Justify Your Reasons By Determining The Postulates, Definitions, Theorems, And Properties Used. (2024)

The results of this test will be used to determine if the average tenure of U.S. workers is significantly different from the stated 4.6 years. If the results are statistically significant, then we can reject the null hypothesis and conclude that the average tenure of U.S. workers is 4.6 years.

Hypothesis: The average tenure of U.S. workers is 4.6 years

Null Hypothesis: The average tenure of U.S. workers is not 4.6 years

Alternative Hypothesis: The average tenure of U.S. workers is 4.6 years

Test Statistic: One-sample t-test

Significance Level: α = 0.05

The purpose of this one-sample t-test is to determine whether the average tenure of U.S. workers is 4.6 years. The null hypothesis states that the average tenure of U.S. workers is not 4.6 years, while the alternative hypothesis states that the average is 4.6 years. The significance level for this test will be set at α = 0.05. The test statistic is a one-sample t-test, which is used to compare the mean of a sample to a known population mean. The results of this test will be used to determine if the average tenure of U.S. workers is significantly different from the stated 4.6 years. If the results are statistically significant, then we can reject the null hypothesis and conclude that the average tenure of U.S. workers is 4.6 years.

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The solution to the monomial in standard form is 0.04b^19.

What is a standard form of a polynomial?

The term "polynomials in standard form" can also refer to a polynomial written in the decreasing order of the degree of the variable.

The degree of the polynomial is significant when writing it in its standard form since the terms are written in descending order of the power of x.

Given that:

= (-0.2b^6)^3*5b

Rewrite using the commutative property of multiplication

= 5(-0.2b^6)^3b

Apply the product rule to −0.2b^6

= 5(-0.2^3)(b^6)^3b

= 5(-0.008b^18)b

= 5(-0.008^19)

= 0.04b^19

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Step-by-step explanation:

The indefinite integral of the polynomial function (x^4 + 2x^3 + 3x^2 + 4x + 5) is:

∫(x^4 + 2x^3 + 3x^2 + 4x + 5)dx = (x^5)/5 + x^4 + (3/2)x^2 + (2/3)x^3 + 5x + C

where C is an arbitrary constant of integration.

Answer:

Step-by-step explanation:

Answer:

960,000

Step-by-step explanation:

Every year, the number of blogs doubled.

The first year:60,000

The Second year: 120,000

The third year: 240,000

The fourth year: 480,000

The fifth year: 960,000

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The perimeter of this rectangle is 94, which is the smallest possible perimeter for a non-square rectangle with integer dimensions that has an area that is triple its perimeter.

Let's call the length of the rectangle "L" and the width of the rectangle "W". The area of the rectangle is then L * W, and the perimeter is 2 * (L + W).

According to the problem, the number of square units in the rectangle's area is triple the number of units in its perimeter:

L * W = 3 * (2 * (L + W))

Expanding the right side and solving for L:

L * W = 6L + 6W

L * W - 6L = 6W

L * (W - 6) = 6W

L = 6W / (W - 6)

Since L and W are both positive integers and L can't be equal to W (because the rectangle can't be a square), we know that W must be greater than 6. Let's try W = 7:

L = 6 * 7 / (7 - 6) = 6 * 7 = 42

This gives us a rectangle with dimensions 42 x 7, which satisfies the conditions of the problem.

The perimeter of this rectangle is 2 * (42 + 7) = 94, which is the smallest possible perimeter for a non-square rectangle with integer dimensions that has an area that is triple its perimeter.

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The situations when you might want to estimate the answer to a division problem are listed below.

What are the situations when you might want to estimate the answer to a division problem?

There are several situations when you might want to estimate the answer to a division problem:

Large numbers: When dividing large numbers, estimation can be quicker and provide a close enough answer.

Complex decimals: Estimating can help when the answer is a complex decimal and you only need a rough idea.

Time constraints: When you're short on time and need a quick answer, estimation can be useful.

Cost calculations: In budgeting or finance, you may need to estimate the cost of an item, which can be done by dividing the total cost by the number of items.

Determining proportions: In many real-world scenarios, you may need to determine the proportion of a certain characteristic, which involves dividing the number of occurrences of that characteristic by the total number of observations.

Quick analysis: In some cases, you might want a quick and rough estimate of the answer to a division problem to see if it falls within a certain range.

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One way we can check this is to simply multiply 15 by 12 to get 180.

15 × 12 = 180

Or you could even switch the numbers around.

12 × 15 = 180

But if we wanted to check it further, we can take the total and divide that by one of the multiplican or multipliers (15 or 12) to get the correct product.

180 ÷ 15 = 12180 ÷ 12 = 15

Therefore, these are some ways to use the numbers 180, 15 and 12 in expressions.

The angle in radians in simplest form is 2π/3 radians.

What is a circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given the radius of the circle = 8

and length of arc = 16π/3

the relation between angle and arc is given by,

s = rθ

where r = radius, s = arc length and θ = angle in radians,

so, θ = s/r

θ = (16π/3)/8

θ = 2π/3 radians

Hence the angle is 2π/3 radians.

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The circ*mstances in which the median rather than the mean is the preferred measure of central tendency is when there is a skewed distribution (a few extreme scores), an open-ended distribution or undetermined scores.

What is central tendency?

Central tendency is defined as the summative measure that tries to describe the entire set of data with a single value representing the mean or center of the distribution.

A skewed distribution occurs when one tail is longer than the other.

Therefore, in this type of distribution, the median should be chosen as the preferred measure of central tendency.

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Area of the backyard is 9000 sq.ft. Area of the flower garden is 60 sq.ft. So the area of backyard planted with grass will be 8940 sq.ft.

Here the backyard is in rectangular shape and the flower garden is a parallelogram.

Backyard has a length of 120ft and a width of 75ft. Area of a rectangle is given by the equation

Area of rectangle = length× width = 120×75 =9000 sq.ft

Area of backyard = 9000 sq.ft

The flower garden is a parallelogram with base 12 ft and height 5 ft.

Area of a parallelogram = Base× height = 12×5 = 60 sq.ft

Area of flower garden = 60 sq.ft

All the remaining area is planted with grass. So, the area of the portion of backyard planted with grass = Total area of backyard- area of the flower garden.

Area planted with grass = 9000-60 = 8940 sq.ft

So the area of the backyard is 9000 sq.ft, area of the flower garden is 60 sq.ft and area planted with grass is 8940 sq.ft.

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Full question is given as image.

The missing measures in △STU are,

⇒ ST = 4

⇒ TU = 8

And, ∠ S = 70°

∠ T = 64°

∠ U = 46°

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ △PQR ~ △STU

Now, By the definition of similar of triangles;

⇒ PQ / QR = ST / TU

⇒ QR / RP = TU / US

Here, we have;

PQ = 14

PR = 21

QR = 28

SU = 6

Hence, We get;

⇒ QR / RP = TU / US

⇒ 28 / 21 = TU / 6

⇒ TU = 28 × 6 / 21

⇒ TU = 8

⇒ PQ / QR = ST / TU

⇒ 14 / 28 = ST / 8

⇒ ST = 8 / 2

⇒ ST = 4

And, All the angles are equal.

⇒ ∠ Q = 180 - (70 + 46)

= 180 - 116

= 64°

Hence, We get;

∠ S = 70°

∠ T = 64°

∠ U = 46°

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The slope of a straight line that is parallel to the vertical axis is zero.

A slope of zero indicates that the line is flat and has no incline or decline. In a two-variable diagram, this means that there is no relationship between the two variables, as a change in one variable does not affect the value of the other. A line with a slope of zero is a horizontal line, and its equation is of the form y = b, where b is a constant value.

In contrast, a line with an infinite slope (or vertical line) would indicate a perfect correlation between the two variables, such that a change in one variable would result in an infinite change in the other. A line with a finite positive or negative slope would indicate a direct or inverse relationship between the two variables, respectively.

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The volume of the pyramid is 66.7 cm cube. Therefore, the answer is c.

How to find the volume of a pyramid?

The above diagram is a square base pyramid. The volume of the square base pyramid can be represented as follows:

volume of the pyramid = 1 / 3 BH

where

B = base areaH = height of the pyramid

Therefore,

base area = l²

where

l = side length

Hence,

base area = 5²

base area = 25 cm²

Therefore, let's find the volume of the pyramid.

Hence,

volume of the pyramid = 1 / 3 × 25 × 8

volume of the pyramid = 200 / 3

volume of the pyramid = 66.6666666667

Therefore,

volume of the pyramid = 66.67 cm³

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The ball is 7 feet high when it leaves the child’s hand

The maximum height is 16 feetIt lands 7 feet from the child

How high is the ball when it leaves the child’s hand?

Given that

h(x) = -x^2 + 6x + 7

When it leaves his hand, we have

x = 0

This gives

h(0) = -(0)^2 + 6(0) + 7

Evaluate

h(0) = 7

What is the maximum height of the ball?

Here, we have

h(x) = -x^2 + 6x + 7

Differentiate and set to 0

-2x + 6 = 0

So, we have

x = 3

The maximum height is

hmax = -3^2 + 6(3) + 7

hmax = 16

How far from the child does the ball strike the ground?

This means that h(x) = 0

So, we have

-x^2 + 6x + 7 = 0

This gives

x^2 - 6x - 7 = 0

Expand

x^2 + x - 7x - 7 = 0

Factor

x(x + 1) -7(x + 1) = 0

So, we have

(x - 7)(x + 1) = 0

Solve for x

x = 7 or x = -1

Hence, the distance is 7 feet

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The value of t is 8 and the value of r is 8√2. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of triangle sides, angles, and relationships is the focus of the mathematical field of trigonometry.

We are given a right angled triangle with an angle 45° and the perpendicular measuring 8.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan 45° = 8/t

⇒1 = 8/t (tan 45° = 1)

⇒t = 8

Similarly,

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos 45° = 8/r

⇒1/√2 = 8/r (cos 45° = 1/√2)

⇒r = 8√2

Hence, the value of t is 8 and the value of r is 8√2.

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Since, there are multiple questions so, the question answered above is attached below.

The function f(x) = 500(1 - 0.19)^x² is an exponentially decaying function.

The rate of decay is 0.19 or 19% and an equivalent expression to it is

f(x) = 500(0.9)^x.

What is a function?

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = 500(1 - 0.19)^x² for the price of a share of stock.

This would be an exponentially decaying function because (1 - 0.19) is less than 1.

The rate of exponential decay is 0.19 or 19%.

An equivalent expression to the function f(x) = 500(1 - 0.19)^x² is,

f(x) = 500(0.9)^x.

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Answer:

4= 16 quarts

Step-by-step explanation:

Answer: 16 quarts

Step-by-step explanation:

1 gallon = 4 quarts

4 gallon = 4 x 4 = 16 quarts

This is a direct proportion

Event R: Drawing a Red Ballot, Event B: Drawing a Blue Ballot, Event Even: Drawing an Even Numbered Ballot, Event Odd: Drawing an Odd Numbered Ballot.

The general election is today, and volunteers are organizing the ballots. Depending on the part of the city in which a citizen lives, he or she receives a different ballot. The types of ballots consist of RED ballots numbered 1, 2, 3, 4 and BLUE ballots numbered 1, 2, 3, 4. First, the volunteers need to define the events of drawing a red ballot and drawing a blue ballot. This can be done by defining the events R and B, respectively. Next, the volunteers need to define the event of drawing an even numbered ballot and the event of drawing an odd numbered ballot. This can be done by defining events Even and Odd, respectively. The volunteers can then use these events to determine which ballots are being drawn by the citizens. For example, they can use the events R and Even to determine which citizens are drawing a red even numbered ballot.

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Answer:

14. cross, bounce, cross

15. cross, bounce

16. [tex]x^{4}-12x^{3}+48x^2-64x[/tex]

Step-by-step explanation:

16.

x(x-4)(x-4)(x-4)

x(x-4)(x^2-8x+16)

x^3-8x^2+16x-4x^2+32x-64

x^4-12x^3+48x^2-64x

Answer:

$ 4564.32

Step-by-step explanation:

APR=2%, monthly interest rate, i=2%/12=0.02/12

Monthly payment, A=250

After 18 monnth, n=18 months,

the balance. Pis therefore

P = A((1+i)^n-1)/i

=250((1+0.02/12)^18-1)/(0.02/12)

=$ 4564.32

Answer:

2.4 lb

Step-by-step explanation:

We know

Alicia paid 1.32 for a bag of pinto beans

The beans cost .55 per lb

How much did the bag of pinto beans weigh?

1.32 / .55 = 2.4 lb

So, the bag of pinto beans weighs 2.4 lb.

Answer:

Green

Step-by-step explanation:

All you have to do is retrace retrace Alison’s steps. Note that there are 10 beads in the pattern, the 10th bead black. 210, 200, 190, 180, 170, 160, 150, 140. The 140th bead is black, because it is a multiple of 10. The 139 bead is black as well, because the end of Alison’s pattern contained 2 black beads. The next bead, bead 138, is green. So your answer would be green.

The simplest form of the polynomial is (x²)-3x+1.

A polynomial is a mathematical expression consisting of constants, variables, and exponents. It can be written in the form of a polynomial equation, which is a mathematical equation with one or more variables.

In this example, we have two functions, f(x) and g(x). The polynomial of these two functions can be written in simplest form by combining the functions together.

The polynomial of f(x) and g(x) is written in simplest form as (x²)-3x+1.

This means that for any value of x, the polynomial will evaluate to the value given by the equation.

If x=2, then the polynomial will evaluate to (2(2)²)-3(2)+1=3.

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The equivalent fractions for their ratios are given as follows:

Puja Limbu: 24/30.Raju Lama: 22/30.

Hence, due to the higher numerator, Puja Limbu had the better performance.

What are equivalent fractions?

Equivalent fractions are fractions that have the same denominator.

The fractions for this problem are given as follows:

Puja Limbu: 8/10.Raju Lama: 11/15.

The common denominator is the least common multiple of 10 and 15, which is of 30, hence the equivalent fractions are given as follows:

Puja Limbu: 24/30. -> multiply numerator and denominator by 3, as 30/10 = 3.Raju Lama: 22/30. -> multiply numerator and denominator by 2, as 30/15 = 2.

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Answer:

141

Step-by-step explanation:

First, you need to identify the pattern. As we have 3 terms, the pattern is +18 then +30. So, we can determine the next term is +18. 75 + 18 = 93. 93 is the 4th term. We can also determine the next term is +30. 93 + 30 = 123. 123 is our 5th term. Based off of what we know, we can determine the next term will be +18. 123 + 18 = 141. This proves our 6th term is 141.

I hope this helped. If this isn't correct, I apologize. This is based off of the 3 terms shown. If this helped, leave a heart and leave stars.

The probability of getting 2 same colour balls in a row = 41/81

Probability:

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.

Probability of an event P(E)

= [ No of favorable outcomes ]/ Total No of outcomes

Here we have

There is a bag filled with 5 blue and 4 red marbles.

Number of balls = 5 + 4 = 9

Marble is taken at random from the bag,

The probability of getting the red ball = 4/9

The probability of getting the blue ball = 5/9

The color is noted and then it is replaced.

Another marble is taken at random.

The probability of getting the red ball 2nd time = 4/9

The probability of getting the blue ball 2nd time = 5/9

The probability of getting red ball in 2 attempts = (4/9)(4/9) = 16/81

The probability of getting blue ball in 2 attempts = (5/9)(5/9) = 25/81

Hence the probability of getting 2 of the same color

= 16/81 + 25/81

= 41/81

Therefore,

The probability of getting 2 same colour balls in a row = 41/81

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According to the random survey, the majors chosen by the freshmen of our university were:

(a) The population is the entering freshmen at the university. (b) The sample is the 10% of the entering freshmen who are randomly surveyed. (c) The parameter is the proportion of entering freshmen who choose a major. (d) The statistic is the proportion of surveyed freshmen who choose a major.

To get a better understanding of the proportions of students choosing certain majors, universities can survey a sample of their entering freshmen. This survey should be representative of the population, so it should be conducted using a randomized sampling technique.

The survey should ask questions about the major the student is planning on pursuing and other relevant information, such as the student's interests and motivations.

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In the inter-quartile graph , the data is contained in about 75% of the total (IQR).

A sort of graph used to show numerical data visually is the box-and-whisker plot. In this graph, the inter-quartile range (IQR) of the data is shown as a rectangular box, and the median is shown as a line extending from the box. The minimum and maximum values of the data are indicated by the whiskers extending from the box. It is clear from the box-and-whisker plot's information that roughly 75% of the data falls inside the inter-quartile range. The first quartile (Q1) is subtracted from the third quartile to determine the IQR (Q3). The median of the lower half of the data is the lower quartile (Q1), and the median of the higher half is the upper quartile (Q3). The dispersion of the middle half of the data is thus indicated by the IQR. When evaluating data, having this knowledge is crucial since it makes it easier to see any outliers or numbers outside the IQR.

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The complete question is

considering the attached box-and-whisker plot, what percent of data lies within the inter-quartile range (iqr) and find the data?

Answer: $140 each weekend

Step-by-step explanation:

$1250 - $130 = $1,120

$1,120 divided by 8 weekends = $140