Solve the equation 4^2x = 9

Answer:

2) 3

Step-by-step explanation:

In the case of the electronic chess game, with a useful life that follows an exponential distribution with a mean of 30 months, we need to determine the length of service time after which the percentage of failed units will approximately equal 50 percent. The options provided are 9 months, 16 months, 21 months, and 25 months.

For the major television manufacturer, the service life of its 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. We are asked to calculate the probability of service lives of at least five years.

1. Electronic Chess Game:

The exponential distribution is characterized by a constant hazard rate, which implies that the percentage of failed units follows an exponential decay. The mean of 30 months indicates that after 30 months, approximately 63.2% of the units will have failed. To find the length of service time when the percentage of failed units reaches 50%, we can use the formula P(X > x) = e^(-λx), where λ is the failure rate. Setting this probability to 50%, we solve for x: e^(-λx) = 0.5. Since the mean (30 months) is equal to 1/λ, we can substitute it into the equation: e^(-x/30) = 0.5. Solving for x, we find x ≈ 21 months. Therefore, the length of service time after which the percentage of failed units will approximately equal 50 percent is 21 months.

2. LED Televisions:

The service life of 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. To find the probability of service lives of at least five years, we need to calculate the area under the normal curve to the right of five years (60 months). We can standardize the value using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. Substituting the values, we have z = (60 - 72) / 0.5 = -24. Plugging this value into a standard normal distribution table or using a calculator, we find that the probability of a service life of at least five years is approximately 1.0000 (or 100% with four digits after the decimal point).

Therefore, the probability of service lives of at least five years for 50-inch LED televisions is 1.0000 (or 100%).

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Answer:

The solution to the system of equations be:

Step-by-step explanation:

Given the system of equations

\(x-2y = 10\)

x + 3y = 5

Solving the system of equations using the elimination method

\(\begin{bmatrix}x-2y=10\\ x+3y=5\end{bmatrix}\)

subtracting the equations

\(x+3y=5\)

\(-\)

\(\underline{x-2y=10}\)

\(5y=-5\)

solving 5y = -5 for y

\(5y=-5\)

Divide both sides by 5

\(\frac{5y}{5}=\frac{-5}{5}\)

Simplify

\(y=-1\)

For x - 2y = 10 plug in y = -1

\(x-2\left(-1\right)=10\)

Apply rule  -a(-a) = a

\(x+2\cdot \:1=10\)

Multiply the numbers:  \(2\cdot \:1=2\)

\(x+2=10\)

subtract 2 from both sides

\(x+2-2=10-2\)

Simplify

\(x=8\)

Therefore, the solution to the system of equations be:

The graph of the solution to the system of equations is also attached below.

Answer with Explanation: We need to find the probability of obtaining the red and tails when the two are flipped at the same time:

The probability of the red and tails or P(Red and Tails) is as follows:

Conclusion: Therefore the probability is (1/4) or 25%.

Hi! I'd be pleased to assist you with your permutations, probability, and position-related query. If a set of 24 children—14 boys and 10 girls—were lined up in a random order, what is the likelihood that the child in the 16th spot is a boy?

Step 1: Compute all possible combinations for the 24 children.

There are 24 children, hence there are 24 possible permutations in all! (Factorial, 24).

Step 2: Determine how many permutations there are with a boy in the sixteenth place.

Consider that there are currently 23 seats available for the remaining 13 boys and 10 girls to do this. The remaining children can be set up in 23! (23 factorial) different ways as a result.

Step 3: Use a to divide the permutations.

Step 4: Calculate the probability.
Probability = (Permutations with a boy in the 16th position) / (Total permutations)
Probability = (14 * 23!) / (24!)

Now, to simplify this expression, we can divide both the numerator and the denominator by 23!:
Probability = (14 * 23!) / (24! * 23! / 23!)
Probability = 14 / 24

Step 5: Simplify the probability.
Probability = 7/12

So, the probability that the person in the 16th position is a boy is 7/12.

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To find the probability that the person in the 16th position is a boy, we need to first calculate the total number of possible permutations in which any person can be in the 16th position. This can be calculated using the formula for permutation, which is n!/(n-r)!, where n is the total number of people and r is the number of positions.

So, the total number of permutations for 24 people in random order is 24!/(24-1)! = 24!

Next, we need to find the number of permutations in which a boy is in the 16th position. Since there are 14 boys and 10 girls, we can choose one of the 14 boys for the 16th position and then arrange the remaining 23 people in any order. This can be calculated using the formula for combination, which is nCr = n!/(r!(n-r)!), where n is the total number of items and r is the number of items chosen.

So, the number of permutations with a boy in the 16th position is 14C1 * 23! = 14 * 23!

Therefore, the probability of a boy being in the 16th position is the number of permutations with a boy in the 16th position divided by the total number of permutations, which is:

(14 * 23!)/24! = 14/24 = 7/12

In conclusion, the probability that the person in the 16th position is a boy is 7/12.

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Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects. A subset is a set that contains only elements that belong to a larger set, called the universal set. In this context, let S, T, X, and Y be subsets of some universal set.

Assuming that S [T X [Y, we can conclude that if a belongs to T, then a belongs to S or a belongs to X or a belongs to Y. This is because T is a subset of S [T X [Y, and any element in T must belong to at least one of these sets.

Assuming that S \T D, we can conclude that if a belongs to T, then a does not belong to S. This is because S \T is the set of elements that belong to S but not to T, and D is the empty set, meaning that there are no elements in the set. Therefore, if a belongs to T, it cannot belong to S \T, and so it must not belong to S.

Assuming that X S, we can use all three assumptions to prove that T Y. Suppose that a belongs to T. Then, using assumption (i), we know that a belongs to S or a belongs to X or a belongs to Y. But since a cannot belong to S (using assumption (ii)), we must have either a belongs to X or a belongs to Y. But since X is a subset of S (using assumption (iii)), we know that if a belongs to X, then a belongs to S. Therefore, we must have a belongs to Y. This holds for any element a in T, so we can conclude that T Y.

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Answer:

about 1 inch

Step-by-step explanation:

The experimental probability of drawing a spade is 0.2

When we perform an experiment N times, and we got a given outcome K times, the experimental probability of said outcome is given by the quotient:

P = K/N

Here the experiment is performed:

N = 6 + 4 + 7 + 3 = 20 times

And a spade is drawn 4 times, then the experimental probability is:

P = 4/20 = 1/5 = 0.20

The correct option is the second one.

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Answer: 4 bedrooms/3 bathrooms/2-car garage

Step-by-step explanation: just did it yw

Answer:

1.400%

2. 55$

3. C

4. 28

5. 19

6. 78

7. 1$

Answer:

12-27+9Y=5+6=90X5=800

Step-by-step explanation:

The missing sides and angles of the triangles are:

1) ∠L = 53°

LA = 23.145 ft

AB = 18.9 ft

2) ∠S = 57.31°

SA = 98.57 cm

SW = 69.12 cm

3) B = 30.71°

C = 99.29°

The law of cosine formula is expressed as:

c² = a² + b² - 2ab cos C

The Law of sines is expressed as:

a/sin A = b/sin B = c/sin C

Thus:

1) ∠L = 180 - (102 + 25)

∠L = 53°

LA/sin 102 = 10/sin 25

LA = 23.145 ft

AB = 10 * sin 53/sin 25

AB = 18.9 ft

2) ∠S = 180 - (79 + 43.69)

∠S = 57.31°

84.5/sin 57.3 = SA/sin 79

SA = 98.57 cm

SW/sin 43.69 = 84.5/sin 57.3

SW = 69.12 cm

3) 15/sin 50 = 10/sin B

sin B = (10 sin 50)/15

sin B = 0.5107

B = sin⁻¹0.5107

B = 30.71°

C = 180 - (50 + 30.71)

C = 99.29°

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Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

Answer: B. The rate is 2, the initial value is 4, and the specific value is 6.

Step-by-step explanation:

for a linear function y = a*x + b

Rate = coefficient that is multiplicating the variable. ( a in this case)

Initial value = value taken of y, when we have x = 0 (b in this case)

Specific value = value forced on y.

In this case, we have:

y = 6 = 2*x + 4

Then:

The coefficient multiplicating x is 2, so the rate is 2.

The constant term is 4, so the initial value is 4.

The value equal to y is 6, so the specific value is 6.

The correct option is B.

Answer:

The answer is: The rate is 2, the initial value is 4, and the specific value is 6.

Step-by-step explanation:

Answer:

\(\huge\boxed{a\in\mathbb{R}}\)

Step-by-step explanation:

\(1\times(a+3)=a+3\\\\a+3=a+3\\\\a-a+3=a-a+3\\\\3=3\qquad\bold{TRUE}\)

Answer:

See the Image below:)

ITS TRUE

SOLUTION ALL REAL NUMBERS

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Suppose a system of equations has 3 equations and 5 variables. additionally, suppose the coefficient matrix for the system has 3 pivot columns. Based on the information provided, it is consistent.

The number of pivot columns in the coefficient matrix of a system of equations determines the rank of the matrix, which is a measure of the number of linearly independent rows or columns. A system of equations is consistent if and only if the rank of the coefficient matrix is equal to the number of unknowns in the system.

In this case, the system has 3 equations and 5 variables, so it is not immediately clear if the rank of the coefficient matrix is equal to the number of unknowns. Additionally, the number of pivot columns alone is not enough to determine the consistency of the system, as there may be additional relationships between the variables that affect the rank.

So,  Based on the information provided, it is consistent.

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Answer:

A.

Step-by-step explanation:

In a direct proporton, the ratio of one quantity to teh other is a constant.

Let's divide each number of crystals by each number of pounds:

7/14 = 1/2

14/28 = 1/2

21/42 = 1/2

28/56 = 1/2

The ratio of crystals to pounds is always 1:2.

This is a proportional relation.

Answer: A.

Statistical conclusion validity is the extent to which inferences and conclusions drawn from statistical data are valid.

The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not.

Statistical conclusion validity is a measure of how valid the conclusions drawn from statistical data are. This is important because it allows us to draw valid inferences from the data. The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not. For example, a study may show that there is a correlation between ice cream sales and crime rate, when in fact it is merely a coincidence that both variables increase during the summer months. By controlling for other variables and using appropriate statistical tests, it is possible to identify and avoid spurious correlations.

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The technique used by the researchers is systematic sampling.

The technique used by the researchers to study alcohol consumption among college students living in campus housing is known as systematic sampling.

In systematic sampling, the researchers select a starting point at random, which in this case is a randomly selected dorm room. Then, they follow a systematic pattern by knocking on every fifth door in the dormitory. This ensures that the sample is representative of the entire population of college students living in campus housing.

Using systematic sampling allows the researchers to obtain a sample that is both random and systematic, reducing bias and providing a fair representation of the population. By using this technique, the researchers can gather data on alcohol consumption among college students living in campus housing.

The researchers employed systematic sampling to study alcohol consumption among college students living in campus housing. This technique helps ensure that the sample is representative and unbiased, allowing for accurate conclusions about the entire population.

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Answer:

63 units

Step-by-step explanation:

d = √(x2-x1)^2 + (y2-y1)^2

Meaning it would look like this

d = √(15+48)^2 + (23-23)^2

we changed the subtraction sign in the first one to an addition sign because it was a double negative

hope this helped

Two of the following are not characteristics of surveys. They are; A. The study compares two or more treatments and B. Statistical analysis is applied to the results of the study. Surveys are important tools that help researchers to collect data for research purposes.

A survey is a research design used to collect data on specific behaviors and attitudes, or attributes of a sample. Surveys typically involve questionnaires that are administered to respondents. The survey questions should be carefully constructed so as to produce valid and reliable data. There are some characteristics of surveys. These characteristics include the following:

The study involves one or more treatment groups and a control group: Surveys typically involve a sample of people who are randomly selected to participate in the study. There is usually one or more treatment groups who receive some type of treatment or intervention, and a control group who do not.Data are gathered during the course of the study: Surveys typically involve collecting data from respondents over a period of time. Data can be collected through various methods such as questionnaires, interviews, or observations.

Statistical analysis is applied to the results of the study: The data collected during the survey is analyzed using statistical techniques. This allows researchers to draw conclusions about the population being studied.The study compares two or more treatments: Surveys can be used to compare two or more treatments. For example, a survey can be used to compare the effectiveness of two different medications for a particular illness.However, two of the following are not characteristics of surveys. They are; A. The study compares two or more treatments and B. Statistical analysis is applied to the results of the study.

Surveys are an important tool that researchers use to collect data on specific behaviors and attitudes or attributes of a sample. Surveys typically involve questionnaires that are administered to respondents. The data collected during the survey is analyzed using statistical techniques. However, the study does not always compare two or more treatments and statistical analysis is not always applied to the results of the study.

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The smallest possible value of is 2, which is the greatest common divisor of the side lengths of the parallelograms bounded by the given lines.

To find the smallest possible value of , we need to determine the common divisor of the areas of the two parallelograms. Let's denote the lengths of the sides of the parallelogram bounded by the lines , , , and as 'a' and 'b', and the lengths of the sides of the parallelogram bounded by the lines , , , and as 'c' and 'd'.

The area of a parallelogram is given by the formula A = base × height. In this case, the bases of the parallelograms are 'a' and 'c', and the heights are 'b' and 'd', respectively.

We are given that the area of the first parallelogram is 18, so we have ab = 18.

Similarly, the area of the second parallelogram is 72, so we have cd = 72.

To find the common divisor of the two areas, we need to find the values of 'a', 'b', 'c', and 'd' that satisfy both equations.

Let's factorize 18 and 72:

18 = 2 × 3²

72 = 2³ × 3²

To minimize , we need to assign the lowest possible values to 'a', 'b', 'c', and 'd' such that the product ab = 18 and cd = 72.

The possible values are:

a = 2, b = 9 (2 × 9 = 18)

c = 4, d = 18 (4 × 18 = 72)

Therefore, the smallest possible value of is the greatest common divisor (GCD) of 'a' and 'c', which is GCD(2, 4) = 2.

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Sure! I can help you with that.

First, we should calculate the profit made by the shopkeeper. To calculate the profit, we will multiply the selling price of the table with 20%, which is 20% of 5400, or 1080.

Next, we should subtract the profit from the selling price to find the cost price of the table.

The cost price of the table = 5400 - 1080

The cost price of the table = 4320

Therefore, the cost price of the table is ₹ 4320.

No, it is not possible to have a simple graph with n vertices, where n is any integer greater than or equal to 5, such that all vertices have different degrees.

In a simple graph, the degree of a vertex refers to the number of edges connected to that vertex. The maximum degree possible in a graph with n vertices is (n-1), which occurs when one vertex is connected to all other vertices.

To create a graph where all vertices have different degrees, we would need to assign a unique degree to each vertex. However, if n is greater than or equal to 5, we cannot assign n unique degrees to n vertices while satisfying the conditions of a simple graph.

To see why, consider the case of n = 5. We need to assign degrees 1, 2, 3, 4, and 5 to the vertices.

The vertex with degree 5 must be connected to all other vertices, leaving us with four remaining degrees (1, 2, 3, and 4) to assign to the remaining four vertices. However, no matter how we distribute these degrees, at least two vertices will have the same degree.

This argument can be extended to any value of n greater than 5. Therefore, it is not possible to construct a simple graph with n vertices where all vertices have different degrees for any integer n ≥ 5.

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Answer:

$2304.5

Step-by-step explanation:

The balance after 8years=P(1+R/100)^t

=1000(1+11/100)^8

=$2304.5

Answer:

-3 + 4 = 1

Step-by-step explanation:

-3 + 4 = 1

Answer:

the anwer is D: 44,44,92

Step-by-step explanation:

2n+10=4n+2 ---->8=2n ------> n=4

11n=11(4)=44

m<N=m<L=44

180-44-44=92

the answer is: 1° equation

2° equation

3° equation

and the 4° equation