A game has a 10-sided die. What is the probability of rolling a number less than 3 or an odd number? All answers should be in FRACTION form ONLY.

Answer:

Step-by-step explanation:

\(\sqrt{81} < \sqrt{84} < \sqrt{100}\)

    \(9 < \sqrt{84} < 10\)

square root of 84 is between 9 and 10.

the probability that the user is fraudulent given that they originate calls from two or more metropolitan areas in a single day is approximately 0.029.

To solve this problem, we can use Bayes' theorem to calculate the probability that a user is fraudulent given that they originate calls from two or more metropolitan areas in a single day.

Let's define the following events:

A: User originates calls from two or more metropolitan areas in a single day.

B: User is fraudulent.

We are given the following probabilities:

P(A|¬B) = 0.01 (probability of legitimate users originating calls from two or more metropolitan areas)

P(A|B) = 0.30 (probability of fraudulent users originating calls from two or more metropolitan areas)

P(B) = 0.001 (proportion of fraudulent users)

We need to find:

P(B|A) = Probability that the user is fraudulent given that they originate calls from two or more metropolitan areas in a single day.

Using Bayes' theorem, we can calculate P(B|A) as follows:

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

To find P(A), we can use the law of total probability:

P(A) = P(A|B) * P(B) + P(A|¬B) * P(¬B)

P(¬B) is the complement of event B, which represents a user being legitimate:

P(¬B) = 1 - P(B)

Now we can calculate P(A):

P(A) = P(A|B) * P(B) + P(A|¬B) * (1 - P(B))

Substituting the given values:

P(A) = 0.30 * 0.001 + 0.01 * (1 - 0.001)

Finally, we can calculate P(B|A):

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

Substituting the given values:

P(B|A) = (0.30 * 0.001) / P(A)

Now, let's calculate P(A) and then find P(B|A):

P(A) = 0.30 * 0.001 + 0.01 * (1 - 0.001)

P(A) = 0.0003 + 0.01 * 0.999

P(A) = 0.0003 + 0.00999

P(A) = 0.01029

P(B|A) = (0.30 * 0.001) / P(A)

P(B|A) = 0.0003 / 0.01029

P(B|A) ≈ 0.0291 (rounded to three decimal places)

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Answer:

(x - 2)(x² + 2x + 4) = 0

Step-by-step explanation:

x³ - 8 ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

x³ - 8

= x³ - 2³

= (x - 2)(x² + 2x + 2²) = (x - 2)(x² + 2x + 4)

Answer:

\(a_{n} =a_{n-1} -5.6\) where \(a_{1} =-2.7\)

Step-by-step explanation:

This is an arithmetic sequence with the first term is \(a_{1}\) = -2.7 and has a common difference of \(d=-5.6\).

Arithmetic Sequence: \(a_{n} =a_{n-1} +d\)

\(a_{n}\) is the nth term and \(d\) is the common difference.

The common difference: -2.7, -8.3, -13.9...

Subtract: -2.7- (-8.3) = -5.6, -13.9 - (-8.3) = -5.6

Common difference: \(d = -5.6\)

Recursive rule: \(a_{n} = a_{n-1} -5.6\)

Answer:

D. a=1 and b=4

Step-by-step explanation:

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

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

x^2-2x +1 =4

(x-1)^2=4

Therefore a=1 and b=4

Answer:

Step-by-step explanation:

Let the number be x.  Then six less than x is y.

Symbolically, this comes out as x - 6 = y

Answer:

y=-4

Step-by-step explanation:

The answer is going to be -4 as when y=-16 x=8.

If the ratio of the two sides of the triangles are the same then the third sides of the triangle will be parallel. Then the correct figure is D.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If the ratio of the two sides of the triangles are the same then the third sides of the triangle will be parallel.

⇒ 5.5/15 = 6.6/18

⇒ 0.366 = 0.366

Then the correct figure is D.

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Based on the geometry of a sphere, we can conclude that two small circles on a sphere will never be parallel unless they are identical or coincide with each other.

To determine whether two small circles on a sphere can be parallel, we need to consider the geometry of the situation. Let's analyze the scenario and draw a sketch to assist in our explanation.

Consider a sphere Q with a small circle on its surface. Points A and B lie on this small circle. We want to explore whether two other small circles on the sphere can be parallel to the given small circle.

First, let's imagine the sphere Q and the small circle with points A and B. Since the small circle does not go through opposite poles (the endpoints of a diameter), we know that it lies on a plane that is tilted relative to the axis of the sphere.

Now, let's take another small circle on the same sphere Q. To be parallel to the given small circle with points A and B, the second small circle would need to lie on a plane that is also tilted at the same angle as the first small circle.

However, since the sphere Q is a three-dimensional object, it is not possible for two planes to be simultaneously tilted at the exact same angle unless they are equivalent or coincide with each other. In other words, two small circles on a sphere cannot be parallel unless they are actually the same circle.

Therefore, based on the geometry of a sphere, we can conclude that two small circles on a sphere will never be parallel unless they are identical or coincide with each other.

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The estimated true population variance in leasing rates for the car dealer is between 3436.02 and 9512.46 with 90% confidence.

To estimate the true population variance in leasing rates with 90% confidence, we can use a confidence interval formula with the t-distribution. The formula for the confidence interval is:

CI = (n-1)*s^2 / chi2(alpha/2, n-1) to (n-1)*s^2 / chi2(1-alpha/2, n-1)

Where CI is the confidence interval, n is the sample size, s is the sample standard deviation, alpha is the level of significance, and chi2 is the chi-squared distribution.

Given the sample of leasing rates, the sample size is 6 and the sample standard deviation is approximately 31.27.

Using a chi-squared distribution table or calculator, we can find the critical values for chi2(0.05, 5) and chi2(0.95, 5) to be approximately 11.07 and 0.83, respectively.

Plugging in the values into the confidence interval formula, we get:

CI = (6-1)*31.27^2 / 11.07 to (6-1)*31.27^2 / 0.83

Simplifying the equation gives:

CI = 3436.02 to 9512.46

Therefore, with 90% confidence, the true population variance in leasing rates for the car dealer is between 3436.02 and 9512.46.

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Answer:

(g∘f)(x) = -20x + 22

Step-by-step explanation:

(g∘f)(x) simply means g(f(x))

We are given;

f(x) = -5x + 4

g(x) = 4x + 6

Thus;

(g∘f)(x) = 4(-5x + 4) + 6

(g∘f)(x) = -20x + 16 + 6

(g∘f)(x) = -20x + 22

Answer:

<1  = 62 degrees

Step-by-step explanation:

<C = 180 - 130

= 50 degrees

<E = 180 - 118

= 62 degrees

<1  = 62 degrees

Approximately 17.4 inches of fabric were used on a headband for each player, and 9.43 inches of fabric were used on a wristband for each player.

Here we want to find how much fabric was used on a headband and wristband for each player, we need to calculate the total fabric used for headbands and wristbands and divide it by the total number of players.

So the formula we need to use is:

Fabric used on a headband  = Total fabric used for headbands / (Number of players + Number of coaches)

Fabric used on a headband  = 853.58 inches / (46 + 3)

Fabric used on a headband = 853.58 inches / 49 = 17.4 inches

And we also need to use:

Fabric used on a wristband  = Total fabric used for wristbands / Number of players

Fabric used on a wristband = 433.78 inches / 46 = 9.43 inches

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The amount of fabric that was used on a headband and wristband for each player is: 28 inches

The parameters given in the question are:

853.58 inches of fabric used for headbands

433.78 inches of fabric on wristbands

She makes 46 headbands for the players and 3 for the coaches: 46 + 3 = 49 headbands

She only makes wristbands for the players: 46 wristbands

Thus:

Fabric used for each headband = 853.58/49 = 17.42 ≈ 18 inches per headband

Fabric used for wristband = 433.78/46 = 9.43 ≈  10 inches per wrist band.

Total fabric used = 18 + 10 = 28 inches

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Answer

The transformation is a dilation with a scale factor of 2.

Explanation

The vertices of the triangle are given as A (1, 3), B(4, 2), and C (3, 8).

Which transformation would produce an image with vertices

A' (2, 6), B'(8, 4), C'(6, 16)?

As we can see from the solution of the transformation, the new coordinates are double the given coordinates.

A rotation, 90º clockwise or anticlockwise interchanges the x and y coordinates somewhat.

A reflection does this interchanging too.

But a dilation with a scale factor changes the size of the figure by multiplying the coordinates of the vertices by the value of the scale factor.

Since the new coordinates are double of the old coordinates, we can see that this transformation is a dilation with a scale factor of 2.

Hope this Helps!!!

The probability that her first flight was delayed exists 0.975.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

Let event that First flight on time be denoted as OT and event that a flight exists delayed be D;

P(OT) = 0.15 and P(D) = 1 - P(OT) = 1 - 0.15 = 0.85

Let event that Luggage will make connecting flight be L and that it won't make it be L',

Given that there is a 0.95 chance that luggage will arrive on time, this is a conditional probability and can be expressed as follows:

P(L/OT) = 0.95 and also P(L/D) = 0.65

From this P(L'/OT) = 1 - P(L/OT) = 1 - 0.95 = 0.05

and P(L'/D) = 1 - P(L/D) = 1 - 0.65 = 0.35

The question is asking for the probability that the first flight was delayed (D) provided that her Luggage was not there (L').

Let the equation of conditional probability be;

P(D/L') = P( D and L')/ P(L')

P(D and L') = P(D) × P(L'/D) = 0.85 × 0.35 = 0.2975

P(L') = P(OT) × P(L'/OT) + P(D) × P(L'/D)

     = 0.15(0.05) + 0.85(0.35)

     = 0.305

P(L/OT) = 0.297/0.305

             = 0.975

Therefore, the probability that her first flight was delayed is 0.975.

The complete question is:

Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight is on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65.

Question: Suppose you pick up Leah in Denver and her luggage is not there.

What is the probability that her first flight was delayed?

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Answer:

1000

Step-by-step explanation:

You just have to multiply by two

Answer:

axis of symmetry: x=1

vertex: (1, -1)

for the sketch, plot these points: (1, -1), (2, 0), (3, 3), (0, 0), (-1, 3)

Step-by-step explanation:

hope this helps :)

Answer:

axis of symmetry= (1,-1)

vertex = (2, -2)

and then I attached a picture of what it should look like on the graph

Recall that the area of a square is:

and the volume of a cube is:

Since the base of the cube has an area of 324 meters squared, then:

Then:

Therefore the volume of the given cube is:

Simplifying the above result we get:

Answer:

The statement " An example of continuous data would be the numbers on baseball player jerseys" is false because the numbers on baseball player jerseys represent a finite set of distinct values, which makes them an example of discrete data, not continuous data.

Continuous data is data that can take on any value within a range or interval. This means that the data can be measured and expressed as a decimal or a fraction, and there are an infinite number of possible values within the range. For example, the height of a person can be any value between 5 feet and 6 feet, including all the possible fractions or decimals in between.

On the other hand, discrete data is data that can only take on certain distinct values. These values cannot be measured or expressed as a decimal or a fraction. Examples of discrete data include the number of children in a family, the number of students in a classroom, or the number of books on a shelf.

In the case of baseball player jerseys, the numbers are assigned to players based on a finite set of integers (typically 0 to 99), and there are no fractional or decimal values in between. Therefore, the numbers on baseball player jerseys are an example of discrete data, not continuous data.

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Answer:

B

Step-by-step explanation:

For the lines to be parallel.

The 2 given angles are corresponding and congruent, that is

4x - 12 = 3x + 17 ( subtract 3x from both sides )

x - 12 = 17 ( add 12 to both sides )

x = 29 → B

The value of x will be 29°. Then the correct option is B.

If two lines are parallel, then the third line. The corresponding angles are equal angles.

We know that the angle (3x + 17) and (4x – 12) are corresponding angle.

(3x + 17) = (4x – 12)

4x – 3x = 17 + 12

          x = 29°

The value of x will be 29°.

Then the correct option is B.

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Answer:

The answer is 3

Step-by-step explanation:

a. The area of the family room is 162 ft².

b. 24 tiles will be needed to cover the floor.

c. Mr. Dieter will have to buy 2 boxes to tile the family room.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are thought to be sufficiently described by the four basic operations, also referred to as "arithmetic operations." The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.

a. There are two different shapes of which one is rectangle and other is triangle.

So,

⇒ Area of rectangle = length x width

⇒ Area of rectangle = 16 x 8

⇒ Area of rectangle = 128 ft²

Also,

⇒ Area of first triangle = \(\frac{1}{2}\) x base x height

⇒ Area of first triangle = \(\frac{1}{2}\) x 4 x 3

⇒ Area of first triangle = 6 ft²

Similarly,

⇒ Area of first triangle = \(\frac{1}{2}\) x base x height

⇒ Area of first triangle = \(\frac{1}{2}\) x 8 x 7

⇒ Area of first triangle = 28 ft²

On adding the three areas, we get

⇒ Area of family room = 128 + 6 + 28

⇒ Area of family room = 162 ft²

b. We will convert the area into inches.

We know that 1 feet = 12 inches.

So, using the multiplication, we get

162 feet = 162 * 12 in²

162 feet = 1944 in²

Now,

⇒ Area of tile = 9 * 9

⇒ Area of tile = 81 in²

So,

⇒ Number of tiles = \(\frac{1944}{81}\)

⇒ Number of tiles = 24

c. Since, tiles are sold in boxes of 12 so, using the division operation, we get

⇒ Number of boxes needed = \(\frac{24}{12}\)

⇒ Number of boxes needed = 2

Hence, the required solution has been obtained.

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Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall.

To determine how many gallons of paint Ms. Paquette used for one coat on the rectangular wall, we first need to calculate the total area of the wall.

Area of the wall = length x width
= 25.5 feet x 10 feet
= 255 square feet

Now, to find out how many gallons of paint are needed for one coat, we need to know the coverage rate of the paint. This information is usually provided on the paint can label. Let's assume that the coverage rate for the paint Ms. Paquette used is 350 square feet per gallon.

To calculate how many gallons of paint are needed, we can divide the total area of the wall by the coverage rate of the paint:

255 square feet ÷ 350 square feet per gallon = 0.7286 gallons

This means that Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall. Since paint is typically sold in 1-gallon containers, she would need to purchase at least one gallon of paint to complete one coat on this wall.

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Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

Answer:

B) The amount of service fee, in dollars

Step-by-step explanation:

Look for words relating to "one time," as that indicates the constant

Answer:

vertex is (6, -11)

Step-by-step explanation:

Given equation
f(x) = x² - 12x + 25

is that of an upward-facing parabola(since the coefficient of x² is positive).

The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x

f'(x) = d/dx(x² - 12x + 25)

= 2x - 12

f'(x) = 0 ==> 2x - 12 = 0

2x = 12

x = 6

Substitute x = 6 in f(x) to get

f(6) = 6² - 12(6) + 25

= 36 - 72 + 25

= -11

So the vertex is at (6, -11)

Answer:20.8 In^2

Step-by-step explanation:

Base=10.4

Height=4

Area of =(base x height)/2

Area of =(10.4x4)/2

Area of =41.6/2

Area of =20.8

Answer:

See below in bold.

Step-by-step explanation:

1. x^2 - 13x - 30

We need 2 numbers whose product is -30 and whose sum = -13.

They are  -15 and + 2:

Answer is (x - 15)(x + 2).

2.   2x^2 + 4x - 126

First we can take 2 out to give:

2(x^2 + 2x - 63)

Now we need 2 numbers whose product is - 63 and sum = +2.

These are +9 and - 7 so

Answer is  2(x - 7)(x + 9).

3. -30x^3 + 3x^2 + 9x

First we can take out -3x to give

-3x(10x^2 - x - 3)

Now we want  2 numbers whose product is 10*-3  = -30 and whose sum is -1. They are  -6 and +5 so we write the above as:

-3x(10x^2 + 5x - 6x - 3)

Now we factor the parentheses by grouping:

= -3x( 5x(2x + 1) - 3(2x + 1)

= -3x(2x + 1)(5x - 3)  Answer.

The answer to the second part is 12x^2 - 13x - 21.

Part 3

1, 18.

2. 6.

3. = 5(2(-3)^2 - 3*3*4 + 4^2) - 3)) - 2(-3)(-3 + 7(4) - 1) - 3*4^2

=  5*(67) - 2(72) - 48

= 143.

4.  (11m^2 - 7) - (6m^2 + 3m - 11) + (3m^2 - m - 9)

= 11m^2 - 7 - 6m^2 - 3m + 11 + 3m^2 - m - 9

=  8m^2 - 4m - 5

A = 8, B = 4 and C = 5.

The common sum is 18 as "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same".

A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. The outcome or conclusion we arrive at when we add two or more numbers is known as the SUM. Addends are the numbers that are added.

Here,

The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these 8 numbers represent all of the vertices of the cube.

=(1+2+3+4+5+6+7+8)/2

=18

Since "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same," the common sum is 18.

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Answer:

-14x+3y+6

Step-by-step explanation:

first do 3x2

then do 2x-16x

then do -4y+7y

Answer:

3x2×3y-14x

Step-by-step explanation:

Combine like terms

-4y and 7y = 3y

-16x and 2x= -14x