Boris is playing a role playing game with his friends. He will roll dice to determine if his character casts a spell. The odds in favor of his character casting a spell are 8/7. Find the probability of his character casting a spell.

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = [tex]\frac{1-7}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

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Answer: hello am I solving for x?

Step-by-step explanation:question

The probability that a randomly chosen person from this group has type B is 0.4.

The probability of type AB is 0.12, and the probability of type B or type AB is 0.52.

We have,

The probability that a randomly chosen person from this group has type B is given by the number of people with blood type B divided by the total number of people in the group:

Probability of type B

= Number of people with type B / Total number of people

In this case, the number of people with blood type B is 20, and the total number of people is 50 (22 + 20 + 6 + 2).

Probability of type B = 20 / 50 = 0.4

Similarly, the probability that a randomly chosen person from this group has type AB is given by the number of people with blood type AB divided by the total number of people:

Probability of type AB = Number of people with type AB / Total number of people

In this case, the number of people with blood type AB is 6, and the total number of people is 50. Therefore,

Probability of type AB = 6 / 50 = 0.12

To find the probability that a randomly chosen person from this group has blood type B or type AB, we need to add the probabilities of both events:

Probability of type B or type AB = Probability of type B + Probability of type AB

Probability of type B or type AB = 0.4 + 0.12 = 0.52

Thus,

The probability that a randomly chosen person from this group has type B is 0.4, the probability of type AB is 0.12, and the probability of type B or type AB is 0.52.

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Answer:

-3x² - x - 5

Step-by-step explanation:

(3x² - 7x - 4) - (6x² - 6x + 1) =
= -3x² - x - 5

Answer:

m<1 = 47 degrees

m<2 = 43 degrees

m<3 = 90 degrees

m<4  = 43 degrees

Step-by-step explanation:

Answer:

-------------------

Let E represent the number of Eagle fans and S represent the number of Spartan fans at the start of the game.

We can set up two equations using the given information:

Now we can solve the equations.

From equation (1), we can replace E in equation (2), the solve for S:

Now find the number of Eagle fans using equation (1):

Answer:

x = 8, m2 = 78, m4 = 102, m6 = 78, m7 = 78,

Step-by-step explanation:

Answer:

1. Find the area of the rectangle in square yards. In this case, the area is 9 yards * 3 yards = 27 square yards.

2. Convert square yards to square feet. There are 9 square feet in 1 square yard. So, the area of the rectangle in square feet is 27 square yards * 9 square feet/square yard = 243 square feet.

Therefore, the area of the rectangle floor in square feet is 243 square feet.

Answer:243

Step-by-step explanation:

(9x3) x (3x3)

27 x 9 = 243

The value of the side BC is equal to 10√21 in the simplest rationalized form using the trigonometric ratio of tangent.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the tangent of angle 60°

tan 60° = BC/(10√7) {opposite/adjacent}

BC = 10√7 × tan 60° {cross multiplication}

BC = 10√7 × √3 {tan 60 = √3}

BC = 10√21

Therefore, the value of the side BC is equal to 10√21 in the simplest rationalized form using the trigonometric ratio of tangent.

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A, percentages

You would see percentages on a circle graph, because it's how many parts of the whole that they take up.

Happy to help, have a great day! :)

The ascending order of the rational numbers are -1.75 < -1.3 < 0.41 < 1.8

Given are the list of the rational numbers, so,

1 4/5, -7/4, 41% and -1.3

So,

1) The fraction form :-

a) 1 4/5 = 9/5

b) -7/4

c) 41% = 41/100

d) -1.3 = 13/10

2) The decimal form :-

a) 1 4/5 = 9/5 = 1.8

b) -7/4 = -1.75

c) 41% = 41/100 = 0.41

d) -1.3 = 13/10 = -1.3

3) The ascending order of the rational numbers =

You can arrange them by seeing the value and sign,

-1.75 < -1.3 < 0.41 < 1.8

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The distribution of the sample means will have a smaller standard deviation

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

Observations = 9

The population is not given

However by the theorem of the central limit; we understand that

The distribution of the sample means will always have a smaller standard deviation

This is because the sample mean selected from the population might not totally represent the whole population, but would have smaller standard deviation

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The value of f(-7) is 172.

To find the value of f(-7) for the given function f(x) = 4x^2 + 6x + 9, we substitute -7 for x in the function and evaluate it.

f(-7) = 4(-7)^2 + 6(-7) + 9

Simplifying the equation:

f(-7) = 4(49) - 42 + 9

= 196 - 42 + 9

= 163 + 9

= 172

Therefore, f(-7) = 172.

By substituting -7 into the function, we obtained the value of 172. This means that when x is equal to -7, the corresponding value of the function f(x) is 172.

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The logo that fits the requirement is the circle logo i.e. logo 1

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

The figures that represent the logos

For the circle logo, we have

Area = 22/7 * 1/2 * 1/2

Convert units to feet using the scale

Area = 22/7 * 1/2 * 7 * 1/2 * 7

Evaluate

Area = 38.5 square feet

Also, we have

Width = 2 * 1/2 * 7 feet

Width = 7 feet

For the plus-shaped logo, we have

Area = 5 * 1/2 * 1/2

Convert units to feet using the scale

Area = 5 * 1/2 * 7 * 1/2 * 7

Evaluate

Area = 61.25 square feet

Also, we have

Width = 3 * 1/2 feet * 7

Width = 10.5 feet

Hence, the logo that fits the requirement is the circle logo i.e. logo 1

This is because its area is not up to the maximum area (40 square feet) and the width is greater than the minimum width (4 feet)

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The time needed before the doctor administers the medication again is given as follows:

d) 22.2 hours.

The exponential function giving the amount of the medicine in the patient's bloodstream after t hours is given as follows:

[tex]A(t) = 500(0.93)^t[/tex]

The medication will be applied when the amount is given as follows:

A(t) = 100.

Hence the time needed is obtained solving the exponential function as follows:

[tex]100 = 500(0.93)^t[/tex]

[tex](0.93)^t = \frac{100}{500}[/tex]

[tex](0.93)^t = 0.2[/tex]

The logarithm of base 10 is the inverse of the exponential, hence:

[tex]t = \frac{\log{0.2}}{\log{0.93}}[/tex]

t = 22.2 hours.

Which is the time needed before the doctor administers the medication again.

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The statement of the function is (b) when x > 0, the graph is positive

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

The functions f(x) and g(x)

In the graph, we can see that

The graph of the function passes through (0, 0)

This means that

When x > 0, the graph is positive

When x < 0, the graph is negative

Hence, the statement of the function is (b)

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y = −(x − 2)(x − 9); the wolf leaped a distance of 7 feet using zeros 2 and 9. Therefore, option B is the correct answer.

Given that, trajectory can be mapped by the equation f(x) = -x² + 11x - 18.

Here, -x² + 11x - 18=0

-x² + 9x+2x - 18=0

-x(x-9)+2(x-9)=0

(x-9)(-x+2)=0

x-9=0 and -x+2=0

x=9 and x=2

Therefore, option B is the correct answer.

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A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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The population grow by 24.7% between the years 2004 and 2009

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

Population in 2004 = 2122

Population in 2009 = 2647

The growth of the population between the years is calculated as

Percentage = Population in 2009/Population in 2004  - 1

Substitute the known values in the above equation, so, we have the following representation

Percentage = 2647/2122 - 1

Evaluate

Percentage = 24.7%

Hence, the population grow between the years by 24.7%

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The probability that this song will be played on exactly 0 days out of 7 days, if The probability that a particular song is played is 0.23 is 0.008.

We have,

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

The probability that a particular song is played is 0.23,

As can be seen that the problem is of combination, so we have to choose 5 out of 7,

Calculate the combination as shown below,

⁷C₅ = 7! / (5! × 2!) = 7 × 6 / 2

⁷C₅ = 7 × 6 / 2

⁷C₅ = 21

Calculate the probability as shown below,

P = ⁷C₅  × (0.23)⁵ × (0.77)²

P = 0.008

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complete question;

During a single day at radio station WMZH, the probability that a particular song is played is 0.23. What is the probability that this song will be played on exactly 0 days out of 7 days? Round your answer to the nearest thousandth.

Answer: Answer is seen below (sorry if its confusing, this is what I got though)

Step-by-step explanation:

Area of triangle A   = 13.5 square units

Area of triangle B   = 10.5 square units

Total area of figure =  24 square units

In the given figure,

It consist of two triangles

Now for triangle A :

Height = 3

Base    = 9

Since we know that,

Area of triangle = (1/2) x base x height

                          = 0.5 x 9 x 3

                          = 13.5 square units

Now for triangle B :

Height = 3

Base    = 7

Since we know that,

Area of triangle = (1/2) x base x height

                          = 0.5 x 7 x 3

                          = 10.5 square units

Now the total are of figure is sum of are of both triangles,

Therefore,

total area of figure,

⇒ 13.5 + 10.5

⇒ 24 square units

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The missing figure of question is attached below:

The maximum value of z = 4x + 4y, subject to the given constraints, is 92/3, which occurs when x = 14/3 and y = 4.

To maximize the objective function z = 4x + 4y subject to the given constraints, we can solve this linear programming problem using the graphical method.

First, let's graph the feasible region determined by the constraints:

1. Graph the line 2x + 4y = 28:

  Rewrite the equation in slope-intercept form: y = -0.5x + 7

  Plot two points on the line: (0, 7) and (14, 0), and draw a line through them.

2. Graph the line 5x + 6y = 50:

  Rewrite the equation in slope-intercept form: y = (-5/6)x + (25/3)

  Plot two points on the line: (0, 25/3) and (10, 5/3), and draw a line through them.

3. Shade the region that satisfies the constraints:

  Shade the region below the line 2x + 4y ≤ 28.

  Shade the region below the line 5x + 6y ≤ 50.

  The feasible region is the intersection of the shaded regions.

Next, we evaluate the objective function at the corner points of the feasible region to determine the maximum value.

The corner points of the feasible region are:

A: (0, 7)

B: (0, 25/6)

C: (14/3, 4)

D: (10, 5/3)

Evaluate the objective function at each corner point:

z(A) = 4(0) + 4(7) = 28

z(B) = 4(0) + 4(25/6) = 50/3

z(C) = 4(14/3) + 4(4) = 92/3

z(D) = 4(10) + 4(5/3) = 140/3

The maximum value of z is obtained at z(C) = 92/3.

Therefore, the maximum value of z = 4x + 4y, subject to the given constraints, is 92/3, which occurs when x = 14/3 and y = 4.

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The difference between 1/5 and 2/10 is that they are different representations of the same value.

The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.

"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.

The diagram can be used to illustrate fraction concepts.

1/5 is simple, but 2/10 can be reduced to 1/5 by dividing both numbers by 2. They are both 0.2 or 20%. 1/5 and 2/10 are different fractions with different purposes.

Use 1/5 for 5 parts and 1/5 (simplified from 2/10) for 10 parts. 1/5 and 2/10 = 0.2, ratio reasoning emphasizes ratios between quantities. A 2:3 boys-to-girls ratio compares the constant ratio between changing quantities.

Proportional reasoning maintains constant ratios between quantities, while ratio reasoning uses fractions or ratios to compare relationships. For instance, if distance doubles, so does speed.

Step 3/5: "Fifth" is the ordinal number for the object five places away in a sequence. See diagram. The fifth circle is 1/5 of a whole in unit fraction sequence. Imagine a rectangle divided into five equal parts, each shaded to show 1/5. Shaded part = 1/5 of whole.

To show 25/7 with area model, make 7x25 rectangle and split into 7 equal parts. 25/7 per part.

1.2 The set model:

To represent 25/7, divide 25 objects into 7 equal sets, resulting in 3 objects per set with 1 left over. This represents the fraction of 25/7.

Step 5/5

Let's assume the width of the rectangular piece of paper as x cm. Then the length of the paper would be:

Now we know that the perimeter of the rectangle is given by the formula:

So, for this rectangle:

54 = 2(5x + x)

Simplifying and solving for x, we get:

54 = 2(6x)

27 = 6x

x = 4.5 cm

Therefore, the width of the paper is 4.5 cm and the length is 5 times the width which is 22.5 cm

The difference between 1/5 and 2/10 is that they are different representations of the same value.

The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.

"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.

The diagram can be used to illustrate fraction concepts.

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Answer:

90

Step-by-step explanation:

This type of problem is an example of combinations. In this case, in one salad, it states that you can chose between 5 bases, 3 proteins, and 6 dressings.

In this problem, you would have to multiply all numbers together.

In this case, 5(bases)x3(protiens)x6(dressings)=90

I hope this helps you!

The graph of the inverse function is given by the image presented at the end of the answer, and the correct option is given by option 3.

The parent function for this problem is the cube function translated up two units, hence it is defined as follows:

y = x³ + 2.

To obtain the inverse function, first we must exchange the variables x and y on the definition of the function, as follows:

x = y³ + 2.

Then we must isolate the variable y, as follows:

[tex]y^3 = x + 2[/tex]

[tex]y = \sqrt[3]{x + 2}[/tex]

Which has the correct dashed graph given by option 3 on the image given.

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If the girls read the book at the same time, who will finish first: A. Shonda will finish first. Her ratio of chapters to hours is 2/1. Corine's rate of chapters to hours is 3/2, and 2/1 is a greater slope than 3/2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = 2/1

Slope (m) = 2.

Based on the table, the slope is the change in y-axis with respect to the x-axis and for Shonda it is equal to 2/1 or 2. Therefore, Shonda would finish before Corine because 2/1 > 3/2.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.