For any given event, the probability of that event and the probability of the _______ of the event must sum to one.

The side length of the small equilateral triangles is 3 cm.

Let's call the side length of the small equilateral triangles "x". Since there are three small triangles, the total perimeter of the small triangles is 3x.

The side length of the large equilateral triangle is 6 cm, so each side of the small triangles is a portion of 6 cm. Specifically, each side of the small triangles is (1/2) of a side of the large triangle.

Therefore, the perimeter of each small triangle is 3x, which is made up of three sides of length (1/2)6 cm or 3 cm. So we have:

3x = 3(3 cm) = 9 cm

Solving for x, we get:

x = 3 cm

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In this situation, Allison's insurance company will pay a total of $400,000.

First, we need to add up the total amount awarded to the people injured in the accident. This is $40,000 x 4 + $80,000 x 2 + $160,000 x 1 = $400,000.

Next, we need to look at Allison's insurance policy. She has 50/250 bodily injury insurance, which means that the insurance company will pay up to $50,000 per person and up to $250,000 per accident.

Since the total amount awarded is $400,000, the insurance company will only pay the maximum amount allowed per accident, which is $250,000.

Therefore, the insurance company will pay $250,000 and Allison will be responsible for the remaining $150,000.

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Answer: Infinite solutions.

Step-by-step explanation:

To graph both these equations, you need to make them slope intercept form (which is y = mx + b):

x + 2y = -2 in slope intercept form is y = -1/2x - 1 (subtract x from both sides then divide both sides by 2).

-3x - 6y = 6 in slope intercept form is y = -1/2x - 1. (add 3x to both sides then divide both sides by -6).

These are the same lines, so there are an infinite number of solutions when you graph.

Hope this helps!

Answer:

[tex]\mbox{\large \boxed{\textsf{5, 849 \;feet}}}[/tex]

Step-by-step explanation:

See figure for information pertaining to this explanation

The figure is self explanatory

The triangle ABC forms a right triangle with the vertical leg of length 14000-h and horizontal length of 58000

The angle opposite side 14000 - h = 8°

By the tangent formula

[tex]\tan 8^\circ = \dfrac{AB}{AC} = \dfrac{14000-h}{58000}[/tex]

Switching sides,

[tex]\dfrac{14000-h}{58000} = \tan 8^\circ[/tex]

[tex]14,000 - h = 58,000 \times \tan 8^\circ\\\\14,000 - h = 8,151.36 \approx 8,151[/tex]

h = 14,000 - 8,151 = 5,849 feet

So the altitude of Colorado Springs is roughly 5,849 feet

This is close to the published value of 6,035 feet. The differences are due to estimate errors in horizontal distance, peak height and angle of depression

The congruency theorem used in each of the triangles are;

14) HL Congruency Theorem.

15) Neither

16) Neither

17) SAS Congruency theorem.

18) Neither

19) AAS congruency theorem.

20) Neither

21) SSS congruency postulate.

14) We are given the hypotenuse side and leg as being congruent and as such the congruency proof here is; HL Congruency Theorem.

15) We are not given any congruent side nor angle and as such we can't determine if they are congruent.

16) We two congruent sides and non-included angle and as such they are not congruent.

17) We are given two congruent sides and the included congruent angle and as such the triangles are congruent by SAS Congruency theorem.

18) We two congruent sides and non-included angle and as such they are not congruent.

19) We are given two congruent angles and the non included side and as such they are congruent by AAS congruency theorem.

20) We two congruent sides and non-included angle and as such they are not congruent.

21) The three sides are shown to be congruent and therefore it is congruent by SSS congruency postulate.

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Answer:

[tex]x=\frac{9}{2}[/tex]

Step-by-step explanation:

[tex]2x=9 \implies x=\frac{9}{2}[/tex]

Answer:

Step-by-step explanation:

2

Answer:

4x+2

Step-by-step explanation:

Add common numbers together.

3x + x = 4x

Therefore, the answer is 4x+2.

Hope this helps ^_^

The total number of bottles that can be filled are 41.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

the volume of a cylinder is given by the formula as

Volume of cylinder = πr²h,

where r is the radius of the cylinder and h is its height.

We are given the radius of the water cooler is 7 inches

also the height of water cooler is 20 inches.

We calculate its volume by substituting the values in the volume formula

Volume of the cooler = π(7²)(20)

Volume of the cooler = 2,940π cubic inches

Now also we given the radius and height of the bottles

We similarly calculate the volume of each bottle by substituting the values in the formula

Volume of the bottle = π(1.5²)(10)

Volume of the bottle = 70.685π cubic inches

Now finally to find the total number of bottles we divide the volume of cooler by the volume of bottles we get

Number of bottles = Volume of the cooler / Volume of the bottle

                                =2,940π) / (70.685π)

                                =41

Therefore, the team manager can completely fill about 41 water bottles.

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The mean income, of people who worked full-time in 2001 and had at least a bachelor's degree, was $53,054. while the median income was $72,674.

The mean is the average value.  The mean is computed as the quotient of the total value divided by the number of values.

The median is the middle value of the data set in an ordered list.

Both the mean and the median are described as measures of central tendency.

Thus, we can identify the mean value as $53,054 since it was the first to be mentioned, followed by the median income as $72,674.

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Which of these numbers is the mean and which is the median? Explain your reasoning.

Answer:

8n^3 + 3n^2 + 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

You're welcome

1. Another point on the graph p(x) is (5, 9)

2. the vertex of the q(x) is (4, 10).

The other two points on the q(x) are (0, 2) and (2, 8).

Parabola is a curve drawn in a plane. Where any point is at an equal distance from a fixed point (the focus ) and a fixed straight line (the directrix ).

Given:

The two equations of the quadratic functions are;

p(x) = -(x - 1)² + 10

q(x) = 1/2(x - 4)² + 10.,

The graph of p(x) and q(x) is given in the image below.

1. Another point on the graph p(x) is (5, 9)

2. the vertex of the q(x) is (4, 10).

The other two points on the q(x) are (0, 2) and (2, 8).

3. Yes the assumption is correct.

Therefore, all the required values are given above.

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Answer: 12 tablespoons

Step-by-step explanation: 3/4 of a cup is equal to 6 fluid ounces or 12 tablespoons.

The correct standard form of the equation of the parabola is,

⇒ y = 1/4(x - 2)² - 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We know that;

The equation of the parabola with vertex (h, k) is,

⇒ y = a(x - h )² + k

Thus, The equation of the parabola is,

⇒ y = a(x - 2)² - 5

To find a, use the fact that the parabola passes through the point (4,−4):

⇒ - 4 = 4a - 5

Solving this equation, we get;

⇒ a = 1/4.

Thus, The equation of the parabola is,

⇒ y = 1/4 (x - 2)² - 5

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Option A is correct.

Selecting eight members randomly and recording whether each member is wearing a blue shirt.

A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Here, in 8 members the person wearing blue will be a success others will be a failure outcome.

Answer:

a

Step-by-step explanation:

Answer: it contains 21 yellow marbles

Step-by-step explanation:

x = 28 x 3/4
canceling method
x = 7 x 3
x = 21

The formulas for the rigid transformations of the figures are listed below:

Case 1: (x, y) → (x - 10, y + 9)

Case 2: (x, y) → (- y, x)

Case 3: (x, y) → (- x, y)

Case 4: (x, y) → (- y, x)

Case 5: (x, y) → (x, - y)

Case 6: (x, y) → (x, y + 10)

In this question we find six cases of rigid transformations applied on figures. The most common rigid transformations are listed below:

Then, by direct inspection, we derive the following rigid transformations:

Case 1 (Translation)

(x, y) → (x - 10, y + 9)

Case 2 (Rotation)

(x, y) → (x · cos (- 270°) - y · sin (- 270°), x · sin (- 270°) + y · cos (- 270°))

(x, y) → (- y, x)

Case 3 (Reflection about y-axis)

(x, y) → (- x, y)

Case 4 (Rotation)

(x, y) → (x · cos 90° - y · sin 90°, x · sin 90° + y · cos 90°)

(x, y) → (- y, x)

Case 5 (Reflection about x-axis)

(x, y) → (x, - y)

Case 6 (Translation)

(x, y) → (x, y + 10)

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59+(40+80)=59+120=179 is implify the expression by Associative property .

What is the associative property?

A mathematical principle known as the associative property states that the product of a multiplication problem is unaffected by the way the factors are organized.

                              The associative quality of addition The amount remains unchanged when the order of the addends is changed. By way of illustration, (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4) 2. plus, left parenthesis, 3. plus, 4. right parenthesis = 2. plus. left parenthesis, 3. plus. right parenthesis.

Associative property

(59 + 40) + 80 = 59 + (40 + 80)

(99) + 80 = 59 + (120)

179 = 179

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The required cost to lay carpet for her entire bedroom is 45,000.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form.

To calculate the cost of carpeting Linda's bedroom, we need to find the area of the rectangle:

Area = length x width

Area = 75m x 50m

Area = 3750 square meters

Then, we can multiply the area by the cost per square meter of carpeting:

Cost = Area x Cost per square meter

Cost = 3750 square meters x AED 12/square meter

Cost = AED 45,000

Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

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The values of x and y are:

x = 3.16

y = 4.47

Trigonometry is a topic which deals with the relation between angles and sides of a right angled triangle. It can be used to determine the value of the  unknown in a given question. The basic functions in trigonometry are: sine, cosine and tangent.

In the given diagram, we have;

i. To determine the value of x,

Tan θ = opposite/ adjacent

Tan 45 = x/ (10)^1/2

x = Tan 45*(10)^1/2

  = 3.16

x = 3.16

ii. To determine the value of y, we have;

Cos θ = adjacent/ hypotenuse

Cos 45 = (10)^1/2 / y

y = (10)^1/2 / Cos 45

 = 4.47

y = 4.47

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Answer:

x=17

Step-by-step explanation:

132 + (-30) = (6x+30) + (-30)

132 - 30 =6x + 30 - 30

102 =6x

6x/6 = 102/6

(This step has a picture)
x=17

The relation which are function is shown below.

In mathematics, a function is represented as a rule that produces a distinct result for each input x.The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.

We know that a relation is said to be function if one input have only one output.

1. The relation is not function because the input 6 have two output values

5 and 10.

2. The relation is a function because the each input have one output values.

3. The relation is a function because the each input have one output values.

4. The relation is not function because the input 4 have two output values .

5. The relation is a function because the each input have one output values.

6. The relation is not function because the input have two output values.

7. The relation is a function because the each input have one output values.

8. The relation is not function because the input have two output values.

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If a bag has 28 orange marbles, then it contain 49 red marbles.

A ratio is a comparison of two quantities or values, expressed in the form of a fraction or a division. Ratios are used to compare the size, magnitude, or quantity of two or more quantities or values.

For example, if there are 10 apples and 5 oranges, we can write the ratio of apples to oranges as 10:5 or 2:1, since there are two times as many apples as oranges. Similarly, if a recipe calls for 3 cups of flour and 1 cup of sugar, we can write the ratio of flour to sugar as 3:1, indicating that there are three times as much flour as sugar.

Ratios can be simplified, converted to equivalent fractions or decimals, or used to solve problems involving proportional relationships between different quantities. They are widely used in many areas of mathematics, science, and everyday life, such as in finance, engineering, and statistics.

We can start by using the given ratio of 7 red marbles for every 4 orange marbles to find the ratio of red marbles to orange marbles in the bag.

For every 4 orange marbles, there are 7 red marbles, so we can write:

7 red marbles / 4 orange marbles

We can simplify this ratio by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. This gives:

7/4

So the bag contains 7 red marbles for every 4 orange marbles.

If the bag has 28 orange marbles, we can use this ratio to find the number of red marbles in the bag. We can set up a proportion:

7/4 = x/28

where x is the number of red marbles in the bag.

To solve for x, we can cross-multiply:

7 × 28 = 4 × x

196 = 4x

Dividing both sides by 4, we get:

x = 49

Therefore, the bag contains 49 red marbles.

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The solution to the radical equation is given as follows:

x = 1.

The radical equation for this problem is defined as follows:

1/x + (x - 1)/9x = 1.

To leave the left side with a common denominator, we can multiply 1/x by 9 in the numerator and in the denominator, hence:

9/9x + (x - 1)/9x = 1.

As the left side has a common denominator, we can add the numerators and keep the denominator constant, as follows:

(9 + x - 1)/9x = 1

(8 + x)/9x = 1.

Applying cross multiplication, the value of x is obtained as follows:

9x = 8 + x

8x = 8

x = 8/8

x = 1.

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Based on the amount deposited into the account every month, the amount that Andrew will deposit in the account is $72,548.64. The interest earned will be $17,451.36.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

here, we have,

What amount does Andrew deposit?

This can be found by the formula:

= Amount deposited every month x Number of years x Number of months in a year

= 503.81 x 12 x 12

= $72,548.64

What amount of interest is earned?

This can be found as:

= Future value of amount - Amount deposited

= 90,000 - 72,548.64

= $17,451.36

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Answer:

(6x+8y)(6x-8y)

Step-by-step explanation:

See attached worksheet.

The slope of the function is equal to: C. 3.

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

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

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (4 - 1)/(0 - (-1))

Slope, m = 3/4=1

Slope, m = 3.

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