consider a double ids with system a and system b. if there is an intruder, system a sounds an alarm with probability .9 and system b sounds an alarm with probability .95. if there is no intruder, the probability that system a sounds an alarm (i.e., a false alarm) is .2 and the probability that system b sounds an alarm is .1. a. use symbols to express the four probabilities just given. b. if there is an intruder, what is the probability that both systems sound an alarm? c. if there is no intruder, what is the probability that both systems sound an alarm? d. given that there is an intruder, what is the probabil

We conclude that there is convincing evidence to reject the null hypothesis. Therefore, the data provide convincing evidence that the distribution has changed.

Based on the given information, a chi-square goodness-of-fit test was conducted to determine whether there is convincing evidence that the distribution has changed. The test statistic is 10.13 and the p-value is 0.0175.

To interpret these results, we need to compare the p-value to a predetermined significance level (α), which is usually set at 0.05.

Step 1: Compare the p-value to the significance level
- If the p-value ≤ α, then there is convincing evidence to reject the null hypothesis (i.e., the distribution has changed).
- If the p-value > α, then there is not enough evidence to reject the null hypothesis (i.e., no convincing evidence that the distribution has changed).

In this case, the p-value (0.0175) is less than the typical significance level (0.05)

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Suppose that the correlation between educational level attained and yearly income is +0.68. This indicates that there is a positive and strong relationship between educational level and yearly income.

It means that as the level of education attained increases, the yearly income also tends to increase. However, it is important to note that correlation does not imply causation, and there could be other factors that contribute to the relationship between education and income.

Based on the provided correlation coefficient of +0.68 between educational level attained and yearly income, we know that there is a positive and moderately strong relationship between the two variables. As a person's education level increases, their yearly income is also likely to increase.

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The original number that Gavyn was thinking of was 15.3.

Let x be the original number.

According to the problem, when Gavyn subtracts 9 from x, he gets an answer of 6.3. This can be written as;

x - 9 = 6.3

To solve for x, we can add 9 to both sides of the equation;

x - 9 + 9 = 6.3 + 9

Simplifying the right side gives;

x = 15.3

Therefore, the original number that Gavyn was thinking of was 15.3.

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A right angled triangle with height = 7, base = 11, by using the Pythagorean theorem, we can calculate the hypotenuse is approximately 13. Therefore, the missing side, x = 13.

In a right angled triangle, using the Pythagorean theorem: sum of the squares of the base and height is equal to the square of the hypotenuse, we can find the hypotenuse x.

[tex]x^2 = 7^2 + 11^2[/tex]

[tex]x^2 = 49 + 121[/tex]

[tex]x^2 = 170[/tex]

Taking the square root of both sides, we get:

x ≈ 13.0384

Rounding this to the nearest tenth, we get:

x ≈ 13.0

Therefore, the length of x is approximately 13.0 units (rounded to the nearest tenth).

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The total surface area of the pyramid is 817 ft squared.

The surface area of the pyramid Jane is painting can be calculated as follows:

area of the pyramid = A + 1 / 2 ps

where

Therefore,

A = 19² = 361 ft²

p = 4(19) = 76 ft

s = 12 ft

Total surface area of the pyramid =  361 + 1 / 2 (76)(12)

Total surface area of the pyramid = 361 + 456

Total surface area of the pyramid = 817 ft²

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The 99% confidence interval for the true proportion of people who prefer x to y is approximately (0.4163, 0.5637).

To calculate the 99% confidence interval for the true proportion of people who prefer x to y, we'll use the following steps:

1. Find the sample proportion (p-hat): Divide the number of people who prefer x by the total number of people surveyed.
p-hat = 147/300 ≈ 0.49

2. Determine the sample size (n): In this case, the researcher surveyed 300 people, so n = 300.

3. Find the standard error (SE) of the proportion: SE = sqrt((p-hat * (1 - p-hat)) / n)
SE ≈ sqrt((0.49 * 0.51) / 300) ≈ 0.0286

4. Identify the 99% confidence level (z-value): For a 99% confidence interval, the z-value is 2.576 (from the standard normal distribution table).

5. Calculate the margin of error (ME): ME = z-value * SE
ME = 2.576 * 0.0286 ≈ 0.0737

6. Determine the lower and upper bounds of the 99% confidence interval:
Lower Bound = p-hat - ME ≈ 0.49 - 0.0737 ≈ 0.4163
Upper Bound = p-hat + ME ≈ 0.49 + 0.0737 ≈ 0.5637

So, the 99% confidence interval for the true proportion of people who prefer x to y is approximately (0.4163, 0.5637).

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If 2 similar "rectangular" shaped prisms have surface-area as 112 cm² and 1008 cm², then base perimeter of larger prism is 36 cm.

In order to calculate the Perimeter, we first calculate the "scale-factor" "k",

The "Scale-Factor" "k" is defined as the ratio of area of two figures which are similar,

So, (area of small rectangular prism)/(area of large rectangular prism) = k²,

Substituting the values of "Area",

We get,

⇒ k² = 112/1008,

⇒ k = 1/3,

Now, we use this "scale-factor" to find the value of the length and width of the "large-rectangular-prism".

For the length:

⇒ (length of small rectangular prism)/(length of large rectangular prism) = k,

⇒ 4/x = k,

⇒ 4/x = 1/3,

⇒ x = 12 cm.

For the width,

⇒ (width of small rectangular prism)/(width of large rectangular prism) = k,

⇒ 2/y = 1/3,

⇒ y = 6.

We know that the Perimeter(P) of base of Larger-Prism is calculated by the formula : 2l + 2w,

Substituting the values of Length(l) = 12 cm and width(w) = 6 cm,

We get,

⇒ Perimeter = 2×12 + 2×6 = 24 + 12 = 36 cm.

Therefore, the required Perimeter is 36 cm.

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Okay, here are the steps to find the probability that Josie will be placed in an A group with an even number:

1) There are 2 possible letters (A or B) and 6 possible numbers (1-6) for the groups. So there are 2 * 6 = 12 possible groups total.

2) Half of the groups (6 groups) will be A groups.

3) Half of the groups (6 groups) will have an even number (2, 4, 6)

4) So there are 6 * 6 / 12 = 1/2 = 0.5 probability that a randomly selected group will be an A group with an even number.

5) Therefore, the probability that Josie will be placed in an A group with an even number is 0.5.

Work shown:

Total groups: 12

A groups: 6

Even number groups: 6

Probability A group with even number: 6 * 6 / 12 = 1/2 = 0.5

Prob Josie in A even group: 0.5

0.5

Let me know if you have any other questions!

Answer: 1/6

Step-by-step explanation:

There are six possible outcomes when rolling a number cube, and two possible outcomes when drawing a letter tile.

To determine the probability that Josie will be placed in an A group with an even number, we need to find the number of outcomes that satisfy this condition and divide by the total number of possible outcomes.

The possible outcomes that satisfy the condition are:

The total number of possible outcomes is:

Therefore, the probability that Josie will be placed in an A group with an even number is:

Therefore, the probability that Josie will be placed in an A group with an even number is 1/6.

The correct answer is a: every individual has an equal chance of being selected. A random sample is a subset of a population that is selected in a way that each member of the population has an equal probability of being chosen.

The randomness of the sample helps to ensure that the results obtained from the sample are representative of the entire population.

Option b, the probabilities cannot change during a series of selections, is a requirement for independent events but not necessarily for a random sample.

Option c, there must be sampling with replacement, is not always required for a random sample. Sampling with replacement means that after an individual is selected, they are returned to the population and can be selected again. This is not always necessary for a random sample.

Therefore, the correct answer is a: every individual has an equal chance of being selected.

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These prompts range from Similarity of triangles to similarity of angles, and transformations here are their answers.

6) ΔADE is similar to Δ ABC on the basis of proportionality.

AB/AC = AD/AE

4/8 = 2/4

1/2 = 1/2

hence on the bases on similar ratios, they are proportional.

7) ABCD transforms to EFGH on the bases of Option C.

8) the following statements about th parallel lines are true:
m∠2=m∠6

m∠1+m∠6 = 180°
x= 120°

If place the spape ABCD on the origin and rotate 180°, them move down ward the axis by 2 units to (0, -4) and two units to the right to (4, -4) you will get the result on the screen hence, the correct answer is Option C.

9) m∠1 = 35°, m∠2=30° (Option B)

Look closely, you would see that there is an angle on a straight line = 115°.

for the triangle of left it shares a co-linear angle with 115° lets call it x

So 80 + m∠1 + x = 180°
since x = 180-115 (angles on straight line) = 65°

Then

80 + m∠1 + 65 = 180

so m∠1= 180-80-65

m∠1 =35°

Using the same approach, we arrive at m∠2 =30°

Hence option B is the right answer.

10)  

(4x+7)  = (5x-10)  by virture of opposite angles.

Thus, (4x+7)  = (5x-10); after collecting like terms we have

⇒ 7+10 = 5x-4x
17= x

or x = 17
so: substituting x into the above expressions, we have

(4(17)+7) = 68 + 7 = 75°

75°

(5x-10) = 5(17) -10 = 85 -10 = 75°

Thus,  (4x+7)  = (5x-10) and are truly opposite angles.

Using x lets test to see if

(3x)° and (4x-14)° are alternate angle.

if they are, the should be equal.

Thus

3x = 3*17 = 51°
4x-14 = 4(17) -14 = 54°

Hence (3x)° ≠ (4x-14)°

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The total pounds of hamburger meat purchased by Sara is equal to 3 and 33/40 pounds in mixed number from.

Weight of one package of hamburger meat =2 and 3/8 pounds

Weight of second package of hamburger meat = 1 and 1/5 pounds

Weight of second package of hamburger meat = 1/4 pounds.

Converting the mixed numbers to improper fractions,

2 and 3/8 = 19/8

1 and 1/5 = 6/5

The total amount of hamburger meat that Sara purchased, add the weights of the three packages is equal to

2 and 3/8 + 1 and 1/5 + 1/4

= 19/8 + 6/5 + 1/4

To add these fractions and mixed numbers,

Convert them to a common denominator.

The least common multiple of 8, 5, and 4 is 40.

Now, rewrite the expression with the common denominator of 40,

= (19/8) × 5/5 + (6/5) × 8/8 + (1/4) × 10/10

= 95/40 + 48 / 40 + 10/40

= ( 95 + 48 + 10 ) / 40

=153/40

Simplifying this fraction to a mixed number, we get,

3 and 33/40 pounds

Therefore, Sara purchased a total of 3 and 33/40 pounds of hamburger meat.

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The length of AD is 2 inches.

Let x be the length of AD. By the Pythagorean theorem in triangle ABD, we have:

[tex]BD^2 + x^2 = AB^2[/tex]

Substituting AB = BC, we get:

[tex]BD^2 + x^2 = BC^2[/tex]

Using the fact that triangle ABC is isosceles, we can use the Pythagorean theorem in triangle ABC to find BC:

[tex]BC^2 = AC^2 - AB^2 = 8^2 - AB^2[/tex]

Substituting this expression for[tex]BC^2[/tex] in the previous equation, we get:

[tex]BD^2 + x^2 = 8^2 - AB^2[/tex]

Since BD is the perpendicular bisector of AC, we have AD = DC = (AC/2) = 4 inches. Therefore, we can write:

AB = AD + DB = 4 + DB

Substituting this expression for AB in the previous equation, we get:

[tex]BD^2 + x^2 = 8^2 - (4 + DB)^2[/tex]

Simplifying this equation, we get:

[tex]BD^2 + x^2 = 16 - 8DB - DB^2 + x^2[/tex]

Solving for DB, we get:

[tex]DB = (16 - BD^2 - x^2)/(8 + DB)[/tex]

Now, we can use the fact that BD is the perpendicular bisector of AC to write:

[tex]BD^2 = AD \times DC = 4x[/tex]

Substituting this expression for[tex]BD^2[/tex] in the previous equation, we get:

[tex]4x = (16 - 4x - x^2)/(8 + DB)[/tex]

Simplifying this equation, we get:

[tex]32x + 4x^2 = 16 - 4x - x^2[/tex]

Solving for x, we get:

x = 2 inches

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The value of the given integral is 116.

To evaluate this integral, by finding an antiderivative of the function and then evaluating it at the limits of integration.

To apply this theorem to our integral, we first need to find an antiderivative of the integrand (the expression inside the integral sign). To do this, we need to use the power rule of integration, which states that the integral of tn is (1/(n+1))tn+1 + C, where C is the constant of integration.

Using this rule, we can find the antiderivative of the integrand as follows:

∫(4 - 2t + 3t²) dt = 4t - t²+ t³ + C

where C is the constant of integration.

[tex]\int\limits^5_1[/tex] (4 - 2t + 3t²) dt = [4t - t² + t³]5^1

= [(4(5) - (5)² + (5)³) - (4(1) - (1)² + (1)³)]

= [(20 - 25 + 125) - (4 - 1 + 1)]

= [120 - 4]

= 116

Therefore, the value of the given integral is 116.

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Answer: 13,-11

Step-by-step explanation: if it's dilation there's a correlation between the two so I think if you just subtract the c from the c now and get 2,1 and you then subtract that from b you should get your answer

a. The velocity at time t is v(t) = t² + 2t - 15 m/s.

b. The distance travelled during the given time interval is [tex]\frac{25}{3}[/tex] meters (or approximately 8.33 meters).

(a) To find the velocity at time t, we need to integrate the acceleration function a(t) from 0 to t and add the initial velocity v(0):

[tex]v(t) = \int a(t) \, dt + v(0) = \int (2t + 2) \, dt - 15 = t^2 + 2t - 15[/tex]

So the velocity at time t is v(t) = t² + 2t - 15 m/s.

(b) To find the distance travelled during the given time interval, we need to integrate the velocity function v(t) from 0 to 5:

s(5) - s(0) = ∫v(t) dt from 0 to 5

Using the formula for v(t) from part (a), we have:

s(5) - s(0) = ∫(t² + 2t - 15) dt from 0 to 5

[tex]\int_{0}^{5} \left( \frac{t^3}{3} + t^2 - 15t \right) \, dt[/tex]

[tex]= \frac{25}{3}+25-75-\frac{0}{3}+0-0=\frac{25}{3}[/tex]

As a result, the distance covered in the allotted time is [tex]\frac{25}{3}[/tex], or roughly 8.33 metres.

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(a) Number of ways to line up 10 members =10! =3,628,800 number of ways so that VP and president are next to each other 2.9!

(b) To line up the ten people if the VP must be beside the president in the photo 725,760 ways.

(c) To line up the ten people if the president must be next to the secretary and the VP must be next to the treasure is:  161,280 ways.

a). To line up the ten people with no restrictions in arrangement; we have;

n! = 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 3,628,800 ways.

b). To line up the ten people if the VP must be beside the president in the photo;

then, there are 9 entities as the VP and president are considered as one entity. However, there are 2! ways to arrange the president and vp, we have:

=> 9! × 2!

=  725,760 ways.

c). To line up the ten people if the president must be next to the secretary and the VP must be next to the treasure we have:

= 8! × 2! × 2!

= 161,280 ways.

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The given question is incomplete, complete question is:

ten members of a club are lining up in a row for a photograph. the club has one president, one vp, one secretary, and one treasurer. (a) how many ways are there to line up the ten people? (b) how many ways are there to line up the ten people if the vp must be beside the president in the photo? (c) how many ways are there to line up the ten people if the president must be next to the secretary and the vp must be next to the treasurer?

The probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.

There cannot be a positive or negative association between a categorical and a numerical variable. here the delivery method is a categorical variable.

We cannot determine what the total number for any of the delivery methods was as we are only given the conditional probability of whether they were returned or not.

We can clearly see that the probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.

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The third side of a triangle must be an integer, so the smallest possible integer solution is 5.

There are infinitely many possible third side lengths for a triangle with sides of length 5.3 and 0.4. To determine the third side length, we need to use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Thus, we have two inequalities:

0.4 + x > 5.3

5.3 + x > 0.4

Simplifying each inequality, we get:

x > 4.9

x > -4.9

The third side must be an integer, so the smallest possible integer solution is 5. Therefore, the length of the third side is 5 units.

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To find the amount of the 1.6 thousand gallons left at the end of the week, we need to determine the demand for the week and subtract it from the initial stock.

First, let's define the function h(x) as the amount left when the demand is x.

1. Identify the demand function for the week. This information is missing in your question, but let's assume it is given as d(x).

2. Calculate the demand for the week by evaluating the function d(x) at the end of the week. Let's assume the week is represented by the variable "t". Evaluate d(t) to find the demand for the week.

3. Subtract the demand for the week from the initial stock to find the remaining amount: h(t) = 1.6 thousand gallons - d(t).

4. Round your answer to three decimal places to get the final result.

Without the specific demand function, I cannot provide a numerical answer.

However, you can follow these steps with the given demand function to find the amount of the 1.6 thousand gallons expected to be left at the end of the week.

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We will use the future value of a series formula to solve this problem. The terms you want me to include are invests, investment, and compounded.

Here's a step-by-step explanation:

1. Bill invests $160 at the start of each month for 22 months. This is a regular investment, and we will treat it as an ordinary annuity.

2. The investment yields 0.5% per month, compounded monthly. We'll convert the percentage to a decimal by dividing it by 100, so the monthly interest rate (r) is 0.005.

3. We will use the future value of an ordinary annuity formula to find the value of the investment at the end of 22 months:

FV = P * [(1 + r)^n - 1] / r

Where FV is the future value of the investment, P is the monthly investment ($160), r is the monthly interest rate (0.005), and n is the number of months (22).

4. Plug in the values and calculate:

FV = 160 * [(1 + 0.005)^22 - 1] / 0.005

FV = 160 * [(1.005)^22 - 1] / 0.005

FV = 160 * [1.113688 - 1] / 0.005

FV = 160 * 0.113688 / 0.005

FV = 3,627.232

The value of Bill's investment at the end of 22 months is approximately $3,627.23.

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On dividing the given two polynomials, we get another polynomial [tex]2x^{4} + 5x^{2}[/tex].

We are given two polynomials. One is 2[tex]x^{5}[/tex] + 5[tex]x^{3}[/tex] and the other polynomial is x. We have to divide the given two polynomials. As we know that when we add, subtract, multiply, or divide two polynomials, the answer is always a polynomial. Therefore, when we divide these two polynomials, the answer we get will also be a polynomial.

= [tex]\frac{2x^{5} + 5x^{3}}{x}[/tex]

We will take x common from the numerator so that we can cancel it out with the x present in the denominator. Therefore, taking x common;

[tex]\frac{x(2x^{4} + 5x^{2})}{x}[/tex]

Cancel out the term x from the numerator and denominator. By doing so, we get;

[tex]2x^{4} + 5x^{3}[/tex]

Therefore, on dividing the given two polynomials, we get the answer as a polynomial [tex]2x^{4} + 5x^{3}[/tex]

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The zeros of the polynomial f(x) are the values of x that make f(x) equal to zero. We can find the zeros of f(x) by setting the polynomial equal to zero and solving for x:

f(x) = (x-5)²6 (x²-25)²7 = 0

The polynomial f(x) has two factors, each of which contributes to the zeros of the polynomial:

Factor 1: (x-5)²6

This factor is equal to zero when x-5=0, or x=5. Therefore, the polynomial f(x) has a zero of multiplicity 6 at x=5.

Factor 2: (x²-25)²7

This factor is equal to zero when x²-25=0, or x=±5. Therefore, the polynomial f(x) has two more zeros at x=±5. Each of these zeros has a multiplicity of 7, since the factor (x²-25) is raised to the 7th power.

Therefore, the zeros of f(x) are x=5 and x=±5, with multiplicities of 6 and 7, respectively.In summary

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Answer:

The figure is trapizium so opposite sides are suplementary which is their sum =180

112° + x = 180°

x = 180° - 112° =68°

Hope it is correct !

The value of x is 3.10

Pythagoras theorem states the sum of the squares of the leg of a right triangle is equal to the square of hypotenuse.

c² = a² + b²

Therefore,

(2x)² = (x-2)² +( x+3)²

4x² = x²- 4x +4 + x²+6x +9

collecting like terms

4x²-x²-x² -6x+4x -13 = 0

2x²-2x-13 = 0

Using formula method

x = (-b ± √b²-4ac)/2a

x = -(-2) ±√ -2)²-4× 2 × -13)/4

= 2±√ 4+104)/4

= 2±√108)/4

x = (2+10.39)/4 or (2-10.39)/4

x = 3.10 or -2.10

therefore the value of x is 3.10

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Answer:

(5x)(2x) = 202.5

10x^2 = 202.5

x^2 = 20.25, so x = 4.5

The area of the parallelogram with vertices K(1,2,3), L(1,3,6), M(3,8,6), and N(3,7,3) is approximately 29.1547.

To find the area of the parallelogram, we need to find the length of one of its base vectors and the perpendicular height.

Let's first find one of the base vectors. We can take KL or MN as the base vector. Let's take KL.

The vector KL = L - K = (1, 3, 6) - (1, 2, 3) = (0, 1, 3).

Next, we need to find the perpendicular height of the parallelogram. We can do this by finding the cross-product of KL and KM, and then taking its magnitude.

The vector KM = M - K = (3, 8, 6) - (1, 2, 3) = (2, 6, 3).

Taking the cross product of KL and KM, we get:

KL x KM = |i j k|

|0 1 3|

|2 6 3|

= i(18) - j(6) + k(-2)

= (18, -6, -2)

The magnitude of KL x KM is:

[tex]|KL x KM| = √(18^2 + (-6)^2 + (-2)^2) = √(340) = 2*√(85)[/tex]

Therefore, the area of the parallelogram is:

Area = base x height = |KL| x |KL x KM| = [tex]√(0^2 + 1^2 + 3^2) * 2√(85) = 2√(10)√(85) = 2√(850) ≈ 29.1547[/tex]

So, the area of the parallelogram with vertices K(1,2,3), L(1,3,6), M(3,8,6), and N(3,7,3) is approximately 29.1547.

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Full Question: The Area of the Parallelogram with Vertices k(1,2,3), l(1,3,6), m(3,8,6), and n(3,7,3) is √265.

Answer:

To find the greatest common factor (GCF) of the list of terms 30x^3, 110x^4, and 60x^5, we can begin by factoring each term into its prime factors:

30x^3 = 2 * 3 * 5 * x * x * x

110x^4 = 2 * 5 * 11 * x * x * x * x

60x^5 = 2 * 2 * 3 * 5 * x * x * x * x * x

Next, we can identify the common factors among the three terms. These are 2, 5, and x^3. The GCF is the product of these common factors:

GCF = 2 * 5 * x^3 = 10x^3

Therefore, the greatest common factor of 30x^3, 110x^4, and 60x^5 is 10x^3.

Step-by-step explanation:

There were 2484 patrons in the theatre that night.

Let n represent the overall number of theatergoers that evening.

Let g represent the number of attendees in the gold seating, s represent the attendees in the silver seating, r represent the attendees in the red seating, and b represent the attendees in the black seating.

Consequently, n = g + s r b.

g = n because of the theatre goers are seated in the gold section.

r + b = n because of the customers are either in the red or the black seating.

The answer is obvious: b = 138.

As a result, r + b = n changes to

r + 138 = n, or r =  n - 138.

Since

n = n + 3(n - 138) + (n - 138) + 138

n = n + n - 414 + n - 138 + `138

n = n + n - 414

n = n - 414

n = 414

n = 2484

Therefore, there were 2484 patrons in the theatre that night.

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As per the probability, the project manager can estimate that the project will take 32.28 weeks to complete with a 90% confidence level.

To convert the project completion distribution to the standard normal distribution, the project manager needs to calculate the z-score, which represents the number of standard deviations away from the mean. The formula for the z-score is:

z = (x - μ) / σ

Where x is the completion time, μ is the mean of the distribution (30 weeks), and σ is the square root of the variance (√(2.78)).

Using a standard normal distribution table or calculator, the project manager can find the z-score corresponding to the 90th percentile, which is approximately 1.28.

To find the completion time that would be exceeded with a probability of only 10%, the project manager can use the inverse of the z-score formula:

x = z * σ + μ

Plugging in the values, the estimated completion time with a 90% confidence level is:

x = 1.28 * √(2.78) + 30 = 32.28 weeks

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