Recta de pendiente 1⁄4 que pasa por (3,0).

A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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(a) The support has length 920 - 720 = 200, so X has probability density

\(f_X(x)=\begin{cases}\frac1{200}&\text{for }720\le x\le920\\0&\text{otherwise}\end{cases}\)

X has mean

\(E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{920}x\,\mathrm dx=\boxed{820}\)

and variance

\(V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2\)

The second moment is

\(E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{920}x^2\,\mathrm dx=\frac{2,027,200}3\)

and so

\(V[X]=\dfrac{2,027,200}3-820^2=\dfrac{10,000}3\)

The standard deviation is the square root of the variance, so

\(SD[X]=\sqrt{V[X]}=\sqrt{\dfrac{10,000}3}\approx\boxed{57.73}\)

(b)

\(P(X<870)=\displaystyle\int_{-\infty}^{870}f_X(x)\,\mathrm dx=\frac1{200}\int_{720}^{870}\mathrm dx=\frac{870-720}{200}=\boxed{0.75}\)

With the help of the given Venn diagram, the answer of n(A∪B) is 44 respectively.

A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects.

Circles that overlap share certain characteristics, whereas circles that do not overlap do not.

Venn diagrams are useful for showing how two concepts are related and different visually.

When two or more objects have overlapping attributes, a Venn diagram offers a simple way to illustrate the relationships between them.

Venn diagrams are frequently used in reports and presentations because they make it simpler to visualize data.

So, we need to find:

A ∪ B

Now, calculate as follows:

The collection of all objects found in either the Blue or Green circles, or both, is known as A B. Its components number is:

8 + 7 + 14 + 6 + 1 + 8 = 44

n(A∪B) = 44

Therefore, with the help of the given Venn diagram, the answer of n(A∪B) is 44 respectively.

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Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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Answer:

6

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

\(\frac{4x}{4} = \frac{64}{4}\)

x = 16

Answer:

axis of symmetry: x=1

Answer:

the closest answer is the last option, so I would say that is the correct one.

Step-by-step explanation:

4.5 x 4.5 x π =

20.25 x π =

63.6172....

On adding the given equation, we get 9x² +2x -5.

Definition of adding 2 and 2 to make a correct guess based on what you see or hear to find something You weren't home so I added 2 and 2 to find you Went back to your office to combine Add to list Share. When you combine things, you combine them to create one of many.

Calculation:-

6x² - 5x + 3 +3x² +7x - 8

= 9x² +2x -5

In some cases, different items are merged by their properties and cannot be separated again but in other cases, the merged items can be individually selected. When we say that two things go together, or one thing goes with another, we mean that they go together or that they cannot be separated. You can see that some colors match and some don't. See the full dictionary entry for together.

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Answer:

10/11

Step-by-step explanation:

The estimated raw material Inventory balance at the end of July is $27,750.

The estimated raw material inventory balance at the end of July, we need to follow the given information and calculations:

a. Each unit of finished goods requires 5 pounds of raw materials. Therefore, the total raw materials needed for production in August can be calculated as follows:

23,000 units (budgeted unit sales for September) × 5 pounds/unit = 115,000 pounds

b. The ending raw materials inventory equals 10% of the following month's raw materials production. Based on the information provided, the estimated raw materials needed to meet production in August is 111,000 pounds.

111,000 pounds × 0.10 (10%) = 11,100 pounds

This means that the ending raw materials inventory for July should be 11,100 pounds.

c. The cost of raw materials is $2.50 per pound. To find the value of the raw material inventory at the end of July, we multiply the pounds by the cost per pound:

11,100 pounds × $2.50/pound = $27,750

Therefore, the estimated raw material inventory balance at the end of July is $27,750.

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There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Answer:

Imao

Step-by-step explanation:

Answer:

14.5 feet

Step-by-step explanation:

the midpoint is halfway from 30 to 45 so be(bart elevation) b.e = 45 - 30 / 2

7.5 m above sea level

__________________________________________________________

We are given:

The elevation of Homer = -30 feet                         [30 feet below sea level]

The elevation of Marge = +45 feet                         [45 feet above sea level]

The elevation of Bart is at the exact mid-point of the elevations of Homer and Marge

The elevation of Bart:

We are given that the elevation of Bart is at the exact mid-point of the elevations of Homer and Marge

So, Half the distance between the elevation of Homer and Marge is the elevation of Bart

Elevation of Bart (with respect to the elevation of Homer) =

(elevation of Marge - Elevation of Homer) / 2

replacing the variables with the suitable values:

(+45 - (-30))/2

(45 + 30) / 2

75 / 2

Elevation of Bart (w.r.t. Homer) = 37.5 feet

Since this is the elevation of Bart with respect to Homer, we can say that Bart is 37.5 m above Homer

So, we can say that:

Elevation of Bart (w.r.t Homer) = Elevation of Bart - Elevation of Homer

replacing the values

37.5 = Elevation of Bart -(-30)

37.5 = Elevation of Bart + 30

Elevation of Bart = 7.5 m above sea level [subtracting 30 from both sides]

The answer is one of the last two. I am pretty sure that it is corresponding but I could be wrong.

Answer:

389202838

Step-by-step explanation:

Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Answer:

42

Step-by-step explanation:

To find out how many widgets he made, you need to find out how much money was earned from all the widgets he made. You know that one day only earns $150 without any widgets but the factory worker earned $370.50 so the difference would be the amount of money earned from the extra widgets.

Amount of money earned from widgets = $370.50 - $150

                                                                  = $220.50

You know each widget costs $5.25, so you can find out how many widgets were made.

No. of widgets made = $220.50 ÷ $5.25

                                   = 42

Answer:

42

Step-by-step explanation:

use the linear equation

y = 5.25x +150 x represents the amount of widgets made and y is the amount earned each day

plug in 370.50 for y then solve for x

370.50 = 5.25x + 150

220.50 = 5.25x

42 = x

so he made 42 widgets

The possible length of the third side will be values that are less than 41 and greater than 5

For three sides to be the sides of a triangle, the sum of any two sides of the triangle must be greater than the third.

Given the two sides of a triangle have lengths 18m and 23m, the sum of the sides is given as:

sum = 18 + 23

Sum = 41

Let the third side be x, such that;

x + 18 >23

23 + x > 18

x >  23 - 18

x > 5

Similarly

x > -5

Hence the possible length of the third side will be values that are less than 41 and greater than 5

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An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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to find the distance between both points, we should first find the coordinates of each one.

From the picture, we can see that point A is located at (-1,2) and point B is located at (1,-2).

Recall that having points (a,b) and (c,d), the distance between them is given by the formula

So, in our case we take a=-1,b=2, c=1 and d=-2. Thus, we get

Using a calculator, we get that

which round to the nearest tenth is 4.5

Answer:

  (c)  The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

Step-by-step explanation:

You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).

The inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...

  f(a) = b

then the graph of f(x) contains the ordered pair (a, b).

The inverse function will have the ordered pair (b, a). That is,

  f⁻¹(b) = a

If an ordered pair (x-intercept) of the inverse function is ...

  (P, 0)

Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.

The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

__

Additional comment

The graphs of the two functions are mirror images of each other across the line y=x.

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(a) Through the conditional probability formula:\(P(B ∩ A) = P(B | A) P(A),\)

\(P(B / A1) P(A1) = 0.50 x 0.20 = 0.10A2 = 0.30 x 0.30 = 0.09A3= 0.40 x 0.50 = 0.20\)

(b)Bayes' theorem gives

\(P(A2 | B) = p(B | A2) p(A2) / [p(B | A1) P(A1) + p(B | A2) P(A2) + p(B | A3) p(A3)]= 0.26Thus, P(A2 | B) = 0.26.\)

(c)the tabular approach can show us

Events      P(Ai)    P(B | Ai)   P(Ai ∩ B)   P(Ai | B)

A1          0.2     0.5       0.1        0.167

A2          0.3     0.3       0.09      0.307

A3          0.5     0.4       0.2        0.526

Therefore,\(P(A1 | B) = 0.167, p(A2 | B) = 0.307, p(A3 | B) = 0.526.\)

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