Answers
Answer: Bottom left corner
[tex]f^{-1}(x) = \frac{-9x-7}{x+6}\\\\[/tex]
=======================================
Work Shown:
[tex]f(x) = \frac{-6x-7}{x+9}\\\\y = \frac{-6x-7}{x+9}\\\\x = \frac{-6y-7}{y+9}\\\\x(y+9) = -6y-7\\\\[/tex]
[tex]xy+9x = -6y-7\\\\xy+6y = -7-9x\\\\y(x+6) = -9x-7\\\\y = \frac{-9x-7}{x+6}\\\\f^{-1}(x) = \frac{-9x-7}{x+6}\\\\[/tex]
Explanation:
I swapped x and y. Then I solved for y to get the inverse.
Related Questions
Jala put $600 in an interest bearing account with a annual compound interest rate of 5%. Jala determined that after seven years, she will have a total balance of $844. 26. Using the rule of 72, t = StartFraction 72 Over r EndFraction how many more years will it be before Jala’s $600 doubles in value? Round to the nearest tenth. 3. 3 years 7. 4 years 10. 3 years 14. 4 years.
Answers
Jala put $600 in an interest bearing account with a annual compound interest rate of 5%. Jala determined that after seven years, she will have a total balance of $844. Hence, Jala will have to wait for D) 4 years.
To determine how many more years it will take for Jala's $600 to double in value, we can use the rule of 72, which states that the time it takes for an investment to double in value can be approximated by dividing 72 by the annual interest rate.
In this case, the annual compound interest rate is 5%.
Using the rule of 72:
t = 72 / r
where t is the time in years and r is the annual interest rate.
t = 72 / 5 = 14.4
Rounding to the nearest tenth, it will take approximately 14.4 years for Jala's $600 to double in value.
Out of the given answer choices, the closest option is 14.4 years, which can be rounded to 14 years. Therefore, the answer is:
4 years.
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The financial statements of the Blue Spruce Corp. reports net sales of $624000 and accounts receivable of $82800 and $45600 at the beginning of the year and end of year, respectively. What is the average collection period for accounts receivable in days
Answers
The average collection period for accounts receivable in days for Blue Spruce Corp. is approximately 59.9 days.
To calculate the average collection period, we need to determine the average accounts receivable balance. We can do this by adding the beginning and ending accounts receivable balances and dividing the sum by 2. In this case, the average accounts receivable balance is ($82,800 + $45,600) / 2 = $64,200.
Next, we need to divide the net sales by the average accounts receivable balance and multiply the result by 365 (the number of days in a year). This gives us ($624,000 / $64,200) * 365 = 3.579 * 365 ≈ 1,306.135.
Therefore, the average collection period for accounts receivable is approximately 59.9 days. This means it takes Blue Spruce Corp. around 59.9 days, on average, to collect payment from its customers. A lower average collection period is generally preferable, as it indicates quicker cash flow and better liquidity for the company.
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you toss a coin four times. what's the probability of tossing tails exactly once? is this an unusual event?
Answers
Step-by-step explanation:
Four tosses of the coin result in 2^4 = 16 possible outcomes of which FOUR
will have ONE tails :
HHHT
HHTH
HTHH
THHH so 4 out of 16 = 4/16 = 1/4 Not very unusual
Ryann is a shareholder of Sigma Corp. and has evidence to suggest that its president/CEO has allowed the corporation to engage in acts that are ultra vires. Based upon this evidence, Ryann contacts an attorney and sues the corporation on behalf of the corporation. The lawsuit Ryann has filed is known as a(n): A direct suit. B derivative suit. C class action suit. D unauthorized suit.
Answers
The lawsuit that Ryann has filed is known as a derivative suit.
In a derivative suit, a shareholder brings a legal action on behalf of the corporation against a third party, typically the corporation's officers or directors, for actions that harm the corporation. The shareholder acts as a representative of the corporation, seeking to enforce the corporation's rights and recover damages on its behalf.
In this case, Ryann is suing Sigma Corp. on behalf of the corporation due to alleged acts by its president/CEO that are ultra vires, meaning they exceed the authority granted to them by the corporation's governing documents or applicable laws. The purpose of a derivative suit is to protect the interests of the corporation and its shareholders.
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Market failure means that Question 17 options: the market has crashed. the market has not provided a socially optimal amount of goods and services. the market has more buyers than sellers. some firms that were in the industry have gone bankrupt.
Answers
The correct option is (C):the market has not provided a socially optimal amount of goods and services. Market-failure means the market has not provided a socially optimal amount of goods and services.
Market failure is a term used to describe a situation where the market has not provided an optimal allocation of goods and services from a social perspective. This means that the market has failed to allocate resources efficiently, resulting in a suboptimal outcome. Market failure can occur due to a variety of reasons, such as externalities, information asymmetry, public goods, and monopoly power. In such situations, government intervention may be required to correct the market failure and ensure the provision of socially optimal goods and services.
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the chemical formula for sodium bromide is NaBr. A chemist measured the amount of sodium bromide produced during an experiment. She finds that 4.90g of sodium bromide is produced. Calculate the number of moles in sodium bromide produced.
Answers
Answer:
Step-by-step explanation:
To calculate the number of moles in sodium bromide (NaBr) produced, we need to use the formula:
Number of moles = Mass / Molar mass
The molar mass of sodium bromide can be determined by adding the atomic masses of sodium (Na) and bromine (Br) together.
The atomic mass of Na is approximately 22.99 g/mol.
The atomic mass of Br is approximately 79.90 g/mol.
So, the molar mass of NaBr is:
Molar mass of NaBr = Atomic mass of Na + Atomic mass of Br
= 22.99 g/mol + 79.90 g/mol
= 102.89 g/mol
Now we can calculate the number of moles:
Number of moles = Mass / Molar mass
= 4.90 g / 102.89 g/mol
Calculating this, we find:
Number of moles = 0.0476 moles (rounded to four decimal places)
Therefore, 4.90 g of sodium bromide is equivalent to approximately 0.0476 moles of sodium bromide.
(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)
(c ^ 2 - (a - b) ^ 2)/(a ^ 2 - (b + c) ^ 2) + (a ^ 2 - (b - c) ^ 2)/(b ^ 2 - (c + a) ^ 2) + (b ^ 2 - (c - a) ^ 2)/(c ^ 2 - (a + b) ^ 2)
Answers
If a + b + c = 0, the value of the expression is 2.
The expression refers to the mathematical equation provided in the previous response. Here is the simplified expression after performing the necessary calculations:
Given that a + b + c = 0, we can simplify the expression as follows:
[tex](c ^ 2 - (a - b) ^ 2)/(a ^ 2 - (b + c) ^ 2) + (a ^ 2 - (b - c) ^ 2)/(b ^ 2 - (c + a) ^ 2) + (b ^ 2 - (c - a) ^ 2)/(c ^ 2 - (a + b) ^ 2)[/tex]
Replacing c with -(a + b), we get:
[tex]((-a - b) ^ 2 - (a - b) ^ 2)/(a ^ 2 - (b + (-a - b)) ^ 2) + (a ^ 2 - (b - (-a - b)) ^ 2)/(b ^ 2 - ((-a - b) + a) ^ 2) + (b ^ 2 - ((-a - b) - a) ^ 2)/((-a - b) ^ 2 - (a + b) ^ 2)[/tex]
Simplifying further:
[tex](4ab)/(a ^ 2 - (a - 2b) ^ 2) + (4ab)/(b ^ 2 - (-a + b) ^ 2) + (4ab)/((a + b) ^ 2 - (-a - b) ^ 2)[/tex]
Since a + b + c = 0, we have c = -(a + b), which implies that c ^ 2 = (a + b) ^ 2.
Substituting this back into the expression:
[tex](4ab)/(a ^ 2 - (a - 2b) ^ 2) + (4ab)/(b ^ 2 - (-a + b) ^ 2) + (4ab)/((a + b) ^ 2 - (a + b) ^ 2)[/tex]
Now, we can simplify the denominators:
[tex](a ^ 2 - (a - 2b) ^ 2) = 4ab\\\\(b ^ 2 - (-a + b) ^ 2) = 4ab\\\\((a + b) ^ 2 - (a + b) ^ 2) = 0[/tex]
Therefore, the expression simplifies to:
(4ab)/(4ab) + (4ab)/(4ab) + 0
Simplifying further:
1 + 1 + 0 = 2
Thus, the value of the expression is 2.
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Your question seems incomplete, the probable complete question is:
If a+b+c=0, then find (c ^ 2 - (a - b) ^ 2)/(a ^ 2 - (b + c) ^ 2) + (a ^ 2 - (b - c) ^ 2)/(b ^ 2 - (c + a) ^ 2) + (b ^ 2 - (c - a) ^ 2)/(c ^ 2 - (a + b) ^ 2)
A firm manufactures aircraft engines for sale to its main client, a producer of small
airplanes. Its client has signed a contract to purchase at least 20 engines this year at a price per
engine given by the formula p = 200 −2q, where p is in thousands of dollars and q is the number
of engines purchased. This pricing formula implies that the price per engine is lower if the client
purchases more engines. The firm has the capacity to produce at most 55 engines per year. What
number of engines purchased would produce the most revenue for the firm?
Answers
To determine the number of engines that would produce the most revenue for the firm, we need to find the quantity at which the marginal revenue equals zero.
In this case, the marginal revenue is the derivative of the revenue function with respect to the quantity of engines sold.
The revenue for the firm can be calculated by multiplying the quantity of engines sold (q) by the price per engine (p). From the given formula, the price per engine is p = 200 - 2q.
The revenue function, R, can be expressed as R = q * p. Substituting the price formula, we have R = q * (200 - 2q).
To find the quantity that maximizes revenue, we differentiate the revenue function with respect to q, set it equal to zero, and solve for q.
Taking the derivative of R with respect to q, we get dR/dq = 200 - 4q.
Setting dR/dq = 0, we have 200 - 4q = 0. Solving for q, we find q = 50.
Therefore, the firm would generate the most revenue by selling 50 engines to its main client.
At this quantity, the price per engine would be p = 200 - 2(50) = 100 thousand dollars. The total revenue would be R = 50 * 100 = 5000 thousand dollars.
Selling more than 50 engines would result in a decrease in revenue due to the declining price per engine as per the pricing formula.
Selling fewer than 50 engines would also result in a lower revenue due to the missed opportunity to sell more engines at a higher price. Thus, 50 engines is the optimal quantity for maximizing revenue for the firm.
Therefore, selling 50 engines would produce the most revenue for the firm.
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the oblique pyramid has a square base with an edge length of 5 cm. the height of the pyramid is 7 cm. an oblique pyramid has a square base with an edge length of 5 centimeters. the height of the pyramid is 7 centimeters. what is the volume of the pyramid?
Answers
The volume of the oblique pyramid is approximately 58.33 cubic centimeters.
To find the volume of the oblique pyramid with a square base and an edge length of 5 cm, and a height of 7 cm, you can follow these steps:
1. Determine the area of the square base:
A = side x side = 5 cm x 5 cm = 25 square centimeters.
2. Apply the formula for the volume of a pyramid:
Volume = (1/3) x Base area x Height = (1/3) x 25 square centimeters x 7 centimeters.
3. Calculate the volume:
Volume = (1/3) x 25 x 7 = 58.33 cubic centimeters (rounded to two decimal places).
So, the volume of the oblique pyramid is approximately 58.33 cubic centimeters.
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The volume of the oblique pyramid with a square base of edge length 5 cm and height 7 cm is 58.33 cubic centimeters.
Explanation:The base of the pyramid is a square with an edge length of 5 cm, so its area is 5cm x 5cm = 25cm2. We multiply this by the height of the pyramid, which is 7 cm, and then divide by 3:
Volume = (25cm2 x 7cm) / 3 = 175cm3 / 3 = 58.333cm3
Therefore, the volume of the oblique pyramid is approximately 58.333 cubic centimeters.
To find the volume of the pyramid, we'll use the formula for volume of a pyramid which is 1/3 * base area * height. For an oblique pyramid with a square base and an edge length of 5 cm, the base area is side length squared, which is 5 * 5 = 25 sq cm. The pyramid's height is given as 7 cm. The volume then becomes 1/3 * (25 sq cm) * (7 cm), which equals 58.33 cubic centimeters.
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Which sociologist(s) first identified the effects of viewer fatigue and created the term narcotizing dysfunction
Answers
Sociologists Paul Lazarsfeld, as well as Robert Merton, were the first to recognize the effects of audience fatigue as well as coined the term narcotizing dysfunction.
Narcotizing dysfunction has become a theory that holds that as the media bombards people with information about a specific issue, it is all about gaining knowledge for action. This theory has its foundation in the development of knowledge for action. It refers to the benefits of the action.
In the article "Mass Communication," a phrase such as "narcotizing dysfunction" experienced coined.
Narcotizing malfunction affects society such as poverty, crime, along with poor health. Narcotizing dysfunction has a negative impact on organizational structure.
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An easement enabling its holder to prevent the possessor of the land subject to the easement from doing certain acts or exercising certain rights of ownership he/she would otherwise have a legal right to is known as a
Answers
An easement enabling its holder to prevent the possessor of the land subject to the easement from doing certain acts or exercising certain rights of ownership is known as a negative easement.
A negative easement grants the holder the right to restrict or prohibit specific activities on the land, even though the possessor of the land would otherwise have the legal right to engage in those activities. It imposes limitations on the use or enjoyment of the land by the possessor.
For example, a negative easement may prohibit the landowner from building any structures that would obstruct the view of the neighboring property or from engaging in any activities that would cause excessive noise or pollution. The holder of the negative easement, such as a neighboring property owner or a conservation organization, can enforce these restrictions to protect their interests or preserve certain conditions.
Negative easements are typically established through legal agreements or by court decisions. They serve to balance the rights of the landowner with the interests of the easement holder, allowing for the protection of specific rights or conditions associated with the land.
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Your parents are redecorating the dining room and want to place two rectangular pictures, each measuring 25 inches across, on the wall, which measures 10 2/3
feet long. They want to place the pictures so that the distance between the pictures and the distances from each picture to the end of the wall are the same, as shown in the diagram below. Write the equation using the variable X.
Answers
Answer:
2X + 25 = 128
Step-by-step explanation:
10 2/3 feet = 10 * 12 + (2/3) * 12 = 120 + 8 = 128 inches.
Now, let's create the equation using the variable X:
X + 25 + X = 128
Adding the distances from each picture to the total width of the pictures (25 inches) and setting it equal to the length of the wall (128 inches).
Simplifying the equation:
2X + 25 = 128
How do you do this question?
Answers
The perimeter of the figure 1 is 36 centimeter.
From the given figure,
1) Missing side = 8-5 = 3 cm
Here, perimeter = 8+10+5+7+3+3 = 36 cm
2) Missing side = 12-8 = 4 cm
Missing side = 9-7 = 2 cm
Here, perimeter = 12+7+4+8+9+2
= 42 cm
3) Missing side = 60-40 = 20 mm
Missing side = 30+15 = 45 mm
Perimeter = 60+15+40+30+20+45
= 210 mm
4) Missing side = 71/2 + 11/2
= 9 m
Missing side = 4+2 = 6m
Perimeter = [tex]7\frac{1}{2}[/tex] + 4+ [tex]1\frac{1}{2}[/tex] +2+9+6
= 9+4+2+9+6
= 30 m
Therefore, the perimeter of the figure 1 is 36 centimeter.
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a square pyramid has a volume of 480 cubic inches and a height of 10 inches. what is the perimeter of the base?
Answers
Answer:
48 in-------------------
The volume of a pyramid is 1/3 of the product of the base area and height.
V = Bh/3Find the area of the base:
480 = B*10/3B = 480*3/10B = 144The base is the square, so each side is the square root of the base area:
a = √Ba = √144a = 12The perimeter of the base is:
P = 4aP = 4(12)P = 48Answer: 48 inches
Step-by-step explanation:
480*3=1440
1440/10=144
each side: 12
12*4=48 inches
Alguien me ayuda con esto??
Answers
Part A: The volume of the right rectangular prism is 40/9 cubic inches.
Part B: 360 small cubes of edge lengths of 1/3 inches can fit in the given right rectangular prism.
To find the volume of the right rectangular prism, we can use the formula:
Volume = Length x Width x Height
Using the given dimensions of the prism, we have:
Volume = (4/3) x 2 x (5/3)
Volume = (4 x 2 x 5) / (3 x 3)
Volume = 40/9
To find how many small cubes of edge lengths of 1/3 inches can fit in the right rectangular prism, we need to calculate the number of small cubes that can fit in each dimension (length, width, height) and then multiply the results together.
For the length of the prism, there are 4 cubes of edge length 1/3 inch that can fit (since 4 x 1/3 = 4/3, which is less than 1(1/3) inch).
For the width of the prism, there are 6 cubes of edge length 1/3 inch that can fit (since 6 x 1/3 = 2 inches).
For the height of the prism, there are 15 cubes of edge length 1/3 inch that can fit (since 15 x 1/3 = 1(2/3) inches).
Multiplying the number of cubes that can fit in each dimension, we get:
Number of cubes = 4 x 6 x 15
Number of cubes = 360
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Determine the domain of the following graph:
Answers
Answer:
D: [-8, 8]
Step-by-step explanation:
Domain refers to allowable x-values. In the graph, x-values from -8 to 8 are used (look at what x values the graph passes through).
We expect the demand curve in the perfectly competitive industry to be Group of answer choices evenly divided horizontal directly sloped vertical negatively sloped
Answers
In a perfectly competitive industry, the demand curve is negatively sloped. so, the correct option is d) Negatively Sloped
In economics, the concept of demand curve plays a crucial role in understanding how prices and quantities of goods or services interact. In a perfectly competitive industry, where there are many buyers and sellers, each having negligible market power, the demand curve takes on a specific shape based on the behavior of buyers in the market.
The demand curve represents the relationship between the price of a product and the quantity demanded by consumers in a particular market. In a perfectly competitive industry, all firms produce identical goods or services, and buyers have access to perfect information. This means that buyers are fully aware of the prices charged by all sellers in the market.
a) Evenly divided: In a perfectly competitive market, the demand curve is not evenly divided. Each individual buyer's demand is a small fraction of the total market demand. However, when we consider the entire market, the demand curve takes on a specific shape.
b) Horizontal: The demand curve in a perfectly competitive industry is not horizontal. A horizontal demand curve would imply that buyers are willing to purchase an unlimited quantity of a good or service at a particular price. However, in reality, buyers have limitations on their purchasing power and preferences.
c) Directly sloped: The demand curve in a perfectly competitive industry is not directly sloped. A directly sloped demand curve would indicate a constant increase or decrease in quantity demanded as the price changes. However, this is not the case in a perfectly competitive industry.
d) Vertical: The demand curve in a perfectly competitive industry is not vertical. A vertical demand curve would imply that the quantity demanded remains constant, regardless of changes in price. In a perfectly competitive market, buyers are generally sensitive to changes in price, which affects the quantity demanded.
e) Negatively sloped: The most appropriate choice for the shape of the demand curve in a perfectly competitive industry is "negatively sloped." In a perfectly competitive market, the demand curve slopes downward from left to right. This means that as the price of a good or service increases, the quantity demanded by buyers decreases, and vice versa. This negative relationship between price and quantity demanded is a fundamental characteristic of the demand curve in a perfectly competitive market.
To summarize, in a perfectly competitive industry, the demand curve is negatively sloped. As the price increases, the quantity demanded by buyers decreases, and as the price decreases, the quantity demanded increases. This behavior reflects the underlying relationship between price and consumer demand in a competitive market.
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Complete Question:
We expect the demand curve in the perfectly competitive industry to be Group of answer choices
a) evenly divided
b) horizontal
c) directly sloped
d) vertical
e) negatively sloped.
The volumes of two mathematically similar objects are 56 cm³ and 875 cm³. The height of the smaller object is 18 cm. Find the height of the larger object.
Answers
Answer:
Therefore, the height of the larger object is 281.25 cm.
Step-by-step explanation:
If two objects are mathematically similar, it means that they have the same shape but different sizes. The ratio of their corresponding dimensions (such as length, width, and height) is the same.
Let the height of the larger object be h cm. Then, since the objects are mathematically similar, we have:
h/18 = (volume of larger object)/(volume of smaller object)
Substituting the given volumes, we get:
h/18 = 875/56
To solve for h, we can cross-multiply and simplify:
h = (875/56) x 18
h = 281.25
To find the height of the larger object, set up a proportion using the volumes of the two objects and solve for the height of the larger object.
Explanation:To find the height of the larger object, we can set up a proportion using the volumes of the two objects. Since the volumes of similar objects are proportional to the cubes of their corresponding lengths, we can write:
(Volume of smaller object) / (Volume of larger object) = (Height of smaller object)³ / (Height of larger object)³
Substituting in the given values, we have:
(56 cm³) / (875 cm³) = (18 cm)³ / (Height of larger object)³
Simplifying the equation, we get:
(56 cm³) * (Height of larger object)³ = (875 cm³) * (18 cm)³
Finally, we can solve for the height of the larger object by taking the cube root of both sides of the equation.
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he eigenvalues of these matrices were different, and they changed in unpredictable ways. however, they each had one eigenvalue in common. explain why this eigenvalue will remain no matter what row operation is performed. (
Answers
Regardless of the row operation performed, the common eigenvalue remains the same because it represents the underlying property of the matrix and is preserved through the row operations.
What is matrix?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
The eigenvalues of a matrix are the values λ for which there exists a non-zero vector v such that Av = λv, where A is the matrix. In other words, the eigenvalues represent the scalars by which certain vectors are stretched or shrunk when multiplied by the matrix.
When performing row operations on a matrix, such as multiplying a row by a scalar, adding or subtracting rows, or swapping rows, the resulting matrix may have different eigenvalues than the original matrix. However, there will always be one eigenvalue that remains the same, regardless of the row operation performed. This eigenvalue is known as the common eigenvalue.
To understand why the common eigenvalue remains unchanged, we can consider the definition of eigenvalues and eigenvectors. Let's assume that λ is a common eigenvalue for a given matrix A and its transformed matrix B after performing a row operation.
If v is an eigenvector of A corresponding to the eigenvalue λ, then Av = λv. After performing the row operation, let's say the transformed vector of v is v'. Since the row operation does not affect the vector v, we have Bv' = λv'.
Since λ is a common eigenvalue for both A and B, we have Av = λv and Bv' = λv'. We can see that the row operation does not change the relationship between the matrix and the eigenvector; it only alters the representation of the eigenvector.
Therefore, regardless of the row operation performed, the common eigenvalue remains the same because it represents the underlying property of the matrix and is preserved through the row operations.
Note that the eigenvectors corresponding to the common eigenvalue may change due to row operations, but at least one eigenvector will exist for the common eigenvalue in both the original and transformed matrices.
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Which number line shows the graph of the inequality x <
38
A.
B.
C.
-3
-3
+++
-2
-2
-2
-2
-1
-1
-1
-1
0
0
0
0
1
2
+++*+
1
2
++*++++++
2
3
2
3
3
3
Answers
My friend has $20$ stuffed animals. All of them are either cats or dogs, and all of them either have short or long fur. ${}12$ of them are cats, $15$ of them have long fur, and $4$ of them are short-furred dogs. How many stuffed animals are long-furred cats?
Answers
Answer:
11
Step-by-step explanation:
There are 8 dogs total with 4 being short furred, so 4 are long furred. If 15 total stuffed animals have long fur and 4 of them are dogs, 11 of them are cats.
What is the equation in point-slope form of the line that passes through the point (2 , 4) and has a slope of 3
Question 9 options:
y+4=3(x+2)
y-2=3(x-4)
y-4=3(x-2)
y+2=3(x+4)
Answers
y - 4 = 3(x - 2)
Therefore, the correct option is:
y - 4 = 3(x - 2)
Answer:
option 3
Step-by-step explanation:
The point-slope formula is:
[tex]\bf{y-y_1=m(x-x_1)}[/tex]
Where [tex]\bf{(x_1,y_1)}[/tex] is a point on the line and m is the slope.
Plug in 4 for [tex]\bf{y_1}[/tex]
[tex]\bf{y-4=m(x-x_1)}[/tex]
Plug in 3 for slope
[tex]\bf{y-4=3(x-x_1)}[/tex]
Plug in 2 for [tex]\bf{x_1}[/tex]
[tex]\bf{y-4=3(x-2)}[/tex]
Therefore, option 3 is correct.
Suppose an isolated box of volume 2V is divided into two equal compartments. An ideal gas occupies half of the container and the other half is empty. When the partition separating the two halves of the box is removed and the system reaches equilibrium again, how does the new (Helmholtz) free energy of the gas compare to the free energy of the original system
Answers
When the partition separating the two halves of the box is removed and the system reaches equilibrium again, the new Helmholtz free energy of the gas remains the same as the free energy of the original system.
The Helmholtz free energy (F) is a thermodynamic potential that represents the energy available to do work in a system at constant temperature and volume. In this scenario, the system consists of an isolated box divided into two equal compartments, where one half is initially occupied by an ideal gas and the other half is empty.
When the partition is removed, the gas particles will distribute themselves evenly throughout the entire volume of the box, reaching equilibrium. At equilibrium, the system has undergone a reversible process and there is no change in the total volume or temperature. Since the process is reversible and the temperature and volume remain constant, the Helmholtz free energy of the gas does not change.
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Express 7.051 in the form of p/q
Answers
7.051 can be written as the fraction 7051/1000.
To express 7.051 as a fraction in the form of p/q, we need to identify the decimal places and convert them to the corresponding fractional parts.
Since 7.051 has three decimal places, we multiply it by 1000 to move the decimal point three places to the right, which gives us 7051.
Now, the numerator (p) of the fraction will be 7051, and the denominator (q) will be the corresponding power of 10, which is 1000.
Therefore, 7.051 can be expressed as 7051/1000.
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
In this case, the GCD of 7051 and 1000 is 1, so the fraction is already in its simplest form.
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Ximena has 1 one dollar 5 quarters 2 dimes ana has the same amount of money in nickels. How many nickles does Ana have
Answers
If Ximena has 1 dollar, 5 quarters, and 2 dimes Ana has 49 nickels.
We need to determine the number of nickels Ana has, given that she has the same amount of money as Ximena.
First, let's calculate the total value of Ximena's coins:
The value of 5 quarters is 5 * 25 cents = 125 cents.
The value of 2 dimes is 2 * 10 cents = 20 cents.
The value of 1 dollar is 1 * 100 cents = 100 cents.
So, Ximena has a total of 125 cents + 20 cents + 100 cents = 245 cents.
Since Ana has the same amount of money as Ximena, we need to find the number of nickels that equals 245 cents.
Since 1 nickel is equal to 5 cents, we can divide 245 cents by 5 cents to find the number of nickels Ana has:
245 cents ÷ 5 cents = 49 nickels.
Therefore, Ana has 49 nickels.
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Sameera height is 110cm and is gaining 4cm pounds each month sara height is 140cm and is gaining 2cm each month how many months h will it take for sameera to weigh the same as sara
Answers
It would take some time due to their initial height difference and the rates at which they gain weight. Sameera starts at a height of 110cm and gains 4cm per month, while Sara begins at 140cm and gains 2cm per month.
Initially, Sameera is 30cm shorter than Sara. In terms of height gain, Sameera is closing the gap by 2cm each month (4cm - 2cm = 2cm). To reach the same height as Sara, Sameera needs to close the 30cm difference, which will take her 30cm / 2cm = 15 months.
Now, let's consider their weight gain. We don't have specific information about their current weights or weight gain rates, so we can't provide an exact answer in terms of weight. However, if we assume their weight gain rates are proportional to their height gain rates, then it would take Sameera the same 15 months to weigh the same as Sara.
In conclusion, assuming the weight gain rates are proportional to the height gain rates, Sameera would need approximately 15 months to catch up with Sara's weight. It's important to note that this calculation is based on the information provided, and if there are additional factors or variations in their weight gain, the actual time required may differ.
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Farmer John produces oranges. He sells half of his inventory to people at his for $20,000 and sells the other half to Tropicali for $15,000. Tropicali uses the oranges to make roadside stand orange juice, which it sells to consumers for $25,000. The impact of these transactions on gross domestic product (GDP) is A. $20,000 008 25000 "i5000 ︵げ000 $45,000 60,000 D. $25,000
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The total impact on GDP from these transactions is $25,000, as it represents the value of the final goods produced and sold to To in the economy. is option D. $25,000
The impact of these transactions on gross domestic product (GDP) is $25,000.
Gross domestic product (GDP) is a measure of the total value of goods and services produced within a country's borders over a specific time period. It includes the value of final goods and services at market prices.
In this scenario, Farmer John sells half of his inventory to people for $20,000 and the other half to Tropicali for $15,000. The $20,000 and $15,000 are both considered as final goods since they are sold directly to the end-users, either consumers or Tropicali, without further processing or resale.
When Tropicali uses the oranges to make roadside stand orange juice and sells it to consumers for $25,000, this transaction also contributes to GDP. The $25,000 represents the value of the final good, which is the orange juice produced by Tropicali and sold to consumers.
Therefore, the total impact on GDP from these transactions is $25,000, as it represents the value of the final goods produced and sold to To in the economy.
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Journalists exhibit selection biases in favor of news stories they view as a. having a great deal of dramatic or entertainment value. b. sympathetic to the government as a whole. c. critical of leaders and issues they oppose. d. favorable to leaders and issues they support.
Answers
Journalists can exhibit selection biases in favor of news stories they view as having a great deal of dramatic or entertainment value. The correct answer is option a.
This bias can lead to the prioritization of stories that are sensational or attention-grabbing, potentially overshadowing other important news that may not have the same level of entertainment value. However, it is important to note that journalists' biases can vary and not all journalists exhibit the same biases.
The media landscape consists of a diverse range of perspectives and approaches. It is the responsibility of journalists to strive for objectivity, balance, and fairness in their reporting, avoiding undue influence from personal biases and ensuring the accurate and comprehensive coverage of news events. Option A.
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In 2012, a sculpture was valued at
£3700.
By the end of 2013, its value had gone up
by 1%.
What was its value at the end of 2013?
Give your answer in pounds (£).
Answers
1% of £3700 is (1/100) * £3700 = £37.
Adding £37 to £3700 gives a value of £3737 at the end of 2013.
the experiment involved tossing three coins simultaneously. the experiment was carried out 100 times, and it was noted that three heads occurred 40 times. what is the difference between the experimental probability of getting three heads and its theoretical probability? write the answer in the simplest form of fraction.(1 point)
Answers
The difference between the experimental probability of getting three heads and its theoretical probability is 11/40.
To find the difference between the experimental probability and the theoretical probability of getting three heads when tossing three coins simultaneously, we need to calculate both probabilities and subtract them.
The theoretical probability is determined by considering all possible outcomes and their likelihood.
When tossing three coins, there are 2³ = 8 possible outcomes since each coin can land either heads or tails.
Out of these 8 outcomes, only one outcome results in three heads.
The theoretical probability of getting three heads is therefore 1/8.
The experimental probability is determined by conducting the actual experiment and recording the observed outcomes.
The experiment was carried out 100 times, and three heads occurred 40 times.
The experimental probability of getting three heads is therefore 40/100 or 2/5.
To find the difference between the experimental probability and the theoretical probability, we subtract the theoretical probability from the experimental probability:
Experimental probability - Theoretical probability = 2/5 - 1/8
To simplify this fraction, we need to find a common denominator:
2/5 - 1/8 = (16/40) - (5/40)
= 11/40
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