A polygraph (lie detector) is said to be 90% reliable in the following sense: There is a 90% chance that a person who is telling the truth will pass the polygraph test; and there is a 90% chance that a person telling a lie will fail the polygraph test. (a) Suppose a population consists of 5% liars. A random person takes a poly- graph test, which concludes that they are lying. What is the probability that they are actually lying? (b) Consider the probability that a person is actually lying given that the poly graph says that they are. Using the definition of reliability, how reliable must the polygraph test be in order that this probability is at least 80%?

Answer:

33

Step-by-step explanation:

Please brainliest, and Hope this helped you, I also answered first! :D

Answer: 33

Step-by-step explanation:

Trains make up approximately 49.04% of the total journeys across all modes of transportation.

We must divide the total number of train trips by the total number of trips made using all modes of transportation, then multiply the result by 100 to get the percentage that trains make up of the total.

There have been 2320 train trips overall, and there have been 4730 trips overall using all forms of transportation.

Trains therefore account for the following proportion of the total:

(2320 / 4730) x 100% = 49.04%

Train travel thus accounts for roughly 49.04 percent of all travels made using all modes of transportation.

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cos(0) and sin(0) both have a value of 0, so they would be selected.

cos(pi)/2 is equal to -0.5, and sin(3(pi)/2) is equal to -1, so they would not be selected.

Answer:

1 | 3 | 5

Step-by-step explanation:

sin 0 sin 3pi/2 and tan pi

cos pi/2 is -.5

cos 0 is 1

Answer:

A commonly used fraction that helps you understand a different size or amount is called a ratio.

Step-by-step explanation:

A ratio is a comparison of two or more quantities or measurements, expressed as a fraction or a colon. Ratios are commonly used to express the relationship between different amounts or sizes, and they can be used to help solve problems involving proportions, rates, and percentages. For example, if you are making a recipe that calls for two cups of flour and one cup of sugar, the ratio of flour to sugar is 2:1, or 2/1. Ratios can also be expressed in decimal or percentage form!

The width of the rectangle whose perimeter is 37 cm is 6.25 cm.

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:

The length of a rectangle is 6 cm more than its width, w cm.

So, the length = w + 6

The perimeter of the rectangle is 37 cm.

Then, Perimeter of the rectangle = 37

2(l+ w) = 37

2( w+ 6 +w )= 37

2(2w + 6)= 37

4w + 12 = 37

4w = 25

w = 6.25 cm

and, length = w+ 6 = 6 + 6.25 = 12.25 cm

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The mean of the sampling distribution is 200, and the standard deviation of the sampling distribution is 4.

The sampling distribution is a theoretical distribution that represents the behavior of sample means from all possible samples of a given size that can be drawn from a population.

However, the standard deviation of the sampling distribution is not the same as the standard deviation of the population.

Mathematically, we can represent the mean of the sampling distribution as follows:

μ(x) = μ = 200

Where μ(x) represents the mean of the sampling distribution and μ represents the mean of the population.

We can also calculate the standard error of the mean using the following formula:

σ(x) = σ / √(n)

Where σ(x) represents the standard deviation of the sampling distribution, σ represents the standard deviation of the population, and sqrt(n) represents the square root of the sample size.

Plugging in the values given in the problem, we get:

σ(x) = 20 / √(25) = 4

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For x = 4.1:

Slope of PQ =5.1

For x = 4.01:

Slope of PQ =6.01

For x = 3.9:

Slope of PQ =15.1

For x = 3.99:

Slope of PQ =105.99

From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.

To find the slope of the secant line PQ, we need to first find the coordinates of point Q in terms of x:

Q = (x, x² + x + 8)

Then, the slope of the secant line PQ is given by:

(yQ - yP) / (xQ - xP)

where yP = 28 and xP = 4, and yQ and xQ depend on the value of x.

For x = 4.1:

Q = (4.1, 4.1² + 4.1 + 8) = (4.1, 28.51)

Slope of PQ = (28.51 - 28) / (4.1 - 4)

= 0.51 / 0.1

= 5.1

For x = 4.01:

Q = (4.01, 4.01² + 4.01 + 8) = (4.01, 28.0601)

Slope of PQ = (28.0601 - 28) / (4.01 - 4)

= 0.0601 / 0.01

= 6.01

For x = 3.9:

Q = (3.9, 3.9² + 3.9 + 8) = (3.9, 26.49)

Slope of PQ = (26.49 - 28) / (3.9 - 4)

= -1.51 / -0.1

= 15.1

For x = 3.99:

Q = (3.99, 3.99² + 3.99 + 8) = (3.99, 26.9401)

Slope of PQ = (26.9401 - 28) / (3.99 - 4)

= -1.0599 / -0.01

= 105.99

As x approaches 4 from both sides, the x-coordinate of Q approaches 4, and the slope of PQ approaches the slope of the tangent line to the curve at P(4,28). From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.

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The coordinates of point l are (8,9).

Numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.


To find this point, we must first calculate the midpoint between j and k. The midpoint can be found by taking the average of the x-coordinates and y-coordinates. The midpoint between j and k is (8,10). Since the ratio of jl:kl is 5:1, we can determine that l is 5 units away from j and 1 unit away from k. This means that l must be 5 units up and 1 unit to the right from the midpoint. Thus, the coordinates of l are (8,9).

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Answer:

x=11.34

Step-by-step explanation:

The library is 20 miles from the community pool as calculated after performing mathematical operations.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, In Hillsdale, the library is due south of the courthouse and due west of the community swimming pool.

Also given,

The distance between the library and the courthouse is 15 miles.

The distance between the courthouse and the city pool is 25 miles,

Using the Pythagorean theorem, we have:

x = 25² - 15²

x² = 625 - 225

x = 400

Taking the square root of both sides, we get:

x = 20

Therefore, the library is 20 miles from the community pool

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The image of the polygon after the rotation is added as an attachment

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

(1, 0), (2, 0), (0, 2) and (2, 2)

The location of point G is

G = (3, -1)

To rotate about point G, we start by subtracting the points from G

So, we have

[(1, 0), (2, 0), (0, 2) and (2, 2)] - (3, -1)

This gives

(-2, 1), (-1, 1), (-3, 3) and (-1, 3)

The rule is 90 degrees clockwise rotation

This is represented as

(x, y) ⇒ (y, -x)

So, we have

(-2, 1), (-1, 1), (-3, 3) and (-1, 3) ⇒ (1, 2), (1, 1), (3, 3) and (3, 1)

Next, we plot (1, 2), (1, 1), (3, 3) and (3, 1)

See attachment for the image of the transformation

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Answer: To simplify the expression, we can start by rewriting it as the product of the first fraction and the reciprocal of the second fraction. Then, we can factor the denominators of each fraction and simplify as much as possible.

x + 1 / (x^2 + x - 6) ÷ (x^2 + 5x + 4) / (x - 2)

= (x + 1 / (x + 3)(x - 2)) ÷ ((x + 4)(x + 1) / (x + 4)(x - 1))

= (x + 1 / (x + 3)(x - 2)) * ((x + 4)(x - 1) / (x + 4)(x + 1)) (reciprocal of second fraction)

= (x + 1 / (x + 3)(x - 2)) * (x - 1 / (x + 1)) (cancel out (x + 4) and simplify)

= (x + 1) * (x - 1) / (x + 3)(x - 2)(x + 1) (multiply the numerators and simplify)

= (x - 1) / (x + 3)(x - 2) (cancel out (x + 1) in the numerator and denominator)

Therefore, the simplified form of the expression is 1 / ((x + 3)(x - 2) / (x - 1)). This can be further simplified to:

1 / ((x + 3)(x - 2) / (x - 1)) = (x - 1) / ((x + 3)(x - 2)) * (x - 1) / 1 = (x - 1)^2 / ((x + 3)(x - 2))

So the answer is: 1 over the quantity (x + 3) times the quantity (x - 2), all multiplied by the quantity (x - 1) squared.

Step-by-step explanation:

The simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

The given expression is:

[tex]\frac{x+1}{x^2+x-6} / \frac{x^2+5x+4}{x-2}[/tex]

When a fraction is in the denominator, we take the reciprocal of the fraction and multiply it with the numerator.

So the expression becomes,

[tex]\frac{x+1}{x^2+x-6} * \frac{x-2}{x^2+5x+4}[/tex]

We can factorize the expression x² + x - 6

x² + 3x - 2x - 6

= x(x+3) -2 ( x+3)

= (x-2) (x+3)

We can also factorize the expression x² +5 x +4

x² + 4x + x +4

= x(x+4) +1 ( x+4)

= (x+1) (x+4)

Substituting these values, the expression becomes as follows:

[tex]\frac{x+1}{(x-2)*(x+3)} * \frac{x-2}{(x+1)(x+4)} = \frac{1}{(x+3)(x+4)}[/tex]

Therefore the simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.

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The value of x in the triangle, given the angle measures of the other angles, is D. 100 degrees

To find the value of x, you first need to find the value of the last interior angle in the triangle.

The sum of the interior angles of a triangle would add up to 180 degrees which means that the angle inside would be :

= 180 - 65 - 35

= 180 - 100

= 80 degrees

Angles on a straight line add up to 180 degrees so the value of x, which is on a straight line with 80 degrees, is :

= 180 - 80

= 100 degrees

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The sine, cosine and tangent are obtained applying the trigonometric ratios presented in this problem.

The three trigonometric ratios are defined as follows:

The hypotenuse is the slanted segment connecting the horizontal and the vertical segment.

For the desired angle, you must identify the adjacent side(between the angle and the angle of 90º) and the opposite side.

The problem is incomplete, hence the concepts needed to obtain the sine, cosine and tangent were presented.

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The rate at which Mandy used up her bags of dog food is 2/3 bags per day

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Slope = change in y /change in x

Here,   Slope = change in bags of food/ /change in days

form the graph = 4/6  = 4  bags per 6 days

4/6 simplifies to 2/3

=>  2/3 bags per day

The rate at which Mandy used up her bags of dog food is 2/3 bags per day

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The equation of the lines with the points (-8, 3) and (-6, 0) is y = -3x/2 + 9.

The equation of the lines with the points (5, 4.5) and (5, -1) is y = 4.5.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (-8, 3), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 3 = (0 - 3)/(-6 + 8)(x + 8)

y - 3 = -3x/2 - 12

y = -3x/2 + 9

For points (5, 4.5) and (5, -1), we have:

At data point (5, 4.5), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4.5 = (-1 - 4.5)/(-5 - 5)(x - 5)

y - 4.5 = 0

y = 4.5

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The distance between the man and the monument is 1060.16 feet.

Here we have the angle of elevation to be 18°

and the angle of depression to be 3°

Let the distance between the man and the monument be x feet

Now for any angle a, tana = opposite angle / adjacent angle

Hence we can sum up the building's height to be

x tan18 + x tan3 = 400

or, x(tan18 + tan3) = 400

or, x(0.3249 + 0.0524) = 400

or, 0.3773x = 400

or, x = 400/0.3773

or, x = 1060.16

Hence the distance between the man and the monument is 1060.16 feet.

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Using the given ratio, we can see that there are 48 teachers.

Here we know that the ratio of teachers to male learners to female learners is:

1:7:8

So for each teacher there are 7 female learners and 8 male learners, for a total of 15.

So we can simplify this and say that there are 15 learners for each teacher.

Then if there are 720 learners, the number of teachers is:

720/15 = 48

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Answer:

9/2

Step-by-step explanation:

True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.

A confidence intervals bar chart (shown as red lines)

In graphs, error bars are used to graphically show data variability and to denote error or uncertainty in reported measurements. They provide a basic indication of a measurement's accuracy or, alternatively, how far the true (error-free) value may deviate from the reported value. The standard deviation of uncertainty, the standard error, or a specific confidence range (such a 95% interval) are frequently represented as error bars. Due to the fact that these values are not the same, the measure chosen needs to be specified clearly in the graph or supporting text.

According to the definition the statement is true.

True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.

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Answer:

they are

Step-by-step explanation:

divide 12*4=3

9*3=3

same ratio

We require x = 170 televisions to minimize total cost

The minimum of a function is the lowest value of that function.

Given that a television manufacturer produces x sets per week so the total cost of production is given by relation C(x) = x² - 195x² + 66000x + 15000.

To find the minimum value, we differentiate C(x) with respect to x and equate to zero.

So,  C(x) = x² - 195x² + 66000x + 15000

dC(x)/dx = d(x² - 195x² + 66000x + 15000)/dx

= dx²/dx - d195x²/dx + d66000x/dx + d15000/dx

= 2x - 195(2)x + 66000 + 0

= 2x - 390x + 66000

= -388x + 66000

Equating to zero, we have

dC(x)/dx = 0

-388x + 66000 = 0

-388x = -66000

x = -66000/-388

x = 170.1

x ≅ 170

So, we require x = 170 televisions to minimize total cost

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The vertical function of the ball can be modelled using the equation h(t) = 16t^2 + 75t + 4, where h(t) is the height of the ball at time t, 16 is the acceleration due to gravity, 75 is the initial velocity of the ball, and 4 is the initial height of the ball.

Acceleration due to gravity is the rate of change of velocity (speed) of an object in free fall due to the force of gravity. It is denoted by g and is equal to 9.80665 m/s2 at sea level. It is the force of gravity that causes objects to fall to the ground and accelerates them as they approach the ground. When an object is in free fall, it accelerates at a rate of 9.8 m/s2. This means that after one second, the object will be travelling at 9.8 m/s, after two seconds it will be travelling at 19.6 m/s, and so on. Without the force of gravity, objects would not accelerate in free fall.

The equation h(t) = 16t^2 + 75t + 4 models the vertical function of the ball by combining the effects of acceleration due to gravity (16), initial velocity (75), and initial height (4). The term 16t^2 represents the acceleration due to gravity, which causes the ball to accelerate in the vertical direction at a rate of 16 meters per second squared. The term 75t represents the initial velocity of the ball, which causes the ball to move in the vertical direction at a rate of 75 meters per second. Finally, the term 4 represents the initial height of the ball, which is 4 meters. By combining these three effects, the equation h(t) = 16t^2 + 75t + 4 accurately models the vertical function of the ball.

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The maximum total deduction that can be claimed is OE. $17,100.

What is deduction ?

Deduction refers to the process of subtracting or taking away something. In the context of taxes, a deduction is a specific amount of money that a taxpayer is allowed to subtract from their income before calculating their tax liability. Deductions are one way to reduce the amount of taxes owed and can help to lower a person's overall tax burden.

There are two main types of deductions in the U.S. tax system: standard deductions and itemized deductions. The standard deduction is a fixed amount that varies depending on the taxpayer's filing status, while itemized deductions are specific expenses that a taxpayer can deduct from their taxable income. Some common examples of itemized deductions include mortgage interest, charitable contributions, medical expenses, and state and local taxes.

It's important to note that not all deductions are available to all taxpayers, and there are specific rules and limits that apply to each type of deduction. It's also important to keep accurate records and documentation to support any deductions that are claimed on a tax return.

The maximum total deduction that can be claimed is OE. $17,100, because that is the sum of the deductible expenses and the standard deduction.

The question is asking for the maximum total deduction that can be claimed, given certain deductible expenses and a standard deduction.

The standard deduction for the tax year is $6,100, and the deductible expenses are $6,000 in mortgage interest and $5,000 in charitable contributions.

Since the deductible expenses ($6,000 + $5,000 = $11,000) are less than the standard deduction of $6,100, it makes sense to use the standard deduction instead of itemizing deductions.

Therefore, the maximum total deduction would be the sum of the deductible expenses and the standard deduction:

$11,000 + $6,100 = $17,100

So, the maximum total deduction that can be claimed is OE. $17,100.

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Answer:

b

Step-by-step explanation:

because u can tell

At the closing of her home purchase, Michelle should expect to pay prepaid interest of $6,934.50. This amount represents the interest accrued from April 8th to the end of the month.

The monthly payment for Michelle's mortgage is calculated as follows:

Principal and interest payment = (95,000 - 15,000) x 0.0495 / 12

This equals a monthly payment of $420.63.

Michelle's total interest over the life of the loan is $119,750. This amount is the sum of her prepaid interest and the total interest she pays over the life of the loan.

Answer:

Step-by-step explanation

The bottle had 20 ounces that before and 8 ounces after

8+x=20

20-x=8

20-8=x

20-8=12

Answer:

25

Step-by-step explanation:

let farhan's age be x and his cousin's age be y

sum of ages = x + y = 38

7 years ago (so x-7 and y-7), farhan was thrice as old as his cousin, so 3 * his cousin's past age = farhan's past age= 3 *(y-7) = x-7

subtract y from both sides in the first equation to solve for x

x = 38-y

substitute this into the second equation

3 *(y-7) = 38-y-7

3y-21 = 31-y

add y to both sides to put all y values on one side

4y  -21 = 31

add 21 to both sides to solve for y

4y = 52

y = 13

sum of ages = x + y = 38 = 13 + x so x = 25 = 38-13

a. Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.

When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.

The correlation coefficent, which expresses correlation on a scale from +1 to -1, is used. Numbers less than 0 indicate a negative connection. An increase in one variable confidently foretells a drop in the other when there is a perfect negative correlation, with a coefficient of -1. Non-zero coefficients between +1 and -1 are used to show lower degrees of connection. 0 means there is no propensity for the variables to change simultaneously, either positively or negatively.

a. A weak negative linear relationship between hours worked and donations collected in this context means that as Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.

b. When we say there is a weak correlation between two variables, we are referring to their level of relationship. The negative correlation in this instance indicates that there is a propensity for the amount of donations collected to decline as the time spent working increases, but the relationship is not very strong, indicating that there is a lot of variability in the data and making firm predictions or conclusions based on this correlation alone is challenging.

c. Tom's boss's claim is wrong as the negative correlation or the decline in donation is a mere coincidence and does not have a relation to Thor's work.

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The probability the card is a diamond or a face card is [tex]\frac{11}{26}[/tex].

Probability refers to the likelihood that any random occurrence will occur. This expression refers to estimating the probability that any specific event will take place. For example, when we throw a coin into the air. Possibility: P(A) = f / N, determines the likelihood that an event will occur. Although probability and ratios are linked, the former dictates the latter. The probability of an occurrence must be known before determining its probability.

When we find the probability, we obtain:

There are 52 cards in a standard deck of cards.As there are four suits, there are 12 face cards, which we identify as the Kings, Queens, and Jacks. There are 13 diamonds total, 3 of which are face cards that have previously been counted. There are thus 10 diamonds without faces.

Out of the 52 cards in the deck, 10 diamonds plus 12 face cards equal 22.

P= [tex]\frac{22}{52}[/tex]= [tex]\frac{11}{26}[/tex].

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