

Expected forward rate for year 3 = (Price of 1-year bond) / (Price of 2-year bond) - 1

By substituting the values, we find:

Expected forward rate for year 3 = ($959.63 / $865.20) - 1 = 0.1088 or 10.88%

If ∆ (delta) is 1%, we can calculate the expected forward rate in the third year as follows:

Expected forward rate for year 3 = (1 + 0.1088) × (1 + 0.01) - 1 = 0.1218 or 12.18%

Therefore, according to the liquidity preference hypothesis, the expected forward rate in the third year, when ∆ is 1%, is 12.18%.

Additionally, the yield to maturity on a three-year zero-coupon bond can be calculated using the formula:

Yield to maturity = (1000 / Price of bond)^(1/n) - 1

Substituting the values, we find:

Yield to maturity = (1000 / $526.64)^(1/3) - 1 = 0.1035 or 10.35%

Hence, the yield to maturity on a three-year zero-coupon bond is 10.35%.

In conclusion, according to the liquidity preference hypothesis, the expected forward rate in the third year when ∆ is 1% is 12.18%, and the yield to maturity on a three-year zero-coupon bond is 10.35%.

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When they work 8 hours, both Jonny and Clara will be paid the same amount of $140.

Let's represent the number of hours worked as 'x'

Total earnings for the first job = (Hourly wage * Number of hours worked) + Bonus

= (10 * x) + 60

Total earnings for the second job = (Hourly wage * Number of hours worked) + Bonus

= (15 * x) + 20

To find the number of hours at which they will be paid the same amount, we can set the two equations equal to each other and solve for 'x':

(10 * x) + 60 = (15 * x) + 20

Now, we can solve the equation:

10x + 60 = 15x + 20

60 - 20 = 15x - 10x

40 = 5x

x = 40/5

x = 8

Total earnings for the first job = (10 * 8) + 60 = $140

Total earnings for the second job = (15 * 8) + 20 = $140

Thus, when they work 8 hours, both Jonny and Clara will be paid the same amount of $140.

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Answer:.35,38% 3/5

Step-by-step explanation:Hope this helped

Answer: 0.35, 38% , 3/5

Step-by-step explanation:

3/5= 0.6= 0.60

38%= 0.38

0.35

Answer:

common fraction is written in the form of two whole numbers, one above the ... For example 3/7 would be 3 divided by 7 = 0.428 571 .