A shopkeeper has 2,625 markers. He would like to pack 25 markers in each box. How many boxes will he need?

Answer:

10=x

Step-by-step explanation:

Intersecting Chords Formula:(segment piece) x (segment piece) =

       (segment piece) x (segment piece)

6*5 = 3*x

30 = 3x

Divide by 3

30/3 = 3x/3

10 =x

Answer:

10 paces East

Step-by-step explanation:

East 20 and West 25 and East 15 = 10 East

10 north and 10 south cancel each other out

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its Denominator, or to eliminate denominators from a radical expression.

To rationalize the denominator 1/7 + 3√2,

A rational number is a number that can be expressed as a ratio of two integers, with the denominator not equal to zero. The fraction 4/5, for example, is a rational number since it can be expressed as 4 divided by 5.

Step-by-Step SolutionTo rationalizes the denominator 1/7 + 3√2, we'll need to follow these steps.

Step 1: First, we need to create a common denominator for the two terms. The common denominator is 7. Thus, we can convert the expression to the following form:(1/7) + (3√2 × 7)/(7 × 3√2).

Step 2: Simplify the denominator to 7. (1/7) + (21√2)/(21 × 3√2).

Step 3: The numerator and denominator can now be simplified. (1 + 21√2)/(7 × 3√2).Step 4: Simplify further. (1 + 21√2)/(21√2).We have successfully rationalized the denominator!

The final answer is (1 + 21√2)/(21√2).

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its denominator, or to eliminate denominators from a radical expression.

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Answer:

What the heII happened? aight nvm It's function

Step-by-step explanation:

my old answer got deleted ;(

Answer:

749.1m

Step-by-step explanation:

Hope this helped!

When dividing the same dividend by 0.1 and 0.01, the quotient obtained by dividing by 0.1 is greater than the quotient obtained by dividing by 0.01. This is because dividing by a smaller decimal results in larger parts

The quotient obtained by dividing the same dividend by 0.1 and 0.01 can be compared by understanding the concept of dividing by decimals.

Let's say the dividend is 10. When we divide 10 by 0.1, we are essentially dividing it by 1/10 or 1 ÷ 10. This means we are dividing 10 into 10 equal parts. Each part would be 1, so the quotient is 1.

When we divide 10 by 0.01, we are dividing it by 1/100 or 1 ÷ 100. This means we are dividing 10 into 100 equal parts. Each part would be 0.1, so the quotient is 0.1.

Comparing the two quotients, we can see that 1 is greater than 0.1. This is because dividing by a smaller decimal results in a larger quotient. In other words, dividing by 0.01 gives smaller parts than dividing by 0.1.

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The volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base.

To find a formula for the volume of the box with surface area A and square base with side x, we first need to find the height of the box. Since the box has a square base, the area of the base is x^2. The remaining surface area is the sum of the areas of the four sides, each of which is a rectangle with base x and height h. Therefore, the surface area A is given by:

A = x^2 + 4xh

Solving for h, we get:

h = (A - x^2) / 4x

The volume V of the box is given by:

V = x^2 * h

Substituting the expression for h, we get:

V = x^2 * (A - x^2) / 4x

Simplifying, we get:

V = (Ax^2 - x^4) / 4

The domain of V is all non-negative real numbers, since both x^2 and A are non-negative.

To graph V as a function of x, we can use a graphing calculator or plot points using a table of values. The graph will be a parabola opening downwards, with x-intercepts at 0 and sqrt(A) and a maximum at x = sqrt(A) / sqrt(2).

To find the maximum value of V, we can take the derivative of V with respect to x and set it equal to 0:

dV/dx = (2Ax - 4x^3) / 4

Setting this equal to 0 and solving for x, we get:

x = sqrt(A) / sqrt(2)

Plugging this value of x into the formula for V, we get:

V = A^1.5 / (4sqrt(2))

Therefore, the maximum value of V is A^1.5 / (4sqrt(2)).

To find the formula for the volume of a box having surface area 10, we simply replace A with 10 in the formula we derived earlier:

V = (10x^2 - x^4) / 4

Simplifying, we get:

V = 2.5x^2 - 0.25x^4

Therefore, the volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base. The domain of V is all non-negative real numbers.

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we have

15!12!(4−1)!

15!12!(3!)=3,758,268,687,305,932,800,000

therefore

the answer is

The rates for the following term in the year a, is \(365\), part b, is \(189\), part c's difference is unclear, and part d's rate for the final term is \(123\).

A term is the name given to each integer in a series. A series has a place for each phrase. Think about the order, for instance Each number in the series is referred to as a word.

The nth term formula, where stood for the term number, can be used to locate any term in a series. Formulas: An arithmetic sequence's nth term is represented by the formula: a n = a + n - 1 d, where is the first word and is a clear differentiation.

(a) To find the rate for the next term in the sequence \(2, 5, 14, 41, 122\)

\(122 + 3(81) = 365\)

The next term in the sequence is \(365\).

(b) To find the rate for the next term in the sequence \(1, 5, 13, 29, 61\)

\(61 + 4(32) = 189\)

So the next term in the sequence is \(189\).

(c) To find the rate for the next term in the sequence \(1, 212, 34, 78, 166\)  the differences between consecutive terms are not following a clear pattern. Therefore, we cannot determine the rate for the next term with the information given.

(d) To find the rate for the next term in the sequence\(6, 9, 15, 27, 51\)

\(51 + 3(24) = 123\)

So the next term in the sequence is \(123\).

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Answer:

Step-by-step explanation:

Back

Area = L * W

L = 20

W = 8

Area = 20 * 8

Area =                                                                       160

2 Triangles

Area = 1/2 one smaller leg*other smaller leg

one smaller leg = 8

The other one = 15

Area = 1/2 8 * 15  =     60

But there are 2 of them 2 * 60 =                            120

Base

L =  20

W = 15

Area = L * W

Area = 20*15 =                                                        300

Front (slanted) Face

L = 20

W = 17

Area = L * W

Area =  20*17                                                         340

Total                                                                        920

The distance from the bottom of the flagpole to any point on the circular path is 40 meters.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since the path has a circumference of 250 meters, we can find the radius as follows:

C = 2πr

250 = 2πr

r = 250/(2π)

r ≈ 39.8

Therefore, we can also say that the distance from the bottom of the flagpole to any point on the b is the radius of the circle.

This is because the flagpole is at the center of the circle, and any point on the circle is at the same distance from the center.

So, if we were to walk around the circular path with a measuring tape, the tape would always read approximately 40 meters from the flagpole, no matter where we stopped on the path.

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The function of the vector field is f ( x , y , z ) = ( 1/2 )x² + (1/2)y² + (1/2)z²

Given data ,

Let the function be F = ∇f,

where F is the given vector field F(x, y, z) = xi + yj + zk, we need to find the components of the gradient of f, denoted as ∇f

Now , The gradient of f is given by ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Comparing the components of ∇f with the given components of F, we get the following equations

∂f/∂x = x

∂f/∂y = y

∂f/∂z = z

We can integrate each of these equations with respect to the respective variable to obtain f(x, y, z)

∫∂f/∂x dx = ∫x dx

f(x, y, z) = (1/2)x² + g(y, z)

∫∂f/∂y dy = ∫y dy

f(x, y, z) = ( 1/2 )x² + (1/2)y² + h(x, z)

∫∂f/∂z dz = ∫z dz

f(x, y, z) = ( 1/2 )x² + (1/2)y² + (1/2)z² + C

Now , the value of C is given by x = 0 , y = 0 and z = 0

So , C = 0

Hence , the function f(x, y, z) = ( 1/2 )x² + (1/2)y² + (1/2)z² is the desired function such that F = ∇f, and f(0, 0, 0) = 0

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I hope and useful for your help

The fee charged for the R 2, 500 withdrawal from TownBank would be R 33. 30.

To find the total fee charged to withdraw the sum of R 2, 500 from TownBank, the formula is :

= 3. 30 + R 1, 20 per R 100

The amount withdrawn was R 2, 500 so the total fee charged would be :

= 3. 30 + 1, 20 x ( 2, 500 / 100 )

= 3. 30 + 1. 20 x 25

= 3. 30 + 30

= 33. 30

= R 33. 30

In conclusion, the total fee charged was R 33. 30.

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First part of the question :

The TownBank current account charges R3,30 plus R1,20 per R100 or part thereof for a cash withdrawal from a TownBank ATM. The first five withdrawals in a month are free. Determine the bank charges for a withdrawal of:

490

472 <490<500

it fits the criteria

Answer:

70

Step-by-step explanation:

Answer:

∠T=70°

Step-by-step explanation:

360-110+(2×90)=70°

∠T=70°

To test a trading rule for statistically and economically significant alpha, follow these steps: gather data, formulate a hypothesis, measure performance, conduct statistical tests, assess economic significance, and perform robustness testing.


To determine if a trading rule generates a statistically and economically significant alpha, several steps can be followed. Alpha refers to the excess return generated by a trading strategy beyond what would be expected from market movements. Here's a summary of the testing process:

To test a trading rule's alpha, you can follow these steps:

1. Data Preparation: Gather historical price data for the assets being traded and any relevant market indices. Ensure the data is clean, consistent, and properly adjusted for dividends and corporate actions.

2. Hypothesis Formulation: Clearly define the trading rule being tested, specifying the entry and exit criteria. Formulate a null hypothesis assuming no alpha exists and an alternative hypothesis suggesting the presence of statistically and economically significant alpha.

3. Performance Measurement: Apply the trading rule to the historical price data and calculate the strategy's performance metrics, including returns, volatility, and risk-adjusted measures like the Sharpe ratio or information ratio.

4. Statistical Significance: Conduct hypothesis testing using appropriate statistical methods such as t-tests or regression analysis to determine if the strategy's excess returns are statistically significant. This helps assess whether the alpha is due to skill or randomness.

5. Economic Significance: Evaluate the economic significance of the alpha by considering transaction costs, liquidity constraints, and realistic trading scenarios. Adjust the returns for these factors to assess if the strategy generates meaningful profits after accounting for expenses.

6. Robustness Testing: Perform sensitivity analysis by varying key parameters of the trading rule and assessing the stability and consistency of the alpha. This helps determine if the strategy's performance is robust across different market conditions and time periods.

By following these steps, you can systematically evaluate a trading rule's alpha generation potential. Remember, it's important to consider statistical significance, economic significance, and robustness to draw meaningful conclusions about a trading strategy's effectiveness.

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Answer:

Diagram number 3 is not a function.

Step-by-step explanation:

It isn't a function because C goes to 2 different numbers.

Explanation:

For choice (3), the input C maps to more than one output (The values 1 and 3 at the same time). A function must have each input map to one and only one output. So this is why relation (3) is not a function.

The other answer choices (1), (2) and (4) have each input point to exactly one output. So these are functions that can be ruled out.

Answer:

x<2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Given

56 - 10x > 20 + 8x ( add 10x to both sides )

56 > 20 + 18x ( subtract 20 from both sides )

36 > 18x ( divide both sides by 18 )

2 > x , thus

x < 2 → D

Answer:

1) 2/5

2) 4/13

3) 1/8

4) 25/4 or 6 + 1/4

Step-by-step explanation:

1) 5/2 * x = 1

x = 1 / (5/2)

x = 2/5

2) (3 + 1/4) * x = 1

13/4 * x = 1

x = 1 / (13/4)

x = 4/13

3) 8 * x = 1

x = 1/8

4) (2/5)^2 * x = 1

2^2 / 5^2 * x = 1

4/25 * x = 1

x = 1 / (4/25)

x = 25/4

x = 6 + 1/4

The two ways to generate fractions equivalent to a given fraction include:

A Multiply the numerator by a nonzero number or divide the denominator by a nonzero number.

B..Multiply or divide the numerator and denominator by the same nonzero number.

It should be noted that equivalent fractions simply means the fractions that are the same when reduced to their lowest terms.

It should be noted that multiplying the numerator by a nonzero number or divide the denominator by a nonzero number as.also.doung the same for the numerator and denominator by the same nonzero number will given an equivalent fraction.

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Answer:

\(Volume = 1017.36\ in^3\) -- Cone

\(Volume = 3052.08\ in^3\) -- Cylinder

\(Volume = 3052.08\ in^3\) -- Sphere

Best Buy: Sphere Clay

Step-by-step explanation:

Given

Solid Shapes: Cone, Cylinder, Sphere

Cost of Cone Clay = $12

Cost of Cylinder Clay = $30

Cost of Sphere Clay = $28

Required

Determine the volume of each shape

Which is the best buy

The volume of a cone is calculated as thus;

\(Volume = \frac{1}{3}\pi r^2h\)

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and \(\pi = 3.14\)

Substitute these values in the above formula;

\(Volume = \frac{1}{3} * 3.14 * 9^2 * 12\)

\(Volume = \frac{3052.08}{3}\)

\(Volume = 1017.36\ in^3\)

The unit cost of the cone is calculated as thus;

\(Volume:Price = \frac{Volume}{Total\ Cost}\)

Where

\(Volume = 1017.36\ in^3\)

\(Total\ Cost = \$12\) (Given)

\(Volume:Price = \frac{1017.36\ in^3}{\$ 12}\)

\(Volume:Price = 84.78 in^3/\$\)

\(Volume:Price = 84.78 in^3:\$1\)

The volume of a cylinder is calculated as thus;

\(Volume = \pi r^2h\)

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and \(\pi = 3.14\)

Substitute these values in the above formula;

\(Volume = 3.14 * 9^2 * 12\)

\(Volume = 3052.08\ in^3\)

The unit cost of the cone is calculated as thus;

\(Volume:Price = \frac{Volume}{Total\ Cost}\)

Where

\(Volume = 3052.08\ in^3\)

\(Total\ Cost = \$30\) (Given)

\(Volume:Price = \frac{3052.08\ in^3}{\$ 30}\)

\(Volume:Price = 101.736\ in^3/\$\)

\(Volume:Price = 101.736\ in^3:\$1\)

The volume of a sphereis calculated as thus;

\(Volume = \frac{4}{3}\pi r^3\)

From the attached diagram

Radius, r = 9 inches; and \(\pi = 3.14\)

Substitute these values in the above formula;

\(Volume = \frac{4}{3} * 3.14 * 9^3\)

\(Volume = \frac{9156.24}{3}\)

\(Volume = 3052.08\ in^3\)

The unit cost of the cone is calculated as thus;

\(Volume:Price = \frac{Volume}{Total\ Cost}\)

Where

\(Volume = 3052.08\ in^3\)

\(Total\ Cost = \$28\) (Given)

\(Volume:Price = \frac{3052.08\ in^3}{\$ 28}\)

\(Volume:Price = 109.003\ in^3/\$\)

\(Volume:Price = 109.003\ in^3:\$1\)

Comparing the Volume:Price ratio of the three clay;

The best buy is the sphere because it has the highest volume:price ratio.

Having the highest volume:price ratio means that with $1, one can get more clay from the sphere compared to other types of clay

it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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Answer: its (4f 5) ^3

Step-by-step explanation:

4 1/6 + 8 3/4 =  12.9166666667

I don't know math honestly

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

Answer:7

Step-by-step explanation:

To find the median you need to first put the number in order from least to greatest this would be 2, 4 ,5, 7, 7, 7, 8

next you have to find the number in the middle

That is your median, 7 is your median.