The value of λ and μ for which the system of equations x+y+z=6,x+2y+3z=10 and x+2y+λz=μ have no solution, are
Aλ=3,μ=10
Bλ=3,μ=10
Cλ=3,μ=10
DNone of these

Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.

What is liability ?

Liability refers to an obligation or debt that an individual, company, or organization owes to another party. In accounting and finance, liabilities are generally classified as current or long-term and can include items such as loans, mortgages, accounts payable, taxes owed, and salaries payable.

The following options would be considered a liability:

Student loan

Money you owe your parents

Mortgage payment

Car payment

Investments and retirement funds would not be considered liabilities as they are assets.

Therefore, Liabilities include student loans, money owed to parents, mortgage payments, and car payments, but investments and retirement funds are considered assets.

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This |x - 32| <= 2 means that the tire pressure can be anywhere between 30 psi and 34 psi.

In order for Ms. Sartain's car to have optimal gas mileage, the tire pressure should remain within 2 psi of 32 psi at all times. This can be modeled with an absolute value inequality.

The absolute value inequality that models this situation is |x - 32| <= 2. This inequality states that the difference between the tire pressure, x, and the optimal pressure, 32, should be less than or equal to 2.

In other words, the tire pressure can be 2 psi above or below the optimal pressure of 32 psi and still be within the acceptable range. This means that the tire pressure can be anywhere between 30 psi and 34 psi.

So the correct answer is |x - 32| <= 2.

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The exact number for tan(t + 71) is -0.5846.

To find tan(t + 71), we can use the formula for the sum of two angles:
tan(t + 71) = (tan t + tan 71)/(1 - tan t * tan 71)

Given that tan t = 5, we can substitute this value into the formula:
tan(t + 71) = (5 + tan 71)/(1 - 5 * tan 71)

To find the exact number for tan 71, we can use a calculator or a table of trigonometric values. The exact value of tan 71 is approximately 2.9042.

Substituting this value into the formula, we get:
tan(t + 71) = (5 + 2.9042)/(1 - 5 * 2.9042)

Simplifying the expression, we get:
tan(t + 71) = (7.9042)/(1 - 14.521)
tan(t + 71) = (7.9042)/(-13.521)
tan(t + 71) = -0.5846

Therefore, the exact number for tan(t + 71) is -0.5846.

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The volume of the cone is  1004.8 cm³.

Let's calculate the volume of the cone with radius 8 cm and the slant height is 17 cm. Therefore, let's find the volume of the cone as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore,

h² = 17² - 8²

h = √289 - 64

h = √225

h = 15 cm

Therefore,

volume of a cone = 1 / 3 × 3.14 × 8² × 15

volume of a cone = 1 / 3 × 3.14 × 64 × 15

volume of a cone = 3014.4 / 3

volume of a cone = 1004.8 cm³

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The hypotenuse of the right triangle is 25.5 inches.

A right triangle is a triangle that has one angle as 90 degrees. The sum of angles in a triangle is 180 degrees.

The right right triangle has the legs as 19 inches and 17 inches. Let's find the hypotenuse.

Using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

c² = 19² + 17²

c² = 361 + 289

c = √650

c = 25.495097568

c = 25.5 inches

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The correct order from least to greatest is: 3.1818181818, 5.55, 5.571, 5.58

To order these numbers from least to greatest, we first need to convert all of them to decimals so that we can compare them easily.

To convert (111)/(20) to a decimal, we can divide 111 by 20 to get 5.55.

To convert 5(7)/(11) to a decimal, we can first multiply 5 by 7 to get 35, and then divide 35 by 11 to get 3.1818181818.

Now we have the following numbers in decimal form:

5.58, 5.55, 5.571, 3.1818181818

Next, we can compare these numbers to determine their order from least to greatest.

3.1818181818 is the smallest number, followed by 5.55, then 5.571, and finally 5.58.

So, the correct order from least to greatest is:

3.1818181818, 5.55, 5.571, 5.58

In the original form of the numbers, the correct order is:

5(7)/(11), (111)/(20), 5.571, 5.58

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Using Poisson distribution, the probability of each scenario is attached below.

(a) The probability of receiving 0 complaints in a 3-day period is given by the Poisson distribution:

P(X=0) = (λ^x * e^(-λ)) / x!

where λ is the expected number of complaints per day, and x is the number of complaints in the time period of interest.

In this case, λ = 1.1 complaints per day, and x = 0 complaints in 3 days.

P(X=0) = (1.1^0 * e^(-1.1 * 3)) / 0! = 0.037

So the probability of receiving 0 complaints in a 3-day period is 3.7%.

(b) The probability of receiving 1 complaint in a 3-day period is:

P(X=1) = (1.1^1 * e^(-1.1 * 3)) / 1! = 0.041

So the probability of receiving 1 complaint in a 3-day period is 4.1%.

(c) The probability of receiving 2 complaints in a 3-day period is:

P(X=2) = (1.1^2 * e^(-1.1 * 3)) / 2! = 0.022

So the probability of receiving 2 complaints in a 3-day period is 2.2%.

(d) The probability of receiving 3 complaints in a 3-day period is:

P(X=3) = (1.1^3 * e^(-1.1 * 3)) / 3! = 0.008

So the probability of receiving 3 complaints in a 3-day period is 0.8%.

(e) The probability of receiving 4 complaints in a 3-day period is:

P(X=4) = (1.1^4 * e^(-1.1 * 3)) / 4! = 0.0022

So the probability of receiving 4 complaints in a 3-day period is 0.22%.

(f) The probability of receiving less than or equal to 4 complaints in a 3-day period is:

P(X ≤ 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) = 0.1102

So the probability of receiving less than or equal to 4 complaints in a 3-day period is 11.02%.

(g) The probability of receiving more than 4 complaints in a 3-day period is:

P(X > 4) = 1 - P(X ≤ 4) = 1 - 0.1102 = 0.8898

So the probability of receiving more than 4 complaints in a 3-day period is 88.98%.

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a. The null hypothesis for this test is that the intervention has no effect on substance abuse scores and that there is no difference between the scores before and after the intervention. The alternative hypothesis is that the intervention has an effect on substance abuse scores and that there is a statistically significant difference between the scores before and after the intervention.

b. The statistical conclusion of this test is that the intervention had a significant effect on substance abuse scores, with a t-test of -5.918 and a p-value of <0.001. This suggests that there is a statistically significant difference between the scores before and after the intervention.

a. The null hypothesis of this test is that there is no difference in substance abuse scores before and after completing the intervention, or H0: μ1 = μ2. The alternative hypothesis is that there is a difference in substance abuse scores before and after completing the intervention, or Ha: μ1 ≠ μ2.

b. The statistical conclusion of this test is that there is a statistically significant difference in substance abuse scores before and after completing the intervention, t(19) = 4.38, p < 0.001. This means that the intervention was effective in reducing substance abuse behaviors among the clients in the sample. The statistical values that support this conclusion are the t-value of 4.38 and the p-value of less than 0.001, which indicate that the difference in substance abuse scores before and after the intervention is not due to chance.

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The domain of the correspondence is {-3, -2.5, 0, 4} and the range is {3, 9, -10}. This correspondence is not a function because it is not a one-to-one correspondence; for example, both -3 and 4 are mapped to the same value of 3.

The question is asking for the domain, range, and whether the correspondence is a function for the given set of ordered pairs: {(-3,3), (-2.5), (0,9), (4,-10)}.

The domain of a correspondence is the set of all possible input values. In this case, the domain is the set of x-values from the ordered pairs: {-3, -2.5, 0, 4}.

The range of a correspondence is the set of all possible output values. In this case, the range is the set of y-values from the ordered pairs: {3, -5, 9, -10}.

A correspondence is a function if each input (x-value) is associated with only one output (y-value). To determine if the given correspondence is a function, we need to check if any x-value is repeated with a different y-value.

In this case, there are no repeated x-values, so each x-value is associated with only one y-value. Therefore, the correspondence is a function.

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The complete factorization of [tex]-3x^2+6x+9[/tex] is -3(x - 3)(x + 1).

A mathematical expression, equation, or polynomial is factorized, sometimes referred to as factored, when it is broken down into factors or simpler expressions.

A technique for factoring a number or a polynomial is called factorisation. The polynomials are divided into the sums of their component parts. As an illustration, x2 + 2x can be factored as x(x + 2), where x and x+2 are the factors that can be multiplied to obtain the original polynomial.

To factor completely [tex]-3x^2+6x+9[/tex], we first need to factor out the greatest common factor, which is -3:

[tex]-3(x^2 - 2x - 3)[/tex]

Now we can factor the quadratic expression inside the parentheses:

-3(x - 3)(x + 1)

Hence, the complete factorization of [tex]-3x^2+6x+9[/tex] is -3(x - 3)(x + 1).

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Answer:

The height of the kite from the ground nearest to the tenth will be 443.6 feet.

Step-by-step explanation:

The equation can be written as: x + 24° = 90°.

The measure of the unknown angle is 66°.

An algebraic equation is an equation that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Let the measure of the unknown angle be x.

Since the angle in the corner measures 90° and one piece of the tile will have a measure of 24°. We can write the equation as:

x + 24° = 90°

The measure of the unknown angle can be determined as follow:

​x + 24° = 90°

x = 90° - 24°

x = 66°

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If ∠PRM = 120°, then the measure of angle MRN is 60°.

Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.

Sum of the measures of angles of linear pair is supplementary.

In the figure, segment PN is a line.

So, the angles formed in between are linear pair of angles.

∠PRM and ∠MRN are linear pair of angles.

∠PRM + ∠MRN = 180°

120 + ∠MRN = 180°

∠MRN = 180° - 120°

∠MRN = 60°

Hence the required angle measure is 60°.

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Answer:
(i) Rs. 3,300, Rs. 4,125, Rs. 1,650, and Rs. 2,475

(ii) 4,950

Step-by-step explanation:

i) To find Mr. Jha's monthly expenditure on each item, we can use the given percentages to calculate the amount he spends on each category:

Food expenditure = 20% of Rs. 16,500 = 0.20 x 16,500 = Rs. 3,300

House expenditure = 25% of Rs. 16,500 = 0.25 x 16,500 = Rs. 4,125

Fuel expenditure = 10% of Rs. 16,500 = 0.10 x 16,500 = Rs. 1,650

Miscellaneous expenditure = 15% of Rs. 16,500 = 0.15 x 16,500 = Rs. 2,475

Therefore, Mr. Jha's monthly expenditure on food, house, fuel, and miscellaneous items is Rs. 3,300, Rs. 4,125, Rs. 1,650, and Rs. 2,475 respectively.

(ii) To calculate how much Mr. Jha saves every month, we can subtract his total expenditure from his monthly income:

Total expenditure = Rs. 3,300 + Rs. 4,125 + Rs. 1,650 + Rs. 2,475 = Rs. 11,550

Savings = Monthly income - Total expenditure = Rs. 16,500 - Rs. 11,550 = Rs. 4,950

Therefore, Mr. Jha saves Rs. 4,950 every month.

Answer: (i) Rs. 3,300, Rs. 4,125, Rs. 1,650, and Rs. 2,475 (ii) 4,950Step-by-step explanation:i) To find Mr. Jha's monthly expenditure on each item, we can use the given percentages to calculate the amount he spends on each category:Food expenditure = 20% of Rs. 16,500 = 0.20 x 16,500 = Rs. 3,300House expenditure = 25% of Rs. 16,500 = 0.25 x 16,500 = Rs. 4,125Fuel expenditure = 10% of Rs. 16,500 = 0.10 x 16,500 = Rs. 1,650 Miscellaneous expenditure = 15% of Rs. 16,500 = 0.15 x 16,500 = Rs. 2,475Therefore, Mr. Jha's monthly expenditure on food, house, fuel, and miscellaneous items is Rs. 3,300, Rs. 4,125, Rs. 1,650, and Rs. 2,475 respectively.(ii) To calculate how much Mr. Jha saves every month, we can subtract his total expenditure from his monthly income:Total expenditure = Rs. 3,300 + Rs. 4,125 + Rs. 1,650 + Rs. 2,475 = Rs. 11,550Savings = Monthly income - Total expenditure = Rs. 16,500 - Rs. 11,550 = Rs. 4,950 so Mr. Jha saves Rs. 4,950 every month. your welcome.

The product of the polynomials (4x-7)^(2) is 16x^(2)-56x+49. This is the final answer expressed as a single polynomial in standard form.

To multiply the polynomials using a special product formula, we can use the formula (a-b)^(2)=a^(2)-2ab+b^(2). In this case, a=4x and b=7. Plugging these values into the formula gives us:
(4x-7)^(2)=(4x)^(2)-2(4x)(7)+(7)^(2)

Simplifying the terms on the right side of the equation gives us:
(4x-7)^(2)=16x^(2)-56x+49

Simplifying, we have (4x-7)2 = 16x2 - 56x + 49, which is our answer expressed as a single polynomial in standard form.

Multiplying polynomials require only three steps.

First, multiply each term in one polynomial by each term in the other polynomial using the distributive law.

Add the powers of the same variables using the exponent rule.

Then, simplify the resulting polynomial by adding or subtracting the like terms.

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To solve the equation, we need to get rid of the fractions by multiplying both sides of the equation by the least common denominator (LCD), which is (b^(2)-9). This will give us:
(8)(b^(2)-9)/(b^(2)-9)-(1)(b^(2)-9)/(b+3)=(1)(b^(2)-9)/(b^(2)-9)
Simplifying the equation gives us:
8-(b^(2)-9)/(b+3)=1
Next, we will isolate the variable term by subtracting 8 from both sides of the equation:
-(b^(2)-9)/(b+3)=-7
Now, we will multiply both sides of the equation by (b+3) to get rid of the fraction:
-(b^(2)-9)=-7(b+3)
Expanding the equation gives us:
-b^(2)+9=-7b-21
Rearranging the equation gives us:
b^(2)-7b-30=0
Factoring the equation gives us:
(b-10)(b+3)=0
Setting each factor equal to zero gives us the possible solutions:
b-10=0 or b+3=0
Solving for b gives us the possible solutions:
b=10 or b=-3
However, we need to check for extraneous solutions by plugging the possible solutions back into the original equation. Plugging in b=10 gives us a true statement, but plugging in b=-3 gives us an undefined expression. Therefore, the only solution is b=10.
Answer: b=10

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The probability of being dealt 5 cards from a standard 52-card deck and getting a four of a kind is 0.00024.

To find the probability of being dealt 5 cards from a standard 52-card deck and getting a four of a kind, first find the total number of ways to get a four of a kind and then dividing that by the total number of possible 5-card hands.

Total number of 5-card hands:

52C5 = 52! / (5!)(47!) = 2,598,960

Total number of ways to get a four of a kind:

There are 13 different ranks in a standard deck, so there are 13 ways to choose the rank of the four of a kind. There are also 48 remaining cards in the deck after the four of a kind has been chosen, so there are 48 ways to choose the fifth card.

13(48) = 624

So the probability of getting a four of a kind is 624 / 2,598,960 = 0.00024.

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a. 39 work sampling observations. b. By selecting a random time and a random employee to observe. c. The 95% confidence interval for the population standard is approximately 83.56 +/- (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

a. To determine the number of work sampling observations necessary to achieve a 95% confidence level with a margin of error of +10%, we need to use the following formula:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = Z-score for the desired confidence level (1.96 for 95% confidence level)

p = proportion of beak adjustments estimated from preliminary investigation (0.3)

E = margin of error (0.1)

Plugging in the values:

n = (1.96^2 * 0.3 * 0.7) / 0.1^2

n = 38.15

Rounding up, we need at least 39 work sampling observations.

b. The random observations should be made by selecting a random time of day, and then selecting a random employee to observe. This should be repeated until the required number of observations has been made. This method ensures that all employees have an equal chance of being observed and that the observations are not biased towards certain times or individuals.

c. To determine the standard in hours per hundred beak adjustments, we need to use the following formula:

Standard = (Total time worked / Total number of beak adjustments) * 100

For the six employees summarized in the table:

Granny:

Standard = (82 / 164) * 100

Standard = 50 hours per hundred beak adjustments

Tweety:

Standard = (80 / 161) * 100

Standard = 49.69 hours per hundred beak adjustments

Item:

Standard = (200 / 185) * 100

Standard = 108.11 hours per hundred beak adjustments

Total:

Standard = (82 + 80 + 200 + 121 + 161 + 185) / (164 + 161 + 185) * 100

Standard = 83.56 hours per hundred beak adjustments

The calculated error is the difference between the estimated standard and the true population standard. Since we do not have the population data, we cannot calculate the error. However, we can calculate the variability in the sample data using the following formula:

Standard Error = Standard Deviation / √(n)

Where:

Standard Deviation = √((Σ(x - x-bar)^2) / (n - 1))

n = sample size

Using the data provided in the table, we can calculate the standard deviation and standard error as follows:

Standard Deviation = √(((82-73.5)^2 + (80-73.5)^2 + (200-119)^2 + (121-82.5)^2 + (161-119)^2 + (185-82.5)^2) / (6-1))

Standard Deviation = 55.88

Standard Error = 55.88 / √(6)

Standard Error = 22.83

This means that there is a 95% chance that the true population standard falls within + or - 2 standard errors of the estimated sample standard. Therefore, the 95% confidence interval for the population standard is approximately 83.56 + or - (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

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The complete question goes thus:

ACME Corp has hired Daffy Duck to conduct a work sampling project to establish standards. 25 employees are part of the operations under scrutiny. The operations include scenery making, coloring, animation, joke writing, duck beak adjustment, and carrot sourcing. A preliminary investigation resulted in the estimate that 30 percent of the time of the group was spent adjusting duck beaks (this is equal to 17,614 beak adjustments). a. How many work sampling observations would be necessary to conduct if a 95 percent confidence that the observed data were within a +10 percent of the population data? b. Describe how the random observations should be made and justify why (Assume that all random observations need to be conducted over a three-week period or 15 working days). c. The Following table illustrates summary data gathered from 6 out of the 25 employees. From this data, determine a standard in hours per hundred beak adjustments. What is the calculated error? Granny 82 164 Tweety 80 Item Total hours worked Total observations (all elements) Observations involving cataloguing Average rating Operators Speedy Taz Glez 78 76 200 121 Foghorn Leghorn 68 Yosemite Sam 81 161 185 144 51 57 29 42 47 55 78 95 120 85 95 99

The rate at which the water was drained from the tank is 6 gallons of water per minute.

Given:

Draining Time (minutes)      10         30

Water in Tank (gallons)     450        330

According to the question,

Now, we calculating the rate at which water was drained at a constant rate.

Rate of water drained = [tex]\frac{Rate of change of water in Tank}{Rate of change Draining Time }[/tex]

Rate of water drained = [tex]\frac{450 - 330}{30 - 10} = \frac{120}{20} = 6[/tex]

The gallon is an important unit of measurement that continues to be used widely today. Specifically, it refers to the amount of space occupied by one US liquid gallon of water, which is equivalent to approximately 3.785 liters. The gallon is commonly used to measure liquids such as gasoline, milk, and water.

The term "gallon" has a long history, dating back to medieval England, where it was used to measure wine and beer. Over time, different countries and regions developed their own variations of the gallon, with the US liquid gallon being slightly larger than the UK imperial gallon. In addition to its use in everyday life, gallons are also used in various industries, including agriculture, manufacturing, and transportation.

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Complete Question:

A tank of water was drained at a constant rate. The table shows the number of gallons of water left in the tank after being drained for two amounts of time. Draining Time (minutes) Water in Tank (gallons) 10 450 30 330

The greatest common factor of the two expressions 18y^(7)w^(2)u^(8) and 30y^(5)w^(4)u^(6) is 6y^(5)w^(2)u^(6).

The greatest common factor (GCF) of two expressions is the largest expression that divides both of the expressions. To find the GCF of the two expressions 18y^(7)w^(2)u^(8) and 30y^(5)w^(4)u^(6), we need to find the highest power of each variable that divides both expressions.

The GCF of the coefficients 18 and 30 is 6.

The highest power of y that divides both expressions is y^(5).

The highest power of w that divides both expressions is w^(2).

The highest power of u that divides both expressions is u^(6).

So, the GCF of the two expressions is 6y^(5)w^(2)u^(6).

Therefore, the greatest common factor of the two expressions 18y^(7)w^(2)u^(8) and 30y^(5)w^(4)u^(6) is 6y^(5)w^(2)u^(6).

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Answer:

30 Stamps

Step-by-step explanation:

Since 40% of Jon's collection has boat stamps, that means that 20% of his total collection would be 6 stamps (40%/2  and  12/2).

All that's left to do now is get that % to 100, and we can do this by multiplying that and the number of stamps by 5.  (20%*5=100,  6*5=30)

This means that Jon has a total of 30 stamps in his collection.

Another way you could do this is simply to multiply 12 by 40%, or 0.4.
This will also give you an answer of 30 stamps.

Answer:

Step-by-step explanation:

No, Selena is incorrect.

answer: Even though there are six

more people than pizzas at the large table and only five more people

than pizzas at the small table, each person at the large table will get

a greater share of pizza than each person at the small table.

The equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

equation of a line using point-slope form is-

y - y1 = m(x - x1)

Points: (17,-12) and  slope -3.

Put the values:

y - (-12) = -3(x - 17)

y + 12 = -3x + 51

y = -3x + 51 - 12

y = -3x + 39

Thus, the equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

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The paper is 147/8 square inches in size. If preferred, this can be condensed to a mixed number or decimal.

A three-dimensional object's surface area is the sum of its sides. It is a measurement of the object's visible surface area. Depending on the shape of the item, different surface area formulas apply. For instance, adding the surface areas of all six sides of a rectangular prism will yield its surface area. The calculation for a rectangular prism's surface area is: Flat area equals 2lw + 2lh + 2wh where the rectangular prism's dimensions are l for length, w for breadth, and h for height.

given

The length and breadth of the postcard must be multiplied to determine its area.

The mixed integers must first be transformed into improper fractions:

5 1/4 = 21/4

3 1/2 = 7/2

We can now multiply:

Area is equal to length times breadth.

Area = (21/4) × (7/2)

Area = (21 × 7) / (4 x 2)

Area = 147/8

The paper is 147/8 square inches in size. If preferred, this can be condensed to a mixed number or decimal.

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Answer: 89 miles

Step-by-step explanation:

Well, if the construction crew added one mile every day for 38 days, then the formula would look like this.

L = 51 + (38)

51 + 38 = 89

L = 89 miles

Answer:

Using the difference of squares formula, we have:

(r³ - 6t¹) (r³ + 6t¹) = r³ × r³ - r³ × 6t¹ - 6t¹ × r³ - 6t¹ × 6t¹

= r^6 - 36t²

Therefore, the expression in simplest form is r^6 - 36t².

Answer:

2:35

Step-by-step explanation:

The result is the 95% confidence interval for µ.

The Metropolis-Hasting (M-H) algorithm is a Markov Chain Monte Carlo (MCMC) method used to sample from a probability distribution. In this case, we want to sample from the posterior distribution of µ, given the recorded data and the prior distribution. The M-H algorithm works by proposing a new value for µ, calculating the acceptance probability, and then deciding whether to accept or reject the proposed value. Here are the steps to construct the M-H algorithm:

Start with an initial value for µ, denoted as µ0.
Propose a new value for µ, denoted as µp, from the proposal distribution q(µ| µo) : N(θ: mean = µp, std = 2).
Calculate the acceptance probability, denoted as α, using the likelihood function L(µ) and the prior distribution p(µ):
α = min{1, [L(µp)/L(µ0)]*[p(µp)/p(µ0)]*[q(µ0| µp)/q(µp| µ0)]}
Generate a random number u from the uniform distribution U(0,1).
If u ≤ α, accept the proposed value and set µ0 = µp. Otherwise, reject the proposed value and keep µ0 unchanged.
Repeat steps 2 to 5 for a specified number of MCMC draws (15000 in this case), and discard the first 1500 draws as the burn-in phase.
Calculate the 95% confidence interval for µ using the remaining 13500 draws.

The 95% confidence interval for µ can be calculated by finding the 2.5th and 97.5th percentiles of the posterior distribution of µ. This can be done by sorting the 13500 draws of µ in ascending order and finding the values that correspond to these percentiles. The result is the 95% confidence interval for µ.

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Step-by-step explanation:

a = 55° because angles on a straight line (around a single point on one side of the line) add up to 180°.

b = 75° because alternate angles (with parallel lines) are equal.

c = 50°, because alternate angles (with parallel lines) are equal.

d = 50°, because corresponding angles (with parallel lines) are equal.

The volume of the composite solid is 5104 cubic ft.

A triangular prism's volume is the area that it takes up in all three dimensions. A prism is a solid object that has the same cross-section throughout its entire length, equal bases, and flat, rectangular side faces. Prisms can be divided into many categories and given different names depending on the form of their bases. A triangular prism has three rectangular lateral sides and two identical triangular bases.

The area of a triangular prism is given as:

V = 1/2(bhl)

Here, h = 22 - 12 = 10 ft.

Substituting the values we have:

V = 1/2(13)(10)(32)

V = 2080 cubic ft.

The volume of the rectangular prism is given as:

V = lwh

V = (28)(9)(12)

V = 3024 cubic ft.

The volume of the composite solid is:

V = V1 + V2

V = 2080 + 3024

V = 5104 cubic ft.

Hence, the volume of the composite solid is 5104 cubic ft.

Learn more about composite solid here:

https://brainly.com/question/23755595

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