least from greatest to least

The corresponding probabilities are: A. P(R) = 0.72 B. P(R') = 0.28 C. P(A ∩ R) = P(R) * P(A | R) = 0.72 * 0.51 = 0.367 D. P(A | R) = 0.51 E. P(A ∩ R') = P(R') * P(A | R') = 0.28 * 0.10 = 0.028 F. P(A' ∩ R) = P(R) * P(A' | R) = 0.72 * 0.49 = 0.352 G. P(A' ∩ R') = P(R') * P(A' | R') = 0.28 * 0.90 = 0.252

(a) The tree diagram with the corresponding probabilities is:

A (0.51) A' (0.49) A (0.10) A' (0.90)

(b) The proportion of students who earn an A and don't attend class regularly is:

P(A ∩ R') = 0.028

(c) The chance that a randomly chosen student will earn an A in the class is:

P(A) = P(A ∩ R) + P(A ∩ R')

= 0.367 + 0.028

= 0.395

(d) Given that a student earned an A, the chance they attend class regularly is:

P(R | A) = P(A ∩ R) / P(A)

= 0.367 / 0.395

≈ 0.9291 (rounded to four decimal places)

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Complete question:

A professor has noticed that students hat attend class regularly, mss no more than two classes per term, generally get better grades. For he class, the overall percent o students who attend regularly s 72% or those who come to class on a regular basis, 51% receive A's. Of those who don't attend regularly, only 10% get A's. (b)Among all students what proportion earn an A and don't attend class regularly?

Answer:

i think it is 30/1 but i could be wrong sorry

Water weighs 4.92892 grams in a US teaspoon. Thus, 1 g of water is equivalent to around 1/5 teaspoon.

The acronym "Tsp" stands for teaspoon, a volumetric measurement commonly used in baking and cooking. A "gram" is a measure of mass or weight. As a result, converting between tsp and grams is not possible.

The density of the material being measured determines how to convert teaspoons to grams. For instance, a teaspoon of water weighs around 5 grams, but a teaspoon of sugar weighs roughly 4 grams.

I'll do my best to estimate the substance's weight in grams if you tell me what it is that you are quantifying in teaspoons.

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Answer:

540$

Step-by-step explanation:

9x9 = 81

9 + 9 + 9 + 9 = 36

36 x 15 =540

The number of X values listed in the first column of the frequency distribution table will be d) 4.

In a frequency distribution table, the first column typically represents the range or interval of the scores. Since the given sample has a range from X = 7 to X = 4, the first column of the frequency distribution table will include the four distinct X values: X = 4, X = 5, X = 6, and X = 7.

hese are the possible values within the given range, and thus, there will be 4 X values listed in the first column. So the correct option is d in this question.

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Ximena wants to design a test for applicants for a statistician position that solely focuses on g factors. Which of the following would it most likely test

Answer: A. Performance of general maths skills The test designed by Ximena for applicants for a statistician position that solely focuses on g factors would most likely test the performance of general maths skills.

A g factor is a concept in psychology that refers to a general intelligence factor that is widely accepted. It is often defined as a mental capacity that is responsible for a person's overall performance on intellectual tasks.

Because general math skills are an essential component of general intelligence, a test for applicants for a statistician position that solely focuses on g factors would most likely test performance of general maths skills.

Therefore, Option A - Performance of general maths skills is the correct answer.

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The score a student would need to have a 30th percentile score on the SAT is approximately 1345. Option B is correct.

To find the score that corresponds to the 30th percentile, we need to use a z-table to determine the z-score that corresponds to a cumulative probability of 0.30.

Using the formula for converting a raw score to a z-score:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and the σ is the standard deviation.

Rearranging this formula to solve for x:

x = z × σ + μ

To find the z-score for a 30th percentile, we can look up the corresponding value in a z-table or use a calculator with a built-in normal distribution function. The z-score corresponding to a cumulative probability of 0.30 is approximately -0.52.

Substituting the known values into the formula above:

x = -0.52 × 312 + 1509

Simplifying:

x ≈ 1345

Hence, B. 1345 is the correct answer.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

5

Step-by-step explanation:

The original number of students scheduled to go on the field trip was 600.

Let the original number of buses be "x" and each bus having "y" students, we can use algebra to solve for the number of students on the field trip.

It is given that; x*y = 600, that is, the original number of students is 600. When the organizer increases the number of buses by 4, the number of buses will be (x + 4), and the number of students per bus decreases by 5. We can express this as y - 5.

Hence, the new number of students will be 600 since no new students were added. We can represent this using the equation (x + 4) * (y - 5) = 600.

Substituting x*y = 600, we get x*(y-5) = (x + 4) * (y - 5).

Expanding the equation above, we get; xy - 5x = xy - 5y + 20.

Rearranging, we have 5x - 5y = 20. Dividing both sides by 5, we get x - y = 4.

Substituting xy = 600, we get x * (x - 4) = 600. Solving this quadratic equation, we get x = 24 or x = - 25.

We discard the negative solution. Therefore, the original number of students scheduled to go on the field trip was

24 * 25 = 600 students.

Therefore, the conclusion is that the original number of students scheduled to go on the field trip was 600.

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Answer:

30/64 inches.

Explanation:

The size of the converted metric part = 0.473 in.

Now, we know that:

Therefore:

Thus, we have that:

To the nearest 64th of an inch, the closest size will be 30/64 inches.

The expression for the length of the sail is x = 7( tan 50° ).

According to the given question.

The sail of a boat is in the shape of a right triangle.

And, the sail of a boat is a right triangle with an acute angle at the tip equal to 50 degrees and the side of the sail which is the hypotenuse to the right triangle is 7 meters long.

Now, the side that measures 7 meters would be the adjacent because its right next to the angle and its not the hypotenuse because its not the largest side

And, the side which we do not know the length to will be the opposite side because it is opposite from where the angle is.  

So, we have the the measure of the adjacent side and the angle of the tip. And we have to find the expression for the length of the sail.

Let the length of the sail be x meters.

Now, in the given right angled triangle

We can say that

tan A = Opposite side/Adjacent side

⇒ tan 50° = x/7

⇒ x = 7( tan 50° )

Hence, the expression for the length of the sail is x = 7( tan 50° ).

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

A point estimate is a single approxmate value of some parameters.

A point estimate for difference in average means is the difference between the sample means .

Point estimator :

In statistics, point estimation uses sample data to compute a single value, called a point estimate, to identify a point in a given parameter space.

Estimator Properties:

Point Estimate of Difference in Average Sales:

Point Estimate of Population Mean The calculation is the sum of all samples divided by the number of values .

Suppose we want to compare the means of two different populations . Each population has a mean and a standard deviation. Take a random sample from Population1 and label the resulting sample statistic with Index1 . Draw a sample from population2 and label its sample statistic with index 2, without reference to the first sample.

It is denoted by " μ1-μ2 " .

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Inverse operations to the rescue!

So, you'd perform 22÷5 (product signals multiplication) to get your answer, 4.4. x=4.4

Mr. Cahn’s total earnings in a year is $18,900.

The total earnings is a function of the annual salary, commission and Christmas bonus.

Total earnings = annual salary + commission + Christmas bonus

Commission = 6% x (160,000 - 20,000)

6% x $140,000

0.06 x 140,000 =  $8,400

Total earnings =  $8,400 + 10,000 + $500 = $18,900

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Answer:

19,680

Step-by-step explanation:

1 lb = 16 ounces

1230 lb = 1230 * 16 ounces = 19,680 ounces

Answer:

It’s (-2,0) and (0,2)

Step-by-step explanation:

The required interval where a local maximum and a local minimum lie is (-2, 0) and (0,2).

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
For a function, the local minimum is defined as at a point the left and right-hand limit should be greater than of the point, while for a local maximum the left and right-hand limit should be lower.
So, while observing the table,
The graph between the interval (-2,0) is increasing, and decreasing so between this interval a local maximum is located,
while between the interval (0,2) graph of the function is decreasing than increasing, so a local minimum is located between the interval.

Thus, the required interval where a local maximum and a local minimum lie is (-2, 0) and (0,2).

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Answer:

Cards with Mark = 30

Cards with Drew  = 120

Cards with Katie = 12

Step-by-step explanation:

The complete question is

Drew has 4 times as many baseball cards as Mark. Katie has 3 fewer than than half as many cards  as Mark. In all they have 162 baseball cards. How many does each have?

Solution -

Let the number of cards with Mark be "X"

Number of cards with Drew = 4 *X = 4X

Number of Cards with Katies = 0.5 X -3

Sum of all the cards is equal to 162

X+4X + 0.5 X -3 = 162

5.5 X = 165

X = 30

Cards with Mark = 30

Cards with Drew = 4 * 30 = 120

Cards with Katei = 15-3 = 12

By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25

The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1

Let us solve this problem by applying the Kuhn-Tucker theorem.

Let us first write down the Lagrangian function:

L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)

Then, we find the first order conditions for a maximum:

Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0

Ly = x - 8λ₁y - 2λ₁x = 0

Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0

Lλ₂ = 2x - y + 1 = 0

The complementary slackness conditions are:

λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0

λ₂(2x - y + 1) = 0

Now, we solve for the above equations one by one:

From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1

Substitute this in equation (1), we get:

8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0

Simplifying, we get:

10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)

From equation (2), we can write x = 8λ₁y + 2λ₁x

Substitute this in equation (1), we get:

8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0

Simplifying, we get:

-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)

Solving equations (4) and (5) for λ₁ and λ₂, we get:

λ₁ = 1/20 and λ₂ = 9/100

Then, substituting these values in the first order conditions, we get:

x = 2/5 and y = 9/5

Therefore, the maximum value of xy is:

2/5 x 9/5 = 18/25

Hence, the required answer is 18/25.

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Answer: 1

Step-by-step explanation:

If heads is 3 more likely to come up than tails, then there are 3 heads for every tails.  

Hope it helps <3

Considering that each input is related to only one output, the correct option regarding whether the relation is a function is:

A. yes.

A relation represents a function when each value of the input is mapped to only one value of the output.

For this problem, we have that:

There are no repeated inputs, hence the relation is a function and option A is correct.

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To find the volume of the solid with equilateral triangular cross-sections, we need to integrate the area of each equilateral triangle over the interval [0,π]. The area of an equilateral triangle with side length s is given by (s^2√3)/4. Since the triangles have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x. Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2√3/4 dx

Simplifying, we get:

V = √3∫[0,π] sin x dx

Using the substitution u = cos x, we get:

V = √3∫[-1,1] √(1 - u^2) du

Using the formula for the integral of the half-circle, we get:

V = (√3/2)π

Therefore, the volume of the solid is (√3/2)π.

To find the volume of the solid with square cross-sections, we need to integrate the area of each square over the interval [0,π]. Since the squares have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x.

Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2 dx

Simplifying, we get:

V = 4∫[0,π] sin x dx

Using the identity ∫sin x dx = -cos x + C, we get:

V = -4cos x ∣[0,π]

Since cos π = -1 and cos 0 = 1, we get:

V = -4(-1 - 1) = 8

Therefore, the volume of the solid is 8.

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Answer:

(B) -8

Step-by-step explanation:

Given the 2-column table below:

\(\left|\begin{array}{c|c}x&y\\--&--\\-3&14\\-1&10\\1&6\\4&0\\8&?\\10&-12\end{array}\right|\)

Taking the pair (-3,14) and (-1,10)

\(Slope, m=\dfrac{10-14}{-1-(-3)} =\dfrac{-4}{2} =-2\)

Taking the pair (1,6) and (4,0)

Slope, \(m=\dfrac{0-6}{4-1} =\dfrac{-6}{3} =-2\)

Since the slope is constant, the table represents a linear function whose slope is -2. Therefore:

Taking the pair (8,y) and (4,0)

Slope, \(m=\dfrac{0-y}{4-8} =-2\)

\(\dfrac{-y}{-4} =-2\\y=-2*4=-8\)

Therefore, the value of ? on the y-column is -8.

Answer:

-8

Step-by-step explanation:

Answer:

1. 142°

2. 137°

3. 140°

Step-by-step explanation:

First we have to assume that each of the statements 1, 2 and 3 are independent of each other, otherwise the results will be inconsistent

Since m and n are parallel to each other and t is a straight line

1. ∠3 =∠7 = 142°

2. ∠1 + ∠2 = 180° ;  ∠2 = 180°-∠1 = 180° - 43° = 137°

3. ∠7 = ∠6 =140°

Answer:

(a) = 0.92
(b) = 0.7613

Step-by-step explanation:

Here are some information to help us answer these problems:

Given That:

P(A) = 0.69
P(B) = 0.23

Then,

Problem (a): P(A ∪ B) when, A ∩ B = ∅:

P(A ∪ B) = 0.69 + 0.23 - 0 = 0.92



Problem (b): P(A ∪ B) when, A ∩ B ≠ ∅:

P(A ∪ B) = 0.69 + 0.23 - (0.69 × 0.23) = 0.7613




I hope you find this easy to understand....

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The comparison of the lengths of the sides based on the angles are given

by sine rule.

The lengths of the sides from greatest to least are;

Reasons:

The given parameters are;

∠A = 78°, ∠B = 56°, ∠C = 46°

By sine rule, we have;

\(\displaystyle \frac{AC}{sin(56^{\circ})} = \frac{AB}{sin(46^{\circ})} = \frac{BC}{sin(78^{\circ})}\)

Given that, sin(46°) ≈ 0.719, sin(56°) ≈ 0.829, sin(78°) ≈ 0.978, we have;

sin(78°) > sin(56°) > sin(46°)

Therefore, applying equal proportions of similar ratios, we have;

BC > AC > AB

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BC > AC > AB

hope this helps >:3

Answer:

Step-by-step explanation:

  If you're allowed to use a calculator, type in 34, the division symbol, 6837, and finally enter:

  34 / 6837 = 0.00497

Answer:

0.00497294135

Step-by-step explanation:

As per the concept of unitary method, the another way to express 8 feet is 2 ²/₃ yards.

In math, unitary method is known as a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.

Here we have given that a clothesline rope is 8 feet long.

Now we need to find another way to express 8 feet.

We know that the formula to convert the measurement it to divide the length by the conversion ratio.

As we know that one yard is equal to 3 feet, then we can use this simple formula to convert is written as

=> yards = feet ÷ 3

Here the equivalent yard measurement is written as,

=> yards = 8 ÷ 3

Then we have to convert the improper fraction into mixed fraction form, then we get,

=> 2 ²/₃ yards.

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Answer:

C. Infinitely many

Step-by-step explanation:

Answer:

2

Step-by-step explanation: