Use the quotient rule to find the derivative of the following.
y = (5x²+ 2)(2x + 3)/y=4x-7 dy/dx = ...

(fg)(x)= x³ - 7x² - 9x + 8

domain is (-∞,∞)

Given: f(x)= x-8, g(x)= x² +1x - 1

To find (fg)(x) we multiply f(x) and g(x)

(fg)(x) = f(x) * g(x)

(fg)(x)= (x-8) (x²+x-1)

(fg)(x)= x³ + x² - x - 8x² - 8x +8

(fg)(x)= x³  - 7x²  - 9x + 8

we know, domain for all cubic function is set of all real numbers

domain is (-∞,∞)

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a. True. Pivot columns of an echelon form of A form a basis for the column space of A.
b. True. Row operations preserve linear dependence relations among the rows of A.
c. False. The dimension of the null space of A is the number of columns of A minus the number of pivot columns.

18. a. If B is any echelon form of A, then the pivot columns of B form a basis for the column space of A.

This statement is true. An echelon form of a matrix is obtained by performing row operations on the original matrix to transform it into a specific triangular form. In this form, the pivot columns correspond to the columns containing the leading entries in each row. The pivot columns of an echelon form of matrix A will also be pivot columns of matrix A itself.

The column space of a matrix is the span of its column vectors. Since the pivot columns of B are a subset of the column vectors of A, they will also span the column space of A. Therefore, the pivot columns of B form a basis for the column space of A.

b. Row operations preserve the linear dependence relations among the rows of A.

This statement is true. When we perform row operations on a matrix, such as multiplying a row by a scalar, adding rows together, or swapping rows, the resulting matrix will have the same row space as the original matrix. This means that the linear dependence relations among the rows of the original matrix will be preserved in the transformed matrix.

c. The dimension of the null space of A is the number of columns of A that are not pivot columns.

This statement is false. The dimension of the null space of A, also known as the nullity of A, is the number of free variables in the reduced row echelon form of A. It is equal to the number of columns of A minus the number of pivot columns. Therefore, the dimension of the null space of A is the number of columns of A minus the number of pivot columns, rather than the other way around.

To summarize:
a. True. Pivot columns of an echelon form of A form a basis for the column space of A.
b. True. Row operations preserve linear dependence relations among the rows of A.
c. False. The dimension of the null space of A is the number of columns of A minus the number of pivot columns.

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Answer:

8 pizzas

Step-by-step explanation:

If each of the 20 people eats 3/8 of pizza, to calculate the total number of pizzas needed, multiply 20 by 3/8 and round up to the nearest whole number.

\(\sf total \ number \ of \ pizzas=20 \times\dfrac38\)

                                  \(=\dfrac{20 \times3}8\)

                                  \(=\dfrac{60}8\)

                                  \(=\dfrac{15}2\)

                                  \(=7.5\)

Therefore, he should buy 8 pizzas for the party.

Answer:

-3

remember, slope is rise over run. It's negative because the line is declining.

Out of 8 members of the committee, it is possible to create two subcommittees only.

We know that in order to create subcommittees. we need to divide the total number of people on the committee into equal parts so that they form subcommittees.

Here, it is given that there are 8 members on the committee.

A subcommittee needs to have 3 people in it.

On dividing 8 people into groups of three, we get

⇒ \(\frac{8}{3}\)

⇒ 2.66..

Here, it is obvious that the 0.66... can not be considered because it is not a whole number and hence, does not mean any number of people.

So, we can create only two different subcommittees from 8 members on the main committee.

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In the figure below, the area of the shaded portion is 31.5 m²

Given the figure which consists of a square and a rectangle, we want to find the area of the shaded portion. We proceed as follows.

We notice that the area of the shaded portion is the portion that lies between the two triangles.

So, area of shaded portion A = A" - A' where

Now, Area of larger triangle, A" = 1/2BH where

So, A" = 1/2BH

= 1/2 × 16 m × 7 m

= 8 m × 7 m

= 56 m²

Also, Area of smaller triangle, A' = 1/2bH where

So, A" = 1/2bH

= 1/2 × 7 m × 7 m

= 3.5 m × 7 m

= 24.5 m²

So, area of shaded portion A = A" - A'

= 56 m² - 24.5 m²

= 31.5 m²

So, the area is 31.5 m²

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The inequality which can be used to determine x, the number of outfits Cameron can purchase while staying within his budget is 720 ≤ 270.4 + 70.25x

Given:

Amount with Cameron = $720

Cost of new bicycles = $200.75

Cost of 4 bicycle reflectors = $12.29 × 4

= $49.16

Cost of bike gloves = $20.49

Cost of new banking outfit = $70.25

let

number of outfits = x

The inequality:

720 ≤ 200.75 + 49.16 + 20.49 + (70.25 × x)

720 ≤ 270.4 + 70.25x

720 - 270.4 ≤ 70.25x

449.6 ≤ 70.25x

x ≤ 449.6 / 70.25

x ≤ 6.4

Therefore, the number of outfits Cameron can purchase is 6 pairs

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Answer:

Y = -1

Step-by-step explanation:

y has multiple meaning

In graphs, y is the coordinate point we need to plot after assuming a promising value of other coordiante like x

see image below for example

Similarly, it can be said that y is a function of variable x , that is the value of y varies with variable x

Answer:The second graph

Step-by-step explanation:Basically since you have y=-6 you can show process of elimination by showing which linear lines cross the -6 crosspoint

The correct answer is a box numbered x can contain a box numbered y if capacity[x] is divisible by capacity[y]. The containment relationships can be determined based on this criterion.

In the given scenario, Amazon ships several parcels each day to multiple locations, and the dispatch center has conveyor belts where the parcel boxes are placed. The boxes in the center are numbered from 0 to (n - 1), and the capacity of each box is denoted by capacity[i]. A box numbered x can contain a box numbered y if the capacity[x] is divisible by capacity[y].

To better understand the situation, let's consider an example. Suppose we have 5 boxes numbered from 0 to 4, and their respective capacities are as follows:

capacity[0] = 10

capacity[1] = 20

capacity[2] = 5

capacity[3] = 2

capacity[4] = 1

Based on the given conditions, the box numbered 0 can contain any other box since any number is divisible by 1. The box numbered 1 can contain boxes 0 and 2, as 20 is divisible by 10 and 5. The box numbered 2 can contain only box 4 since 5 is divisible by 1. The box numbered 3 can contain only box 4 as 2 is divisible by 1. Finally, the box numbered 4 cannot contain any other box since it has the smallest capacity.

So, in this case, the possible containment relationships are as follows:

0 can contain: 1, 2, 3, 4

1 can contain: 0, 2

2 can contain: 4

3 can contain: 4

4 cannot contain any other box

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Yes, that is correct. A matrix A ∈ R^(n×n) is symmetric if and only if A^T = A, which means that the entries of A satisfy a_ij = a_ji for all i, j.

The gradient ∇f(x) of a function f : R^n → R is an n-vector of partial derivatives, given by:

∇f(x) = (∂f/∂x₁, ∂f/∂x₂, ..., ∂f/∂x_n)

Each component of the gradient represents the rate of change of the function with respect to each variable x₁, x₂, ..., x_n.

If you have any further questions or need more clarification, feel free to ask!

what is function?

A function is a mathematical concept that describes a relationship between a set of inputs (called the domain) and a set of outputs (called the range). It assigns each input value to a unique output value. A function can be represented using various notations, such as equations, formulas, graphs, or tables.

In general, a function takes an input value and produces a corresponding output value based on a specific rule or algorithm. The rule or algorithm defines how the function operates and determines the relationship between the input and output values.

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Answer:

40

Step-by-step explanation:

280 divided by 7

Answer:

it's 3/10

Step-by-step explanation:

you would have to multiply all of those fraction so:

3/4 x 4/5 x 1/2=  3/10

i am so so sorry if i am wrong

Answer:

B

Step-by-step explanation:

(hx)(gx)

(2x+5)(3x+2)

6\(x^{2}\)+4x+15x+10

6\(x^{2}\)+19x+10

Answer B

The volume of the recycling bin is given as 576 cubic feet. We know that the bin is a rectangular prism with a base of 12 feet by 6 feet. So, we can use the formula for the volume of a rectangular prism to find the height:

Volume of rectangular prism = base area x height

In this case, the base area is 12 feet x 6 feet = 72 square feet. So, we have:

576 cubic feet = 72 square feet x height

Dividing both sides by 72 square feet, we get:

height = 576 cubic feet / 72 square feet

Simplifying this expression, we get:

height = 8 feet

Therefore, the height of the bin is 8 feet.

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We know that the score is obtained by subtracting the number of incorrect answers from twice the number of correct answers. Let's use "x" to represent the number of correct answers.

According to the question, the player answered 40 questions in total. This means that the number of incorrect answers is 40 - x.
Now we can use the formula for the score:
Score = 2x - (40 - x)
We also know that the player obtained a score of 50. So we can set up the equation:
50 = 2x - (40 - x)
Simplifying the equation:
50 = 3x - 40
90 = 3x
x = 30
Therefore, the player answered 30 questions correctly.
To check, we can plug this value back into the formula for the score:
Score = 2x - (40 - x)
Score = 2(30) - (40 - 30)
Score = 60 - 10
Score = 50
So the score of 50 is correct and the player answered 30 questions correctly.

To find out how many questions the player answered correctly in the trivia game with a score of 50, we can use the given information to set up an equation:
Let x be the number of correct answers and y be the number of incorrect answers. According to the question, the score is calculated by subtracting the number of incorrect answers (y) from twice the number of correct answers (2x). The player answered 40 questions in total, so we have:
x + y = 40
2x - y = 50
Now we can solve this system of equations step-by-step:
1. Solve the first equation for x:
x = 40 - y
2. Substitute this expression for x in the second equation:
2(40 - y) - y = 50
3. Simplify the equation:
80 - 2y - y = 50
4. Combine like terms:
80 - 3y = 50
5. Subtract 80 from both sides:
-3y = -30
6. Divide both sides by -3:
y = 10
7. Substitute the value of y back into the expression for x:
x = 40 - 10
x = 30
The player answered 30 questions correctly in the trivia game with a score of 50.

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Answer:

The answer is 3:4 i believe

Answer:

3:4

Step-by-step explanation:

To model the change in the number of immigrants over time, we can assume a linear relationship between the number of immigrants and the number of years.

To express the number of immigrants, y, in terms of t, we can use the equation of a straight line, y = mx + b, where m is the slope and b is the y-intercept. We have two data points: (t1, y1) = (1950 - 1900, 240,933) and (t2, y2) = (2002 - 1900, 1,102,888). Using these points, we can find the slope as m = (y2 - y1) / (t2 - t1). Substituting the slope and one of the data points into the equation, we can determine the equation expressing the number of immigrants, y, in terms of t.

Using the equation obtained in part a, we can predict the number of immigrants in 2019. We calculate t3 = 2019 - 1900 and substitute it into the equation to find the corresponding value of y.  The validity of using this linear equation to model the number of immigrants throughout the entire 20th century can be evaluated by considering the y-intercept value, b. The y-intercept represents the estimated number of immigrants in the year 1900.

If the number of immigrants in the early 20th century significantly deviates from the y-intercept value, it indicates that a linear model may not accurately capture the immigration patterns over the entire century. It is essential to assess historical data and consider other factors that may affect immigration trends to determine the validity and accuracy of the linear model.

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Answer:

POKEMON YEAH!

Okay, so you first want to take 2485, and subtract it from 4500, because that is the amount of money he has already collected.

4500 - 2485 = 2015

Now you need to find out how many time you can multiply 155, to get 2015, or higher. In this case, I am just gonna divide:

2015/155 = 13

It will take him 13 more weeks to have enough for the Pokemon cards!

Step-by-step explanation:

Hope it helps! =D

Answer:

It is incorrect because the following gives you a total of 171 and not 1.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 TRUE

A number is always 100%  Anyting bigger than 100% is going to be a bigger number

  Anything smaller than 100% is a smaller number

2FALSE   5/100 = 0.05 and NOT 0.5

0.5% is the same as thalf of 100%    = 50%

   50/100  = 5/10  = 0.5

The formula v · v = kvk2 can be seen to hold for all vectors in Rn, as the dot product of a vector and itself is equal to the magnitude of the vector squared.

The formula v · v = kvk2 is true for all vectors v in Rn. This is because the dot product of a vector and itself is equal to the magnitude of the vector squared. The dot product of two vectors is defined as the sum of the products of their components. Therefore, when a vector v is multiplied by itself, the result is the sum of the squares of all its components. The magnitude of a vector is defined as the square root of the sum of the squares of its components. Thus, the formula v · v = kvk2 can be seen to hold for all vectors in Rn, as the dot product of a vector and itself is equal to the magnitude of the vector squared.

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To determine the height of a tree, Joe measures the angle of elevation and finds that it is 34 degrees. He is 8 m from the base of the tree. How tall is the tree? Round to the nearest tenth.

Here is the detailed explanation: Let's assume the height of the tree is h.

From the given data, the angle of elevation of the tree from Joe's position is 34 degrees, and the distance of Joe from the base of the tree is 8 meters.

From the given angle, we can say that tan 34 = h / 8m.

Then, we can evaluate the value of h as h = 8 x tan 34.The value of h is: h ≈ 8 x 0.686 = 5.48 meters.

Hence, the height of the tree is 5.48 meters (rounded to the nearest tenth).

Answer: The height of the tree is 5.48 meters (rounded to the nearest tenth).

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Answer:

x=(14+2)*4x

hope that helps

Answer:

Step-by-step explanation:

There is only one intercepting point, it means one solution.

A) A steer weighing 1000 pounds is 2.78 standard deviations below the mean.

B) A z-score of 1.85 is closer to the mean than a z-score of -2.78, we can conclude that a steer weighing 1000 pounds is more unusual than one weighing 1250 pounds.

A) To find how many standard deviations below the mean a steer weighing 1000 pounds is, we need to use the formula for standard score (or z-score):

z = (x - μ) / σ

where x is the weight of the steer, μ is the mean weight, and σ is the standard deviation. Substituting the values we have:

z = (1000 - 1150) / 54

z = -2.78

B) To determine which is more unusual, we need to compare the z-scores for a steer weighing 1000 pounds and one weighing 1250 pounds. Using the same formula as before:

For a steer weighing 1000 pounds:

z1 = (1000 - 1150) / 54

z1 = -2.78

For a steer weighing 1250 pounds:

z2 = (1250 - 1150) / 54

z2 = 1.85

A positive z-score means the weight is above the mean, while a negative z-score means the weight is below the mean. Therefore, a steer weighing 1250 pounds is 1.85 standard deviations above the mean, while a steer weighing 1000 pounds is 2.78 standard deviations below the mean.

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The conclusion that is correct in a two-tailed test at α = .05 is There appears to be no difference in the mean occupancy rates.

From the given values:

Thus, the P-value = 0.1791

Interpret results. Since the P-value (0.1791) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test, we do not have sufficient evidence in favor of the claim that there is a difference in the mean occupancy rates.

Thus, option A is correct.

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Given

The formula of the volume of a cylinder

Substitute the given to the volume

The volume of a cylinder with a radius of 5 and a height of 3 is

Answer:

normal

Step-by-step explanation:

Dot Product of Vectors

As the dot product of the vectors equals 0, the vectors are normal.

Answer:

The middle between two numbers is the average of those numbers. So we add those two numbers together and divide by two. And the answer is (1 + 6) / 2 = 3.5