What is the following sum?
23/16xy+43,64xy
0 4x(3/2y) + 12x²y3√/2y²
O
08x/xy +12x°y (3{6y )
0 16xy(3,27
0 48xºy(3/2y

Answer: The speed of red horse = 44 feet per second and the speed of black horse = 35.2 feet per second.

Step-by-step explanation:

Given: A red horse and a black horse raced on a 1-mile-long circular racetrack.

Time taken by red horse = 120 seconds

Time taken by black horse = 150 seconds

Speed = \(\dfrac{Distance}{Time}\)

So, speed of red horse =\(\dfrac{1}{120}\text{ mile per second}\)

Since 1 mile = 5280 feet

Speed of red horse = \(\dfrac{5280}{120} =44\text{ feet per second}\)

Similarly,

Speed of black horse = \(\dfrac{5280}{150} =35.2\text{ feet per second}\)

Hence, the speed of red horse = 44 feet per second and the speed of black horse = 35.2 feet per second.

Answer:

Step-by-step explanation:

so,  I was just commenting about word problems to another person and here is a great example of a word problem that is too complex.  They are using the term  "function rule"  that is too broad.  They have probably defined it in some text somewhere and the teacher has mentioned in super briefly, but it's what the question is all about.  We need to understand what "function rule"  really means.   They have also used the varible "s"  which is mostly reserved for  Laplace /  Fourier  transformations.  This is just a really badly written question.   Don't feel bad if  you don't get what it's asking.  it's messy at best.   t(s) is then name of our function,  it's rule ( the function rule)  is 40/s  it's constant of proportionality is 40  ,  This rule would also mean that at the very very start of the race... at .001 into the race, you'll be going 40,000 MPH  , which is obviously not correct.   There probably needs to be some more rule descriptions saying that s is an integer, and it can't be negative. Also note that after 4 hours of racing , the speed would be 40/4 or 10 MPH,  this function rule is probably not accurate after some time.  the speed probably starts out fast,   slows down till the close to the very end of the race... they jumps up dramatically to the finish.   Watch the Tour de France writer of this question.  :D   The riders slow down as the race progress according to this function rule.  But I don't think that's at all accurate for a real bike race.   they slow down only to a point... after the start.... then hold at that speed ... till close to the end.. then speed up a lot... like 50 MPH  :0

Answer:

The solution is -1/343 or (-7)⁻³

Step-by-step explanation:

-7 × (-7)⁻⁴

-7 × 1/(-7)⁴

-7 × 1/2401

-7/2401 = -1/343 = (-7)⁻³

Thus, The solution is -1/343 or (-7)⁻³

-TheUnknownScientist 72

The distance between the two ships is 3.07 miles (approx). The given polar coordinates are converted into rectangular coordinates with the help of sine and cosine functions.

Given data:

The location of two ships from mays landing lighthouse, given in polar coordinates, are 3 mi, 170 and 5 mi, 150.

.To find:Distance between the ships

Formula used:

Distance between the ships = \(sqrt(d1^2 + d2^2 - 2*d1*d2*cos(theta1 - theta2)).\)

where d1 = 3 mi, theta1 = 170°, d2 = 5 mi, theta2 = 150°.

Calculation:Squaring and adding the given distances,sqrt(3² + 5² - 2*3*5*cos(170° - 150°))

:Distance between the ships is 3.07 miles (approx).

:Thus, the distance between the two ships is 3.07 miles (approx). The given polar coordinates are converted into rectangular coordinates with the help of sine and cosine functions. The formula used for finding the distance between the two ships is \(sqrt(d1^2 + d2^2 - 2*d1*d2*cos(theta1 - theta2)).\)

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Answer:

5^3 is the same thing as 5 x 5 x 5. It equals 125

Matrices are rectangular arrays of numbers or elements arranged in rows and columns. They are used in various mathematical operations, such as addition, subtraction, multiplication, and transformation calculations.

Given matrices are \(G_{2\times 3} = \left[\begin{array}{ccc}4&5&-2\\1&6&7\end{array}\right]\)

and \(H_{2\times 3} =\left[\begin{array}{ccc}1&-1&7\\5&1&-7\end{array}\right]\)

We have to find -6G - 3H. Here's how to do it:

First, let's find -6G.

Multiply each element in the matrix G by -6.-6

\(G=\left[\begin{array}{ccc}24&30&12\\-6&-36&-42\end{array}\right]\)

Next, we'll find 3H. Multiply each element in the matrix H by 3.3

\(H=\left[\begin{array}{ccc}3&-3&21\\15&3&-21\end{array}\right]\)

Finally, add the results of -6G and 3H elementwise to get the final answer.-6G - 3H

\(G=\left[\begin{array}{ccc}-21&-27&-9\\9&-33&-63\end{array}\right]\)

So the answer is -6G - 3H

\(G=\left[\begin{array}{ccc}-21&-27&-9\\9&-33&-63\end{array}\right]\)

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Answer:

4. SR= 17 (opposite angle of parallogram are equal)

Answer:

Complementary angles are two angles that add up to 90° in total measurement.

Example:

Angle 1 is 34°. It's complement would be 56°.

\(90 -34=56\)

Brainilest Appreciated.

Answer:

(x+7)(x-7)

Step-by-step explanation:

These are perfect squares. Whenever you have perfect squares, you can take the square root of the constant. The constant is 49 in this case. The square root of 49 is + or - 7. Therefore, you get (x+7) and (x-7) as solutions. Factored form is (x+7)(x-7).

Answer:

20% of 150 is 30. If your looking for the cost of the thing its $120 after markdown

Step-by-step explanation:

To determine when the rate of change of population is fastest, we need to analyze the behavior of the derivative dP/dt. Since the population is at its carrying capacity when P = 75, the rate of change of population is fastest when P is farthest from its carrying capacity. In this case, it would be at the lowest population value, which is P = 0.

The differential equation given is:

dP/dt = 2(1 - P/150)P

To find the carrying capacity, we need to determine the equilibrium point of the population, where the rate of change is zero (i.e., dP/dt = 0).

Setting dP/dt = 0 in the differential equation:

0 = 2(1 - P/150)P

Simplifying:

0 = 2P - \(2P^2\)/150

0 = P - \(P^2\)/75

Rearranging:

\(P^2\)/75 - P = 0

Factoring out P:

P(P/75 - 1) = 0

This equation is satisfied when either P = 0 or P/75 - 1 = 0.

For P = 0, the population is at its lowest and there is no growth.

For P/75 - 1 = 0, solving for P:

P/75 = 1

P = 75

So, the carrying capacity of the population, in this case, is 75.

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find the carrying capacity of differential equation: dP/dt= 2(1-P/150)P Suppose p(t) represents population of species x at time t years. what would be the population when the rate of change of population is fastest?

Given data:

The number of hour Stacy studied maths is 2/6 hour.

The number of hour Stacy studied science is 3/6 hour.

The total number of hours Stacy studied in 5 days is,

Thus, the total number of hours Stacy studied in 5 days is 25/6 hours, so option (D) is correct.

Explanation

We are given the stemplot below:

We are required to determine the highest score received.

A stemplot can be interpreted as follows:

With the illustration above, we can pair the stem and leaf of the stemplot given to determine that the highest score is 100.

Option B is correct. The answer is 100.

if the test statistic falls outside this range, we would reject the null hypothesis and conclude that students take more than 2 classes per quarter on average.

The rejection region is the set of values that, if the test statistic falls within it, would lead us to reject the null hypothesis. In this case, the null hypothesis is that students take an average of 2 classes per quarter.

To determine the rejection region, we need to find the critical value corresponding to the given significance level. Since alpha is 0.01 and the sample size is 16, we can use the t-distribution with n-1 degrees of freedom.

Using a t-distribution table or calculator, we find that the critical value for a two-tailed test at alpha = 0.01 and 15 degrees of freedom is approximately ±2.947.

The rejection region consists of the values outside the interval (-∞, -2.947) and (2.947, ∞).

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The domain of the graphed function is:

D: x ≥ 2

For a function y = f(x), we define the domain as the possible inputs, this is, the possible values of x.

To find the domain, we need to look at the horizontal axis, we can see that the minimum is the leftmost value, which is (2, 3), and it is marked with a  colored dot, so the value x = 2 belongs to the domain.

Then, the line extends to the right side, so the domain is the set of all real values larger than x = 2

The domain is:

D: x ≥ 2

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The inequality for u is \(u \in(-\infty, 24]\)

22+2=u

\(\begin{aligned}&22 \geq u-2 \\&22+2 \geq(u-2)+2 \\&24 \geq u-2+2 \\&24 \geq u \\&u \leq 24 \\&u \in(-\infty, 24]\end{aligned}\)

What is inequality?

A bit represents a portion of a whole. This total can be a region or a grouping. The term" bit" comes from the Latin word" fractio," which means" to break." The Egyptians, the first civilization to study fragments, used fragments to break fine problems similar as the division of food and inventories. fragments were only written in Ancient Rome using words to describe a portion of the whole. fragments were firstly written in India with one number above another( numerator and denominator), but without a line. It was only the Arabs who added the line that separates the numerator and denominator.

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The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.

To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.

Step 1:

Convert the percentage to a decimal.
65.3 / 100 = 0.653

Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

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a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

AB = 10

Step-by-step explanation:

Use the distance formula: √(12 - 18)^2 + (1 - 9)^2

√36 + 64

10

Answer:

10 units

Step-by-step explanation:

Use the distance formula. Substitute the values, (1-9)²+(12-18)²=100. The square root of 100 is 10.

The percentage of fraudulent responses (class 1 response rate) when the model is applied to the data set generated by oversampling depends on the specific circumstances and cannot be determined without evaluating the model's predictions on the oversampled data set.

The percentage of fraudulent responses (class 1 response rate) when the model is applied to the data set generated by oversampling cannot be determined without specific information about the data set, the model, and the results of applying the model.

Oversampling is a technique used to address class imbalance in a dataset, where the minority class (in this case, fraudulent responses) is underrepresented compared to the majority class. By generating additional samples of the minority class, the data set becomes more balanced.

The actual class 1 response rate after applying the model to the oversampled data set will depend on various factors, such as the performance of the model, the quality of the oversampling technique, the characteristics of the data, and the prevalence of fraudulent responses in the original data set.

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The value of y = 11, -4, -9 for each value of x = -1, 2, 3

Here the equation is

5x = -y + 6

We have to find the value of y for x = -1, 2, 3.

So we have,

y = -5x + 6

Now put the value of x =-1

y = -5(-1) +6

  = 5 + 6

  = 11

Now x = 2

y = -5(2) + 6

  = -10+6

  = -4

Now x = 3

y = -5(3) + 6

  = -15 + 6

  = -9

Therefore the value of y = 11, -4, -9 for x = -1, 2, 3 respectively.

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Percentage spent on transportation is 12%

Percentage spent on Property tax is 11%

Percentage spent on utilities is 9%

Percentage spent on food is 20%

Percentage spent on mortgage payment is 30%

Percentage spent on entertainment is 8%

Percentage spent on miscellaneous is 10%

What are the percentages?

Percentage is the fraction of a number expressed as a number out of 100. In order to convert a number of fraction to percentage, multiiply by 100. The sign that is used to represent percentage is %.

Percentage spent on transportation = (576 / 4800) x 100 = 12%

Percentage spent on Property tax = (528 / 4800) x 100 = 11%

Percentage spent on utilities = (432 / 4800) x 100 = 9%

Percentage spent on food = (960 / 4800) x 100 = 20%

Percentage spent on mortgage payment = (1440 / 4800) x 100 = 30%

Percentage spent on entertainment = (384 / 4800) x 100 = 8%

Percentage spent on miscellaneous = (480 / 4800) x 100 = 10%

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The net financing need considering the three accounts is approximately $185,753.42.

To determine the average investment in accounts receivable, inventories, and accounts payable, we need to calculate the Inventory Period, Receivables Period, and Payment Period.

Inventory Period:

The Inventory Period is the average number of days it takes for finished goods to be sold. In this case, the average production process time is given as 40 days, and finished goods are kept on hand for an average of 15 days before they are sold. Therefore, the Inventory Period is the sum of these two periods:

Inventory Period = Production Process Time + Days Kept on Hand

Inventory Period = 40 days + 15 days

Inventory Period = 55 days

Receivables Period:

The Receivables Period is the average number of days it takes for accounts receivable to be collected. It is given that accounts receivable are outstanding for an average of 40 days. Therefore, the Receivables Period is 40 days.

Payment Period:

The Payment Period is the number of days the firm receives credit on its purchases from suppliers. It is given that the firm receives 40 days of credit. Therefore, the Payment Period is 40 days.

Now, we can calculate the average investment in accounts receivable, inventories, and accounts payable.

Average Investment in Accounts Receivable:

Average Investment in Accounts Receivable = (Net Sales / 365) * Receivables Period

Average Investment in Accounts Receivable = ($1,200,000 / 365) * 40

Average Investment in Accounts Receivable ≈ $131,506.85

Average Investment in Inventories:

Average Investment in Inventories = (Cost of Goods Sold / 365) * Inventory Period

Average Investment in Inventories = ($900,000 / 365) * 55

Average Investment in Inventories ≈ $142,191.78

Average Investment in Accounts Payable:

Average Investment in Accounts Payable = (Cost of Goods Sold / 365) * Payment Period

Average Investment in Accounts Payable = ($900,000 / 365) * 40

Average Investment in Accounts Payable ≈ $87,945.21

Finally, to calculate the net financing need, we subtract the average investment in accounts payable from the sum of the average investment in accounts receivable and inventories:

Net Financing Need = Average Investment in Accounts Receivable + Average Investment in Inventories - Average Investment in Accounts Payable

Net Financing Need = $131,506.85 + $142,191.78 - $87,945.21

Net Financing Need ≈ $185,753.42

Therefore, the net financing need considering the three accounts is approximately $185,753.42.

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For the given cubic polynomial function (a) c = -6, d = 9, and k = -4, critical numbers are x = -2 and x = 1/3 (b) The critical number of the function f on the interval [1,3] is 0.

Given cubic polynomial function f(x) = x³ + x² + cx + d, to find the values of c, d, and k, such that 0 is a critical number, (0)=9, and the point (1,-1) is an inflection point of f(x). Inflection point - If the sign of the second derivative of a function changes at a point, then that point is known as the inflection point. Critical number - The critical numbers of a function are those values of x for which f'(x) = 0 or f'(x) does not exist. Now let's solve the question.(1) f(x) = x³ + x² + cx + df(0) = 0³ + 0² + c * 0 + d= 0 + 0 + 0 + d= d ...(i) f(x) = x³ + x² + cx + df'(x) = 3x² + 2x + c

For the critical number, f'(x) = 0 => 3x² + 2x + c = 0 ...(ii).Now (0) = 9 => d = 9 from equation (i).f(1) = 1³ + 1² + c * 1 + 9 = 1 + 1 + c + 9 = c + 11 and the point (1,-1) is an inflection point of f(x).  Therefore, f"(1) = 0 => 6 + c = 0 => c = -6 ...(iii) Substituting equation (iii) in equation (ii),3x² + 2x - 6 = 0 => x² + (2/3)x - 2 = 0 => (x + 2)(x - 1/3) = 0 => x = -2, 1/3 are the critical numbers.

(b) The given function is f(x) = x²√3 - x On differentiating w.r.t x, we get f'(x) = 2x√3 - 1We can observe that f'(x) is defined for all values of x. Hence, there are no critical numbers in the interval [1, 3]. Thus, the critical number of the function f on the interval [1,3] is 0. Answer: (a) c = -6, d = 9, and k = -4, critical numbers are x = -2 and x = 1/3.(b) The critical number of the function f on the interval [1,3] is 0.

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The points (2, 2), (4, - 2), (- 6, - 2), (- 2, 4) are examples of ordered pairs on the coordinate plane.

Coordinate planes are generated by the intersection of two orthogonal axes, a "horizontal" (x-axis) and a "vertical" (y-axis), at a point known as origin. These axes creates four regions known as quadrants, which are introduced in the image attached below.

All the ordered pairs are points of the form (x, y), where x and y represent the orthogonal positions of the point with respect to the origin. Now we proceed to present four examples of ordered pairs, each located in each quadrant: (2, 2), (4, - 2), (- 6, - 2), (- 2, 4).

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all real numbers are greater than or equal to 2

The measure of the inscribed angle is equal to 90 degrees

The inscribed angle theorem mentions that the angle inscribed inside a circle is always half the measure of the central angle or the intercepted arc that shares the endpoints of the inscribed angle's sides. In a circle, the angle formed by two chords with the common endpoints of a circle is called an inscribed angle and the common endpoint is considered as the vertex of the angle.

In this problem, the side length of the square is 5 which forms 90 degrees to all the other sides.

The measure of the circumscribed angle is 90 degree

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When 2 angles and an included side of 1 triangle are congruent to the corresponding piece of another triangle, it is said to be in ASA or AAS congruency

According to the Angle-Side-Angle Postulate (ASA), two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

And as seen in the figure to the right, we prove that triangle ABC is congruent to triangle DEF by the Angle-Side-Angle Postulate.

Contrarily, the Angle-Angle-Side Postulate (AAS) states that two triangles are congruent if their respective non-included sides are congruent with two angles from one triangle and two angles from another.

And as seen in the figure to the right, we prove that triangle ABC is congruent to triangle PQR by the Angle-Angle-Side Postulate.

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By using arithmetic progression, it can be calculated that

i) Distance she ran on 21 days = 37 km

ii) Total distance she ran in 21 days = 525 km

What is arithmetic progression?

Arithmetic progression consist of a sequence of numbers in which the difference between the consequent terms of the sequence are same.

This problem is based on arithmetic progression

Distance an athlete ran on first day = 13 km

She increases the distance she runs each day by 1.2km

So this is an arithmetic progression with first term 13 km and common difference 1.2 km

i) Distance she ran on 21 days = 13 + (21 - 1) \(\times\) 1.2

                                               =  37 km

ii) Total distance she ran in 21 days = \(\frac{21}{2}(13 + 37)\) = 525 km

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The smallest measurement used in the apothecary system for volume is the minim.

The apothecary system is an outdated system of measurements primarily used in pharmacy and medicine. It includes various units for measuring volume, weight, and other quantities.

In the apothecary system, the minim is the smallest unit of measurement for volume. It is equivalent to approximately 0.0616 milliliters.

The minim is a small unit of measurement and is typically used for precise dosing of liquids in the apothecary system. It is commonly used in pharmaceutical compounding and in the preparation of medications.

However, it's important to note that the apothecary system is no longer widely used in modern healthcare practices. The metric system, with units such as milliliters and liters, has become the standard for measuring volume in most countries.

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