Parts of Complex Numbers
z=4.1i+85
Re(z)=_____
Im(z)=_____

a) The cell corresponding to a positive diagnosis when the person has antibodies present as well as the cell for a negative diagnosis when the person has no antibodies present are the cells representing a CORRECT diagnosis.

The cell corresponding to a negative diagnosis when you actually have antibodies present is called a FALSE NEGATIVE and is considered as a TYPE II error.

The cell corresponding to a positive diagnosis when you actually don't have antibodies present is called a FALSE POSITIVE and is considered as a TYPE I error.

For the tree diagram for the questions below, refer to the picture attached.

b) To know the probability that a person without HIV will be diagnosed positive (false positive), we just trace the tree diagram from population to "antibodies not present" to "positive". The tree diagram will give us a value of 0.00588.

ANSWER: The probability of a false positive is 0.00588 or 0.588%.

c) We do the same thing as the previous subproblem to determine the probability that a person with HIV will be diagnosed as negative. We trace the tree diagram from population to "antibodies present" to "negative". The tree diagram will give us a value of 0.003.

ANSWER: The probability of a false negative is 0.003 or 0.3%.

d) Same thing for this subproblem. We trace the tree diagram from population to "antibodies present" to "positive" to know that the value is 0.01997.

ANSWER: The probability that a person with HIV will be diagnosed as positive is 0.01997 or 1.997%.

Answer:

Option A. 68.4 square units.

Step-by-step explanation:

Since sides ED = EF = 13 units

So the given triangle is an isosceles triangle and in an isosceles triangle EFD, perpendicular drawn from E to DF, will be perpendicular bisector of DF.

Moreover, to this perpendicular bisector to DF will be the height of the triangle.

Now Area of a triangle of [tex]\frac{1}{2}[/tex] × base × height.

Sin 63 =  [tex]\frac{Height}{Hypotenuse}[/tex] =  [tex]\frac{h}{13}[/tex]

h = 13 sin 63 = 13 ( 0.891) = 11.583 units

Cos 63 =  [tex]\frac{Base}{Hypotenuse}[/tex] =  [tex]\frac{Base}{13}[/tex]

Base = 13 cos 63 = 13 × (0.454)

                            = 5.90 units

Since DF = 2 × base = 2 × 5.90

                                 = 11.80 units

Now area of EDF =  [tex]\frac{1}{2}[/tex] × 11.80 × 11.583

                             = 68.86 ≈ 68.40 square units.

Option A. 68.4 square units.

To find the town's population in 4 years with an initial population of 6500 and a 4% annual growth rate, we use the exponential growth formula, resulting in an estimated population of approximately 7609.

The population of a town is 6500 and is increasing at a rate of 4% per year. To calculate the town's population in 4 years, we will use the formula for exponential growth:

P(t) = P0(1 + r)^t

Where:

P(t) is the future population

P0 is the initial population

r is the growth rate (as a decimal)

t is the number of years

Step-by-step calculation:

Convert the growth rate from a percentage to a decimal: r = 4% = 0.04

Use the formula with t = 4 years, P0 = 6500, and r = 0.04:

P(4) = 6500(1 + 0.04)⁴

Calculate P(4) = 6500 * 1.04⁴

Approximate the future population after 4 years.

By performing the calculation, the town's population in 4 years will be approximately 7609.

The rectangle has a width of approximately 4.18ft and a length of approximately 7.55ft. These are obtained by setting up and solving a system of equations based on the given information.

Let's start by setting up equations based on the problem statement. Let's denote the width of the rectangle as

w and the length as l. From the problem, we know two things: one is that the length is 5 feet less than three times the width, which can be written as  l = 3w - 5. The second thing we know is that the area of the rectangle, which is obtained by multiplying the length by the width, is 28 square feet, written as l*w = 28 . By substituting the first equation into the second, we can solve for w: (3w - 5)*w = 28

. This simplifies to a quadratic equation 3w^2 - 5w - 28 = 0 which can be solved to give w=~4.18 ft and w=-2.02ft. Because the width cannot be negative, we discard the second solution. Substituting w=~4.18ft into l = 3w -5 gives

l=~7.55 ft . Therefore, the dimensions of the rectangle are approximately 4.18ft (width) and 7.55ft (length).

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Final answer:

To find when the pebble hits the ground, solve for time using the quadratic equation from the given height function, resulting in around 6 seconds.

Explanation:

To find how long the pebble takes to hit the ground, we need to find the time t when its height h becomes 0. This means we need to solve the equation for t when h = 0:

-16t² + 12t + 900 = 0

This is a quadratic equation, and we can solve it using various methods like factoring, the quadratic formula, or completing the square. Here, we'll use the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a = -16, b = 12, and c = 900:

t = (-12 ± √(12² - 4 × -16 × 900)) / (2 × -16)

t = (-12 ± √(614400)) / -32

t ≈ (-12 ± 247.88) / -32

There are two possible solutions:

t1 ≈ 25.50 seconds

t2 ≈ -5.50 seconds (we can discard this since time cannot be negative)

The pebble will hit the ground approximately 6 seconds after it is thrown.

Answer:

1-given

2-if lines are parallel, then corresponding angles are equal

3-Substitution

4-if alternate interior angles are equal then lines are parallel.

Step-by-step explanation:

Given j is parallel to k,[tex]m\angle3 =m\angle 1[/tex]

We have to prove that line l is parallel to m

We  have to match reason with its correct statement in given proof.

1.j is parallel to k,[tex] m\angle 3=m\angle 1[/tex]

Reason:given

2.[tex]m\angle 1=m\angle 2[/tex]

Reason:if the lines are parallel , then corresponding angles are equal.

3.[tex]m\angle 2=m\angle 3[/tex]

Reason: substitution

4.line l is parallel to m

Reason: If alternate interior angles are equal ,then lines are parallel.

Answer:

B.

Step-by-step explanation:

Answer:

The required equation is [tex]g(x)=\frac{3}{x-4}-5[/tex].

Step-by-step explanation:

The given function is

[tex]y=\frac{3}{x}[/tex]

It can be written as

[tex]f(x)=\frac{3}{x}[/tex]

The transformation of a function is defined as

[tex]g(x)=f(x+a)+b[/tex]

Where, a represents the horizontal shift and b represents the vertical shift.

If a>0, then the function f(x) shifts a units left and a<0, then the function f(x) shifts a units right.

If b>0, then the function f(x) shifts b units up and b<0, then the function f(x) shifts b units down.

Since the function translated 4 units to the right and 5 units down, therefore the value of a is -4 and bis -5.

[tex]g(x)=f(x-4)-5[/tex]

[tex]g(x)=\frac{3}{x-4}-5[/tex]                         [tex][\because f(x)=\frac{3}{x}][/tex]

Therefore the required equation is [tex]g(x)=\frac{3}{x-4}-5[/tex].

24.99 + 39.99 = 64.98

69.53-64.98 = 4.55

4.55/69.53 = 0.0654 = 6.5% sales tax

Alice needs to classify her garden quadrilateral to determine if it is suitable for a specific species of flowers. She finds the sides equal in length and consecutive angles supplementary, which leads her to conclude the garden plot is a rhombus, meeting the criteria for her flowers.

Alice designs a garden plot in the shape of a quadrilateral. She knows that for a certain species of flower to grow optimally, her garden must have a specific shape: it needs to be a parallelogram with equal sides but not necessarily equal angles. In order to classify the quadrilateral of her garden, she begins by measuring the sides and finds that they are all of equal length. Then she measures the angles and finds that consecutive angles are supplementary, which means their measures add up to 180 degrees.

To determine if the quadrilateral meets the criteria for the species of flowers, she must classify her garden plot based on her measurements. Is Alice's garden a rectangle, a square, a rhombus, or a parallelogram with unequal angles?

Since the sides of the quadrilateral are all equal and the consecutive angles are supplementary, Alice can conclude that her garden plot is a rhombus, which is a type of parallelogram with all sides equal in length and opposite angles equal. Thus, it fulfills the requirements for her special species of flowers.

Answer:

Answer:  

C: Mia switched the numerator and the denominator.

Step-by-step explanation:

just took the test

30 pounds is available to fill the suitcase with other items.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

An airline requires carry on luggage to weigh at most 40 pounds.

The Suitcase presently carry 10 pounds.

Let  p be the pound available to fill your suitcase with other items.

So, p= 40- 10

p = 30 pounds

Hence, 30 pounds is available to fill the suitcase with other items.

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The relationship where y varies directly as x and inversely as the square root of w can be represented by the equation y = k * (x / sqrt(w)). Here, k is a constant of proportionality.

From the statement given, we can deduce an equation representing a direct proportionality to x and an inverse proportionality to the square root of w.

In mathematics, direct and inverse proportionality relationships are commonly depicted as y = kx and y = k/x respectively, where k is a constant. For direct proportionality, as x increases, y also increases. Contrastingly, for inverse proportionality, as x increases, y decreases.

Given the statement, we can represent the relationship as follows: y = k * (x / sqrt(w)).

Here, y varies directly as x and inversely as the square root of w. The constant k is the constant of proportionality which can be determined based on specific values of x, y and w.

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Answer:

80⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Given:

8x = 90 - x

9x = 90

x = 10⁰

Complement = 90 - 10 = 80⁰

The complement of an angle is 8 times as large as the angle. The measure of other angle is 80⁰.

The complement of an angle is the sum of angles which is equal to 90 degrees.

Let one Angle = x

Complement = 90 - x

The complement of an angle is 8 times as large as the angle.

so,

8x = 90 - x

9x = 90

x = 10⁰

Complement = 90 - 10

                     = 80⁰

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