In Exercises 7 and 8, write a proof.
7. Given: TV = UW, TU > VW
Prove: m m

The first statement, "if 1 + 1 = 2, then 2 + 2 = 1 + 1," is true due to the associative property of addition, which allows us to group the numbers in any order we want.

The first statement, "if 1 + 1 = 2, then 2 + 2 = 1 + 1," is true due to the associative property of addition, which allows us to group the numbers in any order we want.

The second statement, "If 2 + 1 = 21, then everything else must equal 21," is false. If we assume that 2 + 1 = 21, we must know the specific mathematical system being used to determine if everything else equals 21.

Without additional information or constraints, the equation "[tex]3 + y^3 + z^3 = k[/tex] cannot be solved. It is a three-variable equation with only one equation, which means there are an infinite number of solutions depending on the values of y, z, and k.

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Hello!

the equation of the blue line is 3y + 0.5x

Step-by-step explanation:

14 10 is 90 less than the mean 1500

   z score =  - 90 / 75 =  -  1.200

    from a z-score table this represents  .1151  

       or  11.51 % will last LESS than 1410 hrs

The probability that the cause is problem A given that the caller reports a lock-up is 0.25, or 25%.

We have,

We can use Bayes' theorem to solve this problem, which states:

P(A | B) = P(B | A) * P(A) / P(B)

where:

P(A | B) is the probability of event A given that event B has occurred (in this case, the probability that the cause is problem A given that the caller reports a lock up)

P(B | A) is the probability of event B given that event A has occurred (in this case, the probability that the caller reports a lock up given that the cause is problem A)

P(A) is the prior probability of event A (in this case, the probability that the cause is problem A)

P(B) is the prior probability of event B (in this case, the probability that the caller reports a lock up)

We are given that:

P(B) = 0.8 (the probability that the caller reports a lock up)

P(B | A) = 0.5 (the probability that the caller reports a lock up given that the cause is problem A)

We want to find P(A | B) (the probability that the cause is problem A given that the caller reports a lock up)

We don't have the value of P(A), but we can use the fact that the sum of the probabilities of all possible causes (A, B, C, and D) is 1:

P(A) + P(B) + P(C) + P(D) = 1

We also know that the lock up symptom is present in some of the problems, so we can write:

P(B) = P(B | A) * P(A) + P(B | C) * P(C) + P(B | D) * P(D)

Substituting the values we have, we get:

0.8 = 0.5 * P(A) + P(B | C) * P(C) + P(B | D) * P(D)

We don't have the values of P(C) and P(D), but we know that they are not given in the problem statement, so we can assume that they are not relevant for this calculation and that P(C) + P(D) = 0. This allows us to simplify the equation to:

0.8 = 0.5 * P(A) + 0

which gives us:

P(A) = 0.8 / 0.5 = 0.4

Now we can use Bayes' theorem to calculate the probability that the cause is problem A given that the caller reports a lock up:

P(A | B) = P(B | A) * P(A) / P(B) = 0.5 * 0.4 / 0.8 = 0.25

Therefore, the probability that the cause is problem A given that the caller reports a lock up is 0.25, or 25%.

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complete question:

A computer software company receives hundreds of support calls each day. There are several common installation problems, call them A, B, C, and D. Several of these problems result in the same symptom, lock up after initiation. Suppose that the probability of a caller reporting the symptom lock up is 0.80.8 and the probability of a caller having problem A and a lock up is 0.50.5.

Step 1 of 2 :

Given that the caller reports a lock up, what is the probability that the cause is problem A? Round your answer to four decimal places, if necessary.

Answer:

135/176=0.767045

Step-by-step explanation:

1 7/8÷2 4/9

15/8÷22/9

15/8×9/22

135/176

The sentence that uses active voice is: "My friend invited his whole class to Saturday's soccer championship."

Now, let's examine the sentences you provided:

Passive voice: The subject ("the winning homerun") is being acted upon by the action (hit by the worst player).

Active voice: The subject ("my friend") is performing the action (inviting his whole class).

Passive voice: The subject ("the children") is being acted upon by the action (taken to the circus by their doting grandfather).

Passive voice: The subject ("some cookies") is being acted upon by the action (baked by the baker).

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Answer: B |-5+10|

Step-by-step explanation:

with simple addition we can find out that the distance from Mary to the soccer ball is 15 yards (5+10).

-5-10 = -15

|-15| = 15

The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)

From the question, we have the following parameters that can be used in our computation:

log₃(x²∛y²)

The product law of logarithms states that

log(ab) = log(a) + log(b)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  log₃(x²) + log₃(∛y²)

The power law of logarithms states that

log(aᵇ) =  blog(a)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  2log₃(x) + 2/3log₃(y)

This means that the values of A and B are A = 2 and B = 2/3

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The weighted average for the previous week is given as follows:

$161.64.

The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.

Considering the weights, the sum of the observations is given as follows:

1 x 157.01 + 3 x 159.37 + 5 x 159.36 + 7 x 161.78 + 9 x 164.08 = 4041.1.

The sum of the weights is given as follows:

1 + 3 + 5 + 7 + 9 = 25.

Hence the weighted average is given as follows:

4041.1/25 = $161.64.

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The maximum profit that can be obtained is $3160.

Let x be the number of chainsaws to be assembled, and y be the number of wood chippers to be assembled.

We want to maximize the profit, which is given by:

P = 150x + 220y

subject to the following constraints:

4x + 5y ≤ 60 (maximum assembly time available)

x ≥ 0, y ≥ 0 (non-negativity constraints)

We can solve this problem using linear programming.

First, we graph the constraint 4x + 5y ≤ 60 by finding the boundary line:

4x + 5y = 60

y = (-4/5)x + 12

The slope of this line is -4/5, and the y-intercept is 12. We can plot this line on a coordinate plane:

The feasible region is the region that satisfies all the constraints. It is the region below this line, including the non-negativity constraints:

We now evaluate the objective function P at the vertices of the feasible region to find the maximum value of P.

The vertices of the feasible region are (0,0), (0,12), (15,0), and (10,8).

P(0,0) = 0

P(0,12) = 220(12) = 2640

P(15,0) = 150(15) = 2250

P(10,8) = 150(10) + 220(8) = 3160

The maximum value of P is obtained at (10,8), which means that 10 chainsaws and 8 wood chippers should be assembled for maximum profit.

Therefore, the maximum profit that can be obtained is:

P = 150(10) + 220(8) = $3160.

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Answer:

2.5

Step-by-step explanation:

The new triangle is the bigger triangle so it is multiplied

The opposite lines between the two triangles is times 2

(O.G triangle side BC is 8 units while side B'C' is 20 units which is 2.5 times more than the O.G side)

hope that helped

The range of the given function y = |x| is [0, ∞).

As per the question, consider that the absolute value of any real number x is always non-negative.

Therefore, the output of the function y = |x| is always non-negative as well.

Furthermore, for any non-negative real number y, there are two possible inputs x that will produce that value of y: x and -x. For example, if y = 2, then x could be either 2 or -2.

Thus, every non-negative real number is in the range of y = |x|, and no negative numbers are in the range.

Therefore, the range of y = |x| is [0, ∞).

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Answer:

  B.  (4, 8)

Step-by-step explanation:

You want the coordinates of R(1, 5) after translation by (1, -1) and dilation by a factor of 2.

Applying the given transformation, you have ...

  (x, y) ⇒ (x +1, y -1)

  R(1, 5) ⇒ R'(1 +1, 5 -1) = R'(2, 4)

The dilation multiplies each coordinate value by the dilation factor, 2.

  (x, y) ⇒ (2x, 2y)

  R'(2, 4) ⇒ R''(2·2, 2·4)  = R''(4, 8)

The coordinates after translation and dilation are (4, 8).

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The probability that a student who attends the first session also attends the second session is 1/3

Evaluating the probability

We can approach this problem by using conditional probability.

Let's use the notation "S1" to represent the event that a student attends the first session, and "S2" to represent the event that a student attends the second session.

Then we can use the formula for conditional probability:

P(S2 | S1) = P(S1 and S2) / P(S1)

We know that P(S1) = 0.6, since 60% of students attend the first session. We also know that P(S1 and S2) = 0.2, since 20% of students attend both sessions.

So we can plug in these values and solve for P(S2 | S1):

P(S2 | S1) = 0.2 / 0.6

P(S2 | S1) = 1/3

Therefore, the probability that a student who attends is 1/3 or approximately 0.333.

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complete question:

In a cooking class 20% of

the students attend two

sessions. 60% of students

attend the first session of

cooking class. What is the

probability that a student that

attends the first session also

attends the second session?

p + 12 is the resulting expression using commutative law of addition.

Linear expression are expression that has a leading degree of 1.

Given the expression below

4 + (8 + p)

Using the commutative law of addition A + B = B + A, we will have:

4 + (8 + p) = (8 + p) + 4

= (4 + 8) + p

= 12 + p

Applying the commutative law, we will have

12 + p = p + 12

Hence the resulting expression using the commutative law of addition is p + 12

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The solution is, the solution is x > −1.

This means that any value of x greater than −1 satisfies x + 3 > 2.

Inequalities can be represented on a number line such as that shown in the image attached below. The solid line shows the range of values that x can take. We put an open circle at −1 to show that although the solid line goes from −1, x cannot actually equal −1.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.

Suppose we want to solve the inequality x + 3 > 2.

We can solve this by subtracting 3 from both sides:

x + 3 > 2

x > −1

So the solution is x > −1.

This means that any value of x greater than −1 satisfies x + 3 > 2.

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Valid step: Subtract 2 times Row 1 from Row 2. (Adding negative 2 times Row 1 to Row 2 would achieve the same result.)

To reduce the augmented matrix:

Square Row 1: This step is not valid in reducing the augmented matrix. Squaring a row would change the values and potentially lead to incorrect results.

Divide Row 2 by 2 times Row 1: This step is valid. Divide each element in Row 2 by 2 times the corresponding element in Row 1. This operation helps in achieving a leading 1 in the second row.

Multiply Row 1 by Column 1: This step is not valid in reducing the augmented matrix. Multiplying a row by a column does not have a defined operation in matrix reduction.

Add negative 3 times Row 3 to Row 2: This step is valid. Multiply Row 3 by -3 and then add it to Row 2. This operation helps in achieving zeros below the leading 1 in the second row.

After performing the valid steps, the reduced augmented matrix would be:

2 1 4 21

0 2 -6 -14

1 6 2 17

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1296 unit square will be the total surface area of the given figure.

To find the surface area of the given figure. first, we need to separate this graph into two cuboids such that,

The surface area of a cuboid is given by the formula:

A = 2lw + 2hw + 2lh

thus, for the upper cuboid,

A = 2*9*6+2*6*6+2*9*6

A=288

thus, for the lower cuboid,

A = 2*27*6+2*27*12+2*12*6

A=1116

So the total surface area = sum of the surface area of both cuboids - 2* area of the touching side

Total surface area = 1116+288-2*9*6

Therefore total surface area will be 1296.

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According to the information, after 15 days we will have 32,768 beans that will be worth $16,384.

The pattern here is that the number of magical beans is doubling each day. Therefore, we can find the number of beans after 15 days by starting with the initial 2 beans and doubling them 15 times:

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 32,768

So after 15 days, you will have 32,768 magical beans.

How to calculate the value of the beans?

If each magical bean is worth $0.50, then the total value of the beans after 15 days would be:

32,768 x $0.50 = $16,384

Comparing this to the value of your car, which was $65,000, it seems like a bad trade.

How many days would I need to have doubled my beans for the trade to make sense?

To estimate how many days you would need to have doubled your beans for the trade to make sense, we can solve for the number of days in the equation:

According to the above, we would need to have doubled your beans for approximately 16 days to make the trade worth it.

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Expressing her frustration and finding a time to have a conversation, is the most effective way for Kaylin to address the texting issue with CJ. Option A

By clearly communicating her feelings of frustration and the impact that constant texting has on her ability to study effectively, Kaylin can open up a dialogue with CJ. This approach allows both parties to discuss their expectations, needs, and find a mutually beneficial solution. It also demonstrates Kaylin's willingness to address the issue directly and find a resolution.

Option B, turning her phone on silent to study, may help Kaylin focus on her studies, but it doesn't address the underlying issue of CJ's constant texting or Kaylin's frustration with it. It may lead to miscommunication or further misunderstandings between them.

Option C, continuing to text CJ back or texting him when she is finished studying, doesn't address the issue of constant interruptions and the impact it has on Kaylin's ability to concentrate. It may perpetuate the behavior and not effectively communicate her needs and boundaries.

Therefore, option A, expressing her frustration and finding a time to have a conversation, is the most effective way for Kaylin to address the texting issue with CJ.

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Area of quadrilateral BCDE is 20 cm².

From the given figure,

AD/DB=AE/EC=2

AD/AB-AD=AE/AC-AE =2

AB-AD/AD=AC-AE/AE=1/2

AB/AD = AC/AE = 1+1/2

=3/2

Therefore, ratio of areas of triangles ABC and ADE will be

ΔABC/ΔADE = (3/2)² = 9/4

If area of ΔABC =36 cm²,

36/ΔADE = 9/4

Then area of ΔADE =36×4/9 = 16 cm²

Now area of quadrilateral BCED = Area of ΔABC - Area of ΔADE

= 36 - 16

= 20 square cm

Therefore, area of quadrilateral BCDE is 20 cm².

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Kevin make a triangle with an area of 5 is Correct.

To construct a triangle with an area of 5, we need to consider the formula for the area of a triangle: Area = (1/2) x base x height.

Let's choose a base of 4 units and a height of 2.5 units.

Plugging these values into the area formula, we have:

Area = (1/2) x 4 x 2.5

Area = 5

Therefore, we have constructed a triangle with a base of 4 units and a height of 2.5 units, resulting in an area of 5.

This confirms that it is indeed possible to make a triangle with an area of 5 units.

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Answer:

--------------------

The scale factor is the ratio of corresponding sides.

Find the scale factor k for the pictured triangles:

The two equations y - 3 = 2(x − 3) and y + 5 = 2(x + 1) represent (a) the same line

From the question, we have the following parameters that can be used in our computation:

y - 3 = 2(x − 3)

y + 5 = 2(x + 1)

Express the equations in slope intercept form

So, we have

y - 3 = 2x − 6

y + 5 = 2x + 2

These equations give

y  = 2x − 3

y = 2x - 3

The above equations are the same

This means that the two equations represent (a) the same line

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The linear function for the temperature is given as follows:

T(x) = 25 - 3x.

The graph is given by the image presented at the end of the answer.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The slope and the intercept for the function in this problem are given as follows:

Hence the function is given as follows:

T(x) = 25 - 3x.

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5/2 pounds is equal to 40 ounces.

We have to find the 5/2 pounds to ounces

1 pound is equal to 16 ounces.

To convert 5/2 pounds to ounces, we can multiply by 16:

5/2 pounds × 16 ounces/pound = 40 ounces

Therefore, 5/2 pounds is equal to 40 ounces.

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A.  The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.

B. No, the project does not meet the company's cash payback criteria.

C.  Yes, the project does meet the net present value criteria for acceptance.

A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.

                $55,440 / $7,700 = 7.2 years

To solve for the net present value, we say

Net Present Value = ∑ [(Cash inflow in period t) / (1 + [tex]r^{t}[/tex]] - Initial Investment.

NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63

+ ($7,700 / (1 + 0.08)²) = 6601.51

+ .($7,700 / (1 + 0.08)³ = 6112.51

+ ($7,700 / (1 + 0.08)⁴) = 5659.73

+ ($7,700 / (1 + 0.08)⁵) = 5240.49

+ ($7,700 / (1 + 0.08)⁶) = 4 852.31

+ ($7,700 / (1 + 0.08)⁷) = 4492.88

+($7,700 / (1 + 0.08)⁸)  = 4160.07

+ ($27,600 / (1 + 0.08)⁸)) = 14911.42

- $55,440

We add all these values together and subtract by  $55,440

7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440

59160.55 - 55,440

NPV = 3720.55

B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.

C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.

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The circumference of a circle is also referred to as the distance around that circle.

The circumference of the flower garden which is circular in shape is given as = 20 meters

The formula for the circumference of a circle is given as [tex]\bold{2\pi r}[/tex]

We have to find the radius of the circular garden

Hence: [tex]\sf 2\pi r = 20 \ m[/tex]

[tex]\sf \pi = 3.14[/tex]

To find the radius, the formula would be given as

[tex]\bold{r = \dfrac{C}{2\pi}}[/tex]

Where C = Circumference of the circle

[tex]\sf r = \dfrac{20}{2\times3.14}[/tex]

[tex]\sf r = \dfrac{20}{6.28}[/tex]

[tex]\sf r = 3.1847133758 \ m[/tex]

We can find the area of the circle now

The formula for the area of the circle is given as:

[tex]\bold{A = \pi r^2}[/tex]

[tex]\sf A = 3.14 \times 3.1847133758^2[/tex]

[tex]\sf A = 31.847133758 \ m^2[/tex]

[tex]\sf A\thickapprox32 \ m^2[/tex]

Therefore, the area of the flower garden to the nearest whole number is 32m²

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