List 3 sides to a right triangle. explain how you can use three pythagorean theorem to know that your three sides will create a right triangle.

By De Moivre's formula, the square roots of the complex number √(i 2) are √z = 1 + i and √z = - 1 - i, respectively.

In this problem we find a complex number, whose square roots can be determined by De Moivre's formula:

For z = a + i b:

√z = √r · [cos [(θ + 2π · k) / 2] + i sin [(θ + 2π · k) / 2]], for k = {0, 1}

Where:

If we know that r = 2 and θ = π / 2, then the root of the complex number is:

k = 0

√z = √2 · [cos (π / 4) + i sin (π / 4)]

√z = 1 + i

k = 1

√z = √2 · [cos (5π / 4) + i sin (5π / 4)]

√z = - 1 - i

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9.  A normally distributed data set has a µ = 10, the z score for 10 is 0.

10. It is true that the standard deviation is needed to convert a raw score to a z-score.

11. The total percentage between a standard deviation of -2 and 1 is given as follows: 81.85%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score for the mean is given as follows:

Z = 0/s

Z = 0.

The p-values relative to z-scores between -2 and 1 are given as follows:

Hence the percentage is given as follows:

84.13 - 2.28 = 81.85%.

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[tex]36 cm^3[/tex] of pure alcoh ol must be added to the [tex]10 cm^3[/tex] of the 8% solution to obtain [tex]10 + 36 = 46 cm^3[/tex] of an 80% solution.

What is Algebraic expression ?

Algebraic expression can be defined as combination οf variables and constants

Let's first calculate the amount  of pure alcohol in the 8% solution:

Amount of pure alcohol = 8%  of [tex]10 cm^3 = 0.08 x 10 cm^3 = 0.8 cm^3[/tex]

N ow, let's  assume [tex]x cm^3[/tex]of pure alcohol must be added to the 10 cm^3 of the 8% solution to obtain a total volume of [tex]10 + x cm^3[/tex] of an 80% solution. The amount of pure alcohol in the final solution would be:

ο[tex](10 + x) cm^3 = 0.8 (10 + x) cm^3[/tex]

Since we started with [tex]0.8 cm^3[/tex]of pure alcohol and we want to end up with  

[tex]0.8 (10 + x) cm^3[/tex], we can set up the following equation:

[tex]0.8 + x = 0.8 (10 + x)[/tex]ο

Simplifying and solving for x, we get:

[tex]0.8 + x = 8 + 0.8x[/tex]

[tex]0.2x = 7.2[/tex]

[tex]x = 36[/tex]

Therefore, [tex]36 cm^3[/tex] of pure alcohol must be added to the [tex]10 cm^3[/tex]of the 8% solution to obtain [tex]10 + 36 = 46 cm^3[/tex] of an 80% solution.

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Answer:

36cm^3

Step-by-step explanation:

Answer:

The answer is D

Answer:

this does not make sense I mean ate you in un 200lev

Answer:

C

Step-by-step explanation:

Thus, Jamie is wrong. In contrast to Bus C, Bus B has less unoccupied seats as a percentage of total seats.

% is a relative number that is used to represent hundredths of the any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.

Find the complete seating capacity in Bus A first:

Bus A has 28% of the available seats, making its seat count 0.28 x 250 = 70.

Secondly, we can construct an equation system using the number of seats in Bus B compared to Bus C:

The number of seats aboard Bus B will be x.

In that case, Bus C's seating capacity is (2/3)x.

Using the information that there are 250 seats overall, we can find x:

70 (from Bus A) + x (from Bus B) + (2/3)x (from Bus C) = 250

When we simplify this equation, we obtain: (5/3)x = 180

When we solve for x, we get x = 108.

Bus C has (2/3)x = 72 seats, but Bus B has 108 seats.

We can now determine the proportion of vacant seats for each bus:

Out of a total of 108 seats, 38 seats on Bus B are vacant, making the percentage of vacant seats in Bus B (38/108) x 100% = 35.19%.

Out of a total of 72 seats, there are 26 empty seats on Bus C, making the percentage for empty seats there (26/72) x 100% = 36.11%.

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Answer:

what paper is this for this question

The system of linear equations that represents the situation is:

(option 4)  j + s = 120

                 2.5j + 3.5s = 350

Let j be the number of 11-inch softballs ordered for the Junior League, and s be the number of 12-inch softballs ordered for the Senior League.

The total number of softballs ordered is 120, so we have:

j + s = 120

The cost of each 11-inch softball is $2.50, and the cost of each 12-inch softball is $3.50. The total cost of the order is $350, so we have:

2.5j + 3.5s = 350

Therefore, the system of linear equations that represents the situation is:

j + s = 120

2.5j + 3.5s = 350

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Answer:    30

Step-by-step explanation: TRUSy

The new amount due, subtract the discount of $52.57 from the original bill of $2,628.53, giving the new amount due of $2,579.06. Therefore, if you pay the bill within 15 days, you will receive a 2% reduction and your bill will be $2,579.06.

To calculate the amount due if paying within 15 days, you would need to apply the 2% discount to the original amount. To do this, first find the amount of the discount by multiplying the original bill of $2,628.53 by 0.02. This gives a discount of $52.57. To calculate the new amount due, subtract the discount of $52.57 from the original bill of $2,628.53, giving the new amount due of $2,579.06. Therefore, if you pay the bill within 15 days, you will receive a 2% reduction and your bill will be $2,579.06.

Original Bill : $2,628.53

Discount (2%) : $2,628.53 x 0.02 = $52.57

Amount Due (after 15 days) : $2,628.53 - $52.57 = $2,579.06

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The standard deviation is σX ≈ 1.936 (rounded to at least three decimal places).

Standard deviation (σX) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. Here is how to compute it from the given data:\begin{tabular}{cc} \hline Number of Hours & Frequency \\ \hline 0 & 127 \\ 1 & 176 \\ 2 & 348 \\ 3 & 252 \\ 4 & 328 \\ 5 & 239 \\ 6 & 139 \\ 7 & 27 \\ 8 & 60 \\ \hline Total & 1696 \end{tabular}(b) Compute the standard deviation σX​. Round the answer to at least three decimal places.The formula to use is:\[\sigma_X = \sqrt{\frac{\sum f(x_i - \overline{x})^2}{n}}\]where:σX = standard deviation∑ = sum off = frequencyxi = value of i-th datan = total number of data\[\overline{x} = \frac{\sum fx}{n}\]is the sample mean, which we must calculate first.\[\overline{x} = \frac{\sum fx}{n} = \frac{0\cdot127 + 1\cdot176 + 2\cdot348 + 3\cdot252 + 4\cdot328 + 5\cdot239 + 6\cdot139 + 7\cdot27 + 8\cdot60}{1696} \approx 2.7875\]Substituting into the standard deviation formula:\[\sigma_X = \sqrt{\frac{\sum f(x_i - \overline{x})^2}{n}} = \sqrt{\frac{0\cdot(127 - 2.7875)^2 + 1\cdot(176 - 2.7875)^2 + 2\cdot(348 - 2.7875)^2 + 3\cdot(252 - 2.7875)^2 + 4\cdot(328 - 2.7875)^2 + 5\cdot(239 - 2.7875)^2 + 6\cdot(139 - 2.7875)^2 + 7\cdot(27 - 2.7875)^2 + 8\cdot(60 - 2.7875)^2}{1696}} \approx 1.936\]Therefore, the standard deviation is σX ≈ 1.936 (rounded to at least three decimal places).

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Using power reduction formula and half angle formula, the blanks are  "-1/2cos(x)" and "2x", respectively.

We can use the power reduction formula for sine to express sin(3x) in terms of cosines:

sin(3x) = 3sin(x) - 4sin³(x)

= 3(1 - cos²(x)) - 4(1 - cos²(x))sin²(x)

= 3cos²(x) - 4cos⁴(x) - 4sin²(x)cos²(x)

= 3cos²(x) - 4cos⁴(x) - 2sin²(2x)

Now we can substitute this expression into the left-hand side of the identity and simplify using the half angle formula for cosine:

(sin(3x))⁴ = (3cos²(x) - 4cos⁴(x) - 2sin²(2x))⁴

= (3cos²(x) - 4cos⁴(x) - (1 - cos(4x)))⁴

= (3cos²(x) - 4cos⁴(x) - 1 + cos(4x))⁴

= (cos(4x) - 4cos⁴(x) + 3cos²(x) - 1)⁴

Now we can use the half angle formula for cosine again to express cos(4x) in terms of cosines of multiples of x:

cos(4x) = 2cos²(2x) - 1

= 2(2cos²(x) - 1)² - 1

= 8cos⁴(x) - 8cos²(x) + 1

Substituting this expression back into the above identity, we get:

(sin(3x))⁴ = (8cos⁴(x) - 8cos²(x) + 3cos²(x) - 4cos⁴(x) - 1)⁴

= (4cos⁴(x) - 5cos²(x) - 1)⁴

= (-1/2cos(x) + 1/8cos(2x))⁴

Therefore, the blanks in the original identity can be filled with "-1/2cos(x)" and "2x", respectively.

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Answer:

What does the circled part of the picture represent?

A)  a point

B)  a line

C)  line segment

D)  ray

Step-by-step explanation:

it is a btw

The graph of the function has zeros of 0 and 3, two distinct real zeros, and no complex zeros.

What is a function?

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have a function:

y= x²(x² - 6x + 9)

We can write it as a:

y=x²(x-3)²

To find the zeros equate to the function with the zero.

y = 0

x²(x-3)² =0



First, take  x²=0  we get:

x = 0

Now

(x - 3)² =0

x - 3 = 0

x = 3

Thus, the graph of the function has zeros of 0 and 3, two distinct real zeros, and no complex zeros.

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Answer:

B) The mean increases by 2.4 because the mean is 1149 and there 6 outliers.

Edmund spent $63.50 on toys and $28 on new clothes, for a total cost of $91.50.

Edmund had $140 and he decided to spend some of that money on toys and some on new clothes. To calculate how much he spent altogether, we need to first figure out how much he spent on each item. For toys, he spent 3/7 of his total money, which is equal to $63.50. For new clothes, he spent 1/5 of his total money, which is equal to $28. Now that we know how much he spent on each item, we can add these two numbers together to figure out how much he spent altogether. When we add $63.50 and $28, we get a total of $91.50. This means that Edmund spent $91.50 on toys and new clothes altogether.

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The length and width of the rectangle are 7 cm and 8 cm

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

The length and width of a rectangle are consecutive integers

This means that

Length = x

Width = x + 1

So, we have

Area = x * (x + 1)

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

x * (x + 1) = 56

Express 56 as 7 * 8

So, we have

x * (x + 1) = 7 * 8

This means that

x = 7

So, we have

Length = 7

Width = 7 + 1

Length = 7

Width = 8

Hence, the length is 7 cm

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Answer: 2.2

Step-by-step explanation:

Q1 = 7.75th item

Q3 = 23.25th item

Given,For a normal distribution with mean 50 and standard deviation 15,To find Q1 and Q3Formula for Q1 and Q3:Q1 = (n + 1)/4Q3 = 3(n + 1)/4Here, n = total number of observationsn = 2 × 15 = 30Thus, n + 1 = 31We know that for a normal distribution the Z values for Q1 and Q3 are -0.67 and 0.67 respectively.Normal distribution is a statistical model that describes the randomness of a variable in a population. It is symmetric around the mean. The mean is an essential property of a normal distribution. The standard deviation is the amount of variability among the observations that a distribution has.Mean = 50Standard deviation = 15Q1 = (n + 1)/4 = (30 + 1)/4 = 7.75th itemQ3 = 3(n + 1)/4 = 3 × (30 + 1)/4 = 23.25th itemThe 7.75th item and 23.25th item are calculated with the help of the formula.

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By answering the abοve questiοn, we may state that Hence, using divide synthetic divisiοn and the Remainder Theοrem, we have established that P(-1) = -1.

Divisiοn, οne οf the fοur basic mathematical οperatiοns, is the prοcess οf cοmbining twο numbers tο create a new number. Other οperatiοns include additiοn, subtractiοn, and multiplicatiοn. Divisiοn is the reverse οf multiplicatiοn.

When yοu divide twelve intο its three equal parts, yοu get fοur in each grοup when yοu multiply three grοups οf fοur by twelve. Finding οut hοw many equal grοups are generated when sharing fairly—οr hοw many peοple are in each grοup—is the fundamental purpοse οf sharing. Tο divide is tο separate intο twο οr mοre grοups, classes, sectiοns, οr regiοns οf equal size.

In οrder tο evaluate P(c) using synthetic divisiοn and the Remainder Theοrem, we take the fοllοwing actiοns:

[tex]-1 | 3 10 1\s|_______[/tex]

[tex]-1 | 3 10 1\s| \s3[/tex]

[tex]-1 | 3 10 1\s| \s3\s-13[/tex]

Write the sum οf the twο numbers yοu just nοted dοwn underneath the fοllοwing cοefficient, 1:

[tex]-1 | 3 10 1\s| \s3\s-13\s-1[/tex]

The divisiοn's final value is the leftοver amοunt. The Remainder Theοrem states that this number is equal tο P(-1), which is what we were lοοking fοr. Hence, P(-1) equals 1.

Hence, using synthetic divisiοn and the Remainder Theοrem, we have established that P(-1) = -1.

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We can use the Remainder Theοrem tο cοnclude that the value[tex]P(-1) = 3(-1)^2 + 10(-1) + 1 = 3 - 10 + 1 = -6.[/tex]

Synthetic divisiοn is a shοrthand methοd οf dividing a pοlynοmial by a linear factοr οf the fοrm (x - c), where c is a cοnstant. It is a methοd οf pοlynοmial lοng divisiοn that simplifies the prοcess and reduces the number οf steps required.

Tο evaluate P(-1) using synthetic divisiοn and the Remainder Theοrem, we can fοllοw these steps:

Step 1: Write the cοefficients οf the pοlynοmial P(x) in οrder οf decreasing degree, including any missing terms with a cοefficient οf 0. In this case,

[tex]P(x) = 3x^2 + 10x + 1[/tex]

Step 2: Set up the synthetic divisiοn table by placing the value οf c, which is -1 in this case, in the leftmοst cοlumn and writing the cοefficients οf the pοlynοmial in the secοnd cοlumn:

-1 | 3 10 1

Step 3: Bring dοwn the first cοefficient, which is 3, intο the third cοlumn:

-1 | 3 10 1

---------

3

Step 4: Multiply the value in the third cοlumn by the value οf c, which is -1, and write the result in the fοurth cοlumn:

-1 | 3 10 1

---------

3 -3

Step 5: Add the values in the secοnd and fοurth cοlumns and write the result in the fifth cοlumn:

-1 | 3 10 1

---------

3 -3 0

Step 6: The value in the last cοlumn, 0, is the remainder when P(x) is divided by x + c, which is x + 1 in this case. Therefοre, we can use the Remainder Theοrem tο cοnclude that P(-1) = 0.

Thus, [tex]P(-1) = 3(-1)^2 + 10(-1) + 1 = 3 - 10 + 1 = -6.[/tex]

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The expression is always positive Philip's statement is always true.

The expression -p + 5 + p can be written as -p + 5 + p = -p + p + 5,

which simplifies to 5, no matter what the value of p is.

An expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division. Expressions may or may not have an equal sign. Expressions can be evaluated by replacing any variables with specific values and then simplifying the resulting expression using the order of operations.

Therefore, the expression is always positive and Philip's statement is correct.

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The correct answer is option A) Increasing.

The given question is regarding the function and its behavior. To determine whether a given function is increasing or decreasing, we should first find its derivative. Then, if the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.A function is given as: yearn = f (2000, 2015)Here, the independent variable is "year," and the dependent variable is "n." Thus, to find out whether this function is increasing or decreasing, we need to find the derivative of this function:$$\frac{dy}{dx}=\frac{dy}{dn}*\frac{dn}{dx}$$$$\frac{dy}{dx}=0.028$$Since the derivative is positive, it means the function is increasing. Therefore, the correct answer is option A) Increasing.

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The measure of angle H is given as 67.5 degrees

The measure for angle I is 112.5 degrees

The question tells us that ∠F must be 67.5°

from the sign, the angles H and the angle F are vertical angles.

Hence the value of ∠F = ∠H

∠H = 67.5°

From the transversal, we can see that the angle E and angle I are corresponding angles

to get angle E

= 67.5° + ∠E = 180 (angles on a straight line)

∠E = 180 - 67.5

∠E = 112.5 degrees

Since ∠E and ∠I are corresponding angles, ∠I = 112.5 degrees

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The stop sign is a regular octagon, so the measure of ∠F must be 67.5°. What is the measure of angle H? Explain what is the measure of angle i ? explain

The overall area of the exclamation point at the Little Havana billboard is about 24 square ft while rounded to the nearest square foot.

To discover the total area of the exclamation point, we need to calculate the area of the sector and the area of the circle, after which add them collectively.

First, let's find the area of the sector. The formula for the area of a circle area is:

Area of sector = (angle/360) x π x radius^2

Substituting the given values, we get:

Area of sector = [tex](24/360) x π x 9^2 = 16.62 ft²[/tex]

Next, let's find the area of the circle. The components for the area of a circle is:

Area of circle = π x radius^2

Substituting the given value, we get:

Area of circle [tex]= π x 1.5^2 = 7.07 ft²[/tex]

Now, we are able to add the areas of the sector and the circle to get the whole area of the exclamation point:

[tex]6.62 feet² + 7.07 feet² = 23.69 ft²[/tex]

Therefore, the overall area of the exclamation point at the Little Havana billboard is about 24 square ft while rounded to the nearest square foot.

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Answer:

To compare the deals, we need to find the price per milliliter of lemonade for each deal.

For the first deal, the price per milliliter is:

94p / 500ml = 0.188p/ml

For the second deal, the price per milliliter is:

£1.44 / 750ml = 0.192p/ml

Therefore, the first deal is better as it has a lower price per milliliter of lemonade.

The perimeter of the triangle is  72 √5 / 3 units.

The perimeter of a triangle is the sum of the whole three sides of the triangle. The triangle above is an equilateral triangle.

An equilateral triangle has all it sides and angles congruent to each other.

Therefore, the perimeter of the triangle can be found as follows:

Let's find the side of the triangle using trigonometric ratios,

sin 60 = opposite / hypotenuse

sin 60 = 4√15 / h

cross multiply

h = 4√15 ÷ √3 / 2

h = 4√15 × 2 / √3

h = 8√15 / √3

Hence,

hypotenuse side = 8√45 / 3

perimeter of the triangle = 8√45 / 3 + 8√45 / 3 + 8√45 / 3

perimeter of the triangle = 8√45 + 8√45 + 8√45 / 3

perimeter of the triangle = 24√45 / 3

perimeter of the triangle = 72 √5 / 3 units

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Answer:

-7.9,   -7.881,   -7.88,   0.07,   7.03

Step-by-step explanation:

Numbers provided: 0.07, -7.88, -7.9, 7.03, -7.881

Finding the volume of a figure is a useful tool for solving practical problems that involve 3D space and quantities, such as capacity, mass, or density.

Finding the volume of a figure is a common mathematical calculation used in various fields, such as architecture, engineering, physics, and chemistry. The volume of a figure is a measure of the amount of space that it occupies in three-dimensional (3D) space, such as a cube, a cylinder, a sphere, or a complex shape.

One example of a question that can be answered by finding the volume of a figure is "How much water can a swimming pool hold?" The swimming pool is a 3D figure that can be approximated as a rectangular prism, with a length, width, and depth. By multiplying these three dimensions, we can find the volume of the swimming pool, which represents the amount of water it can hold. This information is useful for designing and constructing the swimming pool, as well as for filling and maintaining it.

Another example is "How much concrete is needed to build a retaining wall?" The retaining wall is a 3D figure that can be approximated as a trapezoidal prism, with a length, height, and thickness. By multiplying these three dimensions, we can find the volume of the retaining wall, which represents the amount of concrete required. This information is useful for estimating the cost and resources needed for the project.

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The z-scores for which 50% of the distribution's area lies between -z and z are: z = -0.675 and z = 0.675.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The normal distribution is symmetric, meaning that the middle 50% of the scores is given between these following percentiles:

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