Question 3
Find the slope of each line in the graph. (HINT: Label your x1,y1,x2,y2
on the line). You must show the slope formula with numbers.
*
4-20
Slope of line a
b
20 pts
Slope of line b

The value of x in the inequality is x ≥ -26/3 and can be represented in interval notation as [-26/3, ∞)

An inequality is a relationship between two expressions or values that are not equal to each other. inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In the given problem, we have;

-4 ≥ -3(x + 10)

Open bracket

-4 ≥ -3x - 30

collect like terms

-4 ≥ -3x - 30

-4 + 30 ≥ - 3x

26 ≥ -3x

Divide both sides by the coefficient of x;

x ≥ -26/3

We can write this in interval notation as;

x = [-26/3, ∞)

Learn more on inequality here;

https://brainly.com/question/25275758

#SPJ1

The vertical shift between the Graph A and Graph B is of 3 Units.

The horizontal shift between the Graph A and graph B is 5 units.

Dilation is the transformation due to which the shape and the  orientation of the figure remains same but the size of the figure changes. It is simply the factor by which each linear measure of the figure is multiplied.

For the given graph f(x) = ║x║ the dilation factor is 2 since each linear measure is multiplied by 2 to get the graph.

The equation of the new function g(x) as represented in graph B is given as below

g(x) = 2║(x+5)║-3

#SPJ1

Using Appendix Table or t-distribution table, critical value of two-tailed and one-tailed ( right) test are [tex] t_{ 0.0025,20} = 3.4154[/tex], [tex] t_{ 0.0025,20} = 3.1534[/tex]. Similarly using the Excel technology, critical value of two-tailed and one-tailed ( right) test are [tex] t_{ 0.0025,20} = 3.4154[/tex], [tex] t_{ 0.0025,20} = 3.1534[/tex].

The main work is to determine the t-critical value using the t-distribution table for critical value. From the provide informations, we have to use Appendix Table 5 , present in attached figure and linear interpolation to approximate the critical value, here alpha level = 0.0025, and degree of freedom, df = 20

Using the Appendix Table, critical value for two tailed t-test, [tex] t_{ 0.0025,20} = 3.4154[/tex]

Similarly, for one tailed test ( right tailed),

[tex] t_{ 0.0025,20} = 3.1534[/tex]

For the Verification of approximation values obtained from table, we will using technology or Excel formula : For one-tailed test excel command or formula is written as [tex]= TINV(0.0025,20)[/tex] = 3.4154

Similarly, Excel formula for Two-tailed t-test, [tex]= TINV(2 (0.0025),20)[/tex]

= 3.1534

Hence, required value is 3.1534

For more information about critical values, visit :

https://brainly.com/question/14040224

#SPJ4

The type of sampling technique used by panorex is clustering

From the question, we have the following parameters that can be used in our computation:

Panorex, inc., numbers each city block, then randomly selected ten city blocks from the total.

The above statement means that the sampling technique used is the clustering selection technique

In this case, the ten city block represent the clusters of the whole population and all the city blocks represent the population

Read more about sampling technique at

https://brainly.com/question/11765786

#SPJ4

Rhetorical algebra has never really gone away, as evidenced by a 19th century school notebook that includes a rule for computing the area of a triangle using algebraic operations.


The quote highlights the fact that algebraic methods for solving problems have been around for centuries and continue to be used in modern mathematics. The rule provided demonstrates the use of algebraic operations such as addition, subtraction, multiplication, and the square root function to arrive at a solution for the area of a triangle. This underscores the enduring importance of algebra in mathematical problem-solving and the relevance of historical approaches to modern mathematical education.

The inclusion of a rule for computing the area of a triangle in a 19th century school notebook is evidence that rhetorical algebra has never really gone away. Rhetorical algebra refers to the use of words and symbols to express mathematical ideas and solve problems, and has been an important tool in mathematics for centuries.

The rule provided for computing the area of a triangle involves several algebraic operations, including addition, subtraction, multiplication, and the square root function. The process involves taking half the sum of the three sides of the triangle, subtracting each side severally, multiplying the half sum and the three remainders continually together, and taking the square root of the last product to arrive at the area of the triangle. This rule demonstrates the use of rhetorical algebra to solve a geometric problem, and underscores the enduring importance of algebra in mathematical problem-solving.

Furthermore, the inclusion of this rule in a 19th century school notebook highlights the relevance of historical approaches to modern mathematical education. While the specific methods used in rhetorical algebra may have evolved over time, the underlying principles and problem-solving strategies remain relevant to this day. As such, the study of rhetorical algebra can provide valuable insights into the development of mathematical thought and the historical context in which mathematical ideas have been developed and applied.

In conclusion, the inclusion of a rule for computing the area of a triangle in a 19th century school notebook serves as a reminder of the enduring importance of rhetorical algebra in mathematical problem-solving. This example highlights the use of algebraic operations such as addition, subtraction, multiplication, and the square root function to arrive at a solution for a geometric problem, and underscores the relevance of historical approaches to modern mathematical education.

To know more about algebra  visit:

brainly.com/question/24875240

#SPJ11

The common ratio of the geometric sequence 17, -136, 1088, ... is -8.

Let's first write the given sequence: 17, -136, 1088, ... as an explicit formula. We can do this by using the formula for the nth term of a geometric sequence:

aₙ = a₁ * rⁿ⁻¹

where aₙ is the nth term of the sequence, a₁ is the first term, r is the common ratio, and n is the position of the term in the sequence.

Using this formula, we can find the first three terms of the sequence:

a₁ = 17

a₂ = -136

a₃ = 1088

Plugging these values into the formula, we get:

17 = 17 * r¹⁻¹ = 17 * r⁰ = 17

-136 = 17 * r²⁻¹ = 17 * r

1088 = 17 * r³⁻¹ = 17 * r²

We can simplify the second and third equations by dividing both sides by 17:

-136/17 = r

1088/17 = r²

Simplifying further, we get:

r = -8

r² = 64

Since r² = 64, we know that r = +/- 8. However, we need to choose the negative value of r, -8, because it is the common ratio that produces the sequence 17, -136, 1088, ...

To know more about geometric sequence here

https://brainly.com/question/13008517

#SPJ1

Answer:

Step-by-step explanation:

There are 6 possibilities for each roll: 1, 2, 3, 4, 5 and 6. Each of these has a probability of 1/6.

If you roll the die 30 times, the probability of getting a 6 would be 30 x (1/6) = 5. The answer is 5.

Answer:There are 6 numbers on a die.

The probability of rolling a 6 would be 1/6 for each time you roll the die.

Multiply the number of rolls by 1/6.

30 rolls x 1/6 probability = 5 times.

Step-by-step explanation:

There are a total of 8 microstates possible for a system of 3 particles distributed between 2 boxes.

In a system with 3 particles distributed between 2 boxes, the number of microstates can be determined using combinatorics. There are a few possible arrangements for the particles:

1. All 3 particles in Box 1, and none in Box 2.
2. Two particles in Box 1, and one in Box 2.
3. One particle in Box 1, and two in Box 2.
4. No particles in Box 1, and all 3 in Box 2.

To find the total number of microstates, we calculate the combinations for each arrangement:

1. C(3,3) = 1
2. C(3,2) = 3
3. C(3,1) = 3
4. C(3,0) = 1
To learn more about : microstates

https://brainly.com/question/16693606

#SPJ11

Answer:

When reflecting a point or line segment across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. In this case, we are given the points A (2,5) and B (-3,6) and asked to find their reflections in the x-axis, represented by the points A’ and B’.To reflect point A across the x-axis, we simply change the sign of the y-coordinate while keeping the x-coordinate the same. So, if A is (2,5), its reflection A’ is (2,-5). We can follow the same procedure for point B. If B is (-3,6), its reflection B’ is (-3,-6).From this calculation, we see that answer choice A is the correct one. Therefore, A’(2,-5) and B’(-3,6) represent the points that are the reflections of A and B, respectively, across the x-axis.The reflection of a point across the x-axis can also be visualized as the point being mirrored across the x-axis as if it were a horizontal mirror. In this case, point A is reflected to the point A’ which is the same distance above the x-axis as A is below the x-axis. Similarly, point B is reflected to point B’ which is the same distance below the x-axis as B is above the x-axis.It’s also worth noting that reflecting a point or line segment across the x-axis is an example of a transformation in coordinate geometry. Translations, reflections, rotations, and dilations are all examples of transformations that can be used to manipulate geometric figures on the coordinate plane.Overall, reflecting a point or line segment across the x-axis is a relatively simple calculation that involves negating the y-coordinate. In the context of coordinate geometry, it’s important to understand the basic transformations like these and how they can be used to manipulate shapes and figures on the coordinate plane.

Step-by-step explanation:

i. The probability of exactly 4 students answering yes is 0.1309

ii. The probability of exactly 2 students answering no is 0.3244

iii. The probability of three or fewer students answering yes is 0.6618

iv. The probability of at least 4 students answering yes is 0.0043

The probabilities are determined using the binomial probability formula.

The probability of answering yes is 0.3182, and the probability of answering no is 0.6812.

Therefore, p = 0.3182 and (1-p) = 0.6812.

5 students are randomly from the class, hence n = 5.

i. The probability of exactly 4 students answering yes will be:

P(X=4) = ⁵C₄ * 0.3182⁴ * 0.6812¹

P(X=4) = 0.1309

ii. The probability of exactly 2 students answering no will be:

P(X=2) = ⁵C₂ * 0.6812² * 0.3182³

P(X=2) = 0.3244

iii. The probability of three or fewer students answering yes would be the sum probabilities of 0, 1, 2, or 3 students answering yes:

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

P(X<=3)  = (⁵C₀ * 0.3182⁰ * 0.6812⁵) + (⁵C₁ * 0.3182¹ * 0.6812⁴) +

(⁵C₂ * 0.3182² * 0.6812³) + (⁵C₃ * 0.3182³ * 0.6812²)

P(X<=3)  = 0.6618

iv. The probability of at least 4 students answering yes;

P(X>=4) = P(X=4) + P(X=5)

P(X>=4) = ⁵C₄ * 0.3182⁴ * 0.6812¹ + ⁵C⁵ * 0.3182⁵ * 0.6812⁰

P(X>=4) = 0.0042 + 0.0001

P(X>=4) = 0.0043

Learn more about probabilities at: https://brainly.com/question/25870256

#SPJ1

A variable that cannot be measured in numerical terms is called a qualitative variable. Qualitative variables, also known as categorical variables, are used to describe characteristics or attributes of a population or a sample.

They are typically divided into nominal variables, which do not have a natural order, and ordinal variables, which have a natural order.

Qualitative variables are often used in surveys, polls, and experiments to gather information about people's opinions, preferences, and behaviors. Examples of qualitative variables include gender, race, religion, political affiliation, and educational level. These variables are important in many fields, including sociology, psychology, marketing, and political science. Qualitative data can be analyzed using various statistical techniques, including contingency tables, chi-square tests, and logistic regression.

In summary, qualitative variables are variables that cannot be measured in numerical terms and are used to describe characteristics or attributes of a population or a sample. They are important in many fields and can be analyzed using various statistical techniques.

To learn more categorical variable, click here:

brainly.com/question/24244518

#SPJ11

The Solution of the expression  9+(7+14) is 30.

Now, let's look at the given addition sentence: (9+7)+14=30. This sentence tells us that if we add 9 and 7 first, and then add 14 to that result, we get a total of 30.

To create an equivalent addition sentence that illustrates the associative property of addition, we need to regroup the numbers and the parentheses.

We can do this by adding 7 and 14 first, and then adding 9 to that result, like this: 9+(7+14)=30.

To know more about expression here

https://brainly.com/question/14083225

#SPJ1

The Taylor polynomials T2 and T3 centered at a=0 for the function f(x) = 16 tan(x) are:

T2(x) = 16x + 16x^2

T3(x) = 16x + 16x^2 + (16/3) x^3

The first few derivatives of the function f(x) = 16 tan(x) are:

f(x) = 16 tan(x)

f'(x) = 16 sec^2(x)

f''(x) = 32 sec^2(x) tan(x)

f'''(x) = 32 sec^4(x) + 96 sec^2(x) tan^2(x)

Using these derivatives, we can calculate the Taylor polynomials T2 and T3 centered at a=0 as follows:

T2(x) = f(0) + f'(0)x + (1/2!) f''(0)x^2

= 0 + 16x + (1/2!) (32) x^2

= 16x + 16x^2

T3(x) = f(0) + f'(0)x + (1/2!) f''(0)x^2 + (1/3!) f'''(0)x^3

= 0 + 16x + (1/2!) (32) x^2 + (1/3!) (32 + 96*0) x^3

= 16x + 16x^2 + (16/3) x^3

Therefore, the Taylor polynomials T2 and T3 centered at a=0 are:

T2(x) = 16x + 16x^2

T3(x) = 16x + 16x^2 + (16/3) x^3

To learn more about Taylor polynomials visit : https://brainly.com/question/2533683

#SPJ11

Answer:

➢ Calculating Area of Sector :-

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ \theta \: }{360 \degree \: } \times \pi \: {r}^{2} \\ [/tex]

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 80 \: }{360 \degree \: } \times \frac{22}{7} \times\: {5}^{2} \\ [/tex]

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 8 \: }{36 \degree \: } \times \frac{22}{7} \times \: 5 \times 5 \\ [/tex]

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 8 \: }{36 \degree \: } \times \frac{22}{7} \times\: 25 \\ [/tex]

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 4 \: }{18 \degree \: } \times \frac{22}{7} \times \: 25 \\ [/tex]

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 2\: }{9 \degree \: } \times \frac{22}{7} \: \times 25 \\ [/tex]

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 2 \times 22 \times 25\: }{9 \times 7 \: } \\ [/tex]

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 44 \times 25\: }{9 \times 7 \: } \\ [/tex]

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 1100\: }{63 \: } \\ [/tex]

[tex] \sf \longrightarrow \: Area \: of \: Sector \: = 17.5 \: \: {m}^{2} \\ [/tex]

____________________________

Option D :- 17.5 m²

The interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.

The answer to this question is option D, which is μ - σ to Q3. To understand why this is the correct answer, we need to first understand what each of the intervals represents. Q1 and Q3 are the first and third quartiles of the data set, respectively. μ is the mean of the data set, and σ is the standard deviation.

When we look at the interval μ - σ to Q3, we can see that it includes the upper quartile and some of the data points to the left of it. This means that the area under the normal curve within this interval will be relatively small compared to the other options.

On the other hand, option B includes the mean and a larger range of data points, which would result in a larger area under the curve. Option C includes Q1 and a larger range of data points, which would also result in a larger area. Option A includes both Q1 and Q3, which cover the majority of the data set and would therefore have the largest area under the curve.

In summary, the interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.
Visit here to learn more about normal curve:

brainly.com/question/31391220

#SPJ11

The terms "cross-sectional study" and "time-series study" refer to different types of research designs. A cross-sectional study collects data from a population at a specific point in time, whereas a time-series study collects data from the same population over an extended period.

Based on this definition, it is difficult to classify a graph as either a cross-sectional or time-series study without additional context.

A graph alone does not provide enough information about the research design. It would be best to refer to the accompanying study or research report to determine the type of study represented by the graph.
Therefore, the long answer to your question is that a graph cannot be classified as a cross-sectional or time-series study without further information about the research design.

Know more about the cross-sectional study here:

https://brainly.com/question/30552943

#SPJ11

No, your friend is not entirely correct. It is indeed possible for two of the three equations in a linear system in three variables to have no points in common.

However, this does not necessarily mean that the entire system has no solution.

Consider a simple example of a linear system in three variables with two equations:

2x + 3y - z = 7

4x - y + 2z = -1

These two equations may not have any points in common. For instance, the first equation represents a plane in three-dimensional space, and the second equation represents a different plane. It is possible that these two planes do not intersect at any point.

However, this does not mean that the entire system has no solution. There may be a third equation that intersects both of these planes at a single point, resulting in a consistent system with a unique solution.

Therefore, it is important to consider all of the equations in the linear system and not just focus on the intersections of pairs of equations.

Learn more about linear system at: brainly.com/question/26544018

#SPJ11

The mode salary of a major league baseball player being $600,000 means that more major league baseball players earn $600,000 than any other salary. In this context, "mode" represents the most frequently occurring value in a data-set, which, in this case, is the salaries of major league baseball players.

The correct answer to this question is (a) more major league baseball players earn $600,000 than any other salary. The mode is the value that appears most frequently in a dataset, and in this case, it means that $600,000 is the most common salary among major league baseball players. This doesn't necessarily mean that it's the middle salary or the average salary, as those would be the median and mean respectively. It also doesn't mean that no player makes less than $600,000, as there may be some players who earn less than this amount. Therefore, the correct answer is (a), which is the only option that accurately reflects what the mode represents in this context.

To know more about data-set visit:

https://brainly.com/question/22210584

#SPJ11

Maclaurin series is a Taylor series expansion of a function at x=0, obtained by expressing the function as an infinite sum of terms involving the function's derivatives at 0, multiplied by powers of x.

To find the value of f(3), we need to substitute x=3 into the Maclaurin series formula for the function f:

f(x) = ∑n=0^(infinity) (−4x)^n

Now, we substitute x=3 into the formula:

f(3) = ∑n=0^(infinity) (−4*3)^n

The series is a geometric series with first term a=1 (when n=0, (−4*3)^0 = 1) and common ratio r = -12 (−4*3). To find the sum of an infinite geometric series, we use the formula:

Sum = a / (1 - r)

In this case:

Sum = 1 / (1 - (-12))

Sum = 1 / (1 + 12)

Sum = 1 / 13

So, the value of f(3) is:

f(3) = 1/13

This answer is not among the options provided (A, B, C, D, E). It's possible there is an error in the question or the given answer choices. However, the calculated value of f(3) is 1/13 based on the provided Maclaurin series formula.

To know more about Maclaurin series visit:

https://brainly.com/question/31745715

#SPJ11

The possible lengths for the widths of the machine parts is w = 3.63 inches and w = 3.55 inches

Given data ,

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Now , width of a machine part is designed to be 3.59 inches

And , manufacturing tolerance is within 0.04 inches

So , the possible widths of the machine be w

where w = 3.59 ± 0.04

On simplifying , we get

w = 3.63 inches and w = 3.55 inches

Hence , the percentage error is solved

To learn more about percentage error click :

https://brainly.com/question/28746643

#SPJ1

The probability of event (A or B) is also 2/3.

We have,

P(A) = 12 / 24

P(B) = 20 / 24

P(A and B) = 16 / 24

P(U) = 24

Using, P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 12/24 + 20/24 - 16/24

P(A or B) = 32/24 - 16/24

P(A or B) = 16/24

P(A or B) = 2/3

Thus, the required probability is 2/3.

Learn more about Probability here:

brainly.com/question/11234923

#SPJ1

Answer: 0.66

Step-by-step explanation: the answer is 2/3. The decimal version of 2/3 is 0.66 ( it is the correct answer on Acellus.)

The cost of the backpack is $34.82 and the tax is 9.25%.

To find the final cost, we need to add the cost of the backpack and the tax.

First, we can calculate the amount of tax by multiplying the cost of the backpack by the tax rate:

Tax = $34.82 x 0.0925 = $3.22 (rounded to two decimal places)

Next, we can add the cost of the backpack and the tax to get the final cost:

Final cost = Cost of backpack + Tax = $34.82 + $3.22 = $38.04

Therefore, the final cost of the backpack, including tax, is $38.04.

Learn more about tax here

https://brainly.com/question/30157668

#SPJ11

The directional derivative at (1,1) in the direction i j is -1.

To find the directional derivative at (1,1) in the direction i j, we need to find the unit vector in the direction of i j, which is simply:
u = (1/√2)i + (1/√2)j

Then, the directional derivative is given by:
D_u f(1,1) = ∇f(1,1) · u
where ∇f is the gradient of f.

To find ∇f, we need to compute the partial derivatives of f with respect to x and y, which we are given as:
fx(1,1) = 2 − 2 √ 2
fy(1,1) = −2

So, we have:
∇f(1,1) = (2 − 2 √ 2)i − 2j

Substituting this into the formula for the directional derivative, we get:
D_u f(1,1) = (2 − 2 √ 2)i − 2j · ((1/√2)i + (1/√2)j)
= (2 − 2 √ 2)(1/√2) − 2(1/√2)
= √2 − √2 − 1
= -1

Therefore, the directional derivative at (1,1) in the direction i j is -1.

To learn more about directional derivative visit : https://brainly.com/question/30048535

#SPJ11

Answer:

part 1: white blood cells

part 2: C=3h(6)

Step-by-step explanation:

have a nice day.

A finite group is a group that has a finite number of elements. Now, let us define the center of a group. The center of a group, denoted by Z(G), is the set of all elements in G that commute with every element in G.

Now, we need to prove that if g is a finite group, the index of Z(g) cannot be prime. We can prove this using contradiction. Suppose the index of Z(g) is prime. Let this prime be denoted by p. This means that the number of distinct left cosets of Z(g) in g is p. Therefore, we can write:

|g/Z(g)| = p

where |g/Z(g)| represents the number of distinct left cosets of Z(g) in g.

Now, we can use the fact that the number of left cosets of a subgroup in a group is equal to the index of that subgroup in the group. Therefore, we can rewrite the above equation as:

|g|/|Z(g)| = p

Multiplying both sides by |Z(g)|, we get:

|g| = p|Z(g)|

Since p is a prime number, it can only be divided by 1 and itself. Therefore, the only possible divisors of p|Z(g)| are 1, p, and |Z(g)|.

Now, since |g| is finite, we know that |Z(g)| cannot be infinite. Therefore, the only possible values for |Z(g)| are positive integers that divide |g|. However, since p is a prime number, |Z(g)| cannot be equal to p. This means that the only possible values for |Z(g)| are 1 and |g|.

If |Z(g)| = 1, this means that Z(g) only contains the identity element. Therefore, g does not have any non-identity elements that commute with every other element in g. This is not possible since every group has at least one element that commutes with every other element in the group - the identity element.

If |Z(g)| = |g|, this means that every element in g commutes with every other element in g. This implies that g is an abelian group. However, this contradicts the fact that g is a finite group that is not abelian.

Therefore, we have reached a contradiction in both cases. This means that our assumption that the index of Z(g) is prime is false. Therefore, if g is a finite group, the index of Z(g) cannot be prime.

Learn more about  finite group here:

https://brainly.com/question/29732670

#SPJ11

If a 10 percent cut in price causes a 15 percent increase in sales, then it is likely that the product has an elastic demand. This means that customers are highly responsive to changes in price and are willing to purchase more of the product when it is cheaper.

In this scenario, the decrease in revenue from the price cut may be offset by the increase in sales volume. However, it is important to consider the potential long-term effects on the product's brand value and profitability.

If a 10 percent cut in price causes a 15 percent increase in sales, then:

1. Calculate the new price after the 10 percent cut:
New price = Original price x (1 - 0.10)

2. Calculate the new quantity sold after the 15 percent increase in sales:
New quantity sold = Original quantity sold x (1 + 0.15)

In this scenario, the price elasticity of demand is greater than 1, indicating that the product has elastic demand. This means that a decrease in price will result in a proportionally larger increase in quantity demanded, leading to higher revenue for the seller.

Learn more about elastic demand at: brainly.com/question/30465432

The surface area of the pool float rubber ducky will be 2688 [tex]cm^2[/tex], and the volume of the pool float rubber ducky will be 1990656 [tex]cm^3.[/tex]

Since the bath time rubber ducky and the pool float rubber ducky are similar figures, their corresponding side lengths are proportional.

If we multiply all the dimensions of the bath time rubber ducky by 16, we will get the corresponding dimensions of the pool float rubber ducky.

Let's denote the dimensions of the bath time rubber ducky as x, y, and z, where x, y, and z are the length, width, and height, respectively. Then, the dimensions of the pool float rubber ducky will be 16x, 16y, and 16z.

The surface area of the bath time rubber ducky is:

2xy + 2xz + 2yz = 84

The volume of the bath time rubber ducky is:

xyz = 486

If we multiply all the dimensions of the bath time rubber ducky by 16, the surface area of the pool float rubber ducky will be:

2(16xy) + 2(16xz) + 2(16yz) = 2(16)(2xy + 2xz + 2yz)

                                          = 2(16)(84)

                                         = 2688

The volume of the pool float rubber ducky will be:

(16x)(16y)(16z) = 4096xyz

                      = 1990656

Therefore, the surface area of the pool float rubber ducky will be 2688 [tex]cm^2[/tex], and the volume of the pool float rubber ducky will be 1990656 [tex]cm^3.[/tex]

Learn more about Surface area at

brainly.com/question/29298005

#SPJ1

Ms. Aguilera spent $502.40 on the fencing.

The perimeter of a circle can be calculated using the formula P = πd, where P is the perimeter,

d is the diameter,

and π (pi) is a mathematical constant approximately equal to 3.14.

In this case, the diameter of the pool is 20 meters, so the radius (r) is 10 meters. The perimeter of the pool is:

P = πd

  = π(20m)

  ≈ 62.8m

To fence around the edge of the pool, Ms. Aguilera needs to purchase 62.8 meters of fencing.

The cost of the fencing is $8 per meter, so the total cost of the fencing is:

Total cost = 62.8m x $8/m

                = $502.40

Therefore, Ms. Aguilera spent $502.40 on the fencing.

Learn more about Perimeter at

brainly.com/question/6465134

#SPJ1

To verify that the vector xp is a particular solution of the given nonhomogeneous linear system, we need to substitute xp into the system and check if it satisfies the equation.

The given nonhomogeneous linear system can be written in the form x' = Ax + f, where A is the coefficient matrix (2 1 1 -1) and f is the constant vector (-5 2). The vector xp = (1 3) is a particular solution if it satisfies the equation x' = Ax + f.

Substituting xp into the equation, we get:

x' = (2 1 1 -1) (1 3) + (-5 2)
  = (1 -1 2 -8)

Therefore, the left-hand side of the equation is:

x' = (1 -1 2 -8)

And the right-hand side is:

Ax + f = (2 1 1 -1) (1 3) + (-5 2)
       = (1 -1 2 -8)

Since the left-hand side is equal to the right-hand side, we can conclude that the vector xp = (1 3) is indeed a particular solution of the given nonhomogeneous linear system.

We have verified that the vector xp = (1 3) is a particular solution of the given nonhomogeneous linear system by substituting it into the equation and checking if it satisfies the equation.

To know more about linear system, visit:

https://brainly.com/question/21404414

#SPJ11

The number of distinct sequences of four letters is 240

From the question, we have the following parameters that can be used in our computation:

Word = EQUALS

The above word has 6 letters

If it must begin with L and end with Q, then there are 4 letters remaining

These letters can be arrranged in the following number of ways

4! = 24

Next, we take L and Q as one

So, we have 5 letters i.e. EUAS(LQ)

These letters can be arranged in the following number of ways

5C2 = 5!/(3! * 2!) = 10

So, we have

Total = 24 * 10

Evaluate

Total = 240

Hence, the total number of distance sequences is 240

Read more about combination at

https://brainly.com/question/11732255

#SPJ4