given a j = 3 2 and b j = −3 4 , where j = −1 , find (use just pencil and paper, not software or calculators)

The amounts and the situations are matched as follows:

The situation is modeled by a system of equations, in which the variables are given as follows:

The meaning of each variable is used to build the expressions for this problem.

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Answer:

8.5m

Step-by-step explanation:

K-means clustering is an iterative algorithm that partitions a data set into k clusters, where k is predefined.

It works by first randomly selecting k points as cluster centers, also known as centroids. All points are then assigned to the nearest cluster center based on a distance metric, such as Euclidean distance. This process is repeated until the centroids no longer move, which is when the clusters have stabilized. The formula for calculating the distance between two points is d = sqrt((x1-x2)^2 + (y1-y2)^2).

Hierarchical clustering is a type of clustering algorithm that builds a hierarchy of clusters. It starts by assigning each point to its own cluster, then combines the two closest clusters and repeats the process. The calculation used to determine the distance between two clusters is the distance between their two closest points, also known as the single linkage method. The formula for calculating the distance between two clusters is d = min(d1, d2, ..., dn), where d1, d2, ..., dn are the distances between the two closest points in the two clusters.

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The missing length of the triangle be 7.93725.

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, [tex]$c^2=a^2+b^2$$[/tex], are equal to the total of the squares on the legs.

Remember that in every right triangle, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the two legs side (the two sides that meet at a right angle).

With the aid of the Pythagorean Theorem, we may determine the side lengths of a right triangle by adding the areas of three intersecting squares.

By using Pythagorean Theorem is:

[tex]$c^2=a^2+b^2$$[/tex]

where c exists the hypotenuse and a and b exists the sides.

[tex]$\sqrt{\left(12^2-9^2\right)}=7.93725$$[/tex]

Therefore, the correct answer is 7.93725.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Original equation:}[/tex]
[tex]\mathsf{7.5(22 + 1.2s)}[/tex]

[tex]\huge\textbf{DISTRIBUTE 7.5 within the}\\\\\huge\textbf{parentheses:}[/tex]

[tex]\mathsf{7.5(22 + 1.2s)}[/tex]

[tex]\mathsf{= 7.5(22) + 7.5(1.2s)}[/tex]

[tex]\mathsf{= 165 + 9s}[/tex]

[tex]\mathsf{= 9s + 165}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{9s + 165}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The cost Marie to fill the planter with soil to fill her vegetable planter is $57.

A bag of soil has 64 quarts and is costing 9.50

And required soil is 380 quarts so,

380 → X

64 → 9.50

By using cross multiplication method,

64 × X = 380 × 9.50

X = 3610/64

X = 56.4

X ≈ $57

Cross multiplying is the process of multiplying the denominator of the second fraction by the numerator of the first fraction, which is on one side of the equals to symbol. In a similar way, the denominator of the first fraction is multiplied by the numerator of the second fraction. The butterfly method, also referred to as cross-multiplication, has another name.

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The equation of a quadratic function P with rational coefficients that has a zero of (3 + i) is p(x) = x² - 6x + 10.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The complex number value is given as (3 + i)

Since, x = (3 + i) is a complex zero of p(x), then -

It is known that , the complex zeros occur in pair.

So, x=(3 - i) is also a complex zero of the quadratic function of p(x).

So, {x − (3 + i)} and {x − (3 - i)} are the factors of p(x).

Substitute the values to form a quadratic function -

p(x) = {x − (3 + i)}{x − (3 - i)}

Open the brackets and evaluate -

p(x) = (x - 3 + i)(x - 3 - i)

Use the arithmetic operation of multiplication -

p(x) = x(x - 3 - i) - 3(x - 3 - i) + i(x - 3 - i)

p(x) = x² - 3x - ix - 3x + 9 + 3i + ix - 3i - i²

Collect all the like terms -

p(x) = x² - 3x - 3x - ix + ix + 9 + 3i - 3i - i²

p(x) = x² - 6x + 9 - i²

Substitute the value of  i² = -1 into the equation -

p(x) = x² - 6x + 9 - (-1)

p(x) = x² - 6x + 9 + 1

p(x) = x² - 6x + 10

Therefore, the quadratic function is x² - 6x + 10.

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Answer:

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

The 90° arc is representing the quarter of circle.

Its length is the quarter of the circumference of circle with radius of 8.

The arc length is:

The probability of a randomly selected person from this group visiting a physical therapist is 0.68.

The probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible. Let A denote the event that the person visits a physical therapist, and let B denote the event that the person visits a chiropractor. Now, we need to use the laws of probability to arrive at each individual probability i.e. P(A) and P(B).

Given: P(A∩B)=0.28

(ii) P(AC∩BC)=0.08

(iii) P(A)−P(B)=0.16

Required: P(A)

By the laws of inclusion/exclusion,

P(A∪B)=P(A)+P(B)−P(A∩B)

Therefore,

P(A)+P(B)=P(A∩B)+P(A∪B)

By DeMorgan's Law,

P(AC∩BC)=1−P(A∪B)

Therefore,

P(A)+P(B)=0.28+1−0.08=1.2

By adding the equation,

P(A)−P(B)=0.16

we get

2P(A)=1.36

Therefore, P(A)=0.68

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Attached is a two-way frequency table, to help Hugo organize the results.

A two-way frequency table is a table used to organize and display the relationship between two categorical variables. It is constructed by counting the number of occurrences of each combination of categories and presenting the results in a table format.

1. Identify the categorical variables and list their possible categories.

cat, no cat, dog, no dog

2. Count the number of observations for each combination of categories.

cat = 17

no dog = 20

no cat no dog = 7

3. Organize the counts in a table with the categories of one variable as rows and the categories of the other variable as columns.

          | dog | no dog | total

cat      |        |              |   17  |

no cat |        |     7       |        |

total    |        |     20    |   41  |

4. Fill in the table with the counts of the observed combinations of categories.

cat but no dog = 20 - 7 = 13

both cat and dog = 17 -13 = 4

total no cat = 41 - 17 = 24

total dog = 41 - 20 = 21

dog but no cat = 24 - 7 = 17

          | dog | no dog | total

cat      |   4   |      13     |   17  |

no cat |   17  |     7       |   24  |

total    |   21  |     20    |   41  |

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The sensitivity of the instrument can be calculated as the ratio of true positives (40) to the total number of participants with disease (55) is 73%.

Sensitivity, also known as the true positive rate or recall, is a measure of the accuracy of a diagnostic test or medical screening tool in detecting positive cases. In medical research, sensitivity is an important aspect to evaluate the performance of a diagnostic test.

In a hypertensive study, if a participant has a blood pressure reading above a certain threshold, they are diagnosed as having hypertension (a positive case). Sensitivity is calculated as the proportion of true positive cases (those with hypertension and correctly diagnosed) to the total number of actual positive cases (those with hypertension, both correctly and incorrectly diagnosed).

The formula for sensitivity is:

sensitivity = true positive / (true positive + false negative)

In the example given, the number of true positives is 40 and the total number of participants with disease (true positives plus false negatives) is 55. So, the sensitivity of the instrument is:

sensitivity = 40 / 55 = 0.73 or 73%

This means that out of all the participants with hypertension, the instrument correctly diagnosed 73% of them.

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The following represents a positive correlation

What Is Positive Correlation?

Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. Theoretically, the same external forces can affect both of these separate variables because they travel in the same direction.

A positive correlation may not imply progress or advantage. Instead, it refers to any two or more variables that move in tandem, meaning that as one increases, the other does too.

the following represents a positive correlation

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it will take Isabelle about 10.33 years for her investment to grow to $10,000.

To calculate the time it takes for Isabelle's investment to grow to $10,000, we can use the formula for compound interest:

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

where A is the amount of money at the end of t years, P is the initial amount (4350), r is the interest rate per year (7.6%), n is the number of times compounded per year (4, since it's compounded quarterly), and t is the number of years.

We can rearrange the formula to solve for t:

t = (log(A/P)) / (log(1 + r/n))

Plugging in the values, we get:

t = (log($10,000 / $4350)) / (log(1 + 7.6% / 4))

Using a calculator, t = approximately 10.33 years.

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Answer:

3) m = -3/2

4) m = 3/2

5) m = 5/3

6) m =  7/3

7) m = -3

8) m = 7/3

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

3/ ( -4, 0) ( -2, -3)

The y decrease by 3, and the x increase by 2, so the slope is

m = -3/2

4/ (2,0) (0, -3)

The y decrease by 3, and the x decrease by 2, so the slope is

m = -3/-2 = 3/2

5/ (-1,2) (-4, -3)

The y decrease by 5, and the x decrease by 3, so the slope is

m = -5/-3 = 5/3

6/ (4,3) (1, -4)

The y decrease by 7, and the x decrease by 3, so the slope is

m = -7/-3 = 7/3

7/ (1,2) (3, -4)

The y decrease by 6, and the x increase by 2, so the slope is

m = -6/2 = -3

8/ (0,3) (-3, -4)

The y decrease by 7, and the x decrease by 3, so the slope is

m = -7/-3 = 7/3

This probability is approximately  [tex]\frac{1}{e}[/tex], which is around 0.37, that we collect all n coupons in exactly n weeks.

The probability of collecting all n coupons in exactly n weeks is very low, as it is dependent on getting a unique coupon every week for n weeks. This is known as the "Coupon Collector's Problem".

The probability can be calculated using the formula:

This formula can be broken down as follows:

1/n represents the probability of getting the first unique coupon in the first week, it's 1/n because there are n different types of coupons and all of them are equally likely to be in a box.

So, by subtracting this probability of not getting a unique coupon in n weeks from 1, we get the probability of getting at least one unique coupon in n weeks.

Finally, by multiplying the probability of getting the first unique coupon [tex]\frac{1}{n}[/tex] with the probability of getting at least one unique coupon in the next n-1 weeks, we get the overall probability of collecting all n coupons in exactly n weeks.

Therefore, the probability is approximately [tex]\frac{1}{e}[/tex], which is around 0.37, this is a very low probability, and in practice it would take a much longer time to collect all n coupons.

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Answer:

Step-by-step explanation:

multiply 5km by 3 minutes he would have run the 5km in 1 5 minutes

Answer: Its c

Step-by-step explanation: -2 - 6 is -8

The statement "They can only be integer values" is not true about continuous random variables.

Continuous random variables can take any value within a certain range, not just integers. They are characterized by a probability density function (pdf) that describes the distribution of the variable over a range of values. The pdf is a continuous curve, not a set of discrete points.

The other statements about continuous random variables are true: the entire area under each of the curves does equal 1, some may be described by uniform distributions or exponential distributions, the area under each of the curves represents probabilities, and they have an infinite set of values.

Therefore, The statement "They can only be integer values" is not true about continuous random variables.

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The true statements are Function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

We have to first find the linear equations of the functions.

Given for function A,

Let x be the number of hours.

Function A can be represented as f(x) = 4/5 + 2x

Equation in slope intercept form is y = mx + c, where m is the slope and c is the intercept along Y axis.

Y intercept is the point of the line where it touches the Y axis. x coordinate will be zero here.

x intercept is the point of the line where it touches the X axis. y coordinate will be zero here.

y = 2x + (4/5), in slope intercept form.

Here 2 is the slope and 4/5 is the y intercept.

When y = 0, 2x + (4/5) = 0, then x = -2/5

x intercept = -2/5

For function B,

we have when x = 0, f(x) = y = 2/3

y intercept = 2/3

Slope = [(2/3) - (-25/3)] / [0 - -3]

          = [27/3] / 3

          = 9 / 3

          = 3

Equation in slope intercept form of function B is,

y = 3x + 2/3

When y = 0, 3x + 2/3 = 0, then x = -2/9

x intercept = -2/9

So function B has greater slope as slope is 3 for B and 2 for A.

Function A has greater y intercept as y intercept for A is 4/5 and for B is 2/3.

Function B has greater x intercept as x intercept is -2/9 for B and -2/5 for A.

Hence the correct options are function B has greater slope, Function A has greater y intercept and Function B has greater x intercept.

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Answer:

To find 67% of an amount, we use the percentage multiplier of 0.67.

This is because 67% can be expressed as 67/100, and when we divide a number by 100, we are essentially moving the decimal point two places to the left. So, 67/100 can also be written as 0.67.

Therefore, the percentage multiplier to find 67% of an amount is 0.67.

The polynomial function is f(x) = x(x - 5)(x + 5)² - 8)

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

Zeros: x = 0, 5, -5 + √8

The polynomial can be repesented as

f(x) = product of (x - zeros)

using the above as a guide, we have the following:

f(x) = x(x - 5)(x - (-5 + √8))(x - (-5 - √8))

This can be expressed as

f(x) = x(x - 5)(x + 5)² - 8)

hence, the polynomial is f(x) = x(x - 5)(x + 5)² - 8)

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Answer:

C

Step-by-step explanation:

For the second graph

the equation should be:

y = 1/2 x^2

Which makes the graph true.

You can try plug numbers into x to check your answer.

The speed of wind is 73.335 miles per hour. The distance between San Francisco and New York remains constant and we a considering wind speed is also constant.

It is known that,

The relation between distance , speed

the distance travelled = speed × time

Put the values of given data in above formula.

Then 880×5= 4400 miles

the distance between NY to SF =  4400 miles.

Speed at which the plane was travelling from SF to NY = 4400/6 =733.33 miles per hour.

Differences in the speed is caused by the relative wind speed, which equals (880-733.33)/2 = 146.67/2 =73.335 miles per hour

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Based on the information provided, it appears that Sammi did not make any mistakes in creating the tally chart. The information appears to be correctly recorded and organized.

To create a dot plot, Sammi would simply plot a dot above the appropriate number on the number line for each entry in the "hours" column and mark it the number of times specified in the corresponding entry in the "tally" column.

The answer was determined based on the information provided in the question, which was a 2-column table with 4 rows. The first column was labeled "hours" and had entries of 3, 4, 5, 6. The second column was labeled "tally" and had entries of 4, 6, 3, 5.

Given this information, it can be concluded that Sammi correctly recorded the hours and their respective tallies. Therefore, there is no mistake in the creation of the tally chart.

It is important to note that the question only asks about the creation of the tally chart and not the creation of the dot plot, so the answer is based solely on the information provided in the question and not any assumed knowledge or steps in creating a dot plot.

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Answer:

77.14

Step-by-step explanation:

To find the mean(average) we add all the values and divide the sum by the number of values. Here, we are given 7 total values.

The sum of these values = 79 + 83 + 54 + 77 + 98 + 61 + 88 = 540

Because there are 7 total values we divide the sum by 7 to get the mean

So mean = 540 / 7 = 77.14 (rounded to two decimal places)

By the product rule of differentiation, the derivative of (x² - 3x + 2)(x + 2) with respect to x is: 2x² - 7x + 4.

d/dx [(x² - 3x + 2) (x + 2)]

= (x² - 3x + 2)'(x + 2) + (x² - 3x + 2) (x + 2)'

= (2x - 3) (x + 2) + (x² - 3x + 2) (1)

= 2x² - 7x + 4.

Differentiation is a concept in calculus that involves finding the rate of change or the slope of a function at a particular point. It involves finding the derivative of a function, which is a measure of how the function changes as its input changes. The derivative of a function can be used to determine important features of the function, such as maximum or minimum points, as well as to study the behavior of the function over an interval.

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9sin is the integral of 9cosx (x). 9sin(n*/2) - 9sin(n) is the integral of (n2)* to n* in the expression for 9cosx.

A fundamental trigonometric integration is the integral of 9cosx. The trigonometric substitution formula and the integral of cosx formula, sin, can both be used to calculate this integral (x). This indicates that 9sin is the integral of 9cosx (x).The integral of 9cosx from (n2)* to n* is a little more challenging. The trigonometric substitution formula and the integral of cosx formula can both be used to solve this integral. Sin is the integral of cosx (x). The integral of (n2)* to (n*) of 9cosx is therefore 9sin(n*/2) - 9sin(n). Accordingly, the integral of the function from n* to n* is equal to the difference between the integrals of the functions from 0 to n* and from 0 to n*.

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All the correct statements are,

⇒ ∅ ⊂ R

⇒ {... , - 5, - 4, - 3, - 2} ⊆ T

⇒ T ⊂ I

⇒ 0 ∈ I

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We know that;

For ∅ ⊂ R;

A null set is a subset of R, and in fact every set in general. There are no elements in a null set thus making it automatically a subset of any non-empty set by definition.

Hence, We get;

⇒ ∅ ⊂ R

For 6 ∈ T;

Since T is the set of negative integers less than - 1.

Hence, 6 ∉ T

For {... , - 5, - 4, - 3, - 2} ⊆ T

The set on the left is exactly what is defined on the problem statement for T. (The bar below the subset symbol just means that the subset is not strict, therefore the set on the left can be equal to the set on the right. Without it, the statement would be false since a strict subset requires that the two sets should not be equal).

Hence, {... , - 5, - 4, - 3, - 2} ⊆ T

For T ⊂ I;

Clearly, T is the set of negative integers less than - 1.

Hence, It is subset of integers.

Hence,  T ⊂ I

For 0 ∈ Z;

Zero is indeed an integer thus it is an element of Z.

Hence, 0 ∈ Z

For R ⊂ T

Since, T is the set of negative integers less than - 1.

So, Not all real numbers are some integers. Some real numbers do not meet this criteria.

Hence, R ⊄ T

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The complete question is shown in figure.