2. After running the appropriate statistical tests, Jack finds that life satisfaction was __________ in the older adults (M = 4.9, SD = 1.2) than in middle-aged adults (M = 4.1, SD = 1.8), t(58) = 2.03, p = .047, 95% CI [0.01, 1.59], d = .52. A. From these statistical results, what conclusions can Jack make? Comment on whether there are statistically significant differences between the groups and how you know. B. What should Jack decide about the hypotheses? C. What does the "t(58) = 2.03" tell us? D. What can we conclude from the confidence interval? E. What does the effect size tell us?

The PDF of Y, when X is uniformly distributed between 0 and 1, is given by fY(y) = 1/y for y > 0.

Let's denote the PDF of X as fX(x), which represents the probability density function of X. We want to find the PDF of Y, denoted as fY(y), which represents the probability density function of Y = eˣ.

To derive the PDF of Y, we need to understand the transformation that occurs when we apply the exponential function to X. The transformation Y = eˣ is a monotonic transformation, which means that it preserves the order of the values of X. In other words, if X1 < X2, then eˣ1 < eˣ2.

To find the PDF of Y, we will use the cumulative distribution function (CDF) approach. The CDF of Y, denoted as FY(y), gives us the probability that Y takes on a value less than or equal to y. Mathematically, FY(y) = P(Y ≤ y).

We can express the CDF of Y in terms of the CDF of X. Since Y = eˣ, we have FY(y) = P(eˣ ≤ y). Now, we can solve this inequality for X by taking the natural logarithm (ln) of both sides: ln(Y) ≤ X.

Next, we can write the inequality in terms of the CDF of X. Since X is uniformly distributed between 0 and 1, its CDF, denoted as FX(x), is given by FX(x) = x for 0 ≤ x ≤ 1.

Substituting ln(Y) ≤ X, we get ln(Y) ≤ FX(x). To find the probability that this inequality holds, we integrate the CDF of X from 0 to the value of X that satisfies ln(Y) ≤ X. This gives us:

FY(y) = P(Y ≤ y) = P(ln(Y) ≤ X) = P(ln(Y) ≤ FX(x)) = ∫[0,X] fX(x) dx,

where fX(x) is the PDF of X.

Since X is uniformly distributed between 0 and 1, its PDF is a constant function over the interval [0,1]. Therefore, fX(x) = 1 for 0 ≤ x ≤ 1, and fX(x) = 0 otherwise.

We can now compute FY(y) by evaluating the integral for different values of y. However, to obtain the PDF of Y, we need to differentiate FY(y) with respect to y. By applying the Fundamental Theorem of Calculus, we get:

fY(y) = d/dy [FY(y)] = d/dy ∫[0,X] fX(x) dx.

Since fX(x) = 1 for 0 ≤ x ≤ 1, we can take the derivative of the integral with respect to y, resulting in:

fY(y) = d/dy [FY(y)] = d/dy ∫[0,X] 1 dx = d/dy (X) = d/dy (ln(y)) = 1/y,

where y > 0.

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A bar graph would be the most appropriate graphical representation for the middle school mathematics class's data on travel time to school.The correct answer is option B.

For the given scenario, the most appropriate graphical representation for the data collected from the random sample of 100 students would be a bar graph.

A bar graph is suitable for displaying categorical data, such as the time it takes students to travel to school. The x-axis can represent different categories or ranges of travel time (e.g., 0-5 minutes, 5-10 minutes, 10-15 minutes), while the y-axis represents the frequency or count of students falling within each category.

A circle graph (also known as a pie chart) is more appropriate for displaying proportional data, where the parts make up a whole. It is not suitable for showing individual travel times.

A line plot, also known as a dot plot, is useful for representing a distribution of data with numerical values along a number line. However, it may not be the best choice for displaying the travel times of 100 students, as it could become cluttered and difficult to interpret.

A box plot is typically used to display the distribution, variability, and outliers in a dataset. While it can provide useful insights into the spread of travel times, it may not be the most suitable choice for this particular scenario where the focus is on the frequencies or counts of different travel time categories.

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The probable question may be:

A middle school mathematics class was interested in the amount of time it takes them to travel to school. They gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data. Which graphical representation would be best for their data?

A. Circle graph

B. Bar graph

C. Line plot

D. Box plot

Answer:

= 512 ft²

Step-by-step explanation:

All the rectangular figure:

Area₁ = (32ft + 8ft) (8ft + 8ft)

Area₁ = (40ft)(16ft)

Area₁ = 640ft²

Area of NOT shaded region;

There are 2 similar squares:

Area₂ = 2(8ft*8ft)

Area₂ = 2(64ft²)

Area₂ = 128ft²

Then:

The shaded area is:

Area₁ - Area₂ = Shaded Area

Shaded area = 640 ft² - 128ft²

Shaded area = 512 ft²

Answer:

B) 2x12=24 2x7=14

This equals to 24+14

The density of the material it is made of is equal to 0.9952 g/cm³.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the parameters, we have the following:

Volume, V = 3.14 × 4² × 10

Volume, V = 502.4 cm³.

Density = mass/volume

Density = 500/502.4

Density = 0.9952 g/cm³.

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Answer:

last option shown, 500 milliliters

Step-by-step explanation:

She has approx 3.5 liters of choc milk as shown in the pic.

3.5 liters x 1000 = 3500 milliliters total choc milk.

=3500/7 containers = 500 milliliters in each.

So pick the last option, 500 milliliters.

The local maximums of f(x,y) = sin(x)sin(y) occur at (nπ, mπ) and the local minimums occur at (nπ + π/2, mπ + π/2), where n and m are integers.

The given function f(x,y) = sin(x)sin(y) is a product of two periodic functions, each with a period of 2π. Hence, the function f(x,y) also has a periodicity of 2π in both x and y directions. To find the local maximums and minimums of the function, we need to look for points where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative of f(x,y) with respect to x, we get cos(x)sin(y), which is equal to zero at points (nπ, mπ), where n and m are integers. Similarly, taking the partial derivative of f(x,y) with respect to y, we get cos(y)sin(x), which is also equal to zero at points (nπ, mπ). Therefore, the local maximums of f(x,y) occur at these points.

On the other hand, taking the partial derivative of f(x,y) with respect to x, we get cos(x)sin(y), which is equal to π/2 at points (nπ + π/2, mπ), where n and m are integers. Similarly, taking the partial derivative of f(x,y) with respect to y, we get cos(y)sin(x), which is equal to π/2 at points (nπ, mπ + π/2). Therefore, the local minimums of f(x,y) occur at these points.

In summary, the local maximums of f(x,y) = sin(x)sin(y) occur at (nπ, mπ) and the local minimums occur at (nπ + π/2, mπ + π/2), where n and m are integers.

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The explicit compound interest expression which represents the total value after 19 years is

[tex]560 {(1.0373)}^{19} [/tex]

Compound interest is obtained mathematically using the relation

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

Here ;

A = total value of the investment after the specified period

P = principal amount

r = interest rate

n = number of compounding periods per year, and

t = number of years.

We are given the following parameters;

P = $560 (principal amount)

r = 3.73% = 0.0373

n = 1

t = 19

Plugging the values into the formula , we have

[tex]A = {560(1 + 0.0373)}^{19} [/tex]

Hence, the correct compounding interest expression is

[tex]{560(1 + 0.0373)}^{19} [/tex]

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The number of miles that Hummer H1 can go would be = 230 miles.

To calculate the number of miles the vehicle can travel when a certain amount of gallons are given would be done following the steps below.

The number of miles for 1 gallon of gas = 10 miles

The number of miles for 23 gallons of gas = X miles

That is :

1 gallon = 10 miles

23 gallons = X miles

make X miles the subject of formula;

X miles = 23×10/1

= 230 miles.

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The expected number of days that Kiran wears matching socks is equal to approximately 1.928 days.

To find the expected number of days that Kiran wears matching socks,

Calculate the probability of wearing matching socks on each day and sum up these probabilities.

Let us consider each day of the week separately.

On the first day, Kiran randomly selects two socks.

The probability of wearing matching socks on the first day is 1, as there is no other pair of socks chosen yet.

On the second day, there are 12 socks remaining in the drawer 2 socks from the first day and 10 remaining pairs.

Kiran selects two socks again, and the probability of wearing matching socks on the second day is 1/11,

As there is only one pair of matching socks among the remaining 11 socks.

Similarly, on the third day, the probability of wearing matching socks is 1/9.

On the fourth day is 1/7, on the fifth day is 1/5, on the sixth day is 1/3, and on the seventh day is 1/1.

Now, let us calculate the expected number of days that Kiran wears matching socks,

E = (1 × 1) + (1/11 × 1) + (1/9 × 1) + (1/7 × 1) + (1/5 × 1) + (1/3 × 1) + (1/1 × 1)

  = 1 + 1/11 + 1/9 + 1/7 + 1/5 + 1/3 + 1/1

  ≈ 1.928

Therefore, the expected number of days that Kiran wears matching socks over the course of the week is approximately 1.928 days.

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The exponential regression equation for this set of data is y = [tex]14.129e^{(0.495x)[/tex] and the number of bacteria present after 10 hours is approximately 24684.

The exponential regression equation for this set of data can use a calculator or spreadsheet software.

The equation will have the form y = abˣ a is the initial number of bacteria and b is the growth rate.
Using the given data can create a table of values for the equation:
x                y                   ln(y)
---------------------------------------
0              16                2.773
1               66               4.189
2             311                5.739
3            791                6.672
4          1553                7.349
5          2571               7.853

A regression tool can find that the equation is approximately y = [tex]14.129e^{(0.495x)[/tex] rounded to three decimal places.

The initial amount of bacteria is approximately a = 14.129 and the growth rate is approximately b = 1.649.
The number of bacteria present after 10 hours can plug x = 10 into the equation:
y = [tex]14.129e^{(0.495\times 10)[/tex]

= 24683.522
Rounding to the nearest whole number get that the number of bacteria present after 10 hours is approximately 24684.

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To find Pedro's exam score, we can use the formula for calculating the z-score:

z = (x - μ) / σ,

where z is the z-score, x is the exam score, μ is the mean, and σ is the standard deviation.

Given that Pedro's z-score was 3, we can rearrange the formula to solve for x:

3 = (x - 68) / 10.

Multiplying both sides of the equation by 10, we get:

30 = x - 68.

Adding 68 to both sides, we find:

x = 30 + 68 = 98.

Therefore, Pedro's exam score was 98.

The z-score measures how many standard deviations an individual's score is above or below the mean. In this case, Pedro's z-score of 3 indicates that his exam score was 3 standard deviations above the mean of 68.

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Based on the 30% smoking rate, we can expect that approximately 75 adults out of the group of 250 will be smokers.

To determine the expected number of adults who smoke in a group of 250 adults, we need to consider the smoking rate of 30% in the country. The expected number can be calculated by multiplying the total number of adults by the smoking rate.

Expected number of adults who smoke = Total number of adults × Smoking rate

Given that there are 250 adults in the group, the expected number of adults who smoke can be calculated as follows:

Expected number of adults who smoke = 250 × 0.30 = 75

The expected number is derived by assuming that each adult's decision to smoke is independent of others in the group. While this calculation provides an estimate, it is important to note that individual smoking behavior can vary.

It's also worth considering that the expected number does not account for factors such as age, gender, or other demographic characteristics that could influence smoking rates.

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There is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.

In two- or three-dimensional space, a curve is a mathematical object that symbolises a continuous, smooth path. Curves can be derived from geometric operations, parametric equations, or mathematical equations. They are commonly used to simulate real-world processes in physics, engineering, mathematics, and many other disciplines.

To find the level curve of value c for the given surface [tex]z = f(x, y) = (x^2/4) + (y^2/25) = c[/tex], where c < 0, follow these steps:

Step 1: Write down the equation of the surface.
[tex]z = f(x, y) = (x^2/4) + (y^2/25)[/tex]

Step 2: Replace z with the constant c.
[tex]c = (x^2/4) + (y^2/25)[/tex]

Step 3: Rearrange the equation to isolate [tex]y^2[/tex].
[tex]y^2 = 25(c - (x^2/4))[/tex]

However, note that we're given that c < 0. This means that the value inside the parentheses (c - ([tex]x^2/4[/tex])) must also be negative. Since y^2 can't be negative, there's no real solution for this equation.

In conclusion, there is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.

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Answer:

-72-27m or switch them for -27m-27

Step-by-step explanation:

We are given the problem:

9(-8-3m)

and are asked to combine like terms.

Combining like terms means to combine terms/values that share similar properties.  In this case, it would be single numbers or if we had more than 1 value with "m" as the variable, that.

We would have to use the distributive property in this case to combine like terms, so distribute the 9 to all terms in the parenthesis.

-72-27m

We usually put the variable and coefficient first, so it would be -27m-72.

Hope this helps! :)

The step that is not necessary to conduct each time you use the p-value method is "Multiplying the test statistic by -1."

In hypothesis testing using the p-value method, the general steps include:

Formulating the null and alternative hypotheses.

Selecting an appropriate significance level (alpha).

Collecting and analyzing the data to obtain the test statistic.

Calculating the p-value, which is the probability of observing a test statistic as extreme as or more extreme than the one obtained, assuming the null hypothesis is true.

Comparing the p-value to the significance level.

Making a decision to reject or fail to reject the null hypothesis based on the comparison of the p-value and the significance level.

Providing an interpretation of the results in the context of the problem.

Multiplying the test statistic by -1 is not a standard step in the p-value method. The test statistic itself is calculated based on the data and the hypothesis being tested, and its sign is important in determining the direction of the effect being analyzed.

Multiplying it by -1 would invert the sign, which would change the interpretation and potentially lead to incorrect conclusions. Therefore, this step is not necessary in the p-value method.

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The best method of solving  for -9x^2-12x+12=0 is the factor method.

This is so because it is easier

To solve quadratic equations, there are different methods.

These methods are known as;

From the information given, we have that;

-9x²-12x+12=0

Using the factor method, we have that;

Find the pair factor of the product of 9 and 12 that would add up to given - 12, we have;

-9x² - 18x + 6x + 12 = 0

Group in pairs, we get;

(-9x² - 18x) + (6x + 12) = 0

Factorize

-9x(x + 2) + 6(x + 2) = 0

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The method that is best for solving for 9x^2-12x+12=0 is Quadratic formula method. because we are going to get a comlex roots.

The quadratic formular can be written as;

x = -b ± √(b^2 - 4ac) / 2a

a = 3

b = -4

c = 4.

Then we can substitute as ;

x = -(-4) ± √(-4)^2 - 4(3)(4) /( 2*3)

x = 4 ±√(16 - 48) / 6

x = 4 ± √-32 / 6

x = 4 ± 4i√2 / 6

x = 2 ± 2i√2 / 3

x = 2 + 2i√2/3

x = 2 - 2i√2)/3

x=0.666667+0.942809i

x=0.666667−0.942809i

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Answer:

b.11

Step-by-step explanation:

 b is the answer

The area of the composite shape in this problem is given as follows:

18 inches squared.

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width.

The figure in this problem are composed by two rectangles, with dimensions given as follows:

Hence the area of the shape is given as follows:

A = 2 x 3 + 2 x 6

A = 6 + 12

A = 18 square inches.

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The value of length CD is 5

Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent i.e they are equal.

Also the the ratio of corresponding sides of similar triangles are equal.

Therefore;

25-2x/x = 24/8

25-2x/x = 3/1

25 -2x = 3x

25 = 3x+2x

25 = 5x

divide both sides by 5

x = 25/5

x = 5

therefore the value of CD is 5

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The most general antiderivative of h(t)=-3sin(t)/cos^2(t) is F(t)=3sec(t)+C, where C is a constant of integration.

To find the antiderivative of h(t), we first recognize that -3sin(t)/cos^2(t) can be rewritten as -3cos^(-2)(t) * sin(t). We can then use the substitution u = cos(t), du = -sin(t) dt to obtain ∫ -3cos^(-2)(t) * sin(t) dt = ∫ -3/u^2 du. Integrating with respect to u, we get 3/u + C = 3sec(t) + C, where C is a constant of integration. Therefore, the most general antiderivative of h(t) is F(t) = 3sec(t) + C, where C is a constant of integration.

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The area of the circle in terms of pi, with a diameter of 9.6 meters, is 23.04π square meters.

The diameter of a circle is twice the radius, so if the diameter is 9.6 meters, then the radius is half of that, or:

r = 9.6 / 2 = 4.8 meters

The area of a circle is given by the formula:

A = πr²

Substituting in the value of r, we get:

A = π(4.8)²

Simplifying the expression by squaring 4.8, we get:

A = π(23.04)

So the area of the circle is:

A = 23.04π square meters

Therefore, the area of the circle in terms of pi, with a diameter of 9.6 meters, is 23.04π square meters.

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The description that best defines AB¯¯¯¯¯ is:

"The set of points containing point A and point B."

AB¯¯¯¯¯ represents a line segment with endpoints A and B.

A line segment is a part of a line that connects two points, and it includes all the points that lie between the two endpoints.

Therefore, the set of all points between point A and point B is the most accurate description of AB¯¯¯¯¯.

The set of all points between point A and point B includes both endpoints A and B, as well as all the points that lie in between them. These points can be represented by the notation [A, B].

In other words, AB¯¯¯¯¯ is the line segment that starts at point A and ends at point B, and it includes all the points that lie between A and B.

This definition of AB¯¯¯¯¯ is important in geometry and other related fields. It is used in a variety of applications, including measuring the distance between two points and finding the slope of a line.

Additionally, it is an important concept in trigonometry and calculus, where it is used to define integrals and to calculate the arc length of a curve.

In summary, AB¯¯¯¯¯ is the set of all points between point A and point B, including both endpoints.

This definition is essential to many branches of mathematics and has important applications in geometry, trigonometry, and calculus.

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The first degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T1(x) = f(1) + f'(1)(x-1) = 0 + 1(x-1) = x-1. Therefore, T1(2) = 2-1 = 1.

The second degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T2(x) = T1(x) + f''(1)/2(x-1)^2. We have f''(x) = -1/x^2, so f''(1) = -1. Thus, T2(x) = x-1 - (1/2)(x-1)^2. Therefore, T2(2) = 2-1 - (1/2)(2-1)^2 = 1/2.

The third degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T3(x) = T2(x) + f'''(c)/3!(x-1)^3, where c is some number between 1 and x. We have f'''(x) = 2/x^3, so f'''(c) = 2/c^3.

Thus, T3(x) = x-1 - (1/2)(x-1)^2 + (2/3!c^3)(x-1)^3. To find an upper bound for the error R3 = f(2) - T3(2), we need to find the maximum value of |f'''(x)| on the interval [1,2].

We have |f'''(x)| = 2/x^3, which is decreasing on the interval. Therefore, the maximum value occurs at x = 1, and we have R3 <= (2/3!)(2-1)^3/1^3 = 2/3.

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There is not enough evidence to suggest that Ψ(θ) is significantly different from 2 based on the given data and confidence interval.

Hypothesis testing involves making a decision about a certain claim or hypothesis about the population based on sample data. The claim or hypothesis is typically in the form of a statement about a population parameter such as a mean or proportion.

Confidence intervals, on the other hand, provide a range of values that is likely to contain the true population parameter with a certain level of confidence.

Since the null hypothesis is that Ψ (θ) = 2,

we can use the 95% confidence interval given to determine if there is evidence against the null hypothesis.

If the null value of 2 is not contained in the confidence interval, then we can reject the null hypothesis at the 0.05 level of significance.

Looking at the given confidence interval, we can see that the lower bound is 1.23 and the upper bound is 2.45.

Since the null value of 2 is within this interval, we cannot reject the null hypothesis at the 0.05 level of significance.

Therefore,

There is not enough evidence to suggest that Ψ(θ) is significantly different from 2 based on the given data and confidence interval.

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An estimate of the number of times the 6 - sided spinner will land on 7 is 20 times

Probability is defined as the:

P (E) = number of times a favorable event occurs / number of events

For six-sided spinner:

Outcomes: 9, 1, 2, 3, 4, and 7

Number = 6

P(7)=1/6

If the event takes place 120 times then,

P (7)= number of times it will land on 7/120

1/6 = number of times it will land on 7/120

Number of times it will land on 7 = 20

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the complete question is

This six-sided spinner is decent.

Liz will complete 120 spins of the spinner.

(b) Calculate the likelihood that the spinner will land on 7 a certain number of times.

The required canoeist's paddling rate in calm water is 3 mph.

Let's denote the canoeist's paddling rate in calm water as "x" mph.

When the canoeist paddles upstream against the current, their effective speed is the difference between their paddling rate and the current's rate, or (x - 3) mph. The distance traveled upstream is also 8 miles.

Using the formula:

distance = rate x time

We can set up two equations based on the distance traveled and the effective speed for each leg of the trip:

Downstream leg: 8 = (x + 3) * t1

Upstream leg: 8 = (x - 3) * t2

Since the total time for the round trip is 2 hours, we know that:

t1 + t2 = 2

Now we can solve for x by substituting t1 = 8/(x+3) and t2 = 8/(x-3) into the equation above:

8/(x+3) + 8/(x-3) = 2

Multiplying both sides by (x+3)(x-3) gives:

8(x-3) + 8(x+3) = 2(x+3)(x-3)

Simplifying this expression gives:

16x = 48

x = 3

Therefore, the canoeist's paddling rate in calm water is 3 mph.

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In this case, the distance between u and z is 2sqrt(14).

To find the distance between two vectors, we can use the formula: distance = ||u - z||

where || || denotes the norm (or magnitude) of the vector. In this case, we have:

u = [0, -5, 2]

z = [-4, -1, 8]

So, the difference between the two vectors is:

u - z = [0 - (-4), -5 - (-1), 2 - 8] = [4, -4, -6]

The norm of this vector is:

||u - z|| = sqrt(4^2 + (-4)^2 + (-6)^2) = sqrt(56) = 2sqrt(14)

Therefore, the distance between u and z is 2sqrt(14).

In summary, the distance between two vectors can be found by taking the norm of their difference vector. In this case, the distance between u and z is 2sqrt(14).

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The coterminal angle of 5π/3

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

Examples of coterminal angles are 30°, -330, 390°. We can get the coterminal angles of a given angle by adding or subtracting 360 from the given angle.

5π/3

π is a symbol in radian that is equivalent to 180° in degrees.

therefore;

5 × 180/3

= 5× 60

= 300°

The coterminal angle of 300°

= 300+360

= 660°

converting it back to radian

= 660/180 = 66/18π

= 33/9 = 11/3π

Therefore the coterminal angle of 5π/3 is 11π/3

learn more about coterminal angles from

https://brainly.com/question/23093580

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