find the slopes of the surface z = 5x y at the point (4, 4, 20/4) in the x− and y−directions
slope in the x-direction is
slope in the y-direction is

The cost of each adult ticket for watching movie at the theatre equals to $12.

Given data:

Student ticket price = $7

Group of 4 students and 3 adults paid $64 in all for movie tickets.

The computation of each of the adult ticket cost is as follows:

Let x be the cost of each adult ticket.

Then, cost of 3 adult tickets = 3x.

Now:

The cost of 1 student ticket = $7

The cost of 4 student ticket = $7(4)

Then, we get the following equation:

7(4) + 3x = 64

18 + 3x = 64

3x = 64 - 18

3x = 36

x = 12

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The flexible budget would reflect monthly operating income of $23,000 and $68,500 for 20,000 bottles of spray and 34,000 bottles of spray, respectively. The correct option is A.

The flexible budget is a tool that helps businesses to forecast their costs and revenues under different levels of activity. In this case, the flexible budget for Summer Nights bug spray is based on the following assumptions:

The selling price of each bottle of bug spray is $0.50.

The variable cost of each bottle of bug spray is $3.25.

The fixed cost is $42,000 for volumes up to 40,000 bottles of spray, and $60,000 for volumes above 40,000 bottles of spray.

The operating income for 20,000 bottles of spray is calculated as follows:

Revenue = 20,000 * $0.50 = $10,000

Variable costs = 20,000 * $3.25 = $65,000

Fixed costs = $42,000

Operating income = $10,000 - $65,000 - $42,000 = $23,000

The operating income for 34,000 bottles of spray is calculated as follows:

Revenue = 34,000 * $0.50 = $17,000

Variable costs = 34,000 * $3.25 = $110,500

Fixed costs = $60,000

Operating income = $17,000 - $110,500 - $60,000 = $68,500

Therefore, the flexible budget would reflect monthly operating income of $23,000 and $68,500 for 20,000 bottles of spray and 34,000 bottles of spray, respectively.

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Answer:

\(\begin{array}{ccccc}x & {-8} & {-4} & {4} & {8} & \frac{g(x)}{f(x)} & {-9} & {-5} & {3} & {7} \ \end{array}\)

Step-by-step explanation:

Given

The attached tables of f(x) and g(x)

Required

A new table

For both tables, the x-values are the same.

So, the new table is as follows:

\(\begin{array}{ccccc}x & {-8} & {-4} & {4} & {8} & \frac{g(x)}{f(x)} & {54/-6} & {10/-2} & {18/6} & {70/10} \ \end{array}\) --- i.e. divide g(x) by f(x) of the same x values

After the division, we have:

\(\begin{array}{ccccc}x & {-8} & {-4} & {4} & {8} & \frac{g(x)}{f(x)} & {-9} & {-5} & {3} & {7} \ \end{array}\)

By taking the quotient between the two functions evaluated in one value of x, we will see that the correct option is the third table (counting from the top).

We want to find the table that correctly represents the quotient of the two functions f(x) and g(x).

To do this, let's find each value of that quotient and see which table contains them.

for x = -8 we have:

Then the quotient is:

g(-8)/f(-8) = 54/-6 = -9

There is only one table that contains this value, so only with this, we can conclude that the correct option is the third table (counting from the top).

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Answer:

Eric´s mom had:

31 years 11 months

Step-by-step explanation:

1 year = 12 months

40 years = 39 years + 12 months

40 years 3 months = 39 years + 12 monts + 3 monts = 39 years 15 months

Then:

 40 years 3 months

-   8 years 4 months

it´s equivalent to:

 39 years 15 months

-   8 years  4 months

= 31 years  11 monts

Answer: I calculated the value after 5 years to be 5,734.40 or 5,734

Step-by-step explanation:

Answer:

40.0707

Step-by-step explanation:

because you multiply -0.0035 (-20.2) + 40= 40.0707

Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700

Use the simple interest formula

I = P r t

where I = simple interest

P = principal

r= rate of interest

t= number of years

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

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Answer:

The frequency is -1/pi

Step-by-step explanation:

I am currently taking the test and this is the answer that I got. Please give me brainliest

A sample is said to be picked in such a way that any potential subset of the same size has an equal chance of being chosen is known as simple random sample.

What is  simple random sample ?

A simple random sample, also known as an SRS, is a subset of people (also known as a sample) taken from a larger group of people (also known as a population), where the subset is selected at random and with an equal probability. This procedure involves choosing a sample at random. In SRS, the probability of selecting any subset of k individuals as a sample is the same for all subsets of k individuals.

Therefore, A sample is said to be picked in such a way that any potential subset of the same size has an equal chance of being chosen is known as simple random sample.

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Answer:

16

Step-by-step explanation:

3x + 4 = x + 12  [The straight line on the segments AB and BC indicate that they are the same length]

2x = 8  [Subtract x and 8 from both sides]

x = 4  [Divide both sides by two]

Length AB is equal to (3x + 4) as indicated by the diagram. Substituting x = 4, (3 * 4) + 4 = 16

It is given that Motorists A, B and C are travelling from Town X to Town Y which is 36 km apart.

It is given that when Motorist A is reached town Y , motorist B need to cover 12 km distance to reach town Y and motorist C need to cover 15 km distance to reach town Y.

A can travel 36 km in one hour.

B can travel 24 km in one hour.

C can travel 21 km in one hour.

Now, B can reach to point Y in half hour as there is only 12 km left to cover.

So, in half the C covers only 10.5 km.

And initially it is 15 km apart from point Y but when B reached to point Y.

C left with 4.5 km that is

Hence Motorist C from Town Y when Motorist B reached Town Y is 4.5 km.

1. The graphs and table that represent functions include the following: B, C, and E.

2. The set of ordered pairs that does not represent a function are:

A. {(-4, 9), (-4, 7), (1, -5), (7, -7)}.

C. {(-2, 0), (0, -2), (1, 1), (2, 0)}.

D. {(-5, 4), (-3, 4), (-1, 4), (2, 4)}.

In Mathematics and Geometry, a function is used for defining and representing the relationship that exists between two or more variables in a relation, table, ordered pairs, or graph.

Part 1.

Based on the given graphs and tables, we can logically deduce that the graph of a circle represent a relation because it does not have an inverse function. Also, tables D and F does not represent a function because the input values (domain) are not uniquely mapped to the output values (range).

Part 2.

Based on the given set of ordered pairs, we can logically deduce that only set A represent a function because the input values (domain) its uniquely mapped to the output values (range).

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Step-by-step explanation:

The answer to the question is 3

Answer:

3

Step-by-step explanation:

1 + X = 4

4 - 1 = X

3 = X

To factor a trinomial when a is greater than 1, we can use the AC method

To factor a trinomial when a is greater than 1, follow these steps

Multiply the coefficient of a (the first term) by the constant (the third term).

Find two numbers that multiply to the product obtained in step 1 and add up to the coefficient of b (the second term).

Replace the middle term with the two terms found in step 2.

Factor the resulting four-term polynomial by grouping.

Factor out the greatest common factor from each group.

Factor the resulting binomials.

Combine the factors to obtain the final factorization of the trinomial.

This method is known as the AC method, and it can be used to factor trinomials of the form ax^2 + bx + c, where a is greater than 1.

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Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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The line crosses the y-axis at the y-intercept which is: -6.

The y-intercept of a line can be determined by substituting x = 0 into the equation that represents the line, then solve for y.

Alternatively, if given graph of the line, we can easily determine the y-intercept by finding the value on the y-axis where the line crosses.

The value where the line crosses is the y-intercept of the line.

Given the line in the diagram below, the y-intercept of the line is -6.

This means that the line crosses the y-axis at -6, which is (0, -6).

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An exponential function can represent growth or decay.

The graph represents an exponential growth function is given by  \(y = ab^{x}\).

An exponential function is represented as:

\(y = ab^{x}\)

Where:

a represents any constant value.

b represents the growth or decay rate of the function

When the value of b is greater than 1, then the exponential function represents growth

Graph shown below represents an exponential growth function.

Hence, the graph representing an exponential growth function is graph traced by \(y = ab^{x}\).

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Step-by-step explanation:

Four tosses of the coin result in 2^4 = 16 possible outcomes of which FOUR

will have ONE tails :

HHHT

HHTH
HTHH
THHH      so 4 out of 16  = 4/16 = 1/4    Not very unusual

Answer:

10m + 12n >_ 300

Step-by-step explanation:

Answer:

I think the answer is  12m + 10n ≥ 300

Answer:

the first step is wrong

it should be 4(x-4)/(x+1)(x-4) - (x+2)/(x-4)(x+1)

The minimum number of pounds of mozzarella cheese is necessary to say that your medium pizza ranked in the top 3% of all medium pizzas in terms of cheese content.

P(z < 0.2) = 0.5793

Generally, The normal distribution, also known as the Gaussian distribution, is a kind of probability distribution that is symmetric around the mean. This means that it demonstrates that data that are closer to the mean are more likely to occur than data that are farther away from the mean. When represented graphically, the normal distribution takes the shape of a "bell curve."

In conclusion, To begin, we calculate the z score to determine the crucial value. If

\(z =\frac{ (x - u)}{ s}\)

x = critical value = 0.5

u = mean = 0.495

Hence

\(z =\frac{ (x - u)}{ s}\)

z= 0.2

Therefore, by making use of a table or some other kind of technology, the left-tailed area of this is

P(z < 0.2) = 0.5793

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Complete Question

A pizza shop advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. In addition, it is discovered that the quantity of cheese put on the population of all medium pizzas has a Normal distribution with a mean of 0.495 and standard deviation 0.025. The probability that a randomly selected pizza has less than the advertised amount of mozzarella cheese is:

a) 0.2000

b) 0.5793

c) 0.4207

d) 0.800

To analyze the given function y = -1 - 3csc(pi*x/2 + 3pi/4), let's examine its properties:

Domain: The domain of the function is the set of all real numbers except for the values that make the csc(pix/2 + 3pi/4) term undefined. The csc function is undefined when its argument equals zero, which occurs when pix/2 + 3pi/4 is an odd multiple of pi. So, the domain is the set of all real numbers except for x values that satisfy the equation pi*x/2 + 3pi/4 = (2n + 1)*pi, where n is an integer.

Range: The range of the function y = -1 - 3csc(pi*x/2 + 3pi/4) is all real numbers since the csc function can take on any real value.

Amplitude: The amplitude of the function is the absolute value of the coefficient of the csc term, which is 3 in this case.

Period: The period of the function is determined by the period of the csc function, which is 2pi. However, the period of the given function is affected by the coefficient of x in the argument of the csc function. In this case, the coefficient is pi/2, which means that the period is (2pi) / (pi/2) = 4.

Zeros: To find the zeros of the function, we need to solve the equation y = -1 - 3csc(pi*x/2 + 3pi/4) = 0. However, since the csc function is always positive or negative, it never equals zero. Therefore, the given function has no zeros.

Asymptotes: The asymptotes of the function occur when the csc term approaches positive or negative infinity. This happens when the argument of the csc function equals an odd multiple of pi. So, the vertical asymptotes occur when pix/2 + 3pi/4 = npi, where n is an integer.

In summary: Domain: All real numbers except for x values that satisfy pi*x/2 + 3pi/4 = (2n + 1)*pi

Range: All real numbers

Amplitude: 3

Period: 4

Zeros: None

Asymptotes: Vertical asymptotes occur when pix/2 + 3pi/4 = npi, where n is an integer.

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There have been numerous cases of athletes being accused of using performance-enhancing drugs, and the numbers may vary depending on the sport, country, and time period in question.

Additionally, determining how many athletes were using or not using performance-enhancing drugs would require specific information on individual cases.

Regarding the percentage of athletes falsely accused of using performance-enhancing drugs, it is difficult to determine an accurate figure without examining each case in detail. False accusations may occur due to various reasons, such as flawed testing procedures or contaminated supplements, and the percentage of false accusations may vary depending on the situation.

If you have a specific case or sport in mind, I can try to provide you with more information on that topic.

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Answer:

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

Find each area and then find their difference.

The difference is:

Answer:

$25.99

Step-by-step explanation:

Answer:

(-8,0)

Explanation:

If we have an equation with the form:

y = ax² + bx + c

The x-coordinate of the vertex will be: -b/2a

So, in this case, for the equation:

y = x² + 16x + 64

Where a = 1, b = 16, and c = 64

We get that the x-coordinate of the vertex is:

Then, the y-coordinate can be calculated replacing x by -8 on the initial equation, so:

y = (-8)² + 16(-8) + 64

y = 64 - 128 +64

y = 0

Therefore, the vertex of the parabola is the point (-8, 0)

The measure of the greatest angle in this pentagon is,

a = 88 degree

We have,

The measures of angles of a pentagon from an arithmetic sequence whose common difference is 10.

Let us assume that,

All the five angles of pentagon  whose common difference is 10 are,

⇒ a, a + 10, a + 20, a + 30, and a + 40

Sum of all the angles in pentagon = 540 degree

Hence, We get;

a + a + 10 + a + 20 + a + 30 + a + 40 = 540

5a + 100 = 540

5a = 540 - 100

5a = 440

Divide by 5,

a = 440 / 5

a = 88

Hence, the measure of the greatest angle in this pentagon is,

a = 88 degree

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Given:

Number of spheres = 2

Number of prisms = 3

Number of pyramids = 5

To find:

The probability that a pyramid will be selected.

Solution:

We have,

Favorable outcomes = Number of pyramids

                                  = 5

Total outcomes = Total number of figures

                          = \(2+3+5\)

                          = \(10\)

Now, the required probability is:

\(\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\)

\(\text{Probability}=\dfrac{5}{10}\)

\(\text{Probability}=0.5\)

Therefore, the probability that a pyramid will be selected is 0.5.

The values of a, h and k on the function are given as follows:

The meaning of the transformations is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = 1/x.

Hence the meaning of the transformations is given as follows:

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The series (a) corresponds to the Taylor series expansion of the function f(x) = 1/(4 + x) centered at x = 0. The sum of the series is 1/(4 + x).mThe series (b) corresponds to the Taylor series expansion of the function f(x) = ln(1 + x) centered at x = 0. The sum of the series is ln(1 + x). The series (c) corresponds to the Taylor series expansion of the function f(x) = sqrt(1 - x) centered at x = 0. The sum of the series is sqrt(1 - x).

The Taylor series expansion allows us to approximate a function using a series of terms involving its derivatives. In each case, the series is given in the form of the Taylor series at z = 0.

(a) To determine the function and point, we recognize that the series is in the form of the geometric series with the common ratio of -1/4. By comparing it with the formula for a geometric series, we find that the function is f(x) = 1/(4 + x) and the expansion is centered at x = 0.

The sum of the series can be obtained by using the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

In this case, a = 1/4 and r = -1/4. Plugging these values into the formula, we get the sum as 1/(4 + x).

(b) The series resembles the Taylor series expansion of the natural logarithm function ln(1 + x). By comparing the terms, we identify the function as f(x) = ln(1 + x), and the expansion is centered at x = 0. The sum of the series is ln(1 + x).

(c) The series is reminiscent of the Taylor series expansion of the square root function sqrt(1 - x). By comparing the terms, we recognize that the function is f(x) = sqrt(1 - x), and the expansion is centered at x = 0. The sum of the series is sqrt(1 - x).

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