The probability of a randomly selected adult having a rare disease for which a diagnostic test has been developed is 0.002. The diagnostic test is not perfect. The probability the test will be positive (indicating that the person has the disease) is 0.96 for a person with the disease and 0.01 for a person without the disease. The proportion of adults for which the test would be positive is

Answer:

(x + 8)(x + 4)

Step-by-step explanation:

x² + 12x + 32                    Rewrite

x² + 4x + 8x + 32             Factor

x(x + 4) 8(x + 4)                

(x + 8)(x + 4)                    Final answer

Hope this helps!

Step-by-step explanation:

if x=1 --> 1 + 12 + 32 = 45

if x=2 --> 4+ 24 + 32 = 60

if x=3 --> 9+36+32 = 77

if x=4 --> 16 + 48 + 32 = 96

...

so, with the same logic we'll find the equation:

(x + 8)(x + 4)  

(because it's related to each of the equations on the top )                

I'm not sure if this is what you're looking for, if not tell me in the comments and I'll change my answer. Otherwise, I hope this answers your problem :)

To solve the inequality -1 < 5 - 3x ≤ 20, we need to isolate the variable x. Let's break it down into two separate inequalities: the solution to the inequality -1 < 5 - 3x ≤ 20 is -5 ≤ x < 2.

First, let's solve for the left inequality:

-1 < 5 - 3x

Subtracting 5 from both sides:

-1 - 5 < -3x

Simplifying:

-6 < -3x

Dividing both sides by -3 (remembering to reverse the inequality since we are dividing by a negative number):

-6/(-3) > x

2 > x

Now, let's solve for the right inequality:

5 - 3x ≤ 20

Subtracting 5 from both sides:

5 - 5 - 3x ≤ 20 - 5

Simplifying:

-3x ≤ 15

Dividing both sides by -3 (remembering to reverse the inequality):

-3x/(-3) ≥ 15/(-3)

x ≥ -5

Combining the results, we have 2 > x and x ≥ -5.

In summary, the solution to the inequality -1 < 5 - 3x ≤ 20 is -5 ≤ x < 2.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

Step-by-step explanation:

17

Answer:

Slope is -12.5

x-intercept is 75

y-intercept is 6

Step-by-step explanation:

See attached image

Answer:

3 times as great

Step-by-step explanation:

The most amount of water is 3/4 full

The least amount of water 1/4 full

To get from 1/4 to 3/4, you multiply by 3:

\(\frac{1}{4} * \frac{3}{1} = \frac{3}{4}\)

(I made 3 into 3/1 to show how you multiply across easier)

Answer:

Step-by-step explanation:

x^2-2x

x(x-2)

Answer:

Presumably you want to factor this, as there is no full equation to solve.

In this case you can divide both terms by x, giving you:

x(x - 2).

If you want to factor it into binomials, that's easy enough, as this is very close to being a difference of squares:

(x + x√2)(x - x√2)

You could just factor x out of both terms as well, giving you

x(x - 2)

Given the expression;

a+(b-c)²​

Given the values

a = 2

b = 3

c = -2

To eveluate the expression, we will have to substitute the given values into the expression as shown;

= 2+(3-(-2))²

​

= 2+(3+2)²

= 2+(5)²

= 2 + 25

= 27

Hence the value of the expression is 27.

The airspeed of the plane is approximately 377.8 mph and the speed of the wind is approximately 22.2 mph (rounded to one decimal place).

Let's denote the speed of the plane in still air as "p" and the speed of the wind as "w".

For the flight from Joppetown to Jawsburgh, the effective speed of the plane is reduced by the headwind. The time it takes for this leg of the journey is 4 hours and 30 minutes, which is equivalent to 4.5 hours.

Using the formula distance = speed * time, we can write the equation:

1600 = (p - w) * 4.5

For the return flight from Jawsburgh to Joppetown, the effective speed of the plane is increased by the tailwind. The time it takes for this leg of the journey is 4 hours.

Using the same formula, we can write the equation:

1600 = (p + w) * 4

We now have a system of two equations. Let's solve it to find the values of p and w.

From the first equation, we can express p - w as 1600 / 4.5. Simplifying, we get:

p - w = 355.56

From the second equation, we can express p + w as 1600 / 4. Simplifying, we get:

p + w = 400

Now, we can solve these two equations simultaneously.

Adding the two equations together, we eliminate w and get:

2p = 755.56

Dividing both sides by 2, we find:

p = 377.78

Substituting this value of p back into one of the equations, we can solve for w:

377.78 + w = 400

w = 400 - 377.78

w = 22.22

Therefore, the airspeed of the plane is approximately 377.8 mph and the speed of the wind is approximately 22.2 mph (rounded to one decimal place).

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Answer:

0.15

Step-by-step explanation:

15% = 0.15

__________________________________

Solution,

15%

=15/100

=0.15

So, 0.15 decimal is equivalent to 15%

Hope this helps

Good luck on your assignment

_______________________________

The value of z* should be used to construct a 97 confidence interval of a population mean is 2.17.

A degree of uncertainty and certainty in a sample process is measured by confidence intervals. They can choose from a variety of probability limitations, the most frequent becoming a 95% or 99% confidence level.

Some characteristics of confidence interval are-

Now, according to the question;

The confidence level is given 97%.

Thus, the crucial value of z for a 97% confidence interval is 2.17, as determined by a z score table, which is as follows:

\(P(-2.17 < Z < 2.17)=0.97\)

Therefore the obtained probability for the z-score of 2.17 is 0.97.

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Answer:

Step-by-step explanation:

P= perimeter

P=58 feet

shortest side=a

P= (a+18)+3a+a=58

5a+18=58

5a=58-18

5a=40

a=8 ft

In the given Markov chain, State 1 is absorbing, State 4 is periodic, State 1 is recurrent, and States 3, 4, and 5 are recurrent.

A Markov chain is a stochastic model that represents a sequence of states where the probability of transitioning from one state to another depends only on the current state. Let's analyze the given Markov chain to determine the properties of each state.

State 1: This state has a probability of 1 in the first row, indicating that it is an absorbing state. An absorbing state is one from which there is no possibility of leaving once it is reached. Therefore, statement a) is correct, and State 1 is absorbing.

State 2: There are no transitions from State 2 to any other state, which means it is an absorbing state as well. However, since it is not explicitly mentioned in the question, we cannot determine its status based on the given information.

State 3: This state has non-zero probabilities to transition to other states, indicating that it is not absorbing. Furthermore, it has a loop back to itself with a probability of 1/6, making it recurrent. Hence, statements c) and e) are incorrect, while statement f) is correct. State 3 is recurrent.

State 4: State 4 has a transition probability of 1/3 to State 3, which means there is a possibility of leaving this state. However, there are no outgoing transitions from State 4, making it an absorbing state. Moreover, since there is a loop back to itself with a probability of 2/3, it is also recurrent. Therefore, statement b) is correct, and State 4 is periodic and recurrent.

State 5: Similar to State 4, State 5 has a transition probability of 2/3 to State 3 and no outgoing transitions. Hence, State 5 is also an absorbing and recurrent state. Consequently, statement e) is correct.

To summarize, State 1 is absorbing and recurrent, State 4 is periodic and recurrent, and States 3 and 5 are recurrent.

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The sum of three circles could be equal to 9

We know that a triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

We are given that All triangles have the same value, and all circles have the same value.

WE can see that the triangle = 5

And there are number of circle= 3

Therefore, the sum of three circles =  9

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Answer:

Step-by-step explanation:

find "Y"

180 - 51 - 56 = 73°

the sum of the interior angles in a triangle is 180°

Find "x"

x = 180 - 73 - 72

x = 35

Answer:

x=35

Step-by-step explanation:

Answer:

X= -5

Step-by-step explanation:

Answer:

0.8

Step-by-step explanation:

Start solving.

3n + 3 = 5.4

Simplify

3n = 2.4

Simplify

n = 0.8

Answer:

0.8

Step-by-step explanation:

The growth of Al in business is mainly driven by the desire to increase automation of business processes. Artificial intelligence is a new and quickly growing technology transforming companies' operations.

AI is becoming increasingly common as organizations seek ways to automate various business processes. As businesses seek to improve efficiency and reduce costs, AI has become essential to achieving these goals. AI can perform various tasks, from automating customer service to analyzing large amounts of data for insights.

Businesses have embraced AI because it offers many advantages over traditional decision-making methods. By using AI, companies can improve accuracy and speed, reduce errors and risks, and increase productivity. Therefore, the growth of Al in business is mainly driven by the desire to increase automation of business processes.

The use of AI in companies is becoming increasingly common due to its ability to improve efficiency, reduce costs, increase accuracy and speed, reduce errors and risks, and increase productivity.

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Correlational research is concerned with examining relationships among variables. It focuses on understanding the associations or connections between different variables and how they relate to each other.

This type of research aims to explore the extent and direction of the relationship between variables without manipulating them.

In correlational research, researchers measure two or more variables and analyze their statistical relationship using techniques such as correlation analysis. The goal is to determine whether there is a positive or negative association between the variables, or if they are unrelated.

Correlational research does not involve establishing causation or determining differences between conditions, but rather focuses on understanding the patterns and strength of relationships between variables in order to identify potential associations or predict outcomes.

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Answer:

15.5cm² for number one

Step-by-step explanation:

I will only do number one for you but here how you do it

1/2 (12+9) 10.  

The 12 and 9 come from the top and bottem number and 10 come from the total height

Then we need to calucate

1/2(12+9)+10

1/2*21+10

1/2*31

31/2

15.5

So 15.5cm² is the answer for the first one now I think you can do the rest!

The Area of Trapezoids are:

1. 105 cm²

2. 6.75 ft²

3. 150 mm²

4.  19 ft²

5. 19.6 cm²

6. 331.2 mm²

7.  270.6 ft²

8. 30.36 in²

9.  73.2 cm²

10. 136.17 mm²

The formula of Area of Trapezoids is:

= 1/2 x (Sum of bases) x height

1. Area of Trapezoids is:

= 1/2 x (12 + 9) x 10

= 1/2 x 21 x 10

= 105 cm²

2. Area of Trapezoids is:

= 1/2 x (1.5+ 3) x 3

= 1/2 x 4.5 x 3

= 6.75 ft²

3. Area of Trapezoids is:

= 1/2 x (12 + 18) x 10

= 1/2 x 30 x 10

= 150 mm²

4. Area of Trapezoids is:

= 1/2 x (3 + 6.5) x 4

= 1/2 x 9.5 x 4

= 19 ft²

5. Area of Trapezoids is:

= 1/2 x (9.2+ 2) x 7

= 1/2 x 11.2 x 7

=  19.6 cm²

6.  Area of Trapezoids is:

= 1/2 x (8 + 24) x 20.7

= 1/2 x 32 x 20.7

=  331.2 mm²

7. Area of Trapezoids is:

= 1/2 x (20.1 + 25) x 12

= 1/2 x 45.1

= 270.6 ft²

8. Area of Trapezoids is:

= 1/2 x (3.2 + 5.6) x 6.9

= 1/2 x 8.8 x 6.9

=  30.36 in²

9. Area of Trapezoids is:

= 1/2 x (4.5  + 7.5) x 12.2

= 1/2 x 12 x 12.2

= 73.2 cm²

10. Area of Trapezoids is:

= 1/2 x (14 + 3.8) x 15.3

= 1/2 x 17.8 x 10

= 136.17 mm²

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Answer:

5

Step-by-step explanation:

Slope (m) of RH = 3/4

Distance of RH is d =5 units

Midpoint between points R and H is: M(1, 3.5)

Slope (m) = change in y / change in x = y2 - y1/x2 - x1, where:

R(3, 5) = (x1, y1)

H(-1,2) = (x2, y2)

Plug in the values

Slope (m) = (2 - 5) / (-1 - 3)

Slope (m) = (-3) / (-4)

Slope (m) of RH = 3/4

How to Find the Distance between two Points?

Distance formula used is: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

R(3, 5) = (x1, y1)

H(-1,2) = (x2, y2)

Plug in the values

RH = √[(−1−3)² + (2−5)²]

RH = √[(−4)² + (−3)²]

RH = 5 units

How to Find the Midpoint?

The midpoint formula used is: M[(x2 + x1)/2, (y2 + y1)/2)

R(3, 5) = (x1, y1)

H(-1,2) = (x2, y2)

Substitute the values

M[(-1 + 3)/2, (2 + 5)/2)

M(1, 3.5)

Therefore,

Slope (m) of RH = 3/4

Distance of RH is d =5 units

Midpoint between points R and H is: M(1, 3.5)

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Based on the data above, The five-number summary is 0.00, 0.17, 0.5, 1.43, 292.00.

The following data represent the dividend yields (in percent) of a random sample of 26 publicly traded des.

The following data represents the dividend yields (in percent) of a random sample of 26 publicly traded des:

0.5 0.8 1.75 0.04 0.18 0.35 3.69 0 0.95 0 0.17 1.83 1.33 0 0.54 1.14 0.41 159 21 2.41 292 3.18 3.03 1.43 0.58 0.13 0 0.19

Here, the five-number summary is given by:

Minimum value = 0.00

First Quartile (Q1) = 0.17

Median (Q2) = 0.5

Third Quartile (Q3) = 1.43

Maximum value = 292.00

Therefore, the five-number summary is 0.00, 0.17, 0.5, 1.43, 292.00.

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Answer:

The correct answer to the problem is 9

Step-by-step explanation:

3 x- 1 = 26

3 x = 27

x = 9

Step-by-step explanation:

Piece by piece :

Numerator            5^3 X 5^4  =   5 ^(3+4) = 5^7

Denominator        5^2 X 5^1   =   5^(2+1)   = 5^3

so now you have:

5^7 / 5^3       this equals    5 ^(7-3) = 5^4

then     (5^4 )^3  =  5^(4x3) = 5 ^12

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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The resistance of the heater wire in the electric blanket is approximately 102.56 ohms.

The resistance of the heater wire in the electric blanket, Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I). Since power (P) is equal to voltage multiplied by current (P = V × I),

Voltage (V) = 120 V

Power (P) = 140 W

First, to calculate the current (I) using the formula P = V × I :

I = P / V

I = 140 W / 120 V

I = 1.17 A

Now, calculate the resistance (R) using Ohm's Law:

R = V / I

R = 120 V / 1.17 A

R = 102.56 Ω

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Answer:

Step-by-step explanation:

The answer is D