A toy train set includes a train station building which is a scale model of a real building. The area of the front side of the toy building is 1 square foot. The real building’s front side has an area of 400 square feet. If we view the real building as a dilation of the toy, what is the scale factor?

The probability that fewer than four customers will arrive in a 30-minute segment is 0.0483, rounded to four decimal places.

Based on the given information, we know that the arrivals to the ATM follow a Poisson distribution with a mean of 4 per 15 minutes.

a. To determine the probability that three customers will arrive in a given 15-minute segment, we can use the Poisson probability formula:

P(X = 3) = (e^-4) * (4^3) / 3!

Where X is the number of arrivals, e is the mathematical constant approximately equal to 2.71828, and 3! means 3 factorial, which is 3 * 2 * 1 = 6.

Plugging in the values, we get:

P(X = 3) = (e^-4) * (4^3) / 3! = 0.1954

So the probability that three customers will arrive in a given 15-minute segment is 0.1954, rounded to four decimal places.

b. To find the probability that fewer than four customers will arrive in a 30-minute segment, we need to use the Poisson distribution again, but this time with a mean of 8 (since there are two 15-minute segments in 30 minutes, and the mean for one segment is 4).

We want to find P(X < 4) or P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).

Using the Poisson probability formula with a mean of 8:

P(X = 0) = e^-8 * (8^0) / 0! = 0.0003
P(X = 1) = e^-8 * (8^1) / 1! = 0.0030
P(X = 2) = e^-8 * (8^2) / 2! = 0.0122
P(X = 3) = e^-8 * (8^3) / 3! = 0.0328

Adding up these probabilities, we get:

P(X < 4) = 0.0003 + 0.0030 + 0.0122 + 0.0328 = 0.0483

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The points that would form a square are (2, 2), (2, -2), (-2, 2), (-2, -2)

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

Forming a square

As a general rule

A square has equal sides and the angles at the vertices are 90 degrees

Since it must make a point with origin at its center, then the center must be (0, 0)

So, we have the following points (2, 2), (2, -2), (-2, 2), (-2, -2)

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Answer:

a

Step-by-step explanation:

a

The average of the three points A, B and C is M(x, y) = (- 7 / 9, 17 / 9).

In this problem we need to find the average of three points (A, B, C), each point has different weights. The average can be found by means of following expression:

[tex]M(x, y) = \frac{\sum\limits_{i = 1}^{n} w_{i}\cdot P_{i}(x, y)}{\sum \limits_{i = 1}^{n}w_{i}}[/tex]

Where:

Then, the average of points A, B and C are described below:

M(x, y) = [1 · (8, - 6) + 4 · (9, - 5) + 4 · (- 6, 7)] / (1 + 4 + 4)

M(x, y) = [(8, - 6) + (9, - 5) + (- 24, 28)] / 9

M(x, y) = (- 7, 17) / 9

M(x, y) = (- 7 / 9, 17 / 9)

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Therefore, the approximation of sec(0.08) as 1 is reasonable because 0.08 is a small angle and the linear approximation provides a good estimate of the function near x = 0.

The secant function is defined as sec(x) = 1/cos(x). Thus, if we want to find sec(0.08), we need to find cos(0.08) and then take its reciprocal.

Using a calculator, we find that cos(0.08) is approximately equal to 1.

Now, we can use the linear approximation or differential of the function f(x) = 1/cos(x) to estimate sec(0.08).

The derivative of f(x) is given by:

f'(x) = sin(x) / cos²(x)

Evaluating f'(0), we get:

f'(0) = sin(0) / cos²(0)

= 0/1

= 0

Thus, the linear approximation of f(x) at x = 0 is given by:

L(x) = f(0) + f'(0)(x - 0)

= 1 + 0(x - 0)

= 1

Since 0.08 is very close to 0, we can approximate sec(0.08) using the linear approximation:

sec(0.08) ≈ L(0.08)

= 1

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In hypothesis tests about the population correlation coefficient, the alternative hypothesis of not equal to zero is used when testing whether two variables are correlated or not.

The population correlation coefficient, denoted by ρ (rho), measures the strength and direction of the linear relationship between two variables in a population. If the null hypothesis is that the population correlation coefficient is zero (ρ = 0), then the alternative hypothesis of not equal to zero (ρ ≠ 0) implies that there is some non-zero correlation between the variables. In other words, the null hypothesis assumes that there is no linear relationship between the variables, while the alternative hypothesis allows for the possibility of a positive or negative linear relationship.

To test this hypothesis, a sample of data is collected, and the sample correlation coefficient, denoted by r, is calculated. If the sample correlation coefficient is sufficiently different from zero, then we can reject the null hypothesis in favor of the alternative hypothesis and conclude that there is evidence of a non-zero correlation between the variables. The level of significance and the sample size play important roles in determining the statistical significance of the correlation coefficient.

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The product of 10 by 2 = 20 because when 10 is multiplied twice(2) the result would be = 20.

Multiplication is defined as one of the major arithmetic operations used in solving mathematical questions which involves the duplication of a value.

Other arithmetic operations include addition, subtraction and Division.

The multiplication of a value can also be the product of the value and another value.

That is 10×2 is the product of 10 and 2 which should be = 20.

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The correct answer based on chi-square test is (c) No, because 0.12 > 0.05.

In a chi-square test, the p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. In this case, the null hypothesis is that there is no association between the two variables in the 2 x 2 table.

If the p-value is less than or equal to the significance level (0.05 in this case), then we reject the null hypothesis and conclude that there is a statistically significant association between the variables. However, if the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support a significant association.

In this scenario, the p-value is 0.12, which is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis and conclude that the chi-square test based on the 2 x 2 table is not statistically significant.

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The volume of the NaOH solution is 3.42 L.

To find the volume of the NaOH solution, we can use the formula:

concentration (M) = moles of solute / volume (L)

Rearranging this formula to solve for volume, we get:

volume (L) = moles of solute / concentration (M)

Plugging in the given values, we get:

volume = 1.90 mol / 0.555 M

Simplifying this expression, we get:

volume = 3.42 L

Therefore, the volume of the NaOH solution is 3.42 L.

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To determine the relationship between drag force and speed, you can conduct an experiment using 5 coffee filters and a motion detector. First, set up the motion detector to track the speed of the coffee filters as they fall through the air. Then, drop each coffee filter one at a time and record the drag force measured by the motion detector.

Plot the drag force on the y-axis and the speed on the x-axis, and you should be able to observe a relationship between the two variables. As the speed of the coffee filter increases, the drag force will also increase. This relationship is due to air resistance, which causes the coffee filter to experience a drag force as it falls through the air.

By analyzing the data and creating a graph, you can determine the specific relationship between drag force and speed for these coffee filters. This information can be useful in understanding how air resistance affects the motion of objects and in designing experiments or models that take air resistance into account.

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Answer:

x - 6 < 2x + 2

-8 < x, so x > -8

x = -1 and x = -5 are solutions to this inequality.

The equation that represents the linear form of vector v is given as follows:

v = -9i - 6j.

The general format for the linear form of a vector is given as follows:

v = ai + bj.

In which:

The points of the vector are given as follows:

Hence the horizontal component of the vector is given as follows:

a = 1 - 10

a = -9.

The vertical component of the vector is given as follows:

b = 2 - 8

b = -6.

Hence the linear form of the vector is:

v = -9i - 6j.

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So, approximately 25% of mail deliveries are made after 6:00 p.m.

To determine the percentage of mail deliveries that are made after 6:00 p.m., we need to find the proportion of the continuous uniform distribution that lies between 6:00 p.m. and 7:00 p.m.

The total range of delivery times is 4 hours (from 3:00 p.m. to 7:00 p.m.), so the distribution has a uniform density of 1/4 over this range.

The proportion of deliveries made after 6:00 p.m. is the proportion of the area under the density curve that lies to the right of 6:00 p.m.

The area under the density curve from 3:00 p.m. to 6:00 p.m. is (6:00 - 3:00)/(7:00 - 3:00) = 3/4 of the total area.

Therefore, the proportion of deliveries made after 6:00 p.m. is (1 - 3/4) = 1/4, or 25%.

So, approximately 25% of mail deliveries are made after 6:00 p.m.

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The value of x in the cyclic quadrilateral is 37 degrees

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

Quadrilateral CDEF is inscribed in circle A.

Opposite angles of cyclic quadrilateral add up to 180

So, we have

3x - 10 + 2x + 5 = 180

Evaluate

5x = 185

Divide

x = 37

Hence, the value of x is 37

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Answer:

37

Step-by-step explanation:

The average rate of change in the stock's price between 2014 and 2020 would be $ 1. 89

The formula to find the average rate of change between the two periods is :

Average rate of change = (Stock price in 2020 - Stock price in 2014) / Number of years

The question gives the following details :

Stock price in 2020 = $ 37 .22

Stock price in 2014 = $ 25 .86

The average rate of change is;

= (  37. 22 - 25. 86 ) / 6

= 11. 36 / 6

= $ 1. 89

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Answer: The diver's elevation below sea level after both dives is 22 feet.

The diver starts 16 feet below sea level, and then dives another 6 feet. This means the diver is now 16 + 6 = 22 feet below sea level.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1/3πr²h

Step-by-step explanation:

The formulas for calculating the volume of a cylinder and a cone are:

Volume of cylinder = πr²h

Volume of cone = 1/3πr²h

where r is the radius and h is the height of the shape.

Given that both shapes have a radius of 2 units and a height of 4 units, we can substitute these values into the formulas to calculate the volumes.

For the cylinder:

Volume of cylinder = πr²h

= π(2²)(4)

= 16π cubic units

Therefore, the volume of the cylinder is 16π cubic units.

For the cone:

Volume of cone = 1/3πr²h

= 1/3π(2²)(4)

= 8/3π cubic units

Therefore, the volume of the cone is 8/3π cubic units, which is approximately 8.38 cubic units (rounded to two decimal places).

The equivalent expressions of 3(7+2) is 3(2+7) (optionD)

Equivalent expressions are expressions that work the same even though they look different.

If two algebraic expressions are equivalent, then the two expressions have the same value.

For example, 5(2x+10) is equivalent to 10x+50. And this two expression will have thesame value for any value of x.

Similarly, 3(7+2) is equivalent to 3( 2+7) , because this two will give us the same value.

3(7+2) = 21+6

= 27

also, 3(2+7)

= 6+ 21

= 7

therefore we can say that 3(7+2) is equivalent to 3( 2+7)

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The gate code to a gated community consists of the # key, followed by 3 letters chosen from the English alphabet, followed by 3 digits. The total number of possible gate codes is 17.576,000.

To find the total number of possible gate codes for the gated community, we need to determine the number of choices for each part of the code and multiply them together.
1. The gate code starts with the # key, which is constant, so there's only 1 choice for this part.
2. The next part consists of 3 letters chosen from the English alphabet. There are 26 letters in the alphabet, and each of the 3 positions can be filled with any of those letters. So, the number of choices for this part is 26 * 26 * 26.
3. The last part of the code consists of 3 digits. Since there are 10 digits (0-9), there are 10 choices for each digit. Therefore, there are 10 * 10 * 10 choices for this part.
Now, we'll multiply the number of choices for each part together to get the total number of possible gate codes:
1 * (26 * 26 * 26) * (10 * 10 * 10) = 1 * 17576 * 1000 = 17,576,000
So, there are a total of 17,576,000 possible gate codes for the gated community.

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1. The determination of the predetermined overhead rate using the estimated direct labor costs is $5.30.

2. The actual overhead costs incurred are $2,426,200 while the amount of overhead cost applied to movies using the predetermined overhead rate is $2,438,000.

2b. Overhead is overapplied by $11,800.

3. The journal entry to close the overapplied overhead to the Cost of Goods Sold is as follows:

Debit Manufacturing Overhead $11,800

Credit Cost of Goods Sold $11,800

(To close the overapplied overhead to the cost of goods sold.)

Overhead is overapplied when the applied overhead is more than the actual overhead incurred.

The applied overhead is based on a predetermined overhead rate, which relies on estimates.

Overhead costs = $2,438,000

Direct labor costs = $460,000

Predetermined overhead rate = $5.30 ($2,438,000 ÷ $460,000)

Overhead costs incurred = $2,426,200

Direct labor costs = $460,000

Overhead Applied = $2,438,000 ($5.30 x $460,000)

Overhead overapplied = $11,800 ($2,438,000 - $2,426,200)

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The correct expression for f(x) is f(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + .

The given Maclaurin series suggests that the function f(x) is an even function since all the odd powers of x have coefficients of zero. To find an expression for f(x), we can examine the pattern in the series.

Let's break down the terms in the series:

Term 1: 1

Term 2: x² / (2!)

Term 3: x⁴ / (4!)

Term 4: x⁶ / (6!)

From this pattern, we observe that the coefficient of each term is given by [tex]\dfrac{x^{(2n)}} { (2n)!}[/tex], where n represents the index of the term.

Therefore, an expression for f(x) can be written as:

f(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + .....

This expression represents the summation of terms where each term is the power of x (2n) divided by the factorial of 2n, as indicated in the Maclaurin series.

So, the correct expression for f(x) is:

f(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + .....

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The probability that a student living in a dormitory at ASU does not receive a coupon for a free sandwich is 0.6436.

The probability that a student lives in West Hall is 0.58 and the probability that a student lives in South Tower is 0.42. The probability that a student in West Hall receives a coupon is 0.26, and the probability that a student in South Tower receives a coupon is 0.19.

To find the probability that a student does not receive a coupon, we can use the complement rule: the probability of the event happening plus the probability of the event not happening is equal to 1. So, the probability of a student not receiving a coupon is 1 minus the probability of a student receiving a coupon.

Using a tree diagram, we can find the probability of a student receiving a coupon or not. Starting with the first branch of the tree, we have:

West Hall (0.58)
- Coupon (0.26)
- No Coupon (0.74)

South Tower (0.42)
- Coupon (0.19)
- No Coupon (0.81)

To find the probability of a student not receiving a coupon, we add the probability of no coupon from each branch of the tree and multiply by the probability of being in that branch. So, the probability of a student not receiving a coupon is:

(0.58 x 0.74) + (0.42 x 0.81) = 0.6436

Therefore, the probability that a student living in a dormitory at ASU does not receive a coupon for a free sandwich is 0.6436.
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Answer:

Step-by-step explanation:

Answer:72

Answer:

72 feet square

Step-by-step explanation:

18 x 8 ÷ 2 = 72

So after one hour, the amount of chlorine in the tank has decreased from 20 g to 8.6 g using differential equation.

Let's start by finding the initial amount of chlorine in the tank:

The tank has a capacity of 400 liters and a concentration of 0.05 g of chlorine per liter, so the initial amount of chlorine in the tank is:

400 liters * 0.05 g of chlorine per liter = 20 g of chlorine

Next, we can set up a differential equation to describe how the amount of chlorine in the tank changes over time. We know that the concentration of chlorine in the tank is being diluted by the addition of fresh water at a rate of 4 liters per second, and being removed from the tank at a rate of 10 liters per second. Let C(t) be the amount of chlorine in the tank at time t, in grams. Then we have:

dC/dt = (0.05 g/L * 4 L/s) - (C(t)/400 L * 10 L/s)

The first term on the right-hand side represents the rate at which chlorine is being added to the tank, and the second term represents the rate at which chlorine is being removed from the tank. The factor C(t)/400 L represents the concentration of chlorine in the tank at time t.

We can simplify this equation by multiplying through by 400 L and rearranging:

dC/dt = 2 - (5/2) * C(t)

This is a first-order linear ordinary differential equation. We can solve it using separation of variables:

dC/(2 - (5/2) * C) = dt

Integrating both sides:

(-2/5) * ln|2 - (5/2) * C| = t + constant

Solving for C:

[tex]C(t) = (2/5) * (2 - e^{(-5t/2)})[/tex]

Now we have a formula for the amount of chlorine in the tank as a function of time. To find the amount of chlorine in the tank at a particular time, we can substitute that time into the formula for C(t). For example, to find the amount of chlorine in the tank after 1 hour (3600 seconds), we can calculate:

[tex]C(3600) = (2/5) * (2 - e^{(-5/2 * 3600)})[/tex]

[tex]= (2/5) * (2 - e^{(-9000)})[/tex]

≈ 8.6 g

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Answer: 2019.08

Step-by-step explanation: To find the year when the car had the least value, we need to find the minimum value of the quadratic function V = 20x² - 363.2x + 2500, where x represents the number of years since 2010.

One way to find the minimum value is to use the formula for the vertex of a quadratic function, which is given by:

x = -b / (2a)

where a is the coefficient of the x² term, b is the coefficient of the x term, and x is the x-coordinate of the vertex.

In this case, a = 20 and b = -363.2, so we have:

x = -(-363.2) / (2 x 20)

x = 9.08

This means that the vertex of the parabola occurs at x = 9.08, which represents the year 2010 + 9.08 = 2019.08 (rounded to two decimal places).

Therefore, the car had the least value in the year 2019.

Answer:63

Step-by-step explanation: