4. A sequence of transformations was applied to an equilateral triangle in a coordinate plane.
The transformations used were rotations, reflections, and translations. Which statement about
the resulting figure is true?
A. It must be an equilateral triangle with the same side lengths as the original.
B. It must be an equilateral triangle, but the side lengths may differ from the original
triangle.
C. It may be a scalene triangle, and all the side lengths may differ from the original triangle.
D. It may be an obtuse triangle with at least one side the same length as the original triangle.

Did I read your handwriting correctly? Is this what you wrote? If so the answer is:

\((x( {x}^{2} - 2xy - {y}^{2} ) \div (x + y)(x - y)^{2} \)

The dimensions of the rectangle are 3√13 by 2√13

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

Area = 78 square cm

Dimensions = 3x cm by 2x cm

The area of a rectangle is the products of its dimensions

This means that

Area = 3x * 2x

So, we have

Area = 6x²

This gives

6x² = 78

Divide by 6

x² = 13

So, we have

x = √13

This means that the dimensions of the rectangle are 3√13 by 2√13

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Answer:

x= 63.4°

(the 4th option)

Step-by-step explanation:

Its a right angle triangle, with its opposite and adjacent values given so tan is used.

The ratio of trick-or-treaters who were not dressed as snow white last Halloween is 5/9

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.

It can be expressed in different ways:

1) Use the ":" to separate the values : a : b

2) Use the word "to" : a to b

3) Write it in fraction: a / b

On the other hand, proportion is the equality of two or more ratios.

example: a : b = c : d

If four out of every nine trick-or-treaters that came to your house last Halloween were dressed as snow white, then the rest were not dressed as snow white.

9 - 4 = 5

If five out every nine trick-or-treaters that came to your house last Halloween were not dressed as snow white, we can express the ratio as

5 out of 9 or 5 : 9 or 5/9

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Answer:

1/24

Step-by-step explanation:

fraction of people running = 1 - (5/8 + 1/3) = 1 - 23/24 = 1/24

A. approximately Normal, with a mean of 1100 and a standard error of 204.12.

This is because the Central Limit Theorem (CLT) states that the sampling distribution of the sample mean tends towards a normal distribution with a mean equal to the population mean and a standard error equal to the population standard deviation divided by the square root of the sample size.

In this case, the sample size is 24, so the standard error is 1000/sqrt(24) = 204.12. Therefore, the sampling distribution of the sample mean is approximately normal with a mean of 1100 and a standard error of 204.12.

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Answer:

x= -1/23

Step-by-step explanation:

The running club needs to sell (n - 15) sweatshirts at a price of $10 + $900/(n - 15) per sweatshirt to regain their $900 investment.

What is profit?

Profit is the money that a business or individual earns after taking away all the costs involved in producing or providing a product or service. It is the extra amount of money that is left over once all the bills and expenses have been paid.

A positive profit means that the business has earned more money than it has spent, while a negative profit means that it has lost money. Profit is important for businesses because it helps them stay financially stable and grow, and it is also important for individuals who want to earn a living from their work.

The running club bought a case of sweatshirts for $900, which means the cost per sweatshirt was $900 divided by the number of sweatshirts in the case. Let's assume there were "n" sweatshirts in the case.

Cost per sweatshirt = $900/n

The club needs to sell all but 15 of the sweatshirts at a profit of $10 per sweatshirt to regain the $900 investment. Let's assume they sell "x" sweatshirts at the desired price.

Revenue from selling x sweatshirts = x * ($10 + cost per sweatshirt)

The revenue must be equal to the cost of the investment, which is $900.

x * ($10 + $900/n) = $900

Simplifying the equation:

10x + 9000/n * x = 900

Multiplying both sides by n:

10nx + 9000x = 900n

Simplifying:

10nx = 900n - 9000x

Dividing both sides by 10:

nx = 90n - 900x/10

nx + 900x/10 = 90n

Simplifying:

x(n + 90) = 900

x = 900 / (n + 90)

Since the club needs to sell all but 15 of the sweatshirts, the number of sweatshirts they need to sell is:

n - 15

Therefore, the number of sweatshirts they need to sell, "x", is:

x = 900 / (n + 90)

And the price they need to sell each sweatshirt at is:

($10 + cost per sweatshirt)

= ($10 + $900/n)

Substituting the value of "x" from the previous equation, we get:

Price per sweatshirt = $10 + $900 / (n - 15)

So, to recap, the running club needs to sell (n - 15) sweatshirts at a price of $10 + $900/(n - 15) per sweatshirt to regain their $900 investment.

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In a transportation problem, the activities correspond to the shipping lanes while the supply of each activity is the quantity shipped.

In the transportation problem, activities are the shipping lanes that are taken to transport goods from sources to destinations.

The quantities to be shipped are known as supplies or availabilities. The transportation problem is a linear programming problem that is used to determine how to allocate resources to obtain a minimum cost or maximum profit.The transportation problem is one of the most widely used problems in linear programming. It is used to solve many real-world problems such as supply chain management, production planning, and logistics.

In the transportation problem, we are given a set of sources and a set of destinations. The supply and demand at each source and destination are also given. The objective is to minimize the total cost of transporting the goods from sources to destinations while satisfying the demand and supply constraints.

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Answer:

the nominator could be any number here

Step-by-step explanation:

what do you need ? the equation itself is true, if you put the same number in both places above 21.

any number is possible there, it will not change the equation.

so, again, I am not sure, what you need here.

let's write it with a variable to make my statements clearer :

9 + 1 x/21 = 10 x/21

that is true, because we can combine the whole numbers first giving us 9 + 1 = 10.

and then we add the fraction again (x/21).

again, you can put any number instead of x, and it will always be true.

example

9 + 1 4/21 = 10 4/21

Answer:

42

Step-by-step explanation:

The main goal of data democratization is to make data accessible to all users. Option (a) is correct.

Given the primary goal of data democratization.

Data democratization is the ability to make information in a digital format accessible to the average end user. The goal of data democratization is to allow non-professionals to collect and analyze data without the need for outside help. This requires us to support access with an easy way for people to understand data, so they can use it to accelerate decision-making and uncover opportunities for a business. The goal is for everyone to be able to use the data at any time to make decisions without barriers of access or understanding.

Therefore, the main goal of data democratization is to make data accessible to all users.

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The best buy for granulated sugar is the 4lb option since it is lesser.

To find the best buy for the item , we calculate the cost per pound of the item :

4lb = $2.93

10lb = $8.45

Cost per lb for 4lb :

2.93/4 = $0.7325 per lb

Cost per lb for 10lb :

8.45/10 = $0.845 per lb

Since the cost per lb for 4lb granulated sugar is lesser, then it is the best buy.

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Answer: B= 16

Step-by-step explanation:

The rate at which the sales are changing when the number of units sold is 1,900 is approximately $4,358 per month.

The correct answer is A. $4,358.899/month.

Here, we have,

To find how fast the sales are changing when the number of units sold is 1,900, we need to determine the rate of change of sales with respect to time.

The rate of change of sales can be found using the chain rule.

Given that the profit generated by the product is P(x) = 2√x, where x is the number of units sold, we can express the profit as a function of time, P(t), where t is the time in months.

Since the profit is changing at a rate of $200 per month, we have:

dP/dt = 200

To find dx/dt, the rate of change of sales with respect to time, we need to relate P(x) and x. We can rewrite the profit equation as:

P(x) = 2√x

x = (P(x)/2)²

Now, we differentiate both sides with respect to time, t:

dx/dt = d/dt((P(x)/2)²)

Applying the chain rule, we have:

dx/dt = 2(P(x)/2)(dP/dt)(1/2)(1/x)

= P(x) * dP/dt * (1/2) * (1/x)

Substituting the given values, P(x) = 2√x and dP/dt = 200, we have:

dx/dt = 2√x * 200 * (1/2) * (1/x)

= 200/√x

Now, we can substitute x = 1,900 into the equation to find the rate of change of sales at that point:

dx/dt = 200/√(1,900)

= 200/√(1900)

≈ 200/43.58899

≈ 4.587

Rounding the answer to the nearest dollar per month, we get approximately $4,358.

Therefore, the rate at which the sales are changing when the number of units sold is 1,900 is approximately $4,358 per month.

The correct answer is A. $4,358.899/month.

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Step-by-step explanation:

Probability of A  is  10 + 5  =15

Probability of B is   9 + 5   ( but you already counted the '5')  

 so just count   9

9+ 15 = 24

  this is  24 out of     16 + 10 + 5 + 9 = 40

      or    24/40   which reduces to 3/5   or  .6   or  60%

Using the equation given:

P(A) + P(B) - P(A and B)

  15  + 14    - 5    = 24       this is out of the entire number 40

               24/40 = same as above

Answer:

=13x+12

Step-by-step explanation:

The measure of each of the acute angles of the right triangle is 32° and 58°.

A right triangle is a kind of triangle which has a right angle (90°) and two acute angles (less than 90°).

Let x = measure of one of the acute angles

If the measure of one acute angle of a right triangle is 6 less than twice the measure of the other acute angle, then

measure of the other acute angle = 2x - 6

The sum of all the angles of any triangle is equal to 180°. Hence,

90° + x + 2x - 6 = 180°

Solve for the value of x.

3x = 96

x = 32

Solve for the measure of the other acute angle.

2x - 6 = 2(32) - 6 = 58

Hence, the two angles are 32° and 58°.

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Answer:

#1 = -2

Step-by-step explanation:

First, we need to make -2 2/3 an improper fraction. An improper fraction is a fraction whose numerator is bigger than its denominator.

you first multiply the whole number (ignoring the negative sign for now) by the denominator:

2*3=6

then you add the numerator:

6+2=8

finally you put that number over the denominator and then put the negative sign back:

-8/3

Next, you can use keep change flip to solve the division

You keep the first fraction, change the division sign to a multiplication sign, and flip the numerator and the denominator of the second fraction:

-8/3 divided by 4/3 becomes -8/3 x 3/4

finally you multiply across as you would normally and simplify

-8/3 x 3/4= -24/12

-24/12 simplified is -2

:D

if you need help with the rest just comment on this response and I'll try to answer as soon as I can

If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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Answer:

4

Step-by-step explanation:

an=-4+3(n-1)=-4+3n-3=3n-7

a1=3×1-7=3-7=-4

a5=3×5-7=15-7=8

a1+a5=-4+8=4

Answer:

Kinda confusing, (probably just me) but I think it may be 1,400 rabbits last year.

Answer:

21/56, 40/56, 22/56

10/75, 21/75

Step-by-step explanation:

To get a "like fraction" multiply the top and bottom by the same number. This changes the way the fraction looks, but keeps the value of it the same.

8, 7, and 28 all go into 56. Change the denominator (bottom number) to 56. Use the same multiplier on the top. See image.

For the second problem, multiply by 5/5 and 3/3 to get two fractions that both have 75 in the denominator.

see image.

Rose has $208 in savings if their total savings is $324.

Let's use algebra to solve this problem. We can start by defining variables for each person's savings:
- Let R be the amount of savings Rose has.
- Let C be the amount of savings Cheko has.
- Let Y be the amount of savings Yimin has.

From the problem, we know that:
- R = 4C (Rose has 4 times as much savings as Cheko)
- Y = C + 12 (Yimin has $12 more savings than Cheko)
- R + C + Y = 324 (Their total savings is $324)

Now we can substitute the first two equations into the third equation:
4C + C + (C + 12) = 324

Simplifying gives:
6C + 12 = 324

Subtracting 12 from both sides gives:
6C = 312

Dividing by 6 gives:
C = 52

Now we can use the first equation to find Rose's savings:
R = 4C = 4(52) = 208

So Rose has $208 in savings.

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A person can immigrate to another country for educational purposes.

A person can emigrate to another country for work.

A person can emigrate to another country due to war in their own country.

Migration is when a person moves from one geographical location or another. Immigration and emigration are types of migration.

Immigration is when a person moves to a foreign country. For example, when a US citizen moved to Italy for work. Emigration is when a person lives his home country.

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The stationing of the PT is 153 + 75. The reason is explained below;

Given: Initial grade: +3%

Final grade: +1%

PVC: 101 + 78

PVT: 106 + 72

Superelevation of the horizontal curve: 8%

Radius of the curve = (360/2π) × (30/8) = 137.5 feet

Arc length, L = (75/360) × 2π × 137.5 = 72.03 feet

Two 12-ft lanes, L1 = 12 ft and L2 = 12 ft

Two lanes width, w = L1 + L2 = 24 ft

Let Y be the elevation of the horizontal curve at any point. Thus;

Y = [(x - 150 - 5.25)²/2 × 137.5] × (0.08/24)Y

= [(x - 155.25)²/4125] × 0.08

Where x is the stationing distance in feet from the PI.

The equation for the vertical curve is given by;

Y = ax² + bx + c

Where;

a = -0.001598

b = 0.4424

c = 67.4916x

PVC = 101 + 78 = 179 ft

PVT = 106 + 72 = 178 ft

Therefore, at PVC, x = 78ft Y = -0.001598(78²) + 0.4424(78) + 67.4916 = 99.071 ft

Also at PVT, x = 72ftY = -0.001598(72²) + 0.4424(72) + 67.4916 = 98.956 ft

The difference in the elevation of the vertical curve at PVC and PVT;

∆Y = YPVT - YPVC

= 98.956 - 99.071

= -0.115 ft

The elevation of the pavement at the PT is given by;

YPt = Ypvc + ∆Y

= 99.071 - 0.115

= 98.956 ft

Finally, the stationing of the PT;

Stationing of the PT = 150 + arc

length to the PT = 150 + 72.03

= 153.03 feet

≈ 153 + 75

Therefore, the stationing of the PT is 153 + 75.

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Answer:

4

Step-by-step explanation:

I don't know how to explain this other than use a calculator.

Hope that this helps!

Answer:

The answer is 58 In2

you can take apart some of the parts and multiply them, it may be easier

Answer:

I believe it is acutally 53inches

Answer:

we conclude that Membership grows by 14 each year.

Step-by-step explanation:

Given the equation

\(y=14x+10\)

Comparing the equation with the slope-intercept form

\(y=mx+b\)

Here, m is the slope and b is the y-intercept.

From the equation, we can determine the slope

\(y=14x+10\)

\(m=14\)         ∵  \(y=mx+b\)

Hence, the slope is m=16.

We know that the slope is referred to as the 'rate of change'.

For example, if you have a part-time job at a store. You save for her tour at a rate of $20 every week. It means, your rate of change will be $20 per week.

So given the equation

\(y=14x+10\)

m = rate of change = slope = 24

The slope is basically a vertical change divided by the horizontal change.

Therefore, we conclude that Membership grows by 14 each year.