If xy^2 = 20, and x is decreasing at the rate of 3 units per second, the rate at which y is changing when y = 2 is nearest to?

Answer:

7x = 6(x+15)

Step-by-step explanation:

a pex

The inequality 2.5x ≤ 20 represents the given situation, and Becky can afford at most eight fish.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let x be the number of fish Becky can afford.

We can write an inequality to represent the situation using the cost of the fish and the amount of money Becky has:

2.5x ≤ 20

To solve this inequality, we'll start by isolating the variable x on one side of the inequality. To do that, we'll divide both sides of the inequality by 2.5:

x ≤ 8

This inequality tells us that Becky can afford at most 8 fish.

To check:

20/2.5 = 8 fish

Learn more about the inequalities here:

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To maximize revenue for John Deere's heavy-duty tractors, the optimal unit price is found by determining the vertex of the provided quadratic revenue function R(p). Using the vertex formula, the unit price p that maximizes revenue is $1520.

Maximizing Revenue for John Deere Heavy-Duty Tractors

To find the unit price that maximizes revenue for John Deere heavy-duty tractors, we need to analyze the revenue function R(p) provided, which follows a quadratic format:

R(p) = [tex](-1/2)p^2[/tex]  + 1520p

To find the maximum revenue, we can use the fact that the vertex of a parabola described by a quadratic equation y = ax^2 + bx + c provides the maximum or minimum value of the function. Since our equation is in the form of a parabola opening downwards (because the coefficient of p^2 is negative), the vertex will give us the maximum revenue point.

The formula for the p-coordinate (horizontal axis) of the vertex of a parabola is given by -b/(2a). In this case, a = -1/2 and b = 1520, therefore:

p = -b/(2a) = -1520/(2 * (-1/2)) = -1520/(-1) = 1520

Hence, the unit price p should be set at $1520 to maximize revenue for the sale of heavy-duty tractors. This value is already an integer, so rounding to the nearest dollar is not necessary.

Answer:

The answer is:  [tex]x^3-9x^2+14x+24[/tex]

Step-by-step explanation:

The given expression is:  [tex](x-4)(x^2-5x-6)[/tex]

For getting the product, we need to distribute [tex](x-4)[/tex] with each term in the second parenthesis. So.....

[tex](x-4)(x^2-5x-6)\\ \\ =x^2(x-4)-5x(x-4)-6(x-4)\\ \\ =x^3-4x^2-5x^2+20x-6x+24 \ [using\ distribution\ rule]\\ \\ =x^3-9x^2+14x+24\ [combining\ like\ terms][/tex]

So, the answer is:  [tex]x^3-9x^2+14x+24[/tex]

Answer:

The correct answer is most definitely A. $ 500 credit

Step-by-step explanation:

I am 100% Positive

There are 22,764 possible cones.

To calculate the number of possible cones, we need to consider the number of flavors and the number of scoops. Since a customer can order a single-, double-, or triple-scoop cone, we will consider each case separately.

For a single-scoop cone, the customer can choose one flavor out of the 28 available flavors. Therefore, there are 28 possible single-scoop cones.

For a double-scoop cone, the customer can choose two flavors for the two scoops. Since the order of the flavors matters and repetition is allowed, we can think of this as selecting two flavors with replacement. Using the formula n^r, where n is the number of flavors and r is the number of scoops, there are a total of 28^2 = 784 possible double-scoop cones.

For a triple-scoop cone, the customer can choose three flavors for the three scoops. Again, using the formula n^r, there are a total of 28^3 = 21,952 possible triple-scoop cones.

Therefore, the total number of possible cones is 28 + 784 + 21,952 = 22,764.

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The distance between -3.1 and -5.7 on the number line is 2.6 units.

The distance between two points on the number line is the absolute difference between those two points.

So, the distance between -3.1 and -5.7 is:

[tex]|-3.1 - (-5.7)| = |-3.1 + 5.7| = |2.6| = 2.6[/tex]

Therefore, the distance between -3.1 and -5.7 on the number line is 2.6 units.

Final answer:

To find the amount for the monthly payments for a plasma-screen TV, subtract the down payment from the total cost and divide by the number of installments. The equation is: Monthly Payment = (Total Cost - Down Payment) / Number of Installments, which calculates to $195.75.

Explanation:

The student is seeking to find an equation that represents the cost of a plasma screen television being paid off with a down payment and equal monthly installments. Given the total cost of the television is $5250 and the down payment is $552, we can start by calculating the remaining balance after the down payment, which will be paid in 24 equal monthly payments.

First, subtract the down payment from the total cost to find the balance that needs to be paid in installments:

Next, we divide the balance by the number of monthly payments to find the amount of each payment:

Therefore, the equation that represents the monthly payment after the down payment is:

Monthly Payment = (Total Cost - Down Payment) / Number of Installments

Applying the given numbers we get:

Monthly Payment = ($5250 - $552) / 24

Plugging in the values:

Monthly Payment = $4698 / 24 = $195.75

Answer: No, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).

Step-by-step explanation:

Two lines are called perpendicular to each other if the product of their slope is -1.

Since, the slope of a line having end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Thus, the slope of line Joining points P(–8, –10) and Q(–5, –12),

[tex]m_1=\frac{-12+10}{-5+8}=\frac{-2}{3}=-\frac{2}{3}[/tex]

While, The slope of line Joining points R(9, –6) and S(17, –5),

[tex]m_2=\frac{-5+6}{17-9}=\frac{1}{8}[/tex]

Since,

[tex]m_1\times m_2=-\frac{2}{3}\times \frac{1}{8}=-\frac{1}{12}\neq -1[/tex]

Thus, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).

Answer: B is on bottom, C is on the left

Step-by-step explanation:

A is on top and B is opposite of A. Therefore, it's on bottom and C is on the left as E is on the right.

The bottom of the rectangular prism is side C, and the left side is side B.

To determine which side is the bottom and which side is on the left of the rectangular prism, we need to visualize how the paper was cut and folded. Let's assume that the original piece of paper had the letters A, B, C, D, E, and F on it. After folding, the side with the letter C will be the bottom of the rectangular prism, and the side with the letter B will be on the left. So, the correct answer is A. C is on the bottom, B is on the left.

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The student can match each slice of the surface 2x^2+5y^2+z^2=4 with its correct plot by substituting the slice values into the equation, resulting in a set of new equations each representing a different conic section centered at the origin.

To understand the shapes or plots of the resulting slices when the surface given by 2x^2+5y^2+z^2=4 is sliced by planes of the form x=a, y=b or z=c, you must substitute values of a, b, and c into the equation of the surface to reveal new equations describing the slices.

By comparing these resulting equations with the standard forms of conic sections (circle, ellipse), you can match them with their correct plots.

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Final answer:

The probability that both marbles chosen by Linda are blue is 2/15, calculated by multiplying the probability of selecting a blue marble on each draw without replacement.

Explanation:

To calculate the probability that Linda selects two blue marbles in a row without replacement, we need to consider the number of blue marbles and the total number of marbles in the bag during each draw. Initially, there are 10 marbles in total with 4 blue marbles. The probability of drawing a blue marble on the first draw is therefore 4/10.

Upon successfully drawing a blue marble the first time, the marble is not replaced, meaning there are now only 9 marbles left with 3 being blue. The probability of drawing a second blue marble is now 3/9, which simplifies to 1/3.

To find the total probability of both events occurring in sequence (both draws resulting in blue marbles), we multiply the probabilities of each individual event occurring:

(4/10) × (3/9) = (2/5) × (1/3) = 2/15.

Therefore, the probability that both marbles Linda chooses are blue is 2/15.

Answer:b

Step-by-step explanation:

To convert 15°C to Fahrenheit, we use the formula °F = (9/5 x °C) + 32, which will give us 59°F as the equivalent temperature. The formula is based on the freezing and boiling points of water in the two scales.

To convert a temperature given in degrees Celsius to Fahrenheit, we use the formula °F = (9/5 × °C) + 32. In this case, where the Celsius temperature (x) is 15, we substitute 15 into the formula: °F = (9/5 * 15) + 32. The calculation then becomes °F = 27 + 32 = 59°F, meaning 15°C is equivalent to 59°F on a Fahrenheit scale.

The formula is derived from the fact that the freezing point of water is 0°C (32°F) and the boiling point is 100°C (212°F). On the Fahrenheit scale, that's a range of 180 (212 - 32), and on the Celsius scale, it's 100 (100 - 0), which gives us the ratio 180/100 or 9/5.

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The Answer:

356+56y=-832

Answer:

Step-by-step explanation:

its answer C !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

In Total=560

Step-by-step explanation:

216/6=36

36*10=360

216+360=560

Activities that provide moderate, vigorous, or low exercise levels can be determined by their intensity and duration. Skating involves moderate physical activity, surfing can be considered a vigorous activity, and walking the dog provides a low level of physical exercise.

The level of physical activity involved in various activities usually depends on the intensity and duration of the actions involved. An example of an activity involving a moderate amount of physical activity could be d.) skating, considering the balance, coordination, and movement involved.

A vigorous physical activity, on the other hand, is characterized by increased heartbeat and breathing. Based on this, a.) surfing could be categorized as a vigorous activity as it involves intense body workout and body balance. Lastly, an activity that provides a low level of physical exercise involves less effort and fewer calories burned. A good example of this could be b.) walking the dog, as this activity mostly involves casual walking.

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Answer:

89; the mode

Step-by-step explanation:

Final answer:

The best measure of central tendency for the student's test scores is the mode, which is 89. The mean and median are 86 and 87 respectively, but the mode gives the highest score, hence it is the most favorable for determining the student's final grade.

Explanation:

The question asks for the most favorable measure of central tendency for a student's test scores to determine their final grade. The test scores provided are 89, 81, 85, 82, 89, and 89.

To find the most favorable measure, we need to calculate the mean (average), median, and mode of the test scores. The mean is calculated by adding all the scores together and dividing by the number of tests. The median is the middle number when the scores are listed in order, and the mode is the number that appears most frequently.

Calculating the mean: (89 + 81 + 85 + 82 + 89 + 89) / 6 = 85.83, which we round to the nearest whole number as 86.

To find the median, we order the scores: 81, 82, 85, 89, 89, 89. Since there are an even number of scores, the median is the average of the two middle numbers, in this case, 85 and 89. Thus, the median is (85 + 89) / 2 = 87.

The mode is the most frequent score, which is 89.

Out of the mean, median, and mode, the mode is the highest and most favorable measure of central tendency for the student, resulting in a final grade of 89 when rounded to the nearest whole number.