Différenciation implicit function containing product and quotient. d/dx (2y/5x)

The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

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The owner can advertise 400 different sound systems. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers can be explained using the four fundamental operations, generally known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.

We are given that the owner of a stereo store carries 5 different CD players, 8 different receivers, and 10 different speakers and each sound system consists of one of each item.

So, the different sound systems that the owner can advertise is obtained by using the multiplication operation, which gives:

⇒ Different sound systems = 5 * 8 * 10

⇒ Different sound systems = 400

Hence, the owner can advertise 400 different sound systems.

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Answer:

hope this will help you...

Answer: Increase in percentage by 42% and with baggage 43.2%.

Step-by-step explanation:

we know that the price is increased from $250 to $ 335

the percentage change by increasing the price is

$355 - $ 250 = $105

percentage change will be change/original = 105/250*100 = 42%

additional charges $ 50, $105+ $50 = 155

percentage change = 155/355*100 = 43.2%

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It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.

The total net amount the supermarket owes the wholesaler for the order is $231.31.

A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.

To find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.

The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:

Discounted cost = List price - (Discount rate x List price)

For the soup, the discounted cost per case is:

$18.90 - (0.39 x $18.90) = $11.51

For the baked beans, the discounted cost per case is:

$33.50 - (0.39 x $33.50) = $20.42

Now we can calculate the total net amount owed by the supermarket to the wholesaler:

Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)

Total net amount = (13 x $11.51) + (4 x $20.42)

Total net amount = $149.63 + $81.68

Total net amount = $231.31

Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.

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The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3

What is an absolute value equation?

An absolute value equation can be written as |expression| = value

To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.

We can write,

|x + 5| = 3

To solve for x, we have two cases,

Case 1: x + 5 is positive

If x + 5 is positive, then the equation becomes x + 5 = 3

Solving for x,

x = -2

This matches one of the solutions we want.

Case 2: x + 5 is negative

If x + 5 is negative, then the equation becomes -(x + 5) = 3

Solving for x,

x = -8

This also matches the other solution we want.

Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.

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Answer: What is the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic?

Let's call the number of pulled-pork sandwiches "P" and the number of barbeque chicken sandwiches "C". According to the problem, the organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches. This means that:

P/C = 2/5

To simplify this ratio, we can multiply both sides by a common factor that will make the denominators the same. In this case, the smallest common multiple of 2 and 5 is 10, so we can multiply both sides by 10:

10(P/C) = 10(2/5)

Simplifying this expression, we get:

2P = 4C

Dividing both sides by 2, we get:

P/C = 2/4

Simplifying this fraction, we get:

P/C = 1/2

Therefore, the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic is 1:2.

Step-by-step explanation:

Answer: The formula for compound interest is:

A = P(1 + R/100)^t

where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.

Here, P = Rs. 3,500, R = 8%, and t = 2 years.

So, the amount after 2 years will be:

A = 3,500(1 + 8/100)^2

= 3,500(1.08)^2

= 3,892.32

Therefore, the compound interest for 2 years will be:

CI = A - P

= 3,892.32 - 3,500

= 392.32

Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

D. [tex]8a^{9} -4a^{3} +1[/tex]

Step-by-step explanation:

Given [tex]r(x)=x^{3} -2x+1[/tex] and find [tex]r(2a^{3} )[/tex] :

Solve for [tex]r(2a^{3} )[/tex] :

1. [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]

2. [tex]r(2a^{3} )=8a^{9} -2(2a^{3})+1[/tex]

3. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]

Answer:

So, if [tex]r(x)=x^{3} -2x+1[/tex], then [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1[/tex].

Then the answer is D. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]

A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

How to determine the amount of carpet needed for a rectangular room?

To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.

The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),

18 feet ÷ 3 feet/yard = 6 yards

So the dimensions of the room in yards are 10 yards by 6 yards.

To find the total area of the room, we need to multiply the length and width,

10 yards × 6 yards = 60 square yards

Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

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The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.

To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.

A. 5n = 5(4) = 20

B. n + 30 = 4 + 30 = 34

C. 50 - n = 50 - 4 = 46

D. 80 ÷ n = 80 ÷ 4 = 20

The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n

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Answer:

(3x + y)(2x + 3)

Step-by-step explanation:

6x² = 2 * 3 * x * x

2xy = 2*x * y

Common factor = 2x.

        9x = 3 * 3 * x

        3y = 3 * y

Common factor = 3

Take out the common factor 2x from the first and second term & take out the common factor 3 from third and fourth term.

6x² + 2xy + 9x + 3y = 2x(3x + y) + 3(3x + y)

                              = (3x + y)(2x + 3)

The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of various methods and techniques to gather data from a sample or population and to draw conclusions or make predictions based on that data.

There are two main branches of statistics: descriptive statistics and inferential statistics. Descriptive statistics is the process of summarizing and presenting data in a meaningful way, such as by calculating measures of central tendency (e.g. mean, median, mode), variability (e.g. range, variance, standard deviation), and correlation. Inferential statistics involves using probability theory to make inferences about a larger population based on a sample of data.

Statistics is used in a wide variety of fields, including business, economics, psychology, social sciences, medicine, and engineering. It is often used to test hypotheses, identify trends, and make predictions based on data. The field of statistics has evolved over time, with the development of new techniques and technologies for collecting and analyzing data.

The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying. Surveying a larger group of fifth grade students or every teacher at the school would not be as effective since it would include girls and boys who are not in the fifth grade, and teachers who may not have as much knowledge about the specific video game preferences of fifth grade boys. Surveying every boy who will pass to fifth grade next year would also not be as effective since they are not currently in the fifth grade and their preferences may change by the time they reach that grade. Therefore, surveying the 25 fifth grade boys would provide the most relevant and accurate data for Ryan's study.

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The complete question is:

Ryan wants to find the favorite video game of the fifth grade boys at his school. Which group would be BEST for Ryan to survey? 25 fifth grade boys 25 fifth grade students every teacher at his school every boy who will pass to fifth grade next year

By answering the presented question, we may conclude that As a result, the linear function denoted by the table is y = 2x - 2.

A line's slope shows how steep it is. A mathematical equation for the gradient is referred to as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of vertical change (rise) to horizontal change between two points (run). The slope-intercept form of an equation is used to represent the equation of a straight line, which is written as y = mx + b. The y-intercept is located where the line's slope is m, b is b, and (0, b). The slope and y-intercept of the equation y = 3x - 7 are two examples (0, 7). The line's slope is m. b is b at the y-intercept, and (0, b).

To obtain the slope and y-intercept of a linear function in slope-intercept form, we must first establish the slope and y-intercept.

With two locations on the line, we can first determine the slope. Let us start with the first and last points in the table:

slope = (y change) / (change in x)

slope = (16 - (-8)) / (9 - (-3))

slope = 24 / 12

slope = 2

We can now use the slope and one of the points to get the y-intercept. Let's take the point (1, 0) as an example:

y = mx + b 0 + b b = 2(1) + b b = -2

Hence the linear function's slope-intercept equation is:

y = 2x - 2

As a result, the linear function denoted by the table is y = 2x - 2.

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The probability that y is between 5.1 and 5.7 is approximately 0.4292.

Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.

Since the sample size is large (n = 70), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as normal with mean μ = 5 and standard deviation σ/sqrt(n) = 2/sqrt(70) ≈ 0.24.

Now we want to find the probability that y, the sample mean, is between 5.1 and 5.7. We can use the standard normal distribution to do this by standardizing y:

z = (y - μ) / (σ / sqrt(n)) = (y - 5) / 0.24

The probability that y is between 5.1 and 5.7 is equivalent to the probability that z is between:

z1 = (5.1 - 5) / 0.24 ≈ 0.42

and

z2 = (5.7 - 5) / 0.24 ≈ 2.92

Using a standard normal distribution table or calculator, we can find that the probability of z being between z1 and z2 is approximately 0.4292.

Therefore, the probability that y is between 5.1 and 5.7 is approximately 0.4292.

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The missing step in the proof is: D. ADCA

In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).

Therefore, we have the following proportional sides:

DC/AC = AC/BC

Given that DC = BA (given statement), we can substitute BA for DC in the proportion:

BA/AC = AC/BC

Now, we can cross-multiply to get:

BA * BC = AC²

Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:

BA * BC = AC * AC

Use the definition of congruent sides to replace BA with DC:

DC * BC = AC * AC

And finally, use the substitution property of equality to replace BC with 6 units (given statement):

DC * 6 = AC * AC

From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.

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Answer: The area of the door can be calculated as:

Area of door = width x height

= 0.9 m x 2.1 m

= 1.89 square meters

The area of one window can be calculated as:

Area of window = width x height

= 1.5 m x 1.2 m

= 1.8 square meters

Since there are four windows, the total area of the four windows is:

Total area of four windows = 4 x Area of window

= 4 x 1.8 square meters

= 7.2 square meters

Therefore, the total area of the door and the four windows is:

Total area = Area of door + Total area of four windows

= 1.89 square meters + 7.2 square meters

= 9.09 square meters

Hence, the total area of the door and the four windows is 9.09 square meters.

Step-by-step explanation:

Nick's monthly mortgage payment is $482.16.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To calculate Nick's monthly mortgage payment, we first need to find out the amount he borrowed from the bank, which is 75% of the purchase price:

$145,500 x 0.75 = $109,125

Next, we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate (3.15%) by 12:

3.15% / 12 = 0.002625

Now we can use the following formula to calculate Nick's monthly payment:

M = P [ [tex]i(1 + i)^{n}[/tex] ] / [ [tex](1 + i)^{n}[/tex] – 1]

Where:

M = Monthly payment

P = Loan amount (principal)

i = Monthly interest rate

n = Number of payments (in months)

Plugging in the values we have:

M = $109,125 [ 0.002625 [tex](1 + 0.002625)^{360}[/tex] ] / [ [tex](1 + 0.002625)^{360}[/tex] – 1]

M = $482.16

Therefore, Nick's monthly mortgage payment is $482.16.

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Answer:

To solve this problem, we need to integrate the derivative f'(x) to obtain the function f(x).

∫f'(x) dx = ∫(4x - 3) dx

f(x) = 2x^2 - 3x + C

where C is the constant of integration.

To find the value of C, we need to use the fact that f(0) = 5. Substituting x = 0 into the above equation, we get:

f(0) = 2(0)^2 - 3(0) + C = C

Therefore, C = 5.

Hence, the function f(x) is:

f(x) = 2x^2 - 3x + 5

Now, we can find f(5) and f(-1) and compute their difference:

f(5) - f(-1) = (2(5)^2 - 3(5) + 5) - (2(-1)^2 - 3(-1) + 5)

f(5) - f(-1) = (50 - 15 + 5) - (2 + 3 + 5)

f(5) - f(-1) = 35 - 10

f(5) - f(-1) = 25

Therefore, f(5) - f(-1) = 25.

The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.

Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.

Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.

In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.

The statements that provide support for Chloe's claim are:

A. A<0 because A is to the left of zero.

F. B>0 because B is to the right of zero.

Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.

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5. The real zero occurs located

6. The x-coordinate at which a relative minimum occurs is at

In the context of a graph of a function

A real zero, also known as a root or a solution, is a value of the independent variable (usually denoted as x) for which the value of the dependent variable (usually denoted as y) is equal to zero.

Geometrically, a real zero corresponds to the x-coordinate of a point where the graph of the function intersects the x-axis.

A relative minimum, on the other hand, is a point on the graph where the function has a local minimum value.

Geometrically, a relative minimum corresponds to a point where the graph changes from decreasing to increasing, and is located at the bottom of a valley or a trough.

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All options except "How high you hit the ball" would affect the ball's height and distance.

The following factors would make a difference in the height and distance that the ball goes when an athlete hits a ball:

Therefore, all options except "How high you hit the ball" would affect the ball's height and distance.

When an athlete hits a ball, there are several factors that can affect the ball's trajectory, including the force and angle of the swing, as well as external environmental factors such as wind, temperature, and humidity.

The harder the athlete hits the ball, the more force will be imparted to the ball, and the farther it will travel.

Similarly, the angle of the swing can affect the trajectory of the ball, with a higher or lower angle resulting in different heights and distances traveled.

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When two sample means are significantly different, "the difference is too great to attribute to chance".

The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).

Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.

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Answer:

0.222

Step-by-step explanation:

2 divided by 9 is:

0.222 (rounded to the nearest thousandth)

Answer:

mean: 20mins

Step-by-step explanation:

add them all together to get 240

then divide by how many there are

240÷12=20

so the mean is 20mins

Answer:

84 paid with three 50p coins.

Mohal will be able to paint 9 bookcases for the amount of paint.

An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.

Given that, he has 1 1 /8​ gallons of paint.

Thus, number of bookcases are:

1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9

Hence, Mohal will be able to paint 9 bookcases for the amount of paint.

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Answer:

The Correct answer is Carter