A certain disease has an incidence rate of 0.8%. If the false negative rate is 4% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease.

The probabilities are as follows:

(a) P(A')= 0.7

(b) P(A∪B) =  0.3

(c) P(A'∩B) =  0

(d) P(A∩B') =  0.1

(e) P[(A∪B)'] =  0.7

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7

(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3

(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0

(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1

(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7

Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.

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The relation that is a function is D: {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}.

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, for a relation to be a function, each input can only be related to one output.

In relation D, each input (x-value) has a unique output (y-value), meaning that each x-value is only paired with one y-value. In contrast, relations A, B, and C have repeated x-values with different y-values, which means that they are not functions.

In relation A, the input -1 is paired with two different outputs (2 and 3). In relation B, both inputs 0 and -1 are each paired with two different outputs. In relation C, both inputs 0 and -3 are each paired with two different outputs. Therefore, only relation D satisfies the definition of a function.

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The two possible locations for the fourth vertex are (4, -4) and (-3, -1).

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

To find the location of the fourth vertex of the square, we need to use the fact that a square has four equal sides and four right angles.

The first two vertices given are (4, 3) and (-3, 3), which lie on a horizontal line segment of length 7.

The third vertex is (-3, -4), which is 7 units away from the first two vertices and lies on a vertical line segment.

Since the square has four equal sides, the distance between the third vertex and the fourth vertex must also be 7 units.

And since the square has four right angles, the fourth vertex must be located on a vertical line passing through the first two vertices or on a horizontal line passing through the third vertex.

So, there are two possible locations for the fourth vertex:

(4, -4): This point is located 7 units below the first vertex (4, 3) on the vertical line passing through it.

(-3, -1): This point is located 7 units to the right of the third vertex (-3, -4) on the horizontal line passing through it.

Therefore, the two possible locations for the fourth vertex are (4, -4) and (-3, -1).

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Thus, the height of flagpole from the ground is found as 23.34 feet.

The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.

The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.

Given data:

Using the trigonometric ratios in the right triangle ABE.

tan 35 = h / 30

h = 30* tan(35)

h = 18.34

Height of flagpole = 18.34 + 5 = 23.34 feet

Thus, the height of the flagpole from the ground is found as 23.34 feet.

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Answer:

Step-by-step explanation:

Okay so when a smaller number is divided by a larger number, the quotient is less than 1.  Hope this helps Bye sisters slay.

The per square meter cost of steel will be $32. The solution has been obtained by using the cylinder.

What is a cylinder?

The cylinder, one of the most basic curvilinear geometric shapes, has long been considered to be a three-dimensional solid. It is regarded as a prism with a circle as its basis in elementary geometry.

We are given that the height of cylinder is 8 m and diameter is 10 m.

So, the radius is 5 m.

Now, using the surface area formula, we get

⇒ S = 2πrh + 2π[tex]r^{2}[/tex]

⇒ S = 2π * 5 * 8 + 2π * [tex]5^{2}[/tex]

⇒ S = 2 * 3.14 * 5 * 8 + 2 * 3.14 * 25

⇒ S = 251.2 + 157

⇒ S = 408.2 square meter

Now, it is given that the total cost of the steel will be $13,062.40.

So, per square meter cost will be:

⇒ Cost = [tex]\frac{13,062.40}{408.2\\}[/tex]

⇒ Cost = $32

Hence, the per square meter cost of steel for the cylinder will be $32.

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Check the picture below.

so following the template below, a shift 2 units to the left, means C=2

[tex]G(x)=\sqrt{x+2}[/tex]

Answer:

2.5cm

Step-by-step explanation:

you half the diameter to get the radius

The line graph of Greg's data wood look like "It would move upward."

A graph is a visual representation of data that shows the relationship between two or more variables. There are several types of graphs that can be used to display data

If Greg is measuring the height of the plant each day and the plant is continuing to grow for two weeks, then the line graph of his data would move upward. The graph would show an increasing trend as the plant grows taller each day. Therefore, the correct answer is "It would move upward."

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Answer:1111

Step-by-step explanation:

Answer:

Step-by-step explanation:

We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.

The percent of the box that will remain unwrapped by the 60 square feet of paper is about 20.70%

A percentage is a proportion of a number expressed as fraction of a 100

The dimensions in mixed fractions can be expressed as follows;

Height of the box = 1 2/3 feet = 5/3 feet

Width of the box = 4 feet

Length of the box = 5 1/2 feet = 11/2 feet

Surface area of the box, A = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches

The percent of the box that will remain unwrapped is therefore;

Percentage = 60/(227/3) × 100 ≈ 79.3%

The percentage of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%

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The mean number of bedrooms in a house in this neighborhood will be: 3.824.

In order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.

Next, we will add the products, and then divide by the total frequency. So we can start as follows:

(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478

Total frequency = 7 + 35 + 56 + 27 = 125

Therefore, the mean number of bedrooms = 478 / 125  approximately 3.824

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Answer:

f(x) - g(x) = 2x² + 6x - 4

Step-by-step explanation:

f(x) - g(x)

= 3x² + x - 3 - (x² - 5x + 1) ← distribute parenthesis by - 1

= 3x² + x - 3 - x² + 5x - 1 ← collect like terms

= 2x² + 6x - 4

Answer:

40%

Step-by-step explanation:

2/5=x/100

cross multiply and you get 5x=200

by isolation the variable you will get x=40

therefore, 40% of Canadians read at least 10 books a year

Answer:

We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:

x^2 + 12^2 = 16^2

Simplifying:

x^2 + 144 = 256

x^2 = 112

Taking the square root of both sides:

x ≈ 10.6 feet

Therefore, Brenda is approximately 10.6 feet away from the fish.

The answer of the given question based on the graph is ,  The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.

To dilate line f by scale factor of one half with center of dilation at origin, we  multiply coordinates of each point on line f by 1/2.

The equation of line f can be found by using the points A and B:

slope of line f = (0 - 2)/(2 - 0) = -1

y-intercept of line f = 2

Therefore, the equation of line f is y = -x + 2.

To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:

A' = (0, 2)*1/2 =(0, 1)

B' = (2, 0)*1/2 =(1, 0)

So A' is located at (0, 1) and B' is located at (1, 0) after dilation.

Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.

If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.

To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':

slope of f' = (0 - 1)/(1 - 0) = -1

y-intercept of f' = 0

Therefore, the equation of f' is y = -x.

Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

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The statements are classified as Exponential decay and Linear growth.

a. Exponential decay: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

b. Linear growth: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.

c. Exponential decay: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

d. Linear growth: Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.

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To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.

A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.

This can be written in mathematical notation as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.

In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:

Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks

Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks

Now we can use the Pythagorean theorem to find the distance between their houses:

Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks

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Answer:

FV ≈ $5,673.56

Step-by-step explanation:

To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:

FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))

where:

FV is the future value of the annuity

P is the periodic payment (in this case, $225 per month)

r is the interest rate per year (in this case, 5%)

n is the number of years (in this case, 2)

Substituting the given values, we get:

FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))

Using a calculator, we get:

FV ≈ $5,673.56

Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.

When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle.

When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle.

When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle.

(a) When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle. This is because the intersection of 4th Street and King Avenue creates a right angle, and the car turns northeast, creating another 45-degree angle with the horizontal 4th Street.

(b) When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns left, creating an additional 90-degree angle. Therefore, the total angle is 90 degrees + 45 degrees = 135 degrees.

(c) When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns right, creating another 45-degree angle with the horizontal 3rd Street.

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Answer:

40 cm²

Step-by-step explanation:

you have to multiply the top of the triangle by the base(40) which is 80 then you divide by two since it's a triangle then you get 40 again since your finding the area you have to put the 2 above the cm

Answer: To make soup for 4 people, Lori needs 1 1/4 cups of milk for every 3/4 cup of broth. Therefore, the ratio of milk to broth is:

(1 1/4 cups milk) / (3/4 cup broth) = (5/4 cups milk) / (3/4 cups broth) = (5/3) cups milk per cup of broth

To make soup for 120 people, Lori needs to multiply the ratio by 30 (120/4) to get the total amount of milk and broth needed:

(5/3 cups milk per cup of broth) * 30 = 50 cups of milk per 30 cups of broth

To convert cups to gallons, we divide by 16 (since there are 16 cups in a gallon):

50/16 = 3.125 gallons of milk

30/16 = 1.875 gallons of broth

Therefore, Lori needs a total of 3.125 + 1.875 = 5 gallons of milk and broth combined.

Step-by-step explanation:

Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]

Answer:

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

Use the formula for permutations:

The number of objects is n = 7 books.

Calculate the factorial:

The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.

The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.

The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:

P(vowel and consonant) = P(vowel) x P(consonant)

= 0.25 x 0.75

= 0.1875

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Answer: x=14

Step-by-step explanation:

cb=10.

ac=14

The value of X will be 14.

This is a simple mathematics problem that can be solved by using ratios.

Given, AC : BC : AB = 7 : 5 : 8

AC = X ; BC = 10 ; AB = X + 2

AC/ BC = X/ 10 = 7/5  (Ratios can also be represented as fractions)

X/10 = 7/5

On Transposing,

5X = 70

X = 70/5

X = 14

Alternatively,

BC/AB = 5/8 = 10/ (X + 2)

5/8 = 10/ (X + 2)

On Transposing,

80 = 5X + 10

5X = 70

X = 14

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The plane degrees off course is 6.79 degrees off at a speed of 541. 92 km / hr relative to the ground.

To find the airplane's course deviation and its ground speed, we need to first determine the velocity vectors of the airplane and the wind.

W x = W x cos(225) = 90 x cos(225) = -63.64 km/hr

Wy = W x sin(225) = 90 x sin(225) = -63.64 km/hr

Magnitude: |R| = sqrt(Rx^2 + Ry^2) = √(536.36^2 + (-63.64)^2) = 541.92 km/hr

Direction: θ = arctan(Ry / Rx) ≈ arctan (-63.64 / 536.36) = -6.79 degrees

So, the airplane is 6.79 degrees off course, and its ground speed is 541.92 km/hr.

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Answer:

Step-by-step explanation:

Answer:

You can make 12 possible sundaes with these toppings.

Step-by-step explanation:

Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:

1. Fudge & Chocolate Sprinkles

2. Fudge & Rainbow Sprinkles

3. Marshmallow & Chocolate Sprinkles

4. Marshmallow & Rainbow Sprinkles

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4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.