Find the indefinite integral of each of the following by using [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n #1
(a) e^x (3 - e^x)^4 dx
(b) 3e^2x √(1 + e²x) dx
(c) 3e^-2x / (1 + e^-2x)^3 dx
(d) 4 cos 2x sin³ 2x dx
(e) sec² 3x tan³ 3x dx
(f) 2+tan ² x / cos² x dx​

We have compared the given standard distributions based on their means and standard deviations.

What is the standard deviation?

Standard deviation is a statistical measure of the spread of a dataset, defined as the square root of its variance. It is a way to quantify the amount of variation or dispersion of a set of data values.

(a) The means and the standard deviations of both distributions (1) and (2) are the same. The only difference is that there is an outlier in (2) with the value of 20 that doesn't exist in (1)

(b) The means of both distributions (1) and (2) are the same. However, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)

(c) The means of both distributions (1) and (2) are different, Distribution (2) has larger mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)

(d) The means of both distributions (1) and (2) are different, Distribution (2) has smaller mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)

Hence, we have compared the given standard distributions based on their means and standard deviations.

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In the case of prices of all new cars sold in a month in a large city, the mean is likely to be higher than the median.

The reason is, new car prices range from economy to luxury, and there are high-end cars that are more expensive than the average/median cars, which will pull the mean value to a higher level.

In the case of the heights of all 7-year-old children in a large city, the mean and median are likely to be about equal. The reason is, children's heights are likely to be distributed relatively evenly, and the mean and median are typically close together for a normal distribution.

In the case of shoe sizes of adult women, the median is likely to be higher than the mean. The reason is, the distribution of shoe sizes among adult women is likely to be skewed, with more women having shoe sizes near the middle of the distribution, and fewer women having sizes that are either very small or very large. This will pull the median to a higher level than the mean.

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The different values of x in the equation y = 3 sin (x + π/2) to determine the values of y for different values of x.

The equation of the trigonometric graph is given by y = A sin (Bx + C).

Here, A is the amplitude, B is the angular frequency, and C is the phase shift.

Let's assume that A = 3, B = 1, and C = π/2.

Therefore, the equation of the trigonometric graph is given by y = 3 sin (x + π/2).

To calculate the value of y, we can substitute values of x in the equation.

Let's consider x = 0.

Therefore, the value of y is given by y = 3 sin (0 + π/2).

Using the trigonometric identity sin (π/2 + x) = cos x, we get y = 3 cos 0.

Since cos 0 = 1, y = 3.

Hence, the value of y for x = 0 is 3.

Similarly, we can substitute different values of x in the equation y = 3 sin (x + π/2) to determine the values of y for different values of x.

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Answer: imma be honnest im just trying to get points rn.

Step-by-step explanation: i have no idea but thank you for your time reading my nonescence.

The perimeter of a two-dimensional shape is the distance around the shape. In this case, the paperboard has a semicircle cut out of it, so the perimeter of the paperboard that remains after the semicircle is removed is the distance around the remaining rectangular shape.

To calculate the perimeter of the remaining rectangular shape, you can use the formula: 2(length + width) = 2(26 in + 20 in) = 2(46 in) = 92 in.

It is important to note that the perimeter is a measure of the distance around a two-dimensional shape and it doesn't take into account the area inside the shape. Also it is measured in units, in this case inches.

I hope this helps :)

Length (in ft) x Width (in ft) = area in sq. ft

Hope this helps

I'm not good at math so I got this from my notes :)

If it doesn't help then it was worth an attempt...

Answer:

x=12

y=8

Point form: (12,8)

Step-by-step explanation:

I've done this question before

Answer:

y=8 and x=12

Step-by-step explanation:

2x+y =32

multiply by 1

= 2x+y=32

x+3y=36

multiply by 2

=2x+6y=72

2x+y=32 - 2x+6y=72

=5y/5=40/5

=y=8

2x+y=32

=2x+8=32

=2x=32-8

=2x=24

=2x/2=24/2

=x=12

The total estimated work cost for the project would be $5200 ($5000 + $200).

The formula for calculating the estimated work cost for a project is C = P x T, where C is the estimated cost, P is the hourly rate of the personnel and T is the total amount of time spent working on the project. For example, if the hourly rate of a project manager is $50 and they work 100 hours on the project, the estimated work cost would be $5000 (50 x 100). In addition, any equipment that is used on an hourly rental basis should also be included in the estimated work cost calculation. For example, if a piece of equipment is used for 10 hours at a rate of $20 per hour, the estimated cost for this equipment would be $200 (20 x 10). Therefore, the total estimated work cost for the project would be $5200 ($5000 + $200).

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The area of rectangle ABCD exists 12  sq. units.

A polygon's vertex is a location where the sides or edges of the item or two rays or line segments meet. Vertex is a noun, whereas vertices is the plural.

Vertices are the points at which the edges of the three-dimensional shape converge. Edges are the lines that separate two faces, while faces are flat surfaces.

One of the items that are linked together in a graph is called a vertex (or node). The terms "edges" or "links" refer to the connections between the vertices. a network with ten nodes (or vertices) and eleven edges (links).

The coordinates of point D exists (3,3).

Area of rectangle ABCD = l × b = AB × BC

On further calculation we get

Area of rectangle ABCD = 6 × 2

Area of rectangle ABCD = 12  sq. units

Therefore, the area of rectangle ABCD exists 12  sq. units.

The complete question is:

Three vertices of a rectangle ABCD are A(3,1), B(-3, -1) and C(-3, 3). Plot these points on the graph paper and find the coordinates of the fourth vertex D. Also, find the area of the rectangle ABCD.

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The percent of dry erase markers that are red is 25

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

Number of black dry erase markers= 56

Number of red dry erase markers= 14

Now,

14/56=x/100

56x=1400

x=25

Therefore, the value of red marker in percent will be 25%

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Answer:

angel 2

Step-by-step explanation:

Angle 2 corresponds to angle 6.

Based on this inequality x – 6y < 12, the ordered pair (7, -1) is not a solution.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

In order to determine if (7, -1) is a solution of the given linear equation, we would have to test the given ordered pair by substituting its values into the linear equation as follows;

x – 6y < 12

7 – 6(-1) < 12

7 + 6 < 12

13 < 12 (False).

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Answer:

They have to be similar because careful inspection will show all of their angles (the two triangles) are equal.

One can start with the fact that the two triangles have a common angle.

CAll it x.

x * 40 + q = 180

x + 50 + r = 180

q and r must equal 50 and 40 to satisfy the sum of the interior angles must sum to 180.

The mean of the sample data is 9.91 ounces and the standard deviation is 0.16 ounces.  

To find the 95% confidence interval, we need to calculate the mean and standard deviation of the sample data.  The 95% confidence interval can then be calculated as the mean ± 1.96 times the standard deviation, which is (9.59, 10.23) ounces.

b) The 95% confidence interval for the number of ounces dispensed by the machine is (9.59, 10.23) ounces.

c) 95% confidence means that if the same experiment were to be repeated 100 times, 95 of the confidence intervals would contain the true mean.

d) The confidence interval does not suggest that the company is short-changing their customers because it includes 10 ounces, which is the expected amount of coffee to be dispensed.

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The function uniqueItems takes a list of items and a maximum number of item deletions and returns the number of unique items remained in the bag.

def uniqueItems(items, m):

 uniqueItems = set(items)

 return len(uniqueItems) - m

items = [1,2,3,4,5,6]

m = 2

print(uniqueItems(items, m)) # 4

# First, we create a set using the items list to get a collection of unique items

uniqueItems = set(items)  # {1, 2, 3, 4, 5, 6}

# Then, we subtract the maximum number of items to be deleted from the length of the set to get the number of unique items remained

return len(uniqueItems) - m  # 4

The function uniqueItems takes a list of items and a maximum number of item deletions and returns the number of unique items remained in the bag.

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Answer: D

Step-by-step explanation: A box of apples consists of 20 apples. Since there are a total of 100 apples, you want to find how many boxes makeup 100 apples. 100/20. Then, you would want to multiply that by the cost of each box (i.e. 5 boxes times 17). This is what is done in D when  the order of operations is followed.

The inequality that can be used to solve the possible values of the number is 11 + 3/4x < 112 where the number x is x < 134 2/3

sum of 11 and three-fourths of a number is less than 112.

Let

The unknown number = x

11 + 3/4x < 112

Subtract 11 from both sides

3/4x < 112 - 11

3/4x < 101

divide both sides by 3/4

x < 101 ÷ 3/4

multiply by the reciprocal of 3/4

x < 101 × 4/3

x < 404/3

x < 134 2/3

Therefore, the inequality which represents the situation is 11 + 3/4x < 112.

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Alex's set of ordered pairs would no longer define a function if any of the following actions were taken:

A set of ordered pairs defines a function if, for every element in the domain (the set of first coordinates), there is exactly one element in the range (the set of second coordinates).

For example, if Alex's set of ordered pairs is {(1,2), (2,3), (3,4)}, it would no longer define a function if a new ordered pair of (2,5) is added to it, as it would mean that there are now two different second coordinates (3,5) for the first coordinate 2. This would violate the rule that every element in the domain must have exactly one corresponding element in the range. Similarly, removing one of the ordered pairs, changing the order of the ordered pair, or changing the domain or range would cause the set to no longer to define a function.

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The two Consecutive number is 16 and 17.

What is consecutive number?

Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a 1 difference. The mean and median of a sequence of numbers are equal. If n is a number, then it follows that n, n+1, and n+2 are also numbers. Examples. 1, 2, 3, 4, 5.

Here the according to the question those two consecutive number are multiplied and increased by 17 and answer is not prime number. Now,

=> 1× 2+17 = 2+17 = 19(prime number)

=> 2×3+17=6+17=23(prime number)

=> 3×4 +17 = 12+17 = 29(prime number)

=> 4×5+17 = 20+17 = 37(prime number)

=> 5×6+17 = 30+17 = 47(Prime number)

=> 6×7+17 = 42+17 = 59(prime number)

=> 7×8+17 = 56+17 = 73(prime number)

=> 8×9+17 =72+17 = 89(prime number)

=> 9×10+17 = 90+17= 107(prime number)

=> 10×11+17=110+17 = 127(prime number)

=> 11×12+17=132+17 =149(prime number)

=> 12×13+17=156+17 = 173(prime number)

=> 13×14+17=182+17 = 199(prime number)

=> 14×15+17=210+17 = 227(prime number)

=> 15×16+17 = 240+17=257 (prime number)

=> 16×17+ 17= 272+17 = 289( not prime number)

Hence the two consecutive number is 16 and 17.

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The vertical line that violates the vertical line test is given as follows:

x = -3.

A relation represents a function when each input value is mapped to a single output value.

For the relation graphed, we have that at x = -3, there are two closed bounds of the function, meaning that the input x = -3 is mapped to multiple outputs and thus the relation is not a function.

This also means that a vertical line traced at x = -3 would cross the graph of  the function at two points, thus violating the vertical line test.

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To answer the relevant part of the question, the amount that Norfolk should pay within the discount period is $23,520.

The discount period is based on the credit terms.

For instance, 2/10, n/30 show the discount and credit terms.  The explanation is that a 2% cash discount will be received by the customer if payment is made within 10 days of purchase.

Furthermore, the customer's credit period expires after 30 days.  Thus, from day 11 to day 30, the customer does not qualify for cash discounts.

The catalog list price = $40,000

Trade discount = 40%

Discounted price = $24,000 ($40,000 x (1 - 40%)

Cash discount = $480 ($24,000 x 2%)

Cash payment = $23,520 ($24,000 - $480)

Thus, Norfolk Sporting Goods will pay $23,520 if it utilizes the discount.

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because rules are meant to be guided and I also steps for acquiring what you need

Answer:

AB = 49

ABC = 253

BAC = 156

ABC = 311

Step-by-step explanation:

The whole circle is 360

360 - 107 - 49 = 204  

We now know the measurement of the 3 sections shown.

AB = 49

ABC = 49 + 204 = 253

BAC = 107 + 49 = 156

ACB = 107 + 204 = 311

In a single triangle, there is a 40-degree and a 60-degree angle.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.

Triangles of the scalene, isosceles, and equilateral varieties differ from one another in terms of side length. The triangle is a scalene triangle if the lengths of the three sides are all different. An isosceles triangle is one with all three sides having equal lengths.

A 40-degree and a 60-degree angle are both present in one triangle. three for the side opposite the 40-degree angle, x for the side opposite the 60-degree angle, and six for the third side. A 40 degree angle and an 80 degree angle are present in the second triangle. The third side has a length of 8, the side opposite the 80-degree angle has a length of y, and the side opposite the 40-degree angle has a length of 5.

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The total cost of the items purchased at each store is $68, $52, and $72 respectively.

The total bill at each store can be found by using matrix multiplication. We will create a matrix of the costs of each item, and then multiply it by a matrix of the amounts of each item purchased. The resulting matrix will give us the total cost of the items purchased.

Let x be the matrix of costs per item:

x = [[5, 2.5, 2, 3],

    [4, 2.75, 1.5, 2],

    [6, 3, 1.75, 3.5]]

Let y be the matrix of amounts of items purchased:

y = [[6, 3, 2, 5]]

We can then find the total cost at each store by multiplying x and y together:

xy = [[68, 36.75, 29, 45.5],

     [52, 28.25, 21, 30],

     [72, 40, 33.5, 52.5]]

Interpreting the solution with context to the application, we can see that the total cost of the items purchased at each store is $68, $52, and $72 respectively.

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Answer:

54

Step-by-step explanation:

take the average of the number given

The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.

To find the inverse of the given function as it is not a one to one function (has the same value f(x) for more that one value of x) you restrict the domain to get a function one to one.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

f (x) = 1/3x - 2

Find its inverse as shown below,

Add 2 to x and then divide by 1/3 as shown below,

f⁻¹(x) = (x + 2) / 1/3

f⁻¹(x) = 3(x + 2)

compare with f⁻¹(x) = a (x + 2)

a = 3

Calculate the x-intercept by putting f(x) = 0

0 = x + 2

x = -2

In a quadratic function as given use the vertex to restrict the domain; restrict the domain using coordinate x of the vertex.

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Use a larger confidence level would produce a new confidence interval with larger width (larger margin of error) based on these same data.

How do you calculate the population proportion's 95% confidence interval?

We must determine p′ and q′ in order to construct the confidence interval. p′ = 0.842 is the sample percentage; this is the point estimate of the population proportion.

                               Since CL = 0.95 is the requested confidence level, the calculation is as follows: = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.

What does confidence interval mean?

When you conduct your experiment again or resample the population in the same way, you may anticipate your estimate to fall inside a specific range of values a certain proportion of the time. This is known as the confidence interval.

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