Which statement is missing in the proof?

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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Answer:

\(u = wxv \\ \boxed{ v = \frac{u}{wx} }\)

The equation u = wxv is solved for v and the equation is written as v = u / wx.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

u = wxv

Simplify the equation for v, then the equation is given as,

wxv = u

v = u / wx

The equation u = wxv is solved for v and the equation is written as v = u / wx.

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Answer: C. m = -2; n = -2

have:

x² + 4x + c = (x + m)(x + n)

⇔ x² + 4x + c = x² + (m + n)x + mn

⇒ m + n = 4

    mn = c

=>  M=-2, n=-2 arent possible

Step-by-step explanation:

Answer:

$669.60

Step-by-step explanation:

item with an original price tag of $775.00 that is marked down by 20% will have a sales price of $620.00 plus 8% tax

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

In the equation, we will need to calculate the maximum amount of money Marian can spend on the house.

We can calculate the maximum amount of money Marian can spend on a house by multiplying her monthly income by the number of months she would want to save.

Marian earns $4,100.00 per month

Suppose Marian wants  to save for  x months,  then the maximum amount that she can spend on the house is:

4100  *   x    +  21390

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

Hope this helps!

Area= 69π or 216.77 square units.

Remember that the formula for the area of a circle is the following:

\(A=\pi r^{2}\); where "r" is the radius of the circle.

Hence, the area of the white circle is:

\(A_{WC} =\pi (10)^{2} =100\pi\)

Here you can use the same formula, just need to change the value of the radius:

\(A_{RC} =\pi (13)^{2} =169\pi\)

\(A_{RC} -A_{WC} =169\pi -100\pi =69\pi\)

The area of the shaded region is 69π or 216.77 square units, approximately.

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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

Mutually exclusive events are events that cannot occur at the same time, or that do not have any overlap. In the case of flipping a coin, the possibility of getting a head and the possibility of getting tails are independent of each other, and both can occur simultaneously. Therefore, the chance that you will get heads or tails when you flip a coin once is not mutually exclusive.

On the other hand, the other events listed (B, C, and D) are mutually exclusive. The chance that you will only study for the test alone or with a friend cannot occur simultaneously, as you can either study alone or with a friend, but not both. Similarly, the chance that you will meet your friends for pizza or at a Chinese restaurant for dinner today at 6 cannot occur at the same time, as you can either go to the pizza place or the Chinese restaurant, but not both. And the chance that you will answer the ringing phone or take a walk cannot occur simultaneously, as you can either answer the phone or take a walk, but not both.

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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

this question is related to probability.

mutually exclusive

Mutually exclusive events are those events that do not occur at the same time.

For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.

probability

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Step-by-step explanation:

12x-5=91°

12x=91+5

x =96

12

x=8°

hope it helps.

Answer:

Step-by-step explanation:

I'm sure he was making a joke at the expense of people who rely on mathematics rather than common sense. It is funny, but then Twain was a remarkably funny author..

The problem is that the comparison is apt using some sort of proportion, but it is absurd to think that the land holding the river would also shrink a proportional amount.  

The river reached a minimum (presumably) in 1875 by cutting out all the loops that were there in 1700. The Mississippi was then a straight line from it's beginning to its delta on the gulf of Mexico. It could not get any shorter. Still, Twain managed to get laughs with his whimsical humor.

Thanks for posting. This made my evening.

1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.

2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.

3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.

1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.

2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.

3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.

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Answer:

Step-by-step explanation:Base on the diagram, and the following question, the following are the answers to your question.

#1 Congruent Angle

#2 Congruent Sides

#3 Side Angle Side

I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarification

Answer: negative

Step-by-step explanation:

because –57 + 19= -38

and negative plus positive is negative

so the answer is negative

Hope this helps :)

Answer:

Negative

Compare the absolute values (how far the number is away from zero)

57 is bigger than 19

since 57 is negative and bigger than 19 when they add the sum will still be negative

Step-by-step explanation:

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Kim's test scores indicate that he scored as well as or better than 72% of the test takers, and 28% of the test takers scored better than him. His grade equivalent of 12.1 indicates that he would perform adequately in a twelfth grade science class.

His percentile of 88 indicates that he scored as well as or better than 88% of the test takers. His raw score of 72 does not directly indicate the percentage of questions answered correctly, but it can be assumed that he answered a majority of the questions correctly to achieve his score.

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Answer:

3. 2.4 c.m

The height of the cone 'h' = 2.4 c.m

Step-by-step explanation:

Explanation:-

Given radius of the cone = 2 cm

Given data

The volume of a cone-shaped dessert is 10 cubic centimetres

The Volume of the Cone

                          \(V = \frac{1}{3} \pi r^{2}h\)

                        \(10 = \frac{1}{3} X 3.14 X (2)^{2} X h\)

  cross multiplication , we get

                  \(h = \frac{ 3 X 10}{3.14 X 4}\)

                 h =  2.388 ≅ 2.4 c.m

The height of the cone 'h' = 2.4 c.m

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)

The multiplication of the given values of  321 x 21398 is 6868758.

Multiplication operation can be described as the operation which involves the addition of numbers that are of equal groups which is been performed using the sign *.

When performing a multiplication operation a value will be used to multiply another values, for instance the given question, where  321 was given to multiply 21398,  which can be represented as  (321 x 21398 ) then we now have 6868758 as the result of the multiplication operation.

Therefore, after performing the multiplication operation on the given values the result will be 6868758.

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Answer:

Given:

Amount made by each computer programmer = $10⁵Number of computer programmers = 10⁶

Solution:

  The total money can be found using;                   = Amount made by each programmer x number of programmers 

= $10⁵ x 10⁶   

 = $10¹¹

As a power of ten, the amount made is $10¹¹

In dollar amount  = $100,000,000,000

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 220 engines and the mean pressure was 5.4 pounds/square inch (psi), the level of significance for the hypothesis test is 0.05. This is further explained below.

Generally, the level of significance is simply defined as statistical analysis, the significance level is defined as the likelihood of rejecting the null hypothesis when it is correct.

In conclusion,  The average pressure throughout testing on 220 engines was 5.4 psi, and the significance threshold for the hypothesis test was set at 0.05.

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Answer:

Step-by-step explanation:

The line in slope intercept form :

y = mx + p

Where m is the slope

and p is the y value of the y intercept point

…………………………………………………………………

the y intercept point is (0 , 5) then p = 5

Slope calculation:

(0 , 5) and (2 , 15) are two points of the line , then

\(m=\frac{15-5}{2-0} =\frac{10}{2} =5\)

Conclusion:

y = 5x + 5

Answer:

x ≥ 3

Step-by-step explanation:

- 3(2x - 1) ≤ x - 18 ← distribute parenthesis on left side

- 6x + 3 ≤ x - 18 ( subtract x from both sides )

- 7x + 3 ≤ - 18 ( subtract 3 from both sides )

- 7x ≤ - 21

divide both sides by - 7, reversing the symbol as a result of dividing by a negative quantity.

x ≥ 3

Answer:

2x + 2y + 3y

Step-by-step explanation:

The others are equations ( containing the = sign).

Answer:

2x+2y+3y

Step-by-step explanation:

an expression is not equated to any number but an equation is equated to any number especially zero

Answer:

Max's carton has 2 inches squared more volume than Tucker's carton.

Explanation:

First, calculate the volume of each of the cartons.

Max's Carton

• Height = 6 inches

• Base Area = 12 inches squared.

Max's carton has a volume of 72 cubic inches.

Tucker's Carton

• Height = 7 inches

• Base Area = 10 inches squared.

Tucker's carton has a volume of 70 cubic inches.

Next, we find the difference in volume.

Max's carton has 2 inches squared more volume than Tucker's carton.

Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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The measure of the angle B of the triangle is 78.15 degrees

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

A = 25 degrees

a = 9.5 units

b = 22 units

Using the law of sines, the angle B is calculated as

sin(A)/a = sin(B)/b

So, we have

sin(25)/9.5= sin(b)/22

This gives

sin(b) = 22 * sin(25)/9.5

Evaluate

sin(b) = 0.9787

Take the arc sin of both sides

b = 78.15

Hence, the measure of the angle is 78.15 degrees

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Answer: 3.5

Step-by-step explanation:

Since 10% x 10 = 100%

So we have to do 35 ÷ 10

35 ÷ 10 = 3.5

In conclusion, 10% of 35 = 3.5

Hope this helps!

Answer:

11

Step-by-step explanation:

2^3-(30/5)+9

First, you divide 30/5 because it is in parentheses and we are following this rule for order of operations:

P- parentheses

E- exponents

M- multiplication

D- division

A- addition

S- subtraction

so 30/5 = 6 and plugged in is:

2^3-(6)+9

Next, we do exponents:

2^3 = 2x2x2 = 8

plugged back in:

8-(6)+9

Now, we do the math from left to right so:

8-6=2

2+9=11

11 is your answer

The answer is D: conjecture

The key words in the description are "look for a pattern and then form an educated guess." This suggests making a hypothesis or assumption based on the observed pattern, which is the definition of a conjecture.

The other answer choices are defined as follows:

A. conjugation - the act of changing a verb to agree with its subject

B. conjunction - a connecting word

C. congruence - the state of agreeing, matching, or coinciding

D. conjecture - an opinion or conclusion formed on the basis of incomplete information

So option D, conjecture, is the best match for forming an educated guess based on an observed pattern in induction.