GrumpyCorp drug tests all of the recent college graduates it hires each year. The drug test currently used correctly determines drug users 96% of the time(a Positive test) and correctly determines non-users 90% of the time(a Negative test). A recent study concluded that 36% of college students use drugs. A potential employee has been tested and the result was Negative for drug use.
a) Construct ALL necessary probabilities using proper notation(Example: P(D) for a "drug user"). (Hint: there should be 6 total)
b) Find the Probability of a Negative test, by showing use of the above Probabilities first, and then followed by the proper calculation.
c) Use Bayes' Theorem to find the probability that a person who tests Positive actually was not a Drug User. Set up using Conditional Probability Notation and then substitute in numeric values.

Answer:

The area of a circle is given by the formula A = πr^2, where A is the area, r is the radius, and π is approximately equal to 3.14. Since the diameter of the dartboard is 30 millimeters, the radius is half of that, or 15 millimeters. Therefore, the area of the dartboard is A = π(15^2) = 225π square millimeters.

Step-by-step explanation:

If the mid point of AB is M (-4,-3). and the coordinates of A are (-1,-2), the coordinates of B is solved to be (-7, -4)

The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

From the formula the second end point is calculated

-4= (-1 + x₁)/2

-8 = -1 +  x₁

x₁ = -7

-3 = (-2 + y₁)/2

-6 = -2 + y₁

y₁ = -4

The coordinates of B are (-7, -4)

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Answer:

x = 120

Step-by-step explanation:

the sum of the exterior angles of a triangle is 360°

x is an exterior angle of the triangle , then

x + x + x = 360

3x = 360 ( divide both sides by 3 )

x = 120

Therefore , as a result, the answer to the provided linear equation is 5/23 pounds of cashews and 13/46 pounds of peanuts.

A linear equation is characterized as having a max of just one degree. A Any equation with a maximum degree of 2 or above is considered to be nonlinear. A graph with a linear equation has a straight line. A curve is created on the graph by a nonlinear equation.

Here,

Half of x is equal to the weight of peanuts,

so if x is the weight in pounds of cashews.

Ours has

=>5.75 x + 2.30 (1/2 x)

=>575x+115−230x =190

=> 1.90 x=75/345 = 5/23 pounds of cashews

Pounds of peanuts:

=> 1/2−x=23/46 −10/46= 13/46

As a result, the answer to the provided linear equation is 5/23 pounds of cashews and 13/46 pounds of peanuts.

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Answer:

first number= -2 and the second number = 2

Step-by-step explanation:

x= one number and y= the other

your two equations are x+y=4x+8 and  x-y=3y-10

by solving the first one for y, y=3x+8 so plug that in for y in the second equation

x-(3x+8)=3(3x+8)-10

x-3x-8=9x+24-10

-2x-8=9x=14

11x=-22 so x=-2

now plug that in and solve for y

-2+y=4(-2)+8

y=2

The statements which are always true in the triangle with interior angles, ∠2, ∠3, and m∠5, and exterior angles, ∠1, ∠4, and ∠5 are;

m∠5 + m∠6 = 180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 180°

An exterior angle is an angle that is formed by the extension of a side of the triangle and the side adjacent to the extended side.

The interior angles of the triangle are; angle ∠2, angle ∠3, and angle ∠5

The exterior angles at the interior angles of the triangle ∠2, ∠3, and ∠5 are angles  ∠1, angle ∠4, and angle ∠6 respectively.

Therefore, according to the exterior angle theorem, we get;

m∠1 = m∠3 + m∠5

m∠4 = m∠2 + m∠5

m∠6 = m∠2 + m∠3

The exterior angle and the adjacent internal angle are supplementary angles, therefore;

m∠2 + m∠1 = 180°

m∠3 + m∠4 = 180°

m∠5 + m∠6 = 180°

The angle sum property of a triangle indicates that the sum of the interior angles of a triangle is 180°, therefore;

m∠2 + m∠3 + m∠5 = 180°

The statements that are always true are therefore;

m∠5 + m∠6 = 180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

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The approximate area of the shaded sector is 97 cm^2

What is area of circle ?

area of circle can be defined as the product of pi and square of radius ,the value of pi is 22/7 or 3.14 .

Given , diameter = 12

We need to convert diameter to r

d =2r

d/2 =r

12/2=r

6 =r

The radius is 6

A= pi *6^2

A = 36 *(3.14)

A = 113.04 cm^2

Now the fraction of the circle that is shaded is 301degrees out of 360

(A circle is 360 degrees)

=310/360 * area of a circle

=310/360 * 113.04

= 97.34

Hence , The approximate area of the shaded sector is 97 cm^2 .

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Answer:

461.814 is part A

103.67 is part

The required function g(x) = 4x² and the related graph is a parabola that is opened upwards on the x-axis  

The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. This means that when we replace x - coordinate with a numerical value in the expression, we get the y-value for the given function f(x).

Here we have

f(x) = x²  

Given that g(x) = f(2x)

To find the g(x) take x = 2x

=> f(2x) = (2x)²

=> g(x) = 4x²  

Therefore,

The required function g(x) = 4x² and the related graph is a parabola that is opened upwards on the x-axis  

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The value of k from the equation is k = 4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = ( 2 - k ) / ( 5x + k )   be equation ( 1 )

Now , the equation passes through the point P ( 3 , -2/19 )

On simplifying the equation , we get

Substituting the values of x and y in the equation , we get

y = ( 2 - k ) / ( 5 ( 3 ) + k ) )

-2/19 = ( 2 - k ) / ( 15 + k )

Multiply by ( 15 + k ) on both sides of the equation , we get

-2 ( 15 + k ) / 19 = 2 - k

Multiply by 19 on both sides of the equation , we get

-30 - 2k = 38 - 19k

Adding 2k on both sides of the equation , we get

38 - 17k = -30

Subtracting 38 on both sides of the equation , we get

17k = 68

Divide by 17 on both sides of the equation , we get

k = 4

Hence , the value of k = 4

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Answer:

[tex]\displaystyle \frac{\sqrt{5}-1}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{2}{1+\sqrt{5}}\\\\=\frac{2}{1+\sqrt{5}}*\frac{1-\sqrt{5}}{1-\sqrt{5}}\\ \\=\frac{2(1-\sqrt{5})}{1-5}\\ \\=\frac{2(1-\sqrt{5})}{-4}\\\\=\frac{\sqrt{5}-1}{2}[/tex]

The value of y is 2/3, and RS = 9 and ST = 9.

What is the value of​ y?

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The known quantities are then identified using the visual overview as a guide, and they are q1 q2 q3 x1 and x2. The unknown quantity is then x3

Based on the details provided;

e charge 1 is located at the origin of the x-axis and the positive x-axis points to the right. Let x1, x2, and x3 denote the positions of charge 1, charge 2, and charge 3, respectively

Considering that charge 1 is thought to be at the source;

The known quantities are then identified using the visual overview as a guide, and they are:

q1 q2 q3 x1 and x2

However, given that we are unsure of its precise position x3,

The unknown quantity is then x3

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a. At the end of the 3 1/2 years, the amount of interest Damian has paid is $4,288.73.

b) When Damian pays off his credit card, the total amount (principal and interest) he has paid will be $14,488.73.

The interest is computed using an online finance calculator, setting the following parameters, based on the compounding interest system.

The calculator also shows the total payments made for the duration of the credit balance.

N (# of periods) = 42 months (3.5 years x 12)

I/Y (Interest per year) = 21%

PV (Present Value) = $10,200

FV (Future Value) = $0

Results:

PMT = $344.97

Sum of all periodic payments = $14,488.73

Total Interest = $4,288.73

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Answer:

To divide using long division, we first divide the leading term of the dividend (3r³) by the leading term of the divisor (r) to get the first term of the quotient (3r²). Then, we multiply the divisor (r + 4) by the quotient term (3r²) and subtract it from the dividend. We then bring down the next term of the dividend (11r²) and repeat the process. This will give us the quotient and the remainder.

The long division process is as follows:

(r + 4) | (3r³ +11r²-6r-18)

| 3r² (3r²)

|__

| -9r² +11r²-6r-18

|____

| -2r-18

|____

| +12r + 72

|____

| -36

|____

So the quotient is 3r² - 2r + 12 and the remainder is -36

And we can write the division as (3r³ +11r²-6r-18)÷(r + 4) = 3r² - 2r + 12 +(-36)/(r + 4)

Answer: ±1.4

Step-by-step explanation:

f(x)=ax^2+c

The graph passes through (2,2) and (-2,2)

Vertex:(0,-2)

f(x)=ax^2-2

4a-2=2

4a=4

a=1

f(x)=x^2-2

if f(x)=0

x^2-2=0

x^2=2

x=±[tex]\sqrt{2}[/tex]=±1.414

x=±1.4

The required order of buttons to press on a scientific calculator to enter 2.8 x 10⁷ is  [2] [.] [8] [EE] [7] . Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
While using the calculator, for the expression 2.8 × 10⁷,
We have to tap on tabs as,  [2] [.] [8] [EE] [7] where [.]  is the multiplication operator and {EE} is the exponential operator.

Thus, the required order of buttons to press on a scientific calculator to enter 2.8 x 10⁷ is  [2] [.] [8] [EE] [7] . Option A is correct.

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CV stands for standard deviation divided by sample mean multiplied by 100.

CV = (std. deviation*100)/mean = 41.2 %

for SAT score:

CV = (std. deviation*100)/mean = 17.55%

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The area of the mirror is 480 square inches

From the question, we have the following parameters that can be used in our computation:

A mirror that has the shape of a parallelogram (see attachment)

From the attachment, we have the following dimensions

Base length = 5 units

Height = 6 units

The area is the product of the dimensions

Since the side length of each square tile is 4 in, then we have

Area = 4 * 4 * 5 * 6

Evaluate

Area = 480

Hence, the area is 480 square inches

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If there were 50 workers, they would set 2,500 stones each day.

Total number is a term used to describe the sum of all the values or items within a set. It is usually used to calculate an aggregate or grand total, such as the sum of all the numbers in a list or the total number of people in a population. Total number can also be used to describe the absolute value or quantity of something, such as the total number of days in a year.

Assuming each worker set the same number of stones each day, the total number of stones set each day would be 50 times the number of workers. For example, if there were 20 workers, they would set 1,000 stones each day.
The number of stones set each day could also vary depending on the number of workers and the number of days they worked in a week. For example, if the workers worked a six day week and worked 50 out of the 52 weeks each year, the total number of stones set each day would be 50 times the number of workers multiplied by six. For example, if there were 20 workers, they would set 12,000 stones each day. If there were 50 workers, they would set 30,000 stones each day.

The number of stones set each day can also be affected by the production rate of the workers, the quality of the stones, and the amount of time required to set each stone. If the production rate was low, the number of stones set each day would also be lower. Similarly, if the quality of the stones was poor, the workers would likely take longer to set each stone, thus reducing the number of stones set each day.

Overall, the exact number of stones set each day depends on the number of workers, the number of days they work each week, their production rate, and the quality of the stones.

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Answer:

yes

Step-by-step explanation:

Answer:

Choice B

Step-by-step explanation:

The y increases by 3 every time that the x increases by 1.

Hope this helped! :)

The figure shows intersecting lines k and m, the measure of angle a is 94 degrees.

What are parallel lines ?

parallel lines can be defined as the lines which are equi distant from each other and which never meet or intersect each other.

Given,

In the figure the lines k and m are intersecting.

so,

by adding 86 degrees with a it should result into 180 degrees.

86+a  = 180

a = 180 - 86

a = 94

Hence, The figure shows intersecting lines k and m,  the measure of angle a is 94 degrees.

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The slope is (2/3 - 2/(3+h))/ h and as h is made closer and closer to 0, the slopes of the lines tend toward the derivative of the function f(x) at x = 3.

a) To find the slope of the line between the points (3, f(3)) and (3.1, f(3.1)), we use the formula m = (f(3.1) - f(3)) / (3.1 - 3) = (f(3.1) - f(3)) / 0.1

b) To find the slope of the line between the points (3, f(3)) and (3.01, f(3.01)), we use the formula m = (f(3.01) - f(3)) / (3.01 - 3) = (f(3.01) - f(3)) / 0.01

c) To find the slope of the line between the points (3, f(3)) and (3.001, f(3.001)), we use the formula m = (f(3.001) - f(3)) / (3.001 - 3) = (f(3.001) - f(3)) / 0.001

As h is made closer and closer to 0, the slopes of the lines tend toward the derivative of the function f(x) at x = 3.

Now to find a simplified rational expression for the slope of the line between (3, f(3)) and (3 + h, f(3 +h)), (h 0) :

The slope is equal to (f(3+h) - f(3)) / h

With f(x) = 2/x, we substitute it into the equation above and we get (2/(3+h) - 2/3) / h

The simplified rational expression for the slope is (2/3 - 2/(3+h))/ h

The graph of y = f(x) = 2/x between x = 1/2 and x = 4 :

This is the graph of a hyperbola that is symmetric about the y-axis and passes through the origin (0,0) and as x increases from 1/2 to 4, y decreases from 4 to 1/2.

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The 95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is given as follows:

($629, $727).

The bounds of the confidence interval are given as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The parameters for this problem are of:

[tex]\overline{x} = 678, \sigma = 560, n = 500[/tex]

Hence the lower bound of the interval is of:

[tex]678 - 1.96\frac{560}{\sqrt{500}} = 629[/tex]

The upper bound of the interval is of:

[tex]678 + 1.96\frac{560}{\sqrt{500}} = 727[/tex]

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The exact values of the trigonometric functions for an angle are:

The direction of an angle (θ), in degrees, with respect to origin is determine by coordinates on the terminal side. For a point in rectangular format we can determine the exact values of two fundamental trigonometric functions (sine, cosine) and four derivate trigonometric functions (tangent, cotangent, secant, cosecant:

For P(x, y) = (x, y)

Sine

sin θ = y / √(x² + y²)

Cosine

cos θ = x / √(x² + y²)

Tangent

tan θ = sin θ / cos θ

Cotangent

cot θ = 1 / tan θ

Secant

sec θ = 1 / cos θ

Cosecant

csc θ = 1 / sin θ

If we know that x = 2 and y = - 7, then exact values of trigonometric functions are, respectively:

Sine

sin θ = - 7 / √[2² + (- 7)²]

sin θ = - 7 / √53

sin θ = - 7√53 / 53

Cosine

cos θ = 2 / [2² + (- 7)²]

cos θ = 2 / √53

cos θ = 2√53 / 53

Tangent

tan θ = [- 7√53 / 53] / [2√53 / 53]

tan θ = - 7 / 2

Cotangent

cot θ = 1 / (- 7 / 2)

cot θ = - 2 / 7

Secant

sec θ = 1 / (2 / √53)

sec θ = √53 / 2

Cosecant

csc θ = 1 / (- 7 / √53)

csc θ = - √53 / 7

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A grid that correctly graphs the points A (3, 1), B (0, 3), and C (1, 3) include the following: B. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units above the origin. Point C is plotted 1 unit to the right and 3 units above the origin.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.

Next, we would use an online graphing calculator to plot the above set of data points with a point of intersection at (2, 3) as shown in the graph attached below.

By critically observing graph B of the given set of data points, we can logically deduce that it correctly graphs the points A(3, 1), B(0, 3), and C (1, 3) as shown in the image attached below.

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Complete Question:

Which of the following grids correctly graphs the points A (3, 1), B (0, 3), and C (1, 3)?

A. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units to the right of the origin. Point C is plotted 1 unit to the right and 3 units above the origin.

B. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units above the origin. Point C is plotted 1 unit to the right and 3 units above the origin.

C. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 1 unit to the right and 3 units above the origin. Point B is plotted 3 units above the origin. Point C is plotted 3 units to the right and 1 unit above the origin.

D. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 1 unit to the right and 3 units above the origin. Point B is plotted 3 units to the right of the origin. Point C is plotted 3 units to the right and 1 unit above the origin.

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Step-by-step explanation: