the conditions for sample proportions to be approximately normal distribution are group of answer choices dependent samples and both np ≥ 10 and n(1 − p) ≥ 10 independent samples and both np < 10 and n(1 − p) < 10 dependent samples and both np < 10 and n(1 − p) < 10 independent samples and both np ≥ 10 and n(1 − p) ≥ 10

The conditions that are not possible are e) {(33), (19)} and g) {(11), (19)}.

To determine the conditions that are not possible, we need to analyze the interleaving of the two transactions and consider the serializability of their execution. Let's go through each option:

a) {(3), (13)}: This is possible. Transaction T1 updates the value from 1 to 3, and then T2 updates it from 3 to 13.

b) {(33), (39)}: This is possible. Transaction T1 updates the value from 3 to 9, and then T2 updates it from 9 to 39.

c) {(3), (9)}: This is possible. Transaction T1 updates the value from 1 to 3, and then T2 updates it from 3 to 9.

d) {(13), (19)}: This is possible. Transaction T1 updates the value from 1 to 3, and then T2 updates it from 3 to 13, and finally, T1 updates it again from 13 to 19.

e) {(33), (19)}: This is not possible. Transaction T1 updates the value from 1 to 3, and then T2 updates it from 3 to 13. Therefore, T1 cannot update it from 13 to 19 since the value is already 13.

f) {(11), (13)}: This is possible. Transaction T2 updates the value from 1 to 11, and then T1 updates it from 11 to 13.

g) {(11), (19)}: This is not possible. Transaction T2 updates the value from 1 to 11, and then T1 cannot update it from 11 to 19 since the value is already 11.

Therefore, the conditions that are not possible are e) {(33), (19)} and g) {(11), (19)}.

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Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.

The statement is True only for independent events and False otherwise. The statement "p (A ∩ B) = p(A). p(B)" is not always true for any two events A and B defined on a sample space S of an experiment.

This equation only holds true if A and B are independent events, meaning that the occurrence of one event does not affect the probability of the other event happening. In other words, p(A|B) = p(A) and p(B|A) = p(B).

If A and B are dependent events, meaning that the occurrence of one event affects the probability of the other event happening, then the equation does not hold true. In this case, the probability of A and B occurring together (p(A ∩ B)) would be less than the product of the probabilities of A and B occurring separately (p(A).p(B)).

Therefore, the statement is not always true and depends on whether A and B are independent or dependent events.

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Answer:

Average speed = 100 km/h

Step-by-step explanation:

Given:

Total distance covered = 250 km

Total time taken = 8:30 am - 6:00 am = 2:30 hours = 2.5

Find:

Average speed.

Computation:

⇒ Average speed = Total distance covered / Total time taken

⇒ Average speed = 250 / 2.5

⇒ Average speed = 100 km/h

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The standard matrix A of T, i.e., T(x)=Ax. Also,find T(x), where x=(2,-3) is T(x) = (-13, -11, 6, 8).

The standard matrix A of T can be found by using the formula A = [T(e1) T(e2)], where T(e1) and T(e2) are the images of the standard basis vectors e1 and e2 under the transformation T. In this case, T(e1) = (1, 2, 3, 4) and T(e2) = (5, 5, 0, 0), so the standard matrix A of T is:

A = [T(e1) T(e2)] = [(1, 2, 3, 4) (5, 5, 0, 0)] = [[1, 5], [2, 5], [3, 0], [4, 0]]

To find T(x), where x = (2, -3), we can use the formula T(x) = Ax. Substituting the values of A and x into this formula gives:

T(x) = Ax = [[1, 5], [2, 5], [3, 0], [4, 0]] * [(2), (-3)] = [(2*1 + (-3)*5), (2*2 + (-3)*5), (2*3 + (-3)*0), (2*4 + (-3)*0)] = [(-13), (-11), (6), (8)]

So the answer is T(x) = (-13, -11, 6, 8).
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The problem asks to find how many problems Nona has left to do if he solved 30 problems and completed 5/12 of his homework on Monday and 1/3 of his homework on Tuesday.

On Monday, Nona did 5/12 of his RSM homework, which means he has 1 - 5/12 = 7/12 of the homework left to do. If he solved 30 problems already, then the total number of problem is:

30 = (5/12)x + (1/3)x

30 = (15/36)x + (12/36)x

30 = (27/36)x

x = (30 × 36)/27

x = 40

So Nona has a total of 40 problems to do. He has already solved 30 problems, so he has 40 - 30 = 10 problems left to do.

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Answer:

this is tricky ngl

The volume V of a rectangular prism is given by the formula:

V = l x w x h

where l is the length, w is the width, and h is the height.

In this case, we have:

l = 12 inches

w = 25 inches

h = 20 inches

Substituting these values into the formula, we get:

V = 12 inches x 25 inches x 20 inches

Multiplying, we get:

V = 6,000 cubic inches

Therefore, the volume of the rectangular prism is 6,000 cubic inches.

The examples that represent the importance of determining the number of bacteria in a sample are determining the quality of milk, assessing the purity of food or water , testing to see if a patient has a bladder infection.

It is necessary to count the number of organisms present in a sample of a material, such as water, food, or a bacterial culture. Bacterial pathogens, for instance, can enter food at any point, including during growth/production at the farm, processing, handling, and packaging, as well as when the food is prepared in the kitchen . While pathogenic bacteria in tiny quantities are typically not harmful, poor storage and/or cooking practices can cause these germs to grow to dangerously high concentrations .Another method bacteria can be introduced into water is by faecal contamination . Gram-negative, non-spore-forming bacteria called coliforms can ferment lactose to create acid and gas. Fecal coliforms are a subset of these bacteria that are prevalent in both human and animal intestines. Other fecal coliform bacteria are frequently utilized as indicator species since they are rarely observed thriving in nature when there is no fecal pollution. The presence of E. coli signals the presence of feces, which raises the possibility of the presence of dangerous pathogens including Salmonella species and Campylobacter species.

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Answer: 10

Step-by-step explanation:

10 times 10 = 100

So square root of 100 = 10

Answer:

I think if you take the x out it would be equivalent

Step-by-step explanation:

3•3•3

a.  x ≡ 16 (mod 141) is the solution to the congruence 19x ≡ 4 (mod 141) using the modular inverse. b. x ≡ 1156 (mod 89) is the solution to the congruence 55x ≡ 34 (mod 89) using the modular inverse. c. 178x · z

a) To solve the congruence 19x ≡ 4 (mod 141) using the modular inverses found in parts (b), (c), and (d) of Exercise 5, we can apply the concept of modular inverse and modular arithmetic.

In modular arithmetic, the modular inverse of a number a (mod n) is another number x (mod n) such that ax ≡ 1 (mod n). In other words, the modular inverse of a allows us to cancel out a in modular equations.

In Exercise 5, the modular inverses of certain numbers were found. Let's assume the modular inverse of 19 (mod 141) is denoted as x. Therefore, we have 19x ≡ 1 (mod 141).

Now, to solve the congruence 19x ≡ 4 (mod 141), we can multiply both sides of the congruence by 4, which gives us:

(19x)(4) ≡ 4(4) (mod 141)

76x ≡ 16 (mod 141)

Next, we can multiply both sides by the modular inverse of 76 (mod 141) to cancel out 76:

76x · x^(-1) ≡ 16 · x^(-1) (mod 141)

Since 76 · x^(-1) ≡ 1 (mod 141), we have:

x ≡ 16 · x^(-1) (mod 141)

Therefore, x ≡ 16 (mod 141) is the solution to the congruence 19x ≡ 4 (mod 141) using the modular inverse found in Exercise 5.

b) To solve the congruence 55x ≡ 34 (mod 89), we need to find the modular inverse of 55 (mod 89) based on the information from Exercise 5.

Let's assume the modular inverse of 55 (mod 89) is denoted as y. Therefore, we have 55y ≡ 1 (mod 89).

To solve the congruence 55x ≡ 34 (mod 89), we can multiply both sides by 34:

(55x)(34) ≡ 34(34) (mod 89)

1870x ≡ 1156 (mod 89)

Next, we multiply both sides by the modular inverse of 1870 (mod 89) to cancel out 1870:

1870x · y ≡ 1156 · y (mod 89)

Since 1870 · y ≡ 1 (mod 89), we have:

x ≡ 1156 · y (mod 89)

Therefore, x ≡ 1156 (mod 89) is the solution to the congruence 55x ≡ 34 (mod 89) using the modular inverse found in Exercise 5.

c) To solve the congruence 89x ≡ 2 (mod 232) using the modular inverse found in Exercise 5, we can follow a similar approach.

Let's assume the modular inverse of 89 (mod 232) is denoted as z. Therefore, we have 89z ≡ 1 (mod 232).

Multiplying both sides of the congruence 89x ≡ 2 (mod 232) by 2, we get:

(89x)(2) ≡ 2(2) (mod 232)

178x ≡ 4 (mod 232)

Next, we multiply both sides by the modular inverse of 178 (mod 232) to cancel out 178:

178x · z

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Answer:

rational, simplified number is -0.5

Step-by-step explanation:

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The rate of dan that can eat three bananas in 90 seconds would be equal to 1banana/30sec.

The average Rate of Change of the function f(x) can be calculated as;

\(f(x) = \dfrac{f(b) - f(a)}{b-a}\)

Most of the times, you will get some other facts or information by which the unknown values of those items can be known. For simple daily life cases, we can use variables, which are nothing but just placeholders for those unknown values. We can then operate on those variables assuming them to be actual values, thus, getting near to their original values.

Given that Dan can eat three bananas in 90 seconds

Now

3banana= 90sec

1banana = 90/3

=30sec

Therefore, the rate of dan will be 1banana/30sec.

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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You can solve this by doing Pythagorean theorem. I think thats what its called... a^2+b^2=c^2. So 24 squared plus 18 squared is 900. The square root of 900 is 30. The legnth of the third side is 30.

The distance from the top of the flagpole to the ground is 30 feet.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

Given the distance from the base of a flagpole to a point on the ground = 24 feet

height of flagpole = 18 feet

the distance from the top of the flagpole to the ground is x

by Pythagorean theorem, we can find the distance

h² = b² + p²

h = hypotenuse = x

b = base = 24 feet

h = height = 18 feet

x² = 24² + 18²

x² = 576 + 324

x = √900

x = 30 feet

Hence the value of x is 30 feet.

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Given p(a) = 0.77 p(b) = 0.05 p(a and b) = 0.5, the probability of either event A or event B occurring is 0.82.

To find the probability of either event A or event B occurring, we can use the formula for the union of two events. The formula is given as:

p(A or B) = p(A) + p(B) - p(A and B)

Given the values provided, we have p(A) = 0.77, p(B) = 0.05, and p(A and B) = 0.5. Plugging these values into the formula, we get:

p(A or B) = 0.77 + 0.05 - 0.5 = 0.82

Therefore, the probability of either event A or event B occurring is 0.82, indicating a relatively high likelihood of at least one of the events happening.

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The composite function g(h(8)) when evaluated is 94.

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

g(a) = 4a - 2

h(a) = 3a

To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.

h(a) is defined as 3a, so h(8) = 3(8) = 24.

Now we can plug in 24 for a in g(a) and simplify:

g(a) = 4a - 2

g(h(8)) = g(24) = 4(24) - 2 = 94

Therefore, g(h(8)) = 94.

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Using either the law of sines or the law of cosines   a = (c * sin(24°)) / sin(96°)

To find the indicated side, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

Let's label the sides of the triangle as follows: side a is opposite to angle A, side b is opposite to angle B (given as 24°), and side c is opposite to angle C (given as 96°).

Using the Law of Sines, we have the following proportion:

a / sin(A) = c / sin(C)

We are given the values of angles B and C, so we can substitute the known values into the equation:

a / sin(24°) = c / sin(96°)

Now we can solve for side a by multiplying both sides by sin(24°):

a = (c * sin(24°)) / sin(96°)

Substituting the known values, we have:

a = (c * sin(24°)) / sin(96°)

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The context that could be modeled by a linear function is "snow was falling at a rate of 2 inches per hour."

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. In other words, a function takes an input and produces a corresponding output. It is often represented as a mathematical equation or a graph. Functions are used to model real-world phenomena and are an important tool in many areas of mathematics, science, and engineering.

Here,

A linear function describes a constant rate of change, and in this context, the rate of snowfall is constant at 2 inches per hour. The other contexts involve exponential or percentage change, which cannot be modeled by a linear function.

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The probability of a defect in the production process, based on the given specifications, is approximately 0.0228 (rounded to 4 decimals), indicating a relatively low likelihood of encountering defective items within the defined weight range.

To determine the probability of a defect, we need to calculate the area under the normal distribution curve that falls outside the acceptable weight range. In this case, the acceptable range is defined as plus or minus 2.4 standard deviations from the mean.

First, we calculate the range of acceptable weights by multiplying the standard deviation (0.14) by 2.4 and subtracting and adding this value to the mean weight (12 ounces). The lower limit is 12 - (2.4 * 0.14) = 11.664 ounces, and the upper limit is 12 + (2.4 * 0.14) = 12.336 ounces.

Next, we calculate the z-scores for these limits using the formula z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation. For the lower limit, the z-score is (11.664 - 12) / 0.14 = -2.4, and for the upper limit, the z-score is (12.336 - 12) / 0.14 = 2.4.

Using a standard normal distribution table or a calculator, we find that the area to the left of -2.4 is approximately 0.0082, and the area to the right of 2.4 is also approximately 0.0082. Since we want the probability of a defect, which includes both tails, we multiply this probability by 2 to get 0.0082 * 2 = 0.0164.

Therefore, the probability of a defect in the production process is approximately 0.0164, or 0.0228 when rounded to 4 decimal places.

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The required probability is 0.4966.

According  to our question-

The probability mass function of poisson distribution:

Where λ is called parameter.

It is given that The farmer counted 3,500 borers in the 5,000 ears.

Thus, the value of the parameter is:

The probability that an ear of corn selected at random will contain no borers is:

Hence, the required probability is 0.4966.

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Answer:

x = 30, -30

Step-by-step explanation:

Answer: Willis will take 3 hours to paint the room by himself.

Step-by-step explanation:

Given: Time taken by James to complete job by himself = 6 hours

Let Time taken by Willis to complete job by himself = t hours

Together they take 2 hours.

\(\dfrac{1}{6}+\dfrac{1}{t}=\dfrac{1}{2}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{2}-\dfrac{1}{6}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3-1}{6}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{2}{6}\\\\\Rightarrow\ t=\dfrac{6}{2}\\\\\Rightarrow\ t=3\)

So,  Willis will take 3 hours to paint the room by himself.

Answer:

The product of 6 numbers is negative only is the number of negatives is odd.

If the number of negative roots is even, then their product will be positive.

The greatest odd number less than 6, is 5. It means the smallest number of positive numbers is 6 - 5 = 1.

So the least number of positive roots is one.

Answer:

1. alternate exterior angles

2. co-interior angles

3. corresponding angles

4. alternate interior angles

5. corresponding angles

6. co-interior angles

Answer:

20 mins

Step-by-step explanation:

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