The lengths of the three sides are given for several right triangles. For each, write an equation that expresses the relationship between the lengths of the three sides. ​5,2. 2360679775,5. 47722557505

Answers

Answer 1

An equation that expresses the relationship between the lengths of the three sides is a^2 + b^2 = c^2.

In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.

The relationship between the lengths of the three sides in a right triangle is described by the Pythagorean Theorem, which states that the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

Mathematically, this can be represented as:

a^2 + b^2 = c^2

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

For the given right triangle with lengths 5, 2.2360679775, and 5.47722557505, we can plug in the values of a, b, and c to get:

5^2 + 2.2360679775^2 = 5.47722557505^2

which simplifies to:

25 + 5 = 30

This equation is true, indicating that the given lengths do indeed form a right triangle according to the Pythagorean Theorem.

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Related Questions

I need some help please

Answers

Answer:

A. 2

Step-by-step explanation:

Let's interpret the function.

First, let's look at the top section:

[tex]f(x)=x+2[/tex] if [tex]x < 1[/tex]

So, if the value of x is less than 1, to find f(x), we should add 2 to x.

Let's check if x is less than 1:

[tex]x=3\\x < 1\\3 < 1[/tex]

3 is not less than one, so to find f(x), we cannot add 2 to x.

The second part of the function is:

[tex]f(x)=x-1[/tex] if [tex]x\geq 1[/tex]

So, if the value of x is greater than or equal to 1, to find f(x), we should subtract 1 from x.

Let's check if x is greater than or equal to 1:

[tex]x=3\\x\geq 1=\\3\geq 1[/tex]

3 is greater than or equal to 1, so to find f(x), we should use x-1.

[tex]x-1=\\3-1=\\2[/tex]

Thus, f(3) = 2; the answer is A.

When analyzing difference in means between treatments in a single factor, a completely randomized model means that

Answers

A completely randomized model in a single factor study means that the assignment of treatments is completely random, with no underlying pattern or bias.

What do you know about completely randomized model?

When analyzing the difference in means between treatments in a single factor, a completely randomized model means that each individual or unit in the study has an equal chance of being assigned to any of the treatment groups.

In other words, the assignment of treatments is completely random, with no underlying pattern or bias.

This type of experimental design is important because it helps to minimize the effects of confounding variables and other sources of bias.

By randomly assigning treatments to study participants, researchers can be confident that any observed differences in the outcome variable are due to the treatment itself, rather than to other factors that may vary between the groups.

In statistical analysis, a completely randomized model can be used to test whether there are significant differences in the means between the different treatment groups.

This can be done using methods such as analysis of variance (ANOVA) or t-tests, depending on the number of treatment groups and the type of outcome variable being measured.

Overall, the completely randomized model is an important tool for ensuring that the assignment of treatments in a single factor study is unbiased and that the resulting data are suitable for statistical analysis.

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Simplify 7/8x1/3x2/3=

Answers

Therefore, the simplified form of the given expression is 7/36.

What is expression?

In mathematics, an expression is a combination of numbers, variables, and operators that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve one or more operations or functions. Expressions are an important concept in mathematics and are used in a wide range of applications, from simple arithmetic calculations to advanced mathematical modeling and analysis.

Here,

To simplify this expression, we can multiply the numerators of the fractions and multiply the denominators of the fractions, and then simplify the resulting fraction:

7/8 x 1/3 x 2/3 = (7 x 1 x 2)/(8 x 3 x 3)

= 14/72

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

14/72 = (2 x 7)/(2 x 36)

= 7/36

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Which proportion can be used to find 180% of 45?

Answers

The answer to this question is 180% of 45 is 81.

pls answer fast
q is below:

Answers

It would be number 2 the second option

Estimate the measure of this
angle within 15°

Answers

When the line is right should be 90°, an estimate for the angle would be 120°

Within 15° angle {15°,30°45°,60°75°,90°,105°,120°}

Should be 120°

Use a graph to write an equation for the proportional relationship between the number of hours Corrie works, h, and her total pay, P.

Answers

The equation for the proportional relationship between the number of hours Corrie works, h, and her total pay, P, can be represented as [tex]P = Ph[/tex].

Which equation represent the proportional relationship?

If we assume that Corrie's pay rate is P dollars per hour, then the equation for the proportional relationship between the number of hours Corrie works, h, and her total pay, P, can be represented as P = Ph, which simplifies to:

P = hP

Here, the P is the pay rate in dollars per hour, and h is the number of hours worked. Note that this equation is similar to the original equation e = 23h, except that the constant of proportionality has been replaced with the pay rate, P.

Full question "The proportional relationship between the number of hours Corrie works, h, and his total earnings in dollars and cents, e, can be represented by the equation e = 23h. Write an equation for the proportional relationship between the number of hours Corrie works, h, and her total pay, P."

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A karate studio owner wants to make a
representation that shows the ages of all students at
his studio, which offers karate classes for ages 2 to 18
Select all graphical representations that will best
display the data.
O Box plot
O Line plot
O Histogram
O Stem-and-leaf plot

Answers

I would recommend using a histogram to display the ages of all students at the karate studio. A histogram can clearly show the distribution of ages and provide insight into the number of students in each age group. A box plot or a stem-and-leaf plot could also be useful, but a histogram is likely the best option for this scenario. A line plot may not work as well since it is typically used to show changes over time rather than frequency distributions.

Miguel has $783 in
each pay period, which is deducted from his
paycheck to pay for taxes, insurance, and a retirement plan.
OA. net pay
OB. gross earnings
C. withholdings
OD. paystubs

Answers

On solving the provided query we have   His net pay would be the amount he receives after this $783 has been subtracted from his gross income. This $783 reflects his withholdings.

What is equation?

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

The amount that an employer withholds from an employee's paycheck to pay for taxes, insurance premiums, and other deductions like retirement contributions or wage garnishments is known as a withholding. Before the employee receives their net pay—the amount they actually take home after all deductions are done—these deductions are made.

For Miguel, taxes, insurance, and retirement plan payments total $783, and these are taken from each pay period. His net pay would be the amount he receives after this $783 has been subtracted from his gross income. This $783 reflects his withholdings.

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Answer: C. Withholdings

Step-by-step explanation:

just did it and got it right

write the equations of all the circles

Answers

The equation of a circle with center (a, b) and radius r is:

(x - a)^2 + (y - b)^2 = r^2

(x, y) represents any point on the circle

What is a circle?

A circle is described as a shape consisting of all points in a plane that are at a given distance from a given point, the center.

The properties of the circle are as follows:

The circles are said to be congruent if they have equal radii.The diameter of a circle is the longest chord of a circle.Equal chords of a circle subtend equal angles at the centre.The radius drawn perpendicular to the chord bisects the chord.

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Triangle ABC will be rotated 270 degrees clockwise with the origin as the center of rotation

Answers

The new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

To rotate a triangle 270 degrees clockwise with the origin as the centre of rotation, you can follow these steps:

Draw the coordinates of the vertices of the triangle. Let's assume that the coordinates of vertex A are (x₁, y₁), the coordinates of vertex B are (x₂, y₂), and the coordinates of vertex C are (x₃, y₃).

To rotate the triangle 270 degrees clockwise, you need to reflect it first over the x-axis, and then over the y-axis.

To reflect the triangle over the x-axis, you need to change the sign of the y-coordinates of each vertex. So the new coordinates of vertex A would be (x₁, -y₁), the new coordinates of vertex B would be (x₂, -y₂), and the new coordinates of vertex C would be (x₃, -y₃).

To reflect the triangle over the y-axis, you need to change the sign of the x-coordinates of each vertex. So the final coordinates of vertex A would be (-y₁, x₁), the final coordinates of vertex B would be (-y₂, x₂), and the final coordinates of vertex C would be (-y₃, x₃).

These final coordinates represent the vertices of the rotated triangle.

So, the new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

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There are three angles measured in degrees of a triangle where x is the largest angle, y is the middle angle, and z is the smallest angle.

The measure of the largest angle is 40 degrees less than twice the sum of the measure of the other two angles.

The measure of the largest angle is twice the smallest angle plus 10 degrees.

The sum of the angles of a triangle can be written as x + y + z = 180.

What are the other equations that represent this system of equations?

Select each correct answer.
a.) x=2y+10
b.) x=2z+10
c.) x=40-2(y+z)
d.) x=2z+y-40
e.) 2(y+z)-40

Answers

What is angles ?

An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.

From the given information, we have the following equations:

[tex]x = 2(y+z) - 40[/tex] (the largest angle is 40 degrees less than twice the sum of the other two angles)

[tex]x = 2z + 10[/tex] (the largest angle is twice the smallest angle plus 10 degrees)

[tex]x + y + z = 180[/tex] (the sum of the angles of a triangle is 180 degrees)

To simplify the system of equations, we can use the second equation to substitute for x in the first equation:

[tex]2z + 10 = 2(y+z) - 40[/tex]

Simplifying this equation, we get:

[tex]y = z + 25[/tex]

Now we can substitute x and y in terms of z into the third equation:

[tex]x + (z+25) + z = 180[/tex]

Simplifying this equation, we get:

[tex]x + 2z = 155[/tex]

Finally, we can substitute x in terms of z from the first equation into this last equation:

[tex]2(y+z) - 40 + 2z = 155[/tex]

Simplifying this equation, we get:

[tex]y + 3z = 97[/tex]

Therefore, the equations that represent this system are:

[tex]x = 2(y+z) - 40\\y = z + 25\\x + 2z = 155\\y + 3z = 97[/tex]

So the correct answers are:

[tex]a.) x=2y+10\\d.) x=2z+y-40\\e.) 2(y+z)-40[/tex]

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The equations that represent this system are:

a.) x=2y+10

d.) x=2z+y-40

e.) 2(y+z)-40

What is angles ?

An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.

From the given information, we have the following equations:

=> x=2(y+z)-40 (the largest angle is 40 degrees less than twice the sum of the other two angles)

=> x=2z+10 (the largest angle is twice the smallest angle plus 10 degrees)

=> x+y+z=180  (the sum of the angles of a triangle is 180 degrees)

To simplify the system of equations, we can use the second equation to substitute for x in the first equation:

=> 2z+10=2(y+z)-40

Simplifying this equation, we get:

y=z+45

Now we can substitute x and y in terms of z into the third equation:

x+z+25+z=180

Simplifying this equation, we get:

=> x+2z=155

Finally, we can substitute x in terms of z from the first equation into this last equation:

2(y+z)-40+2z=155

Simplifying this equation, we get:

y+3z=97

Therefore, the equations that represent this system are:

a.) x=2y+10

d.) x=2z+y-40

e.) 2(y+z)-40

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In the picture below Pac-Man, from the video game PAC-MAN, is shown eating ghosts. In the picture his mouth is open 60° and the radius of the circle is 13 mm. What is the area of the Pac-Man, to the
nearest tenth mm²?

Answers

The area of Pac-Man to the nearest tenth mm² is 11.4 mm².

What is area of circle?

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius.

To find the area of Pac-Man, we need to calculate the area of the sector that corresponds to the angle of his open mouth and subtract the area of the isosceles triangle formed by the two radii of the sector and the chord that represents the straight edge of his mouth.

First, we need to calculate the angle in radians that corresponds to the 60° angle given:

angle in radians = (60/360) x 2π = π/3 radians

Next, we can use the formula for the area of a sector:

Area of sector = (angle in radians / 2π) x πr²

where r is the radius of the circle.

Area of sector = (π/3 / 2π) x π(13mm)² ≈ 84.95 mm²

Now, we need to calculate the area of the triangle. We can use the formula for the area of an isosceles triangle:

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

where the base is the chord that represents the straight edge of Pac-Man's mouth, and the height is half the length of the chord times the sine of half the angle of the mouth opening.

The base of the triangle is given by the formula:

base = 2r x sin(angle/2)

base = 2(13mm) x sin(30°) ≈ 22.52 mm

The height of the triangle is given by the formula:

height = (base / 2) x sin(angle/2)

height = (22.52 mm / 2) x sin(30°) ≈ 6.53 mm

Therefore, the area of the triangle is:

Area of triangle = (1/2) x base x height ≈ 73.5 mm²

Finally, we can subtract the area of the triangle from the area of the sector to get the area of Pac-Man:

Area of Pac-Man ≈ 84.95 mm² - 73.5 mm² ≈ 11.4 mm²

Therefore, the area of Pac-Man to the nearest tenth mm² is 11.4 mm².

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Jerome is a photographer. He earns $125 per hour

Answers

The graph of the data from the table is added as an attachment

Creating a graph of the data from the table.

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

Jerome is a photographer. He earns $125 per hour

This means that the equation of the function is

f(x) = 125x

Where x is the number of hours he works

Using the above as a guide, we have the following table of values

x    f(x)

1     125

2    250

3    375

4    500

5    625

6     750

Next, we plot the graph from the table of values and the function f(x) = 125x

The graph of the function is added as an attachment

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Chapter 10: Quadratic Relations and Conic Sections Answers

Answers

To solve problems related to quadratic relations and conic sections, use the following formulae, respectively:

1. ax^2 + bx + c = 0

2. (x - h)^2 + (y - k)^2 = r^2

How to resolve quadratic relations and conic sections

A quadratic relation is a type of equation in which the highest power of the variable is two. The general form of a quadratic equation is:

ax^2 + bx + c = 0

where a, b, and c are constants and x is the variable.

This is closely related to conic sections which are geometric shapes that can be obtained by intersecting a plane with a double-napped cone. If we assume the equation of a circle with center (h, k) and radius r is, a good equation that can be used to resolve this will be:

(x - h)^2 + (y - k)^2 = r^2.

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Suppose that 20% of a group of people have hazel eyes, what is the probability that the eighth passenger boarding a plane is the third one having hazel eyes? assume that passengers boarding the plane form a randomly chosen group

Answers

Answer:       This is called percent error this is how i solve.

                    8     20%

                    3     100%

          800. 60 =               48000          

Can a subset of A contain elements of AC ? Why or why not?

Answers

It is not possible for a subset of A to contain elements of Ac

To answer the question, "Can a subset of A contain elements of Ac?" we must first understand what these terms mean.

A subset of A is a set that contains only elements that are also in A. On the other hand, Ac is the complement of A, which is the set of all elements that are not in A. Therefore, an element that is in Ac is not in A.

Now, let us consider the possibility of a subset of A containing elements of Ac. If an element is in Ac, it is not in A. Therefore, it cannot be in any subset of A, as all elements of a subset must be in A. This means that it is not possible for a subset of A to contain elements of Ac.

In summary, It is not possible for a subset of A to contain elements of Ac because the complement of A includes all the elements that are not in A. Therefore, any element that is in Ac cannot be in any subset of A

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Complete Question:

Can a subset of A contain elements of Ac? Give reason.

Rewrite 10 to the 32 power times 10 to the 6

Answers

Answer:

[tex] {10}^{32} {10}^{6} = {10}^{38} [/tex]

I am an even whole number. I am greater than 0 and I am also less than 20. If you multiply me by 2 the product will be less than 3.

Answers

The even whole number that satisfies the given conditions is 1.

If we multiply 1 by 2, the product is 2, which is less than 3.

Therefore, the even whole number that is greater than 0, less than 20, and whose product when multiplied by 2 is less than 3, is 1.

Input➡️x4➡️-5➡️output.

If the input is the same as the output what is the input

Answers

The value of the system in which newton's law of motion is applicable is (a) 25 (b) 10 (c) if output is x , 4y -x-15 =0

What about newton's law of motion?

Newton's laws of motion are three fundamental laws in classical physics that describe the behavior of objects in motion. They were first presented by Sir Isaac Newton in his work "Philosophiee Naturalis Principia Mathematica" in 1687. The three laws are:

The Law of Inertia: An object at rest will remain at rest, and an object in motion will continue in a straight line with constant velocity, unless acted upon by an external force.

The Law of Acceleration: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.The Law of Action-Reaction: For every action, there is an equal and opposite reaction. This means that when an object exerts a force on another object, the second object exerts an equal and opposite force back on the first object.

According to the given information:

a) When input is 10.

   output= 10×4 - 15 =25

b) From the question output is 25

  Because input* 4 -15= output. So (output +15) / 4= input

  so input =[tex](25+15)/4[/tex] =10

c) if output is x. So y × 4 - 1 5 = x , 4y - x - 15 = 0

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The value of the system in which newton's law of motion is applicable is (a) 25 (b) 10 (c) if output is x , 4y -x-15 =0

What about newton's law of motion?

Newton's laws of motion are three fundamental laws in classical physics that describe the behavior of objects in motion. They were first presented by Sir Isaac Newton in his work "Philosophiee Naturalis Principal Mathematical" in 1687. The three laws are:

The Law of Inertia: An object at rest will remain at rest, and an object in motion will continue in a straight line with constant velocity, unless acted upon by an external force.

The Law of Acceleration: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.

The Law of Action-Reaction: For every action, there is an equal and opposite reaction. This means that when an object exerts a force on another object, the second object exerts an equal and opposite force back on the first object.

According to the given information:

a) When input is 10.

  output= 10×4 - 15 =25

b) From the question output is 25

 Because input* 4 -15= output. So (output +15) / 4= input

 so input = =10

c) if output is x. So y × 4 - 1 5 = x , 4y - x - 15 = 0

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find the slope of (-7,2) and (-4,1)

Answers

Answer:

-1/3

Step-by-step explanation:

Use the formula [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] to find the slope given the 2 points:

1-2

------

-4-(-7)

-1/3 is your slope

HELP IS THE ANSWER 638.30 OR 106.38?
Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.4 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.

2,553.20 cubic inches
638.30 cubic inches
425.53 cubic inches
106.38 cubic inches

Answers

The amount of juice that can be poured into 6 cups with a diameter of 4.4 inches and a height of 7 inches is 638.30 cubic inches (rounded to the nearest hundredth).

Solution:We can use the formula to find the volume of a cylinder,V = πr²hwhere V is the volume of the cylinder, r is the radius of the base, h is the height of the cylinder, and π is the mathematical constant approximately equal to 3.14.To begin solving this problem, we must first find the radius of the base of the cylinder.

Since the diameter of each cup is given as 4.4 inches, the radius is half of this, or 2.2 inches.Now we can use the formula for the volume of a cylinder, with r = 2.2 inches and h = 7 inches.V = πr²hV = 3.14(2.2)²(7)V ≈ 106.38 cubic inches

This is the volume of juice that can be poured into a single cup. To find the total volume of juice that can be poured into 6 cups, we multiply this by 6.6(106.38) ≈ 638.30 cubic inches

Therefore, the answer is 638.30 cubic inches.

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What is the geometric mean between 1/4 and 12?
A. √12
B. √12 1/4
C. √3
D.1/2

Answers

D. Is the answer you’re looking for

The geometric mean of the given number is √3.

Hence option C is correct.

Use the concept of geometric mean  defined as:

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers.

In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

The given numbers are,

1/4 and 12

Take a = 1/4 and b = 12

Now since we know the geometric mean of a and b = √ab

geometric mean  = [tex]\sqrt{\frac{1}{4}\times 12[/tex]

geometric mean  = √3

Hence,

The geometric mean for the given numbers is √3.

So option C is correct.

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Need help with all please

Answers

Answer:

Step-by-step explanation:

1 )

a) quotient of powers as dividing two powers with the same base, we subtract the exponents.

b) product of powers when you are multiplying two terms with the same base, you add their exponents

c) property of negative exponents. According to the rules of exponents, a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.

2)

Yes, when raising a fraction to a power with parentheses, the same principles apply as when raising a fraction to a power without parentheses. When evaluating expressions with fractions and exponents, the order of operations, including parentheses, is followed. To re-write the expressions (1/3)^2 is = (1/9) and (1/3)^-2 is equal to 9 9*(1/9) is 1 which is the rule of the product of powers. then the same applies to the second expression

3)

[tex](-2.3^{2})^{6}[/tex]  power to a power rule

[tex](\frac{1}{4}) ^{3}[/tex] power of a quotient

[tex]6^{4}[/tex] power to a power rule

[tex]7^{-1}[/tex] product of powers

ps: please grade me appropriately if you need more help with problems I am glad to help and these stars mean a lot to me. make sure you study your exponent laws and all the best!

The table shows items sold at a food stand during a basketball game.
Sports Drink Bottled Water No Drink Total
5
175
35
145
10
80
50
400
Hot Dog
Candy
No Food
Total
0.0875
What is the probability that a person who buys candy at the food stand will not get a drink?

Answers

Answer:

c

Step-by-step explanation:

Answer:

0.0875

Step-by-step explanation:

The number of people who will get candy and no drink is 35 people.

and we know that there are 400 people in total.

So it should be 35/400 = 0.0875

Maverick spins a spinner 15. The spinner has 5 equal parts numbered 1-5. Which is the best prediction of the number of times Maverick should spin a 4?

Answers

The best prediction of the number of times Maverick should spin a 4 is 3 times.

How to determine the best prediction of the number of times Maverick should spin a 4

Assuming the spinner is fair and unbiased, the best guess for how many times Maverick should spin a 4 is three.

The expected number of times a 4 should appear can be calculated by calculating the probability of spinning a 4 (1/5, or 0.2) by the total number of spins (15):

Expected number of 4's = Probability of spinning a 4 x Total number of spins

Expected number of 4's = 0.2 x 15

Expected number of 4's = 3

Therefore, the best prediction of the number of times Maverick should spin a 4 is 3 times.

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which of the following statements is true? group of answer choices in general, it is no more difficult to solve an integer programming model than a linear programming one. all of these answers. an integer programming solution is better than the linear programming solution to the same problem rounding does not necessarily provide feasible solutions and feasible solutions from rounding are not necessarily optimal.

Answers

The true statement is that An integer programming solution can be better than the linear programming solution to the same problem. So, option(b) is right one.

In integer linear programming is harder than linear programming, because the branch-and–bound method requires many iterations of the simplex method, integer programming problems, So, option(a) is false one.

It usually takes longer than linear programming problems of the same size.Integer programming is a mathematical method that produces numerical solutions to linear programming problems.In integer programming, obtained integer solutions that should be neither feasible nor optimal. So, option(c) is also false.

Hence, required answer is option(b).

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Complete question :

which of the following statements is true? group of answer choices

a) in general, it is no more difficult to solve an integer programming model than a linear programming one.

b) an integer programming solution is better than the linear programming solution to the same problem rounding does not necessarily.

c) provide feasible solutions and feasible solutions from rounding are not necessarily optimal.

d) all of these answers

assertion: if p and q are integers and is represented in the form of p/q then it is a rational number
reason: 17/3 is a rational number

Answers

The assertion will be correct and the reason provided is also correct.

A rational number is termed as a number which can be represented as the ratio of the two integers, where the denominator (q) will be not equal to zero. In other words, a rational number can be expressed in the form of a p/q, where p and q are the integers and q ≠ 0.

In the given reason, 17/3 is cited as an example of a rational number. Since both 17 and 3 are integers, and 3 ≠ 0, 17/3 can be expressed as the ratio of two integers, making it a rational number.

Therefore, the assertion will be true, and the reason provided is correct.

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Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials. a. (2xy2 − 3xy3)(2xy2 + 3xy3) b. (2xy2 − 3xy3)(2xy2 − 3xy3) c. (4xy2 + 9xy3)(xy2 − xy3) d. (4xy2 − 9xy3)(xy2 − xy3)

Answers

Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials. (2xy2 − 3xy3)(2xy2 + 3xy3). So, correct answer is A.

To multiply two binomials, we use the FOIL method which stands for First, Outer, Inner, Last. For option A, using the FOIL method, we get

(2xy² - 3xy³)(2xy² + 3xy³) = (2xy²)² - (3xy³)² = 4x²y⁴ - 9x²y⁶

This is the given polynomial, so option A is correct.

For other option, we have two identical binomials multiplied together, which would give us a trinomial with three terms, so it cannot be a product of two binomials.

Option C is also incorrect because when we multiply the two binomials, we do not get the given polynomial. Option D is incorrect as well because the signs are incorrect and we would get a different polynomial when we multiply the two binomials.

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--The given question is incomplete, the complete question is given

" Given the polynomial 4x²y⁴ − 9x²y⁶, rewrite as a product of polynomials. a. (2xy² − 3xy³)(2xy² + 3xy³) b. (2xy² − 3xy³)(2xy² − 3xy³) c. (4xy² + 9xy³)(xy² − xy³) d. (4xy² − 9xy³)(xy² − xy³)"--

develop an estimate regression equation with both television advertising and newspaper advertising as independent variables. what are the correct interpretations of the estimated regression parameters? are this interpretation reasonable?

Answers

In a regression equation, the estimated coefficients represent the change in the dependent variable for a one-unit increase in the corresponding independent variable, holding all other independent variables constant.

For example, if the estimated coefficient for television advertising is 0.5, then we can interpret it as a $0.5 increase in the dependent variable (such as sales) for every one-unit increase in television advertising expenditure, holding newspaper advertising constant.

Whether the interpretations of the estimated coefficients are reasonable depends on the data and the research question being investigated. It is important to examine the statistical significance, magnitude, and direction of the estimated coefficients, as well as their practical relevance and theoretical soundness, to evaluate the validity and usefulness of the regression model.

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