a permutation is any arrangement of r objects selected from n possible objects. which formula is used to calculate the number of permutations?

Answer:

336in^2

Step-by-step explanation:

6 x 4 x 14

"The buetiful thing about learning is that no one can take it away from you" :)

Answer: 336

Step-by-step explanation: I just multiplied them all

So the total area of the figure is 171 square meters.

Area is a measure of the size of a two-dimensional surface or region. It is usually expressed in square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). The concept of area is used in mathematics, geometry, and various fields such as architecture, engineering, and physics.

Here,

To find the total area of the figure, we need to find the areas of the rectangle and the triangle, and then add them together. The area of the rectangle is:

A = length x width

= 12 m x 9 m

= 108 m²

The area of the triangle is:

A = (1/2) x base x height

= (1/2) x 9 m x 14 m

= 63 m²

The base of the triangle is the same as the width of the rectangle, since they are adjacent and parallel. The other side of the triangle is the hypotenuse, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the legs of the right triangle, and c is the hypotenuse. In this case, we can use a = 9 m (the width of the rectangle) and b = 5 m (the distance between the rectangle and the triangle):

9² + 5² = c²

81 + 25 = c²

106 = c²

c ≈ 10.3 m

Therefore, the total area of the figure is:

total area = area of rectangle + area of triangle

total area = 108 m² + 63 m²

total area = 171 m²

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Answer:

To find the equation of the linear function, we need to first determine its slope, which is the rate of change of the function with respect to its input. We can use the slope formula: slope = (change in y) / (change in x) Using the two given points, we have: slope = (30 - 24) / (6 - 4) = 3 Now that we know the slope, we can use the point-slope form of the equation of a line to find the equation of the function: y - y1 = m(x - x1) where m is the slope, and (x1, y1) is one of the given points. Let's use the point (4, 24): y - 24 = 3(x - 4) Expanding and simplifying, we get: y = 3x -

Now, we can construct the confidence interval: [tex]0.4 ± 1.96 * 0.0157 ≈ 0.4 ± 0.0308. [/tex]The resulting interval is 0.3692 to 0.4308, which is closest to option e. 0.374 to 0.426

5. To calculate the sample proportion, divide the number of consumers who shop online at least once a week (121) by the total number of consumers surveyed (484). So, the sample proportion is[tex] 121/484 = 0.25.[/tex] The correct answer is c. 0.25.

6. A sample proportion is a statistic because it is a measure derived from a sample of the population. The correct answer is a. statistic.

7. To construct a 95% confidence interval for the proportion of OSU undergraduates with full-time jobs, we first find the sample proportion:[tex] 368/920 = 0.4[/tex].

Next, we find the standard error (SE) for the sample proportion: SE = sqrt(0.4 * (1 - 0.4) / 920) ≈ 0.0157. For a 95% confidence interval, the critical value (z-score) is approximately 1.96.

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Given statement "f the null hypothesis is correct, the probability of getting a sample mean greater than $189,500 is .0668" is true. Because, It's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.

The null hypothesis is a general statement that there is no significant effect or difference between the considered groups or variables.

In this case, the null hypothesis would be that the true mean valuation of homes is equal to or less than $189,500.
The probability of 0.0668, mentioned in the question, represents the likelihood of getting a sample mean greater than $189,500 if the null hypothesis is true.

In other words, it's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.

This probability (0.0668) is also known as the p-value.

The p-value helps to determine the significance of the results.

If the p-value is less than a predetermined significance level (usually 0.05), the null hypothesis is rejected in favor of the alternative hypothesis.
In this case, the p-value of 0.0668 is higher than the common significance level of 0.05.

We cannot reject the null hypothesis, meaning the probability of getting a sample mean greater than $189,500 is indeed 0.0668 if the null hypothesis is correct

Hence, the statement is true.
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Therefore, the expression that can be used to find the probability that a boy will be chosen, and the arrow will land on "Free assignment" is 2/13.

Which expression can be used to find the probability that this week a boy will be?

chosen and the arrow will land on "Free assignment"?

The probability of a boy being chosen is the ratio of the number of boys to the total number of students, which is:

[tex]P(boy) = 12 / (12 + 14) = 12/26 = 6/13[/tex]

The probability of the arrow landing on "Free assignment" is 1/3, since there are 3 equal sectors on the spinner.

To find the probability that both events occur (i.e., a boy is chosen and the arrow lands on "Free assignment"), we multiply the probabilities:

[tex]P(boy and "Free assignment") = P(boy) x P("Free assignment")[/tex]

[tex]P(boy and "Free assignment") = (6/13) x (1/3) = 2/13[/tex]

Therefore, the expression that can be used to find the probability that a boy will be chosen, and the arrow will land on "Free assignment" is 2/13.

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The probability that the large-cap domestic stock fund has a return of at least 17% is approximately 0.2776 or 27.76%.

To calculate the probability that the large-cap domestic stock fund has a return of at least 17%, we need to find the z-score first.

The z-score formula is:

Z = (X - μ) / σ

Where X is the desired return (17%), μ is the mean of 14.4%, and σ is the standard deviation of 4.4%.

Z = (17 - 14.4) / 4.4 = 2.6 / 4.4 ≈ 0.591

Now, using a z-table or calculator, we can find the probability associated with this z-score. The area to the left of the z-score in a standard normal distribution is approximately 0.7224. Since we want the probability of a return of at least 17%, we need to find the area to the right of the z-score.

P(X ≥ 17%) = 1 - P(X < 17%) = 1 - 0.7224 = 0.2776

So, the probability that the large-cap domestic stock fund has a return of at least 17% is approximately 0.2776 or 27.76%.

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Step-by-step explanation:

Look at point A ====>  A'

  x goes from 1 to 4           so X:  x + 3

  y goes from 7 to 3          so Y:   y - 4

The possible unit rate for Josh is 2.91 minutes per mile. However, keep in mind that this is just one possible rate and there could be other values that satisfy the conditions given in the problem.

Unit rate is a rate that is simplified to have a denominator of 1.

In other words, it is a ratio that compares two measurements with one of the measurements set to 1.

For example, if a car travels 100 miles in 2 hours, the unit rate for the car's speed would be 50 miles per hour.

Kody's unit rate can be found by dividing the time taken by the distance covered:

Unit rate = Time / Distance = 80 minutes / 35 miles = 2.29 minutes per mile (rounded to two decimal places).

To find a possible unit rate for Josh, we can use the fact that he rode at a faster rate per mile than Kody. Let's say that Josh's unit rate is x minutes per mile. Since he rode for 102 minutes, we can set up the following equation:

35 miles x (minutes per mile) = 102 minutes

Solving for x, we get:

x = 102 minutes / 35 miles = 2.91 minutes per mile

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Answer:

C.)

Step-by-step explanation:

1.) First find the slope of the perpendicular line. The slope of the perpendicular line is the number that when multiplied by the slope of the initial line, you get -1. The slope of the line is 3/8, and -8/3 * 3/8 is -1, therefore -8/3 is the slope of the new line.
2.) Now, since we have a slope if you look at the options, there is only one option with the slope -8/3, which is option C.).

The appropriate test to compare one sample to another sample to see if one is greater than another in some way is called a "two-sample hypothesis test."

In a two-sample hypothesis test, the null hypothesis states that there is no significant difference between the means of the two samples, while the alternative hypothesis states that there is a significant difference between the means.

The specific type of test used depends on several factors, including the type of data being compared, the sample sizes, and the level of significance desired. Commonly used tests include the t-test, z-test, and ANOVA.

It is important to choose the appropriate test for the data being analyzed to ensure accurate results and conclusions.

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Answer:

C. ∠ZXY and D. YX

Step-by-step explanation:

C. ∠ZXY

because the middle letter is always the angle or the turning point of an angle and also it is in order based on the diagram. The angle won't change even if you look at it on a different point of view or if the diagram was flipped.

D. YX

because the line YX is a true statement because XY or YX is on the same line that goes on and on. You can tell because there's arrows on the end of the line.

Answer:

True

Step-by-step explanation:

If you took a true if-then statement, inserted not in each clause and reversed the clauses you will have created the contrapositive. The contrapositive of an if-then statement has the same true value as the original statement.

Statement:

If p, then q.

Contrapositive:

If not q, then not p

If the statement is true, then the contrapositive is also true.

Answer:

The first step is to convert the annual interest rate to a monthly rate. We divide 14% by 12 months to get a monthly interest rate of 1.17%.

Next, we need to calculate the total number of months for the loan. Since the loan is for 2 years, or 24 months, we will make 24 payments.

To calculate the interest paid, we can use the formula:

I = P[(1 + r)^n - 1]

where:

I = interest paid

P = principal (amount borrowed) = $1200

r = monthly interest rate = 0.0117

n = total number of compounding periods = 24

Plugging in these values, we get:

I = 1200[(1 + 0.0117)^24 - 1]

I = $357.72

Therefore, the interest paid is $358.

Hope This Helps!

Answer:

They are 50 and 20 years old.

Step-by-step explanation:

5 years ago jack was 45 and his son was 15, which makes jack 3 times older than his son and has a 30 year difference.

The total number of hours Erica works in a week when she babysits for 8 hours can be expressed using the following equation: Total Hours Worked = 8 x Number of Babysitting Days per Week In this case, since Erica babysits for 8 hours.

To calculate the total number of hours Erica works in a week, we need to consider the number of days she babysits and the number of hours she works per day. Erica babysits for 8 hours per day. Therefore, we can use the equation

Total Hours Worked = Number of Days x Hours per Day

To calculate the total number of hours she works in a week. We can substitute these values into the equation:

Total Hours Worked = 1 x 8 = 8 hours.

This means that Erica works a total of 8 hours per week when she babysits for 8 hours.

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If we know that f(-4) = 0, we can say that:

x + 4 is a factor of the function f(x).

This is because when we substitute x = -4 into the function, we get:

f(-4) = (-4)^4 + 2(-4)^3 - 9(-4)^2 - 2(-4) + 6 = 0

This means that (x + 4) is one of the factors of the function.

Now, we can use polynomial division or synthetic division to find the other factors. If we divide the function f(x) by (x + 4), we obtain:

           x^3 - 2x^2 - 17x + 3

We can use the Factor theorem on this cubic function f(x) = x^3 - 2x^2 - 17x + 3.

If we try to substitute a = 1 we find that f(1) = -15 which is not zero. If we try to substitute a = -1, we find that f(-1) = 23 which is not zero.

Now we can solve as follows:

Let x = t - 2/3. After substitution we get a cubic equation.

t^3 -25/3 t - 85/27 = 0

We can find one root of this cubic by rational root theorem which is t = 5 or t = -17/3.

Now, we can use synthetic division again to divide f(x) by the binomial (x - 5). This gives us:

        (x - 5)(x^2 + 3x - 1)

Therefore, the complete factorization of f(x) is:

f(x) = (x + 4)(x - 5)(x^2 + 3x - 1)

Therefore, the zeros of the function are:

x = -4, 5, (-3 ± √13)/2

Thus, these are the zeros of the polynomial.

The improper fraction [(n² + 4)] / [(n + 5)] is not in simplest form for 2024 integers between 1 and 2023 inclusive.

We notice that the numerator of the fraction is always of the form n² + 4, which is always greater than or equal to 4 for any n. Also, the denominator is always positive, since n + 5 is always positive for n ≥ -5.

For the fraction to not be in simplest form, the greatest common divisor of the numerator and denominator must be greater than 1. Let's try to find the factors of the numerator:

n² + 4 = (n + 2i)(n - 2i)

where i is the imaginary unit. Therefore, the fraction [(n² + 4)] / [(n + 5)] is not in simplest form if and only if n + 5 is divisible by one of the factors (n + 2i) or (n - 2i), for some integer i ≠ 0.

Since n + 2i and n - 2i differ by 4i, they are either both odd or both even. Therefore, for n + 5 to be divisible by either of them, n must have the same parity (evenness or oddness) as i. If n is even, then n + 2i and n - 2i are also even, and their greatest common divisor is even. If n is odd, then n + 2i and n - 2i are also odd, and their greatest common divisor is odd.

Therefore, for each even n between 1 and 2023 inclusive, there are no factors (n + 2i) or (n - 2i) that divide n + 5, since they would have to be even and n + 5 is odd. For each odd n between 1 and 2023 inclusive, there are two factors (n + 2i) and (n - 2i) that divide n + 5, namely i and -i. Therefore, the improper fraction [(n² + 4)] / [(n + 5)] is not in simplest form for exactly 2 times the number of odd integers between 1 and 2023 inclusive.

There are (2023 - 1) / 2 + 1 = 1012 odd integers between 1 and 2023 inclusive, so the answer is 2 * 1012 = 2024. Therefore, the improper fraction [(n² + 4)] / [(n + 5)] is not in simplest form for 2024 integers between 1 and 2023 inclusive.

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The value of x in given figure is a whole number that is x = 6.6

When two tangent segment are drawn from an outside point to a circle, the sum of the dimensions of the first tangent segment and its exterior tangent segment equals the sum of the dimensions of the other secant segments and its exterior secant segment.

Given the image and the labelled measurement of two secant segments outside the predetermined circle that have a similar endpoint. We are required to determine what x's value is.

With these measurements, we can use the secant-secant theorem to solve for the value of x as we refer to and analyse the figure. We will therefore have this theorem applied.

(5) [(5) + ( x+4)] = (6) [6 + 7]

(5) [5+x+4] = (6) [13}

5 [9 + x] = 78

45 + 5x = 78

5x = 33

x = 6.6

Therefore the value of x is 6.6

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The graph represents a proportional relationship is a false statement.

Based on the graph, it appears to represent a linear relationship, where there is a constant rate of change between the two variables. However, it is not possible to determine if it represents a proportional relationship without knowing the specific context of the data being plotted.

If the variables represented in the graph have a proportional relationship, then the graph should be a straight line that passes through the origin (0,0). This is because in a proportional relationship, as one variable increases, the other variable increases or decreases in proportion to the change in the first variable. Therefore, the ratio between the two variables should remain constant.

If the graph in this example does not pass through the origin, then it is likely that the relationship between the variables is not proportional.

As sufficient data is not provided so this statement is false.

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to find two values for x that make an inequality true, we can choose values that satisfy the inequality, while to find two values that make it false, we can choose values that do not satisfy the inequality.

How to solve inequality?

A. x+3>70

To make this inequality true, we can choose x = 67 or x = 100. For x = 67, we have 67 + 3 > 70, and for x = 100, we have 100 + 3 > 70. To make the inequality false, we can choose x = 68 or x = 69. For x = 68, we have 68 + 3 < 70, and for x = 69, we have 69 + 3 < 70.

B. x+3<70

To make this inequality true, we can choose x = 0 or x = 1. For x = 0, we have 0 + 3 < 70, and for x = 1, we have 1 + 3 < 70. To make the inequality false, we can choose x = 67 or x = 100. For x = 67, we have 67 + 3 > 70, and for x = 100, we have 100 + 3 > 70.

C. -5x<2

To make this inequality true, we can choose x = 0 or x = -1/5. For x = 0, we have -5(0) < 2, and for x = -1/5, we have -5(-1/5) < 2. To make the inequality false, we can choose x = -2 or x = 1/5. For x = -2, we have -5(-2) > 2, and for x = 1/5, we have -5(1/5) > 2.

D. 5x<2

To make this inequality true, we can choose x = 0 or x = 1/5. For x = 0, we have 5(0) < 2, and for x = 1/5, we have 5(1/5) < 2. To make the inequality false, we can choose x = -2 or x = -1/5. For x = -2, we have 5(-2) > 2, and for x = -1/5, we have 5(-1/5) > 2.

In summary, to find two values for x that make an inequality true, we can choose values that satisfy the inequality, while to find two values that make it false, we can choose values that do not satisfy the inequality.

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We can conclude that 10% of the football players complete their degree in five years.

How to investigate the university's claim?

To investigate the university's claim, we can set up a hypothesis test.

Null hypothesis: The proportion of football players who complete their degree in five years is 0.9.

Alternative hypothesis: The proportion of football players who complete their degree in five years is less than 0.9.

We can use a one-tailed binomial test to test this hypothesis. The test statistic is the number of football players who received their degree in our sample of 20. Under the null hypothesis, this follows a binomial distribution with n=20 and p=0.9.

We can calculate the probability of observing 14 or fewer football players receiving their degree if the true proportion is 0.9:

P(X ≤ 14) = Σ P(X = i) for i = 0 to 14

= binom.cdf(14, n=20, p=0.9)

≈ 0.001

This means that the probability of observing 14 or fewer football players receiving their degree in a random sample of 20, if the true proportion is 0.9, is only 0.001.

If we use a significance level of 0.05, this means we reject the null hypothesis if the p-value is less than 0.05. Since our p-value is much smaller than 0.05, we can reject the null hypothesis and conclude that the proportion of football players who complete their degree in five years is less than 0.9.

Therefore, based on the given sample, we cannot conclude that 90% of the football players complete their degree in five years.

So, we can conclude that 10% of the football players complete their degree in five years.

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We can conclude that 10% of the football players complete their degree in five years.

To investigate the university's claim, we can set up a hypothesis test.

Null hypothesis: The proportion of football players who complete their degree in five years is 0.9.

Alternative hypothesis: The proportion of football players who complete their degree in five years is less than 0.9.

We can use a one-tailed binomial test to test this hypothesis. The test statistic is the number of football players who received their degree in our sample of 20. Under the null hypothesis, this follows a binomial distribution with n=20 and p=0.9.

We can calculate the probability of observing 14 or fewer football players receiving their degree if the true proportion is 0.9:

P(X ≤ 14) = Σ P(X = i) for i = 0 to 14

= binom.cdf(14, n=20, p=0.9)

≈ 0.001

This means that the probability of observing 14 or fewer football players receiving their degree in a random sample of 20, if the true proportion is 0.9, is only 0.001.

If we use a significance level of 0.05, this means we reject the null hypothesis if the p-value is less than 0.05. Since our p-value is much smaller than 0.05, we can reject the null hypothesis and conclude that the proportion of football players who complete their degree in five years is less than 0.9.

Therefore, based on the given sample, we cannot conclude that 90% of the football players complete their degree in five years.

So, we can conclude that 10% of the football players complete their degree in five years.

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The quadratic function graphed is defined as follows:

C) y = x² - x - 2.

The factored format of a quadratic function is given as follows:

y = a(x - x*)(x - x**)

In which the parameters are given as follows:

From the graph, we have that it crosses the x-axis at x = -1 and x = 2, hence the x-intercepts are given as follows:

x* = -1, x** = 2.

Hence:

y = a(x + 1)(x - 2)

y = a(x² - x - 2).

When x = 0, y = -2, hence the leading coefficient a is given as follows:

-2a = -2

a = 1.

Thus the equation is:

y = x² - x - 2.

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The required probability of the candies in the bag having width between 1200 and 1225 is given by 16.67%.

The range of the number of skittles in the bag is 1150 to 1300 candies and is uniformly distributed.

This implies that the probability density function is a horizontal line over this interval.

The width of the interval we are interested in is 1225 - 1200 = 25 candies.

The total width of the interval is 1300 - 1150 = 150 candies.

The probability that the bag contains between 1200 and 1225 candies is equals to,

= ( Width of the required interval ) / (Total width of the interval )

= 25 / 150

= 0.1667

This means that the probability is 16.67% accurate to two decimal places.

Therefore, the probability of the bag contains candies between 1200 and 1225 is equal to 16.67%.

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Answer:

The area of rectangle is Length × Breadth

Step-by-step explanation:

You have already learnt that perimeters of plane figures and areas of squares and rectangles. Perimeter is the distance around a closed figure while area is the part of plane or reason occupied by the closed figure.

[tex] \sf \: Squares \: and \: Rectangles[/tex]

Ananya and samira made pictures. Ananya made her picture on a rectangular sheet of length 60 cm and breadth 20 cm while samira made hers on a rectangular seat of length 40 cm and breadth 35 cm. Both these pictures have to be separately framed and laminated.

Who has to pay more for farming is the cost of farming is $3.00 per cm?

If the cost of lamination is $2.00 per cm², who has to pay more for lamination?

For finding the cost of farming, we need to find perimeter and then multiply it by the rate for farming. For finding the cost of lamination we need to find area and then multiply it by the rate of lamination.

Find the area of the rectangle whose Length is 4 cm and breadth/width is 6 cm .

Answer:

The area of the rectangle is 24 cm²

Step-by-step explanation:

Length of rectangle = 4 cm

Breadth of rectangle = 6 cm

[tex] \bf \: Formula \: used[/tex]

[tex] \sf \: Area_ { \{Rectangle \}} = Length × Breadth[/tex]

Now put values

[tex] \sf \: Length = 4 cm [/tex]

[tex] \sf \: Breadth = 6 cm[/tex]

[tex] \sf \: Length × Breadth = 4 × 6 \: cm [/tex]

[tex] \sf \implies 24 \: cm \ {}^{2} [/tex]

Always remember if we find area :-

After units like centimetres,metres we always put (²) on these units.

Like :- 26 cm², 56 m ²

In words = Twenty six centimetre square, Fifty six centimetre square

The area of rectangle is 24 cm²

Perimeter

Area

♦ Area of Rectangle

[tex] \underline{ \rule{140pt}{4pt}}[/tex]

Area - Region occupied by figure is called area.

[tex] \large \bf{ \mathfrak{{More \: Formulas \: \red{( Area)}}}}[/tex]

[tex] \large \sf \leadsto \: triangle = \frac{1}{2} \times bh[/tex]

[tex]\large \sf \leadsto \: \: Rectangle \: = \: lb[/tex]

[tex]\large \sf \leadsto \: \: Square \: = {s}^{2} [/tex]

[tex]\large \sf \leadsto \: \: Parallelogram \: = \: bh[/tex]

[tex]\large \sf \leadsto \: \: Rhombus \: = \: \frac{1}{2} \times \: d1 \times d2[/tex]

[tex]\large \sf \leadsto \: \: Trapezium \: = \frac{1}{2} \times (x + y) \times h[/tex]

[tex]\large \sf \leadsto \: \: Quadrilateral \: = \: \frac{1}{2} \times d(h1 + h2)[/tex]

[tex]\large \sf \leadsto \: Circle \: = {\pi \: r}^{2} [/tex]

[tex]\large \sf \leadsto \: \: Equilateral \triangle \: = \frac{ \sqrt{3} }{4} \times {s}^{2} [/tex]

Answer:  5

Step-by-step explanation:

Answer: y= 2x-5

Step-by-step explanation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To get the equation into slope-intercept form, you need to isolate the y-term on one side of the equation and simplify the rest of the equation. So, let's start with 6x - 3y - 15:

6x - 3y - 15 = 0 (I'm assuming this equation represents a line)

Now, let's isolate the y-term by subtracting 6x from both sides:

-3y = -6x + 15

Finally, let's solve for y by dividing both sides by -3:

y = 2x - 5