Before making a final decision on the production plan to adopt, the bakery's manager decides to contact Professor Leung in the Math Department to conduct a market research survey. The results of the survey will indicate either favourable or unfavourable market conditions for premium breads.

In the past, when there was medium demand, Professor Leung's predictions were favourable 46% of the time. The professor's predictions have also been unfavourable given low demand 85% of the time, and favourable given high demand 69% of the time.

Assume prior probabilities of 0.2 and 0.3 for high and low demand respectively.
Calculate posterior (revised) probabilities and enter them in the table below.
Round answers to 3 decimal places; do not round intermediate results.

Note:
  The first cell of the table represents P(Low | Favourable)
  The last cell of the table represents P(High | Unfavourable)
Low Medium High
Favourable
Unfavourable

Determine the marginal probabilities of favourable and unfavourable predictions.

P(Favourable)=P(Favourable)=

P(Unfavourable)=P(Unfavourable)=

Answer:

TSP RSU

Step-by-step explanation:

Hope this helps!

(x - 2)² = 25

24 = x² - 4x + 3

rewritting:

x² - 4x = 24 - 3

x² - 4x = 21

using the completing the square:

coefficient of x = -4

square half the coefficient of x = (-4/2)² = (-2)²

Add the square half the cofficient of x to both sides of the equation

x² - 4x + (-2)² = 21 + (-2)²

taking out -4x:

(x - 2)² = 21 + 4

(x - 2)² = 25

The equation above is in the form (x + c)^2 = d or (x – c)^2 = d

The hourly wage in 10 years = $12.37,  In this scenario, automobile plant workers' hourly wages increased from $6.10 to $8.58 over a period of 7 years, with the wages growing exponentially.

To calculate their hourly wage in 10 more years, we will use the exponential growth formula:

Final Amount = Initial Amount * (1 + Growth Rate)^Years

First, we need to find the annual growth rate. To do this, we can rearrange the formula as follows:

Growth Rate = [(Final Amount / Initial Amount)^(1 / Years)] - 1

Plugging in the given values:

Growth Rate = [(8.58 / 6.10)^(1 / 7)] - 1
Growth Rate ≈ 0.0476

Now that we have the annual growth rate, we can calculate their hourly wage in 10 more years:

Hourly Wage in 10 Years = 8.58 * (1 + 0.0476)^10
Hourly Wage in 10 Years ≈ $12.79

Therefore, the automobile plant workers' hourly wage will be approximately $12.79 in 10 more years, assuming their wages continue to grow exponentially at the same rate.

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It is not reasonable to use the least-squares regression model to predict attendance per game for 0 wins because it involves extrapolation beyond the range of the observed data

Using the least-squares regression model to predict attendance per game for 0 wins is not reasonable because it would involve extrapolating the regression line beyond the range of the data.

In other words, the least-squares regression model is designed to capture the relationship between two variables within the range of the observed data. If we attempt to use this model to make predictions outside of this range, the results may not be reliable or accurate.

For example, if we were to use a least-squares regression model to predict attendance per game based on the number of wins a sports team had, and the range of wins in our data set was from 10 to 80, then any predictions we make for 0 wins (which is outside of this range) would be extrapolations rather than interpolations.

Extrapolation can be risky because it assumes that the relationship between the two variables continues beyond the range of the data. However, this assumption may not hold true in reality, and therefore the predictions made using extrapolation may not be accurate.

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To solve, we'll work left to right.

First, we have division. When we are dividing terms with exponents, given that the base is the same, then we need to subtract the exponents.

10^4 / 10^3 = 10^1

Next, we have multiplication. When we are multiplying terms with exponents, given that the base is the same, then we need to add the exponents.

10^1 x 10^9 = 10^10

Answer: 10^10

Hope this helps!

The statement "Choosing a smoothie containing apple and choosing a smoothie containing blueberry are not mutually exclusive events." can be inferred from the calculation.

Firstly, we identify the total number of each type of smoothies available. We have 12 apple smoothies, 7 blueberry, 8 other, and 3 smoothies that are common to both apple and blueberry. This brings our total smoothies to 30.

a) To find the probability that a smoothie contains either apple or blueberry, we need to consider the apple smoothies and smoothies that are common to both apple and blueberry then blueberry smoothies and smoothies that are common to both apple and blueberry. So, we add up the numbers of these smoothies and divide by the total number of smoothies.

P(contains apple) = (12 apple + 3 common) / 30 total = 15 / 30 which equals 0.5

P(contains blueberry) = (7 blueberries + 3 common) / 30 total = 10 / 30 which equals 0.33

Then, we find P(contains apple) + P(contains blueberry) = 0.5 + 0.33 which equals 0.83.

b) To find the probability that a smoothie contains apple or blueberry, we add up the number of apple smoothies, blueberry smoothies and smoothies common to both, then divide by the total number of smoothies.

P(contains apple or blueberry) = (12 apple + 7 blueberries + 3 common) / 30 total = 22/30 which equals 0.73.

c) The events of choosing a smoothie containing apple and choosing a smoothie containing blueberry are mutually exclusive if P(contains apple) + P(contains blueberry) is equal to P(contains apple or blueberry). As 0.83 is not equal to 0.73, these are not mutually exclusive events.

Therefore, the statement "Choosing a smoothie containing apple and choosing a smoothie containing blueberry are not mutually exclusive events." can be inferred from the calculation.

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Answer:

After a year you would have $1,825

Step-by-step explanation:

Amount for one cat a day in cents

10x25=250

Amount for one cat for a year in cents

250x365=91,250

Amount for both cats for a year in cents

91,250x2=182,500

Amount for both cats for a year dollars

182,500/100=1,825

The correct options are:

1) the triangle is isosceles.

2) the leg-to-hypotenuse ratio is 1:√2  

3) the non-right angles are congruent.

4) the ladder represents the longest length in the triangle.

For given question,

the length of the ladder is 12 feet.

the distance from the wall to the base of the ladder is 6√2 feet

Let x be the height of the wall.

Using Pythagoras theorem,

⇒ x² + (6√2)² = 12²

⇒ x² = 72

⇒ x = 8.5 ft

So, the triangle is right triangle.

Here, the hypotenuse = 12 ft

And, the leg-to-hypotenuse ratio is,

6√2 : 12 = 1:√2

We know that the right triangle is an isosceles triangle.

Since the right triangle is an isosceles  triangle, the non-right angles are congruent.

We know that, the hypotenuse is the longest length in the triangle.

So, the ladder represents the longest length in the triangle.

Therefore, the correct options are:

1) the triangle is isosceles.

2) the leg-to-hypotenuse ratio is 1:√2  

3) the non-right angles are congruent.

4) the ladder represents the longest length in the triangle.

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Answer:

1, 2, 4, and 5

Step-by-step explanation:

Edge 2022

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

According to the statement seen in this question, the line segments RT and  ST are collinear to each other. Mathematically speaking, the length of the line segment ST can be found by using the following formula:

RT = RS + ST

ST = RT - RS

ST = 19 - 6

ST = 13

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

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Lorraine can fill 8 jars with the tomatoes from the 2.5-gallon pot.

First, we need to convert the volume of the pot from gallons to quarts, since the jars are measured in quarts:

2.5 gallons = 2.5 * 4 quarts = 10 quarts

Next, we can divide the total volume of the pot in quarts by the volume of each jar in quarts to find the number of jars Lorraine can fill:

10 quarts / 1.25 quarts per jar = 8 jars

So Lorraine can fill 8 jars with the tomatoes from the 2.5-gallon pot.

Mensuration is a branch of mathematics that deals with the measurement of various geometric figures and objects, such as lengths, areas, and volumes. It is concerned with finding the size, shape, and measurement of geometric objects, such as points, lines, circles, polyggon, and solids.

Mensuration is used in various areas of mathematics, science, and engineering to solve problems involving measurements, such as finding the area of a rectangle, the volume of a cylinder, the circumference of a circle, or the surface area of a sphere.

Mensuration provides a set of mathematical formulas and methods for measuring geometric objects, and it requires knowledge of basic concepts such as perimeter, area, volume, and surface area. These concepts are used to find the size of objects and to compare different objects to one another based on their measurements.

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Calculating this expression will give us the probability that a random sample of 60 households in the town contains exactly 20 households that have 3 or more vehicles.

To solve this probability problem, we need to use the binomial probability formula.

The binomial probability formula calculates the probability of getting a specific number of successes in a fixed number of independent Bernoulli trials.

In this case, the probability of success is 30% (0.30), which represents the probability that a household owns 3 or more vehicles. The probability of failure is 70% (0.70), which represents the probability that a household does not own 3 or more vehicles.

Let's denote X as the number of households in the sample of 60 that have 3 or more vehicles. We want to find the probability that X = 20.

The formula for the probability mass function (PMF) of a binomial distribution is:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the number of combinations of n items taken k at a time (n choose k),

p is the probability of success,

n is the total number of trials,

k is the number of successes.

In our case:

p = 0.30 (probability of success)

n = 60 (total number of trials)

k = 20 (number of successes)

Now, we can calculate the probability:

P(X = 20) = C(60, 20) * (0.30)^20 * (1 - 0.30)^(60 - 20)

Using the combination formula, C(n, k) = n! / (k! * (n - k)!), we can calculate:

P(X = 20) = (60! / (20! * (60 - 20)!)) * (0.30)^20 * (0.70)^40

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The conversion method from milimeter to nanometer is Quantity in nanometer = quantity in milimeter × 10⁶.

In the question, the two short forms mm and nm are representative of milimeter and nanometer. As per the known information, the milimeter represents 1/10³ meters and nanometer represents 1/10⁹ meters. So, we see that the difference between the exponents of 10 is 6 (as 9 - 3 = 6).

Therefore, the conversion of milimeter to nanometer will be through the mentioned formula -

Quantity in nanometer = quantity in milimeter × 10⁶

For instance, the quantity 3 mili meters in nanometer will be calculated as follows.

Quantity in nanometer = 3 × 10⁶ nanometer

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Answer:

1. SSS

Step-by-step explanation:

AB = AC

BD = BD

AD = AD

Option(C), The sampling distribution used when making inferences about a single population's variance is a chi-square distribution.

The sampling distribution used when making inferences about a single population's variance is a chi-square distribution. This distribution is used when we want to estimate the population variance based on a sample of observations. The chi-square distribution is derived from the normal distribution and is used when we have a sample size greater than 30. This distribution is commonly used in inferential statistics, especially in hypothesis testing. The chi-square distribution is a non-negative, right-skewed distribution, and its shape changes based on the degrees of freedom. The degrees of freedom are calculated by subtracting one from the sample size. The chi-square distribution is a critical tool used in many areas, including quality control, genetics, and social sciences. It is important to understand the properties and uses of the chi-square distribution when working with samples to make inferences about a population's variance.

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thanks, this is a answer (:

The measure of angle OTQ is 166 degrees.

What are parallel lines?

Parallel lines are two or more lines in a plane that never intersect each other, no matter how far they are extended.

Since line NP is parallel to line OU, we can conclude that angles NRS and STU are corresponding angles, meaning they have the same measure. Therefore:

5X + 12 = 3X + 8

2X = 4

X = 2

Now that we know X, we can find the measure of angle STR:

3X + 8 = 3(2) + 8 = 14

Since angle STR is a straight angle with angle OTQ, we can find the measure of angle OTQ by subtracting the measure of angle STR from 180 degrees:

180 - 14 = 166

Therefore, the measure of angle OTQ is 166 degrees.

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Answer:

umm

Step-by-step explanation:

what? XD wdym

confusion...

If the hypotenuse is given to the 45 45  90 triangles, the leg of the triangle is calculated after dividing the hypotenuse by \(\sqrt{2}\).

The 45, 45, and 90 triangle is a type of isosceles triangle where the two legs are the same as each other and other non-right angles are both 45 degrees. Most of the time, Pythagoras' theorem is used for finding out the missing legs and hypotenuses of 45, 45, and 90 triangles.

If the leg of the triangle is equal to a, then:

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A derivative is a mathematical concept that represents the rate at which a function is changing at a given point. It is a measure of how much a function changes in response to a small change in its input.

We can start by finding the first derivative of the function:

f(x) = x^2 - 4x

f'(x) = 2x - 4

Then, we can find the second derivative:

f''(x) = d/dx (2x - 4) = 2

So, f''(2) = 2.

the value of f''(2) is 2.

what is function?

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function is typically represented by an equation or rule that assigns a unique output value for each input value.

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Maya is playing a trivia game with multiple choice questions. Each question has 222 correct answers among 555 answer choices. Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random.

The probability that maya's first guess is correct and her second guess is incorrect is 0.24.

From the question given above, the following data were obtained:

Correct answer (C) = 222

Total answer = 555

Incorrect answer (I) = 555 – 222 = 333

Next, we shall determine the probability that her 1st guess is correct.

Correct answer, nC = 222

Total answer, nS= 555

Probability of correct answer, P(C) =?

P(C) = nC / nS

P(C) = 222 / 555

Next, we shall determine the probability that her 2nd guess is incorrect

Incorrect answer, nI = 333

Total answer, nS = 554

Probability of incorrect answer, P(I) =?

P(I) = nI / nS

P(I) = 333 / 554

Finally, we shall determine the probability that her first guess is correct and her second guess is incorrect.

Probability of correct answer, P(C) = 222 / 555

Probability of incorrect answer, P(I) = 333 / 554

Probability of 1st correct and 2nd incorrect, P(C n I) =?

P(C n I) = P(C) × P(I)

P(C n I) = (222 / 555) × (333 / 554)

P(C n I) = 0.24

Hence the answer is, The probability that maya's first guess is correct and her second guess is incorrect is 0.24.

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Answer:

0.3

Step-by-step explanation:

Khan Academy ;)

To calculate real interest rates, you need to take into account inflation. The formula for real interest rate is: Real interest rate = Nominal interest rate - Inflation rate.

To calculate nominal interest rates, you simply divide the interest rate by 100 and multiply it by the principal amount. For example, if the nominal interest rate is 5% and you put $100 in the bank, you would earn $5 in interest ($100 x 0.05).

To calculate real interest rates, you need to take into account inflation. The formula for real interest rate is:

Real interest rate = Nominal interest rate - Inflation rate

For example, if the nominal interest rate is 5% and the inflation rate is 2%, the real interest rate would be 3% (5% - 2%). This means that your $100 in the bank would earn $3 in real terms after accounting for inflation.

In summary, to calculate nominal interest rates, simply multiply the principal by the interest rate, while to calculate real interest rates, subtract the inflation rate from the nominal interest rate.

Nominal interest rate is the rate at which you earn interest on your deposit without accounting for inflation. Let's assume you deposit $100 in a bank that offers a 5% annual nominal interest rate. To calculate the interest earned in one year, you would use the following formula:

Interest earned = Principal amount x Nominal interest rate
Interest earned = $100 x 0.05
Interest earned = $5

Now, to calculate the real interest rate, you need to consider the inflation rate. The real interest rate is the nominal interest rate adjusted for inflation, and it provides a more accurate representation of the true return on your investment. To calculate the real interest rate, use the Fisher equation:

Real interest rate ≈ Nominal interest rate - Inflation rate

Assuming the annual inflation rate is 2%, you would calculate the real interest rate as follows:

Real interest rate ≈ 0.05 - 0.02
Real interest rate ≈ 0.03 (or 3%)

So, in this example, your real interest rate is 3%, which takes into account the effects of inflation on your $100 deposit.

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The volume of the sphere figure is 697.19 cubic yards

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

The sphere

The volume of a sphere can be calculated as

V = 4/3πr³

Where

r = Radius

In this case,

r = 11/2

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

V = 4/3 * 22/7 * (11/2)³

Evaluate

V = 697.19

Hence, the volume is 697.19 cubic yards

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Answer:

2100

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

The equation of a line in point slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Given

y - 4 = \(\frac{1}{4}\) (x - 8)

with m = \(\frac{1}{4}\) and (a, b) = (8, 4 )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then

y = \(\frac{1}{4}\) x + c ← is the partial equation

To find c substitute (8, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = \(\frac{1}{4}\) x + 2 ← equation in slope- intercept form

Answer:1400.812

Step-by-step explanation:

Answer: 1,400.812

Step-by-step explanation: This looks like an addition problem

685.488 + 715.324 = 1,400.812