The probability for a disease X is 0.01. - if a person has the disease, the test results are positive with probability 0.90, and - if the person does not have the disease, the test results are negative with probability 0.80. Which of the following statements is true? Show your work. 1. The test results are positive with probability 0.2 when a person does not have the disease (false positives). 2. When a person has the disease, the test results are negative (false negatives) with probability 0.2.

The number of distinguishable large equilateral triangles can be constructed is 336.

To solve this case, we use the Burnside's Lemma and examine 3 rotations of 0 degrees, 120 degrees, and 240 degrees.

We also examine 3 reflections from the 3 lines of symmetry in the triangle. So, we must divide by 3 + 3 = 6 for our final count.

Case 1: 0-degree rotation.

This is known as the identity rotation, and there are 6^4 = 1296 choices because we do not have any restrictions.

Case 2: 120-degree rotation.

Note that the 3 outer sides of the triangle must be the same during this, and the middle one can be anything. So, we have 6 * 6 = 36 choices from this.

Case 3: 240-degree rotation.

Similar to the 120-degree rotation, each have to be the same except for the middle. We have 6 * 6 = 36 choices from this.

Case 4: Symmetry about lines.

We must multiply by 3 for these since the number of colorings fixed under symmetry are the exact same each time. Two triangles do not change under this, and they have to be the same. The other two triangles (1 middle and 1 outer) can be anything since they stay the same during the reflection. We have 6 * 6 * 6 = 216 ways for one symmetry. Since there are 3 symmetries, so there are 216 * 3 = 648 combinations in all.

Now, add all the cases up:

1296 + 36 + 36 + 648 = 2016

Then, divide by 6:

2016 / 6 = 336

Hence, the number of distinguishable large equilateral triangles can be constructed is 336.

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Chebyshev's inequality provides a bound on the probability that a random variable deviates from its mean by a certain number of standard deviations.

According to Chebyshev's inequality, for any value k greater than 1, the probability that a random variable deviates from its mean by more than k standard deviations is at most 1/k^2.

(a) To find the percentage of gasoline stations with prices within 3 standard deviations of the mean, we can use the complement of Chebyshev's inequality. The probability that a random variable deviates from its mean by more than 3 standard deviations is at most 1/3^2 = 1/9. Therefore, the probability that the price of gasoline is within 3 standard deviations of the mean is at least 1 - 1/9 = 8/9, which is approximately 0.889 or 88.9%.

(b) To find the percentage of gasoline stations with prices within 1.5 standard deviations of the mean, we can apply the same logic. The probability that a random variable deviates from its mean by more than 1.5 standard deviations is at most 1/(1.5)^2 = 1/2.25 ≈ 0.444 or 44.4%. Therefore, the probability that the price of gasoline is within 1.5 standard deviations of the mean is at least 1 - 0.444 = 0.556 or 55.6%.

To determine the gasoline prices that are within 1.5 standard deviations of the mean, we can calculate the interval. Given the mean price of $3.45 per gallon and a standard deviation of $50.08, the lower bound of the interval is $3.45 - 1.5 * $50.08 = $3.45 - $75.12 = $-71.67 (negative values are not meaningful in this context, so we can consider it as the minimum price to be 0) and the upper bound is $3.45 + 1.5 * $50.08 = $3.45 + $75.12 = $78.57.

(c) The minimum percentage of gasoline stations that had prices between $3.29 and $3.61 cannot be determined using Chebyshev's inequality alone. Chebyshev's inequality provides a lower bound on the probability, but it does not give the exact probability in this case. To determine the exact probability, additional information about the distribution of gasoline prices or a specific probability distribution model would be needed.

Using Chebyshev's inequality, we can determine the percentages of gasoline stations with prices within certain standard deviations of the mean. However, it is important to note that Chebyshev's inequality provides a lower bound on these probabilities and does not give the exact probabilities or the specific prices within the given intervals.

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Answer:

she should buy 3 quarts and keep the remainder which can possibly cover 30 square feet.

Answer:

h

Step-by-step explanation:

h

Answer:

36 cm

Step-by-step explanation:

The formula to find the area of a triangle is A=1/2bh where b stands for base and h for height.

So, 8 times 9 equals 72, and 72 divided by 2 is 36.

There is a profit of $39.7.

It is given that there 100 tickets costing $10 per ticket.

You must look first for the probability of the 4 prizes which are $475, $195, $30, and no prize.

P ($475 prize) = 1/100 or 0.01

P ($95 prize) = 2/100 or 0.02

P ($30 prize) = 4/100 or 0.04

P (No prize) = 100/100 – 1+2+4/100 =93/100 .93

Expected gain or loss is computed by: (P(x)* n)

E= (475-10)*.01 + (95-10)*0.02 + (30-10)* 0.04 + (-10)*.93

= 46.5 + 1.70 + 0.8 – 9.3

E = 39.7

There is a profit of $39.7.

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Answer:

The second train speed is 356.4 miles per hour

And, the first train speed is  361 miles per hour

Step-by-step explanation:

The computation of the speed of each train is as follows

Given that

The Sum of the speed of two trains is 717.4 miles per hour

Let us suppose the second train speed be x

So for the first train, the speed is x + 4.6

Now the equation is

x + x + 4.6 = 717.4

2x + 4.6 = 717.4

2x = 717.4 - 4.6

2x = 712.8

x= 356.4

Therefore the second train speed is 356.4 miles per hour

And, the first train speed is = 356.4 + 4.6 = 361 miles per hour

Answer:

Step-by-step explanation:

Expanding this equation and replacing r²(t) and y²(t), we get:(r²(t)/9) + (y²(t)/16) = 1(r²(t)/9) + (y²(t)/16) 1⇒ (9sin²t/9) + (16cos²t/16)  1⇒ sin²t/1 + cos²t/41/9⇒ (y/4)² + (r/3)² = 1This is the required Cartesian equation.

The Cartesian equation that is equivalent to the given parametric equations r(t) = 3sint and y(t) 4cost is the equation given by (y/4)² + (r/3)²1. Given parametric equations :r(t) = 3sinty(t)

= 4costThe above equations describe a curve in the plane and to convert it into a Cartesian equation, we need to eliminate the parameter t.

We know that\(sin²t + cos²t = 1\), therefore, we can square the first equation to get: r²(t) = 9sin²tSimilarly, squaring the second equation yields:y²(t) = 16cos²tNow, we can use the Pythagorean theorem to  16cos²t = 9 + 7cos²tWe can see that this equation gives a relationship between r and y but it still has the parameter t.

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a) The probability of completing the exam in one hour or less is equivalent to finding the probability of completing the exam in 60 minutes or less. To find this probability, we need to standardize the value using the z-score formula. z = (x - μ)/σ, where x is the time required to complete the exam, μ is the mean time, and σ is the standard deviation.

Hence, z = (60 - 80)/10 = -2. We then look up the corresponding probability from the standard normal distribution table, which is 0.0228. Therefore, the probability of completing the exam in one hour or less is 0.0228 (rounded to four decimal places).

(b) The probability that a student will complete the exam in more than 60 minutes but less than 75 minutes is equivalent to finding the area between the z-scores of -2 and -1.5 (since 60 minutes is -2 standard deviations from the mean and 75 minutes is -1.5 standard deviations from the mean).

Using the standard normal distribution table, we find that the area between -2 and -1.5 is 0.0808. Therefore, the probability of completing the exam in more than 60 minutes but less than 75 minutes is 0.0808.

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Goodwill acquired and associated legal fees: In the question, XYZ Ltd acquired 100% of Red-X Ltd on 1 July 2021. For this acquisition, XYZ Ltd paid the shareholders of Red-X Ltd a combination of cash, plant and equipment, and land. There are also legal fees of $249,267 involved in acquiring Red-X Ltd. Red-X Ltd’s statement of financial position shows total assets of $393,579 and liabilities of $393,575 on 1 July 2021.In order to determine whether goodwill has been acquired as a result of the acquisition, we first need to calculate the fair value of the consideration transferred.

The fair value of the consideration transferred is as follows: Cash consideration paid: $91,835Fair value of plant and equipment transferred: $327,983Fair value of land transferred: $393,579Total fair value of the consideration transferred: $813,397As we can see, the fair value of the consideration transferred exceeds the fair value of the net assets acquired ($1,049,544 - $393,575 = $655,969). Therefore, goodwill has been acquired as a result of the acquisition. The amount of goodwill acquired can be calculated as follows:Goodwill = Fair value of the consideration transferred - Fair value of the net assets acquiredGoodwill = $813,397 - $655,969Goodwill = $157,428Therefore, goodwill of $157,428 has been acquired as a result of the acquisition.Regarding the potential for including associated legal fees into the cost of acquiring Red-X, the IFRS 3 Business Combinations standard provides guidance on this matter. According to this standard, the costs of acquiring a business should be included in the cost of the acquisition. These costs include professional fees, such as legal and accounting fees, that are directly attributable to the acquisition. Therefore, the legal fees of $249,267 involved in acquiring Red-X Ltd should be included in the cost of acquiring Red-X Ltd.

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If XYZ Ltd were following ASPE, they could capitalize the legal fees and include them in the cost of acquiring Red-X Ltd and include them in the cost of acquiring Red-X Ltd.

Part 1: Calculation of Goodwill

Goodwill is calculated as the difference between the fair value of consideration paid and fair value of net assets acquired.

Let us calculate the fair value of consideration paid to the shareholders of Red-X Ltd.

Cash 91 835 Plant and equipment fair value $327 983; carrying amount in the books of ABC Ltd $222 912

Land fair value $393 579; carrying amount in the books of ABC Ltd $262 386

Fair value of consideration paid = $91,835 + $327,983 + $393,579 = $813,397

Fair value of net assets acquired = Total assets - Total liabilities

Fair value of net assets acquired = $1,049,544 - $393,575

= $655,969

Goodwill = Fair value of consideration paid - Fair value of net assets acquired

= $813,397 - $655,969

= $157,428

Therefore, the amount of goodwill acquired by XYZ Ltd is $157,428.

Part 2: Accounting Treatment of Legal Fees

According to the International Financial Reporting Standards (IFRS), the legal fees associated with the acquisition of a company are recognized as an expense in the statement of profit or loss and are not included in the cost of the acquisition.

Therefore, XYZ Ltd cannot include the legal fees of $249,267 in the cost of acquiring Red-X Ltd.

However, the Accounting Standards for Private Enterprises (ASPE) allow the capitalization of legal fees incurred during the acquisition process.

These legal fees are included in the cost of the acquisition.

If XYZ Ltd were following ASPE, they could capitalize the legal fees and include them in the cost of acquiring Red-X Ltd.

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The asset's variance is approximately 0.0358, and its standard deviation is approximately 0.1891.

To calculate the variance and standard deviation of the asset's returns, we'll follow the steps mentioned earlier using the given probability distribution:

⇒ Calculate the expected return (μ):

μ = (0.27 * 0.25) + (0.18 * 0.25+) + (0.10 * 0.30) + (0.04 * 0.20+)

  = 0.0675 + 0.045 + 0.03 + 0.008

  = 0.1505

⇒ Calculate the variance (σ^2):

σ^2 = [(0.27 - μ)^2 * 0.25] + [(0.18 - μ)^2 * 0.25+] + [(0.10 - μ)^2 * 0.30] + [(0.04 - μ)^2 * 0.20+]

Substituting the values and simplifying:

σ^2 = [(0.27 - 0.1505)^2 * 0.25] + [(0.18 - 0.1505)^2 * 0.25+] + [(0.10 - 0.1505)^2 * 0.30] + [(0.04 - 0.1505)^2 * 0.20+]

    = [(0.1195)^2 * 0.25] + [(0.0295)^2 * 0.25+] + [(-0.0505)^2 * 0.30] + [(-0.1105)^2 * 0.20+]

    = 0.017972 + 0.00021617 + 0.0030309025 + 0.01459516

    = 0.0358141325

⇒ Calculate the standard deviation (σ):

σ = √(σ^2)

  = √(0.0358141325)

  ≈ 0.1891

Therefore, the asset's variance is approximately 0.0358 and the standard deviation is approximately 0.1891.

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Using the property of fractions, we know that Frank ran 2.79 miles.

So, in this case, we have the mixed fraction:

Convert in proper fractions as follows:

We know, 1 km = 0.62 miles.

So, now converting 4.5km into miles as follows:

Therefore, using the property of fractions, we know that Frank ran 2.79 miles.

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Answer:

B

Step-by-step explanation:

In each one, they add two arrows that are to the right as much as they possibly can be

a. Null hypothesis is a statement that suggests no significant difference or relationship exists between two variables or populations. It is the starting point of hypothesis testing, and the aim is to prove it wrong.
b. Alternative hypothesis is a statement that suggests there is a significant difference or relationship between two variables or populations. It is the opposite of the null hypothesis and is supported if there is enough evidence to reject the null hypothesis.
c. Critical values are the values that divide the rejection region from the acceptance region in hypothesis testing. They are determined based on the chosen alpha level and the degrees of freedom.
d. Rejection region is the area in the distribution where the null hypothesis is rejected. It is determined by comparing the test statistic with the critical values.
e. Test statistic is a calculated value that measures the difference between the observed sample data and the expected values under the null hypothesis. It is used to determine whether the null hypothesis should be rejected.
f. Alpha level is the significance level set by the researcher, which determines the probability of rejecting the null hypothesis when it is true. It is typically set at 0.05 or 0.01, indicating a 5% or 1% chance of rejecting the null hypothesis when it is true. The alpha level is used to determine the critical values and the rejection region.

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Answer:

Step-by-step explanation:

Simplifying

4(t + 1) = 6(g + -4)

Reorder the terms:

4(1 + t) = 6(g + -4)

(1 * 4 + t * 4) = 6(g + -4)

(4 + 4t) = 6(g + -4)

Reorder the terms:

4 + 4t = 6(-4 + g)

4 + 4t = (-4 * 6 + g * 6)

4 + 4t = (-24 + 6g)

Solving

4 + 4t = -24 + 6g

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-4' to each side of the equation.

4 + -4 + 4t = -24 + -4 + 6g

Combine like terms: 4 + -4 = 0

0 + 4t = -24 + -4 + 6g

4t = -24 + -4 + 6g

Combine like terms: -24 + -4 = -28

4t = -28 + 6g

Divide each side by '4'.

t = -7 + 1.5g

Simplifying

t = -7 + 1.5g

A normal probability plot (also known as a normal plot or a probability plot) is a graphical tool that can be used to assess whether a set of data follows a normal distribution.

When the data being plotted follows a normal distribution, the points on the plot will appear roughly linear, with deviations from linearity being relatively minor. In other words, the plot will form a straight line.

If the plot deviates significantly from a straight line, it suggests that the data may not be normally distributed. The shape of the plot can indicate whether the data is skewed or has heavy tails compared to a normal distribution.

Therefore, a normal probability plot appearing linear indicates that the data follows a normal distribution. It is important to note that this is only one way to check for normality, and it is always recommended to use multiple methods to verify the normality assumption before applying statistical tests that assume normality.

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Answer:

$2/croissant

Step-by-step explanation:

$10÷ 5croissants = $2/ 1 croissant

Answer:

maybe the answer ris 36×4 and then 30×4 and subtract the result?!?!

To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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When you cjoose marbles and replace it, the marbles are independent. One marble does not affect the outcome of the other.

Multiply the probability of pulling out one big marble by the probability of pulling out a small marble:

Then, the probability of pulling out one big marble, replacing it, then pulling out a small marble is 0.249 or 24.9%

Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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Draw the circle with the center at the intersection of the perpendicular bisectors and the radius equal to the distance found in step 4.

When constructing a circle circumscribed about a triangle, the following step is needed:

Identify the three vertices of the triangle.

Let's say the triangle has vertices A, B, and C.

Find the perpendicular bisectors of the triangle's sides.

For each side of the triangle, construct a line that is perpendicular to the side and passes through its midpoint.

Locate the point of intersection of the perpendicular bisectors.

The point where all three perpendicular bisectors intersect is the center of the circumscribed circle.

Measure the distance from the center to any of the triangle's vertices.

This distance is the radius of the circumscribed circle.

By following these steps, you can construct a circle that passes through all three vertices of the triangle. This circle is known as the circumscribed circle or circumcircle of the triangle. It is unique to each triangle and provides a useful geometric property that can be applied in various mathematical and geometric contexts.

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Given:

The point, (4, -3)

The line,

To find an equation in slope-intercept form for the line that passes through (4,-3) and is parallel to the given line:

The slope of the line is,

Since the given line is parallel to the new line, so the slope will be same for the both.

Using the point-slope formula,

Substitute the point and slope we get,

Hence, the equation in slope-intercept form for the line is,

Answer:

Step-by-step explanation:

The monthly interest rate is the annual rate (APR) divided by 12.

  19%/12 ≈ 1.5833%

The loan will be paid in fewer than 91 months, because Zach will be paying at least $10 per month on his current balance of $910. The attached spreadsheet shows it will take 73 payments to pay off the loan.

Answer:

  (c)  20

Step-by-step explanation:

You want to find x, given that the external angle adjacent to a base angle of an isosceles triangle is (5x +12)°, and the other base angle is marked (3x +8)°.

The base angles of an isosceles triangle are congruent, so the other base angle is congruent to the marked base angle.

The external angle and the adjacent base angle are a linear pair, hence supplementary.

  (5x +12)° +(3x +8)° = 180°

  8x +20 = 180 . . . . . . . divide by °, collect terms

  8x = 160 . . . . . . subtract 20

  x = 20 . . . . . divide by 8

As per the 95% confidence interval, the true average age of all students in the university is approximately 23 to 24.

Confidence interval

Confidence interval means the interval calculation, obtained from the observed data that holds the actual value of the unknown parameter.

Given,

A random sample of 64 students at a university showed an average age of 23 years and a sample standard deviation of 3 years.

And we need to find the 95% confidence interval for the true average age of all students in the university.

While we looking through the given question we have identified the following,

Number of samples = 64

Average age = 23

Standard deviation = 3

Confidence interval = 95%

Based on this confidence interval, the z score is 1.96

According to the formula,

u = 23 ± 1.96 x 3/√64

u = 23  ± 1.96 x (3/8)

u = 23  ± 1.96 x 0.375

u = 23  ± 0.735

u = 23.735, 22.635

Therefore, the average age of the student is approximately 23 to 24.

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The real distance between towns X and Y measuring 11.2 cm apart on a map with a scale 1: 100,000 is 11.2 km.

Given the scale = 1: 100,000, which means that 1 cm on the map represents 100,000. Thus, 11.2 cm on the map represents 11.2* 100,000 = 1,120,000cm.

We know that 1 km = 100,000cm

Therefore 1,120,000 cm = 1,120,000/100,000

= 11.2 km

Therefore, the real distance between towns X and Y is 11.2km.

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