Mr. Adam bought a total of 20 muffins and cookies. Each muffin cost $1.50 and each cookie cost $0.50. The cookies were $5 more than the muffins. How many items of each type did he buy?

We can use the formula for the confidence interval for a population mean with a known standard deviation. Plugging in the values, we get the interval  (6817.22, 7182.78).

To find the 99% confidence interval for the scholarship averages of thirty students, we need to use the following formula:

CI = X ± zα/2 * (σ/√n)

Where

X = sample mean ($7,000 in this case)

zα/2 = the z-score corresponding to the desired confidence level (99% in this case), which is 2.576

σ = population standard deviation ($500 in this case)

n = sample size (30 in this case)

Substituting these values into the formula, we get:

CI = 7000 ± 2.576 * (500/√30)

Simplifying this expression, we get:

CI = 7000 ± 182.78

Therefore, the 99% confidence interval for the scholarship averages of thirty students is

(7000 - 182.78, 7000 + 182.78)

= (6817.22, 7182.78)

So we can say with 99% confidence that the true population mean scholarship amount lies within this interval.

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Therefore, the reliability of the results may be questioned due to the small sample size and the fact that the observed and expected counts in some cells are too small.

The fact that two of the six observed counts are 5 or less should make you the most worried about the reliability of the results of the test in this case. This is because when the observed counts in a cell are too small, it is difficult to draw reliable conclusions from them. In such cases, the chi-squared statistic may not accurately reflect the true relationship between the variables being studied. This is because the chi-squared statistic is based on the difference between the observed counts and the expected counts, and if the observed counts are too small, the chi-squared statistic may be biased and not accurately reflect the true relationship between the variables.
Moreover, the fact that two of the six expected counts are less than 5 also raises concerns about the reliability of the results. This is because when the expected counts in a cell are too small, it may indicate that the sample size is too small or that the sample is not representative of the population being studied. In this case, the sample size was only 300 black women, which may not be representative of all black women.

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If the points  D(−3,−4), E(5,0), F(3,4), and G(−5,0) form rectangle DEFG then the area  is 40 square units.

The length of the rectangle can be found by finding the distance between D and E (or F and G), which is:

√(5 - (-3))² + (0 - (-4))²] = √8² + 4²

= √80

= 4√5

The width of the rectangle can be found by finding the distance between D and G (or E and F), which is:

√-5 - (-3))² + (0 - (-4))²

= √(-2)²+ 4²

= √20

= 2√5

Therefore, the area of the rectangle is:

length x width = 4√5 x 2√5

= 8 x 5

= 40

Hence,  40 square units is area of the given rectangle DEFG.

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Answer:

[tex]x^{0} =105^{0}[/tex]

Step-by-step explanation:

[tex]x^{0} =180-(180-(180-110)-(180-145))[/tex]

[tex]x^{0} =180-(180-70-35)[/tex]

[tex]x^{0} =180-75[/tex]

[tex]x^{0} =105[/tex]

Hope this helps

Answer:

x=105

Step-by-step explanation:

Two methods

Method 1. Solving with Exterior Angles

Method 2. Solving with Interior Angles

Method 1. Solving with Exterior Angles

So that we can keep things organized, let's call the angle in the bottom left of the triangle, Angle 1, the angle in the top of the triangle, Angle 2, and the angle in the bottom right of the triangle, Angle 3.

An Exterior Angle is formed by continuing the line segment of a side, and is the angle that forms a linear pair with the interior angle.

Observe that all of the angles given are Exterior Angles to the Polygon (in this case, a triangle), and only one exterior angle is given for each vertex (we don't want to double-count things).

For any polygon, the sum of its exterior angles is always 360 degrees.

Therefore, we can setup the following equation:

[tex]360^o=m \angle 1_{exterior} + m \angle 2_{exterior} + m \angle 3_{exterior}[/tex]

[tex]360^o=(145^o) + (110^o) + (x^o)[/tex]

Combining like terms on the right hand side...

[tex]360^o=x^o +255^o[/tex]

Isolating x by subtraction 255 degrees from both sides...

[tex](360^o)-255^o=(x^o +255^o)-255^o[/tex]

[tex]105^o=x^o[/tex]

So, x = 105

Method 2. Solving with Interior Angles

An Interior Angle is the angle we usually think of inside of a polygon (in this case, a triangle).

The sum of the Interior angles of any polygon is given by [tex]Interior~Angle~Sum=180^o*(n-2)[/tex], where "n" is the number of sides of the polygon.  For triangles, n=3, so

[tex]Interior~Angle~Sum=180^o*((3)-2)[/tex]

[tex]Interior~Angle~Sum=180^o*(1)[/tex]

[tex]Interior~Angle~Sum=180^o[/tex]

In this case, we're given exterior angles for two of the vertices, and we've been asked to find the exterior angle for the third vertex.  Each Exterior angle forms a linear pair with the interior angle, and thus is supplementary, meaning a pair of Interior and Exterior angles have measures that add to 180 degrees.

Keeping with our angle numbering described in Method 1, we have the following 3 true equations about each interior/exterior pair, where we can substitute in the known values, and solve for / isolate the unknown angle measure (in the last case, we'll get an expression containing "x" for its measure):

[tex]\begin{array}{ccc}180^o=m \angle 1+m \angle 1_{exterior}&180^o=m \angle 2+m \angle 2_{exterior}&180^o=m \angle 3+m \angle 3_{exterior}\\180^o=m \angle 1+(145^o)&180^o=m \angle 2+(110^o)&180^o=m \angle 3+(x^o)\\180^o-145^o=m \angle 1&180^o-110^o=m \angle 2&180^o-(x^o)=m \angle 3\\35^o=m \angle 1&70^o=m \angle 2&180^o-(x^o)=m \angle 3\end{array}[/tex]

Additionally, since the sum of the interior angles of a triangle is 180 degrees, we also have the following equation...

[tex]m \angle 1 + m \angle 2 + m \angle 3 = 180^o[/tex]

Making substitutions with the quantities found above...

[tex](35^o) + (70^o) + (180^o-x^o) = 180^o[/tex]

Rewriting subtraction as addition of a negative...

[tex]35^o + 70^o + 180^o + (-x^o) = 180^o[/tex]

Adding x degrees to both sides, and subtracting 180 degrees from both sides...

[tex]35^o + 70^o =x^o[/tex]

Combining like terms..

[tex]105^o =x^o[/tex]

So, again, x=105

Answer:

-5 and 5

Step-by-step explanation:

[tex]-5*5=-25\\\\-5+5=0[/tex]

Answer: 7, 6 ,7

Step-by-step explanation:

Within the relevant range, a curvilinear cost function can be graphed as a curved line. A curvilinear cost function is a cost function where the total cost changes as a function of the level of activity, but not at a constant rate.

This means that as the level of activity increases, the cost per unit may increase or decrease, resulting in a curved relationship between the level of activity and the total cost. In order to determine the optimal level of activity, a manager can use calculus to find the point where the marginal cost equals the marginal revenue.

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As a bank officer, Elena's claims would not be enough to encourage me to approve the loan. It's important to look at the details of her business plan, her financial history and her credit score before making a decision. Even if Elena believes that her business idea cannot fail, there is always a risk involved in lending money. It's important to assess the risk and make a decision based on the facts, rather than on promises or guarantees.

Answer:

Step-by-step explanation:

Her claims encourage you.

The solution to all parts is shown below.

1. Using a standard normal distribution table (z-table), the corresponding percentile left of the score for a z-score of 1.93 is approximately 97.65. Therefore, the percentile can be written as an integer of 98.

2. The percentile left of the score corresponding to z-score 1.94 can be found using a standard normal distribution table (z-table).

Looking up the value of 1.94 in the z-table, we find the area under the curve to the left of 1.94 is 0.9732, or 97.32% when rounded to two decimal places.

Therefore, the corresponding percentile left of the score for z-score 1.94 is 97%.

4. Since the normal distribution is symmetrical, we know that the area in the right tail is also 0.0158.

Therefore, the total area of the shaded region is:

= 0.0158 + 0.0158 = 0.0316

7. To determine the percentage of test takers who scored lower than Lorena, we need to find the area to the left of her z-score on the standard normal distribution.

First, we calculate the z-score of Lorena's score:

z = (554 - 495) / 20 = 2.95

Using a standard normal distribution table or calculator, we find that the area to the left of z = 2.95 is approximately 0.9985. This means that approximately 99.85% of test takers scored lower than Lorena.

Therefore, Lorena scored better than about

100% - 99.85% = 0.15% of test takers, which can be rounded to 0.2%.

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The measure of angle FCD is given as follows:

m < FCD = 28º.

First we consider that the given angles are bisected, meaning that they are divided into two equal parts, hence:

Consecutive angles on a rhombus are supplementary, hence the value of x is obtained as follows:

6x + 2 + 16x - 20 = 180

22x = 198

x = 198/22

x = 9.

Then the measure of angle E is given as follows:

m < E = 6 x 9 + 2

m < E = 56º.

Opposite angles on a rhombus are congruent, hence the measure of angle C is given as follows:

m < C = m < E = 56º.

Considering the bisection, the measure of angle FCD is given as follows:

m < FCD = 0.5 x 56º = 28º.

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The most general antiderivative of f(x) = 9sqrt(x) + 3cos(x) is:

F(x) = 6x^(3/2) + 3sin(x) + C

To find the most general antiderivative of the function f(x) = 9sqrt(x) + 3cos(x), we can integrate each term separately.

The antiderivative of 9sqrt(x) can be found by using the power rule of integration. We add 1 to the exponent (1/2) and divide by the new exponent:

∫9sqrt(x) dx = 9 * (2/3)x^(3/2) + C = 6x^(3/2) + C

The antiderivative of 3cos(x) can be found using the integral of the cosine function:

∫3cos(x) dx = 3sin(x) + C

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Answer:

Step-by-step explanation:

to figure out the distributive property of 13(2+9), we multiply the outside number (in this case 13), into the inside numbers (2 and 9). so, 13*2 and 13*9. in this equation the 2 and 9 are separate by a + sign meaning we separate it again by the + sign. (13*2+13*9). making D the correct answer.

Approximately 897 liters of oil would be required to supply the electrical energy needs of an average home for a year. Keep in mind that this is a rough estimate, as factors like energy consumption and power plant efficiency can vary.

To answer your question, we need to consider a few factors such as the size of the home and the energy consumption of the household. However, on average, a household consumes around 10,000 kilowatt-hours (kWh) of electricity per year. If we convert this into liters of oil, we can use a conversion factor of 0.2778 liters of oil per kWh. Therefore, an average household would require around 2,778 liters of oil per year to supply their electrical energy needs.
It is important to note that this is just an estimate and the actual amount of oil required may vary depending on various factors such as the efficiency of the heating system and the energy usage habits of the household. It is also worth considering alternative energy sources such as solar or wind power, which can reduce the dependence on oil and lower the carbon footprint of the household.
In conclusion, an average household would require approximately 2,778 liters of oil to supply their electrical energy needs for a year. However, it is important to explore alternative energy sources and implement energy-saving measures to reduce the reliance on oil and minimize environmental impact.
The number of liters of oil required to supply the electrical energy needs of an average home for a year depends on the home's energy consumption and the efficiency of the power plant converting the oil into electricity. On average, a US household consumes about 10,649 kilowatt-hours (kWh) of electricity per year.
A typical oil-fired power plant can produce around 1,885 kWh of electricity from one barrel (159 liters) of oil, with an efficiency rate of around 33%. To calculate the number of liters needed for a year, we can use the formula:
(Number of kWh per year) / (kWh per liter of oil) = Liters of oil needed
First, let's find the kWh per liter of oil: 1,885 kWh/barrel * (1 barrel/159 liters) ≈ 11.86 kWh/liter
Now we can calculate the liters of oil needed: 10,649 kWh/year / 11.86 kWh/liter ≈ 897 liters/year
So, approximately 897 liters of oil would be required to supply the electrical energy needs of an average home for a year. Keep in mind that this is a rough estimate, as factors like energy consumption and power plant efficiency can vary.

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There are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.

To determine the number of possible configurations, we multiply the number of choices available for each component of the system. Since the customer can choose one of two amplifiers, one of four CD players, and one of eight speaker models, the total number of possible configurations is given by:

2 (amplifiers) × 4 (CD players) × 8 (speakers) = 64

Therefore, there are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.

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Step-by-step explanation:

green is 6 out of  a total of ( 8+6+6 = 20 ) beads

   so  6/20 ths of the time it should be a green bead

              6/20  * 150 = 45 times should be green

The farming conglomerate will use approximately 36,912.51 megaliters of water 5 years from now.

To calculate the amount of water the farming conglomerate will use 5 years from now, we can use the given information that its water usage increases at a rate of 7% every year.

Let's denote the current water usage as W₀ and the water usage after 5 years as W₅.

We know that W₅ = W₀ * (1 + r)^n, where r is the growth rate (in decimal form) and n is the number of years.

In this case, W₀ = 28,390 megaliters, r = 7% = 0.07, and n = 5.

Substituting these values into the formula, we have:

W₅ = 28,390 * (1 + 0.07)^5

Calculating this expression, we get:

W₅ ≈ 28,390 * (1.07)^5 ≈ 36,912.51 megaliters

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The term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.

To find the limit of the given sequence, we can use the ratio test:

StartFraction
(9(n+1)+1)! / (9(n+1))!
Over
(9n+1)! / (9n)!
EndFraction

Simplifying the expression, we get:

StartFraction
(9n+10)(9n+9)(9n+8)...(9n+2)(9n+1)
Over
(9n+1)(9n)(9n-1)...(2)(1)
EndFraction

The terms cancel out and we are left with:

StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction

Taking the limit as n approaches infinity, we get:

lim (n → ∞) StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction

= lim (n → ∞) StartFraction
81n² + 81n + 90
Over
81n² + 9n
EndFraction

= lim (n → ∞) StartFraction
n² + n + 10 / n² + n / 9
EndFraction

As n approaches infinity, the higher order terms dominate, so we can ignore the constants and simplify the expression to:

lim (n → ∞) StartFraction
n² / n²
EndFraction

= 1

Since the limit exists and is finite, the sequence converges. Therefore, the limit of the sequence is 1.

To find the limit of the given sequence or determine if it diverges, consider the sequence:

a_n = (9n+1)! / (9n)!

We can rewrite the sequence using the properties of factorials:

a_n = [(9n+1)(9n)(9n-1)...(9n-(9n-1))] / (9n)!

a_n = (9n+1)

Now, we'll examine the limit as n approaches infinity:

lim (n -> ∞) a_n = lim (n -> ∞) (9n+1)

Since the term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.

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Given the pattern:

In words, this pattern represents:

The numbers are obtained by squaring the integers 3, 4, 5, 6, and 7, respectively.

Algebraically, we can represent the pattern using the formula:

The value of p(2) = 7, p(0) = -3 , p(-1) = -17 and p(-2) = -53 when polynomial is p(x) = 2x³ - 5x² + 7x - 3 with one variable.

Given that,

The polynomial is p(x) = 2x³ - 5x² + 7x - 3

We have to find the value of p(2), p(0), p(-1) and p(-2).

We know that,

Take polynomial,

p(x) = 2x³ - 5x² + 7x - 3

Now, to find p(2) take x = 2 in polynomial

By substituting,

p(2) = 2(2)³ - 5(2)² + 7(2) - 3

p(2) = 16 - 20 + 14 - 3

p(2) = 30 - 23

p(2) = 7

Now, to find p(0) take x = 0 in polynomial

p(0) = 2(0)³ - 5(0)² + 7(0) - 3     [multiplication]

p(0) = 0 - 0 + 0 - 3

p(0) = -3

Now, to find p(-1) take x = -1 in polynomial

p(-1) = 2(-1)³ - 5(-1)² + 7(-1) - 3

p(-1) = -2 - 5 - 7 - 3                  [subtraction]

p(-1) = -17

Now, to find p(-2) take x = -2 in polynomial

p(-2) = 2(-2)³ - 5(-2)² + 7(-2) - 3

p(-2) = -16 - 20 - 14 - 3

p(-2) = -53

Therefore, The value of p(2) = 7, p(0) = -3 , p(-1) = -17 and p(-2) = -53.

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The value of sample space are:

⇒ (B,A), (B,B), (B,C), (C,A), (C,B), (C,C)

We have to given that;

When entering class, each student is given a card labeled with either A, B or C.

And, The sample space showing the possibilities for being given a letter over two days can be represented as {(A,A), (A,B), (A,C), __}.

Hence, the possible outcomes for being given a letter over two days are:

{(A,A), (A,B), (A,C), (B,A), (B,B), (B,C), (C,A), (C,B), (C,C)}

So, the options that would be part of the sample space are:

(B,A), (B,B), (B,C), (C,A), (C,B), (C,C)

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The variance is 7521.2 and the standard deviation is 86.7.

The variance is 18630.08 and the standard deviation is 136.4.

The variance is 0.0325 and the standard deviation is 0.18.

The variance is 252.8418 and the standard deviation is 15.91.

We have,

1)

Step 1: Find the mean

Mean = (106 + 121 + 152 + 234 + 347) / 5 = 192

Step 2: Find the variance

Variance = [(106-192)^2 + (121-192)^2 + (152-192)^2 + (234-192)^2 + (347-192)^2] / 5

Variance = 37606 / 5 = 7521.2

Step 3: Find the standard deviation

Standard deviation = sqrt(Variance) = sqrt(7521.2) = 86.7

2)

Step 1: Find the mean

Mean = (1450 + 1250 + 1776 + 1388 + 1340) / 5 = 1440.8

Step 2: Find the variance

Variance = [(1450-1440.8)^2 + (1250-1440.8)^2 + (1776-1440.8)^2 + (1388-1440.8)^2 + (1340-1440.8)^2] / 5

Variance = 93150.4 / 5 = 18630.08

Step 3: Find the standard deviation

Standard deviation = sqrt(Variance) = sqrt(18630.08) = 136.4

3)

Step 1: Find the mean

Mean = (7.7 + 7.4 + 7.3 + 7.9) / 4 = 7.575

Step 2: Find the variance

Variance = [(7.7-7.575)^2 + (7.4-7.575)^2 + (7.3-7.575)^2 + (7.9-7.575)^2] / 4

Variance = 0.0325

Step 3: Find the standard deviation

Standard deviation = sqrt(Variance) = sqrt(0.0325) = 0.18

4)

Step 1: Find the mean

Mean = (112 + 100 + 127 + 120 + 134 + 118 + 105 + 110) / 8 = 117.375

Step 2: Find the variance

Variance = [(112-117.375)^2 + (100-117.375)^2 + (127-117.375)^2 + (120-117.375)^2 + (134-117.375)^2 + (118-117.375)^2 + (105-117.375)^2 + (110-117.375)^2] / 8

Variance = 2022.7344 / 8 = 252.8418

Step 3: Find the standard deviation

Standard deviation = sqrt(Variance) = sqrt(252.8418) = 15.91

Therefore,

The variance is 7521.2 and the standard deviation is 86.7.

The variance is 18630.08 and the standard deviation is 136.4.

The variance is 0.0325 and the standard deviation is 0.18.

The variance is 252.8418 and the standard deviation is 15.91.

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Edwin eats approximately 9 kilograms of granola in a year.

To calculate how much granola Edwin eats in a year, we need to determine the total amount of granola consumed in a month and then multiply it by the number of months in a year.

Given that Edwin eats about one 750-gram bag of granola every month, we can simply multiply this by the number of months in a year, which is 12.

750 grams * 12 months = 9,000 grams

To convert grams to kilograms, we divide by 1,000 since there are 1,000 grams in a kilogram.

9,000 grams / 1,000 = 9 kilograms

Therefore, Edwin eats approximately 9 kilograms of granola in a year.

It's important to note that this calculation assumes that Edwin's granola consumption remains consistent throughout the year and that he consumes exactly one 750-gram bag each month. Variations in actual consumption may lead to slightly different results.

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[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill PQ=\sqrt{(~~ 3- 1~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill PQ=\sqrt{( 2 )^2 + ( -2)^2} \implies \boxed{PQ=\sqrt{ 8}}[/tex]

[tex]Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad R(\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill QR=\sqrt{(~~ 1- 3~~)^2 + (~~ -1- 1 ~~)^2} \\\\\\ ~\hfill QR=\sqrt{( -2)^2 + ( -2)^2} \implies \boxed{QR=\sqrt{ 8}} \\\\\\ R(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1}) ~\hfill RS=\sqrt{(~~ -2- 1~~)^2 + (~~ -1- (-1)~~)^2} \\\\\\ ~\hfill RS=\sqrt{( -3)^2 + ( 0)^2} \implies RS=\sqrt{ 9}\implies \boxed{RS=3}[/tex]

[tex]S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad P(\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) ~\hfill SP=\sqrt{(~~ 1- (-2)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill SP=\sqrt{( 3)^2 + ( 4)^2} \implies SP=\sqrt{ 25}\implies \boxed{SP=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{\sqrt{8}+\sqrt{8}+3+5} ~~ \approx ~~ \text{\LARGE 13.7}[/tex]

Answer:

To work out 3.4 cos 13 degrees, you can use a calculator or a table of trigonometric functions that includes cosine values.

Using a calculator, you can simply enter "3.4 * cos(13)" and get the answer. Rounding to 2 decimal places gives:

3.4 * cos(13) ≈ 3.298

Therefore, 3.4 cos 13 degrees, rounded to 2 decimal places, is approximately equal to 3.30.

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Answer:

sec² [㏑(ax + b)] X a/(ax +b)

Step-by-step explanation:

chain rule is if y = f(c) and z = f(e), and y = f[f(e)], then:

dy/de = dy/dc X dc/de

This might look complicated. Much easier with example, as in this question.

y = tan [㏑(ax + b)]

y = tan (u),

where u =㏑(v), v = ax + b

so we have y = tan (u), u = ㏑(v), v = ax + b.

dy/du = sec² (u), du/dv = 1/v, dv/dx = a.

dy/dx = dy/du X du/dv X dv/dx

        = sec² (u) X (1/v) X a

        = sec² [㏑(v)] X (1/(ax + b)) X a

        = sec² [㏑(ax + b)] X a/(ax + b)

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta = \frac{2\pi }{3} \end{cases}\implies A=\cfrac{~~ \frac{2\pi }{3 }6^2 ~~}{2}\implies A=12\pi \stackrel{ using~\pi =3.14 }{\implies A=37.68}[/tex]

Step-by-step explanation:

'y - intercept'  is shorthand for ' y-axis intercept' ....or the value of the graph where it crosses the y - axis

this one is     point (0,3)  or  y-intercept  = 3