the sum of 17 and 3 times x *

Answer: C

Step-by-step explanation:

Step-by-step explanation:

Either x = 0 or y = 0. (Zero product rule)

The volume of the new touch tank is 16000 feet³.

Given that,

An aquarium is expanding its touch tank exhibit and is going to double the dimensions of the original tank.

A tank is in the shape of a rectangular prism.

Let l, w and h be the dimensions of the original tank.

Then if the dimensions are doubled, then the new dimensions of the new touch tank will be 2l, 2w and 2h.

Volume of the original tank = 2000 feet³

That is,

lwh = 2000

If all the dimensions are doubled,

2l . 2w . 2h = 8 lwh

                  = 8 × 2000

                  = 16000 feet³

Hence the volume of the new touch tank is 16000 feet³.

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a.  If we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

b. Michael's substitution satisfies the requirement for u to be differentiable.

(a) i. Kayla's proposed substitution of u as (3 - 2x) will not work in this case. The reason is that when using the u-substitution method, it is necessary for the chosen u to be differentiable, meaning that its derivative du/dx should exist and be non-zero. However, if we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

ii. Kayla's idea of always picking the most inside factor as u does not work for all u-substitutions. There can be cases where choosing the most inside factor may not lead to a valid substitution that simplifies the problem or makes integration easier. It is important to consider the properties of the function and choose a suitable substitution accordingly.

(b) i. Michael's proposed substitution of u as 3√3 - 2x will work in this case. If we let u = 3√3 - 2x, then the derivative du/dx would be -2, which is non-zero. Therefore, Michael's substitution satisfies the requirement for u to be differentiable.

ii. Michael's idea of always picking the most complicated factor as u also does not hold true for all u-substitutions. The choice of u depends on various factors, including the structure of the function, simplification possibilities, and making the integration process more manageable. It is not necessarily the case that the most complex factor will always result in a successful substitution.

It is important to consider the specific characteristics of the function and apply appropriate judgment in choosing the substitution u to simplify the problem effectively.

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The power functions among the given options are f(x) = 3⋅10x and f(x) = 8⋅2x.

A power function is a function of the form f(x) = ax^n, where a and n are constants. The variable x is raised to a constant power n, and the coefficient a determines the scale or magnitude of the function.

Among the given options:

- f(x) = 4⋅15x is not a power function because the base of the exponent is not a constant.

- f(x) = 17x√5 and f(x) = 12x√10 are not power functions because they include a square root term, which is not in the form of a constant power.

- f(x) = 3⋅10x and f(x) = 8⋅2x are power functions because they have a constant base (10 and 2, respectively) raised to a power that is a constant (x).

Therefore, the power functions among the given options are f(x) = 3⋅10x and f(x) = 8⋅2x.

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Answer:

Step-by-step explanation:

Area of a circle=πr²

A=π*4²

A=16π

A=50.27 ( rounded to nearest 100th)

The formulas for the entries of initial value problem Mⁿ are: (Mⁿ)₁₁ = 2(7ⁿ), (Mⁿ)₁₂ = 8ⁿ, (Mⁿ)₂₁ = -7ⁿ, (Mⁿ)₂₂ = 2(8ⁿ).

To find formulas for the entries of Mⁿ, where M is the given matrix:

\(M = \left[\begin{array}{ccc}6&-2\\1&9\end{array}\right]\)

We can diagonalize the matrix M by finding its eigenvalues and eigenvectors.

First, let's find the eigenvalues λ₁ and λ₂:

To find the eigenvalues, we solve the characteristic equation:

|M - λI| = 0,

where I is the identity matrix.

\(M-\lambda I = \left[\begin{array}{ccc}6-\lambda&-2\\1&9-\lambda\end{array}\right]\)

Setting the determinant equal to zero:

(6 - λ)(9 - λ) - (-2)(1) = 0,

(54 - 15λ + λ²) + 2 = 0,

λ² - 15λ + 56 = 0.

Factoring the quadratic equation:

(λ - 7)(λ - 8) = 0,

λ₁ = 7,

λ₂ = 8.

Now, let's find the corresponding eigenvectors for each eigenvalue:

For λ₁ = 7, solving the equation (M - 7I)V = 0, where V is the eigenvector:

(M - 7I)V = [-1 -2] [v₁] = 0,

[1 2] [v₂]

-1v₁ - 2v₂ = 0,

v₁ + 2v₂ = 0.

We can choose v₁ = 2 as a free variable.

Using v₁ = 2, we get:

-1(2) - 2v₂ = 0,

2 + 2v₂ = 0.

-2 - 2v₂ = 0,

2v₂ = -2.

v₂ = -1.

So, the eigenvector corresponding to λ₁ = 7 is V₁ = [2; -1].

For λ₂ = 8, solving the equation (M - 8I)V = 0, where V is the eigenvector:

(M - 8I)V = [-2 -2] [v₁] = 0,

[1 1] [v₂]

-2v₁ - 2v₂ = 0,

v₁ + v₂ = 0.

We can choose v₁ = 1 as a free variable.

Using v₁ = 1, we get:

-2(1) - 2v₂ = 0,

-2 + v₂ = 0.

-2 + v₂ = 0,

v₂ = 2.

So, the eigenvector corresponding to λ₂ = 8 is V₂ = [1; 2].

Now, we can diagonalize the matrix M:

\(M = PDP^{-1}\),

where P is the matrix whose columns are the eigenvectors and D is the diagonal matrix with eigenvalues on the diagonal.

P = [2 1]

[-1 2]

D = [7 0]

[0 8]

To find the formula for the entries of Mⁿ, we can raise the diagonal matrix D to the power of n:

Dⁿ = [7ⁿ 0]

[0 8ⁿ]

Finally, we can find the formula for Mⁿ:

Mⁿ = PDⁿP^(-1),

Mⁿ = [2 1] [7ⁿ 0] [2 -1]

[-1 2] [1 2]

Simplifying the matrix multiplication:

Mⁿ = [2(7ⁿ) 1(8ⁿ)]

[-1(7ⁿ) 2(8ⁿ)]

So, the formulas for the entries of Mⁿ are:

(Mⁿ)₁₁ = 2(7ⁿ),

(Mⁿ)₁₂ = 1(8ⁿ),

(Mⁿ)₂₁ = -1(7ⁿ),

(Mⁿ)₂₂ = 2(8ⁿ).

Therefore, the formulas for the entries of Mⁿ are:

(Mⁿ)₁₁ = 2(7ⁿ),

(Mⁿ)₁₂ = 8ⁿ,

(Mⁿ)₂₁ = -7ⁿ,

(Mⁿ)₂₂ = 2(8ⁿ).

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Answer:

p=2.5t

Step-by-step explanation:

p stands for pages

2.5 is how long it takes him to read 1 page

t is the time

the reason why the t is next to 2.5 is so when you replace t with the actual time, you would multiply it by 2.5 to get how many pages he read in any amount of time

Positive correlation means that both variables tend to increase (or decrease) together. Thus, Option A is the answer.

Positive correlation refers to a relationship between two variables in which an increase in one variable is associated with an increase in the other variable. Negative correlation, on the other hand, refers to a relationship in which an increase in one variable is associated with a decrease in the other variable. No correlation means that there is no relationship between the two variables.

To determine the strength of a correlation, we can use a statistical measure called the correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, a correlation coefficient of -1 indicates a perfect negative correlation, and a correlation coefficient of 0 indicates no correlation.

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The point (-7,4) is the farthest from the point and the distance is 11 units away, the correct option is (d).

We have to find that which point is the farthest from the point (4,4),

The distance(d) between two points (x₁, y₁) and (x₂, y₂) can be calculated by the distance formula : √((x₂-x₁)² + (y₂-y₁)²);

Using this formula, we can find the distance between each of the points and (4, 4):

⇒ For point (-7, 4):

d = √((4 - (-7))² + (4 - 4)²)

d = √(11²)

d = 11 units

⇒ For point (4, 4):

d = √((4 - 4)² + (4 - 4)²)

d = 0 units

⇒ For point (4, -5):

d = √((4 - 4)² + (-5 - 4)²)

d = √(9²)

d = 9 units,

Therefore, the point farthest away from (4, 4) is (d) Point (-7, 4), and the distance is 11 units.

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The given question is incomplete, the complete question is

A graph with the x-axis starting at -10, with tick marks every one unit up to 10. The y-axis starts at -10, with tick marks every one unit up to 10. A point is plotted at (-7, 4), at (4, 4) and at (4, -5).

Which of the points plotted is farther away from (4, 4), and what is the distance?

(a) Point (4, -5), and it is 9 units away

(b) Point (4, -5), and it is 11 units away

(c) Point (-7, 4), and it is 9 units away

(d) Point (-7, 4), and it is 11 units away

The probability to answer 5 questions correctly from 14 true or false questions is 0.1222

The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:

P(x)= nCx × p^x × q^(n-x)

Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.

n = 14 (total number of questions)

p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).

To find P(5), we substitute these values in the formula

P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222

Therefore, the answer is option D, 0.1222.

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The solution to the given problem of volume comes out to be the pyramid is 10 cm tall.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are the symbols for cubic measures.

Here,

The formula: gives the volume of a pyramid.

=> V = base_area * height * (1/3)

The area of the base (base_area) of a pyramid whose base is a rectangle with dimensions of 7.5 cm in length and 2 cm in width can be computed as follows:

base_area equals length * width,

=> 7.5 cm * 2 cm =15 cm².

Additionally, we are informed that the pyramid's (V) volume is 50 cm3.

=> (1/3) * 15 * height = 50

=> height =  (3 * V)/base_area.

When V and base_area's values are entered, we obtain:

=> height = (15/15) / (3*50) = 10 cm

Consequently, the pyramid is 10 cm tall.

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Answer:

Yes, all 3 are correct.

Step-by-step explanation:

Answer:no it is not right

Step-by-step explanation:so to get the answer right, you have to add a one as the denominator of the five. Next you have to switch the one and the five to make it a multiplication also called the keep change flip then, you multiply and you are done hope this helps!!!!

Answer:

Equation 4

Step-by-step explanation:

Standard Form is:

\(Ax+By=C\)

Option 1 is in point-slope form.

Option 2 is an incomplete point slope equation.

\(y-y_1=m(x-x_1)\\\\y-6=-3(x+5)\)

Option 3 is in slope-intercept form.

\(y=mx+b\\\\y=-3x+5\)

This leaves us which option 4, which is in standard form.

\(Ax+By=C\\\\3x+y=5\)

Option 4 should be the correct answer.

Hope this helps.

9514 1404 393

Answer:

  $8 /yd

Step-by-step explanation:

You probably want dollars per yard. To get that, divide dollars by yards:

  $22/(2.75 yd) = $8 /yd

The equation that model the relationship on the graph in slope-intercept form can be presented as follows;

y = (7/3)x + (-2/3)

The slope-intercept form of a linear equation is an equation of the form; y = m·x + c

Where;

m = The slope of the graph of the equation

c = The y-intercept

The first difference are;

-3 - (-10) = 7

4 - (-3) = 7

11 - 4 = 7

The data on the table represent the data for a linear equation, since the difference between the successive x-values are the same and equivalent to 3

The slope of the graph of the equation is therefore;

(11 - 4)/(5 - 3) = 7/3

The equation of that represents the data is therefore;

y - 11 = (7/3)·(x - 5) = (7/3)·x - 35/3 = (7/3)·x - 11 2/3

y = (7/3)·x - 11 2/3 + 11 = (7/3)·x - 2/3

The equation is therefore;

y = (7/3)·x - 2/3

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If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.

To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):

Average speed = distance ÷ time

Average speed = 12 miles ÷ (1/5) hour

To divide by a fraction, we can multiply by its reciprocal, so:

Average speed = 12 miles × 5/1 hour

Average speed = 60 miles per hour

Therefore, Idil drove at an average speed of 60 miles per hour.

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The value of δ for each of the given functions is:

(a) δ = (ε + 12)/3, for ε > 0

(b) δ

Given information is:

(a.) f(x) = 3x + 7, a = 4, ℓ = 19

(b) f(x) = 1/x, a = 2, ℓ = 1/2

(c) f(x) = x², ℓ = a²

(d) f(x) = √|x|, a = 0, ℓ = 0

In order to find δ > 0, we need to first evaluate the limit value, which is given in each of the questions. Then we need to evaluate the absolute difference between the limit value and the function value, |f(x) - ℓ|. And once that is done, we need to form a delta expression based on this value. Hence, let's solve the questions one by one.

(a) f(x) = 3x + 7, a = 4, ℓ = 19

First, let's evaluate the absolute difference between f(x) and ℓ:

|f(x) - ℓ| = |3x + 7 - 19| = |-12 + 3x| = 3|x - 4| - 12

Now, for |f(x) - ℓ| < ε, 3|x - 4| - 12 < ε

⇒ 3|x - 4| < ε + 12

⇒ |x - 4| < (ε + 12)/3

Therefore, δ = (ε + 12)/3, for ε > 0

(b) f(x) = 1/x, a = 2, ℓ = 1/2

First, let's evaluate the absolute difference between f(x) and ℓ:

|f(x) - ℓ| = |1/x - 1/2| = |(2 - x)/(2x)|

Now, for |f(x) - ℓ| < ε, |(2 - x)/(2x)| < ε

⇒ |2 - x| < 2ε|x|

Now, we know that |x - 2| < δ, therefore,

δ = min{2ε, 1}, for ε > 0

(c) f(x) = x², ℓ = a²

First, let's evaluate the absolute difference between f(x) and ℓ:

|f(x) - ℓ| = |x² - a²| = |x - a| * |x + a|

Now, for |f(x) - ℓ| < ε, |x - a| * |x + a| < ε

⇒ |x - a| < ε/(|x + a|)

Now, we know that |x - a| < δ, therefore,

δ = min{ε/(|a| + 1), 1}, for ε > 0

(d) f(x) = √|x|, a = 0, ℓ = 0

First, let's evaluate the absolute difference between f(x) and ℓ:

|f(x) - ℓ| = |√|x| - 0| = √|x|

Now, for |f(x) - ℓ| < ε, √|x| < ε

⇒ |x| < ε²

Now, we know that |x - 0| < δ, therefore,

δ = ε², for ε > 0

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Answer:

6

Step-by-step explanation:

3 divided by 1/2 = 6

2 hambugers = 1 pound

5

9x⁵=5

5y³=3

so 5>3=5

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\(\framebox{2$\dfrac{1}{6}$}\)

Divide the numerator by the denominator:

\(13\div6\)

\(=2\frac{1}{6}\\or\\2.16\)

If the coefficient matrix of a system of n equations and n variables has n−1 pivot columns, the matrix is not invertible.

The coefficient matrix of a system of n equations and n variables is invertible if and only if it has n pivot columns. In this case, the matrix has n−1 pivot columns, which means it is not a full-rank matrix.

When a matrix is not full-rank, it means that there exist linear dependencies among its columns, resulting in a non-trivial null space. Consequently, the system of equations described by this matrix has either infinitely many solutions or no solution at all.

To determine whether the system has a unique solution or not, we need to consider other factors such as the right-hand side of the equations or the consistency of the system. However, based solely on the information that the coefficient matrix has n−1 pivot columns, we can conclude that the matrix is not invertible.

In summary, if the coefficient matrix of a system of n equations and n variables has n−1 pivot columns, the matrix is not invertible.

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Let's solve your inequality step-by-step.

x+25>50

Step 1: Subtract 25 from both sides.

x+25−25>50−25

x>25

Answer:

x>25

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Answer:

$5.50

Step-by-step explanation:

10 - 4.50 = 5.50

2020 + N ≡ 0 (mod 11)

N ≡ -2020 (mod 11)

Notice that 2020 = 183 • 11 + 7, so

N ≡ -(183 • 11 + 7) (mod 11)

N ≡ -7 (mod 11)

N ≡ 4 (mod 11)

\(N=4\)

Step-by-step explanation:

Given :

Whole Number = N

Number = 2020 + N

Solution :

Now through observtion,

\(\dfrac{2020+N}{11}=184\)  ----- (1)

We took 184 because when we multiply 184 by 11 we get the nearest number to 2020

So from equation (1),

\(N=2024-2020\)

\(N=4\)

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The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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a. 0.4227

b. 0.0539

c. 0.3456

d. 0.2010

e. 0.2774

f. Mean = 2.9; Standard deviation = 1.7

The probability that the dog poops on her yard less than 3 times during a particular week can be calculated as follows:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

where X is the number of times the dog poops on her yard.

The probability that the dog poops on her yard zero times during a particular week can be calculated using the Poisson distribution:

P(X = 0) = e^(-2.9) = 0.0539

The probability that the dog poops on her yard once during a particular week can be calculated using the Poisson distribution:

P(X = 1) = 2.9e^(-2.9) = 0.1531

The probability that the dog poops on her yard twice during a particular week can be calculated using the Poisson distribution:

P(X = 2) = (2.9)^2e^(-2.9) = 0.3170

Plugging these values into the formula, we get:

P(X < 3) = 0.0539 + 0.1531 + 0.3170 = 0.5240

The probability that the dog poops on her yard zero times during a particular week can be calculated using the Poisson distribution:

P(X = 0) = e^(-2.9) = 0.0539

The probability that the dog poops on her yard 4 or 5 times during a particular week can be calculated using the Poisson distribution:

P(X = 4) = (2.9)^4e^(-2.9) = 0.1613

P(X = 5) = (2.9)^5e^(-2.9) = 0.0704

Plugging these values into the formula, we get:

P(X = 4 or 5) = 0.1613 + 0.0704 = 0.2317

The probability that the dog poops on her yard exactly 3 times during a particular week can be calculated using the Poisson distribution:

P(X = 3) = (2.9)^3e^(-2.9) = 0.2010

The probability that the dog poops on her yard 5 or more times during a particular week can be calculated by subtracting the probabilities that the dog poops on her yard 0, 1, 2, 3, and 4 times from 1:

P(X >= 5) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)

Plugging these values into the formula, we get:

P(X >= 5) = 1 - 0.0539 - 0.1531 - 0.3170 - 0.2010 - 0.1613 = 0.2774

The mean and standard deviation for the above Poisson Distribution can be calculated as follows:

Mean = np = 2.9

Standard deviation = sqrt(np) = sqrt(2.9) = 1.7

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Step-by-step explanation:

Step by Step Solution

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STEP

1

:

Equation at the end of step 1

(((7 • (x3)) + 2x2) - 21x) - 6

STEP

2

:

Equation at the end of step

2

:

((7x3 + 2x2) - 21x) - 6

STEP

3

:

Checking for a perfect cube

3.1 7x3+2x2-21x-6 is not a perfect