Let T: R³ → R² be the linear transformation that first projects points onto the yz-plane and then reflects around the line y=-z. Find the standard matrix A
for T.

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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[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 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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Answer:

+ 12

Step-by-step explanation:

Inverse means the opposite of the operation, and if the operation is subtraction the inverse would be addition. Add 12 to undo the -12.

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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The average complexity of linear search for a list of size n is O(n).

The average complexity of linear search for a list of size n is calculated by taking the sum of the number of comparisons for each possible position of the search element, and then dividing it by the total number of possible positions.

For example, if we have a list of size n = 10, and the search element is equally likely to be found in any position, then the number of comparisons to find the element in each position is as follows:

Position 1: 1 comparison Position 2: 2 comparisons Position 3: 3 comparisons Position 4: 4 comparisons Position 5: 5 comparisons Position 6: 6 comparisons Position 7: 7 comparisons Position 8: 8 comparisons Position 9: 9 comparisons Position 10: 10 comparisons

Therefore, the average number of comparisons to find the search element in the list is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 10 = 5.5

This means that the average complexity of linear search for a list of size n is O(n).

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The value of x determined from the area of parallelogram is 6 units.

A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposing sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height.

Given that the area of the parallelogram is 24 square units.

The area of the parallelogram is given by the formula:

A = (b)(h)

Substitute the value of A = 24, and b = 8 as given in the figure:

24 = 8(h)

h = 3

The measure of the height is 3 units.

For the triangle, we can observe that it is a right-angled triangle and the angle given is 30 degrees.

Using trigonometric functions, we have:

sin 30 = h / x

Substitute the values:

0.5 = 3 / x

x = 6

Hence, the value of x determined from the area of parallelogram is 6 units.

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Answer:

Step-by-step explanation:

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

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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ALL the statements about the number 2⁻³that are true are:

An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in an unequal way. It can be used most frequently by comparing the sizes of two numbers on a number line.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. Therefore, inequality comes from an imbalance.

The phenomena of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is known as inequality.

Inequalities can be shown in the speed limits on roads, the minimum age for watching particular movies, or even in how long it takes to walk to the park. Inequalities don't represent a precise sum.

First

2⁻³ = -8

So, 2⁻³ is equal to −8 is true

2⁻³ is greater than 3⁻²

No, as negative odd exponent will result in negative number while negative even exponent would result in positive number.

2⁻³  multiplied by −1 equals 2³

Yes, -8 × -1 = 8 = 2³

2⁻³  is less than 1

As negative odd exponent is there

2⁻³  raised to the third power equals 1, Nope.

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The digits {1,2,...,5} are randomly arranged in a row so total 5 ordered elements are in the sample space.

The digits {1,2,...,5} are randomly arranged in a row.

We have determine how many ordered elements are in the sample space.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

So, we use the combination formula

[tex]^nC_{r} = \frac{n!}{r!(n-r)!}[/tex]

Total digits are 5. So,

Sample space = [tex]^5C_{1}[/tex]

Sample space = [tex]\frac{5!}{1!(5-1)!}[/tex]

Sample space = [tex]\frac{5!}{1!4!}[/tex]

Sample space = [tex]\frac{5\times 4!}{1\times 4!}[/tex]

Sample space = 5

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From a position 17 cm from the circle's center, the tangent to it is 8 cm long.

Distance from a circle's center to any point along its perimeter is known as the radius of the circle. R or r are frequently used to indicate it.

Almost every formula involving circles makes use of this amount.

A circle's radius is used to determine both its surface area and circumference.

Give the circle's radius, r.

Given:

PQ=8cm

PO=17cm

OQ=r

Since the radius across the point of contact is perpendicular to any point on a line, it follows that any point on a line must be.

According to Pythagoras' Theorem, in OPQ, OP 2 = PQ 2 + OQ 2.

(17) ²  = (8) ² +r ²

⇒ r=  √289−64  = √225  =15cm

Consequently, the circle has a 15 cm radius.

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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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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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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.

Para completar la piramide hay que ir sumando los polynomios que  hay en cada bloque.

Para construir las piramides, solo debes sumar los polinomios de los bloques inferiores para obtener los superiores.

La primer piramide tiene los valores en los dos bloques de la izquierda:

2r - 3s y 5s - r

Si los sumamos, obtendremos:

(2r - 3s) + (5s - r) = (2r - r) + (-3s + 5s) = r + 2s

Entonces eso es lo que colocamos en el bloque que esta justo arriba.

Si vemos el segundo y el tercero son:

5s - r y 7r - 6s

Sumandolos obtenemos:

5s - r + 7r - 6s = 6r - s

Y eso va en el bloque que esta justo arriba, y asi de a poco vamos completando la piramide.

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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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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 value of the function when evaluated is 1/2

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

f(x)=2/√10-6

Express properly

So, we have the following representation

f(x)=2/√(10-x)

Substitute the known values in the above equation, so, we have the following representation

f(-6)=2/√10+6

Evaluate the like terms

f(-6)=2/√16

So, we have

f(-6) = 1/2

Hence, the function value is 1/2

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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.

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:

700

Step-by-step explanation:

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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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:

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)

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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By graphing, the solution to the given system of equations is: (2, 4).

To solve a system of equations by graphing:

The graph of y = 7/2x - 3 is the red line while that of y = –3/2x + 7 is the red line. They intersect at (2, 4).

Therefore, the solution of the system of equations is: .

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