what is the z formula

Let A be a symmetric matrix, which means that A is equal to its own transpose, i.e., A = Aᵀ. We want to prove that if A is invertible, then its inverse A⁻¹ is also symmetric.

To show that A⁻¹ is symmetric, we need to show that (A⁻¹)ᵀ = A⁻¹.

We know that A is invertible, so A⁻¹ exists. Taking the transpose of both sides of the equation A = Aᵀ, we get:

(Aᵀ)ᵀ = A

which simplifies to:

A = Aᵀ

Multiplying both sides of this equation by A⁻¹, we get:

A⁻¹ A = A⁻¹ Aᵀ

Using the property of transpose (i.e., (AB)ᵀ = Bᵀ Aᵀ), we can rewrite the right-hand side of the equation as:

A⁻¹ Aᵀ = (A A⁻¹)ᵀ = Iᵀ = I

where I is the identity matrix.

Substituting this back into the original equation, we get:

A⁻¹ A = I

Taking the transpose of both sides of this equation, we get:

(A⁻¹ A)ᵀ = Iᵀ

which simplifies to:

Aᵀ (A⁻¹)ᵀ = I

Using the property of transpose again, we can rewrite the left-hand side of the equation as:

(A⁻¹)ᵀ Aᵀ = (A A⁻¹)ᵀ = Iᵀ = I

Substituting this back into the equation, we get:

(A⁻¹)ᵀ Aᵀ = I

which can be rearranged as:

(A⁻¹)ᵀ = (Aᵀ)⁻¹

Since we know that A = Aᵀ, we can substitute this into the equation to get:

(A⁻¹)ᵀ = A⁻¹

which shows that A⁻¹ is symmetric. Therefore, if a symmetric matrix is invertible, then its inverse is symmetric also.

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65  °F is equal to 18.3333 °C.

A temperature unit developed from the SI (International System of Units) is Celsius (symbol: °C).

Prior to the adoption of the metric system, Fahrenheit (symbol: °F) was a commonly used measurement of temperature.

To convert a temperature from Fahrenheit (°F) to Celsius (°C),

We can use the following formula:

°C = (°F - 32) x 5/9

Where °C is the temperature in Celsius

°F is the temperature in Fahrenheit.

Substituting 65 for °F,

We get:

°C = (65 - 32) x 5/9

Simplifying the expression:

°C = 33 x 5/9

°C = 18.3333333333

Therefore, 65 degrees Fahrenheit is equal to nearly 18.3333 degrees Celsius (rounded to four decimal places).

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We can convert milliliters to teaspoons using the formula 1 milliliters = 0.202 teaspoons as per the standard US unit conversion.

The milliliters is the unit of volume. A teaspoon is likewise a volume unit, however it is a smaller unit and usually it is used on the dinner tables.

As per the standard conversion rates, one milliliters is equal to 0.202 US teaspoons.

As a consequence, we may use the unit conversion concept to describe the connection.

One milliliter is equivalent to 0.202 US teaspoons.

For instance, 8 milliliters is equal to 1.61 teaspoons.

As a result, we now have a standard formula for calculating the value of volume in small amount in teaspoons to milliliters and milliliters to teaspoons.

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The distribution is roughly symmetric and unimodal, and the median and IQR best represent the data set.

If you plot a histogram of the data;

the distribution appears to be roughly symmetric and unimodal.

We can also calculate some summary statistics to better understand the center and spread of the data:

The range is a simple measure of spread, but it can be heavily influenced by outliers.

The IQR is a more robust measure of spread that is less affected by outliers.

Finally, the standard deviation is a commonly used measure of spread that takes into account how far each data point is from the mean.

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The answer is 84 pairs of pants.

Explanation:
According to the problem, she donated half of her pants to charity, which means she donated (1/2)x pairs of pants.

After donating half of her pants, she kept her 7 favorite pairs of pants. So, the number of pairs of pants she kept is 7.

The problem states that she was left with 35 pairs of pants after donating half of her pants and keeping her 7 favorite pairs. This means that the remaining number of pairs of pants is (x/2) - 7 = 35.

Solving for x, we get:

(x/2) - 7 = 35

x/2 = 42

x = 84

Therefore, Kim had 84 pairs of pants in the beginning.

Answer:

my guess is 17 .,.

Step-by-step explanation:

Nominal, ordinal, interval, and ratio are measurement scales used in statistics to categorize and rank data.

Nominal, ordinal, interval, and ratio are four sorts of information estimation scales utilized in measurements.

Nominal scales are utilized to mark or classify information into particular gatherings, where each gathering is fundamentally unrelated and altogether comprehensive. Instances of ostensible information incorporate orientation, race, and occupation.

Ordinal scales include positioning information in a particular request, however the distinctions between values are not significant. Instances of ordinal information incorporate positioning motion pictures in view of their prominence or understudy execution on a test.

interval scales include positioning information in a particular request, however the distinctions between values are significant, and there is no obvious zero point. Instances of stretch information incorporate temperature, intelligence level scores, and time.

ratio scales are like span scales, however they have a genuine zero point, implying that values can be duplicated and partitioned. Instances of proportion information incorporate weight, level, and pay.

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The complete question is:

what is the nominal, ordinal, interval and ratio?

The antiderivative of sin is -cos(x) + C.

The antiderivative of a function is the inverse operation of differentiation which is is also known as its indefinite integral.

So, the integral of sin

                 ∫sin(x) = -cos(x) + C

where C = constant of integration.

This can be verified by differentiating -cos(x) + C with respect to x, which gives sin(x).

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Answer:

[tex] \frac{23}{10} [/tex]

the shaded segment PQR will be 18.265m².

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angle of triangle = 180

the diagram shows a sector OPQR of a circle, centre O and radius 8 cm.

Area of shaded part = Area of quadrant − Area of triangle

=πr²/ 4 - 1/2 bh

= π × 8²/ 4  - 1/ 2 × 8× 8

= 18.265m².

Hence the shaded segment PQR will be 18.265m².

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Online calculator of variable cost is used to Total Variable Cost = Total Cost-Fixed Costs to calculate the Total Variable Cost.

A variable cost is an expense that changes as a company's production output rises and falls. Variable expenses vary according on the amount of output produced. Basic variable costs include, in large part:

Variable costs are frequently employed in business and are a crucial component of the analysis of the company's break-even point. The revenue or unit that must be sold to cover all costs is examined using the break-even approach.

The following calculation is the break-even point:

Break-even point in units = Fixed costs/(Sales price per unit – Variable cost per unit)

Variable costs are crucial for successful investors because they help them calculate the proportion of the set price and predict how the company will respond to various operational scenarios.

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108ft is the length of the of the guy wire

Triangles are known to be similar if the ratio of the similar sides of the triangle are equal.

From the given diagram, we need to determine of the guy wire. Using the similarity theorem of a triangle;

8/2 = l/25+2
8/2 = l/27

2l = 8 * 27

l = 4 * 27

l = 108 ft

Hence the length of the of the guy wire, to the nearest foot is 108ft

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The value of x is 2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The point as far as she can tell are (3,5) and (x,10).

Slope is -5.

-5=10-5/x-3

-5=5/x-3

-5(x-3)=5

Apply distributive property

-5x+15=5

Substitute 15 from both sides

-5x=-10

Divide both sides by 5

x=2

Hence, the value of x is 2.

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Work Shown:

5/32 divide 25/4

(5/32) * (4/25)

(5*4)/(32*25)

(5*4)/(8*4*5*5)

(1)/(8*5)

1/40

Answer:

9 units bro

Step-by-step explanation:

The correct answer is:

greater than zero for all values of x.

Probability is a way of evaluating how likely something is to happen. Several things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.  One is the probability of every event in a sample space.

Now in the given question ,

A probability density function (PDF) of a continuous random variable x is a function that describes the relative likelihood of x taking on different values in a continuous range. The PDF is defined such that the area under the curve between any two values a and b represents the probability of x being in that range, i.e., P(a ≤ x ≤ b).

Since probabilities are non-negative, the PDF of a continuous random variable must also be non-negative. That is, f(x) > 0 for all values of x. This condition ensures that the area under the curve is non-negative, which is necessary for it to represent a valid probability distribution.

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The integral of sec(x) is ln |sec(x) + tan(x)| + C.

The integral of sec(x) is:

∫sec(x) dx = ln |sec(x) + tan(x)| + C

where C is the constant of integration.

To solve this integral, you can use the method of substitution. Let u = sec(x) + tan(x). Then [tex]du/dx = sec(x)tan(x) + sec^2(x)[/tex], which can be simplified to du/dx = u tan(x). Rearranging, we get du/u = tan(x)dx.

Substituting these expressions into the integral, we have:

∫sec(x) dx = ∫(sec(x) + tan(x))/(sec(x) + tan(x)) dx = ∫(1/u) du

Integrating this expression gives:

∫(1/u) du = ln |u| + C = ln |sec(x) + tan(x)| + C

Therefore, the integral of sec(x) is ln |sec(x) + tan(x)| + C.

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70 degrees Fahrenheit is equal to approximately 21.1111 degrees Celsius (rounded to four decimal places).

The Celsius (symbol: °C) is an SI (International System of Units) derived unit of temperature.

The Fahrenheit (symbol: °F) is a unit of temperature that was widely used prior to metrication.

To convert a temperature from Fahrenheit (°F) to Celsius (°C),

We can use the following formula:

°C = (°F - 32) x 5/9

Where °C is the temperature in Celsius and °F is the temperature in Fahrenheit.

Substituting 70 for °F, we get:

°C = (70 - 32) x 5/9

Simplifying the expression:

°C = 38 x 5/9

°C = 21.1111111111

Therefore, 70 degrees Fahrenheit is equal to approximately 21.1111 degrees Celsius (rounded to four decimal places).

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The number of $56 dollar tickets to center section was 200 and the number of tickets costing $38 to the left and right sections were 200.

Let us consider the number of tickets to the center section be x and right and left sections be y.

Here the total number of tickets sold are 540.

So,  x+ y = 540  ---------> i

The cost of tickets cost $56 will be 56x

The cost of tickets cost $38 will be 38y.

The total cost was given as $24120

So, 56x+ 38y = 24120 -----------> ii

Multiplying equation i with 56,

56x + 56y = 30240  ------------> iii

Subtracting equation ii from equation iii

   56x+ 56y = 30240

-   56x + 38y = 24120

So 18y = 6120

      y = 6120/18 = 340

Since x+ y = 540

          x+ 340 = 540

          x = 540- 340 = 200

So the number of $56 ticket sold is 200 and the number of $38 ticket sold is 340.

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There are 6 employees who play musical instruments.

What is the ratio?

A ratio is a relationship between two quantities, indicating how many times the first quantity contains the second. Ratios are often expressed as a fraction or in the form "a:b", where "a" and "b" are the two quantities being compared.

The given ratio of employees who play musical instruments to employees who play sports is 3:20. This means for every 3 employees who play musical instruments, there are 20 employees who play sports.

We are given that there are 40 employees who play sports. We can use this information to find the number of employees who play musical instruments as follows:

Let's start with the ratio of employees who play sports to employees who play music, which is 20:3. This means that for every 20 employees who play sports, there are 3 employees who play music.

We know that there are 40 employees who play sports, so we can set up a proportion to find the number of employees who play music:

20/3 = 40/x

where x is the number of employees who play music.

To solve for x, we can cross-multiply:

20x = 3 * 40

20x = 120

Then, we can solve for x by dividing both sides by 20:

x = 6

Therefore, there are 6 employees who play musical instruments.

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The correct answer is option B and it is equal to 30% of 81 because it shows 0.30 x 81.

We have to find that how much is equal to the 30% of 81.

We can use the percentage formula here and that is,

%age = Obtained value/total value x 100

Here in this case, we have to find the obtained value and the total value is 81 and the percentage that we are going to get  is equal to 30.

So, putting all the values, we get,

obtained value = 30 x 81/100

obtained value = 0.30 x 81

Hence, the value 0.30 x 81 is equal to 30 % of 81. hence option B is the correct answer.

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Complete question - Which of the following options have the same value as 30% of 81?

A. 0.03 x 81

B. 0.3 x 81

C. 0.03 x 81

D. 3 x 81

Answer:

Below

Step-by-step explanation:

21 is to 27    as x-3   is to    x-1

21/27 =  x-3/x-1    cross multipliy , solve for x = 10

Answer:

Step-by-step explanation:

x-3/21 = x-1/27

27(x-3) = 21(x-1)

27x-81 = 21x-21

27x-21x = -21+8

6x = 60

x = 60/6

x = 10

_____________________

Hope this helps! :)

Answer:

ED = 57 , AB = 19

Step-by-step explanation:

the midsegment FC is half the sum of the parallel bases , that is

[tex]\frac{AB+ED}{2}[/tex] = FC

[tex]\frac{4x+3+18x-15}{2}[/tex] = 38 ( multiply both sides by 2 )

22x - 12 = 76 ( add 12 to both sides )

22x = 88 ( divide both side by 22 )

x = 4

then

ED = 18x - 15 = 18(4) - 15 = 72 - 15 = 57

AB = 4x + 3 = 4(4) + 3 = 16 + 3 = 19

The amount of money that the salesman will earn from 10 vans is:

$138,352

The profit from selling 1 van is shared between the salesman and Asco Motor in the ratio of 2:3. This means that for every $5 of profit, the salesman gets $2 and Asco Motor gets $3.

To determine the amount of money that the salesman will earn from 10 vans, we first need to calculate the profit from selling 10 vans. Since the profit from selling 1 van is $34,588, the profit from selling 10 vans will be:

$34,588 × 10 = $345,880

Now we need to calculate the salesman's share of this profit. Since the profit is shared in the ratio of 2:3, the salesman's share will be:

$345,880 × (2/5) = $138,352

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At the end of 18 years, there will be a total of $5,890.37 in the account.  

Compound interest is a powerful financial tool that can help you grow your money over time.

In the case of the $1,800 deposited into an account earning 6% interest compounded weekly, the total amount in the account at the end of 18 years can be calculated as follows:

Let P be the principal balance, r be the interest rate, n be the number of times the interest is compounded per year, and x be the number of years. Using the compound interest formula, we can calculate the amount in the account at the end of 18 years:

A = P(1 + (r/n))ⁿˣ

A = 1800 * (1 + (0.06/52))⁵²ˣ¹⁸

A = 5,890.37

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Part A) Solve for x because it has a coefficient of 1 in both equations.

Part B)  The solution is,

⇒ (x, y) = (57/8, 16/3)

Part C) The slope is,

⇒ m = 128/171

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

Given that;

The system of equation are,

⇒ x + y = 10

⇒ 2y = x + 6

Now, We can solve the equation as,

⇒ x + y = 10

⇒ 2y - x = 6

Add both equation,

⇒ 3y = 16

⇒ y = 16/3

⇒ x + y = 10

⇒ x + 16/13 = 10

⇒ x = 10 - 16/13

⇒ x = 57/8

Hence, The solution is,

⇒ (x, y) = (57/8, 16/3)

Thus, The slope is,

⇒ m = (16/3) / (57/8)

       = 16×8 / 3×57

       = 128/171

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Solving an equation, the number of textbooks sold by the textbook store, which sold a combined total of 236 in a week is as follows:

An equation is a mathematical statement that two or more algebraic expressions are equal or equivalent.

Equations are differentiated from mathematical expressions by the use of the equal sign (=).

The total number of math and physics textbooks sold in a week = 236

Let the number of physics textbooks sold = x

Let the number of math textbooks sold = x + 52

2x + 52 = 236

2x = 236 - 52

2x = 184

x =92

The number of textbooks sold for the week:

Physics textbooks sold = 92

Math textbooks sold = 144 (92 + 52)

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In 1 billion, the probability of division being incorrect would be : {1/(11 x 10⁹)²}.

In science, the probability of an event is a number that indicates how likely the event is to occur.

Given is that the manufacturer initially claimed that the chance of any particular division being incorrect was only 1 in 11 billion.

The probability of division being incorrect would be -

P{incorrect} = (1/11 x 10⁹)

In 11 billion, the probability of division being incorrect is (1/11 x 10⁹).

Then, in 1 billion, the probability of division being incorrect would be -

{1/(11 x 10⁹)²}

Therefore, in 1 billion, the probability of division being incorrect would be : {1/(11 x 10⁹)²}.

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Answer:

Step-by-step explanation:

0.0869

Answer: look at the image for the answer and explanation

Step-by-step explanation:

The solution to the system of inequalities is (80, 50).

At least two linear inequalities in the same variables make up a system of a linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

Given:

To raise money for the show,

the drama club is selling tickets.

Let x be the number of student tickets sold and y represents the number of adult tickets sold.

According to the question,

x + y ≤ 130

5x + 10y ≥ 900.

We have drawn a graph of the system of inequalities.

And the graph is given in the attached image.

Therefore, the solution is (80, 50).

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Slope of relationship between length of icicle and time = −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches .The correct option is D.

What is slope?

The slope of a line is defined as the change in vertical coordinate with respect to the change in horizontal coordinate of that line.

Given,

A student is measuring the length of an icicle, y, every hour, x

At present icicle is 9 inches long

melting at rate of 0.6 per hour

y = 9 - 0.6 x

Where y is the length of the icicle after x hours

comparing with slope intercept form of line: y = m x + c

slope m = -0.6

Hence, - 0.6 is the slope, represents that the length of the icicle decreases by 0.6 inches every hour.

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