Mark wants to make an enclosure for his cows.
He has 44 metres of fencing.
He wants the width to be 8 metres less than the length.
What dimensions should the field have?
?

Answer:

1

Step-by-step explanation:

0.81666666666

Answer:

5/12+2/5

That is the answer as the real decimal is 0.81666 repeating

Step-by-step explanation:

The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:

On the interval (-∞, -3), f(x) is increasing.

On the interval (-3, 0), f(x) is decreasing.

On the interval (0, 3), f(x) is increasing.

On the interval (3, ∞), f(x) is decreasing.

We have,

To determine the increasing and decreasing behavior of the function f(x) = x / (x² - 9) on the given intervals, we can evaluate the sign of the derivative of the function.

Taking the derivative of f(x) with respect to x and simplifying, we have:

\(f'(x) = (-x^2 + 9 - x(2x)) / (x^2 - 9)^2\\= (-x^2 + 9 - 2x^2) / (x^2 - 9)^2\\= (-3x^2 + 9) / (x^2 - 9)^2\)

To identify the increasing and decreasing behavior, we need to examine the sign of f'(x) on each interval.

For the interval (-∞, -3):

Plugging in a value less than -3, such as -4, into f'(x) yields a positive result.

Plugging in a value between -3 and 0, such as -2, into f'(x) gives a negative result.

Therefore, f'(x) is positive for x < -3 and negative for -3 < x < 0, indicating that f(x) is increasing on the interval (-∞, -3) and decreasing on the interval (-3, 0).

For the interval (-3, 3):

Plugging in a value between -3 and 0, such as -2, into f'(x) yields a negative result.

Plugging in a value between 0 and 3, such as 1, into f'(x) gives a positive result.

Therefore, f'(x) is negative for -3 < x < 0 and positive for 0 < x < 3, indicating that f(x) is decreasing on the interval (-3, 0) and increasing on the interval (0, 3).

For the interval (3, ∞):

Plugging in a value between 3 and 4, such as 3.5, into f'(x) yields a positive result.

Plugging in a value greater than 4, such as 5, into f'(x) gives a negative result.

Therefore, f'(x) is positive for 3 < x < 4 and negative for x > 4, indicating that f(x) is increasing on the interval (3, 4) and decreasing on the interval (4, ∞).

Thus,

The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:

On the interval (-∞, -3), f(x) is increasing.

On the interval (-3, 0), f(x) is decreasing.

On the interval (0, 3), f(x) is increasing.

On the interval (3, ∞), f(x) is decreasing.

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Answer:

The formula of pi is approximately 3.14 2×3.14

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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Answer: I would suppose 2.

The validity of short forms may be reduced because they contain fewer items compared to the full-length version. Short forms of tests or questionnaires are often used in research and clinical settings due to their convenience and efficiency.

This means that the short form may not fully capture the construct being measured and may not accurately reflect the individual's true scores. Additionally, the items selected for the short form may not be representative of the full range of the construct, leading to bias and limited generalizability.

Therefore, researchers and clinicians should consider the trade-offs between convenience and validity when deciding to use short forms.

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Answer:

greater than 5 and less than 35

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is

difference of 2 sides < x < sum of 2 sides, that is

20 - 15 < x < 20 + 15

5 < x < 35

Thus the third side is greater than 5 and less than 35

Answer:

A 5 and B 35

Step-by-step explanation:

sides are 15 and 20 the third side has to be

grater than 20-15=5 and

less than 15+20 =35

because the third side has to be between the

diference of sides 1 and 2  < 3rd side < sum of side 1 and 2

Answer

Option A is correct.

B' (15, 6) is the answer.

Explanation

To dilate a given coordinate (x, y) about the origin by a scale factor of n, we will obtain (nx, ny).

So, for the given coordinate (5, 2), dilating by the scale factor of 3, we will obtain

B (5, 2) = B' (5×3, 2×3) = B' (15, 6)

Hope this Helps!!!

The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer: \(1\ \text{USD}\ \equiv\text{jmd}\$120\)

Step-by-step explanation:

Given

Shantel converted jmd$16,200 to USD $135

Using unitary method 1 USD is equivalent to

\(jmd\$16,200\equiv USD\$135\\\\USD\$135\equiv jmd\$16,200\\\\1\ \text{USD}\ \equiv \dfrac{16,200}{135}\\\\1\ \text{USD}\ \equiv\text{jmd}\$120\)

Answer:

Step-by-step explanation:

The correct answer is (b) The central limit theorem is applicable for the sample mean.

The condition that the population size be at least 10 times the sample size is necessary to ensure that the sample mean follows a normal distribution, as required by the central limit theorem. The central limit theorem states that the sample mean will be approximately normally distributed, regardless of the underlying population distribution, as long as the sample size is large enough. In this case, the condition is necessary to ensure that the sample size is sufficiently large for the central limit theorem to be applicable. Options (a), (c), (d), and (e) are not the correct answers because they do not directly relate to the condition that the population size be at least 10 times the sample size.

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X represents the number of arrangements.

If Noah earns £160 a week and pays £55 in tax, he has £160 - £55 = £160-£55 = £105 to spend.

Subtraction is a mathematical procedure that includes subtracting one number from another. For example, if we have five apples and subtract three of them, we are left with two apples. Beginning with the bigger number and deducting the smaller number from it is how subtraction is done. Subtraction is denoted by the minus symbol (-). A difference is the outcome of a subtractive operation.

We may better grasp how to solve issues requiring the removal of one or more elements from a set by understanding the fundamental mathematical formula of subtraction. It is employed in many different scenarios, such as when we need to subtract incomes on a regular basis.

How to solve?

The formula for the money Noah has to spend each week is m = w - t.

£160 - £55 = £160 - £55 = £105

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The height of the person's shadow on the wall is decreasing at a rate of 1/4 ft/sec when the person is 10 ft from the wall.

Let the distance between the person and the wall be x ft. Then, by similar triangles, the height of the person's shadow on the wall is (5/40)x = (1/8)x ft.

Taking the derivative with respect to time t, we get:

dh/dt = (1/8)(dx/dt)

We are given that dx/dt = -2 ft/sec (since the person is walking towards the wall). We want to find dh/dt when x = 10 ft. Plugging in these values, we get:

dh/dt = (1/8)(-2) = -1/4 ft/sec

Therefore, the height of the person's shadow on the wall is decreasing at a rate of 1/4 ft/sec when the person is 10 ft from the wall.

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Answer:

the P is 25% for all positions

Step-by-step explanation:

P = (1/n)

P = probability

1 = the total of the whole

n = number of options

P = 1/4

P = .25

To calculate the derivative of the function f(x) = (3 - 4x + 2x²)⁻², we can use the Chain Rule and the Power Rule. The derivative can be expressed as f'(x) = -2(3 - 4x + 2x²)⁻³(4 - 4x).

To find the derivative of f(x), we apply the Chain Rule and the Power Rule. The Chain Rule states that if we have a composition of functions, such as f(g(x)), the derivative is given by f'(g(x)) multiplied by g'(x).

First, we focus on the inner function g(x) = 3 - 4x + 2x². The derivative of g(x) is g'(x) = -4 + 4x.

Next, we differentiate the outer function f(g) = g⁻². Using the Power Rule, the derivative of f(g) is f'(g) = -2g⁻³.

Combining the results, we have f'(x) = f'(g(x)) * g'(x), which gives us f'(x) = -2(3 - 4x + 2x²)⁻³(4 - 4x).

Therefore, the derivative of f(x) is f'(x) = -2(3 - 4x + 2x²)⁻³(4 - 4x).

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Answer:

4.9,5.0

Step-by-step explanation:

Thier is two open spaces and the decimals are decreasing by 1 tenth. So if 1 tenth is being decreased the order would be 4.9, 5.0, 5.1, 5.2, 5.3, 5.4.

Answer:

4.9, 5 , 5.1 , 5.2 , 5.3 , 5.4

Step-by-step explanation:

5.4-5.3 = 0.1

5.3-5.2 = 0.1

5.2-5.1 = 0.1

then the pattern is : adding 0.1 to the number to get the next number

5.1 - 0.1 = 5

5 - 0.1 = 4.9

the total area under the standard normal curve to the left of z = -2 or to the right of z = 2 is by using a standard normal distribution table or a statistical calculator.

the standard normal distribution table provides the area under the standard normal curve for any given z-score. The table is divided into two parts, one for the left-tail probabilities and the other for the right-tail probabilities. To find the total area to the left of z = -2, one needs to look up the z-score -2 in the left-tail probability section and read the corresponding area under the curve, which is 0.0228. Similarly, to find the total area to the right of z = 2, one needs to look up the z-score 2 in the right-tail probability section and read the corresponding area under the curve, which is also 0.0228.

the total area under the standard normal curve to the left of z = -2 is 0.0228, and the total area to the right of z = 2 is also 0.0228.
To find the total area under the standard normal curve to the left of z = -2 or to the right of z = 2, you will add the areas corresponding to z = -2 and z = 2 using a standard normal table or calculator.


1. Locate the area corresponding to z = -2 in the standard normal table or using a calculator. This value represents the area to the left of z = -2.
2. Since the standard normal curve is symmetrical, the area to the right of z = 2 is equal to the area to the left of z = -2.
3. Add the areas found in steps 1 and 2 to get the total area under the curve to the left of z = -2 or to the right of z = 2.

By following these steps, you can find the total area under the standard normal curve to the left of z = -2 or to the right of z = 2 using a standard normal table or calculator.

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Based on the total budget of Mr. Bell for the incentive and the cost of a pizza box, the equation that matches the word problem is 60 ≥ 9.25x

The amount that Mr. Bell will spend at the most is the budget for the incentive of $60.

He will not spend more than this amount but will spend a maximum of it. This amount of $60 is therefore equal to or greater than the cost of the pizzas:

60 ≥ cost of the pizza

The cost of the pizza is:

= Cost per pizza box x number of boxes

= 9 × x

= 9x

The equation is therefore:

60 ≥ 9.25x

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The function whose graph is given below is y = tan (x).

Therefore, for x = 0, y = 0 for the given function

Now, at x = 0,

y = sec (0) = 1

y = tan (0) = 0

y = cosec (0) = Not defined

y = cot (0) = Not defined

Now, it is clear that, the function y = tan (x) represents the given graph.

The complete question is:

Choose the function whose graph is given below.

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Answer:

30.9 mb

Step-by-step explanation:

The probability of getting 2 tails is option (b) 37.5%

The event of "2 tails" can occur in three possible outcomes: {htt, tht, tth}, so the probability of getting 2 tails is the sum of the probabilities of these three outcomes.

Each toss of a fair coin is independent and has a 50% chance of landing tails. Therefore, the probability of each of these three outcomes is:

P(htt) = 1/2 × 1/2 × 1/2 = 1/8

P(tht) = 1/2 × 1/2 × 1/2 = 1/8

P(tth) = 1/2 × 1/2 × 1/2 = 1/8

So, the probability of getting 2 tails is:

P(2 tails) = P(htt) + P(tht) + P(tth) = 1/8 + 1/8 + 1/8 = 3/8

= 0.375

0.375 multiplied by 100% gives:

P(2 tails) = 37.5%

Therefore, the correct option is (b) 37.5%

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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Step-by-step explanation:

First, we can try to factor out the greatest common factor, which is 1 in this case. Then, we can try to factor by grouping:

x³ - 5x² - 8x + 12

= x²(x - 5) - 4(x - 3)

= x²(x - 5) - 4(x - 3)

Now we can see that we have a common factor of (x - 3), which we can factor out:

x²(x - 5) - 4(x - 3)

= (x - 3)(x² - 4x + 4)(x - 5)

The expression is now fully factorised, so the complete factorisation of x³ - 5x² - 8x + 12 is:

(x - 3)(x - 2)²(x - 5)

The appropriate family of distributions to approximate the probability of rolling a 6 on a fair die is the discrete uniform distribution, which assumes equal probabilities for each outcome. In this case, the probability of rolling a 6 would be approximately 1/6 based on the assumption of fairness.

For the problem of approximating the probability of rolling a 6 on a fair die, an appropriate family of distributions to consider is the discrete uniform distribution.

The discrete uniform distribution is commonly used to model situations where each outcome has an equal probability of occurring. In the case of rolling a fair die, the die has six equally likely outcomes (numbers 1 to 6).

Each outcome has a probability of 1/6 of occurring, making the discrete uniform distribution a suitable choice.

By assuming a discrete uniform distribution, we can assign equal probabilities to each outcome (1/6 for rolling a 6) and approximate the probability of rolling a 6 based on the assumption of fairness.

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Answer:

\(J.(x,y)\) → \((9x,9y)\)

\(--------\)

hope it helps..

have a great day!!

Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

\(( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2=\cfrac{1-\cos(\theta )}{1+\cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2\implies \csc^2(\theta )-2\csc(\theta )\cot(\theta )+\cot^2(\theta ) \\\\\\ \cfrac{1^2}{\sin^2(\theta )}-2\cdot \cfrac{1}{\sin(\theta )}\cdot \cfrac{\cos(\theta )}{\sin(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\implies \cfrac{1}{\sin^2(\theta )}-\cfrac{2\cos(\theta )}{\sin^2(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\)

\(\cfrac{\cos^2(\theta )-2\cos(\theta )+1}{\sin^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{\sin^2(\theta )} \\\\\\ \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{1-\cos^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1]}\)

\(\cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1^2]}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos(\theta )-1][\cos(\theta )+1]} \\\\\\ \cfrac{\cos(\theta )-1}{-[\cos(\theta )+1]}\implies \cfrac{-[\cos(\theta )-1]}{\cos(\theta )+1}\implies \cfrac{1-\cos(\theta )}{1+\cos(\theta )}\)