Find the probability of exactly three
successes in eight trials of a binomial
experiment in which the probability of
success is 45%.
P(3) = 8C3 (0.45)³ (0.55)8-3
Solve part of the answer.
8C3 = [?]

pi x 2r = circ

2r = circ/pi

r = circ /(2 x pi) =  65.94/(2 x 3.14) = 10.5 feet

The total distance run by each runner is 1/12 mile.

A relay race is a track and field event where athletes compete as part of a team, taking turns running a certain distance and passing a baton to the next runner until all team members have completed their portion of the race.

Here we have

A relay race is 1 /4 space mile

The number of relay runners on the team is 3

Let each runner, runs for x miles  

The total distance run by 3 relays = 3x

From the data,

The relay race is 1/4 miles

=> 3x = 1/4 miles

=> 12x = 1 miles

=> x = 1/12 miles  

Hence,

The total distance run by each runner is 1/12 mile.

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The probability of getting an 8 or 4 on the spinner is 1÷4 or 25%.

What is Probability ?

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

the probability of getting an 8 or 4 by assuming that the spinner has equally likely outcomes for each number from 1 to 8.

There are two possible outcomes that satisfy the condition of getting an 8 or 4: either the spinner lands on 8 or it lands on 4.

Since there are 8 equally likely outcomes on the spinner, the probability of getting an 8 or 4 is:

P(8 or 4) = number of favorable outcomes ÷ total number of outcomes

= 2 ÷ 8

= 1÷4

Therefore, the probability of getting an 8 or 4 on the spinner is 1÷4 or 25%.

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Scarcity principle: Resources are limited and choices must be made, b. Rational person: Makes decisions based on logical thinking and self-interest, c. Economic surplus: Net gain to society from producing and consuming a good, d. Marginal benefit: Additional benefit from consuming one more unit of a good or service.

A statement is a declarative sentence that expresses a fact, opinion, or idea. It is a sentence that makes a claim or assertion that can be true or false, and it can be either affirmative (positive) or negative. A statement can be a simple sentence, or it can be a complex sentence that includes multiple clauses

a. The scarcity principle is the economic principle that states that resources are limited and cannot satisfy all human wants and needs. This principle recognizes that we live in a world of limited resources, and therefore, we must make choices about how to allocate those resources to satisfy our wants and needs. For example, a farmer may have limited land and water resources to cultivate crops, and he must choose which crops to grow based on their profitability, water requirements, and market demand.

b. A rational person is an individual who uses logical thinking and makes decisions based on self-interest to achieve the best possible outcome. A rational person weighs the pros and cons of each option and selects the alternative that maximizes their satisfaction or utility. For example, a consumer may compare prices and quality of different brands before purchasing a product to get the best value for their money.

c. Economic surplus is the difference between the total value that consumers place on a good or service and the total cost of producing it. It represents the net gain to society from producing and consuming the good or service. For example, if a firm produces 100 units of a product at a total cost of $500 and sells them for a total of $700, then the economic surplus is $200.

d. Marginal benefit is the additional benefit that a person receives from consuming one more unit of a good or service. It is the change in total benefit divided by the change in the quantity consumed. For example, if a consumer derives 10 units of satisfaction from consuming the first slice of pizza and 8 units of satisfaction from consuming the second slice, then the marginal benefit of the second slice is 8-10=-2 units of satisfaction.

Therefore, a. Scarcity principle: Resources are limited and choices must be made, b. Rational person: Makes decisions based on logical thinking and self-interest, c. Economic surplus: Net gain to society from producing and consuming a good, d. Marginal benefit: Additional benefit from consuming one more unit of a good or service.

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Answer:

4

Step-by-step explanation:

The product of eight and two is 8 x 2 = 16.

The product of three and four is 3 x 4 = 12.

So, the expression "the product of eight and two, minus the product of three and four" can be written as:

16 - 12 = 4

Therefore, the answer is 4.

These dimensions would work for the swimming pool are

9 feet by 70 feet

10 feet by 63 feet

14 feet by 45 feet

15 feet by 42 feet

18 feet by 35 feet

21 feet by 30 feet

How to find dimensions of the swimming pool?

to find the dimensions of the swimming pool that covers an area of 630 square feet, we can use the formula:

Area = Length x Width = 394

Let x and y be the length and width of the

swimming pool, respectively. Then we have:

x * y = 630

We need to find the values of x and y that satisfy this equation. We can do this by finding the factors of 630 and checking which pairs multiply to 630.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630

From this list, we can see that the following dimensions would work for the swimming pool:

9 feet by 70 feet

14 feet by 45 feet

10 feet by 63 feet

21 feet by 30 feet

15 feet by 42 feet

18 feet by 35 feet

So, the dimensions that would work for the swimming pool.

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The value of the equation are 1. (-2√3 + 2)(√3 - 5) = -16 + 8√3 2. (5 - 4√5)(-2 + √5) = -30 + 21√. 3. (-2 - 3√5)(5 - √5) = -5 - 17√5. 4. (√5 - √3)(√5 + √3) = 2.

An expression is a mathematical sentence without the equal sign that can include variables, operators, and integers. Although it can be appraised or simplified, there isn't a single perfect answer. An expression is, for instance, 3x + 2y.

A mathematical statement that has an equal sign and expresses the equivalence of two expressions is called an equation, on the other hand. To determine the values of variables that meet an equality, equations can be solved. One equation is 3x + 2y = 7, for instance.

1. Multiplying (-2√3 + 2)(√3 - 5), we get:

= -2√3 × √3 + (-2√3 × -5) + (2 × √3) + (2 × -5)

= -2√(3 × 3) + 10√3 - 2√3 - 10

= -2(3) + 8√3 - 10

= -16 + 8√3

Therefore, (-2√3 + 2)(√3 - 5) = -16 + 8√3.

2. Multiplying (5 - 4√5)(-2 + √5), we get:

= 5(-2) + 5√5 + (-4√5)(-2) + (-4√5)(√5)

= -10 + 13√5 + 8√5 - 4(5)

= -30 + 21√5

Therefore, (5 - 4√5)(-2 + √5) = -30 + 21√5.

3. Multiplying (-2 - 3√5)(5 - √5), we get:

= (-2 × 5) + (-2 × √5) + (-3√5 × 5) + (-3√5 × -√5)

= -10 - 2√5 - 15√5 + 3(5)

= -5 - 17√5

Therefore, (-2 - 3√5)(5 - √5) = -5 - 17√5.

4. Multiplying (√5 - √3)(√5 + √3), we get:

= (√5 × √5) - (√3 × √3)

= 5 - 3

= 2

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Without the specific details or an image of the line segment on the coordinate grid, I'm unable to provide you with the specific numbers included in the range.

To help you generally, a line segment is a part of a line with two endpoints, and it is located on a coordinate grid, which is a two-dimensional plane formed by the intersection of horizontal and vertical lines (x and y axes).

To determine the range of the line segment, you need to identify the y-coordinates of the two endpoints.

The range includes all the y-coordinates between those two points, inclusive of the endpoints. To find the range, observe the line segment and note the y-coordinates of both endpoints. Then, list all the numbers (whole or fractional) between those values, including the endpoints themselves.

Once you have the necessary details or an image of the line segment, feel free to ask again, and I'll be happy to help you identify the numbers within the range.

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Function[tex]y = arcsin(x)[/tex]is symmetric with respect to the origin, while function [tex]y = arccos(x)[/tex] is not. This is as inverse sine function is an odd function, while inverse cosine function is an even function.

If [tex]f(-x) = -f(x)[/tex] for all values of x in the function's domain, then the function is symmetric with regard to the origin. In other words, a function is said to be symmetric with regard to the origin if it passes through the origin and has the same shape on each side of the y-axis.

We must substitute -x for x in each function and simplify to find out if the functions [tex]y = arcsin(x)[/tex] and [tex]y = arccos(x)[/tex] are symmetric with respect to the origin.

According to the equation [tex]y = arcsin(x)[/tex], we get:

[tex]-arcsin = arcsin(-x) (x)[/tex]

Because it is odd, the function[tex]y = arcsin(x)[/tex] is symmetric with respect to the origin.

According to the equation [tex]y = arccos(x)[/tex]:

[tex]x(-arccos) = -arccos (x)[/tex]

Because it is not odd, the function[tex]y = arccos(x)[/tex] is not symmetric with respect to the origin.

In conclusion, [tex]y = arccos(x)[/tex]is not symmetric with regard to the origin, but [tex]y = arcsin(x[/tex] is. Due to the fact that the inverse cosine function is an even function, whereas the inverse sine function is an odd function, this is the case.

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Answer:

1 ⅓

Step-by-step explanation:

there 4 glasses and you put ⅓ in each one therefore 4 x ⅓ = 1 ⅓

The value of X when <1 = 3x+15 = 25. Then the value of the missing part of the sides of the kite (KITE) is given as follows;

X = 25

a.) ET = 60

b.) KE = 20

One of the properties of a kite is that it has two pairs of adjacent equal sides and the longer diagonal bisects the shorter one with the formation of angle 90°.

Therefore to calculate for X when <1 = 3x+15 is as follows;

<1 = 90°

90= 3x+15

3x = 90-15

3x = 75

X = 75/3

X = 25

But IT = ET

Given IT = 2x +20

X = 25

IT = ET = 2(20)+20

= 40+20 = 60

But KI = KE

Given that KI = 2x-30

X = 25

KI= KE = 2(25)-30

= 50-30 = 20

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Answer:

1 shorter than 2 longer than 3 short

Answer:

When you have a negative base and an odd exponent, you always get a negative answer.  For example, (-9)^3 written out is -9 * -9 *-9.  Although the answer becomes positive for the first two 9s (81) it becomes negative again for the third 9 (-729).  A base with a positive exponent will always yield a positive number.  Positive numbers are greater than 0 and are always greater than negative numbers.

Cheryl ran a total of 8 miles in five days.

1 + 1 + 1 + 2 + 3 = 8

Written as a decimal, this is 8.0 miles.

Answer:108 degrees

Step-by-step explanation:easy

The area of the figure is approximately 163.8 square units, rounded to the nearest tenths place.

To find the area of this figure, we need to find the area of the parallelogram and the area of the semicircle, and then add them together.

The area of the parallelogram is given by the formula:

A = base x height

In this case, the base is 12 and the height is 9, so:

A_parallelogram = 12 x 9 = 108

The area of a semicircle is given by the formula:

[tex]A = (πr^2)/2[/tex]

where r is the radius of the semicircle.

The diameter of the semicircle is equal to the base of the parallelogram, which is 12. So, the radius of the semicircle is half of the diameter, or 6.

Substituting the values, we get:

A_semicircle = [tex](π x 6^2)/2 = 18π[/tex]

Adding the areas of the parallelogram and the semicircle, we get:

A = A_parallelogram + A_semicircle = 108 + 18π

Using a calculator to approximate π to the nearest tenths place, we get:

A ≈ 108 + 18 x 3.1 = 163.8

Therefore, the area of the figure is approximately 163.8 square units, rounded to the nearest tenths place.

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Move the figure 2 units to the right  and  Move the figure 3 units downwards are the rules to translate any point on the red figure to the corresponding point on the orange figure, and vice versa

To describe the translation rule for the red figure to the orange figure, we need to determine how the red figure was moved to obtain the orange figure.

First, we can see that the orange figure is shifted to the right of the red figure. This means that the x-coordinate of every point on the orange figure is greater than the corresponding point on the red figure.

Second, we can see that the orange figure is shifted downwards from the red figure. This means that the y-coordinate of every point on the orange figure is less than the corresponding point on the red figure.

Therefore, the translation rule for the red figure to the orange figure is:

• Move the figure 2 units to the right (add 2 to the x-coordinate of every point), and

• Move the figure 3 units downwards (subtract 3 from the y-coordinate of every point).

We can use this rule to translate any point on the red figure to the corresponding point on the orange figure, and vice versa. This translation rule can be used in various applications such as computer graphics, engineering, and architecture, where precise translations of objects are necessary.

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As a result, the original figure's corresponding sides and those of its enlarged image are parallel.

A quadrilateral is a closed, two-dimensional form in geometry that has four straight sides. Four sides, four edges, and four angles make up the polygonal shape. The total of a quadrilateral's internal angles is 360 degrees. Kites, squares, rectangles, parallelograms, and trapezoids are examples of quadrilaterals.

given

Each side of the original figure is expanded to meet the dilation scale factor when a quadrilateral is dilated from an outer centre of dilation, and the sides of the dilated image are parallel.

Parallel lines continue to be parallel after scaling because dilatation scales each side of the quadrilateral by a constant factor.

As a result, the original figure's corresponding sides and those of its enlarged image are parallel.

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On a number line graph, the inequality X > 12 would be represented as follows:

A number line is a mathematical tool used to represent and visualize numbers, particularly real numbers, in a linear manner.

On a number line graph, the inequality X > 12 would be represented as follows(check attachment)

The line represents all real numbers, with the arrow pointing towards the right indicating that any number greater than 12 is a solution to the inequality. The circle at the end of the line is an open circle, indicating that 12 is not included in the solution set because the inequality is strict, i.e., X is strictly greater than 12.

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Answer: -31x

Step-by-step explanation:

|x|31 becomes -x31 which is -31x

The value of arc angle FH is 102⁰.

The value of arc angle FH is calculated by first; determining the value of the bigger arc HGF by applying the intersecting chords theorem.

The intercepting chord theorem, also known as the tangent chord theorem, states that when a tangent line intersects a chord of a circle at a point on the chord, then the measure of the angle formed by the tangent line and the chord is equal to half the measure of the intercepted arc (the arc that lies between the endpoints of the chord).

arc HGF = 2 x 129⁰

arc HGF = 258⁰

The value of arc FH is calculated as;

arc FH = 360⁰ - 258⁰ ( sum of angles in a circle)

arc FH = 102⁰

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The area of the ripple at t=2 is 32π square inches.

What is area ?

Area is the measure of the size of a two-dimensional surface enclosed by a closed boundary, such as a polygon or a circle. It is typically measured in square units such as square meters, square feet, or square inches.

The equation for the radius of the circular ripple is given by r(t) = √(15t+2). The equation for the area of a circle with radius r is A(r) = πr².

Therefore, the area of the ripple as a function of time is given by:

A(t) = π[r(t)]²

Substituting the expression for r(t), we get:

A(t) = π[(√(15t+2))²]

A(t) = π(15t+2)

A(t) = 15πt + 2π

To find the area of the ripple at t=2, we substitute t=2 into the expression for A(t):

A(2) = 15π(2) + 2π

A(2) = 30π + 2π

A(2) = 32π

Therefore, the area of the ripple at t=2 is 32π square inches.

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Using the area formula for square, we can find that the area of square CDEF is = 289-unit².

In geometry, a square is a two-dimensional plane object with four equal sides and four equal, 90° angles. Although a rectangle only has its opposite sides equal, a rectangle and a square have some properties in common. As a result, a rectangle can only be described as a square if its four sides are equal in length.

As per the question,

In right-angled ΔABC, as per Pythagoras theorem:

AC = √ (AB² + BC²)

= √ (12² + 9²)

= √ 225

= 15.

Similarly, in ΔACD as per Pythagoras theorem:

CD = √ (AC² + AD²)

= √ (15² + 8²)

= √289

= 17

Now, in square CDEF:

Side of square CDEF, CD = 17.

Area = side²

= 17²

= 289-unit².

Therefore, area of square CDEF is = 289-unit².

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Answer:

I think a

good luck

have a good day

the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.

Why is it?

To find the distance from the first plant to the last plant, we need to add up the distances between each adjacent pair of plants. Since there are 8 plants, there are 7 pairs of adjacent plants, and each pair is separated by 1.5 feet.

So, the total distance from the first plant to the last plant is:

7 ×1.5 = 10.5 feet

Therefore, the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.

Distance refers to the measurement of the physical space between two points or objects. It is a scalar quantity that only considers the magnitude of the separation between two points and does not take into account the direction of the separation.

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In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]

An integer is a positive, negative, or zero-valued whole number. It is a number without a fractional or decimal component.

To find all integer solutions of the given system of equations:

[tex]x + y &= 3 \[/tex]

[tex]3xy - z^2 &= 9[/tex]

We can start by solving the first equation for one of the variables. Let's solve for y in terms of x:

[tex]x + y &= 3 \[/tex]

[tex]y &= 3 - x[/tex]

Now we substitute this expression for y into the second equation:

[tex]3xy - z^2 &= 9 \[/tex]

[tex]3x(3-x) - z^2 &= 9 \quad \text{Substituting } y = 3-x \[/tex]

[tex]9x - 3x^2 - z^2 &= 9 \[/tex]

[tex]3x^2 + z^2 &= 9x - 9 \[/tex]

[tex]3x^2 - 9x + z^2 &= -9 \quad \text{(1)}[/tex]

Now we will examine equation (1) for integer solutions.

Case 1: [tex]z= 0[/tex]

If  then equation (1) becomes:

[tex]3x^2 - 9x &= -9 \quad \text{(1a)} \[/tex]

[tex]3x(x-3) &= -9[/tex]

Since we are looking for integer solutions, 3x and x-3 must have opposite signs. The possible pairs of factors of -9 with opposite signs are (3,-3) and (-3,3). So we have two possible sets of equations to solve:

The discriminant is negative, there are no integer solutions. Therefore, there are no integer solutions for the original system of equations when [tex]z \neq 0.[/tex]

In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]

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Answer: The commission rate for the real estate agency is 7.5% of the sale price, which is:

0.075 x 343000 = $25,725

The agent's commission is 30% of the amount the agency gets, which is:

0.3 x 25725 = $7,717.50

Therefore, the real estate agency made $25,725 on the house and the agent earned a commission of $7,717.50.

Step-by-step explanation:

By answering the presented question, we may conclude that Therefore, the solution set to the equation f(x) = 0 is {0}.

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

the equation:

[tex]3x^2 + x^2 = 0\\4x^2 = 0\\x^2 = 0\\x = 0[/tex]

Therefore, the solution set to the equation f(x) = 0 is {0}.

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