It is given & = {x: 1 ≤ x ≤ 10, x is an integer); P= {odd numbers); Q= {prime numbers) and R= {1,2,3,4,5} List the elements of each of the following sets. (a) (PNQ)UR (b) (RMP)'UQ (c) Q'N(PUR) (d) (PUQUR)' (POR)​

Answer:

425.39 ft

Step-by-step explanation:

[tex]\frac{1}{2}mv^2=mgh\\\frac{1}{2}v^2=gh\\v^2=2gh[/tex]

h = [tex]\frac{v^2}{2g} = \frac{165^2}{2 * 32}=\frac{27225}{64}=425.39ft[/tex]

a) The Test statistic of the hypothesis is; 0.81

b) The p-value from the test statistic is; 0.20897.

c) The final conclusion is that there is not sufficient evidence to reject the null hypothesis that (p1 - p2) = 0

Test statistic is defined as a number, calculated from a statistical test, used to find if your data could have occurred under the null hypothesis. In this case, we are dealing with proportions and as such the test statistic has the formula;

z = (p1 - p2)/standard error

p1 = 53/90 = 0.59; s1 = √(0.59 * 0.41/90) = 0.052

p2 = 48/90 = 0.53; s2 = √(0.53 * 0.47/90) = 0.053

Hence, for the distribution of differences, the mean and the standard error are given as follows:

Mean: p = 0.59 - 0.53 = 0.06

Standard error: s = √(0.052² + 0.053²) = 0.074

a) Test statistic = p/s = 0.06/0.074

Test statistic = 0.81

b) From p-value from z-score calculator, we get that;

p-value = 0.20897.

c) The p-value is greater than the significance value of 0.05, we fail to reject the null hypothesis and conclude that there is not suffucuent evidence to reject the null hypothesis that (p1 - p2) = 0

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Hence, the driving second car cost Romney per year pays is $ [tex]16364[/tex].

What is the selling price?

The selling price of a product or service is the seller’s final price, i.e., how much the customer pays for something. The exchange can be for a product or service in a certain quantity, weight, or measure.

Here given that,

Romney bought a car with $[tex]6000[/tex] down payment, and paid the remaining cost by installments, which totaled $[tex]15000[/tex]. Romney then sold the car after [tex]10[/tex] years for $[tex]5500[/tex].

So, he sold his car in $[tex]15000(6000)=90000000[/tex].

And he is paying installment in every month which is $ [tex]15000[/tex].

So, in case of second car he paied $ [tex]5500[/tex] and his installments of every month would be

[tex]\frac{90000000}{5500}=16364[/tex] $

Hence, the driving second car cost Romney per year pays is $ [tex]16364[/tex].

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The center of the circle lies on the x-axis. The radius of the circle is 3 units. The radius of this circle is the same as the radius of the circle whose equation is x² + y² is 9.

The radius of a circle is the distance between the circle's centre and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.

The standard equation of a circle is expressed as:

x² + y²+2gx+2fy+C=0

Centre is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is 2+ y²-2x-8=0.

Get the centre of the circle

2gx = -2x

2g=-2

g=-1

Similarly, 2fy = 0

f=0

Centre = (-(-1), 0) = (1, 0)

This shows that the center of the circle lies on the x-axis

r = radius = √g²+f²-C

radius = √1²+02-(-8)

radius =√9 = 3 units

The radius of the circle is 3 units.

For the circle x² + y² = 9, the radius is expressed as:

r² = 9

r = 3 units

Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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Based on the given parameters, the value of the money to invest initially is $994.8

The given parameters about the compound interest are

Principal Amount, P = $2130

Interest Rate, R = 6.4%

Time, t = 12

Number of times, n = 12 i.e. monthly

To calculate the amount, we have:

A = P + CI

Where

C = P(1 + R)^t

So, we have

A = P(1 + R)^t

This can be rewritten as

A = P(1 + R/n)^nt

Substitute the known values in the above equation

2130 = A * (1 + 6.4%/12)^(12*12)

So, we have

A = 2130/[(1 + 6.4%/12)^(12*12)]

Evaluate the expression

A = 994.8

Hence, the amount of the investment is $994.8

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The rental cost for each movie and each video game is 2.25.

One month Trey rented three movies and five video games for a total of 35.

3 M + 5V = 33

6 M + 2 V = 24

Divides bottom equation by 2:

3 M + 5 V = 35

3 M + V = 20

subtracts:

 4V = 21

 V = 21/4 = $5.25

3 M + 5.25 = 12

3 M = 6.75

M = 2.25

Let x = cost to rent a movie and y = cost to rent a video game

3x + 5y = 33

6x + 2y = 24

Multiply the first equation by -2:

-6x - 10y = -66

6x + 2y = 24

Add the equations to get -8y = -42

So, y = 5.25 and x = 2.25.

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The p-value of the test is 0, which is less than the standard significance level of 0.05, thus we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.7.

We may test the following using the example data:

In reality, 812.35 respondents identified as better drivers than average.

We can infer that the proportion of respondents who rated themselves as above average drivers is greater than 0.7 because the test's p-value is 0, which is less than the standard significance level of 0.05. 77% of the sample of 1055 adults rated themselves as above average drivers, so 0.77(1055) = 812.35.

As a result, 812.35 respondents actually assessed themselves as better drivers than average.

We examine if the proportion is 7/10=0.7 at the null hypothesis.

H0 is that, with p = 0.7.

If the proportion is larger than 70%, we test for the alternative hypothesis, which is H1:p>=0.7.

The test statistic comes from:

The parameters for this issue are p dash = 0.77, p = 0.7, and n = 1055.

As a result, the test statistic's value is:

z = 351.758 root

The likelihood of discovering a sample proportion above 0.77, calculated as 1 minus the p-value of z = root of 351.758, is the test's p-value.

According to the z-table, the p-value for z = root of 351.758 is 1, and 1 - 1 equals 0.

Since the test's p-value is zero and is below the conventional significance level of 0.05, we can infer that a higher proportion of respondents than 0.7 evaluated themselves as above-average drivers.

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The equations are 3x - 3y = 4 and 3x + 2y = -6.

What is a system of linear equations in matrices?

A system of linear equations can be represented in matrix form using a coefficient matrix, a variable matrix, and a constant matrix. Consider the system, 2x+3y=85 and x−y=−2. The coefficient matrix can be formed by aligning the coefficients of the variables of each equation in a row.

In the given matrix,

The first equation would be

3x - 3y = 4

and the second equation would be

3x + 2y = -6

Hence, the equations are 3x - 3y = 4 and 3x + 2y = -6.

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Answer:

6x² + 5x + 1

Step-by-step explanation:

(4x² + x − 4) + (2x² + 4x + 5)

1. Expand the brackets to get
4x² + x − 4 + 2x² + 4x + 5

2. Group common terms (terms with same power as well as the constant)
4x² + 2x² + x + 4x - 4 + 5

3. Simplify
4x² + 2x² = 6x²
x + 4x = 5x
-4 + 5 = 1

4. Solution is
6x² + 5x + 1

A student selected at random from the class has a 0.5 is 50% chance of not participating in sports, according to the probability notion.

A probability is calculated by dividing the entire number of possible outcomes by the desired outcomes.

In this issue:

The total number of students is 30 (8 + 7 + 3 + 12).

3 + 12 = 15 of the total don't participate in sports.

Hence:

p =D/T = 15/30 = 0.5

There is a 50% chance that a student who was randomly selected from the class does not participate in sports.

A student selected at random from the class has a 0.5 is 50% chance of not participating in sports, according to the probability notion.

The complete question is :in a class of students, the following data table summarizes how many students playing instrument or a sport. What is the probability that student plays an instrument given that they play a sport?

play an instrument and a sport: 3

play an instrument but does not play a sport: 8

does not play an instrument but plays a sport: 7

does not play an instrument or a sport: 12

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According to the question
Let the number be x

[tex]x+\frac{1}{x}=\frac{5}{2} \\\\\ \frac{x^{2}+1}{x} = \frac{5}{2} \\\\\\\ By \\ cross-multiplication \\\\x^{2}+1 = \frac{5}{2} * x\\\\2x^{2}+2 = 5x\\\\2x^{2}-5x+2 = 0\\\2x^2-4x-1x+2 = 0\\2x(x-2)-(x-2)=0\\(2x-1)(x-2)=0\\\\therefore,\\\\x = \frac{1}{2}\\or\\x = 2[/tex]

The value of X is 9 units it is solved by using the properties of Similar Triangles

What are Similar Triangles?

Two objects are comparable in Euclidean geometry if they have the same form or one has the same shape as the mirror image of the other. More exactly, one can be created by evenly scaling the other, potentially with extra translation, rotation, and reflection.

Solution:

In the given question

Triangle ABC and Triangle DEC are similar by AAA property

By using the properties of Similar Triangle

We can say that AC/DC = BC/EC

26/8 = (x+4)/4

13 = x + 4

x = 9 units

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Answer:

x = 35

Important things to know:

1. A + (x + 110) will equal 180 degrees

2. The interior angles of a triangle will equal 180 degrees.

With these two pieces of knowledge, you can substitute the value of A as "180 - (x+110)" because A = 180-(x+110)

Step-by-step explanation:

The time when the money will double is 11.6 years

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

When the money doubles, the amount is

A = 900 * 2

A = 1800

The compound interest formula is given as

A = P(1 + r/n)^nt

Also from the question, we have

n = 12

This is so because the loan is compounded 12 times in a year as a result of being compounded monthly

Solving further, we replace the variables with their values in the above equation

1800 = 900 * (1 + (6%)/12)^(t*12)

Divide both sides by 900

2 = (1 + (6%)/12)^(t*12)

Also, we have

2 = (1.005)^(t*12)

Take the logarithm of both sides

12t = log(2)/log(1.005)

Evaluate the quotients

12t = 139

Divide both sides by 12

t = 11.6

Hence, the number of years is 11.6 years

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Answer:

To solve this equation, you can use cross multiplication to eliminate the fractional terms. Doing so gives you 11 * 17 = 13 * x. Solving for x gives you x = (11 * 17)/13. Dividing these two numbers gives you approximately x = 8.46. Rounding this number to the nearest tenth gives you x = 8.5. Therefore, the value of x that makes the equation true is approximately 8.5.

The value of z in the equation 1/3(6z + 7.2) = 0.5(8z + 2) - 0.4 is z=0.9

How to solve the equation?

1/3(6z + 7.2) = 0.5(8z +2) -0.4

(6/3)z + 7.2/3 = (8/2)z + 2/2 - 0.4

2z + 2.4 = 4z + 1 - 0.4

2z - 4z = 0.6 - 2.4

-2z = -1.8

z= 0.9

Hence, the value of z in the equation 1/3(6z + 7.2) = 0.5(8z + 2) - 0.4 is z=0.9

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Hello,

I hope you and your family are doing well!

The function y = |20x+15| is an absolute value function. Absolute value functions have the form y = |f(x)|, where f(x) is a linear function.

In this case, the linear function is 20x+15, so the absolute value function is:

y = |20x+15|

The absolute value function takes the absolute value of the output of the linear function. This means that if the output of the linear function is positive, the absolute value function returns the same value. If the output of the linear function is negative, the absolute value function returns the opposite of that value.

For example, if x = -1, then the output of the linear function is 20(-1)+15 = -5. The absolute value of -5 is 5, so the absolute value function returns y = 5.

On the other hand, if x = 1, then the output of the linear function is 20(1)+15 = 35. The absolute value of 35 is 35, so the absolute value function returns y = 35.

Overall, the absolute value function returns the distance of the output of the linear function from 0, without considering the sign of the output.

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Happy Holidays!

Answer: Muffins > 15 (Greater than 15)

Step-by-step explanation: If the most Scott can eat without feeling sick is 15 muffins, this means that any more muffins would make him sick. The amount of muffins to make Scott sick would have to be greater than 15.

Step-1) Determine the value of the x and y variables

To verify if (2, -3) is a solution to the system of equations provided in the question, we will need to determine the value of the x and y variables.

To do this, we will have to compare the coordinates of the point (2, -3) with the "original form" of the coordinate point (x, y). Then, we will have to identify the values (from the coordinates) in their respective order.

Example: (4, 5) = (x, y) ⇒ x = 4; y = 5

Step-2) Substitute the x and y values into one of the equations

The next step is to substitute the value of the variables. This is a required step for the coordinate provided to be verified. Once you substitute the value of the variables, you can move on to the next step process.

Step-3) Simplify the equation completely until it is in simplified form

Then, we will have to simplify the equation completely.

This is also a required step because simplifying is a process where we can convert an expression to a specific numerical value, which can help us create final conclusions to a problem. It can also help us obtain a specific numerical value from any large/small expression provided.

Step-4) Compare both sides and verify if they are equal/not equal

If both sides of the equation do not receive the same value, then the point (2, -3) is not a solution to the provided system of equation.

Given Information (Provided in the question):

Step-1) Determine the x and y variables from the coordinates:

Step-2) Substitute the variables into any equation:

Step-3) Simplify both sides of the equation:

Therefore, (2, -3) is not a solution to the system of equations.

The difference between the boards’ total lengths is  86 inches.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The difference between the total lengths of the boards is the positive value when we subtract one from another.

The total length of the red cedar board is = (8×10.25) = 82 inches.

The total length of the tiger maple board is = (16×10.5) = 168 inches.

∴ The difference is (168 - 82) = 86 inches.

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The information provided indicates that the means test is too narrow because it excludes factors like the type of engineer, amount of education, and experience. The type of engineer or educational level may be a reflection of the gender with lower earnings.

Additional information on the factors, including gender, education, and the type of engineer, could enhance the research.

Then, it is advised to build a multiple regression where the wage is the dependent variable and the other four variables are independent variables. The "difference in means" test is not appropriate for identifying gender bias in salary setting due to the significance of the omitted variable.

The variables which  are likely useful to add to the regression to control for important omitted​ variables are excessive drug or alcohol use and their gang activity.

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In a one-tailed T-test, if the test statistics and the t-value are under the null hypothesis, then p-value = ρ > to alternate hypothesis is true.

Critical zones in hypothesis testing are ranges of distributions where the values correspond to outcomes that are statistically significant. Analysts set the significance level (alpha) and whether the test is one-tailed or two-tailed in order to determine the size and location of the key regions.

The likelihood of rejecting an accurate null hypothesis is the significance level.

A test statistic's sample distribution assumes that the null hypothesis is true.

As a result, you need to shade the necessary fraction of the distribution to depict the crucial areas on the distribution for a test statistic. You shade 5% of the distribution using the typical significance threshold of 0.05.

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cylinder

A cylinder is a three-dimensional solid figure with two identical circular bases connected by a curved surface at a specified distance from the center, which is the height of the cylinder. Toilet paper wicks and cold drink cans are examples of cylinders.

A cone is a three-dimensional shape that smoothly narrows from a flat base (usually a circular base) to a point called the vertex or apex that forms the axis to the center of the base. A cone can also be defined as a pyramid with a circular cross-section instead of a cone with a triangular cross-section. These cones are also known as circular cones.

The cylinder and cone have the same radius because they both have the same base area.

The volumes of the cylinder and the cone are equal,

Cylinder Volume = Cone Volume

; Ûr2h=1/3 Ûr2h

(5×5)= 1/3×5×h

h=12

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The solution of the system of equation y = -x + 3 and y = 3x + 7 will be (-1,4).

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

As per the given system of equations,

y = -x + 3 and y = 3x + 7

Compare both,

3x + 7 = -x + 3

3x + x = 3 - 7

x = -1

y = -(-1) + 3 = 4

So the solution will be (-1,4).

Hence "The system of equations y = -x + 3 and y = 3x + 7 will have the following solution: (-1,4).".

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The area of a rectangle is given as:

Area = Length x width

The area of the rectangle is 57 square feet.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Length = 19 feet

Width = 3 feet

The area of the rectangle.

= 19 x 3

= 57 square feet.

Thus,

The area of the rectangle is 57 square feet.

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The solution for the given system of inequalities is (5,-2). which is the correct answer would be an option (A).

The first inequality, 2x + y > 3, can be rewritten in slope-intercept form as y > -2x + 3. This represents a line with a slope of -2 and a y-intercept of (0,3).

The second inequality, x - y > 1, can also be rewritten in slope-intercept form as y < x - 1. This represents a line with a slope of 1 and a y-intercept of (0,-1).

When you graph these two lines, you will get two lines that intersect at some point. The region of the graph that satisfies both inequalities will be the area that is bounded by these lines and lies above or below them, depending on the inequality symbol.

In this case, the solution to the system of inequalities is the region of the graph that is above the line y = -2x + 3 and below the line, y = x - 1. This region is shaded in the graph below.

From the graph, you can see that the solution includes all points in the shaded region. You can also see that points B (0,-5), C (0,0) , and D (0,5) is not included in the solution, while point A (5,-2) included in the solution.

Therefore, the correct answer is A (5,-2).

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After writing y = kx, we'll solve for k putting the given corresponding values of x and y.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Suppose we have two variables x and y and they are directly proportional and some values of x and y are given.

If we see that y has a bigger corresponding value than x, we'll write

y = kx,

In the case of inverse variation, we write y = k/x.

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Explanation:

1/4 = 0.25

1/2 = 0.5

24 & 1/2 = 24.5

The rope is 24.5 ft long and you want sections of length 0.25 ft each.

Let x be the number of sections we can make.

1 section is 0.25 ft long

x of them combine to 0.25x feet long

Set this equal to 24.5 and solve for x

0.25x = 24.5

x = (24.5)/(0.25)

x = 98

There will be 98 sections of equal length (each being 0.25 ft)

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

Another way to look at it:

1 foot of rope gets you four sections of 0.25 ft each

24 feet of rope gets you 24*4 = 96 sections.

Another 0.5 ft adds another 0.5*4 = 2 sections to get to a total of 96+2 = 98