Solve 1 and 2 please help

The matrix's entry of 1.00 on the diagonal denotes that it is an identity matrix, which means that all values besides 1 along the diagonal are 0.

The matrix is an identity matrix, as evidenced by the entry of 1.00 on its diagonal. A square matrix called an identity matrix is one in which the primary diagonal's elements are all ones and the other components are all zeros. The letter "I" stands for this particular sort of matrix. In several branches of mathematics, such as matrix theory and linear algebra, identity matrices are employed. Calculations and equations can also be made simpler by using identity matrices. An identity matrix, for instance, is created by multiplying it by any other matrix. This characteristic can be used for matrix inversion or to solve a set of linear equations. In group theory and abstract algebra, the identity element is also represented by identity matrices.

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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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According to the linear equation, because 8.8 rounds to 9 and 2.7 rounds to 3, division rounds to 3. His solution of 4.14 equals 4. As a result, it is illogical.

A linear equation is an equation having one or more variables, the maximum power of which is one. A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

The following expression is:

Given expression is:

8.8 ÷ 2.7

≈ 9 ÷ 3

= 3

His answer is 4.14 ≈ 4.

According to the linear equation, division rounds to 3 since 8.8 rounds to 9 and 2.7 rounds to 3. His solution of 4.14 equals 4. It is thus irrational.

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Answer:

Since 6/7  rounds to 1 and 4 4/5 rounds to 5, the sum rounds to 6. Her answer of 5 22/23 rounds to 6. So it is reasonable.

Step-by-step explanation:

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.

Answer:

kaoajaoàwkwk2k2kwkw

Step-by-step explanation:

[tex] \boxed{ \sf \: \\ \\ \\ \\ \\ \\ \\ } \: \: \: \: \: \: \: \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \boxed{ \colorbox{blue}{ \: }}[/tex]

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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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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Answer:

700

Step-by-step explanation:

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 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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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.

6x² - 31 x + 40, after factorization we get: (2x - 5) (3x - 8).

correct option: a

Expanding brackets is done in reverse when factorising. By eliminating the most common factors, an expression is fully factored when it is enclosed in brackets. The simplest method of factorization is to identify the term in the equation with the largest common factor. The Grouping technique, the Difference in Two Squares, the Sum or Difference in Cubes, and the Greatest Common Factors (GCF) are the four primary methods of factoring.

Similar to this, factoring is a very useful technique in algebra that is utilised at all levels. Additionally to, of course, simplifying complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.

= 6x² - 31 x+40

= 6x² - 15 x - 16 x +40

= 3x (2x - 5) - 8 (2x - 5)

= (2x - 5) (3x - 8)

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In order for a function to be continuous at a point, then,

The limit of f(x) as x approaches the x coordinate of the point from the left and the right equals the value of the function at that point.

What does the term "continuous function" mean?

A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap.

                            This indicates that there aren't any discontinuities, or sharp shifts in value.

What does it mean when a function is continuous or discontinuous?

If one can sketch a function without picking up a pencil, one can say that it is continuous. A function is considered discontinuous if it is not.

                          If there is no break in the graph of the given function at the point, then a function f(x) in calculus is continuous at x = c.

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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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The digit in the ones place of 2^90 is 4. The pattern of the digits in the ones place for powers of 2 follows a repeating cycle of 0, 2, 4, 6, 8, 0, 2, 4, 6, 8 and so on.

The digit in the ones place of 2^88 is 6 because the last digit of 2^88 is 6. The pattern of the digits in the ones place for powers of 2 is 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, etc. Therefore, the digit in the ones place of 2^90 is 4 since the pattern starts over again at 0 after 8.

The pattern of the digits in the ones place for powers of 2 follows a repeating cycle of 0, 2, 4, 6, 8, 0, 2, 4, 6, 8 and so on. This pattern is a result of the fact that 2^n is divisible by 10 for all integers n greater than or equal to 0. Since 10 is divisible by 10, the remainder of 2^n divided by 10 will always be the same for certain powers of 2. The remainder for 2^0 is 0, 2^2 is 4, 2^4 is 6, 2^6 is 8 and 2^8 is 0. This pattern then repeats with 2^10 being 2 and so on. Therefore, the digit in the ones place of 2^90 is 4, since the pattern starts over again at 0 after 8.

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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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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 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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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:

C

Step-by-step explanation:

15 (-42 x + 40) = 15 (- 8 x + 244)

15 cancelled on each side

-42x+40= -8x+244

move all the x to one side & numbers to the other,

-34x =204

x=6

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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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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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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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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Salut/Hello!

Answer:

Step-by-step explanation:

x = 5 : 6 + (10 - 2x - 20)
x= 0,8(3) + 10 - 2x - 20
2x + x = 0,8(3) + 10 - 20
3x = 0,8(3) + 10 - 20
3x = -10,8(3)
x = -3.6(1)

I hope it was helpful! :]

Answer:

y=-4x+2

Step-by-step explanation:

y2-y1/x2-x1

= 10-(-2)/-10-5

=12/-15 (divide by 3)

= -4/5x ---(Slope)

y=mx+b

-2=(-4/5)(5)+b

-2=-4+b (Add 4 on both Sides)

2=b

Put it all together

y=mx+b

Therefore,the equation is : y=-4/5x+2

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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There are 7.58 ounces of silver are in the bar.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

A metal bar weights 8.15 ounces.

And, 93% of the bar is silver.

Now, Let the amount of silver in the bar = x

So, We can formulate;

⇒ x = 93% of 8.15

⇒ x = 93/100 × 8.15

⇒ x = 7.58

Thus, the amount of silver in the bar = 7.58 ounces

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