More Examples TT = 2 • Let A be the area of the region that lie under the curve f(x) = cos x between x = 0 and x = E Using right endpoints, find an expression for A as limit. Do not evaluate the limit • Estimate the area by using 3 subintervals and left endpoints.

Answer: triangle, rectangle, pentagonal

Step-by-step explanation: b x h and length x width = base.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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The translation of the sentence "If Daenerys loves Jon but Jon doesn't love Daenerys, then neither no one rides a dragon nor someone doesn't deceive Cersei" into predicate logic is as follows:

(Ldja ∧ ¬Ljd) → (¬(∃x)(Rxd ∨ ¬Dxc))

Breaking it down:

(Ldja ∧ ¬Ljd): Daenerys loves Jon, but Jon doesn't love Daenerys.

(∃x)(Rxd ∨ ¬Dxc): There exists an x (someone) who either rides a dragon (Rxd) or doesn't deceive Cersei (¬Dxc).

¬(∃x)(Rxd ∨ ¬Dxc): It is not the case that there exists someone who either rides a dragon or doesn't deceive Cersei.

So, the translated sentence states that if Daenerys loves Jon but Jon doesn't love Daenerys, then it is not the case that there exists someone who either rides a dragon or doesn't deceive Cersei.

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1a. The interest that Thato will pay equals to R3,840.

1b. The final amount he will pay for the bicycle will be R 11 840.

a) To calculate the interest that Thato will pay, you can use the following formula:

Interest = Principal * Rate * Time

Interest = R 8,000 * 0.14 * 3

Interest = R3 840

Final amount = Principal + Interest

Final amount = R 8,000 + R 3,840

Final amount = R 11,840

Cost price per rose = Total cost of roses / Number of roses

Cost price per rose = R 900 / 200

Cost price per rose = R 4.50

Selling price per rose = Price of bouquet of 5 roses / Number of roses in the bouquet

Selling price per rose = R 35 / 5

Selling price per rose = R 7.00

Profit per rose = Selling price per rose - Cost price per rose

Profit per rose = R 7.00 - R 4.50

Profit per rose = R 2.50

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The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Using the concept of rates, the machine will complete 9 9/64 inches in 8.67 minutes

To determine how long it will take to turn a particular length of iron, we can calculate the rate at which it works and it must be in a definite proportion.

If the lathe moves 3/128 in one revolution.

And the machine completes 45 revolutions in 1 minutes, we can determine how many inches in moves in that minute.

3/128 in = 1 rev

x in = 45

45 * (3/128) = 45 revolutions = 1 minute

1.054 inches in 1 minute.

We can further use this to determine the time it takes to move 9 9/64 inches

1.054 inches = 1 minute

9 9/64 inches = x minute

cross multiply both sides and solve

x = 8.67 minutes

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Answer: 4q-4

Step-by-step explanation:

2(q+q-2) = 2(2q-2) = 4q-4

The expression that represents the total number of comic books Ray, Janet, and Simone have altogether is: x + 4x + 12

This expression is obtained by adding up the number of comic books each person has. Ray has x comic books, Janet has 4 times as many comic books as Ray, which is 4x, and Simone has 12 comic books.

Adding these quantities together gives the total number of comic books:

Ray's comic books + Janet's comic books + Simone's comic books = x + 4x + 12

Simplifying the expression gives:

5x + 12

This is the final expression that represents the total number of comic books that Ray, Janet, and Simone have all together, in terms of the number of comic books that Ray has.

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Answer:

3 months

Step-by-step explanation:

So 60 dollar down and 70 per month

130 (60+70)

200

270

now 90 per month but no down

90

180

270

So 3 months

The number of months will be 3 is it until your cost is the same as Mega-er-Gym. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mega-Gym costs a one-time $60 membership fee and then charges $70 per month, while Mega-er-Gym does not charge a membership fee but costs $90 per month.

Cost of Megagym = 60 + 70m

Cost of Mega-er-Gym = 90m

90m = 60+70m

20m = 60

m = 60 / 20

m = 3 months

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False. The statement "Solving the system of linear equations by elimination -2x+y=3 and 3x+2y=-15" is not a true or false statement. It is a method used to solve the given system of equations.

The process of solving a system of linear equations by elimination involves eliminating one variable by adding or subtracting the equations to create a new equation with only one variable. The goal is to eliminate one variable so that the resulting equation becomes solvable for the remaining variable.

In the given system of equations -2x+y=3 and 3x+2y=-15, the process of elimination can be used to eliminate one variable and solve for the other. By multiplying the first equation by 3 and the second equation by 2, the coefficients of the x term can be made equal, allowing the x variable to be eliminated. Adding the resulting equations will eliminate x, and solving the resulting equation will yield the value of y.

Therefore, the statement provided in the question is not a true or false statement but rather a method used to solve the system of linear equations. The actual solution to the system can be determined by applying the elimination method and finding the values of x and y that satisfy both equations.

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Answer:

2500

Step-by-step explanation:

5×5 ( 5×5×5 - 5×2 )

25 ( 125 - 25 )

25 ( 100)

25 × 100

= 2500

Solution:

Here we use a law of exponent i.e.

\( {a}^{m} \times {a}^{n} = {a}^{m + n} \\ \\ \)

So,

5² × 5³ × 5²

\( = {5}^{2 + 3 + 2} \\ \\ = {5}^{7} \\ \\ = 78125 \\ \\ \)

Therefore the answer is 78125 or simply 5⁷

Hope it helps you :)

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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Answer:

26771.8115

Step-by-step explanation:

24500(1.03)=25235 then continue doing this 2 more times and you get 26771.8115

Answer:

$18 less than the cost of 5 hot dog combos

Step-by-step explanation:

First, we see from the minus sign that this will be subtraction.  PEMDAS (order of operations) says we do the multiplication first, then the subtraction.

Let's define the following variables:

x = the amount of pure acid (100%) in liters

y = the amount of 20% acid in liters

If mixing the two liquids makes 52 L, then we can say that: (equation1)

In addition, 100% of x liters + 20% of y liters will make 52L of 40% solution then, we can also say that: (equation 2)

Using this two equations, we can solve for the values of x and y using elimination. Here the steps:

1. Subtract equation 2 from equation 1.

2. Divide both sides of the equation by 0.8.

Therefore, the value of y = 39. The amount of 20% acid solution added to the mixture is 39 liters.

3. Plug in the value of y in the equation 1 to solve for x.

The value of x is 13. Hence, the amount of pure acid that was added to the mixture is 13 liters.

Answer:

Step-by-step explanation:I don't say you have to mark my ans as brainliest but if you think it has really helped you plz don't forget to thank me...

If all of the 720 pairs of shoes are sold at $25.00 per pair with a profit margin of 25%, the shoe store will make $4,500.00.

Selling price is the amount of money that a seller charges for a particular product or service in order to make a profit.

The selling price of a pair of shoes is $25.00, and the profit for the shoe store is 25% of the selling price, or 0.25 x $25.00 = $6.25.

To find out how much the shoe store will make if all of the shoes are sold, we need to multiply the number of pairs of shoes by the selling price and then by the profit margin:

Total revenue = Number of pairs of shoes x Selling price x Profit margin

Total revenue = 720 pairs x $25.00 x 0.25

Total revenue = $4,500.00

Therefore, if all of the 720 pairs of shoes are sold at $25.00 per pair with a profit margin of 25%, the shoe store will make $4,500.00.

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The expression "x - y + z" can be simplified and rearranged using the associative property and commutative property of addition. Let's break it down step by step:

1. x - y + z

According to the associative property of addition, the grouping of terms does not affect the result when only addition and subtraction are involved. Therefore, we can choose to group "y" and "z" together:

2. x + (-y + z)

Next, using the commutative property of addition, we can rearrange the terms "-y + z" as "z + (-y)":

3. x + (z + (-y))

Now, we have the expression "x + (z + (-y))". According to the associative property of addition, we can group "x" and "z + (-y)" together:

4. (x + z) + (-y)

Finally, we can rewrite the expression as "(x + z) - y", which is equivalent to "(x - y) + z":

5. (x + z) + (-y) = (x - y) + z

Therefore, "x - y + z" is indeed the same as both "x - (y + z)" and "(x - y) + z" due to the associative and commutative properties of addition.

Answer:

YES

Step-by-step explanation:

The 7 in (0,7) is the y-intercept given in the equation y = 3x + 7

Check the picture below.

Answer:

14.1

Step-by-step explanation:

You add all of your numbers up, and then you divide by how many numbers you have.

Answer:

No Solution

Step-by-step explanation:

It's false there's no solution

Answer:39084620

Step-by-step explanation:

New questions in Mathematics

19 ft 4 ft l Find l. l = √ [?] ft

flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet stream, the same jet travels 5360 miles in 4 hours. What is the rate…e of the jet in still air and what is the rate of the jet stream?

Please help! Express the area of the region bounded by the x-axis, y = 1/2x - 2, and y equals the cubed root of x, using definite integrals.

Solve the equation 7/4x-2=-5x+1

How to Convert 11010112 to base 10?

Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation…. (b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k2 x,k2 y,k2 z)

Evaluate each expression if a=2,b=-3,C=-1, and d=4 5+d(3b-2d)

(a) To prove or disprove the statement "if f(x) is o(g(x)), then 2f(x) is o(2g(x))", we can use the definition of little-o notation.

Recall that f(x) is o(g(x)) if and only if, for any positive constant ε, there exists a positive constant M such that |f(x)| ≤ ε|g(x)| for all x > M.

Using this definition, let's consider the statement in question.

Suppose f(x) is o(g(x)), which means that |f(x)| ≤ ε|g(x)| for some positive constant ε and all x > M.

Now let's consider 2f(x). We can write this as 2f(x) = 2 * f(x), and since f(x) is o(g(x)), we know that |f(x)| ≤ ε|g(x)|. Therefore,

|2f(x)| = |2 * f(x)| ≤ 2 * |f(x)| ≤ 2ε|g(x)|

So we can see that |2f(x)| ≤ 2ε|g(x)|, which means that 2f(x) is also o(g(x)). Therefore, the statement is true.

(b) Now let's consider the statement "if f(x) is o(g(x)), then (f(x))2 is o(g(x))2". Again, we can use the definition of little-o notation.

Suppose f(x) is o(g(x)), which means that |f(x)| ≤ ε|g(x)| for some positive constant ε and all x > M.

Now let's consider (f(x))2. We can write this as (f(x))2 = f(x) * f(x), and since f(x) is o(g(x)), we know that |f(x)| ≤ ε|g(x)|. Therefore,

|(f(x))2| = |f(x) * f(x)| = |f(x)| * |f(x)| ≤ ε|g(x)| * ε|g(x)| = ε2|g(x)|2

So we can see that |(f(x))2| ≤ ε2|g(x)|2, which means that (f(x))2 is also o(g(x))2. Therefore, the statement is true.

In conclusion, we have proven both (a) and (b) to be true.

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Answer:

Triangle MBT

Step-by-step explanation:

Congruent basically means an identical triangle in this situation, so the congruent triangle to VET would be MBT

Answer:

triangle mbt is congruent to triangle vet by sas

Step-by-step explanation:

sas stands for side angle side.

angle t is congruent for both triangles

the lines show that line mt and vt are congruent, and line et and bt are too.

since angle t is between both lines that are congruent, it would be through sas

Answer:

I'm sorry the calculator for geometry isn't working right. I'm so sorry

Step-by-step explanation:

The researcher would likely use an independent samples t-test.

The researcher would likely use an independent samples t-test to test the hypothesis that men and women differ in the amount of time they spend exercising weekly.

This is because an independent t-test is appropriate when comparing the means of two independent groups, in this case, men and women.

However, before conducting the t-test, the researcher should check if the data meets the assumptions of normality and equal variance. If these assumptions are not met, alternative tests such as the Wilcoxon rank-sum test may be more appropriate.

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(a) Researchers did not allow the subjects to choose whether to be in the sleep deprivation group or the unrestricted sleep group for several reasons:First, self-selection could result in an unrepresentative sample that could jeopardize the study's validity. If the participants are allowed to choose, the self-selected groups may be biased.

Second, self-selection could result in a biased sample of motivated volunteers who are not representative of the population being studied.

(b) The actual experiment marked a value with a blue line in the figure. The conclusion that can be drawn from this is that there is a significant difference between the sleep-deprived group's time improvement and the unrestricted sleep group's time improvement. The group that was allowed unrestricted sleep improved by an average of 37.5 milliseconds on the visual discrimination test, while the sleep-deprived group improved by an average of 20 milliseconds.

(c)  A type I error occurs when we reject the null hypothesis when it is true. A type II error occurs when we accept the null hypothesis when it is false. In this case, if we conclude that there is a significant difference between the two groups when there is not, we would be making a type I error. If we conclude that there is no significant difference between the two groups when there is, we would be making a type II error.

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Answer:

x=-12

Step-by-step explanation:

it would be -2=-x-14 then solve as normal algebraic equation

add 14 to each side 12=-x

then divide by -1 on each side so you get x=-12 for the final answer hope this helps

The inverse of a function can be determined graphically by reflecting the graph over line y =x, the correct option is D.

An inverse of a function can be determined by interchanging variables in the function, y is interchanged by x in an f(x,y) function and then the equation is solved for y to determine the inverse of a function.

The equation is y = 2x+3

The inverse of a function is determined graphically the graph will be reflected in the line y =x.

The graph is attached with the answer.

Therefore, the correct option is D.

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