The diagram shows a right angled triangle.
The length of the base of the triangle is 2 square root 3 cm. the length of the hypotenuse of the triangle is 6cm. The area of the triangle is A cm squared.
Show that A = k square root 2 giving the value of k.

Answer and Step-by-step explanation:

Solve for the middle side, then  for x using Pythagorean Theorem.

\(A^2 + B^2 = C^2\\\\\\6^2 + 8^2 = C^2\\\\100 = C^2\\\\C = 10\\\\\\\\A^2 + 10^2 = 12^2\\\\A^2 + 100 = 144\\\\A^2 = 44\\\\A^2 = 2\sqrt{11} <-Answer\)

#teamtrees #PAW (Plant And Water)

The probability of having an error when confidence limits are 3 standard deviations far from the mean is approximately 0.27.

Assume that the data is normally distributed. For a normal distribution, approximately 99.7% of the data is within 3 standard deviations of the mean.

As a result, if the lower and upper specification limits are 3 standard deviations away from the mean, they encompass 99.7% of the data.

As a result, there is only a 0.3% chance of an error. Since this is a two-tailed test, the probability of an error on each side is 0.15%

As a result, the probability of an error when the lower and upper specification limits are 3 standard deviations away from the mean is approximately 0.27.

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The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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Answer:

x = your number

3 / ( x + 8 ) = 2 / ( x + 3 )

Cross multiply

3 ∙ ( x + 3 ) = ( x + 8 ) ∙ 2

3 x + 9 = 2 x + 16

Subtract 2 x to both sides

x + 9 = 16

Subtract 9 to both sides

x = 7

Answer:

2.4 or 2 2/5 bottles of water

Answer:125.666

Step-by-step explanation:

Answer:

El monomio equivalente es \(\cos 5x \cdot \cos 2x\).

Step-by-step explanation:

Un monomio es una entidad algebraica consistente en un componente, el polinomio dado puede ser transformado mediante el uso de la siguientes propiedades trigonométricas:

\(\cos (\alpha + \beta) = \cos \alpha \cdot \cos \beta - \sin \alpha \cdot \sin \beta\)

Es decir:

\(\cos 7x + \sin 5x \cdot \sin 2x\) Dado

\(\cos (5x+2x) + \sin 5x\cdot \sin 2x\)

\(\cos 5x \cdot \cos 2x - \sin 5x \cdot \sin 2x + \sin 5x \cdot \sin 2x\)

\(\cos 5x \cdot \cos 2x\)

El monomio equivalente es \(\cos 5x \cdot \cos 2x\).

(a) 125 is the smallest positive integer greater than 100 that can be expressed in two different ways as a sum of two squares. (b) The 20th smallest number that is a sum of two squares in two different ways is 197.

(a) To show that 125 is the smallest positive integer greater than 100 that can be expressed in two different ways as a sum of two squares, we need to find two distinct pairs of integers (a, b) and (c, d) such that:

125 = a² + b² = c² + d

We can start by listing the squares of integers and checking for sums that equal 125:

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

From the list, we can see that 125 is not a perfect square. However, we can express it as the sum of two squares in two different ways:

125 = 5² + 10² = 11² + 2²

Therefore, 125 is the smallest positive integer greater than 100 that can be expressed in two different ways as a sum of two squares.

(b) To find the 20th smallest number that is a sum of two squares in two different ways, we can use a systematic approach. We can start with the smallest numbers that can be expressed as a sum of two squares and check if they have multiple representations.

Starting from the smallest non-zero-sum of squares:

1² + 0² = 1

We continue to find more numbers that can be expressed as a sum of two squares:

2² + 1² = 5

1² + 2² = 5

3² + 1² = 10

1² + 3² = 10

4² + 1² = 17

1² + 4² = 17

And so on...

By following this process, we can find the 20th smallest number that can be expressed as a sum of two squares in two different ways:

20th number = 49² + 2² = 7² + 8² = 197

Therefore, the 20th smallest number that is a sum of two squares in two different ways is 197.

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For S:{20} the inequality 4(n − 8) < 2(n + 6) will be True where n is natural number

In the above question, an inequality is given where n is natural number

4(n − 8) < 2(n + 6)

We need to find the value of n from the given options for which this inequality is true

To do so, we'll put the values one by one and check

1) S:{44}

4(n − 8) < 2(n + 6)

4(44 − 8) < 2(44 + 6)

144 < 100

Which is not true

2) S:{32}

4(n − 8) < 2(n + 6)

4(32 − 8) < 2(32 + 6)

96 < 76

Which is not true

3) S:{22}

4(n − 8) < 2(n + 6)

4(22 − 8) < 2(2 + 6)

56 < 16

Which is not true

4) S:{20}

4(n − 8) < 2(n + 6)

4(20− 8) < 2(20 + 6)

48 < 52

Which is true

Hence, For S:{20} the inequality 4(n − 8) < 2(n + 6) will be True where n is natural number

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a) The 90% confidence intervals for the population mean 30-year fixed mortgage rate is (0.0762, 0.0708)

b) The 99% confidence intervals for the population mean 30-year fixed mortgage rate is (0.07394, 0.07306)

Given,

Mean fixed mortgage rate = 30

Random sample, n = 14

Sample mean, x = 7.35% = 0.0735

Population Standard Deviation, σ = 0.6% = 0.006

We have to compute 90% and 99% confidence interval for the population mean;

Here,

Formula to find confidence interval for population standard deviation;

x ± tₙ₋₁, ∝/2 σ/√2

Now,

a) Significance Level, ∝ = 1 - 0.90 = 0.1

Critical Value, tn-1 ∝ = t₂₇, ₀.₀₅ = 1.703

Now, the 90% confidence intervals for the population mean 30-year fixed mortgage rate will be:-

0.0735 ± (1.703) 0.006/√14

= 0.0735 ± 0.0027

= (0.0735 + 0.0027, 0.0735 - 0.0027)

= (0.0762, 0.0708)

b) Significance Level, ∝ = 1 - 0.99 = 0.01

Critical Value, tn-1 ∝ = t₂₇, ₀.₀₀₅ = 0.2771

Now, the 99% confidence intervals for the population mean 30-year fixed mortgage rate will be:-

0.0735 ± (0.2771) 0.006/√14

= 0.0735 ± 0.00044

= (0.0735 + 0.00044, 0.0735 - 0.00044)

= (0.07394, 0.07306)

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To find the vertical asymptote of the function f(x) = 17x - 5, we need to determine the value of x for which the function approaches infinity or negative infinity as x approaches that value.

The vertical asymptote occurs when the denominator of the fraction approaches zero, leading to an undefined value.

The given function f(x+4) can be obtained by substituting x+4 for x in the original function f(x) = 17x - 5.

So, f(x+4) = 17(x+4) - 5 = 17x + 68 - 5 = 17x + 63.

It is important to note that shifting the function horizontally by adding 4 does not affect the vertical asymptote; it only changes the position of the graph.

Therefore, the vertical asymptote of f(x+4) is the same as the vertical asymptote of the original function f(x), which is x = -4. This means that as x approaches -4, the function approaches infinity or negative infinity.

Moving on to the second part of the question, let's analyze the function \(f(x) = (7x^2 - 41)/(10x^2 + 15).\)

To determine the horizontal asymptote, we look at the behavior of the function as x approaches positive infinity or negative infinity.

To find the horizontal asymptote, we compare the degrees of the numerator and denominator of the rational function. In this case, both the numerator and denominator have a degree of 2, as the highest power of x is 2. When the degrees of the numerator and denominator are the same, the horizontal asymptote can be determined by dividing the leading coefficients of both the numerator and denominator.

In the given function, the leading coefficient of the numerator is 7, and the leading coefficient of the denominator is 10. Dividing these coefficients, we get 7/10. Therefore, the horizontal asymptote of f(x) is

y = 7/10 or y = 0.7.

In summary, the answer to the given question is:

A. The vertical asymptote of f(x+4) is x = -4.

B. The horizontal asymptote of \(f(x) = (7x^2 - 41)/(10x^2 + 15)\) is y = 7/10 or y = 0.7.

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For which population is 636363 wins a legitimate estimate of the average longest streak: Only the top 200200200 longest streaks worldwide in June

Mean = sum of data / Number of data

The 200200200 longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada, but they are the top 200200200 longest streaks of all players. So,

Only the top 200200200 longest streaks worldwide in June will win.

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The slope of the line is undefined.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-4, 6) and (-4, 1)

Now,

Since, The equation of line passes through the points (-4, 6) and (-4, 1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 6) / (-4 - (-3))

m = - 5 / 0

m = ∞

Thus, The slope of the line is undefined.

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Answer:

\(54c^3+68c^2-72c\)

Step-by-step explanation:

\(6c(9c^2+11c-12)+2c^2\\=(6c)(9c^2)+(6c)(11c)+(6c)(-12)+2c^2\\=54c^3+66c^2-72c+2c^2\\=54c^3+68c^2-72c\)

Answer:

1100

Step-by-step explanation:

3300 ÷ 0.5 = 6600

6600 ÷ 6 = 1100

Answer:

10 km/h

Step-by-step explanation:

I'm not really sure about this but no ones answering your question and I wanna help.

So basically to calculate the average speed you need to divide the distance travelled by time taken

But you do not have the distance traveled. But it is mentioned that it takes u 30 minutes to walk from home to school when walking at 5 km/h so to find the distance all you have to do is... 30 x 5 = 150 km

Now that we have the time and distance all we have to do is find the average speed.

Average Speed = distance ÷ time

So 150 ÷ 15 = 10 km/h

The tax rate given as a percentage, can be used to find out the amount

to be paid as tax.

Correct response:

The given parameters are;

Susan Wong's taxable income last year = $52,915

The income tax rate = 2%

Required:

Susan Wong's tax last year

Solution:

The tax rate is given as a percentage of the taxable income.

The amount payable as tax = The tax rate × The taxable income

Therefore;

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Answer:

The slope of the curve is 2 and its y-intercept is 4.

Hope this helps

Answer:

The slope of the curve is 2 and its y-intercept is 4.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

The easiest way to tell if a relation is a function is to look at the values of the x's. If more than one x is the same, it cannot be a function. In contrast, if more than one y is the same, it is okay. The answers A, B, and D are functions because the x's are all different. Looking at the table for the answer C, you can see that two x's are the same (there are two x's with the value of 1).

Hope this helps!! Have a wonderful day :D

The exact value of the expression tan(π/6) sin(5π/3)⋅cos(-3π/4) is -√3/2.

We have tan(π/6). The angle π/6 is equivalent to 30 degrees. The tangent of 30 degrees is √3/3.

We have sin(5π/3). The angle 5π/3 is equivalent to 300 degrees. In the unit circle, the sine value at 300 degrees is -√3/2.

Finally, we have cos(-3π/4). The angle -3π/4 is equivalent to -135 degrees. In the unit circle, the cosine value at -135 degrees is -√2/2.

Multiplying these values together, we have (√3/3) * (-√3/2) * (-√2/2). Simplifying, we get (√3 * √3 * √2) / (3 * 2 * 2) = (√3 * √2) / 12.

Taking the negative sign into account, the final value is -√3/2, which is approximately -0.866.

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Answer:

The mean is 67

Step-by-step explanation:

Answer:

Step-by-step explanation:

The hypotenuses(x) of the triangle whose legs are 12 cm and 16 cm is 20 cm.

As we know that in a right angled triangle there are base, perpendicular and hypotenuse. a hypotenuse is the longest side of a right triangle. In other words, the side opposite to the right angle is called the hypotenuse.

Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

By Pythagoras theorem, hypotenuse (x)  = √(a² + b²)

                                                                        =  √(16² + 12²)

                                                                        = 20 cm

Answer:

Step-by-step explanation:

The sum of two supplementary angles is 180

Let A be the larger angle and B be the smaller angle

A+B=180

Given A=5B-18

5B-18+B=180

6B=180+18=198

B=198/6=33

A=180-B=180-33=147

Hence A=147, B=33

Answer:

0.99925077115

To calculate the mean price per item when a total of $68.80 is spent on the purchase of 15 items, we need to divide the total amount by the number of items. This gives us the average cost per item.

Here are the steps to solve the problem:1. The total amount spent is $68.80.2. The total number of items purchased is 15.3. To find the mean price per item, we need to divide the total amount spent by the total number of items.  This gives us:

Mean price per item = Total amount spent / Total number of items

Mean price per item = $68.80 / 15= $4.5867 (rounded to four decimal places)

Therefore, the mean price per item is $4.5867.

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Answer:

Step-by-step explanation:

57.6

Answer:

57.6

Step-by-step explanation:

You multiply 72 by .8 because you have to change the percent into a decimal place to multiply it by. 0.8 is 80 hundredths and fractions are numbers out of 100. I hope I could help you :)