what is the product of (2m-3n)(2m-3n)?​

The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

In the question ,

it is given that ,

the initial point of the vector = (1 , -1)

the terminal point of the vector = (4,2)

we know that the vector with initial point (x₁ , y₁) and (x₂ , y₂) is calculated using the formula

V = (x₂ - x₁)i + (y₂ - y₁)j

Substituting the values from the point ,

we get the vector as

V = (4 - 1)i + (2 -(-1))j

V = 3i + (2 + 1)j

V = 3i + 3j

Therefore , The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

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For the given situation, we can clearly say that the change in one quantity will also cause a change in the second quantity.

Correlation is a relationship between the values ​​of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.

Causality means that one event causes another. Well-designed experiments can only determine causality. In such experiments, similar groups receive different treatments, and the results of each group are examined.

The collected data on the number of miles driven and fuel expenses. we found that number of miles driven tended to be lower when fuel expenses were high, and the number of miles driven tended to be higher when fuel expenses sales were high.

We do not conclude that more fuel expenses mean fewer miles driven. Likely, an Increased in fuel expenses and the number of miles driven may be caused by a third factor, car mileage. So, the present case is a case of negative correlation.

Negative correlation: y decreases as x increases.

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\(\huge\underline\mathtt\colorbox{cyan}{320}\)

Step-by-step explanation:

The firm will shut down in the short run due to the inability to cover total costs with the marginal cost (MC) below both the average total cost (ATC) and the marginal revenue (MR). Thus, the correct option is :

(c) shut down in the short run.

To analyze the firm's situation, we need to consider the relationship between costs, revenues, and profits.

Option a. "maximize its profit by producing in the short run" is not correct because the firm is experiencing losses. When MC is below ATC, it indicates that the firm is making losses on each unit produced.

Option b. "minimize its losses by producing in the short run" is also not correct. While producing in the short run can help reduce losses compared to not producing at all, the firm is still unable to cover its total costs.

Option d. "realize a loss of $5 per unit of output" is not accurate based on the given information. The exact loss per unit of output cannot be determined solely from the given data.

Now, let's discuss why option c. "shut down in the short run" is the correct choice.

In the short run, a firm should shut down when it cannot cover its variable costs. In this scenario, MC is equal to AVC at $8, indicating that the firm is just able to cover its variable costs. However, MC is below both ATC ($12) and MR ($7), indicating that the firm is unable to generate enough revenue to cover its total costs.

By shutting down in the short run, the firm avoids incurring further losses associated with fixed costs. Although it will still incur losses equal to its fixed costs, it prevents additional losses from adding up.

Therefore, the correct option is c. "shut down in the short run" as the firm cannot cover its total costs and is experiencing losses.

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Answer:

Answer is option (B)......

Answer:

(-8,-1)

Step-by-step explanation:

More information or diagram needed.

The problem provides a circle with center E and three points A, B, and C on the circumference. Using the properties of circles and triangles, we can solve for the unknown length AC. First, we observe that since E is the center of the circle, the length of segment EB is equal to the length of segment EC. Next, we can apply the inscribed angle theorem to triangle ABC to find that angle AEC is a right angle, since it intercepts the diameter of the circle. Therefore, we can use the Pythagorean theorem to find the length of AC, where AC^2 = AE^2 + EC^2. Substituting EB for EC and simplifying, we get AC^2 = AE^2 + EB^2. Finally, we can plug in the given values to obtain AC = sqrt(2.4^2 + 5.2^2) = sqrt(34) ≈ 5.83. Therefore, the length of AC is approximately 5.83.

The regression line is a statistical tool that can be used to analyze the relationship between two variables.

It helps identify trends in the data and can be used to make predictions about future values. It can also be used to assess the accuracy of the model and to determine the strength of the relationship between the two variables.

By examining the slope of the regression line, we can assess the direction and strength of the linear relationship between the two variables.

Additionally, the y-intercept of the regression line can provide insight into the value of the dependent variable when the independent variable is equal to zero.

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Step-by-step explanation:

Use the Distributive Property for the left side of the equation.

\(a( b+ c) = ab + ac\)

Use the Distributive Property:

\(3x + 6 + 8x = 11x + 7\)

\(11x + 6 = 11x + 7\)

x has no solution.

Answer:

see explanation

Step-by-step explanation:

cos C = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{24}{51}\) = \(\frac{8}{17}\)

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

tan Z = \(\frac{opposite}{adjacent}\) = \(\frac{XY}{ZY}\) = \(\frac{15}{20}\) = \(\frac{3}{4}\)

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

sin C = \(\frac{opposite}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{60}{65}\) = \(\frac{12}{13}\)

The speed of the bottom of the ladder moving along the ground when the bottom is 8 ft from the wall is 3.75 ft/sec.

What is speed?

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Let us take x = the distance from the base of the ladder to the base of the wall.

y = the distance from the tip of the ladder to the base of the wall, we have:

=> \(x^2 + y^2 = 17^2\)

=> \(y^2=17^2-x^2=17^2-8^2=289-64=225=15^2\)

=> y = 15 ft.

Now differentiate then,

=> 2x dx/dt + 2y dy/dt = 0

=> 2 * 8 * dx/dt + 2 * 15 * (-2) = 0

=> 16 dx/dt = 60

=> dx/dt = 60/16= 3.75 ft/sec

Hence the bottom of the ladder moving along the ground when the bottom is 8 ft from the wall is 3.75 ft/sec.

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Answer:

-6\(\geq\)x\(\geq\)12

Step-by-step explanation:

I can't match it to one of your solutions but I can explain this:

-8\(\geq\)x-2\(\geq\)10

We can add 2 to each side to eliminate the -2 in the centre.

-6\(\geq\)x\(\geq\)12

Answer:

Step-by-step explanation:

Given μA = $2.78, σA = $0.25, μB = $2.45, σB = $0.20, you want ...

The probabilities of interest are found using the CDF function of a suitable calculator or spreadsheet.

(a) P(A < $2.50) ≈ 0.1314

(b) P(B < $2.50) ≈ 59.87%

(c) P(B > $2.78) ≈ 0.0495

__

Additional comment

We note that you have provided your own answers to these questions. The answer you give for question B is not given as the percentage requested.

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The probability of selecting a person who is either a Democrat or a woman is 0.8, or 80%.

Probability is a branch of mathematics that deals with the study of random events. It is used to predict the likelihood of an event occurring.

Let's start by finding the probability of selecting a Democrat. We are given that there are 60 Democrats in the group of 100 people. Therefore, the probability of selecting a Democrat at random is:

P(Democrat) = 60/100 = 0.6

Next, let's find the probability of selecting a woman. We are given that there are 60 women in the group of 100 people. Therefore, the probability of selecting a woman at random is:

P(Woman) = 60/100 = 0.6

Now, we need to find the probability of selecting both a Democrat and a woman. We are given that 40 of the Democrats are women. Therefore, the probability of selecting a woman who is also a Democrat is:

P(Democrat and Woman) = 40/100 = 0.4

To find the probability of selecting a person who is either a Democrat or a woman, we add the probabilities of selecting a Democrat and selecting a woman, and then subtract the probability of selecting both a Democrat and a woman. Therefore, the probability of selecting a person who is either a Democrat or a woman is:

P(Democrat or Woman) = P(Democrat) + P(Woman) - P(Democrat and Woman)

= 0.6 + 0.6 - 0.4

= 0.8

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Answer:

x^2 + y^2 = z^2

There are infinitely many choices for whole numbers x, y, and z.

Step-by-step explanation:

y=mx+b

200 = 8x + 40

Rearrange,

x = 160/8 = 20

He would need to save $20 a week

200= 20 × 8 + 40

Answer:

Step-by-step explanation:

Required inequality:

Answer:

The complex number is B, \(3\sqrt{\frac{7}{5}}+\sqrt{-\frac{9}{5}}\)

Step-by-step explanation:

A complex number should be written in the form \(a+bi\), where a and b are real numbers, and i is an imaginary number.

Recall that \(\sqrt{-1}=i\). Since letter B has the second term \(\sqrt{-\frac{9}{5}}\), we can say

\(\sqrt{-\frac{9}{5}}=\sqrt{-1\cdot\frac{9}{5}}=i\sqrt{\frac{9}{5}}\)

Therefore, the number can be written as

\(3\sqrt{\frac{7}{5}}+i\sqrt{\frac{9}{5}}\).

Answer:

$9.60

Step-by-step explanation:

The question above is a simple interest question.

The formula for the amount of money after a given period of time using simple interest is given as:

A = P(1 + rt)

Where

P = Initial Amount saved or invested = $8

R = Interest rate = 5%

t = Time in years = 4

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year.

Solving our equation:

A = 8(1 + (0.05 × 4)) = 9.6

A = $9.60

The amount of money that will be in a bank account after 4 years is $9.60

Answer:

Theres no Picture added.

Step-by-step explanation:

Answer:

The answer That I would expect from any question is in stuff like a paper or a file.

Step-by-step explanation:

Because that's where most questions and answers come from.

Let the speed of the southbound train be x mph. then the speed of the northbound train will be x - 14 mph.

Both trains are traveling in the opposite direction and going away from each other.

The distance traveled by southbound train in 3 hours will be 3x miles. The distance traveled by southbound train will be 3(x - 14) miles.

Therefore, the sum of distance covered by both the trains will be equal to 498 miles.

Thus, the speed of the southbound train is 90 mph and the speed of the northbound train is 76 mph.

Let  be the number of pennies,  be the number of nickels, and  be the number of dimes that Vern has. The given ratios tell us that  and  Therefore,  so we haveTo turn this into a ratio of integers, we multiply every part of the ratio by  Doing this, we see that Therefore, we can think of Vern's collection as consisting of several groups, each of which contains  pennies,  nickels, and  dimes. Let  be the number of such groups of coins that Vern has. Then Vern has  pennies,  nickels, and  dimes. Since a penny is worth  cent, a nickel is worth  cents, and a dime is worth  cents, the total worth of Vern's coins in cents is  However, we know Vern has  or  cents, so we can write an equation:Simplifying the left-hand side, we get  Dividing both sides by  we get  This tells us that Vern has  groups of  coins, for a total of  coins.

328

The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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The graph of ƒ has a point of inflection  is (D) -3.259, 0, and 1.603

To determine if a function has a point of inflection, we need to find the values of x where the second derivative changes sign from positive to negative or vice versa. The sign of the second derivative at a point determines the concavity of the function at that point. If the second derivative is positive, the function is concave up, and if it is negative, the function is concave down.

Since ƒ"(a)=x² cos(2a+22), we can see that the second derivative is positive for x²>0. So the function is concave up when x²>0, which means when x is in the interval (-∞,0)∪(0,∞).

Since the interval (-4,3) includes both negative and positive values of x, the graph of ƒ may have a point of inflection within this interval. To determine the exact points of inflection, we need to find the values of x where the second derivative equals zero or is undefined.

Therefore, the answer is (D) -3.259, 0, and 1.603.

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The value of  Q(x) =   x² - 1  

R(x) = 4

What is Long Division?

Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.

By long Division method:

                        x² - 1            

                     _______________________________

         (3x - 4) | 3x³ - 4x² - 3x

                       3x³ - 4x²

                       _________________

                            0 - 0   - 3x      

                                       - 3x + 4  

                                ___________________

                                          0  + 4

Q(x) =   x² - 1  

R(x) = 4

Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1  ) + 4

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The value of the constant "a" is -1/4.

To find the value of the constant "a", we need to use the given information that the definite integral of the function 2x^2 + x - a over an unspecified interval is equal to 24.

The integral can be evaluated using the power rule of integration:

fo(2x^2 + x - a) dx = (2/3)x^3 + (1/2)x^2 - ax + C

where C is the constant of integration.

Since we are given that the integral equals 24, we can substitute this value into the above equation and solve for "a":

(2/3)x^3 + (1/2)x^2 - ax + C = 24

Simplifying and setting C = 0 (since it's an unspecified constant), we get:

(2/3)x^3 + (1/2)x^2 - ax = 24

Now, we don't have enough information to solve for "a" yet, as we don't know what interval the definite integral is taken over. However, we can use the fact that the integral is linear, meaning that if we multiply the integrand by a constant, the value of the integral will also be multiplied by that constant.

In other words, if we let f(x) = 2x^2 + x - a, then fo f(x) dx = 24 is equivalent to:

fo (2f(x)) dx = 48

Now we can solve for "a" using the same method as before:

(2/3)x^3 + x^2 - 2ax = 48

Again, we don't know the interval over which the integral is taken, but that doesn't matter for finding "a". We can now compare the coefficients of x^2 to get:

1/2 = -2a

Solving for "a", we get:

a = -1/4

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Answer:

I don't see a picture but the circumcenter is usually inside the triangle.

There are 15C5 or 3003 possible combinations in the sample space.There are 20C5 or 15504 possible combinations in the sample space.

A number is a mathematical object used to count, measure, and label. Numbers can be represented in many different forms such as natural numbers, integers, real numbers, and complex numbers. They can also be classified as scalar numbers (which have a magnitude or value only) or vector numbers (which have both magnitude and direction). Numbers can be used to represent many different things, including measurements, distances, money, and quantities.

A) Sample Space: The sample space for selecting a set of 5 questions from a set of 15 questions is the set of all possible combinations of 5 questions from 15 questions. There are 15C5 or 3003 possible combinations in the sample space.

B) Sample Space: The sample space for forming a committee of 5 from a membership of 20 is the set of all possible committees that can be formed from 20 members. There are 20C5 or 15504 possible combinations in the sample space.

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The original price of the pearl was 52 euros.

Price is the monetary value of a product, service, or asset. It is one of the most important factors in a customer's decision to purchase something. Price also determines the amount of profit a business makes on a particular product or service. Price is a key component of the marketing mix, and it can be used to create a sense of value for customers. Price can also be used to differentiate a product from competitors, as well as to indicate quality levels and to create loyalty.

a) One of the cheapest pearls costs 41 euros.

b) This necklace costs 2153 euros, which is the sum of all the pearls.

c) The pearl with the crack originally cost 52 euros. The price was reduced by 1/5, which is 10.4 euros, making the price of the pearl 41.6 euros. The decrease in price of the necklace was 6.5 euros, which means the reduction in price of the pearl was 6.5 euros. Therefore, the original price of the pearl was 52 euros.

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If speed is important and the array is large, the a. Binary search algorithm should be used. This algorithm is designed to efficiently search through sorted arrays by repeatedly dividing the search interval in half.

It has a time complexity of O(log n), which means that as the size of the array increases, the time it takes to search for an item will not increase at the same rate.
On the other hand, ascending bubble sort and other sorting algorithms such as selection sort and insertion sort have a time complexity of O(n^2), which means that as the size of the array increases, the time it takes to sort the array will increase exponentially. Therefore, these algorithms are not efficient for large arrays and should not be used if speed is important.
In summary, when dealing with large arrays and speed is important, binary search is the best algorithm to use for searching, while ascending bubble sort and other sorting algorithms with a time complexity of O(n^2) should be avoided.

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Answer:

A

Step-by-step explanation:

Simplify both sides x+38.18=82.06

subtract 38.18 from both sides

x+38.18-38.18=82.06-38.08

x=43.88