How do I do part 2 and 3?? Please show all steps of working. I have no clue how to do this!

The fourth root of -81 is not a real number is 3√i.

A number that can be represented in the form a + bi is an imaginary number. In this case, a and b are real numbers, while I is the imaginary unit, which is equal to the square root of -1. In mathematics, imaginary numbers are used to expand on the real number system and to describe values that cannot be stated using real numbers.

Complex numbers, which are numbers of the type a + bi, where a and b are real numbers, are one of the principal applications for imaginary numbers. Several mathematical and scientific disciplines, such as electrical engineering, signal processing, and quantum physics, require complex numbers.

The value of -81 can be written as i²(3)⁴.

Taking the fourth root of the number we get 3√.

Hence, the fourth root of -81 is not a real number is 3√i.

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Step-by-step explanation:

Two ends' area = 2 * pi r^2       r is radius = 1/2 diameter = 4m

                            2 * 3.14 * (4^2) = 100.48 m^2

Sidewall is   cicumfernce ( = pi *d)  times the height ( =7m)

      3.14 * 8 *7=175.84 m^2

Cost = (100.48 +175.84) m^2   *   $ 29 /m^2 = $ 8013.28

The correct option is B. 5/14, which is equivalent to approximately 0.357 or 35.7%

The probability of selecting a chocolate ice cream bucket is calculated by dividing the number of chocolate ice cream buckets by the total number of buckets:

P(chocolate) = number of chocolate ice cream buckets / total number of buckets

P(chocolate) = 5 / 14

P(chocolate) = 0.35714285714285715

To simplify the fraction, we can express it as a decimal or a percentage:

P(chocolate) ≈ 0.357 or P(chocolate) ≈ 35.7%

Therefore, the probability of selecting a chocolate ice cream bucket is approximately 0.357 or 35.7%. The probability of selecting a chocolate ice cream bucket can be calculated by dividing the number of chocolate ice cream buckets by the total number of buckets. The number of chocolate ice cream buckets is 5, and the total number of buckets is 14. Therefore, the probability of selecting a chocolate ice cream bucket is: 5/14

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14 because 14+28=42.

The surface area of the prism from the net is 260.5 cm².

The rectangular prism has dimensions of length, width, and height given by 5 and three-fourths cm, 4 cm, and 11 and three-fourths cm respectively.

To find the surface area of the prism, we need to find the area of each of its six faces and then add them up.

So, we have

Area = 2 * (5 3/4 * 4 + 5 3/4 * 11 + 4 * 11)

Evaluate

Area = 260.5

Therefore, the surface area of the prism is 260.5 cm².

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As a result, the company produced number of rods are **56** rods.

What exactly is radius?

A radius is a section of a straight line in geometry that connects a circle's or sphere's center to its edge or surface Its length is divided by the circle's diameter by two.

Each rod has a diameter of 6 centimeters, hence the radius is 3 centimeters. Each rod has a 20-centimeter height.

The following formula can be used to determine a cylinder's volume:

V = πr²h

where V stands for volume, r for radius, which is equal to half of the diameter, and h for height.

Adding these values to the formula yields the following results:

V = π(3)²(20) (20)

V = 180π

The volume of each rod is therefore 180 cubic centimeters.

30520.8 cubic centimeters of steel were used to make how many rods?

To find out,

divide the total volume of steel by the volume of each rod:

30520.8 / (180π) ≈ **56** rods

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The required balance of Hall's account after 11 years is [tex]$A = 2145.1$[/tex].

The formula to calculate compound interest is:

[tex]$A = P(1 + \frac{r}{n})^{nt}$[/tex]

Where:

A = Final amount

P = Principal amount

r = Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Time (in years)

Here, P = 920, r = 0.08, n = 1 (compounded annually), and t = 11 years.

Plugging in the values:

[tex]$A = 920(1 + \frac{0.08}{1})^{1\times 11}$[/tex]

[tex]$A = 920(1.08)^{11}$[/tex]

[tex]$A = 2145.1$[/tex]

Therefore, the balance of Hall's account after 11 years is [tex]$A = 2145.1$[/tex].

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Answer:

A 1x3 matrix only has one entry, so there is only one minor, which is the determinant of the matrix itself.

For example, if A = [a, b, c], then the minor of A is simply:

|A| = det(A) = a

Since the determinant of a 1x1 matrix is just its single entry.

Step-by-step explanation:

Answer: The length of the prism is 8 yards

Step-by-step explanation:

First, take the volume of the prism, divide it by the width (2 1/2). Once you get that divide that answer by height (5 3/4) getting you the length of the prism (8 yards)

Answer:

1. pyramid

2. cylinder

3. sphere

4. cone

5. cube

6. rectangular prism

7. pyramid

8. sphere

9. cylinder

10. pyramid

11. cube

12. cube

13. cone

14. cylinder

15. sphere

16. cylinder

Step-by-step explanation:

Compare each one to the sample diagrams shown on the top of the paper.

(D) |k - 7| < - 6 has no solution is not a true statement because an absolute value can never be negative, so the inequality has no solution.

Inequality refers to the state of being unequal or not equal in some respect. It can refer to various forms of disparities or differences, such as differences in income, wealth, education, opportunities, health, or social status, among others. Inequality can occur between individuals, groups, communities, or nations, and it can be caused by various factors, such as discrimination, historical legacies, social structures, policies, or economic systems. Inequality is often considered a social problem because it can lead to social tension, unrest, and injustice, as well as undermine economic growth and human development.

(D) |k - 7| < - 6 has no solution is not a true statement because an absolute value can never be negative, so the inequality has no solution.

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The solution for the equation √(x-1) = x - 13 is x = 17, the correct option is C.

We have the following equation.

√(x-1) = x - 13

If we apply the square exponent in both sides, we will get:

x - 1 = (x - 13)²

x - 1 = x² - 26x + 169

x² - 27x  + 170 = 0

Using the quadratic formula we get:

[tex]x = \frac{27 pm \sqrt{(-27)^2 - 4*170*1} }{2} \\\\x = \frac{27 pm 7}{2}[/tex]

We only care for the positive solution, which is:

x = (27 + 7)/2 = 17

The correct option is C.

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The solution to the given equation is 14 by squaring both sides of the equation and simplifying. Therefore, the solution to the equation is option A.

To solve the equation √x-1=x-13, we first square both sides to eliminate the square root.

That results in the equation x - 2*x +1 = x - 13. Simplify this to get -x + 14 = 0. Further simplifying, x = 14 is the solution. Therefore, the solution to the equation is 14 (option A).

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Answer:

B is greater than A by 1/4 of A

Step-by-step explanation:

Let's use the information given in the problem to write expressions for the values of a and b:

a = b - (1/5)b = (4/5)b

b is greater than a by the difference:

b - a = b - (4/5)b = (1/5)b

To express this difference as a fraction of a, we divide by a:

(b - a)/a = ((1/5)b)/((4/5)b) = 1/4

Therefore, b is greater than a by 1/4 of a.

The height of the cliff diver after 1.25 seconds is 35 feet.  

The concept used is evaluating a function at a given input or value. In this case, we are evaluating the height function H(t) at t = 1.25 to find the height of the cliff diver after 1.25 seconds. The formula for the height function is given as H(t) = -16t^2 + 32t + 20.

Here we have

A cliff diver's height (in feet) after t seconds is given by the model

H(t)=-16t² +32t +20  

Given time t = 1.25 seconds

To find the height after 1.25 seconds, we simply need to evaluate H(1.25) using the given formula:

H(1.25) = -16(1.25)² + 32(1.25) + 20

On Simplifying the expression we get:

H(1.25) = -16(1.5625) + 40 + 20

H(1.25) = -25 + 60

H(1.25) = 35

Therefore,

The height of the cliff diver after 1.25 seconds is 35 feet.  

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After plotting the points A (-5, -2), B (-3, -2), and D (-5, -4) in the 4th quadrant as shown in the attached graph, we can see that to make the square we have to plot point C, at (-3, -4).

Simply said, the graph is a structured representation of the data. Because of this, it is simpler for us to understand the facts. Data is the term used to describe the numerical information obtained through observation.

The word data is derived from the Latin word datum, which meaning "something delivered."

After developing a research question, data are progressively obtained through observation. The information is then organised, categorised, and visually shown.

Here in the question,

After plotting the points A (-5, -2), B (-3, -2), and D (-5, -4) in the 4th quadrant as shown in the attached graph, we can see that to make the square we have to plot point C, at (-3, -4).

And the coordinate rule that will rotate the rectangle to the fourth quadrant, with vertex C’ at point (4, -3) is known as reflection.

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(A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

What is the rate of change?

The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.

A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.

Using the formula for an annual rate of change (r):

final value = initial value * [tex](1 - r)^t[/tex]

where t is the number of years and r is the annual rate of change expressed as a decimal.

Substituting the given values, we get:

$15,000 = $44,000 * (1 - r)¹⁴

Solving for r, we get:

r = 0.0804

So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.

B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:

r = 0.0804 * 100% = 8.04%

C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.

Substituting the known values, we get:

value in 2009 = $15,000 * (1 - 0.0804)³

value in 2009 = $11,628.40

Rounding to the nearest $50, we get:

value in 2009 = $11,650

Hence, (A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

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Determine the point estimate of the population mean and the margin of error for the given confidence interval. Lower bound: 12 Upper bound: 20To determine the point estimate of the population mean, we simply take the average of the lower and upper bounds of the confidence interval: Point estimate = (Lower bound + Upper bound) / 2 = (12 + 20) / 2 = 16 Therefore, the point estimate of the population mean is 16. To calculate the margin of error, we need to determine the distance between the point estimate and either the lower or upper bound of the confidence interval. We can do this by subtracting the point estimate from the upper bound (or vice versa): Margin of error = (Upper bound - Point estimate) / 2 = (20 - 16) / 2 = 2 Therefore, the margin of error for this confidence interval is 2.

Answer: its 16 I think

Step-by-step explanation:

the sales of portable MP3 players in 2008 will be approximately $3.50 billion. To predict the sales of MP3 players in 2008, we need to first understand the exponential growth pattern of sales from 2001 to 2005.

We are given that sales grew approximately exponentially from $0.07 billion in 2001 to $0.91 billion in 2005. This means that the sales data can be modeled by an exponential function of the form:

[tex]S(t) = a * b^t[/tex]

where S(t) is the sales at year t, a is the initial sales value (in 2001), and b is the growth factor per year. We can find the values of a and b by using the given sales data.

When t = 0 (in 2001), S(t) = $0.07 billion. So, we have:

[tex]0.07 = a * b^0\\a = 0.07[/tex]

When t = 4 (in 2005), S(t) = $0.91 billion. So, we have:

[tex]0.91 = 0.07 * b^4b = (0.91/0.07)^(1/4) = 1.770[/tex]

Therefore, the exponential function that models the sales data is:

[tex]S(t) = 0.07 * (1.770)^t[/tex]

To predict the sales of MP3 players in 2008, we need to find the value of S(7) (since 2008 is 7 years after 2001). We have:

[tex]S(7) = 0.07 * (1.770)^7= $3.50 billion[/tex]

Therefore, we can predict that the sales of portable MP3 players in 2008 will be approximately $3.50 billion.

It is important to note that this is a prediction based on the data we have and the model we have used. The actual sales value in 2008 could be different due to various factors such as market changes, competition, and technological advancements.

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The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

[tex]SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}[/tex]

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

[tex]SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))[/tex]

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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well, since all interior angles in a triangle add up to 180°, by definition A = 44°, since B and A are complementary anyway.

[tex]\cos(46^o )=\cfrac{\stackrel{adjacent}{9}}{\underset{hypotenuse}{c}}\implies c=\cfrac{9}{\cos(46^o)}\implies c\approx 13.0 \\\\[-0.35em] ~\dotfill\\\\ \tan(46^o )=\cfrac{\stackrel{opposite}{b}}{\underset{adjacent}{9}}\implies 9\tan(46^o )=b\implies 9.3\approx b[/tex]

Make sure your calculator is in Degree mode.

Ahmed placed a chocolate slice is $1.75.

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given: Ahmed and Tiana buy a cake for $14 that is half chocolate and half vanilla. They cut the cake into 8 slices.

Denoting the value of the slice of chocolate as C and V as the vanilla slice then

4 slices × C + 4 slices *V = $14

if Ahmed  likes 4 times more the chocolate than the vanilla slice, then he finds C four times more valuable than V, thus

C = 4*V

4 slices × 4V + 4 slices ×V = $24

20 slices × P = $14

P = $0.7/slice

V = 4 × P = 4 × $0.7/slice  = $2.8/slice

for a slice that is half chocolate and half vanilla

value= 1/2 slice × C + 1/2 slice × V = 1/2 slice ($0.7 /slice + $2.8/slice) =  $1.75

Hence,  Ahmed placed a chocolate slice is $1.75.

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The numerical sign of the limiting value is significant because it indicates the general direction of the function's behavior (increasing or decreasing) within the given interval,

Hi there! In Exploration 5.3.2, Question 3 required finding multiple average rates of change for different intervals, and in Question 6, you discussed the limiting value that those average rates are approaching. The significance of the numerical sign of the limiting value found in Question 6, addressed in Question 7, is as follows:

The sign of the limiting value (positive or negative) indicates the general direction of the function's behavior during the given interval. A positive limiting value means that the function is generally increasing, while a negative limiting value suggests that the function is generally decreasing.

Understanding the sign of the limiting value is essential as it provides insight into the overall trend of the function in the specified range. This information can be useful in various applications, including predicting future behavior and identifying potential maximum or minimum points of the function.

In summary, providing valuable information about the function's characteristics and trends.

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Answer:

Step-by-step explanation:

Reflecting a point across the x-axis negates the y-coordinate, so the point (-5, 7) reflected across the x-axis becomes (-5, -7).

Reflecting a point across the y-axis negates the x-coordinate, so the point (-5, -7) reflected across the y-axis becomes (5, -7).

Therefore, the third point is (5, -7).

Answer:

The answer is the first option

Step-by-step explanation:

The reason why it is the first option is because if we add up the total amount of things sold (candy, snacks, automotive supplies, and beverages) we would see that together the store sold 500 items. Using that we can diving the amount of candy, snacks, automotive supplies, and beverages by the total amount of things sold to get the percentages.

Ex: 75/500 = 0.15*100 = 15%
     100/500 = 0.20*100 = 20%
     etc.

Answer:

the correct answer is the last one i think

Step-by-step explanation:

Will put in chat if correct or not if i remember  to do it.

Quotient ➔ 2x² - 7x + 18

Remainder ➔ - 37

━━━━━━━━━━━━━━━━━━━━━━

SolutioN ::

ㅤ

[tex]\begin{gathered} \\ \\ \qquad{\rule{120pt}{7pt}} \\ \\ \end{gathered}[/tex]

VerificatioN ::

ㅤ

[tex]\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf {x(2x^{2} - 7x + 18) + 2(2x^{2} - 7x + 18) + ( - 37)} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^{3} - 7x^{2} + 18x + 4x^{2} - 14x + 36 - 37} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^{3} - 7x^{2} + 4x^{2} + 18x - 14x - 1} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf \pink{2x^{3} - 3x^{2} + 4x - 1} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf \pink{2x^{3} - 3x^{2} + 4x - 1} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {LHS = RHS} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \underline{\boxed{\sf{Verified}}} \; \pmb{\red{\bigstar}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ {\underline{\rule{150pt}{10pt}}} \end{gathered}[/tex]

[tex]\blue{\huge {\mathrm{DIVIDING \; POLYNOMIALS}}}[/tex]

[tex]\\[/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]

[tex]\qquad\begin{aligned}\sf \blue{2x^2 - 7x + 18} \:\:\:\:\:\:\:\:\:\: &\\\sf x + 2 \: \: ) \overline{2x^3 - 3x^2+4x-1} \quad&\\\sf \: \: \underline{ - 2x^3 - 4x^2 \qquad\qquad \: \: \: \: } \\\sf - 7x^2 + 4x \qquad \: \: \: \\\sf \:\:\: \underline{ - 7x^2 + 14x \qquad \: } \\ \sf 18x - 1 \: \: \: \\ \underline{ \sf{ - 18x - 36 \: }} \\ \sf \red{ - 37} \end{aligned}[/tex]

[tex]{===========================================}[/tex]

[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023[/tex]

the length of EF is 11 units.

How to solve similar triangles?

Since triangles DEF and GHF are both right triangles, we can use the Pythagorean theorem to find the length of EF.

Let's first find the lengths of DE and EF.

DE = DF + FE = 13 + x, where x is the length of FE.

GF = DE - DG = (13 + x) - 4 = 9 + x.

GH = 4.

Now, using the Pythagorean theorem in triangle GHF, we have:

GH² + HF² = GF²

4²+ HF² = (9 + x)²

16 + HF² = 81 + 18x + x²

And in triangle DEF, we have:

DE²+ EF² = DF²

(13 + x)² + EF² = 13²

169 + 26x + x²+ EF² = 169

Simplifying the above equation, we get:

EF²= -26x - x²

Substituting this into the equation we got from the GHF triangle, we have:

16 + HF² = 81 + 18x + x² - EF²

16 + HF² = 81 + 18x + x²+ 26x + x²

HF² = 97 + 44x + 2x²

Now, using the fact that HE + EF = HF, we have:

8 + x = √(97 + 44x + 2x²)

Squaring both sides and simplifying, we get:

4x² + 16x - 225 = 0

Solving this quadratic equation, we get:

x = (-16 ± √(16² - 44(-225)))/(2*4) = (-16 ± 34)/8

Since x has to be positive, we take the positive solution:

x = 3

Therefore, EF = HE + FE = 8 + 3 = 11.

So the length of EF is 11 units.

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Buzz earned $65 - $55 = $10 more than Woody for his pink bear.

How to calculate earnings?

Woody sold his bear for $50 + 10% of $50 = $55.

Buzz sold his bear for $50 + 30% of $50 = $65.

Therefore, Buzz earned $65 - $55 = $10 more than Woody for his pink bear.

To determine how much more money Buzz earned than Woody for their pink bears, we first needed to calculate the selling price for each of them.

We know that both of them bought their bears for $50. Woody sold his bear for 10% more, which means his selling price was $50 + 10% of $50 = $55. Buzz sold his bear for 30% more, which means his selling price was $50 + 30% of $50 = $65. Therefore, Buzz earned $65 - $55 = $10 more than Woody for his pink bear.

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The best choice is B. Saving Bonds, Stock Market, Mutual

Investments are defined as assets bought or invested in with the goal of increasing wealth and setting aside funds from salary or capital gains. The main goal of an investment is to generate extra income or to make money on an investment over a certain amount of time.

Generally speaking, the following is the order of investments from the lowest risk to the greatest risk:

Bonds for savings, mutual funds, and the stock market

As a result, list B is the one that runs from investment with the lowest risk to investment with the greatest risk. Stock market, mutual funds, and savings bonds.

The sequence of mutual fund investments, Savings Bonds, and Stock Market in Option A is not in decreasing order of danger.

Savings Bonds, the stock market, and mutual funds are listed in Option C's order, and this is also not from lowest to greatest risk.

Stock markets, mutual funds, and savings bonds are listed in Option D's order of greatest to lowest risk.

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