How many terms are there in the expression?

-11 - 7c + 5 - 2x - 13b - 7

The directional derivative of given function at (0,6) in θ= 2π/3 is given as 7.732 approximately.

The rate at which any function varies at any specific location in a specified direction is known as the directional derivative. Any derivative's vector form is that. It describes the function's immediate rate of alteration. It broadens the perception of a partial derivative.

The rate of growth of a function on a given point in a certain direction is known as the directional derivative.

For a function f(x, y, z) , its directional derivative on point (x₁, y₁, z₁) in direction of unit vector u is evaluated as:

\(f(x_1,y_1,z_1)=\frac{\partial f}{\partial y } |u_x| + \frac{\partial f}{\partial x } |u_y|+\frac{\partial f}{\partial z } |u_z|\)

where \(u_x,u_y,u_z\)  components of the considered unit vectors in direction of coordinate axes, and that |u| like symbol means magnitude of that component.

For the given case, the function is

f(x, y) = 2ye⁻ˣ

The point at which directional derivative of given function is to be found is (0,6), and direction is θ = 2π/3

\(\frac{\partial f}{\partial x } =-2ye^{-x}\\\\\frac{\partial f}{\partial y }=2e^{-x\)

Thus, the directional derivative is found as:

f(0, 6) = 6 + \(\sqrt{3}\) = 7.732.

Thus, the directional derivative at (0,6) in θ = 2π/3 is 7.732.

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Complete question:

Find the directional derivative of f at the given point in the direction indicated by the angle θ. f(x, y) = 2ye−x, (0, 6), θ = 2π/3

Answer:

\(x = \frac{2}{3} \: \: or \: \: x = - 3\)

Step-by-step explanation:

\(3 {x}^{2} + 7x = 6 \\ 3 {x}^{2} + 7x - 6 = 0 \\ 3 {x}^{2} + 9x - 2x - 6 = 0 \\ 3x(x + 3) - 2(x + 3) = 0 \\ (3x - 2)(x + 3) = 0 \\ \\ 3x - 2 = 0 \\ 3x = 2 \\ x = \frac{2}{3} \\ \\ x + 3 = 0 \\ x = - 3\)

The simplest polynomial function with the given zeros 2, -1, and -8 is:

f(x) = x³ + 7x² - 6x - 16.

Given the roots or zeroes: 2, -1, and -8

Polynomial function f(x) = ?

If the given zeros are 2, -1, and -8, then the corresponding factors of the polynomial function are:

(x - 2), (x + 1), and (x + 8).

The simplest polynomial function with these zeros is the product of these factors:

(x - 2)(x + 1)(x + 8)

Expanding this product gives:

x³ + 7x² - 6x - 16

Hence;

The polynomial function is f(x) = x³ + 7x² - 6x - 16.

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Answer:

Deal A is best

Step-by-step explanation:

Given

Deal A:

3/4 lb for $2.50

Deal B:

2/10 lb for $5.25

Required

Which deal is the better

To do this, we simply calculate the lb/dollar ratio

i.e.

\(Ratio = \frac{Amount}{Size}\)

For Deal A:

\(Ratio = \$2.50/\frac{3}{4}lb\)

\(Ratio = \$2.50 * \frac{4}{3}lb\)

\(Ratio = \frac{\$10}{3}lb\)

\(Ratio = \$3.33/lb\)

For Deal B:

\(Ratio = \$5.25/\frac{2}{10}lb\)

\(Ratio = \$5.25 * \frac{10}{2}lb\)

\(Ratio = \frac{52.5}{2}lb\)

\(Ratio = \$26.25/lb\)

The better deal is the least expensive:

Hence: Deal A is better

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The required answer is  sec θ = -√2.

Explanation:-

Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).

To determine three possible angles θ,  the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore  conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.

Therefore, sec θ = 1/cos θ.To find cos 11π/4,  the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.

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To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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The terms minimum and infimum are both related to the concept of lower bounds in mathematics. A minimum is the smallest value in a set of numbers, whereas an infimum is the greatest lower bound of a set.

A minimum is a value that is less than or equal to all other values in the set, while an infimum is a value that is less than or equal to all other values in the set, but not necessarily the smallest value.

For example, if we consider the set {2, 4, 6}, the minimum is 2 and the infimum is also 2. However, if we consider the set {2, 4, 6, 8}, the minimum is 2 and the infimum is 4. In the latter set, 4 is the greatest lower bound, meaning that all other values in the set are greater than or equal to 4.

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The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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Answer:

4+3x esa es la suma de cuatro y el producto de tres y un número x

Answer:

10

Step-by-step explanation:

-12+22

10

Answer:

10

Step-by-step explanation:

Its A because i checked myself

Answer:

answers is 78 because if 6x45 that 87

Answer

Option A is correct.

Only (3, 2) is a solution of this equation given.

Explanation

The ordered pair which is a solution of this equation will be the option that satisfies the equation given when the values are inserted.

4x - 1 = 3y + 5

Option A

(3, 2)

x = 3

y = 2

4x - 1 = 3y + 5

4(3) - 1 = 3(2) + 5

12 - 1 = 6 + 5

11 = 11

This satisfies the given equation.

Option B

(2, 3)

x = 2

y = 3

4x - 1 = 3y + 5

4(2) - 1 = 3(3) + 5

8 - 1 = 9 + 5

7 ≠ 14

This does not satisfy the equation.

Option C

Only one of the answers is correct.

So, this option is wrong

Hope this Helps!!!

Answer: x = 2 - 1/2 y

Step-by-step explanation:

12x + 6y = 24

12x = 24 - 6y

x = 2 - 1/2 y

The ratio of p:q:r is 1 : 6 : 5 / 6

Ratio compares values. Ratios compares relationship between two numbers of same units. Ratios can be express in fraction too.

Therefore,

p:q = 1/3 : 2  = 1 / 3 × 1 / 2 = 1 / 6

p : r = 3/4:1/2  = 3 / 4 × 2 / 1 = 6 / 5

p:q  = 1 /  6

p / q = 1 / 6

p = 1 / 6 q

q = 6p

Therefore,

p : r = 6 / 5

p / r = 6 / 5

6r = 5p

r = 5 / 6 p

Therefore,

P : q: r = p : 6p : 5 /6 p

Therefore,

P : q: r = 1 : 6 : 5 / 6

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The normal approximation relies on certain assumptions about the underlying distribution, and if these assumptions are not met, the approximation may not be accurate.

To determine whether the normal approximation is appropriate, we need to consider the sample size and the distribution of the data. If the sample size is large enough (typically n > 30) and the data follow a roughly symmetric distribution, then the normal approximation can be used.

However, if the proportion of individuals holding multiple jobs is close to 0 or 1, or if the sample size is small, the normal approximation may not be valid. In such cases, it is better to use exact methods or alternative distributions, such as the binomial distribution.

Without additional information about the sample size and the distribution of the data, it is not possible to definitively determine whether the normal approximation is appropriate.

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Answer:

46 and 22

Step-by-step explanation:

let the father b (f) and d son is (s)

so

f=3s.....(1)

(f+10) +(s+10)=68 .... (2)

substitute f=3s in equation (2)

we have

(3s+10)+(s+10)=68

4s+20=68

4s=68-20

4s=48

s=12 .......(3)

substitute (3) in (1)

f=3*12

which f=36

in 10 year time

f+10 =46

s+10=22

Answer:

The percent for games that were won is 59.375%.

Step-by-step explanation:

Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

Answer:

758

Step-by-step explanation:

The largest number that can be made is 875 but it ends in 5 which makes it an odd number.

The only even number is 8 so we have to use it last.

7 is bigger than 5 so 7 goes first which means it's 758

Answer:

Step-by-step explanation:

Let the packages contain maximum amount of plates.

Find the GCF of both numbers:

Lisa bought:

Greg bought:

The probability that the mean number of raisins in a sample of 17 randomly selected Happy Trail Mix bags is more than the mean number of raisins in a sample of 17 randomly selected generic trail mix bags is approximately 0.954, or 95.4%.

To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means tends to be approximately normal, regardless of the shape of the population distribution, when the sample size is sufficiently large. In this case, we have a sample size of 17 for both the Happy Trail Mix and the generic trail mix.

We can calculate the mean and standard deviation of the sampling distribution of the mean for each trail mix. The mean of the sampling distribution for the Happy Trail Mix is equal to the population mean, which is 33.6, while the mean of the sampling distribution for the generic trail mix is equal to the population mean, which is 28.8.

The standard deviation of the sampling distribution for the Happy Trail Mix is equal to the population standard deviation divided by the square root of the sample size, which is 8.4 divided by the square root of 17. Similarly, the standard deviation of the sampling distribution for the generic trail mix is equal to 12.7 divided by the square root of 17.

To find the probability that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix, we can calculate the z-score using the formula: z = (sample mean of Happy Trail Mix - sample mean of generic mix) / (standard deviation of Happy Trail Mix - standard deviation of generic mix).

Once we calculate the z-score, we can then look up the corresponding probability using a standard normal distribution table or calculator. In this case, the calculated z-score corresponds to a probability of approximately 0.954, or 95.4%.

Therefore, the probability that the mean number of raisins in a sample of 17 randomly selected Happy Trail Mix bags is more than the mean number of raisins in a sample of 17 randomly selected generic trail mix bags is approximately 0.954, or 95.4%.

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The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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The odds of selecting a number in your phone that is not your family are approximately 0.9423 or 94.23%.

To calculate the odds of selecting a number in your phone that is not your family, we need to determine the number of contacts that are not family members and divide it by the total number of contacts.

Given that you have 52 contacts in total, and you have the numbers of your dad, mom, and brother, we can assume that these three contacts are family members. Therefore, we subtract 3 from the total number of contacts to get the number of non-family contacts.

Non-family contacts = Total contacts - Family contacts

Non-family contacts = 52 - 3

Non-family contacts = 49

So, you have 49 contacts that are not family members.

To calculate the odds, we divide the number of non-family contacts by the total number of contacts.

Odds of selecting a non-family number = Non-family contacts / Total contacts

Odds of selecting a non-family number = 49 / 52

Simplifying the fraction:

Odds of selecting a non-family number ≈ 0.9423

Therefore, the odds of selecting a number in your phone that is not your family are approximately 0.9423 or 94.23%.

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Answer:

1 1/3 tubs per min.

2 mph.

50 mph.

9 cups per bag.

Step-by-step explanation:

Multiply the numerator of the first number by the denominator of the second number, then divide the product by the denominator of the first number. Hope this helps :)

Answer:

1. Hence, the answer is $74.50

2. Hence, the answer is 16.

Step-by-step explanation:

1. Given: Natalie and her friends decide to rent 4 lanes at regular cost for a party. Ten people need to rent shoes, adn 4 people are members.

To find: What is the total cost for the party?

Solution:

Since Natalie and her friends wanted to rent four lanes, we need to calculate this at REGULAR cost.

4 * 9 .75 = 39

Now since 10 people want to rent shoes, and 4 people are members, we subtract.

10 - 4 = 6

6 nonmembers

4 members

6 times the amount of shoe rental for 6 * 3.95 - 23.70

non members

4 times the number of members shoe rental 4* 2.95

11. 80

Now add the quantities

39 + 11.80 + 23.70 += 50.80 + 23.70 =

74.50

Now, our answer is 74.50

2.

Solution:

20 / 1.25 = 16

So the possible amount that can be bought is 16 medium sodas.