5. What are the real and complex solutions of the polynomial equation? (1 point)
x^3-8=0
01+i3, and 1-i√√3
O2,-1+13, and-1-i√√3
O2, 1+2i √√3, and 1-2i √√3
02, 2+2i √√3, and 2-2i

Answer:

1: Narrower

2: Wider

Step-by-step explanation:

The magnitude of 'a' increases, the parabola becomes more and more wider.

A parabola is a curve where any point is at an equal distance from a fixed point (the focus), and a fixed straight line (the directrix).

Given is a parabola.

The parametric form of equation of parabola is given by -

y² = 4ax

Here, distance 'a' is called focus of parabola.

For a constant value of x - coordinate, take different values of 'a'. For constant x, we get the following relation -

y² \(\alpha\) a

As the magnitude of 'a' increases, the y coordinate increases and parabola becomes more and more wider.

Therefore,  the magnitude of 'a' increases, the parabola becomes more and more wider.

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So there are 6 permutations possible with the letters "ABC". These are: ABC, ACB, BAC, BCA, CAB, CBA.

Permutations are a way of arranging objects in a specific order. The number of permutations of a set of n distinct objects is given by n!, where n! denotes the factorial of n.

In the case of the letters "ABC", there are three distinct objects: A, B, and C. Therefore, the number of permutations possible with these letters is:

3! = 3 x 2 x 1 = 6

This means that there are 6 possible ways of arranging the letters "ABC" in a specific order. These permutations are:

ABC

ACB

BAC

BCA

CAB

CBA

To see why there are 6 possible permutations, consider the first position. There are three letters to choose from, so there are three possible choices for the first position. Once the first letter is chosen, there are two letters left to choose from for the second position. Finally, there is only one letter left to choose from for the third position. Therefore, the total number of permutations is:

3 x 2 x 1 = 6

In summary, the number of permutations of a set of n distinct objects is given by n!, and in the case of the letters "ABC", there are 3! = 6 possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA.

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The values for f(1), f(2), f(3), f(4), and f(5) using the recursive formula f(n+1) = 3^(f(n)/3) are:

f(1) = 3, f(2) = 3, f(3) = 3, f(4) = 3, f(5) = 3.

To find the values of f(1), f(2), f(3), f(4), and f(5) for each given recursive definition, we can use the initial condition f(0) = 3 and the recursive formulas.

(a) f(n+1) = -2f(n):

Using the recursive formula, we can find the values as follows:

f(1) = -2f(0) = -2(3) = -6

f(2) = -2f(1) = -2(-6) = 12

f(3) = -2f(2) = -2(12) = -24

f(4) = -2f(3) = -2(-24) = 48

f(5) = -2f(4) = -2(48) = -96

So, the values for f(1), f(2), f(3), f(4), and f(5) using the recursive formula f(n+1) = -2f(n) are:

f(1) = -6, f(2) = 12, f(3) = -24, f(4) = 48, f(5) = -96.

(b) f(n+1) = 3f(n) + 7:

Using the recursive formula, we can find the values as follows:

f(1) = 3f(0) + 7 = 3(3) + 7 = 16

f(2) = 3f(1) + 7 = 3(16) + 7 = 55

f(3) = 3f(2) + 7 = 3(55) + 7 = 172

f(4) = 3f(3) + 7 = 3(172) + 7 = 523

f(5) = 3f(4) + 7 = 3(523) + 7 = 1576

So, the values for f(1), f(2), f(3), f(4), and f(5) using the recursive formula f(n+1) = 3f(n) + 7 are:

f(1) = 16, f(2) = 55, f(3) = 172, f(4) = 523, f(5) = 1576.

(c) f(n+1) = f(n)^2 - 2f(n) - 2:

Using the recursive formula, we can find the values as follows:

f(1) = f(0)^2 - 2f(0) - 2 = 3^2 - 2(3) - 2 = 1

f(2) = f(1)^2 - 2f(1) - 2 = 1^2 - 2(1) - 2 = -3

f(3) = f(2)^2 - 2f(2) - 2 = (-3)^2 - 2(-3) - 2 = 7

f(4) = f(3)^2 - 2f(3) - 2 = 7^2 - 2(7) - 2 = 41

f(5) = f(4)^2 - 2f(4) - 2 = 41^2 - 2(41) - 2 = 1601

So, the values for f(1), f(2), f(3), f(4), and f(

using the recursive formula f(n+1) = f(n)^2 - 2f(n) - 2 are:

f(1) = 1, f(2) = -3, f(3) = 7, f(4) = 41, f(5) = 1601.

(d) f(n+1) = 3^(f(n)/3):

Using the recursive formula, we can find the values as follows:

f(1) = 3^(f(0)/3) = 3^(3/3) = 3^1 = 3

f(2) = 3^(f(1)/3) = 3^(3/3) = 3^1 = 3

f(3) = 3^(f(2)/3) = 3^(3/3) = 3^1 = 3

f(4) = 3^(f(3)/3) = 3^(3/3) = 3^1 = 3

f(5) = 3^(f(4)/3) = 3^(3/3) = 3^1 = 3

So, the values for f(1), f(2), f(3), f(4), and f(5) using the recursive formula f(n+1) = 3^(f(n)/3) are:

f(1) = 3, f(2) = 3, f(3) = 3, f(4) = 3, f(5) = 3.

Note: In the case of (d), the recursive formula leads to the same value for all values of n.

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Answer:

\(y=-2x+6\)

Step-by-step explanation:

Equation of the line

First, we find the slope of the line.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

The two points are (1,4) and (2,2), thus:

\(\displaystyle m=\frac{2-4}{2-1}=\frac{-2}{1}\)

\(m=-2\)

The equation of a line passing through (h,k) and slope m is:

\(y-k=m(x-h)\)

\(y-4=-2(x-1)\)

Note we used the point (1,4). If we used the other point, the result would have been the same. Operating the equation:

\(y-4=-2x+2\)

Adding 4:

\(y=-2x+6\)

The slope-intercept form of the line is

\(\boxed{y=-2x+6}\)

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\(\sigma\))= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n\(=(2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n\(=(2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5)^2

n=(15.996)^2

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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Answer:

X is 17

Step-by-step explanation:

Answer:

49 in the first box and 7 in the second one

25 in the 3rd box and 5 in the 4th

Answer:

c=68 and b=112

Step-by-step explanation:

When the area corresponding to the critical value is in the lower tail of the sampling distribution, the p-value is the area under the curve less than or equal to the critical value. Therefore, the correct answer is a. less than or equal to the critical value.

The critical value is the point on the sampling distribution that separates the rejection region from the non-rejection region. If the test statistic falls in the rejection region, we reject the null hypothesis. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, given that the null hypothesis is true. If the p-value is less than or equal to the critical value, we reject the null hypothesis.

In the case of a lower-tailed test, the critical value is in the lower tail of the sampling distribution, and the p-value is the area under the curve to the left of the test statistic. If the p-value is less than or equal to the critical value, it means that the test statistic falls in the rejection region and we reject the null hypothesis.

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Answer: subtract 5 from the input to get the output.

Step-by-step explanation:

The steps for adding and subtracting fractions with whole numbers:

- Write the whole number in the form of a fraction.

- Convert the fractions to like fractions.

- Add/Subtract the numerators while the denominator remains the same.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part of fraction is denominator.

consider a fraction 1/8.

Here, numerator is 1, denominator is 8

When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8

In case of adding and subtracting fractions with whole numbers:

Let us assume that 'a' represents the whole number and \(\frac{x}{y}\) be fraction

First we write the whole number in the form of a fraction.

So, a = \(a = \frac{a}{1}\)

Now we find the LCM of the denominators of fractions \(\frac{a}{1} ,\frac{x}{y}\) and then convert the given fractions to like fractions.

Let m be the LCM of the denominators of fractions \(\frac{a}{1} ,\frac{x}{y}\)

So, the fractions becomes  \(\frac{a}{m} ,\frac{x}{m}\)

Last we Add/Subtract the numerators while the denominator remains the same.

i.e., \(\frac{a\pm x}{m}\)

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The complete question is:

How to add /subtract fractions with whole numbers?

1. (y+2)dx + (x+y^2)dy = 0 is a separable differential equation.

2. (2x−y)dx + (x−2y)dy = 0 is a separable differential equation.

3. (x^2+y^2)dx − 2xydy = 0 is a homogeneous differential equation

1. (y+2)dx + (x+y^2)dy = 0

To determine the type of this equation, let's rearrange it as follows:

(y+2)dx = -(x+y^2)dy

This equation is separable because it can be written in the form M(x)dx + N(y)dy = 0, where M(x) = -(x+y^2) and N(y) = y+2.

2. (2x−y)dx + (x−2y)dy = 0

Rearranging the equation, we have:

(2x−y)dx = -(x−2y)dy

This equation is also separable since it can be expressed as M(x)dx + N(y)dy = 0, where M(x) = -(x-2y) and N(y) = 2x-y.

3. (x^2+y^2)dx − 2xydy = 0

Rearranging the equation, we get:

(x^2+y^2)dx = 2xydy

This equation is homogeneous because it can be written in the form M(x, y)dx = N(x, y)dy, where M(x, y) = 2xy and N(x, y) = x^2 + y^2.

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False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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Answer:

its 64cm

Step-by-step explanation:

Answer:

answer in picture

Step-by-step explanation:

Answer:

4.85 ft

Step-by-step explanation:

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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Answer:

4

Step-by-step explanation:

Since the base angles are the same, the side have to be the same

ML = MN

4x = x+3

Subtract x from each side

4x-x = x+3-x

3x= 3

Divide by 3

3x/3 = 3/3

x = 1

We want the length of MN

MN = x+3 = 1+3 = 4

The measurement of MN side is 4

The properties of the triangle are:

1. The sum of all the angles of a triangle (of all types) is equal to 180°.

2. The sum of the length of the two sides of a triangle is greater than the length of the third side.

3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

Since the base angles are the same, the side have to be the same

ML = MN

4x = x+3

Subtract x from each side

4x-x = x+3-x

3x= 3

Divide by 3

3x/3 = 3/3

x = 1

We want the length of MN

MN = x+3 = 1+3 = 4

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Answer:

2x^2+x-6

Step-by-step explanation:

Use the F.O.I.L method

2x^2+4x-3x-6

Answer:

Step-by-step explanation:

\(4-2b^2 +3c\\b =2\\c = -1\\4-2(2)^2 +3(-1)\\4- 2(4) -3\\4-8-3\\= -7\)

Answer:

-7

Step-by-step explanation:

Sub in the numbers

4 - 2(2)2+ 3(-1)

4 - 8 + (-3)

 = -7

According to the information in the table, the histogram would be as shown in the attached image.

To graph the information in the table we must take into account the relationship of the data. On the one hand we have the frequency, which is the data that varies, and the different variations of time.

In accordance with the above, what we want to demonstrate with this table are the different frequencies of time that students take to do their math homework. Additionally, most students take between 10 and 25 minutes to do their math homework.

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Answer:$8,890.83

Step-by-step explanation:

Answer:

Step-by-step explanation:put (-5,0) on top and (4,18) on the bottom subtract the two and you will get the answer

Answer:

1/81

Step-by-step explanation:

In h(x)=3^x, replace each instance of x with -4:

h(-4) = 3^(-4), or

                 1

h(-4) = ----------- = 1/81

              3^4

\(\huge{\mathbb{\tt { PROBLEM:}}}\)

if h(x)=3^x then h (-4) =

\(\huge{\mathbb{\tt { ANSWER:}}}\)

\( \frac{1}{81} \)

\(\huge{\mathbb{\tt { EXPLANATION:}}}\)

In h(x) = 3^x , you must replace each instance of with -4:

h(-4)=3^(-4)

\(h(4)= \frac{1}{3^4} = \frac{1}{81} \)

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When x = π/2, the rate at which x is changing can be calculated by using the chain rule. The rate at which x is changing is equal to \(-5e^{(-sin(\pi /2))\), or -5.

We are given that \(y = 2e^{cos(x)\) and that y is increasing at a constant rate of 5 units per second. To find the rate at which x is changing when x = π/2, we need to differentiate y with respect to time using the chain rule.

Using the chain rule, we differentiate \(y = 2e^{cos(x)\) as follows: dy/dt = dy/dx * dx/dt. Since we know that dy/dt is 5 units per second, we can rewrite the equation as 5 = dy/dx * dx/dt.

To find dx/dt when x = π/2, we substitute x = π/2 into the equation. Now we need to find dy/dx. Taking the derivative of \(y = 2e^{cos(x)\) with respect to x, we get \(dy/dx = -2e^{cos(\pi /2)} sin(\pi /2)\)

Substituting x = π/2 into dy/dx, we have \(dy/dx = -2e^{cos(\pi /2)} sin(\pi /2)\). Since cos(π/2) = 0 and sin(π/2) = 1, we can simplify dy/dx to -2e⁰ * 1 = -2.

Finally, we can rearrange the equation 5 = dy/dx * dx/dt and substitute dy/dx = -2 to solve for dx/dt. We get -2 * dx/dt = 5, which implies dx/dt = -5/2 or -2.5.

Therefore, when x = π/2, the rate at which x is changing is -2.5.

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The distance between the height of the platform and the depth below water is 47ft . The concept of depth describes how far something extends.

A deep area in a body of water is what the word "DEPTH" means.

Ocean depth is most frequently and quickly measured using sound. Sonar, which stands for sound navigation and range, is a technique that allows ships to map the topography of the ocean below. The instrument uses sound waves to send to the ocean's bottom and time how long it takes for an echo to come back.

Water depth is the distance in feet between the ocean's surface and bottom, as determined by mean lower low water.

Use the following formula for measuring ocean depth.

D = V Times 1/2 T D

Depth (in meters) T= Time (in seconds) V = 1507 m/s (speed of sound in water)

In the question we have,

Platform to surface of water = 33ft

Platform to depth below water = 33+14 = 47ft

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Answer:

Similar to the question: They figure that they will drive 792 miles round trip. If their car gets 25 miles per gallon and the current cost of gasoline is $2.35, what will the gas for their trip cost? $74.45 George is taking the same trip to San Antonio (792 miles)

Step-by-step explanation:

Hope it helps :)

Answer:

y + 11 = 14

Step-by-step explanation:

Answer:

The equation is y + 11 = 14

The answer to that equation is 3

Step-by-step explanation:

y + 11 = 14

   -11     -11

y = 3

If Neptune's distance from the sun is about 4.5 billion km and Venus distance is 2×\(10^{8}\) km, then its 22.5 times farther is Neptune from the sun than Venus.

The Neptune's distance from sun = 4.5 billion km

we know

1 billion = \(10^{9}\)

The Venus's distance from sun = 2×\(10^{8}\) km

How many times farther is Neptune from the sun than Venus = The Neptune's distance from sun / The Venus's distance from sun

Substitute the values in the equation

= (4.5×\(10^{9}\))÷(2×\(10^{8}\))

= 22.5

Hence, If Neptune's distance from the sun is about 4.5 billion km and Venus distance is 2×\(10^{8}\) km, then its 22.5 times farther is Neptune from the sun than Venus.

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The day the two bags will have the same weight is the 24th day.

The linear equation that can be used to determine the pound of dog food left is:

Amount of dog food left = capacity of the bag - (number of days x amount the dog eats per day)

Amount of dog food left = 34 - (1 x p)

Amount of dog food left = 34 - 1p

The linear equation that can be used to determine the pound of cat food left is:

Amount of cat food left = capacity of the bag - (number of days x amount the cat eats per day)

Amount of cat food left = 16 - (1/4 x p)

Amount of cat food left = 16 - 1/4p

On the day the two bags will have the same weight, the two above equations would be equal:

16 - 1/4p = 34 - 1p

p - 1/4p = 34 - 16

3/4p = 18

p = (18 x 4) / 3

p = 24 days

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