In his suitcase, Jack has 3 shirts, 4 pants, 2 socks (pairs of socks), and 2 shoes (pairs of shoes). How many unique ways can Jack get fully dressed? Show your work and explain.

Answer:

B) The diagonals of the parallelogram are congruent.

Step-by-step explanation:

Since, If the diagonals of a parallelogram are equal in length, then is the parallelogram a rectangle.

For proving this statement.

Suppose PQRS is a parallelogram such that AC = BD,

In triangles ABC and BCD,

AB = CD,   ( opposite sides of parallelogram )

AD = CB,   ( opposite sides of parallelogram )

AC = BD ( given ),

By SSS congruence postulate,

[tex]\triangle ABC\cong \triangle BCD[/tex]

By CPCTC,

[tex]m\angle ABC = m\angle BCD[/tex]

Now, Adjacent angles of a parallelogram are supplementary,

[tex]\implies m\angle ABC + m\angle BCD = 180^{\circ}[/tex]

[tex]\implies m\angle ABC + m\angle ABC = 180^{\circ}[/tex]

[tex]\implies 2 m\angle ABC = 180^{\circ}[/tex]

[tex]\implies m\angle ABC = 90^{\circ}[/tex]

Since, opposite angles of a parallelogram are congruent,

[tex]\implies m\angle ADC = 90^{\circ}[/tex]

Similarly,

We can prove,

[tex]m\angle DAB = m\angle BCD = 90^{\circ}[/tex]

Hence, ABCD is a rectangle.

That is, OPTION B is correct.

Answer:

B

Step-by-step explanation:

I just took it

Answer:

Step-by-step explanation:

You can actually answer this question without graphing the equation, but a graph confirms the answers.

__

A cubic with a positive leading coefficient will be negative and increasing on any interval* whose left end is -∞. Similarly, it will be positive and increasing on any interval whose right end is +∞.

The answer choices tell you ...

The function is increasing up to the first turning point and after the second one.

The function is negative up to the first zero and between the last two.

_____

* We say "any interval" but we mean any interval whose boundary is a zero or turning point, and which properly describes an interval where the function is one of increasing, decreasing, positive, or negative.

To graph the polynomial function f(x) = x^3 - 6x^2 + 3x + 10, we need to find the x-intercepts, y-intercept, and determine the behavior of the graph. Then, using test points, we can determine the intervals where the function is increasing or decreasing, and where it is positive or negative.

To graph the polynomial function f(x) = x3 - 6x2 + 3x + 10, we can start by finding the x-intercepts, y-intercept, and identifying the behavior of the graph. The x-intercepts are the points where the graph intersects the x-axis, and they can be found by setting f(x) = 0 and solving for x using factoring or other methods. The y-intercept is the point where the graph intersects the y-axis, and it can be found by evaluating f(0). Finally, to identify the behavior of the graph, we can examine the signs of the coefficients of the polynomial.

To find the x-intercepts, we set f(x) = 0:

x3 - 6x2 + 3x + 10 = 0

At this point, we can either try factoring the polynomial or use more advanced methods like synthetic division or the rational root theorem. Let's use a graphing calculator to find the approximate x-intercepts. From the calculator, we find that the x-intercepts are approximately x = -1.01, x = 1.25, and x = 6.76.

The y-intercept is the point where the graph intersects the y-axis, which occurs when x = 0. We can find the y-intercept by evaluating f(0):

f(0) = 03 - 6(0)2 + 3(0) + 10 = 10

The y-intercept is (0, 10).

By examining the signs of the coefficients of the polynomial, we can determine the behavior of the graph.

For x3, the coefficient is positive, which means the graph will be “up” on the left side and “down” on the right side. For -6x2, the coefficient is negative, which means the graph will be “down” on the left side and “up” on the right side. The positive coefficient of 3x indicates that the graph will have a “upward” trend on both sides. Finally, the constant term 10 does not have an effect on the overall behavior of the graph.

Based on the information gathered, we can sketch the graph of the polynomial function f(x) = x3 - 6x2 + 3x + 10. By plotting the x-intercepts (-1.01, 0), (1.25, 0), and (6.76, 0) and the y-intercept (0, 10), and considering the behavior of the graph, we can roughly sketch the shape of the graph.

Based on the sketch of the graph, we can now identify the intervals where the function f(x) is increasing or decreasing, and where it is positive or negative. We can use test points within each interval to determine the sign of the function. For example, to determine the sign of f(x) within the interval (-∞, 0.27), we can choose a test point like x = -1. Plugging in this value, we find that f(-1) = -11. Since f(-1) is negative, we can conclude that f(x) is negative within the interval (-∞, 0.27). Similarly, we can choose test points in the other intervals to determine the signs of f(x) and complete the statement.

The graph of the polynomial function f(x) = x3 - 6x2 + 3x + 10 has x-intercepts at approximately x = -1.01, x = 1.25, x = 6.76, and a y-intercept at (0, 10). The graph has a certain behavior, with an upward trend on both sides. Using test points, we can determine that f(x) is negative on the intervals (-∞, 0.27) and (3.73, ∞), positive on the intervals (-1, 2) and (5, ∞), and positive on the intervals (-∞, -1) and (2, 5).

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For this case we have that by definition, the equation of a line in the point-slope form is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

m: It is the slope of the line

[tex](x_ {0}, y_ {0})[/tex]: It is a point that belongs to the line

According to the statement we have the following point:

[tex](x_ {0}, y_ {0}): (- 10,8)[/tex]

Substituting we have:

[tex]y-8 = m (x - (- 10))\\y-8 = m (x + 10)[/tex]

Thus, the most appropriate option is option C. Where the slope is[tex]m = -0.2[/tex]

Answer:

Option C

Answer:

  x⁵ +x⁴ +x³ +x² +x +1

Step-by-step explanation:

Your expression matches the pattern with n=6, so fill in that value of n in the quotient the pattern shows:

  [tex]\dfrac{x^6-1}{x-1}=x^5+x^4+x^3+x^2+x+1[/tex]

Answer: 95% confidence interval for the proportion of yellow is (0.125,0.275).

Step-by-step explanation:

Since we have given that

n = 22+22+22+12+15+15=108

x = yellow = 22

So, [tex]\hat{p}=\dfrac{22}{108}=0.20[/tex]

We need to find the 95% confidence interval.

So, z = 1.96

So, Interval would be

[tex]\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.20\pm 1.96\times \sqrt{\dfrac{0.2\times 0.8}{108}}\\\\=0.20\pm 0.075\\\\=(0.20-0.075, 0.20+0.075)\\\\=(0.125, 0.275)[/tex]

Hence, 95% confidence interval for the proportion of yellow is (0.125,0.275).

Answer:

[tex]H_0: p =0.62\\H_a: p\geq 0.62[/tex]

Step-by-step explanation:

Given that a presidential candidate claims that the proportion of college students who are registered to vote in the upcoming election is at least 62% .

Let p be the proportion of college students who are registered to vote in the upcoming election

we have to check the claim whether p is actually greater than or equal to 62%

For this a hypothesis to be done by drawing random samples of large size from the population.

The hypotheses would be the proportion is 0.62 against the alternate that the proportion is greater than or equal to 0.62

[tex]H_0: p =0.62\\H_a: p\geq 0.62[/tex]

(right tailed test at 5% level)

The probability of having 0 typographical errors on an article of 10 pages is approximately 0.8187. The probability of having 2 or more errors is approximately 0.0176.

To find the probability of certain events happening, we can use the Poisson distribution. In this case, the Poisson distribution can be used to model the number of typographical errors on a page. The parameter of the Poisson distribution, lambda (λ), is equal to the expected number of errors on each page, which is 0.2.

(a) To find the probability of 0 errors on an article of 10 pages, we can use the Poisson distribution with λ = 0.2 and x = 0. We can plug these values into the formula:

P(X = x) = (e^-λ * λ^x) / x!

So for (a), the probability is:

P(X = 0) = (e^-0.2 * 0.2^0) / 0! = e^-0.2 ≈ 0.8187

(b) To find the probability of 2 or more errors on an article of 10 pages, we can calculate the complement of the probability of 0 or 1 errors. The complement is 1 minus the sum of the probabilities of 0 and 1 errors:

P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) ≈ 1 - 0.8187 - (e^-0.2 * 0.2^1) / 1! ≈ 1 - 0.8187 - 0.1637 ≈ 0.0176

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Using the Poisson distribution with λ = 0.2, we find the probability of 0 errors on a page and 2 or more errors in a 10-page article, offering insightful predictions.

The given situation involves a Poisson distribution, as it deals with the number of events (typographical errors) occurring in a fixed interval of time or space. The expected number of errors per page is λ = 0.2, and the total number of pages is 10.

(a) To find the probability of 0 errors on a page, we use the Poisson probability mass function:

P(X = k) = (e^(-λ) * λ^k) / k!

For k = 0:

P(X = 0) = (e^(-0.2) * 0.2^0) / 0!

Solving this gives the probability of having 0 errors on a single page.

(b) To find the probability of 2 or more errors, we sum the probabilities for k = 2, 3, ..., up to the total number of pages (10):

P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)

This accounts for the complement probability that there are 0 or 1 errors, leaving us with the probability of 2 or more errors on at least one page.

In summary, the Poisson distribution helps model the likelihood of different numbers of typographical errors on a page, providing a useful tool for analyzing such scenarios.

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Chain rule when it's one function inside another.

d/dx f(g(x)) = f’(g(x))*g’(x)

Product rule when two functions are multiplied side by side.

d/dx f(x)g(x) = f’(x)g(x) + f(x)g’(x)

Final answer:

The chain rule is used when you have a composite function, while the product rule is used when you have a product of two functions.

Explanation:

The chain rule and product rule are both rules used in calculus to differentiate functions.

The chain rule is used when you have a composite function, where one function is inside another function. To differentiate a composite function, you multiply the derivative of the outer function by the derivative of the inner function.

For example, if you have y = f(g(x)), where f(x) and g(x) are functions, the chain rule states that dy/dx = f'(g(x)) * g'(x).

The product rule is used when you have a product of two functions. To differentiate a product, you take the derivative of the first function times the second function, plus the first function times the derivative of the second function.

For example, if you have y = f(x) * g(x), the product rule states that dy/dx = f'(x) * g(x) + f(x) * g'(x).

Answer:

420 ft

Step-by-step explanation:

The given equation of a parabola is

[tex]y=630[1-\left(\frac{x}{290}\right)^{2}][/tex]

An arch is 630 ft high and has 580=ft base.

Find zeroes of the given function.

[tex]y=0[/tex]

[tex]630[1-\left(\frac{x}{290}\right)^{2}]=0[/tex]

[tex]1-\left(\frac{x}{290}\right)^{2}=0[/tex]

[tex]\left(\frac{x}{290}\right)^{2}=1[/tex]

[tex]\frac{x}{290}=\pm 1[/tex]

[tex]x=\pm 290[/tex]

It means function is above the ground from -290 to 290.

Formula for the average height:

[tex]\text{Average height}=\dfrac{1}{b-a}\int\limits^b_a f(x) dx[/tex]

where, a is lower limit and b is upper limit.

For the given problem a=-290 and b=290.

The average height of the arch is

[tex]\text{Average height}=\dfrac{1}{290-(-290)}\int\limits^{290}_{-290} 630[1-\left(\frac{x}{290}\right)^{2}]dx[/tex]

[tex]\text{Average height}=\dfrac{630}{580}[\int\limits^{290}_{-290} 1dx -\int\limits^{290}_{-290} \left(\frac{x}{290}\right)^{2}dx][/tex]

[tex]\text{Average height}=\dfrac{63}{58}[[x]^{290}_{-290}-\frac{1}{84100}\left[\frac{x^3}{3}\right]^{290}_{-290}][/tex]

Substitute the limits.

[tex]\text{Average height}=\dfrac{63}{58}\left(580-\frac{580}{3}\right)[/tex]

[tex]\text{Average height}=\dfrac{63}{58}(\dfrac{1160}{3})[/tex]

[tex]\text{Average height}=420[/tex]

Therefore, the average height of the arch is 420 ft above the ground.

The average height of the arch above the ground is approximately  420 feet.

To find the average height of the arch, we need to find the average value of this function over the interval x=0 to x=580 (the base of the arch).

[tex]\[ \text{Average height} = \frac{1}{580 - 0} \int_{0}^{580} 630 \left(1 - \left(\frac{x}{290}\right)^2\right) \, dx \]\[ = \frac{630}{580} \int_{0}^{580} \left(1 - \left(\frac{x}{290}\right)^2\right) \, dx \]\[ = \frac{630}{580} \left(x - \frac{1}{3} \cdot \frac{x^3}{290^2}\right) \Bigg|_{0}^{580} \]\[ = \frac{630}{580} \left(580 - \frac{1}{3} \cdot \frac{580^3}{290^2} - 0\right) \][/tex]

[tex]\[ = \frac{630}{580} \left(580 - \frac{1}{3} \cdot \frac{580^3}{290^2}\right) \]\[ = \frac{630}{580} \left(580 - \frac{1}{3} \cdot \frac{580^3}{290^2}\right) \]\[ \approx \frac{630}{580} \times 420 \]\[ \approx 420 \text{ ft} \][/tex]

Answer:

75.5 pounds

Step-by-step explanation:

He needs 200

He already has 11.25

He needs:

200 - 11.25 = $188.75 more

1 pound of candy costs 2.50, so x pounds would cost 2.50x

This would need to equal 188.75 (the amount he needs to break even). We can write an equation in x and solve:

[tex]2.50x=188.75\\x=\frac{188.75}{2.50}\\x=75.5[/tex]

James needs 75.5 pounds more to break even

Final answer:

James needs to sell an additional 75.5 pounds of candy to break even, after taking into account the $11.25 he has already earned towards his $200 goal by dividing the remaining amount needed ($188.75) by the price per pound of candy ($2.50).

Explanation:

James is selling candy at a local marketplace and needs to earn at least $200 to break even. He has already earned $11.25. The price of one pound of candy is $2.50. To find out how many more pounds of candy, x, he has to sell to break even, we need to calculate the remaining amount he needs to earn and divide it by the price per pound of candy.

First, subtract the amount already earned from the total needed to break even:

$200 - $11.25 = $188.75

Then, divide this amount by the price per pound of candy to find out how many more pounds he needs to sell:

$188.75 / $2.50 = 75.5

Therefore, James needs to sell an additional 75.5 pounds of candy to break even.

Answer:

4%

Step-by-step explanation:

1. Convert the problem to an equation using the percentage formula: P% * X = Y.

2. P is 10%, X is 150, so the equation is 10% * 150 = Y.

3. Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.

Answer:

416025

Step-by-step explanation:

For confidence interval of 99%, the range is (0.005, 0.995). Using a z-table, the z-score for 0.995 is 2.58.

Margin of error = 0.2% = 0.002.

Proportion is unknown. So, worse case proportion is 50%. p = 50% = 0.5.

\\ [tex]n = \left(\frac{\texttt{z-score}}{\texttt{margin of error}} \right )^2\cdot p\cdot (1-p) \\ = \left(\frac{2.58}{0.002} \right )^2\cdot 0.5\cdot (1-0.5)=416025[/tex]

So, sample size required is 416025.

Final answer:

The value of a car worth $18,500 that loses 10.3% annually decreases by approximately $158.8 per month.

Explanation:

To find the approximate monthly decrease in value of a car worth $18,500 that loses 10.3% of its value every year, we first calculate the annual decrease and then divide by 12 to get the monthly decrease.

The annual decrease is calculated as 10.3% of $18,500, which is:

0.103 imes $18,500 = $1,905.50 per year.

To find the monthly decrease, we divide the annual decrease by 12:

$1,905.50 \/ 12 \\approx $158.79 per month.

Therefore, the car's value decreases approximately $158.8 per month.

Answer:

$6000

Step-by-step explanation:

Profit from the investment of $8000 in fund A

= 10% × $8000

= $800

Let the amount invested in fund B be $Y

Profit from the investment of $Y in fund B

= 3% × $Y

= $0.03Y

if both funds together returned a 7% profit

800 + 0.03Y = 7% (8000 + Y)

800 + 0.03Y = 560 + 0.07Y

Collect like terms

0.07Y - 0.03Y = 800 - 560

0.04Y = 240

Y = 240/0.04

Y = 6000

Amount invested in Fund B is $6000

Answer:

I got 469.8 kilowatt-hours. I got this by taking the total of Frank's bill, which was $85.78, and subtracting the flat monthly fee of $20.00. I did this because I need to find out the number of kilowatt-hours Frank used. Then, I divided $65.78 by $0.14 since that is the price per kilowatt-hour and got about 469.8 kilowatt-hours used by Frank.

The power utilised by frank in the month of march is 470 kilowatts - per hour.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Franks's electric bill for the month of March was $85.78. The electric company charged a flat monthly fee of $20.00 for service plus $0.14 per kilowatt-hour of electricity used.

The equation will be written as,

B = 20 + 0.14K

85.78 = 20 + 0.14k

k = ( 80.78 - 20 ) / 0.14

K = 65.78 / 0.14

K = 470 Kilowatt-hour

Therefore, the power utilised by frank in the month of march is 470 kilowatts - per hour.

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Answer:

144

Step-by-step explanation:

We simply need to input these values into the equation.

S = (ab + ac + bc)

Where: a = 12 b = 6 and c = 4

S = ( 12 × 6 + 12 × 4 + 6 × 4)

S = 72 + 48 + 24 = 144 inch^2

Answer:

the correct answer is c (288 in. squared)

Step-by-step explanation:

i got i correct on the quiz;)

hope this helps you out

(also please let me know if i am wrong)

Answer:

The margin of error is multiplied by [tex]\sqrt{2}[/tex]

Step-by-step explanation:

margin of error (ME) from the mean can be calculated using the formula

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

Since margin of error is proportional with inverse of [tex]\sqrt{N}[/tex],

if we cut the sample size in half, the margin of error is multiplied by [tex]\sqrt{2}[/tex].

Cutting the sample size in half increases the margin of error. The new margin of error will be approximately 1.414 times larger than the original margin of error. Essentially, this effect multiplies the margin of error by 2.

If you cut the sample size in half, the margin of error will increase. The margin of error is inversely proportional to the square root of the sample size. Specifically, the margin of error is multiplied by the square root of the ratio of the original sample size to the new sample size.

Mathematically, if the original sample size is N and the new sample size is N/2, the margin of error (MOE) changes as follows:

Since √(N/2) = √(N) / √(2), the new margin of error will be:

New MOE = Original MOE × √(2) approximately equal to Original MOE × 1.414.

Therefore, cutting the sample size in half multiplies the margin of error by 1.414, roughly 2 times.

Complete Question:

All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? ME= 2·5/√(n) . The margin of error is multiplied by √(0.5)· The margin of error is multiplied by √(2)· The margin of error is multiplied by 0.5. The margin of error is multiplied by 2.

Calculate the mean and standard deviation for the binomial distribution, adjust for continuity correction, find the z-score, and use the standard normal distribution to estimate the probability of scoring at least 10 correct out of 47 purely guessed multiple-choice questions.

To estimate the probability of a student guessing and scoring at least 10 correct answers out of 47 multiple-choice questions using normal approximation to binomial distribution, we start by finding the mean ( extmu) and standard deviation ( extsigma) of the binomial distribution. Since each question has five options, the probability of guessing a question correctly (p) is 1/5, and the probability of guessing incorrectly (q) is 4/5.

The expected number of correct answers (mean) is  extmu = np = 47(1/5) = 9.4, and the variance ( extsigma^2) is npq = 47(1/5)(4/5) = 7.52. So, the standard deviation is  extsigma =  extsqrt{7.52}.

To apply the continuity correction, we adjust the score of 10 down by 0.5, giving us a z-score. The z-score is calculated by (X -  extmu)/ extsigma, where X is the adjusted score. Finally, we use the standard normal distribution to find the probability associated with this z-score, which will yield the likelihood of the student scoring at least 10 correct answers.

Answer:

Step-by-step explanation:

12) A(x, 5) and B(-4,3)

slope = -1

We want to determine the value of x so that the line AB is parallel to another line whose slope is given as -1

Slope, m is expressed as change in y divided by change in x. This means

Slope = (y2 - y1)/(x2 - x1)

From the information given

y2= 3

y1 = 5

x2 = -4

x1 = x

Slope = (3-5) / (-4-x) = -2/-4-x

Recall, if two lines are parallel, it means that their slopes are equal. Since the slope of the parallel line is -1, therefore

-2/-4-x = -1

-2 = -1(-4-x)

-2 = 4 + x

x = -2 - 4 = - 6

x = -6

13) R(3, -5) and S(1, x)

slope = -2

We want to determine the value of x so that the line RS is parallel to another line whose slope is given as -2

Slope = (y2 - y1)/(x2 - x1)

From the information given

y2= x

y1 = -5

x2 = 1

x1 = 3

Slope = (x - -5) / (1 - 3) = (x+5)/-2

Since the slope of the parallel line is -2, therefore

(x+5)/-2 = -2

x + 5 = -2×-2

x + 5 = 4

x = 4 - 5 = - 1

Answer: it will take him 4.5 hours to cover same distance

Step-by-step explanation:

Marathon runner covered the whole distance in 4 hours running at a constant speed of 8.1 km per hour.

Speed = distance / time

Distance = speed×time

Therefore, distance covered by the marathon runner in in 4 hours, running at a speed of 8.1 km per hour is

8.1 × 4 = 32.4 kilometers

if he decreased the speed to 7.2 km per hour, the distance remains 32.4 kilometers. Therefore,

At 7.2 km per hour, the time it would take him to cover the same distance would be

Distance/ speed = 32.4/7.2 = 4.5 hours

Answer:

Your answer id D.

Step-by-step explanation:

PLEASE MARK BRAINLIEST!!!

Answer:

322.21 feet

Step-by-step explanation:

Flying rate = 6 ft/s

Angle of depression from his balloon to a friend's car= 35 °

One and half minutes later, he observed the angle of depression to be 39°

Time = 1 mins 1/2 seconds

= 3/2 mins

= 3/2 * 60

= 3*30

= 90 secs

Speed = distance /time

Distance = speed * time

= 6*90

= 540 ft

The angle on the ground = 180° - 35° - 39°

= 180° - 74°

= 106°

Let the distance between him and his friend be x

Using sine rule

x/sin 35 = 540/sin 106

x = (540sin 35) / sin 106

x = 322.21ft

Answer:

Step-by-step explanation:

y = (-1/4)x - 4 has a y-intercept of (0, -4).  Place a dark dot at (0, -4).  

Now we use the info from the slope, -1/4:

Starting with your pencil point on the dot (0, -4), move the pencil point 4 units to the right and then 1 unit down.  You will now be at (4, -5).  Place a dark dot there.  

Then draw a straight, solid line through (0, -4) and (4, -5).

Answer:

In a one-way ANOVA, the [tex]SS_{within}[/tex] is calculated by taking the squared difference between each person and their specific groups mean, while the [tex]SS_{between}[/tex] is calculated by taking the squared difference between each group and the grand mean.

Step-by-step explanation:

The one-way analysis of variance (ANOVA) is used "to determine whether there are any statistically significant differences between the means of two or more independent groups".

The sum of squares is the sum of the square of variation, where variation is defined as the spread between each individual value and the mean.

If we assume that we have p groups and each gtoup have a size [tex]n_j[/tex] then we have different sources of variation, the formulas related to the sum of squares are:

[tex]SS_{total}=\sum_{j=1}^{p} \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]

A measure of total variation.

[tex]SS_{between}=\sum_{j=1}^{p} n_j (\bar x_{j}-\bar x)^2 [/tex]

A measure of variation between each group and the grand mean.

[tex]SS_{within}=\sum_{j=1}^{p} \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]

A measure of variation between each person and their specific groups mean.

Answer:

x=2

Step-by-step explanation:

9-10x=2x+1-8x

9-10x=1-6x

8=4x

x=2

Combine like terms in the equation 9 − 10x = 2x + 1 − 8x to simplify it to 9 − 10x = −6x + 1. Rearranging the equation to -4x = -8 and dividing by -4, we find that x = 2.

The solution for x in the equation 9 − 10x = 2x + 1 − 8x can be found by first combining like terms on both sides of the equation.

On both the left and right side, the terms involving x are −10x and 2x − 8x respectively. After combining, the equation simplifies to 9 − 10x = −6x + 1.

Then, we can solve for x by shifting terms around. Getting all x-terms on one side and constant terms on the other side, we get -10x + 6x = 1 - 9. This simplifies to -4x = -8.

Finally, dividing the equation by -4 which is the coefficient of x, we obtain the solution x = 2.

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Answer:

(a)€2048

(b)€4095

Step-by-step explanation:

So the amount of money we would save at nth month is

[tex]2^{n-1}[/tex] where n = 1, 2, 3, 4, ...

At the 12th month, meaning n = 12, we would save

[tex]2^{12-1}[/tex] = €2048 for that month

The total amount we would save in a year is

1 + 2 + 4 + 8 + 16 + ... + 2048

[tex]2^{n} - 1 = 2^{12} - 1 [/tex] = €4095

Answer: population; independently

Step-by-step explanation:

A random sample selected from an infinite population is a sample selected such that each element selected comes from the same *population* and each element is selected *independently*.

Each element in a random sample is selected independently and comes from the same population, with the principle goal of achieving representation and independence in sample selection.

A random sample selected from an infinite population is a sample selected such that each element selected comes from the same population and each element is selected independently. The crux of random sampling theory is ensuring each member of the population has an equal chance of being selected, maintaining the independence of each selection. For example, if a student wanted to make a study group out of a class of 31 students, she could write each student's name on a separate piece of paper, put all the names in a hat, and pick out three without looking. This is a classic case of simple random sampling, each selection being representative and independent.

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Answer:

65.56°

Step-by-step explanation:

We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them

That is let p and q be any two vectors and A be the angle between them

So, p·q=|p|*|q|*cosA

⇒[tex]cosA=\frac{u.v}{|u||v|}[/tex]

Given u=-8i-3j and v=-8i+8j

[tex]|u|=\sqrt{(-8)^{2}+ (-3)^{2}} =8.544[/tex]

[tex]|v|=\sqrt{(-8)^{2}+ (8)^{2}} =11.3137[/tex]

let A be angle before u and v

therefore, [tex]cosA=\frac{u.v}{|u||v|}=\frac{(-8)*(-8)+(-3)*(8)}{8.544*11.3137} =\frac{40}{96.664}[/tex]

⇒[tex]A=arccos(\frac{40}{96.664} )=arccos(0.4138 )=65.56[/tex]

Therefore angle between u and v is 65.56°

Answer:

66% have graduated within five years.

Step-by-step explanation:

It is given that 70% of freshmen went to public schools. Then the rest 30% i.e.,  [tex]$ \frac{30}{100} = 0.3 $[/tex] should have gone to other schools.

Now, the number the freshmen in public schools is considered as 100% or 1.

60% of the freshmen from public schools have graduated means out of the total freshmen from public schools, 60% of them have graduated. That is why it is denoted as 0.6 and those not graduated as 0.4.

Note that 60% of total students have graduated.

Let us assume there were 100 students initially. Then 70 students went to public school. Number of students graduated = 60%

[tex]$ \implies \frac{60}{100} \times 70  = 42 $[/tex]

That is 42 students have passed from public school.

Now, the ones in other schools:

80% of them have graduated in other schools. That means out of total students 80% of them have graduated.

That means [tex]$ \frac{80}{100} \times 30 = 24 $[/tex]

24 students from other schools have passed.

Therefore, totally 66 students have passed. i.e., 66 percent have passed.

Answer:

$792.50

Step-by-step explanation:

As the mortgage rate is 3.75% APR , One has to pay 3.75% of the amount of home in a year as Interest .

Amount of home = $253,600.00

One year interest one has to pay in a year  = [tex]\frac{3.75}{100}[/tex]×253,600

                                                        = $9510.

So, In one month , he has to pay amount $[tex]\frac{9510}{12}[/tex] .

                                                                   = $792.5.