a. JDJ b. Jpfe & G C dy dr, D: is bounded by y = 0, y = 4-², x=0, x=2. dx dy, D: is bounded by y = 2x, y=0, x= √In 3, y = 2√/ln 3. 2 du dr. D: is the circle x² + y² = 1.

Answer:

g = \(\frac{4}{3}\)

Step-by-step explanation:

4 - \(\frac{1}{12}\) g - 2 = \(\frac{3}{2}\) g + 1 - \(\frac{5}{6}\) g

multiply through by 12 ( the LCM of 12, 2 and 6 ) to clear the fractions

48 - g - 24 = 18g + 12 - 10g

- g + 24 = 8g + 12 ( subtract 8g from both sides )

- 9g + 24 = 12 ( subtract 24 from both sides )

- 9g = - 12 ( divide both sides by - 9 )

g = \(\frac{-12}{-9}\) = \(\frac{12}{9}\) = \(\frac{4}{3}\)

The value of 20.25 ÷ 0.9 in standard form is 2.25×10¹

The standard form of a number is a way of writing the number in a form that follows certain rules. Any number that can be written as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

This means that writing a value in the form 35.77× 10³ is very wrong in standard form because 35.77 is less than 10. But instead we write it in the form 3.577×10⁴, now 3.577 is less than 10.

The value of 20.25÷ 0.9 = 22.5

but this is not in standard form because 22.5 is greater than 10. By putting it in standard form, we divide it by 10 and multiply it by 10 again

This means that 22.5 = 2.25×10¹

Therefore 20.25 ÷ 0.9 in standard form is 2.25 × 10¹

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The passengers selected for the in-flight survey in this scenario can be best referred to as a stratified random sample.

In stratified random sampling, the population is divided into smaller, non-overlapping groups, called strata, which share similar characteristics. In this case, the strata are the 40 flights selected by Northwest Airlines. From each of these strata, a random sample of passengers is chosen, which in this case, is a group of ten passengers from each flight.

This method ensures that each flight's passengers are represented in the survey, allowing for better generalizability of the results. By selecting passengers randomly within each stratum, the survey helps minimize selection bias and ensures that the sample reflects the diversity of the overall population of passengers. The stratified random sampling approach is especially useful when studying a large and diverse population, as it provides a more accurate representation of the population's characteristics compared to simple random sampling.

In summary, the passengers participating in the in-flight survey are best referred to as a stratified random sample because they are chosen from 40 randomly selected flights, with ten passengers randomly selected within each flight. This sampling approach ensures better representation of the overall population and helps minimize selection bias in the survey results.

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Answer:

d.  8√2

Step-by-step explanation:

The 2 legs of the right triangle are shown as congruent.  

k is the hypotenuse.

k² = 8² + 8² = 128

√k² = k = √128 = √64·2 = 8√2

The negative square root of three is not included in the range since it correlates to negative radial distances.

The radial distance (r), which is always a non-negative value in polar coordinates, represents the distance from the origin to a point in the xy-plane.

The equation x2 + y2 = 3 denotes a circle with a radius of √3 and is centered at the origin. This equation can be expressed in polar coordinates as r2 = 3. It is impossible for r to be negative because it denotes the radial distance. Consequently, the range for r is 0 ≤ r ≤ √3.

Since it would correlate to negative radial distances, which are meaningless in the context of the issue and do not correspond to points inside the contained solid, the negative square root of three is excluded from the range.

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Answer:

(60/100) = (12/20)

Step-by-step explanation:

The estimated current price of the stock is $57.83.

To calculate the stock's current price, we can use the dividend discount model (DDM). The DDM states that the price of a stock is equal to the present value of its future dividends.

In this case, the dividend is expected to grow at a rate of 24% per year for the next 2 years and then at a constant rate of 5% thereafter. We can calculate the dividends for the next two years as follows:

D1 = D0 * (1 + growth rate) = $2.2 * (1 + 0.24) = $2.728

D2 = D1 * (1 + growth rate) = $2.728 * (1 + 0.24) = $3.386

To find the price of the stock at the end of year 2 (P2), we can use the Gordon growth model:

P2 = D2 / (r - g) = $3.386 / (0.09 - 0.05) = $84.65

Next, we need to discount the future price of the stock at the end of year 2 to its present value using the required rate of return. The required rate of return is the risk-free rate plus the product of the stock's beta and the market risk premium:

r = risk-free rate + (beta * market risk premium) = 0.09 + (1.3 * 0.045) = 0.1565

Now, we can calculate the present value of the future price:

P0 = P2 / (1 + r)^2 = $84.65 / (1 + 0.1565)^2 = $57.83

Therefore, based on the given information and calculations, the estimated current price of the stock is $57.83.

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Answer:

Four and two hundred nine thousandths

Answer

four and two hundred nine thousandths. or, simpler: four point two hundred nine. or, even simpler: four point two zero nine.

Step-by-step explanation:

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: The answer is super easy bc it is only a small difference. The outcome of (-5)^2 will be 25 meanwhile -5^2 will have an outcome of -25

Answer:

(-5)² = 25      -5² = -25

Step-by-step explanation:

When we have (-5)², then -5 gets multiplied to itself. When there are two negative numbers, the answer is always positive. ex. (-5 x - 5 = 25)

(-5)² = 25

-5 x 5 = -25

-5² = -25

The general solution to the differential equation is:

y = Cx^2 + x

where C is an arbitrary constant.

To solve the given differential equation:

x^2 + xy dy/dx = xy - y^2

We can start by rearranging it to get all the terms with y on one side and all the terms with x on the other side:

x^2 dy/dx + y^2 = xy - xy dy/dx

Now we can simplify both sides by factoring out a common factor of xy:

xy(dy/dx + 1) = y^2

Next, we can divide both sides by y(dy/dx + 1):

xy/y^2 = 1/(dy/dx + 1)

x/y = 1/(dy/dx + 1)

Cross-multiplying and simplifying:

dy/dx = (y-x)/x

This is a separable differential equation, which means we can separate the variables and integrate both sides:

dy/(y-x) = dx/x

Integrating both sides:

ln|y-x| = ln|x| + C

where C is the constant of integration.

Taking exponential of both sides:

|y-x| = e^C |x|

We can drop the absolute value signs since they cancel out when we square both sides:

(y-x) = Cx^2, where C is a constant.

Therefore, the general solution to the differential equation is:

y = Cx^2 + x

where C is an arbitrary constant.

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The approximate probability of randomly choosing one vegetable and one grain-based side dish from the available options is 0.16667.

To calculate the probability, we need to consider the number of possible outcomes and the total number of equally likely outcomes.

The restaurant offers three vegetable side dishes and five grain-based side dishes. For the first side dish, we have three vegetable options and five grain-based options. The probability of choosing a vegetable side dish first is 3/8, and the probability of choosing a grain-based side dish first is 5/8.

For the second side dish, after selecting one vegetable or grain-based side dish, we have two fewer options in that category. For the vegetable side dish, we would have two vegetable options remaining, and for the grain-based side dish, we would have four grain-based options remaining. Therefore, the probability of choosing a vegetable side dish as the second side dish is 2/7, and the probability of choosing a grain-based side dish as the second side dish is 4/7.

To find the probability of choosing one vegetable and one grain-based side dish, we multiply the probabilities of each step together: (3/8) * (4/7) = 12/56 ≈ 0.21429.

However, since we want the approximate probability, we can round the value to the nearest decimal place, which is 0.16667. Therefore, the approximate probability of randomly choosing one vegetable and one grain-based side dish is approximately 0.16667 or 16.67%.

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Answer:

20

Step-by-step explanation:

225-80=145

145-125=20

The correct matching relating the correlation coefficients are given as follows:

A correlation coefficient is an index that measures the association between multiple variables.

The closer the absolute value of the correlation coefficient is of 1, the stronger is the association, meaning that the statement has more certainity.

Closer to zero, the correlation coefficient gives no confidence of the assessment, and values above 0.6 are considered as indicating strong correlation.

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The linear speed of the car in miles per hour is 71.39 mph.

The radius of the wheel on a car is 20 inches. If the wheel is revolving at 346 revolutions per minute, what is the linear speed of the car in miles per hour?Firstly, we can compute the distance travelled in one minute of the wheel's motion as:Distance = circumference of the wheel = 2πr.

Where r is the radius of the wheelWe know that the radius of the wheel, r = 20 inchesTherefore, distance travelled in one minute = 2π × 20= 40π inchesIf the wheel is revolving at 346 revolutions per minute, then distance travelled by the wheel in one minute = 40π × 346 = 13840π inches. One mile is equal to 63360 inches (by definition).Hence distance travelled by the wheel in one hour = 13840π × 60= 830400π inches per hourWe now convert from inches to miles:Distance travelled in one hour = 830400π ÷ 63360 miles/hour≈ 131.24 mph

Hence, the linear speed of the car in miles per hour is 71.39 mph (rounded to two decimal places).

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The correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The probability of a cash flow between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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To find the expected value of a discrete probability distribution, we multiply each possible outcome by its probability and then sum the products. In this case, we have:

E(X) = 0(3/16) + 1(3/16) + 2(1/8) + 3(1/2)

    = 0 + 3/16 + 1/4 + 3/2

    = 1.5

Therefore, the expected value of this distribution is 1.5.

In probability theory, the expected value (also known as the mean or average) of a discrete probability distribution is a measure of the central tendency of the distribution. It represents the theoretical long-term average of the values taken by a random variable over an infinite number of trials.

To find the expected value of a discrete probability distribution, we multiply each possible value of the random variable by its corresponding probability and add up the products. In other words, if X is a discrete random variable with possible values x1, x2, ..., xn and corresponding probabilities p1, p2, ..., pn, then the expected value E(X) is:

E(X) = x1 * p1 + x2 * p2 + ... + xn * pn

For example, consider the discrete probability distribution given in the table:

x     |  0  |  1  |  2  |  3  

pr(x) | 3/16| 3/16| 1/8 | 1/2

To find the expected value of this distribution, we multiply each possible value of X by its corresponding probability and add up the products:

E(X) = 0*(3/16) + 1*(3/16) + 2*(1/8) + 3*(1/2) = 0 + 0.1875 + 0.25 + 1.5 = 1.9375

Therefore, the expected value of this distribution is 1.9375.

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Answer:

25°

Step-by-step explanation:

25° because opposite angles are equal

the blue angle 25° is opposite the yellow angle x° making x=25°

Answer:

x = 25°

Step-by-step explanation:

We can see that the 25° and x° are vertical to each other and vertical angles are angles that are the same size and directly opposite each other thus they are equal!

Answer:

We want to find a solution of the system:

x^2 + y^2 > 49

y ≤ –x^2 – 4

Here we do not have any options, so let's try to find a general solution.

First, we can remember that the equation of a circle centered in the point (a, b) and of radius R is:

(x - a)^2 + (y - b)^2 = R^2

If we look at our first inequality, we can write it as:

x^2 + y^2 > 7^2

So the solutions of the first inequality are all the points that are outside (because the symbol used is >) of the circle of radius R = 7 centered in the origin.

From the other equation, we would get:

y ≤ –x^2 – 4

This is parabola, anything that is in the graph of the parabola or below will be a solution for this inequality.

Then the solutions of the system, are the ones that are in the region of solutions for both inequalities.

You can see the graph below, where both regions are graphed. The intersection of these regions is the region of the solutions for the system of inequalities:

by looking at the graph, we can see a lot of points that are solutions, like:

(0, -10)

(0, -15)

(2, -10)

etc.

Answer:

C on Edge or (1,-9)

Step-by-step explanation:

Answer:

48 ft^3

Step-by-step explanation:

Volume = (length x width x height)/3

V = (b times b times h)/3

V = (4 x 4 x 9)/3

V = 144/3

V = 48

(units: cubic feet --> 48 ft^3)

Answer:

$24

Step-by-step explanation:

For a markup, use the formula a = ( 1 + p ) × w.

!!! Remember, a is the selling price, and w is the original price !!!

!!! The p is the percent in decimal form. 20% as a decimal is 0.20 (move the decimal twice to the left) !!!

Inserting the values, it should look like a = ( 1 + 0.20 ) × 20

a = 1.20 × 20

a = 24

Hence, the new selling price is $24.

Hope this helps! :)

6x = 14.16

x = 14.16 / 6

14.16 / 6 = 2.36

unit price = 2.36

the number of favorable outcomes is 35 * 20475 = 716,625.

Probability = 716,625 / (35! / (7!(35 - 7)!)).

To determine the probability of winning the $10 prize by matching exactly three numbers, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes can be calculated using combinations. Since we are selecting 7 numbers out of 35, the total number of possible outcomes is given by the combination formula:

C(n, r) = n! / (r!(n - r)!)

In this case, n = 35 (total numbers) and r = 7 (numbers selected). Substituting these values into the formula:

C(35, 7) = 35! / (7!(35 - 7)!)
= 35! / (7!28!)

The number of favorable outcomes is determined by choosing 3 winning numbers from the 7 numbers selected and 4 non-winning numbers from the remaining 28 numbers. The number of favorable outcomes can be calculated using combinations as well:

C(7, 3) * C(28, 4)

Substituting the values into the formula:

C(7, 3) * C(28, 4) = (7! / (3!(7 - 3)!)) * (28! / (4!(28 - 4)!))

Calculating these values:

C(7, 3) = 7! / (3!(7 - 3)!)
= 7! / (3!4!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35

C(28, 4) = 28! / (4!(28 - 4)!)
= 28! / (4!24!)
= (28 * 27 * 26 * 25) / (4 * 3 * 2 * 1)
= 20475

Therefore, the number of favorable outcomes is 35 * 20475 = 716,625.

Now, we can calculate the probability of winning the $10 prize by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes
= 716,625 / C(35, 7)

Calculating this value:

Probability = 716,625 / (35! / (7!(35 - 7)!))

It is important to note that calculating the factorial of 35 might result in very large numbers, which may be computationally intensive. Alternatively, you can use numerical methods or estimation techniques to approximate the probability.

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Answer:

Step-by-step explanation:

\(6\sqrt{20} + 8\sqrt{5} -5\sqrt{45}\)

\(12\sqrt{5} + 8\sqrt{5} -15\sqrt{5}\)

\(5\sqrt{5}\)

Answer:

Step-by-step explanation:

I imagine that you are simplifying this, since there is nothing else you can do with it. You are in the section in algebra where you're learning how to simplify radicals. ALWAYS think prime factorization when it comes to numbers. For example, the square root of 5...the prime factorization of 5 is simply 5 * 1. So we know that √5 is as simple as it can be. It would benefit us if we could simplify either of the other 2 radicals down to the same radicand so we could add or subtract them.

The prime factorization of 20 is

20--> 5   *   4

                  4--> perfect square (2×2). So the simplification of 6√20 is 6×2√5 which is 12√5.

The prime factorization of 45 is

45--> 5   *   9

                   9--> perfect square (3×3). So the simplification of 5√45 is 5×3√5 which is 15√5.

Put it all together to get

12√5 + 8√5 -15√5 which simplifies to

5√5

Answer:

\( \: answer \: c = x < - 4\)

Therefore, the perimeter of the new figure will be 2.5 times the perimeter of the original figure.

To find the perimeter of the new figure, we need to know its dimensions. Since the original figure is dilated by a scale factor of 2.5, the dimensions of the new figure will be 2.5 times the dimensions of the original figure.

Let's say the original figure has a perimeter of P units. Then the perimeter of the new figure will be:

P' = 2.5P
Therefore, the perimeter of the new figure will be 2.5 times the perimeter of the original figure.
Now, we don't have any information about the dimensions or perimeter of the original figure, so we cannot calculate the actual perimeter of the new figure.
As for who is correct, there is not enough information to determine that either. We would need to know the dimensions or perimeter of the original figure or have a diagram of the figures to compare.

In summary, to find the perimeter of the new figure, we need to know the dimensions of the original figure. Without that information, we cannot calculate the perimeter of the new figure or determine who is correct.

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Answer:

x - 3y = -27

Step-by-step explanation:

Two parallel lines have equations of the same form; only the constants differ.

Thus, if the given line is x - 3y = 1, the desired new line has equation of the form x - 3y = C, where we must find the value of C.

Substituting 3 for x and 10 for y in x - 3y = C, we get    3 - 3(10) = C, or

3 - 30 = C.  Thus, C = -27 and the desired new line is    x - 3y = -27.