a plane slices the three rectangular faces of a right triangular prism but neither of its bases. the plane is not parallel to the bases of the prism. show and describe the plane section that results from the slice

The probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

We can use Bayes' theorem to calculate the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids. Let A be the event that a randomly selected bicyclist uses steroids, and B be the event that a randomly selected bicyclist tests positive for steroids. Then, we want to find P(A|B), the probability that a bicyclist uses steroids given that they test positive for steroids:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of testing positive given that the bicyclist uses steroids, P(A) is the prior probability of a bicyclist using steroids, and P(B) is the probability of testing positive for steroids.

We are given that P(A) = 0.08, P(B|A) = 0.94, and P(B|not A) = 0.09. We can calculate P(B) using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= 0.94 * 0.08 + 0.09 * 0.92

= 0.0976

where P(not A) = 1 - P(A) = 0.92.

Substituting the values we have:

P(A|B) = 0.94 * 0.08 / 0.0976

= 0.763

Therefore, the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

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Answer:

-8.5 and 7.5

Step-by-step explanation:

Let's call the two numbers x and y. We know that their difference is 16, so we can write:

x - y = 16 or x = y + 16

We want to find the values of x and y that minimize the expression:

x + y + xy

Substituting x = y + 16, we get:

(y + 16) + y + (y + 16)y

Simplifying and expanding, we get:

y^2 + 17y + 16

To minimize this expression, we can take its derivative with respect to y and set it equal to 0:

d/dy (y^2 + 17y + 16) = 2y + 17 = 0

Solving for y, we get:

y = -8.5

Substituting y = -8.5 into x = y + 16, we get:

x = 7.5

Therefore, the two numbers with a difference of 16 such that the result of adding their sum and their product is a minimum are -8.5 and 7.5.

Answer:

Let's start by using algebra to represent the given information.

Let the son's current age be "s" and the mother's current age be "m". We know from the problem that:

m = 3s (the mother is 3 times as old as her son is now)

and

m - 14 = 10(s - 14) (fourteen years ago, the mother was 10 times as old as her son was then)

Now we can solve for the son's age:

m - 14 = 10s - 140 (distribute the 10)

m = 10s - 126 (add 14 to both sides)

3s = 10s - 126 (substitute m = 3s)

7s = 126

s = 18

Therefore, the son is currently 18 years old. To check this answer, we can use the first equation to find the mother's current age:

m = 3s = 3(18) = 54

So the mother is currently 54 years old, and 14 years ago the son was 4 years old and the mother was 40 years old, which is 10 times as old as the son.

Step-by-step explanation:

The missing sides are:

x = 13

y =  13*√2

The triangle is isosceles, so the value of x is also 13, and it is also a right triangle, so the value of y is given by:

y² = 13² + 13²

y = √( 13² + 13²)=  13*√2

These are the missing values.

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We can expand 12.907.054 as 1 × 10,000,000,000 + 2 × 1,000,000,000 + 9 × 100,000,000 + 0 × 10,000,000 + 7 × 1,000,000 + 0 × 100,000 + 5 × 10 + 4 × 1.

To expand a decimal number by showing each digit by value, we need to break it down into its place values. For example, in the number 12.907.054, the first digit to the left of the decimal point is in the billions place, the second digit is in the hundred millions place, and so on.

So, we can expand 12.907.054 as follows:

1 × 10,000,000,000 + 2 × 1,000,000,000 + 9 × 100,000,000 + 0 × 10,000,000 + 7 × 1,000,000 + 0 × 100,000 + 5 × 10 + 4 × 1

This means that 12.907.054 can be written as the sum of its place values. The first digit to the left of the decimal point is worth 10 billion, the second digit is worth 1 billion, and so on until we reach the ones place.

Expanding a decimal number by showing each digit by value is a way to better understand the place values of each digit and to break down the number into smaller parts for easier analysis.

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An equation in slope-intercept form for the line shown in the graph is x = -1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 3)/(-1 + 1)

Slope (m) = -3/0

Slope (m) = 0.

At data point (-1, 3) and a slope of 0, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 0(x - (-1))

y - 3 = 0

y = 3.

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Answer:

  a) '34'

Step-by-step explanation:

You want the result of executing the Python expression "3" +"4".

The tokens "3" and "4" are both strings. In this context, the "+" operator does concatenation of the strings, so the result is the string "34". The Python interpreter outputs this as '34'.

Answer:

The Circumference of the circle shown in the picture is 87.96

Step-by-step explanation:

The formula in order to find the circumference is C=2πr.

r in this example is 14

so C= 2 * π * 14

π is always a constant value so all you have to do is add it to the calculator to get your answer.

Hope this helps!

The domain of the expression is all real numbers except -7 and 5. In interval notation, the domain can be expressed as (-∞, -7) U (-7, 5) U (5, ∞).

The simplified form of the expression is:

(12 - X) / (x² + 2x - 35) * (x² + 7x) / (x² - 12x)

And the domain of the expression is all real numbers except for values of x that make the denominators equal to zero, as division by zero is undefined.

To find the values of x that make the denominators equal to zero, we can set the denominators equal to zero and solve for x:

x² + 2x - 35 = 0

(x + 7)(x - 5) = 0

x + 7 = 0 or x - 5 = 0

x = -7 or x = 5

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Answer:

x = 12

Step-by-step explanation:

If you're bored of solving equations the normal way, why not try this fun and easy method? Just follow these simple steps:

Subtract 3/10 x from both sides to eliminate the x term on the right side. This is like getting rid of the annoying person who always sits next to you in class.

4/5 x - 3/10 x + 15 = 21

Simplify the left side by finding the common denominator and combining the fractions. This is like putting all your candy in one bag and eating it faster.

(8/10 - 3/10) x + 15 = 21

5/10 x + 15 = 21

Subtract 15 from both sides to isolate the x term on the left side. This is like taking away your allowance and making you do chores.

5/10 x = 21 - 15

5/10 x = 6

Multiply both sides by 10/5 to solve for x. This is like giving you a magic wand that makes everything easier.

(10/5) (5/10) x = (10/5) (6)

x = 12

This is the solution of the equation. You can check it by plugging it back into the original equation and verifying that both sides are equal. Or you can just trust me

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

The equation that can be used to represent number of people who can go to the amusement park is 12 + 33.75x = 215.50.

We have,

the total amount to spent on amusement park = $214.50

And the parking fees = $12

The ticket cost per person = $33.75

let the number of person be x.

Then, the equation can become as

12 + 33.75x = 215.50

Simplifying the equation we get

33.75x = 215.5 - 12

33.75x = 203.5

x= 6.02

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Answer:

Example of the distributive property: a(b + c) = ab + ac

Question #1:

a) 6(3a + 2) = 18a + 12

b) 2(7 - 5y) = 14 - 10y

c) 3(r + 1/3) = 3r + 1

d) 8(2m - 3/8) = 16m - 3

e) 5(x/5 + 4) = x + 20

Question #2:  

a) 3y + 1/4 = 4

4 (3y + 1/4) = 4 (4)

12y + 1 = 16

b) x/6 + 7 = 10

6 (x/6 + 7) = 6 (10)

x + 42 = 60

c) 11/3 - 4c/3 = 2

3 (11/3 - 4c/3) = (3) 2

11 - 4c = 6

d) 2n - 1 = 1/2

2 (2n - 1) = 2 (1/2)

4n - 2 = 1

e) r/2 + 8 = 1/2

2 (r/2 + 8) = 2(1/2)

r + 16 = 1

Hope this helped!

Answer:5000 meters

Step-by-step explanation:1km=1000m

The system of equations are solved and x = 1 and y = -2

Given data ,

Let the system of equations be A and B

where 5x + 4y = -3

y = 2x - 4

Substituting the value of y in equation (1) , we get

5x + 4 ( 2x - 4 ) = -3

On simplifying the equation , we get

5x + 8x - 16 = -3

Adding 16 on both sides , we get

13x = 13

Divide by 13 on both sides , we get

x = 1

Now , when x = 1

y = -2

Hence , the equations are solved

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Juliana and Brody hiked a total distance of 6 1/2 miles, which is the sum of the distances of the two trails they hiked 3 2/3 miles and 2 5/6 miles.

To find the total distance hiked by Juliana and Brody, we need to add the distances of the two trails they hiked.

3 2/3 + 2 5/6 can be written as a common fraction by finding the least common multiple (LCM) of the denominators, which is 6.

3 2/3 can be written as 11/3, and 2 5/6 can be written as 17/6.

So, 3 2/3 + 2 5/6 = 11/3 + 17/6

We need to find a common denominator, which is 6

11/3 + 17/6 = 22/6 + 17/6

Adding the two fractions, we get

22/6 + 17/6 = 39/6

Simplifying the fraction, we get

39/6 = 6 3/6

Therefore, Juliana and Brody hiked a total distance of 6 3/6 or 6 1/2 miles.

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The scale factor is one half

To find the scale factor, we can compare the side lengths of triangle D and triangle D′.

Let's compare the side lengths that are given for both triangles:

Triangle D has a side length of 4.2, and triangle D′ has a corresponding side length of 2.1.

Scale factor = (Side length of triangle D′) / (Side length of triangle D)

Scale factor = 2.1 / 4.2

Scale factor = 0.5

The scale factor used is 0.5, which corresponds to the first option, "one half".

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The solutions to the system of equations f(x) = x² + x - 6 and g(x) = -2x² - 2x + 12 are (-3, 0) and (2, 0). So, correct option is 1.

To graph the functions f(x) and g(x) using a calculator, we can enter the equations into the calculator's graphing function and choose an appropriate window to display the graph. Once the graphs are displayed, we can look for the points of intersection to find the solution to the system of equations.

Using a graphing calculator, we can see that the graphs of f(x) and g(x) intersect at two points: (-3, 0) and (2, 0). These points represent the x-coordinates of the solutions to the system of equations.

To verify that these points are indeed the solutions, we can substitute each of them into both equations and check that they satisfy both equations simultaneously.

For point (-3, 0):

f(-3) = (-3)² + (-3) - 6 = 0

g(-3) = -2(-3)² - 2(-3) + 12 = 0

Therefore, (-3, 0) is a solution to the system of equations.

For point (2, 0):

f(2) = 2² + 2 - 6 = 0

g(2) = -2(2)² - 2(2) + 12 = 0

Therefore, (2, 0) is also a solution to the system of equations.

The point (0, -6) and (0, 12) are not the points of intersection and (-6, 12) is not a solution to the system of equations.

Therefore, the answer is option 1.

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The following are the correct vertical translation and you can use this information to fill the table in the picture:

A vertical translation refers to a type of transformation that moves a function or graph vertically up or down without changing its shape. Specifically, a vertical translation of distance c is given by the function:

f(x) + c

where f(x) is the original function and c is a constant that determines the amount and direction of the translation. If c is positive, the graph of the function is shifted upwards; if c is negative, the graph is shifted downwards.

For example, the function f(x) = x^2 has a graph that is a parabola opening upwards. If we apply a vertical translation of 2 units, the resulting function is:

f(x) + 2 = x^2 + 2

The graph of this function is also a parabola, but it has been shifted vertically upwards by 2 units. Similarly, a vertical translation of -3 units would give us the function f(x) - 3 = x^2 - 3, which is the same parabola shifted downwards by 3 units.

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The function has been solved, and f (t) = 15 - 3t, with n days equal to 5.

Given data ,

There were 15 inches of snow on the ground on Monday morning. As the temperature increased, 3 inches of snow had evaporated by Tuesday morning. By Wednesday morning, three more inches had melted, and the pattern persisted.

The following factors affect this situation:

Time: Indicates how many days have elapsed since Monday morning.

Measures how much snow is still on the ground in inches.

Given that the amount of snow is reducing by a given amount every day, the situation may be modelled using a linear function.

f(t)= 15-3t

when f ( t ) = 0

15 = 3t

Divide by 3 on both sides:

t = 5 days

Therefore, after 5 days, all of the snow will have melted.

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The required value of probability P(B|A) is approximately 0.837.

As mentioned in the question,
P(A)=0.3, P(B)=0.57 and P(A and B)=0.251,

We can use the formula for conditional probability to find P(B|A):

P(B|A) = P(A and B) / P(A)

Substituting the given values, we get:

P(B|A) = 0.251 / 0.3 = 0.83667

Rounding to the nearest thousandth, we get:

P(B|A) ≈ 0.837

Therefore, the value of P(B|A) is approximately 0.837.

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Count the significant digits in the number.

Since there are no captive zeros or trailing zeros, only the two non-zero digits (3 and 6) are significant.

The time measurement 0.0036 seconds has 2 significant digits.

Significant digits in the time measurement 0.0036 seconds, let's first define what significant digits are and then determine the number of significant digits in the given measurement.
Significant digits are the meaningful digits in a number that contribute to its precision.

These digits help to reduce any ambiguity when reporting measurements.
To determine the significant digits in the number 0.0036 seconds:
Identify non-zero digits.
All non-zero digits (1-9) are always considered significant.

The non-zero digits are 3 and 6.
Identify leading zeros.
Leading zeros are the zeros that appear before the first non-zero digit.

These zeros are not considered significant.

The leading zeros are the three zeros before the 3.
Identify trailing zeros.
Trailing zeros are the zeros that appear after the last non-zero digit.

If the number has a decimal point, these zeros are considered significant.

There are no trailing zeros.
Identify captive zeros.
Captive zeros are the zeros that appear between non-zero digits.

These zeros are always considered significant.

There are no captive zeros.
Count the significant digits in the number.

Since there are no captive zeros or trailing zeros, only the two non-zero digits (3 and 6) are significant. So, the time measurement 0.0036 seconds has 2 significant digits.

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Answer:

The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius. The value of π is 3.14 or 22/7.

The correct option is (C) Triangle HJK is congruent to triangle NLM

A triangle is a closed, two-dimensional geometric figure with three sides and three angles. It is the simplest polygon and is formed by connecting three non-collinear points with line segments.

Congruent is a term used in geometry to describe two or more geometric figures that have the same shape and size. If two geometric figures, such as triangles or line segments, are congruent, it means that they are identical in shape and size, and they can be superimposed onto each other.

According to the given information:

In Triangle HKJ

Angle H is 58 degrees.

Angle J is 62 degrees.

Angle K is 60 degrees

In Triangle LMN (Arranging in the same order as the angles above)

Angle N is 58 degrees.

Angle L is 62 degrees.

Angle M is 60 degrees.

Therefore, we can say that:

Triangle HJK is congruent to Triangle NLM.

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The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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In the above isosceles trapezoid,

Since R is the midpoint of HN, HR = RN. Similarly, since T is the midpoint of KJ, KT = TJ.

Let's use these properties to write expressions for HJ and NK in terms of x:

HJ = 5x + 9

NK = 3x - 2

Since NKJH is an isosceles trapezoid, we know that HJ = NK + 2RT. Substituting the expressions we found earlier, we get:

5x + 9 = (3x - 2) + 2(3x + 6)

Simplifying this equation gives:

5x + 9 = 9x + 10

Subtracting 5x from both sides gives:

4 = 4x

Dividing both sides by 4 gives:

x = 1

Now that we know x, we can find the values of HJ, NK, and RT:

HJ = 5x + 9 = 14 cm

NK = 3x - 2 = 1 cm

RT = 3x + 6 = 9 cm

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