Moving vertically up from the origin is movement in the direction of positive z
The first hook will be hung at a point 4 feet east of the origin and 7.5 feet above the origin. The second hook will be hung at a point 5 feet east of the origin, 12
feet north of the origin, and 8 feet above the origin.
Provide the coordinates of the following points:
1. the first hook
2. the second hook
3.
the point on the string joining the hooks that is exactly halfway between the hooks

The joint probability mass function given by PX, Y(a, b) = {1/4a, for 1≤ b≤a≤4, otherwise is indeed a joint probability mass function because the sum of all the joint probabilities is equal to 1.

To find the marginal probability mass function of X, we need to sum the joint probabilities over all possible values of Y:

PX(a) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4

To find the marginal probability mass function of Y, we need to sum the joint probabilities over all possible values of X:

PY(b) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4

To find P(X = Y + 1), we need to find the joint probability of X = a and Y = a-1, where a = 2,3.

P(X = Y + 1) = PX, Y(2,1) + PX, Y(3,2) = (1/42) + (1/43) = 1/4 + 3/12 = 5/12

So the probability that X is one more than Y is 5/12.

It's important to note that the given joint probability mass function is valid as it satisfies the non-negativity and the condition of summing to 1.

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Two boys, Zach and Carlos, go for a walk. Zach begins walking 20 seconds earlier than Carlos and they both walked the same distance.

How to calculate the distance?

To calculate the distance that the boys walked, you would need to know their speed and the duration of their walk.

Speed is typically measured in units such as miles per hour (mph) or kilometers per hour (kph). If you know the speed of the boys and the duration of their walk in hours, you can calculate the distance they walked using the formula: distance = speed x time.

The sentence is describing a scenario in which two boys, Zach and Carlos, go for a walk. It is stated that Zach begins walking 20 seconds earlier than Carlos. This means that Zach starts his walk 20 seconds before Carlos does. It is also stated that both boys had walked exactly the same distance. This means that despite Zach starting his walk 20 seconds earlier than Carlos, they both covered the same distance during their walk.

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The probability that a student studied for 5 hours is 0.2 or 20%.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

A table is given where the first column represents the number of hours a student studied Math and the second column represents the number of students.

The sum of the second column is 35 so it is the total number of students

And only 7 of them studied mathematics for 5 hours.

Therefore, The probability that a student studied for 5 hours is,

= 7/35

= 0.2 or 20%.

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The number of yards of the automobile of length 'x' meters will be 1.10x yeads.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

A meter is about 1 ¹/₁₀ yards.

Convert the mixed fraction number to a decimal number. Then we have

1 meter = 1 ¹/₁₀ yards

1 meter = 1 + ¹/₁₀ yards

1 meter = 11 / 10 yards

1 meter = 1.10 yards

Let the length of the automobile be 'x' meters. Then the number of yards in 'x' meters is given as,

⇒ x × (1.10)

⇒ 1.10x yards

The number of yards of the automobile of length 'x' meters will be 1.10x yeads.

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Answer:

$ balance = 120*(1+6.4%/4) ^4t

Step-by-step explanation:

principal =120

r =6.4% annual = 1.6% per quarter compounding every quarter

so 4 times a year, for t years

$ balance = 120*(1+6.4%/4) ^4t

The function that represents the balance of the investment account after t years is  [tex]y = 120 (1.016)^{4t[/tex].

The formula for calculating the balance of an investment account that earns compound interest is:

[tex]A = P (1 + \dfrac{r}{n})^{nt}[/tex]

where:

A = the balance after t years

P = the principal (initial amount deposited)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

In this case, we have:

P = $120

r = 6.4% = 0.064 (as a decimal)

n = 4 (compounded quarterly)

Therefore, the function that represents the balance y (in dollars) of the investment account after t years is:

[tex]y = 120 *(1 + \dfrac{0.064}{4})^{4t}[/tex]

Simplifying the expression inside the parentheses, we get:

[tex]y = 120 (1.016)^{4t[/tex]

This is the function that represents the balance of the investment account after t years.

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The initial deposit was $8000 and after 18 years the simple interest earned is $12960. So, the total amount for Melissa in college account is $20,960.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

The amount that was put in college fund for Melissa, P = $8000

The rate at which interest was earned is, R = 9%

The time period after which the account was checked, T = 18 years

The formula for Simple Interest is -

S.I. = (P R T)/100

Substitute the values into the equation -

S.I. = (P R T)/100

S.I. = (8000 × 9 × 18)/100

S.I. = 1296000/100

S.I. = 12960

The amount of interest earned in 18 years is $12960.

The total amount after 18 years will be -

Total Amount = Initial deposit + Interest earned

Total Amount = $8000 + $12960

Total Amount = $20960

Therefore, the total amount after 18 years is $ 20,960.

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When Melissa was born, her parents put $8,000 into a college fund account that earned 9% simple interest. After 18 years, she had $20,960 in the account. How did this happen?

On solving the given equation,  the value of x = -4.

Finding the value of f(x) =... or y =... that corresponds to a certain value of x is what it means to evaluate a function.

Simply swap out all instances of x with the value of x to do this. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.

Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

Given,

[tex]\frac{2x + 4}{2} - \frac{3x}{x-2} = x\\ \\[/tex]

Taking LHS

⇒ [tex]\frac{2x^2 - 4x + 4x - 8 - 6x}{2(x-2)} \\[/tex]

⇒ [tex]\frac{x^2-4-3x}{(x-2)}[/tex]

Equating both sides,

⇒ [tex]\frac{x^2-4-3x}{(x-2)} = x\\x^2-4-3x = x^2 - 2x\\x = -4[/tex]

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The movie gross is $701

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total amount earned from the movie and the sequel = $1518

Amount earned from the movie = x

Amount earned from the sequel = x + $116

Now,

x + (x + 116) = 1518

2x + 116 = 1518

2x = 1518 - 116

2x = 1402

x = 1402/2

x = 701

Now,

x = $701

x + 116 = 701 + 116 = $817

Thus,

The movie gross is $701

The sequel gross is $817

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A graph that satisfies the given requirements 1 ≤ x ≤ 3 and 2 ≤ y ≤ 7 is shown in the image attached below.

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

For the domain of this graph, the x-value would be placed at point 1 and then dragged to point 3 on the x-coordinate. Similarly, the y-value for the range of this graph would be placed at point 2 and then dragged to point 7 on the y-coordinate as shown in the image attached below.

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There is a distance of 656.088 feet to the bottom of the well.

What is Speed?

Speed is the ratio between the distance an object travels and the time it takes to cover that distance.

Since speed just has magnitude and no direction, it is a scalar quantity.

Because the amount of time that passes after you drop the rock is made up of both the amount of time it takes for it to fall to the bottom of the hole and the amount of time it takes for the sound of the impact to reach you,

Let t be the moment when a rock was attained at depth d, which is the well's bottom.

And this is the moment when you hear the sound of impact.

t + t' = 7 seconds

⇒ t' = 7 - t

Speed = Distance / Time

1100 feet per second = d / t'

d = 1100 t

Also d = 16t²

1100 t' = 16t²

1100 (7 - t) = 16t²

7700 - 1100t = 16t²

16t² + 1100t - 7700 = 0

4t² + 275t - 1925 = 0

This is a quadratic equation.

Discriminant = √(b² - 4ac) = √[275² - (4 × 4 × -1925)] = 326.228

t = (-275 ± 326.228) / (2 × 4)

t = 6.404 or t = -75.15

t = -75.15 is not possible because it is negative and t + t' = 7 seconds.

So t = 6.404 seconds

t' = 7 - 6.404 = 0.596 seconds

d = 16 × (6.404)² = 656.088 feet

Hence the distance from the well to the bottom is 656.088 feet.

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Note that the next number in the progression or sequence or pattern is 35,585.

Note that a number pattern is a series of numbers that adheres to a set of criteria. The rule might be mathematical, such as adding a constant value to each item in the series, or it can be based on some other logical relationship.

The next term in the sequence or pattern is derived as follows:

3x5 -3 = 12

5x12 -5 = 55

12x55 -12 = 648

55x648 -12 = 35,585

Therefore, it is correct to state that 35,585 is the next term in the sequence

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The ways to represent 3+3+3+3+3 with multiplication are:

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, an expression 3+3+3+3+3

To represent this in multiplication terms,

We need to figure out what the expression tells us. So, there are 5 terms all terms have a value of 3.

Thus,

represent a way to show 3+3+3+3+3 with multiplication is either 3*5 or 5*3.

Therefore, The correct ways of representing the expression 3+3+3+3+3 are:

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A symmetric matrix is a square matrix that is equal to transpose of itself. If A is a symmetric matrix, then it satisfies the condition: A = AT. (AT is the inverse of A )

A square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix. Or we can say when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

Suppose  λ and  μ are 2 distinct values of matrix  A.

For the matrix to be Symmetric,

                 ( Ax,y)=(x,Ay)

 condition needs to be satisfied.

Here, ( x,y) is dot product between vectors  x and  y

                 λ (u,v) = (λu,v)

 where  u,v are eigen vectors for eigen values  λ and  μ

             λ(u,v) = (Au,v)

             λ(u,v) = (u,Av)

             λ(u,v) = μ(u,v)

             λ(u,v) = μ(u,v)

but  λ≠μ

                             ∴ (u,v) = 0.

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The complete question is :

If a matrix is symmetric then show that any two eigenvectors of that matrix corresponding to different eigenvalues are orthogonal. Assume square matrix.

The values of variables a to d are

Polynomial 1

This is given as

x² - 8x + 15 = (ax + b)(cx + d)

The factors of 15 that add up to -8 are

-3 and -5

This means that

b = -3 and d = -5

Because the coefficient of x² is 1, then

a = 1 and c = 1

Polynomial 2

This is given as

2x³ - 8x² - 24x = 2x(ax + b)(cx + d)

Divide through by 2x

x² - 4x - 12 = (ax + b)(cx + d)

The factors of -12 that add up to -4 are

2 and -6

This means that

b = 2 and d = -6

Because the coefficient of x² is 1, then

a = 1 and c = 1

Polynomial 3

This is given as

6x² + 14x + 4 = (ax + b)(cx + d)

Factorize

(x + 2)(6x + 2) = (ax + b)(cx + d)

By comparison, we have

a = 1, b = 2. c = 6 and d = 2

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Average speed is determined by dividing the total distance you traveled by the total time,

In order to calculate average velocity, divide the change in position or displacement (x) by the time intervals (t) during which the displacement takes place. Depending on the displacement's sign, the average velocity can either be positive or negative. The SI unit for average speed is meters per second (m/s or ms-1).

Average speed is determined by dividing the total distance you traveled by the total time, whereas average velocity is determined by dividing your displacement, which is a vector pointing from your initial location to your end position, by the whole time.          

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The amount that you would have to pay in federal income tax if you claim 3 allowances would be:  $65.46

To calculate the amount you will pay in federal income tax using the percentage method of withholding, you will need to know the withholding percentage for your gross pay and the number of allowances you are claiming.

If you claim 3 allowances, each allowance is $80.80, and you gross pay for the week is $710, your taxable income is:

$710 - 3*$80.8 = $710 - $242.4 = $467.6

To find the amount of federal income tax you will pay, you will need to use the withholding percentage for your taxable income. You can find this information by consulting the IRS Circular E (Employer's Tax Guide) or by using an online withholding calculator.

If we use the IRS Circular E, we can find that if you are single and claim 3 allowances, the withholding percentage for a taxable income of $467.6 is 14%.

So the amount you will pay in federal income tax is:

$467.6 * 14% = $65.46

Therefore, you will pay $65.46 in federal income tax if you claim 3 allowances, and your gross pay for the week is $710.

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The inverse of the function as it has been written is f(x) = (x - 32) 5/9.

We know that the inverse of a function can easily be obtained as long as we have the function as we do in the question here. The function has been given to us as; f(x)=9/5 x + 32.

Let y = f(x)

Hence;

y=9/5 x + 32

y - 32 + 5/9 = x

We would then have the inverse of the function as;

f(x) = (x - 32) 5/9

This is the procedure that would help us to obtain the inverse of the function that have been given here.

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Missing parts;

Given f(x)=9/5 x + 32, find the following;

Inverse of the function

Slope of regression is 0.8710 and at 4 tons top speed of boat is 111.064 mph.

Linear regression is a data analysis technique that predicts the value of unknown data by using another related and known data value. It mathematically models the unknown or dependent variable and the known or independent variable as a linear equation.

Given, In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded.

Solution(a)

Given in the question

Dependent variable is top speed of a boat (in mph) Independent variable is weight of boat (in tons)

from the coefficient table of Enova summary we can write least square regression line as follows

Top speed = 107.58 +0.8710* Weight of boat

Here intercept of regression line = 107.58

Slope of regression line = 0.8710

Solution(b)

if X = 4 tons

than predictive value of the top speed of a boat can be calculated as

Top speed = 107.58 +0.8710 * 4 = 107.58 +3.484 = 111.064 mph predictive value of the top speed of a boat = 111.064 mph if its weigh It is 4 tons.

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Complete question:

The median for average life of a particular brand of a T.V sets from the following data is given as follows:

17.5.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.

The total number of observations in this problem is given as follows:

2 + 16 + 26 + 39 + 43 + 21 + 8 + 4 = 159.

This is an odd cardinality, hence the median is found in the class when the counter hits:

(159 + 1)/2 = 80.

Which is the class 15-20, as 2 + 16 + 26 < 80 and 2 + 16 + 26 + 39 > 80, and the median value is given as follows:

(15 + 20)/2 = 17.5.

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The following are not characteristics of surveys :

A. The study involves on or more treatment groups and a control group

B. The study compared two or more treatments

A survey is a research technique used to gather data from a predetermined sample of respondents in order to learn more and acquire insights into a range of interesting topics.

There are Characteristics of an Effective Survey :

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According to the information, Aaliyah is going to need 8.75 hours to read 50 more pages than Yohance.

To calculate how many hours Aaliyah will beed to read, we have to perform the following mathematical procedure

First, we have to calculate how many pages Yohance is going to read this week, so if she is going to read during 7.5 hours we have to multiply the number of pages she read per hour by time (7.5 hours).

So, Yohance is going to read 300 pages. Now if we want to know how many hours needs Aaliyah to read 50 more pages we have to perform the following operation:

According to the above, Aaliyah needs to read for 8.75 hours to complete 50 more pages than Yohance.

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X intercept: 10/5

Y intercept: 0

To find the intercepts of a linear equation, you need to set either the X or Y variable to 0 and then solve for the other variable.

For example, if you have the equation 5x - 2y = 10, you can set X equal to 0 and solve for Y to find the Y intercept, or you can set Y equal to 0 and solve for X to find the X intercept.

X Intercept:

To find the X intercept, set Y equal to 0 and solve for X.

5x - 2(0) = 10

5x = 10

x = 10/5

X intercept = 10/5

Y Intercept:

To find the Y intercept, set X equal to 0 and solve for Y.

5(0) - 2y = 10

-2y = 10

y = -10/2

Y intercept = 0

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Answer:

Jade will be farther by 0.6 or .6 miles in 3 hours

Step-by-step explanation:

Jade walks at a speed of 3 miles per hour so 3×3=9 miles per hour

Elena walks at a speed of 2.8 miles per hour so 2.8×3=8.4 miles per hour

Next,the question is how much farther will Jade walk after 3 hours so that means 9-8.4 which is 0.6 or .6 in decimals and we read it as six tenths

hope it helps you

Answer:

  957,697,598

Step-by-step explanation:

You want a number that has 7 different prime factors.

If we choose 7 primes at random from the first 20, we might have the list ...

  {2, 11, 13, 23, 41, 53, 67}

The product of these primes will have 7 different prime factors.

  2 × 11 × 13 × 23 × 41 × 53 × 67 = 957,697,598

The number 957,697,598 has exactly 7 different prime factors.

__

Additional comment

Any of these factors might have a power greater than 1 without changing the number of different primes. We chose to keep it simple.

The second attachment shows the first 20 prime numbers.

The type of sampling design is used: simple random sample

The correct answer is an option (a)

We know that in data analysis, the sampling is nothing but the selecting the group or subset of the population to make statistical inferences.

The types of probability sampling are:

Simple random sampling, Systematic sampling, Stratified sampling and Cluster sampling.

In simple random sampling, the researcher randomly selects a subset of data from the population.

In Stratified random sampling, the population is divided into smaller subgroups called as strata.

In case of clustered random sampling, the population is divided into clusters, and then we randomly select some of these clusters as sample.

As we know multistage sampling is a type of cluster sampling.

Here,  it has been decided to randomly select 4 of the 10 lab sections.

This means, simple random sampling design is used in given scenario.

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The complete question is:

a. suppose there are 10 lab sections of a statistics class that each have the same number of students enrolled. a class evaluation is about to be administered to some of the students. it has been decided to randomly select 4 of the 10 lab sections and give the evaluation to all the students in those sections. What type of sampleing design is used?

a) Simple random sample

b) Stratified random sample

c) Clustered random sample

d) Multistage sample

The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:

C) Translation (x,y) -> (x + 7, y), and reflection over the x-axis.

The glide reflection is a combination of a reflection with a translation.

The vertices of the original triangle are given as follows:

A(-3,-2), B(-6,-5) and C(-1,-4).

The vertices of the reflected triangle are given as follows:

A'(4,2), B'(1,5) and C'(6,4).

The composite rule for these two transformations is given as follows:

(x,y) -> (x + 7, -y).

The transformation y -> -y is a reflection over the x-axis, hence the correct option is given by option C.

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Event A is the event that the sum of the numbers rolled on the two dice is divisible by 4. Event B is the event that the sum of the numbers rolled on the two dice is less than 4.

(a) The total number of possible outcomes in this experiment is 36 (6 possible outcomes for each die).

(b) Outcomes in A are (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (12, 1), (12, 2), (12, 3), (12, 4), (12, 5), and (12, 6).

(c) Outcomes in B are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), and (2, 6).

(d) P(A) is 5/36. (e) P(B) is 6/36. (f) P(A U B) is 11/36. (g) P(A n B) is 0 (there are no outcomes that belong to both A and B). (h) Events A and B are not independent because P(A U B) does not equal P(A) + P(B).

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The perimeter of the rectangular park is 423/4 units.

The lengths of a shape's edges and sides are added to find its perimeter.

The length of a two-dimensional shape's boundary is its perimeter. It is frequently referred to as the sum of the lengths of the sides of the object. That shape's perimeter is equal to the side lengths added together algebraically.

The perimeter of a shape is equal to the length of its boundary or whole circumference. The perimeter of a closed 2D form is the product of its sides.

Given : Length = 20 1/4

                        = 81/4

          Width = 32 5/8

                     = 261/8

So, Perimeter = 2 ( L + B)

                      = 2 ( 81/4 + 261/8)

                      = 2 ( 423/8)

                     = 423/4 units.

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Answer:

arrange in ascending order

14,15,16,17,18,20,25

there are odd number of terms so

median = (n+1/2) th observation

here n = 7 which is odd

therefore, 7+1/2 th observation

which is 4th observation

ans) 17