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1) The discount percentage is 16.07%.

2) The discounted price of F₁, F₂ is $470,000

3) The amount that Adam had after purchasing F₁, F₂ is $530,000.

The discount percentage is a product of the discount amount divided by the original cost, multiplied by 100.

Price of item F = $280,000

Discounted price = $235,000

Discount amount = $45,000 ($280,000 - $235,000)

Discount rate = 16.07% ($45,000/$280,000 x 100)

Discounted price of F₁, F₂ = $470,000 ($235,000 x 2)

The amount that Adam had before the purchase = $1,000,000

The amount he had after purchasing F₁, F₂ = $530,000 ($1,000,000 - $470,000).

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We can compute various descriptive statistics such as the mean, median, mode, range, variance, standard deviation, sum of values, and sum of squared deviations.

The sample mean, also known as the average, provides information about the central tendency of the variable X. It represents the typical or average number of coupons used by the shoppers in the sample. In this case, calculating the mean of the given data would provide an estimate of the average number of coupons used over the 6-month period.

The sample standard deviation measures the dispersion or variability of the data points around the mean. It indicates how much the individual observations deviate from the mean value. A higher standard deviation implies greater variability, indicating a wider range of coupon usage among the shoppers in the sample.

By computing the sample mean and standard deviation, we can understand the average coupon usage and the degree of variability in the data. These statistics help us summarize and interpret the characteristics of the variable X, allowing us to make comparisons, identify outliers, assess the spread of the data, and make inferences about the larger population from which the sample was drawn.

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The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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The central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

To find the central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

If you want the central angle in degrees, you can convert it using the fact that there are 2π radians in a full circle (360 degrees):

Central angle (in degrees) = (Arc length / Radius) * (180 / π)

Make sure to use consistent units for the arc length and radius, such as meters or centimeters, to obtain accurate results.

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The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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The samples of size n = 2 that can be drawn from this population is 28

From the question, we have the following parameters that can be used in our computation:

Population, N = 8

Sample, n = 2

The samples of size n = 2 that can be drawn from this population is calculated as

Sample = N!/(n! * (N - n)!)

substitute the known values in the above equation, so, we have the following representation

Sample = 8!/(2! * 6!)

Evaluate

Sample = 28

Hence, the number of samples is 28

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Complete question

A finite population consists of 8 elements.

10,10,10,10,10,12,18,40

How many samples of size n = 2 can be drawn this population?

The central metaphor which is presented in six degrees of separation is:

This refers to the figure of speech which makes use of comparison to show the similarity between two different things.

With this in mind and from the concept of six degrees of separation, we can see that it is based on the theory that people are about six or fewer connections away from each other.

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The studentized range statistic (q) is used in multiple comparison tests to determine significant differences between group means. To find the df for the error term, we need to look at the table provided.

From the table, we can see that the degrees of freedom (df) are given for different values of q. For example, when q is 2.95, the df for the error term is 2.92. Similarly, for q = 3.58, the df is 3.44.

To determine the df for the error term, we need to find the corresponding value of q in the table and read off the df.

In conclusion, to find the df for the error term, you need to match the value of q in the table and read off the corresponding df. Make sure to check the values in the table for the exact match.

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Angles can be measured using one of two standard units. Degrees are the most widely used unit of measurement.

∠ABD = 39°

Therefore, the correct option is c) 39°

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Answer:

For a problem like this there is no one solution.  It is an inequality.  When you graph it you would start with the Y-intercept at (0,10) then you move down 2 on the y axis and move the the right 1 on the x axis as that is your slope.  Do that a couple times until you can connect the dots.  You will draw a solid line to connect, and shade everything to the left and below the line.  Everything in the shaded area are the potential solutions for the inequality.

To your question about (0, -4) that would be in the solution set.

I hope this helps

The correct response is (f) 26 ft. The radius of the cylinder is approximately 26 ft.

To solve for the radius, we can use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. We can plug in the given values to get:

63,679 = πr²(30)

Dividing both sides by 30π gives:

r² = 676

Taking the square root of both sides gives:

r ≈ 26

Rounding to the nearest whole number gives the answer of 26 ft. Therefore, the correct response is (f) 26 ft.

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Complete Question:

A cylinder has a height of 30 ft and a volume of 63,679 ft³. what is the radius of the cylinder? round your answer to the nearest whole number. responses

a) 676 ft

b) 676 ft  

c)338 ft

d) 338 ft

e) 52 ft

f) 26 ft.  

Answer:

Volume = ( About ) 2406.165 cm^3

Step-by-step explanation:

If you consider a cube or a rectangular prism, you could identify it's volume through the multiplication of it's Base by height. A pyramid has 1 / 3rd that volume, so in order to take a volume of the figure to the left, we would multiply Base * height and take 1 / 3rd of that;

\(Square Pyramid,\\Base ( Square ) = a^2, a = length = 17.2 cm\\Height = 24.4 cm\\\\Volume = 1 / 3 ( Base ) ( Height ),\\Volume = 1 / 3 ( ( 17.2 )^2 )( 24.4 ),\\Volume = 1 / 3( 295.84 )( 24.4 ),\\\\Volume = 98.6133333333( 24.4 ),\\Volume = 2406.16533333,\\\\Volume = ( About ) 2406.165\)

Solution ⇒ ( About ) 2406.165 cm^3

Hope that helps!

The vector electric field at point (1,1,1) is:

E = E_xî + E_yĵ + E_zk = 0î - 8ĵ + 14k

To find the electric field components and vector at point (1,1,1), we need to take the negative gradient of the electric potential V(x, y, z) at that point.

The gradient of V is given by the vector:

∇V = (∂V/∂x)î + (∂V/∂y)ĵ + (∂V/∂z)k

where î, ĵ, and k are the unit vectors in the x, y, and z directions, respectively.

Taking partial derivatives of V with respect to x, y, and z, we get:

∂V/∂x = 4xy - 4z^4

∂V/∂y = 2x^2 + 6y^2z

∂V/∂z = 2y^3 - 16z^3x

Evaluating these partial derivatives at (1,1,1), we get:

∂V/∂x = 4(1)(1) - 4(1)^4 = 0

∂V/∂y = 2(1)^2 + 6(1)^2(1) = 8

∂V/∂z = 2(1)^3 - 16(1)^3(1) = -14

Therefore, the components of the electric field at point (1,1,1) are:

E_x = -∂V/∂x = 0

E_y = -∂V/∂y = -8

E_z = -∂V/∂z = 14

So the vector electric field at point (1,1,1) is:

E = E_xî + E_yĵ + E_zk = 0î - 8ĵ + 14k

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Answer:

B

Step-by-step explanation:

M is a factor of N and \((1+r)^t\), which is not influenced by N. This is because N is just the initial amount of people, and does not change no matter the rate of new members. Hope this helps!

Answer:

can you show us the graph

Answer:

Locate (0,-6), move up 2, right 1

Step-by-step explanation:

Hi there!

To graph a linear function, we first locate the-intercept, then graph the next point according to the slope.

We're given that the y-intercept is -6. The y-intercept occurs when x=0, so therefore, the point (0,-6) falls on the line.

Locate (0,-6)

Now, to graph the next point, we look at the slope. The slope in this case is 2. This means every time the line travels to the right by 1 unit, it travels up 2 units.

Move up 2, right 1

I hope this helps!

Answer:

one and thirty-seven thousandths

or simpler one point zero three seven

Step-by-step explanation:

a) The probability that the demand will exceed 200 cfs during the early after- noon on a randomly selected day is 0.1353.

b)  The water-pumping capacity that the station should maintain during early afternoons is 460.52 cfs, so that the probability that demand will exceed capacity on a randomly selected day is only 0.01.

a) The given probability distribution of the demand for water during the early afternoon hours is given as exponentially distributed with a mean of 100 cfs. Therefore, the random variable X, representing the demand for water during early afternoon hours, follows exponential distribution with parameter λ = 1/100. We are required to find the probability that the demand will exceed 200 cfs during the early afternoon on a randomly selected day. By definition of probability density function of exponential distribution, the probability that the demand for water during early afternoon hours will exceed 200 cfs on a randomly selected day is:  

P(X > 200) = e-2  ≈ 0.1353

b) Given that the probability that demand will exceed capacity on a randomly selected day is only 0.01, we can write this in terms of the probability density function of exponential distribution as:

P(X > c) ≤ 0.01, where c is the water-pumping capacity that the station should maintain during early afternoons.

If X ~ Exponential distribution with parameter λ, the probability density function is given by:

f(x) = λ e-λx;  x > 0

For the probability P(X > c) ≤ 0.01, we have:

P(X > c) = e-λc ≤ 0.01 (probability distribution function of exponential distribution)

⇒ e-λc = 0.01

⇒ λc = ln(100) = 4.6052

⇒ c = 4.6052 * 100 = 460.52 cfs

Therefore, the station should maintain a pumping capacity of 460.52 cfs.

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Answer:

Step-by-step explanation:

Cylinder volume formula: V= πr²h

Given

Volume of soup pod

In a hyperbolic plane, a Lambert quadrilateral ABCD with right angles at A, B, and C. This result tells us about the properties of hyperbolic geometry.

In hyperbolic geometry, the sum of angles in a triangle is less than 180 degrees, which means that a right angle is acute. Therefore, in a Lambert quadrilateral ABCD, angle D is acute. Additionally, in hyperbolic geometry, parallel lines diverge from each other, which means that the sides adjacent to D in a Lambert quadrilateral are greater than their respective opposite sides. This property holds true for all sides adjacent to an acute angle in a Lambert quadrilateral.

Thus a  Lambert quadrilateral ABCD in a hyperbolic plane with right angles at A, B, and C implies that angle D is acute and the sides adjacent to D are greater than their respective opposite sides, highlighting the properties of hyperbolic geometry and the absence of rectangles in the hyperbolic plane.

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By using the given table, we can see that the expected value is 20.97 AED.

The expected value is given by the sum between the products between the value of each outcome and the probability of said outcome.

Then, by using the table, we can write the expected value as:

\(12*0.8 + 18*0.15 + 20*0.31 + 22*0.08 + 24*0.15 + 25*0.23 = 20.97\)

Then we can see that the correct option is C, the expected value is 20.97 AED.

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The required sample size is given as follows:

n = 62.

The bounds of the confidence interval are given by the rule presented as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is given as follows:

\(M = z\frac{\sigma}{\sqrt{n}}\)

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The parameters for this problem are given as follows:

\(M = 500, \sigma = \sqrt{4000000} = 2000\)

Hence the sample size is obtained as follows:

\(500 = 1.96\frac{2000}{\sqrt{n}}\)

\(500\sqrt{n} = 1.96 \times 2000\)

\(\sqrt{n} = 1.96 \times 4\)

n = (1.96 x 4)²

n = 62.

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Answer:

36 yards

Step-by-step explanation:

The triangle is a 3-4-5 right triangle with a scaling factor of 12. No complicated Pythagorean theorem has to be used in this case.

60/12 = 5

48/12 = 4

3 is the only base number remaining.

3(12) =36

Answer:

h = 14

Step-by-step explanation:

just substitute the x value and calculate for h

x = (-18)

h = 17 + -(18)/6

h = 17 + (-3)

h = 17 - 3 = 14

Solution

David simplified a polynomial

For the first step

Open the brackets

The first step is correct.

For the second step

Collect like terms

The second step is correct

For the third step

Add up the like terms

The third step is correct.

Hence, David did not make a mistake

Answer:

yes

Step-by-step explanation:

they both simplify to 3:1

Answer:

Yes

Step-by-step explanation:

To see whether two fractions are equivalent or not we need to simplify them

9:3 can be simplified to 3:1 as the biggest common divisor of 9 and 3 is 3

6:2 can be simplified to 3:1 since the biggest common divisor of this set is 2

as seen we can simplify both to 3:1 so yes, they are equivalent

The pattern to the number series 5, 12, 26, ____, 110, 222 is 50. There are different methods to solve the pattern. For example, you can find the difference between consecutive numbers and check if it follows a pattern.

The pattern to the number series 5, 12, 26, ____, 110, 222 is 50.

How?

There are different methods to solve the pattern. For example, you can find the difference between consecutive numbers and check if it follows a pattern. Here, I am using this method to explain the answer. To start, we will find the difference between consecutive numbers.

5 to 12 = 7 (12 - 5 = 7)

12 to 26 = 14 (26 - 12 = 14)

26 to ____ = ?

____ to 110 = 84 (110 - ____ = 84)

110 to 222 = 112 (222 - 110 = 112)

Now, we will find the difference between the second difference.

7 to 14 = 7 (14 - 7 = 7)

14 to ____ = ?

____ to 84 = 70 (84 - ____ = 70)

84 to 112 = 28 (112 - 84 = 28)

Since we are given 5, 12, 26, ____, 110, 222

fill in the patterning blank, we need to find the blank space. So, let's work on that.

7 to 14 = 7 (14 - 7 = 7)

14 to ____ = ?

7 + 7 = 14

____ = 28 (14 + 14 = 28)

28 to 84 = 56 (84 - 28 = 56)

84 to 112 = 28 (112 - 84 = 28)

28 + 28 = 56

Hence, the blank in the patterning is 50. This number series has a pattern to solve. If you learn how to solve such patterns, you can easily find the blank in any patterning series. There are different methods to find the answer, as explained above, but the one I used is the most common one. Here, we found the difference between consecutive numbers and checked if it follows a pattern. The pattern we found is that the second difference is constant. The second difference is the difference between the first difference of the consecutive numbers. When we calculated the second difference, we found that the blank in the patterning series is 50. It means that the difference between 26 and the blank is 28, and the difference between the blank and 110 is 84.

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The correct logic translation of "some people are afraid of some animals" is:

∃x∃y, Person(x) ∧ Animal(y) ∧ Afraid(x, y)

This translates to "There exist some person x and some animal y such that x is afraid of y, and x is a person, and y is an animal." This statement asserts the existence of at least one person who is afraid of at least one animal.

To break down the statement, the quantifier ∃x asserts that there is at least one person x who is afraid of some animal, and the quantifier ∃y asserts that there is at least one animal y that some person is afraid of. The predicates Person(x), Animal(y), and Afraid(x, y) specify the properties of x and y, where Person(x) means x is a person, Animal(y) means y is an animal, and Afraid(x, y) means x is afraid of y. The ∧ symbol represents the logical operator "and," which combines the predicates to form a single statement.

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Answer:

Use colon method

Step-by-step explanation:

So it is more easy