Look at the figure. If m 2JKM = 48, find m2).

The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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The probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

Let's use the following notation:

P(TB) represents the probability that an adult has tuberculosis, which is given as 0.05.

P(POS|TB) represents the probability that the test is positive given that an adult has tuberculosis, which is given as 0.746.

P(NEG|TB) represents the probability that the test is negative given that an adult has tuberculosis, which is 1 - P(POS|TB) = 0.254.

We are asked to find the probability of an adult getting a NEG result and truly having tuberculosis, which can be calculated using Bayes' theorem as follows:

P(TB|NEG) = P(NEG|TB) * P(TB) / P(NEG)

We can calculate P(NEG) using the law of total probability, which considers the two possible cases for an adult: having tuberculosis (TB) or not having tuberculosis (TB').

P(NEG) = P(NEG|TB) * P(TB) + P(NEG|TB') * P(TB')

= 0.254 * 0.05 + 0.7653 * 0.95

= 0.7352

Now we can substitute the values into Bayes' theorem:

P(TB|NEG) = 0.254 * 0.05 / 0.7352

= 0.01725

Therefore, the probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

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The translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5). (option b)

To translate the triangle two units to the left, we need to subtract 2 from the x-coordinates of each vertex, while leaving the y-coordinates unchanged. This is because moving the triangle left means we're decreasing its x-values.

So, let's apply this transformation to each point.

The first point, (-1, -1), becomes (-1 - 2, -1), which simplifies to (-3, -1).

The second point, (-1, -5), becomes (-1 - 2, -5), or (-3, -5).

The third point, (0.5, -5), becomes (0.5 - 2, -5), or (-1.5, -5).

These new coordinates give us the vertices of the triangle after it has been translated two units to the left.

Now that we have the new vertices, we can label them A', B', and C' to distinguish them from the original vertices. So, the translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5).

This is the second option in the answer choices given.

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Answer:

\(x^{3}\) - 7x + 1

Step-by-step explanation:

(\(x^{4}\) - 5\(x^{3}\) - 7\(x^{2}\) + 36x - 5) ÷ ( x - 5)

Factor the expressions that are not already factored.

\(\frac{(x - 5) (x^{3} - 7x + 1)}{x - 5}\)

Cancel out x − 5 in both numerator and denominator.

\(x^{3}\) - 7x + 1

Answer:

stop cheating

Step-by-step explanation:

no

The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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Answer:

lateral area = pi x radius x slant height

slant height = 40^2 + 30^2 = 1600 + 900= \(\sqrt{2500}\) = 50

3.14 x 30 x 50 = 4710m^3

Hope that answers your question

Don't hesitate to leave a comment if you are confused about something

Step-by-step explanation:

We can conclude that the socioeconomic class of the offender is related to the likelihood of arrests.

Based on the information provided, we can conclude that there is a significant relationship between arrests and the socioeconomic class of the offender.
Identify the chi-square critical score: 9.488

Identify the chi-square test statistic: 12.2
Compare the test statistic to the critical score:

If the test statistic (12.2) is greater than the critical score (9.488), then there is a significant relationship between the variables.
In this case, 12.2 > 9.488, so there is a significant relationship between arrests and the socioeconomic class of the offender.
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Answer: 5(a+4)

Step-by-step explanation:

An expression that is equivalent to 5a + 20 is: 5 ( a + 4 ).

Since 5 times a equals 5a and 5 times 4 equals 20.

Therefore, 5 (a + 4) is equivalent to 5a + 20.

When he rests for a few hours after coming back from ice-store he rests for 2 hours the time the plane takes off is 9:10 pm.

Total distance traveled is 151 miles.

Dave spends 25 + 10 + 55 + 25 = 115 minutes (or 1 hour and 55 minutes) on stops.

Dave rests for 2 hours.

To calculate the time the plane takes off, we need to add up all the time Dave spends on driving, stops, and rests, and then add that time to the time he starts (12:45 pm).

Time to drive from A to C and back to A: 2 * 6 / 60 = 0.2 hours

Time to drive from A to C to D to B to A: (6 + 24 + 24 + 3) / 60 = 0.95 hours

Time to drive from A to C to D to home to E to market to E: (6 + 24 + 24 + 40 + 5 + 5) / 60 = 2.33 hours

Time to rest: 2 hours

Total time spent: 0.2 + 0.95 + 2.33 + 1.92 = 5.4 hours

Time of departure: 12:45 pm + 5.4 hours = 6:25 pm

Adding 45 minutes for the luggage check and boarding, the plane takes off at 6:25 pm + 0.45 hours = 7:10 pm

Adding another 2 hours for the time zone difference, the plane takes off at 7:10 pm + 2 hours = 9:10 pm.

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If Ariana removes the $4,800 rent from the set, the mean and median of the remaining rents will decrease because $4,800 is a very high value compared to the other rents.

Before removing the $4,800 rent, the mean can be calculated by adding up all the rents and dividing by the total number of rents (5):

Mean = (1,000 + 1,200 + 1,300 + 1,400 + 4,800) / 5 = 2,540

The median is the middle value in the set, which is 1,300.

After removing the $4,800 rent, the new mean can be calculated by adding up the remaining rents and dividing by the new total number of rents (4):

New Mean = (1,000 + 1,200 + 1,300 + 1,400) / 4 = 1,225

The new median is still 1,300 because it is the middle value in the remaining set.

Therefore, removing the $4,800 rent will decrease both the mean and median of the remaining rents.

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Explanation: We subtract the given value from 1

1-0.31 = 0.69

The complement of an event is the complete opposite.

Example: heads vs tails

Answer:

a) \(a_n=3n-1\)

b) \(a_n=2n+7\)

Step-by-step explanation:

a)  From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:

14 - 11 = 3

11 - 8 = 3

8 - 5 = 3

5 - 2 = 3

(so the common difference = 3)

General equation of arithmetic sequence:  \(a_n=a+(n-1)d\)

(where \(a\) is the first term and \(d\) is the common difference between terms)

Given:

\(\implies a_n=2+(n-1)3\)

\(\implies a_n=2+3n-3\)

\(\implies a_n=3n-1\)

b)  From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:

17 - 15 = 2

15 - 13 = 2

13 - 11 = 2

11 - 9 = 2

(so the common difference = 2)

General equation of arithmetic sequence:  \(a_n=a+(n-1)d\)

(where \(a\) is the first term and \(d\) is the common difference between terms)

Given:

\(\implies a_n=9+(n-1)2\)

\(\implies a_n=9+2n-2\)

\(\implies a_n=2n+7\)

Answer:

Step-by-step explanation:

x= 180-110(angles on a straight line)

x= 70

y=x=70 (alternate angles)

z= 110(alternate angles)

Answer:

Here is your answer

((9 * 7) ^ 8) ^ 6 =

(63 ^ 8) ^ 6 =

248155780267521 ^ 6 = 233531986596828998799172199566520716360870650059740845218613277797210219279668591621121

Step-by-step explanation:

Answer:

1)

x = 10.3

2)

x = 5.65

3)

x = 12.08

4)

x = 13.74

5)

x = 18.43

6)

x = 15.52

Answer:

1.72m^2x              5.=168f^2t^2x

2.63m^2x             6.=4\sqrt{257}imx\sqrt{im}

3.=55f^2t^2x

4.=90m^2x

Answer:

isnt that extrapolation?

Step-by-step explanation:

The solution to the coupled differential equations dx/dt= 2.x1 +x2 is x1 = t^2 + 2t and x2 = t^2, We can then integrate both sides of the equation to get the following: ln(2.x1 +x2) = t + c

To solve this set of differential equations, we can use the method of separation of variables. This method involves separating the variables in each equation so that they can be solved independently. In this case, we can separate the variables as follows: dx/(2.x1 +x2) = dt

We can then integrate both sides of the equation to get the following: ln(2.x1 +x2) = t + c

where c is an arbitrary constant. We can then exponentiate both sides of the equation to get the following 2.x1 +x2 = e^t.e^c

We can then substitute the initial conditions into this equation to get the following 2.x1 +x2 = e^t.1

where x1(0) = 0 and x2(0) = 0. This gives us the following solution for x1 and x2 x1 = t^2 + 2t and x2 = t^2

Here are some additional explanations:

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Answer:

25%

Step-by-step explanation:

Given:

The man buys the car for 80000 units.

For repairing the car, the man spends 20000 units.

The man sells the car for 125000 units.

To find:

The gain percent of the man.

Solution:

The man buys the car for 80000 units.

For repairing the car, the man spends 20000 units.

∴ Total expenditure of the man for the car_

(80000 + 20000) units.

= 100000 units.

The man sells the car for 125000 units.

∴ Gain = (125000 - 100000) units

= 25000 units.

∴ Gain % = (25000×100)/100000

= (25000/1000)

= 25 %.

∴ The gain of the man is 25 %.

Answer:

His gain is 25%.

Answer:

A≈12.57cm²

Step-by-step explanation:

A=1

4πd2=1

4·π·42≈12.56637cm²

Answer:

area of a circle with a diameter of 4cm=π(d/2)²

=π(4/2)²=π2²=4π cm ² is your answer or 4×3.16=12.48 cm²

Answer:

∠α = 5.001°

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The set consists of elements of the form y = x^2 - 1, where x is an integer. To find the four smallest elements of the set, we can substitute different integer values for x and determine the corresponding values of y. The four smallest elements can then be listed.

1. Start by substituting an integer value for x in the equation y = x^2 - 1.

2. Calculate the corresponding value of y.

3. Repeat steps 1 and 2 for different integer values of x.

4. Identify the four smallest values of y obtained from the calculations.

5. List these four values as the four smallest elements of the set.

The exact values of the four smallest elements will depend on the range of integer values chosen for x. The list of the four smallest elements should be provided as a comma-separated list.

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6 number of stickers diana given to her sister.

A division is a process of splitting a specific amount into equal parts.

Diana had 41 stickers and she put them in 7 equal groups. To find out how many stickers she put in each group, we can divide 41 by 7:

41 ÷ 7 = 5 with a remainder of 6

This means that Diana put 5 stickers in each of the 7 groups, and she had 6 stickers leftover.

She gave the leftover stickers to her sister, so she gave her sister 6 stickers.

Hence, 6 number of stickers  diana given to her sister.

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To calculate the cost of holding stock for a year, we need to determine the carrying cost per unit and multiply it by the number of units being held in stock.

First, let's calculate the economic order quantity (EOQ) for the computing systems:

EOQ = sqrt((2DS)/H)

where

D = annual demand = 25 systems

S = setup cost per order = $6,000

H = holding cost per unit per year = ?

Assuming a holding cost of 20% of the unit cost, we have:

H = 20% of unit cost = 0.20*$6,000/46 = $24.78 per unit per year

So, the EOQ is:

EOQ = sqrt((225$6,000)/$24.78) = 46.17 (rounded to 46)

Since the EOQ is 46 systems, we need to order 46 systems at a time to minimize our total inventory costs.

The cost of holding stock for a year is then:

Cost of holding stock = number of units held in stock * holding cost per unit per year

= 46 * $24.78

= $1,139.88

Therefore, it will cost your company $1,139.88 to hold 46 computing systems in stock for a year.

The next step would be to factor the left-hand side of the equation as (x - 3)^2 - 8 = 0, which can be solved using the square root method or by adding 8 to both sides and then taking the square root.

The first step when solving the equation x^2 - 6x - 40 = 0 by completing the square is to add the square of half the coefficient of x (which is (-6)/2 = -3) to both sides of the equation:

x^2 - 6x - 40 + (-3)^2 = (-3)^2

This simplifies to:

x^2 - 6x + 1 = 0

what is equation?

In mathematics, an equation is a statement that two expressions are equal. It contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. The goal of solving an equation is to determine the value or values of the variables that make the equation true. Equations are used to model real-world situations and to solve problems in various fields, such as science, engineering, economics, and physics.

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In a regression analysis, if SST = 4500 and SSE = 1575, then the coefficient of determination is 0.65.

The given data is as follows:

SST = 4500 ------ the total sum of squares

SSE = 1575 ---------the sum of squares error

In a regression model, the coefficient of determination is a statistical measurement that determines the proportion of variance for an independent variable.

The coefficient of determination (R²) is calculated using the following formula :

\(R^{2} = (\frac{SST - SSE}{SST} )\)

Substituting the values of SST and SSE in the coefficient of determination (R²) equation:

\(R^{2} = (\frac{4500-1575}{4500} )\)

\(R^{2} = \frac{2925}{4500}\)

R = 0.65

Therefore, we can conclude that  the coefficient of determination is 0.65

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The equation for the diameter is d = 8.65 ± 0.05.

The minimum possible diameter of the soccer ball is 8.60 inches and maximum possible diameter of the soccer ball is 8.70.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

diameter of soccer ball = 8.65 inches

Also, there is an allowable margin of error = 0.05 inch.

The equation for the diameter of the new soccer ball can be written as,

d = 8.65 ± 0.05

The minimum possible diameter of the soccer ball can be

= 8.65-0.05

= 8.60 inches

The maximum possible diameter of the soccer ball can be

= 8.65 + 0.05

= 8.70 inches

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Given the average, sum, and one of a list, the greatest integer that can be on the list is 235.

The average of a data set can be obtained by adding up all the data values, then dividing by the number of data.

Information from the problem:

Sum = 350

Average = 50

xₙ = 100

          Average = sum of all data / number of data

                    50 = 350 / number of data

number of data = 350 / 50

                          = 7

To find out the greatest member on the list, we want the other numbers to be as small as possible.

As the list members should be positive integers, first we can assume the first 5 numbers are 1, 2, 3, 4, and 5; and the 6th number is 100

Sum of all data = x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇

350 = 1 + 2 + 3 + 4 + 5 + 100 + x₇

350 = 115 + x₇

x₇ = 350 - 115

   = 235

Now the list consists of 1, 2, 3, 4, 5, 100, 235. Its sum is 350 and the average is 50, which is consistent with the given problem.

Thus, the biggest number that can be on the list is 235.

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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