Reasoning A cylindrical water tank holds 26 litres when full. The water tank is 36 cm tall.
Work out the radius of the tank to 2 d.p.
(4 marks)

The null hypothesis for the single factor ANOVA states that all means are equally true.

The null hypothesis for a single-factor ANOVA (analysis of variance) states that all means are equal.

The alternative hypothesis, on the other hand, suggests that at least one of the means is different from the others.

The purpose of the ANOVA test is to determine whether there is sufficient evidence to reject the null hypothesis and conclude that there are significant differences between the means. A statistical formula used to compare variances across the means (or average) of different groups.

Hence, the statement is true .

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The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Answer:

Step-by-step explanation:

To multiply the binomials, use the distributive property of multiplication:

The equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is 2400.

To relate the flow of water from the 8-inch pipe to the flow of water from the 4-inch pipe, we can use the equation of continuity, which states that the product of the cross-sectional area of a pipe and the velocity of the fluid is constant.

Let's assume that the velocity of water flowing through the 8-inch pipe is V1 and the velocity of water flowing through the 4-inch pipe is V2. The cross-sectional area of the 8-inch pipe is A1 = π\((8/2)^2\) = 64π square inches, and the cross-sectional area of the 4-inch pipe is A2 = π\((4/2)^2\) = 4π square inches.

According to the equation of continuity, A1 * V1 = A2 * V2.

Substituting the given values, we have:

64π * V1 = 4π * V2

Simplifying, we get:

16V1 = V2

So, the equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is:

1600 * 16 = 2400

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The sum of the series s = ∑n=4^∞ 1/(n(n−1)) is 1/4.

To write the series s = ∑n=4^∞ 1/(n(n−1)) as a telescoping series, we need to manipulate the terms to cancel each other out and simplify the expression.

We can rewrite the series as:

s = ∑n=4^∞ (1/n - 1/(n-1))

Expanding the summation:

s = (1/4 - 1/3) + (1/5 - 1/4) + (1/6 - 1/5) + ...

Notice that the term -1/(n-1) in each subsequent term cancels out with the 1/n term in the next term, except for the first term (1/4 - 1/3).

We can simplify the expression by canceling out the terms:

s = 1/4 - 1/3 + 1/5 - 1/4 + 1/6 - 1/5 + ...

The consecutive terms cancel out, leaving only the first term:

s = 1/4

Therefore, the sum of the series s = ∑n=4^∞ 1/(n(n−1)) is 1/4.

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In perimeter, The cost to frame Joy's math certificate in a fancy frame is $138.00.

The dimensions of Joy's math certificate are 10 inches tall and 13 inches wide.

Joy wants to frame it in a fancy frame that costs $3.00 per inch.

To determine the total cost of framing the certificate, we need to find its perimeter and then multiply that by the cost per inch.

The perimeter of the certificate is:

Perimeter = 2 × (height + width)

Substituting the given values, we get:

Perimeter = 2 × (10 + 13)Perimeter = 46 inches

Therefore, the total cost of framing Joy's math certificate is:

Total cost = Perimeter × Cost per inch

Total cost = 46 × 3.00Total cost = $138.00

Thus, the cost to frame Joy's math certificate in a fancy frame is $138.00.

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Answer:

  ₹168 per hour

Step-by-step explanation:

The hourly rate at which Tamara is paid can be found by dividing her ₹1050 pay by the 6:15 hours that she worked.

We know there are 60 minutes in an hour, so the fraction of an hour represented by 15 minutes is ...

  (15 min)/(60 min/h) = (15/60) h = 1/4 h = 0.25 h

Added to the 6 whole hours Tamara worked, her pay is for 6.25 hours.

The pay per hour is found by dividing pay by hours.

  ₹1050/(6.25 h) = ₹168/h

Tamara's hourly rate of pay is ₹168 per hour.

The correct option is OA. y+4= -3(x-3). L 4.6.3 Test (CST): Linear Equations Solution: We are given that a line passes through (3,-4) and has a slope of -3.

We will use point slope form of line to obtain the equation of liney - y1 = m(x - x1).

Plugging in the values, we get,y - (-4) = -3(x - 3).

Simplifying the above expression, we get y + 4 = -3x + 9y = -3x + 9 - 4y = -3x + 5y = -3x + 5.

This equation is in slope intercept form of line where slope is -3 and y-intercept is 5.The above equation is not matching with any of the options given.

Let's try to put the equation in standard form of line,ax + by = c=> 3x + y = 5

Multiplying all the terms by -1,-3x - y = -5

We observe that option (A) satisfies the above equation of line, therefore correct option is OA. y+4= -3(x-3).

Thus, the correct option is OA. y+4= -3(x-3).

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a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

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To determine the number of ways that the letters of a word can be arranged in a row if two letters must remain next to each other, we can treat these two letters as a single unit. Therefore, the problem reduces to finding the number of ways to arrange this new "unit" and the remaining letters.

So, to answer the question directly, the number of ways that the letters of a word can be arranged in a row if two letters must remain next to each other is (n-1) x 2!
To solve this problem, we will treat the two letters that must remain next to each other as a single unit, and then find the total number of arrangements. Here's the step-by-step explanation:

1. Combine the two letters that must remain next to each other into a single unit. This will temporarily reduce the total number of items to arrange by one.

2. Count the total number of items (including the combined unit) that you need to arrange.

3. Calculate the factorial of the total number of items. This will give you a number of ways to arrange these items in a row.

4. Finally, since the two letters inside the combined unit can be arranged in two ways (either the first letter comes first or the second letter comes first), multiply the result from step 3 by 2.

By following these steps, you will get the total number of ways the letters of a word can be arranged in a row with the constraint that the two specified letters must remain next to each other.

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Answer:

p = \(\frac{q-7r}{9}\)

Step-by-step explanation:

Given

9p + 7r = q ( subtract 7r from both sides )

9p = q - 7r ( isolate p by dividing both sides by 9 )

p = \(\frac{q-7r}{9}\)

Answer: p = q - 7r   ÷    9

Answer:

Step-by-step explanation:

Answer:

C is correct

Step-by-step explanation:

I'm not sure what the substituting part has to do anything, but here is how I got the answer

4(x+x+7)-2x+8-4

4(2x+7)-2x+4

8x+28-2x+4

6x+32

Factor and you get

2(3x+16), which is answer choice C

You can check that the answer is right by plugging in x=1 and x=2 into the original equation and the answer choice, which may be what that is asking.

Answer:

\(\huge\boxed{P\approx267.75m}\)

Step-by-step explanation:

Look at the picture in the attachment.

x it's the quarter of  the circle with the radius r = 75m.

The formula of a circumference of a circle:

\(C=2\pi r\)

Therefore

\(x=\dfrac{1}{4}\cdot2\pi r=\dfrac{1}{2}\pi r\)

Substitute r = 75m:

\(x=\dfrac{1}{2}\pi\cdot75=37.5\pi(m)\)

The PERIMETER of the shaded region:

\(P=2\cdot75+37.5\pi=(150+37.5\pi)m\\\\\pi\approx3.14\)

substitute

\(P\approx150+37.5\cdot3.14=150+117.75=267.75(m)\)

Answer:

m<2=m<5=50

m<4=85

m<6=45

Step-by-step explanation:

Answer:

1:85 2:50 3:45 4:85 5:50 6:45

Step-by-step explanation:

pls give brainliest

1 should be like 4 and 3 should be like 6.

Like 6+1 is 130 so 2 is 50

The expressions that represent the derivative of the function y = f(x) are:

- dy/dx

- f'(x)

- lim(h→0) [f(x+h) - f(x)]/h

- lim(h→0) [f(x) - f(x-h)]/h

So, the correct options are:

- dy/dx

- f'(x)

- lim(h→0) [f(x+h) - f(x)]/h

- lim(h→0) [f(x) - f(x-h)]/h

Option (C) and option (D) are the same expressions, just with a different notation.

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Answer:

Surface area: 199.27 cm

Volume: 129.8 cm³

Step-by-step explanation:

Answer:

If you start at 0, 51.  If you start with 2, 50.

Step-by-step explanation:

The amount of numbers that will be said are simply 100/2 which is 50 since counting by two is the same as the amount of even numbers up to 100.  If you start at 0, simply add an additional count, making 51.

Cheers.

True, a data warehouse allows users to specify certain dimensions or characteristics.

In a data warehouse, dimensions represent the different aspects or characteristics by which data can be categorized or analyzed. These dimensions can include various attributes or variables that provide context and organize the data.

Users of a data warehouse can specify these dimensions based on their analytical needs and the nature of the data being stored.

For example, in a sales data warehouse, common dimensions may include product, customer, time, and location.

By specifying these dimensions, users can slice and dice the data based on different criteria and gain insights from various perspectives.

By defining dimensions, users can navigate through the data warehouse and perform multidimensional analysis using tools such as OLAP (Online Analytical Processing).

Dimensions provide a structure for organizing and querying data in a way that facilitates analysis and reporting.

In summary, a data warehouse allows users to specify dimensions or characteristics that help organize and analyze the data stored in the warehouse. These dimensions provide a framework for users to navigate and explore the data from different perspectives.

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The number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

To calculate the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels, we can use the concept of stars and bars.

First, we need to ensure that we have at least one of each type of bagel. So, we take one bagel of each type, which leaves us with 14 bagels to buy.

Now, we can use stars and bars to distribute the remaining 14 bagels among the 6 types of bagels. We represent the 14 bagels as stars and the 5 possible locations between the types of bagels as bars.

Using this method, we need to distribute 14 stars among 5 bars, which can be done in

(14+5-1) choose (5-1) = 18 choose 4 = 3060 ways.

Therefore, the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

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The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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Using a worksheet, we can get different polynomial models. For example, a second-degree polynomial:

We can see that the model is good, however, if we try with a third-degree polynomial, we get the following:

The adjustment is perfect. Thus, the third-degree polynomial fits best.

If we get the graph of the square root of the period and time, we get the following:

As we can see, in this case, the second-degree polynomial fits best than the second-degree polynomial of the data without the square root.

However, if we display the third degree of the square root of the data, we can see in the image below that the model fits as best as the data without root.

Therefore, the only ones we can compare are the second-degree polynomials (as the third degree are both the same), that when compared, the model that best fits is the one with the square root of the data.

To find the maximum likelihood estimator (MLE) for λ, we need to maximize the likelihood function L(λ) with respect to λ of the Poisson distribution

First, let's write the probability density function (PDF) of the Poisson distribution:
P(X = k) = (e^(-λ) * λ^k) / k!

The likelihood function can be defined as the product of the probabilities for each observation in the random sample. Since the sample is independent and identically distributed, we can write the likelihood function as:
L(λ) = P(x1, x2, ..., xn | λ) = P(x1 | λ) * P(x2 | λ) * ... * P(xn | λ)

Taking the logarithm of the likelihood function (log-likelihood) will simplify the calculations. The log-likelihood function is:
log(L(λ)) = log(P(x1 | λ)) + log(P(x2 | λ)) + ... + log(P(xn | λ))

Now, let's calculate the derivative of the log-likelihood function with respect to λ:
d/dλ log(L(λ)) = d/dλ (log(P(x1 | λ)) + log(P(x2 | λ)) + ... + log(P(xn | λ)))
= d/dλ (log(P(x1 | λ))) + d/dλ (log(P(x2 | λ))) + ... + d/dλ (log(P(xn | λ)))

To find the MLE, we set the derivative equal to zero and solve for λ:
d/dλ log(L(λ)) = 0

The derivative of log(P(x | λ)) with respect to λ can be calculated using the logarithmic differentiation technique. After taking the derivative, we equate it to zero and solve for λ.

By solving the equation, we will obtain the MLE for λ.

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Answer:

2

Step-by-step explanation:

(1/8) to the power of -1/3

=> 2.66

Answer:

The answer for x is 28°

Step-by-step explanation:

x+62=90°

x=90-62

x=28°