Find the gradient vector field of f. f(x,y,z) =(x^2+y^2+z^2)^1/2

A manufacturer A supplies 297 blankets with irregular workmanship, while Manufacturer B supplies 3500 blankets without irregularity.

Manufacturer A supplies a total of 3300 blankets, and 9% of them are irregular in workmanship. Therefore, the number of blankets with irregular workmanship from Manufacturer A is 3300 * 0.09 = 297. On the other hand, Manufacturer B supplies a total of 3500 blankets, and since there is no mention of irregular workmanship for their blankets, we can assume that all 3500 blankets are without irregularity.

To summarize, Manufacturer A supplies 3300 blankets, with 297 of them having irregular workmanship, while Manufacturer B supplies 3500 blankets, all of which are without irregularity. It is important for relief organizations to consider the quality of the blankets when distributing them to ensure the recipients receive blankets that meet the necessary standards.

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Using the substitution sec(u) = √(tan^2(u) + 1), the integral becomes:

(1/8) ∫ √(tan^2(u) + 1) du

To find the indefinite integral of arcsec(8x) dx, we can use integration by substitution.

Let u = 8x. Then, du = 8 dx, and dx = du/8.

Substituting these values into the integral, we have:

∫ arcsec(8x) dx = ∫ arcsec(u) (du/8)

Now, we need to express arcsec(u) in terms of its corresponding inverse trigonometric function, sec(u).

Recall the identity: sec^2(u) - 1 = tan^2(u)

Rearranging the equation, we get: sec^2(u) = tan^2(u) + 1

Taking the reciprocal of both sides, we have: 1/sec^2(u) = 1/(tan^2(u) + 1)

Simplifying further, we get: cos^2(u) = 1/(tan^2(u) + 1)

Taking the square root of both sides, we obtain: cos(u) = 1/√(tan^2(u) + 1)

Since sec(u) = 1/cos(u), we have: sec(u) = √(tan^2(u) + 1)

Now, substituting back into the integral, we have:

∫ arcsec(8x) dx = ∫ arcsec(u) (du/8)

                 = (1/8) ∫ arcsec(u) du

This integral can be further simplified using trigonometric identities and techniques. However, the solution involves elliptic integrals, which cannot be expressed in terms of elementary functions. Therefore, the indefinite integral of arcsec(8x) dx cannot be expressed using standard mathematical functions.

For the second question regarding the indefinite integral of 5x arcsin(x) dx, a similar process can be applied using integration by parts. However, it also leads to an expression involving elliptic integrals and cannot be expressed using elementary functions.

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Therefore, the image is formed at a distance of approximately 46.03 cm behind the mirror, and its height is approximately 2.98 cm.

We'll use the mirror formula and magnification to find the height of the image produced by the convex mirror.
1/f = 1/do + 1/di
do = object distance = 17 cm
f = focal length = -59 cm
Now, let's solve for the image distance (di):
1/-59 = 1/17 + 1/di
1/di = 1/-59 - 1/17
1/di ≈ -0.0217
di ≈ -46.03 cm
The magnification (M) is given by:
M = -di/do
M ≈ 46.03/17
M ≈ 2.71
Now, let's find the height of the image (hi):
hi = M * object height
hi = 2.71 * 1.1
hi ≈ 2.98 cm

Therefore, the image is formed at a distance of approximately 46.03 cm behind the mirror, and its height is approximately 2.98 cm.

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Answer:

Step-by-step explanation:

The null hypothesis (H0) would be: Less than or equal to 84% of the school graduates passed the TSI before the 12th grade.

The alternative hypothesis (H1) would be: More than 84% of the school graduates passed the TSI before the 12th grade.

Option A. The correct system of inequalities to determine the possible number of sweatshirts, s, and t-shirts, t, they would need to sell is:

In this system:

s ≥ 2 represents the fact that they expect to sell at least 2 sweatshirts.

t ≥ 10 represents the fact that they expect to sell more than 10 t-shirts.

25s + 10.5t ≥ 400 represents their goal of making at least $400 from selling sweatshirts at $25 each and t-shirts at $10.50 each.

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Complete questiom

Gabriela and her mother sell sweatshirts for $25 and tie dyed t-shirts for $10.50. They are positive more than 10 t-shirts and at least 2 sweatshirts will be sold this weekend. If they want to make at least $400, which system could be used to determine the possible number of sweatshirts, s, and t-shirts, t, they would need to sell?

s≥2

t≥ 10

25s + 10.5t ≥ 400

s22

t> 10

25s+10.5t ≥ 400

S>10

t≥2

10.5s + 25t≥ 400

s≥2

t> 10

10.5s+ 25t≥ 400

Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

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The triple integral becomes:

∫[θ=0 to 2π] ∫[φ=0 to π] ∫[ρ=0 to 1] ρ²sin(φ)[tex]e^{(\rho^2)^{(3/2)[/tex] dρdφdθ

The coordinate system primarily utilised in three-dimensional systems is spherical coordinates of the system, represented as (r,, ). The spherical coordinate system is used to determine the surface area in three dimensions.

To evaluate the triple integral using spherical coordinates, we need to express the integrand and the volume element in terms of spherical coordinates.

In spherical coordinates, we have the following relationships:

x = ρsin(φ)cos(θ)

y = ρsin(φ)sin(θ)

z = ρcos(φ)

The volume element in spherical coordinates is given by dV = ρ²sin(φ)dρdφdθ.

Now, let's express the given triple integral in terms of spherical coordinates:

∫∫∫U [tex]e^{(x^2+y^2+z^2)^{(3/2)[/tex] dV

U represents the solid unit sphere, which is defined by ρ ≤ 1.

The limits of integration for ρ are 0 to 1, since it represents the distance from the origin to a point on the sphere.

The limits of integration for φ are 0 to π, representing the polar angle from the positive z-axis to the point.

The limits of integration for θ are 0 to 2π, representing the azimuthal angle around the z-axis.

With these limits, the triple integral becomes:

∫[θ=0 to 2π] ∫[φ=0 to π] ∫[ρ=0 to 1] ρ²sin(φ)[tex]e^{(\rho^2)^{(3/2)[/tex] dρdφdθ

Now, you can evaluate the integral using these spherical coordinates and the given limits of integration.

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A construction of the line plot for the given data set is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would make use of an online graphing calculator (tool) to graphically represent the given data set on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 5 1/2 or 5.5 because it has the highest frequency of 3.

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Without seeing the algorithm, it is impossible to provide an answer.

The question states that there is a cumulative algorithm using an array and a range-based loop, but the actual algorithm is not provided. Therefore, without knowing what the algorithm is doing or what values are being used, it is impossible to determine what will be printed.

The question is incomplete as it does not provide the cumulative algorithm that is being referred to. Therefore, no answer can be provided without additional information.
That without the specific algorithm and code snippet, I am unable to determine what will be printed. For a proper explanation, please provide the cumulative algorithm using an array and a range-based loop that you mentioned.

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The Boolean expression that is not equivalent to the given expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

What is Boolean expression?

A Boolean expression is an expression or equation that evaluates to true or false. It includes the use of logical operators such as AND, OR, and NOT, as well as comparison operators such as equal to (=), greater than (>), less than (<), and more.

The Boolean expression that is not equivalent to the expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

Let's break down each option and evaluate its equivalence to the given expression:

A. (num < 0) AND (num * -1 = 10)

This expression checks if "num" is negative and if the absolute value of "num" is equal to 10. It does not directly represent the condition "num * -1 ≥ 10," so it is not equivalent.

B. (num < -10) OR (num = -10)

This expression checks if "num" is less than -10 or if "num" is exactly equal to -10. It also does not directly represent the condition "num * -1 ≥ 10," so it is not equivalent.

C. (num * -1 > 10) OR (num = -10)

This expression checks if the negative value of "num" is greater than 10 or if "num" is exactly equal to -10. Although it involves the negative value of "num," it represents the condition "num * -1 > 10" when "num" is positive. Therefore, it is equivalent to the given expression.

D. NOT num * -1 < 10

This expression checks if the negative value of "num" is not less than 10. While it involves the negative value of "num," it does not directly represent the condition "num * -1 ≥ 10." Additionally, the use of "NOT" operator flips the condition, which makes it different from the original expression. Hence, it is not equivalent.

Therefore, the Boolean expression that is not equivalent to the given expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

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The true statement is that 25% of the students are 16 years old. The Option C.

The lower quartile also known as first quartile is the value under which 25% of data points are found when they are arranged in increasing order

To determine correct statement, let's analyze the given information and the options as First quartile (Q1) represents the value below which 25% of the data falls.

In this case, Q1 is 16 years old.

This means that 25% of the students have an age of 16 or below. Therefore, the Statement C "25% of the students are 16 years old," is consistent with the given information.

Full question:

The 1st quartile of the ages of 250 fourth year students is 16 years old. which of the following statements is true?

A. most of the students are below 16 years old

B. 75% of the students are 16 years old and above

C. 25% of the students are 16 years old

D. 150 students are younger than 16 years.

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A recursive formula defines each term in relation to preceding terms, while an explicit formula directly calculates each term based on its position or index in the sequence.

We have,

A recursive formula for a sequence gives the nth term of the sequence as a function of one or more preceding terms in the sequence.

It defines the sequence recursively by expressing each term in terms of earlier terms in the sequence.

On the other hand,

An explicit formula for a sequence gives the nth term as a function of the term's position number or index.

It directly provides a formula or equation that can be used to calculate any term in the sequence without relying on previous terms.

Thus,

A recursive formula defines each term in relation to preceding terms, while an explicit formula directly calculates each term based on its position or index in the sequence.

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(a) The type of polar curve is a horizontal line.

(b) The polar equation that represents the graph is r = 1.

B. (a) The given polar curve is a horizontal line, which means it extends infinitely in the radial direction while maintaining a constant angle. It does not form any specific shape or pattern.

(b) The polar equation r = 1 represents a horizontal line in polar coordinates. In polar coordinates, the radial distance (r) from the origin is constant (in this case, 1) regardless of the angle (θ). This equation generates a line at a fixed distance from the origin, extending horizontally in both positive and negative x-directions.

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1. the distribution function of X is [tex]F_X(x)[/tex] = 1 - [tex]e^{-x[/tex] for x ≥ 0, and the distribution function of Y is [tex]F_Y(y)[/tex] = 1 for y ≥ 0.

2. The function F(x, y) is not the joint distribution function of any pair (X, Y) of random variables.

Let's analyze each case separately:

(a) F(x, y) = 1 - [tex]e^{-x - y[/tex] if x, y ≥ 0, and F(x, y) = 0 otherwise.

To determine if F is the joint distribution function of some pair (X, Y) of random variables, we need to check if F satisfies the properties of a distribution function:

1. Non-negativity: F(x, y) ≥ 0 for all (x, y).

2. Monotonicity: F(x, y) is non-decreasing in both x and y.

3. Right-continuity: F(x, y) is right-continuous in both x and y.

4. Marginal distribution: The marginal distribution functions, [tex]F_X(x)[/tex] and [tex]F_Y(y)[/tex], can be obtained by integrating F(x, y) over the respective variables.

In this case, the function F(x, y) satisfies the properties of a distribution function:

1. Non-negativity: F(x, y) = 1 - [tex]e^{-x - y[/tex] ≥ 0 for all x, y ≥ 0.

2. Monotonicity: The partial derivatives of F(x, y) with respect to x and y are non-negative for x, y ≥ 0, which implies that F(x, y) is non-decreasing in both x and y.

3. Right-continuity: The function F(x, y) is continuous for all x, y ≥ 0.

4. Marginal distribution: To find the marginal distribution functions, we can integrate F(x, y) over the respective variables.

Let's find the distribution functions of X and Y separately:

[tex]F_X(x)[/tex] = ∫[0 to ∞] F(x, y) dy

      = ∫[0 to ∞] (1 - [tex]e^{-x - y[/tex]) dy

      = [y - [tex]e^{-x - y[/tex]]|[0 to ∞]

      = ∞ - (0 - [tex]e^{-x - 0[/tex])

      = 1 - e[tex]e^{-x[/tex]

[tex]F_Y(y)[/tex] = ∫[0 to ∞] F(x, y) dx

      = ∫[0 to ∞] (1 - [tex]e^{-x - y[/tex]) dx

      = [x - [tex]e^{-x - y[/tex]]|[0 to ∞]

      = ∞ - (0 - [tex]e^{-\infty - y[/tex])

      = 1

Therefore, the distribution function of X is [tex]F_X(x)[/tex] = 1 - [tex]e^{-x[/tex] for x ≥ 0, and the distribution function of Y is [tex]F_Y(y)[/tex] = 1 for y ≥ 0.

(b) F(x, y) = 1 - [tex]e^{-x[/tex] = x [tex]e^{ - y[/tex] if 0 ≤ x ≤ y, and F(x, y) = 0 otherwise.

Let's analyze this case using the same criteria:

1. Non-negativity: F(x, y) = 1 - [tex]e^{-x[/tex] = x [tex]e^{- y[/tex] ≥ 0 for 0 ≤ x ≤ y.

2. Monotonicity: The partial derivatives of F(x, y) with respect to x and y are positive for 0 ≤ x ≤ y, indicating that F(x, y) is increasing in both x and y.

3. Right-continuity: F(x, y) is continuous for 0 ≤ x ≤ y.

4. Marginal distribution: We need to find the marginal distribution functions [tex]F_X(x)[/tex] and [tex]F_Y(y)[/tex] by integrating F(x, y) over the respective variables.

Let's find the distribution functions of X and Y separately:

[tex]F_X(x)[/tex] = ∫[x to ∞] F(x, y) dy

      = ∫[x to ∞] (1 - [tex]e^{-x[/tex]) dy

      = (y - [tex]e^{-x[/tex] y)|[x to ∞]

      = ∞ - (x - [tex]e^{-x[/tex] x)

      = 1 - x [tex]e^{-x[/tex] for x ≥ 0

[tex]F_Y(y)[/tex] = ∫[0 to y] F(x, y) dx

      = ∫[0 to y] (1 - [tex]e^{-x[/tex] y [tex]e^{- y[/tex]) dx

      = (x -[tex]e^{-x[/tex] x [tex]e^{- y[/tex])|[0 to y]

      = y -[tex]e^{- y[/tex] y [tex]e^{- y[/tex]

      = y(1 - [tex]e^{ - y[/tex]) for y ≥ 0

Therefore, the distribution function of X is F_X(x) = 1 - x [tex]e^{-x[/tex] for x ≥ 0, and the distribution function of Y is [tex]F_Y(y)[/tex] = y(1 - [tex]e^{- y[/tex]) for y ≥ 0.

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The lateral limits for the function f(x) are given as follows:

[tex]\lim_{x \rightarrow 0^{-}} = 1[/tex] and [tex]\lim_{x \rightarrow 0^{+}} = 0[/tex]

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

On the graph of a function, the limit of f(x) as x approaches a value of a is defined considering it's lateral limits, that is:

If the lateral limits are different, then the limit does not exist.

To the left of x = 0, the graph of the function approaches the value of y = 1, hence the limit is given as follows:

[tex]\lim_{x \rightarrow 0^{-}} = 1[/tex]

To the right of x = 0, the graph of the function approaches the value of y = 0, hence the limit is given as follows:

[tex]\lim_{x \rightarrow 0^{+}} = 0[/tex]

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The correct option is the second one "This system is inconsistent. This means the system has no solution."

When we have the graph of a system of equations, to find the solutions, we need to identify the points where the curves intercept.

Particularly, for a system of linear equations we can have some cases:

One intersection ---> One solution.

Infinite intersections ---> Infinite solutions (both lines are the same one)

No intersections ---> No solutions (case of parallel lines)

Here the lines are parallel, then the correct option is "This system is inconsistent. This means the system has no solution."

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a) This is the general expression for the z-value corresponding to X - 40

b) P(Z > z) = 1 - P(Z < z)

P(Z > z) = 1 - 0.1393

What is Standard Deviation?

Definitely! In statistics, standard deviation is a measure of the amount of variation or dispersion in a set of values. It quantifies how much individual data points differ from the mean (mean) of the data set.

(a) To compute the z-value corresponding to X - 40, we need to use the formula:

z = (X - μ) / σ

Substituting the given values, we have:

z = (X - (μ - 53)) / (σ - 12)

Since we want to find the z-value when X = 40, we substitute X = 40 into the equation:

z = (40 - (μ - 53)) / (σ - 12)

Note that we don't have specific values for μ and σ in this question, only the expressions μ - 53 and σ - 12. Therefore, we cannot calculate the exact z-value without knowing the actual values of μ and σ. We can, however, simplify the expression:

z = (40 - μ + 53) / (σ - 12)

z = (93 - μ) / (σ - 12)

This is the general expression for the z-value corresponding to X - 40.

(b) The area under the standard normal curve to the left of the z-value found in part (a) is given as 0.1393. This means:

P(Z < z) = 0.1393

To find the area to the right of this z-value, we subtract the given area from 1:

P(Z > z) = 1 - P(Z < z)

P(Z > z) = 1 - 0.1393

(c) The area under the normal curve to the right of X - 40 can be found using the z-value from part (a). However, since we don't have specific values for μ and σ, we cannot calculate the exact area. We can only calculate the area if we know the specific values for μ and σ.

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She would be able to fill only one spherical mold with a diameter of 5 cm.

To calculate the number of spherical molds with a diameter of 5 cm that Carmen can fill with the same amount of powder, we need to compare the volumes of the two different sizes of molds.

The formula for the volume of a sphere is given by:

V = (4/3) * π * r^3

where V is the volume and r is the radius of the sphere.

Let's calculate the volumes of the two different sizes of molds:

For the molds with a diameter of 4 cm:

- Radius (r) = diameter / 2 = 4 cm / 2 = 2 cm

- Volume (V1) = (4/3) * π * (2 cm)^3 ≈ 33.51 cubic centimeters

For the molds with a diameter of 5 cm:

- Radius (r) = diameter / 2 = 5 cm / 2 = 2.5 cm

- Volume (V2) = (4/3) * π * (2.5 cm)^3 ≈ 65.45 cubic centimeters

Now, let's calculate the number of molds with a diameter of 5 cm that can be filled with the same amount of powder:

Number of molds = V1 / V2 = 33.51 cubic centimeters / 65.45 cubic centimeters ≈ 0.512

Since we can't have a fraction of a mold, Carmen would be able to fill 0 molds with a diameter of 5 cm with the same amount of powder. In other words, she would not be able to fill any spherical molds with a diameter of 5 cm using the given amount of powder.

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The χ2 values for interval estimation for a sample size of 12 at 95% confidence level are approximately 21.920 and 2.179.

For the χ2 values for interval estimation at a 95% confidence level for a sample size of 12, we need to determine the critical values associated with the chi-square distribution.

The chi-square distribution is determined by two parameters: the degrees of freedom (df) and the confidence level.

For interval estimation, the degrees of freedom are equal to the sample size minus 1, which in this case is 12 - 1 = 11.

To find the critical values, we need to identify the chi-square values that leave a total probability of 0.05 (5%) in the tails of the distribution.

Since we are interested in a two-tailed interval estimation, we need to divide this probability equally between the two tails, resulting in 0.025 (2.5%) in each tail.

Using statistical tables or software, we can find the chi-square value associated with a 2.5% probability in the upper tail of the distribution with 11 degrees of freedom.

Similarly, we can find the chi-square value associated with a 2.5% probability in the lower tail.

For a sample size of 12 and a 95% confidence level, the critical chi-square values would be approximately:

Upper tail (2.5%): χ2 = 21.920

Lower tail (2.5%): χ2 = 2.179

Therefore, the χ2 values for interval estimation at a 95% confidence level with a sample size of 12 are approximately 21.920 and 2.179.

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The slope of the line in the given graph is 0.5

From the question, we are to calculate the slope of the line in the given graph

To calculate the slope, we will pick two points on the line shown in the graph

Picking the points (1, 1) and (3, 2).

Using the formula,

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (2 - 1) / (3 - 1)

Simplify the expression on the right side

Slope = 1 / 2

Slope = 0.5

Hence,

The slope of the line is 0.5

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The equation of the tangent line to the curve [tex]\(f(x) = \cos\left(\frac{2x}{\pi} - 1\right)\) at \(x = \frac{\pi}{2}\) is \(x = \frac{\pi}{2}\).[/tex]

What are Tangent lines?

Lines that touch a curve at a certain location and have the same slope as the curve are known as tangent lines. In other words, the slope or instantaneous rate of change of a curve at a specific point is represented by a tangent line to a curve. The curve near that point is approximated linearly by it. Calculus frequently makes use of tangent lines to analyze the behavior of functions and pinpoint crucial elements like derivatives, rates of change, and local linearity.

Let's find the equation of the tangent line to the curve [tex]\(f(x) = \cos\left(\frac{2x}{\pi} - 1\right)\) at \(x = \frac{\pi}{2}\).[/tex]

The equation of a tangent line to a curve can be written in the form [tex]\(y = mx + b\),[/tex] where [tex]\(m\)[/tex] is the slope of the tangent line and b is the y-intercept.

To find the slope of the tangent line, we take the derivative of [tex]\(f(x)\)[/tex] with respect to x:

[tex]\[f'(x) = -\frac{2}{\pi} \sin\left(\frac{2x}{\pi} - 1\right)\][/tex]

Substituting [tex]\(x = \frac{\pi}{2}\) into \(f'(x)\),[/tex] we have:

[tex]\[f'\left(\frac{\pi}{2}\right) = -\frac{2}{\pi} \sin\left(\frac{2}{\pi} \cdot \frac{\pi}{2} - 1\right) = -\frac{2}{\pi} \sin(0) = 0\][/tex]

Since the slope of the tangent line is 0, the equation of the tangent line is simply the vertical line [tex]\(x = \frac{\pi}{2}\).[/tex]

Therefore, the equation of the tangent line to the curve [tex]\(f(x) = \cos\left(\frac{2x}{\pi} - 1\right)\) at \(x = \frac{\pi}{2}\) is \(x = \frac{\pi}{2}\).[/tex]

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Answer:

1.=7

2.=1

3.=6

4.=3

5.=12

6.=9

7.=2

8.=11

9.=0

10.=10

11.=8

12.=4

where does seaweed look for a job:

Thekelpwantedsection

To find each dimensions from the square hole, we would need to subtract TWICE of the border width from its original dimensions of the matte board.

Give:

Side length of the matte board = 15 1/2 inches

Border width= 2/34

To find the dimensions of the square hole, We would need to subtract TWICE of the border width from the side length of the matte board.

Length of the Square hole = Length of the matte board - 2* Border width

Width of the Square hole = Width of the matte board - 2* Border width

Converting the mixed numbers to just improper fractions:

Side length of the matte board = 31/2 inches

Border width = 11/4 inches

Calculation of the dimensions of the Square hole:

Length of the square hole = 31/2 inches - 2*11/4 inches

Width of the square hole = 31/2 inches - 2*11/4 inches

The final steps from this is to Simplify the calculations we have.

Length of the square hole = 31/2 inches - 22/4 inches = (31/2) - (11/2) = 20/2 = 10 inches

Width of the square hole = 31/2 inches - 22/4 inches = (31/2) - (11/2) (20/2) = 10 inches

As a result, the dimensions that mr Hawk cuts  of the square hole would be 10 inches on each side.

The surface area of this triangular prism is 784 sq cm.

Let's find rectangular areas first.

16×24 + 10×16

Adding both areas of both rectangles

384+160

= 544 sq cm

Now lets find the side triangles.

Area of triangle =1/2×base×height

Remove 1/2 because you have 2 triangles, 1/2×2 = 1

24×10

= 240

Total surface area =240 sq cm + 544 sq cm

= 784 sq cm.

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A. 280 students chose lifting weights as their favorite exercise.

B. 70 more students chose lifting weights than walking.

Based on the given information, we can answer both Part A and Part B.

Part A:

To find the number of students who chose lifting weights, we need to calculate 20 percent of the total number of students surveyed (1,400).

Number of students choosing lifting weights = 20% of 1,400

= (20/100) * 1,400

= 0.2 * 1,400

= 280

Part B:

To determine how many more students chose lifting weights than walking, we need to calculate the difference between the percentages of students who chose lifting weights and walking, and then apply that difference to the total number of students surveyed (1,400).

Percentage difference between lifting weights and walking = 20% - 15%

= 5%

Number of students who chose lifting weights more than walking = 5% of 1,400

= (5/100) * 1,400

= 0.05 * 1,400

= 70

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Answer:

Step-by-step explanation:

(a) 2p - 3q + r

= 2(2i + 3j) - 3(i + j) + i - 2j

= 4i + 6j - 3i - 3j + i - 2j

= 2i + j.

(b) The vector in the opposite direction is -2i - j.

Its magnitde is √((-2i)^2 + (-j^2))

= √5.

So its unit vector is

-2i/√5 - j/√5.

(c) First find the dot prodct of the 2 vectors

This is 2*1 - 3*2

= -4.

Magnitde of 2i + 3j = √13

Magnitde of i - 2j = √5.

Angle between the vectors

= arcsin  (-4) / (√13*√5).

= -29.75

= 330 degrees to nearest degree.

Answer:

128 km

Step-by-step explanation:

Length

128

Kilometer

=

79.5355

[tex]V_{\text{water}}=V_{\text{aquarium}}-V_{\text{cube}}\\\\V_{\text{aquarium}}=10\text{ in}\cdot5 \text{ in}\cdot15\text{ in}=750\text{ in}^3\\\\V_{\text{cube}}=(3\text{ in})^3=27\text{ in}^3\\\\V_{\text{water}}=750\text{ in}^3-27\text{ in}^3=723\text{ in}^3[/tex]

Answer:

Step-by-step explanation:

−−−√2

We know that −a=−1.a

⟹−1.6−−−−√2

Apply ab−−√c=a−−√cb√c

−1−−−√26–√2

Remember that −1−−−√=i

i26–√2

Apply x−−√2=|x|

|6|i2=6i2

Use i2=−1

⟹−6