Numeros que multiplicados den 30 y sumados o restados den -11

Answers

Answer 1

Los dos números que multiplicados den 30 son 5 y 6. Para encontrar dos números que sumados o restados den -11, debemos verificar todas las posibles combinaciones. Al hacerlo, descubrimos que -5 y -6 sumados dan -11. Por lo tanto, los dos números son 5 y -6.

Answer 2
The answer is 29 because 30-11=29

Related Questions

what is the value of the expression
y(1/2 + z) +6
when Y= 2 and z = 3/4
a 57/8
b 19/2
c 17/2
d 22/3

Answers

Answer: C.17/2

Step-by-step explanation: because 2(1/2+3/4)+6

So first (1/2+3/4)= 5/4

Then 2(5/4)=5/2

Finally 5/2+6=17/2

please answer i really need it

Answers

The answer of the question based on the container is in the shape of cube answer is, the volume of the container is (1/512)t⁹u¹², not 1/24t⁹u¹² as Parker claimed.

What is Volume?

A volume is  measure of  amount of space occupied by  three-dimensional object. It is typically measured in a cubic units, like  cubic meters, cubic centimeters, or cubic feet.

Parker is not correct.

The volume of a cube is calculated by multiplying the length, width, and height of the cube. In this case, the length of the container is given as 1/8t³u⁴, but we do not have any information about the width and height. Assuming that the width and height are also 1/8t³u⁴, the volume of the cube would be:

V = (1/8t³u⁴) x (1/8t³u⁴) x (1/8t³u⁴)

V = (1/512)t⁹u¹²

Therefore, the volume of the container is (1/512)t⁹u¹², not 1/24t⁹u¹² as Parker claimed.

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The radius, , R of a sphere is 5.6 cm. Calculate the sphere's volume, V. use 3.14 for pie will give brainliest

Answers

After addressing the issue at hand, we can state that Hence, the sphere's linear equatiοn vοlume is rοughly 904.32 cm3.

What is a linear equatiοn?

The algebraic equatiοn y = mx + b is knοwn as a linear equatiοn. M serves as the y-intercept, and B serves as the slοpe. The previοus clause has twο variables, y and x, and is sοmetimes referred tο as a "linear equatiοn with twο variables". Bivariate linear equatiοns are thοse with twο independent variables. The fοllοwing are a few examples οf linear equatiοns: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equatiοn takes the fοrm y = mx + b, with m denοting the slοpe and b denοting the y-intercept, it is referred tο as being linear. The term "linear" refers tο an equatiοn having the fοrm y=mx+b, where m stands fοr the slοpe and b fοr the y-intercept.

The fοllοwing equatiοn determines a sphere's vοlume:

V = (4/3)πR³

where R is the sphere's radius and is a cοnstant that rοughly equates tο 3.14.

R = 5.6 cm and = 3.14 are substituted intο the equatiοns tο yield:

V = (4/3) x 3.14 x (5.6)³

V = 4.19 x (5.6) x (5.6) x (5.6)³

V= 904.32 cm³ (rοunded tο twο decimal places)

Hence, the sphere's vοlume is rοughly 904.32 cm³.

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1. Explain what Marc did in steps 4 and 5.

2. Why did he do this?

3. Create your own radical equation and explain how to solve it.

4. Is there an extraneous solution to your equation?

Answers

A radical equation is √(x + 2) = 4 - x and the extraneous solution is x = 7

How to solve

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

The solution to a radical equation

In steps 4 and 5, we have

x = ∛5 * 5 * 5 * 5

x = 5∛5¬ * 5¬ * 5¬ * 5

The above steps are carried out because it would simplify the radical expression to its simplest form

The reason it is done is to have the value of x in its simplest form

Create a radical expression

Here's an example of a radical equation:

√(x + 2) = 4 - x

Square both sides

x + 2 = 16 - 8x + x^2

Evaluate the like terms

x^2 - 9x + 14 = 0

Factor the quadratic equation

(x - 2)(x - 7) = 0

Solve for x:

x = 2 or x = 7

Is there an extraneous solution to your equation?

For x = 2:

√(2 + 2) = 4 - 2

√4 = 2

2 = 2

This is true, so x = 2 is a valid solution.

For x = 7:

√(7 + 2) = 4 - 7

√9 = -3

3 = -3

This is not true, so x = 7 is not a valid solution.

So, there is an extraneous solution

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Carrie missed 9.6% of the problems on a test. The test had a total of 125 problems. Which of the following is the best estimate of the number of problems Carrie missed?

Answers

The best estimate οf the number οf problems she missed is 12

What are number problems ?

When sοlving a number prοblem, yοu are provided with hints about one or more numbers, and you must use these hints to create an equation. The Problem-Solving Strategy can be practised with number problems, which don't occur frequently but are a gοod starting point.

To find the best estimate οf the number of problems Carrie missed, we can start by calculating what 9.6% of 125 is:

9.6% οf 125 = 0.096 x 125 = 12

This means that Carrie missed apprοximately 12 problems on the test. Therefore, the best estimate of the number of problems she missed is 12.

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Complete Questiοn:

Carrie missed 9.6% οf the problems on a test. The test had a total of 125 problems. Which of the following is the best estimate of the number of problems Carrie missed? F 123 G 13 H2 3 113 OPEN ENDED QUESTION This is a proportion question: What numbers would you fill into the ratios? 6 d a= b= C= ulube d='

Simplify: (9x^3+2x^2-5x+4)-(5x^3-7x+4)
Show all steps used to solve this problem and write your final answer in factored form in the space provided.

Answers

To simplify (9x^3+2x^2-5x+4)-(5x^3-7x+4), we can start by combining like terms.

First, we need to distribute the negative sign to the second set of parentheses:

(9x^3+2x^2-5x+4) - 1(5x^3-7x-4)

= 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4 (distributing the negative sign)

= (9x^3 - 5x^3) + 2x^2 - 5x + (4 - 4 + 7x) (grouping like terms)

= 4x^3 + 2x^2 + 2x (combining like terms)

Therefore, the simplified expression is 4x^3 + 2x^2 + 2x.

We cannot factor this expression further as there are no common factors between the terms.

1) Remove parentheses.

[tex]9x^{3}+ 2x^{2} -5x+4-5x^{3} +7x-4[/tex]

2) Collect like terms.

[tex](9x^{3}-5x^{3})+2x^{2} +(-5x+7x)+(4-4)[/tex]

3) Simplify.

[tex]4x^{3}+2x^{2}+2x[/tex]

--------------------------(DONE)---------------------------------

Joules and calories are two different units of energy. The equation j=0. 239c

relates the measures, where c

stands for calories and j

stands for joules

Answers

If the equation j=0. 239c, the food that contains 200 calories provides 47.8 joules of energy.

To convert the energy in calories to joules using the equation j = 0.239c, we can simply substitute the given value of c (200 calories) into the equation and solve for j:

j = 0.239c

j = 0.239 x 200

j = 47.8 joules

It's important to note that joules are the standard unit of energy in the International System of Units (SI), while calories are more commonly used in nutrition and food science.

The conversion factor between joules and calories is not exact, as it depends on the definition of the calorie used.

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Complete question is:

Joules and calories are two different units of energy. The equation j=0. 239c relates the measures, where c stands for calories and j stands for joules. If a food contains 200 calories, how many joules of energy does it provide?

A 10ft pole casts a 30ft shadow. What is the angle of elevation of the sun? For full credit, you must draw the triangle, label the sides and angle, and determine the answer. You may use a calculator for this problem.

Answers

18.43°

Given:A 10ft pole casts a 30ft shadow.To find:The angle of elevation of the sun.Diagram:Let AC be the height of the pole and BC be its shadow cast on the ground by the pole.Now, AB represents the ray of the sun. Angle ABC is the angle of elevation of the sun.Measurement:We have AC = 10ft, BC = 30ft.Let x be the angle of elevation of the sun. Then we have, tan(x) = opposite side/adjacent side = AC/BC = 10/30 = 1/3.To find the value of x, we have to take an inverse tangent of 1/3 on the calculator. We have,x = tan-1(1/3)x = 18.43°Therefore, the angle of elevation of the sun is 18.43°.

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Figure ABCD has vertices A(−3, 2), B(2, 2), C(2, −4), and D(−3, −2). What is the area of Figure ABCD?
a
5 square units
b
20 square units
c
25 square units
d
40 square units

Answers

After using the formula of a trapezoid, we know that the area is 25 units².

What is the area?

The size of a patch on a surface is determined by its area.

Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The shape can also be placed on a grid, and the number of squares can be counted: The area of the rectangle is 15.

For instance, if each square is 1 meter in size, the area is 15 m² (15 square meters).

So, we  have the vertices as follows:

A(−3, 2), B(2, 2), C(2, −4), and D(−3, −2)

See, the plotted vertices on the graph.

The figure is a trapezoid.

The area of a trapezoid is as follows:

A = 1/2(AD+BC)AB

Now, find the distance:

AD = 4

BC = 6

AB = 5

Substitute as follows:

A = 1/2(4+6)5 = 25 units²


Therefore, after using the formula of a trapezoid, we know that the area is 25 units².

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Please please PLEASE HELP!!!

Answers

Answer:

47.5

Step-by-step explanation:

We know that a semicircle is half the area of a circle so to answer this question we can simply find the area of a circle with a diameter of 11cm and then half it!

The area of a circle can be found using the equation: πr²

The radius of the circle would be 5.5cm as we have to be half the diameter.

This means to work it out we would be doing...

π × 5.5² = 95.0331777711

Now we have to half it...

95.0331777711 ÷ 2 = 47.5165888855 or 47.5 rounded to 1d.p

Hope this helps, have a lovely day! :)

How many different ways can the letters of ​"notebook​" be​ arranged?

Answers

There are 40,320 different ways to arrange the letters of the word "notebook".


The word "notebook" contains 8 letters.

To calculate the number of different ways the letters can be arranged,

we can use the formula for permutations,

which is: n! / (n-r)!

where, n is the total number of items and r is the number of items selected.

For "notebook",

We want to find the number of permutations of all 8 letters,

So, n = 8 and r = 8.

Plugging these values into the formula,

we get: 8! / (8-8)! = 8!
Simplifying, 8! is equal to: 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320


Therefore, there are 40,320 different ways to arrange the letters of the word "notebook".


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Divide and simplify. Please show all steps to simplifying.


(1/x+4) ÷ (x-3/ x²+7x+12)

Answers

The polynomial fraction division (1/x + 4) ÷ (x - 3/x² + 7x + 12) = (x + 3)/(x - 3)

What is a polynomial?

A polynomial is a mathematical expression in which the least power of the unknown is 2.

Since we are given the polynomial expression

(1/x + 4) ÷ (x - 3/x² + 7x + 12).

We proceed to divide and simplify as follows.

(1/x + 4) ÷ (x - 3/x² + 7x + 12) = (1/x + 4) × (x² + 7x + 12)/(x - 3)

= (x² + 7x + 12)/(x - 3)(x + 4)

To simplify further, we factorize the numerator. So, we have that

x² + 7x + 12 = x² + 4x + 3x + 12

Factorizing, we have that

x² + 4x + 3x + 12 = x(x + 4) + 3(x + 4)

= (x + 3)(x + 4)

So, we have that

x² + 7x + 12 = (x + 3)(x + 4)

So, substituting this into the fraction, we have that

(x² + 7x + 12)/(x - 3)(x + 4) = (x + 3)(x + 4)/(x - 3)(x + 4)

Cancelling out (x + 4), we have that

(x² + 7x + 12)/(x - 3)(x + 4) = (x + 3)/(x - 3)

So, we have (1/x + 4) ÷ (x - 3/x² + 7x + 12) = (x + 3)/(x - 3)

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Ruben and Estelle just had business cards made. Ruben's printing company charged a one-time setup fee of $8 and then $18 per box of cards. Estelle, meanwhile, ordered hers online. They cost $6 per box. There was no setup fee, but she had to pay $20 to have her order shipped to her house. By coincidence, Ruben and Estelle ended up spending the same amount on their business cards. How much did each spend? How many boxes did each buy?

Answers

Ruben ordered 0 boxes of cards and Estelle ordered 2 boxes of cards. Ruben spent $8 and Estelle spent $20 + $6(2) = $32.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's start by setting up equations for the total cost of Ruben and Estelle's business cards. Let R be the number of boxes of cards Ruben ordered and E be the number of boxes Estelle ordered. Then we have:

Ruben's cost = 8 + 18R

Estelle's cost = 6E + 20

We know that Ruben and Estelle spent the same amount, so we can set their costs equal to each other and solve for R and E:

8 + 18R = 6E + 20

18R - 6E = 12

3R - E = 2

This equation tells us that Ruben ordered two more boxes of cards than Estelle. We can use trial and error to find the values of R and E that satisfy this equation and give us the same cost:

If R = 4 and E = 2, then Ruben's cost = 8 + 18(4) = 80 and Estelle's cost = 6(2) + 20 = 32, which are not equal.

If R = 3 and E = 1, then Ruben's cost = 8 + 18(3) = 62 and Estelle's cost = 6(1) + 20 = 26, which are not equal.

If R = 2 and E = 0, then Ruben's cost = 8 + 18(2) = 44 and Estelle's cost = 6(0) + 20 = 20, which are not equal.

If R = 1 and E = -1, then Ruben's cost = 8 + 18(1) = 26 and Estelle's cost = 6(-1) + 20 = 14, which are not equal.

If R = 0 and E = -2, then Ruben's cost = 8 + 18(0) = 8 and Estelle's cost = 6(-2) + 20 = 8, which are equal.

Therefore, Ruben ordered 0 boxes of cards and Estelle ordered 2 boxes of cards. Ruben spent $8 and Estelle spent $20 + $6(2) = $32.

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Determine the indicated probability for a Poisson random variable with the given values of λ and t. Λ = 0. 8, t = 5, P(More than 3)

Answers

The probability of obtaining more than 3 events in a Poisson random variable with a mean of λ = 0.8 and a time period of t = 5 is approximately 0.3272 or 32.72%.

To determine the probability of obtaining more than 3 events in a Poisson random variable with a mean of λ = 0.8 and time period of t = 5, we can use the Poisson probability distribution formula, which is:

P(X > k) = 1 - P(X ≤ k)

= 1 - e^(-λ) * ∑(i=0 to k) (λ^i / i!)

where X is the Poisson random variable, k is the number of events, λ is the mean or expected number of events, and e is the mathematical constant approximately equal to 2.71828.

In this case, we want to find P(X > 3), which means we need to compute P(X ≤ 3) first:

P(X ≤ 3) = e^(-λ) * ∑(i=0 to 3) (λ^i / i!)

= e^(-0.8) * [1 + 0.8 + (0.8^2 / 2!) + (0.8^3 / 3!)]

= 0.6728

Then, we can find P(X > 3) using the formula:

P(X > 3) = 1 - P(X ≤ 3)

= 1 - 0.6728

= 0.3272

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Please help I really struggle with these !!!

Answers

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =312 \end{cases}\implies s=\cfrac{(312)\pi (4)}{180}\implies s=\cfrac{104\pi }{15}\implies s\approx 21.8[/tex]

The point Q(4,-3) is rotated 180° clockwise around the origin. What are the coordinates of the resulting point, Q'?

Answers

Check the picture below.

Work out the size of angle x give reasons for your answer

Answers

Answer:

x° = 80

Step-by-step explanation:

Remember a line is 180°

Because B is = 100°

B and x are interior angles meaning B + x = 180°

100° + x = 180°

x = 80°

Answer:

80 °

Step-by-step explanation:

[tex]\frac{360-2*100}{2} = 80[/tex]

An auditorium has 288
seats distributed evenly in
6 rows. Find the unit rate of seats per row.

Answers

288/6 = 48 not sure if this is the answer you are looking for though

Answer: To find the unit rate of seats per row, we can divide the total number of seats by the number of rows:

288 seats ÷ 6 rows = 48 seats per row

Therefore, the unit rate of seats per row is 48.

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*see image* The number of wolves in a forest
increases by 25% each year.
This year, there are 400 wolves in the
forest.
Calculate the number of wolves that there
will be in the forest
a) after 1 year.
b) after 2 years.

Answers

Answer:

Below

Step-by-step explanation:

After 1 year there will be 25 % more than 400   or    1.25 * 400 = 500 wolves      after two years there will be 25 % more than 500 wolves

   = 1.25 * 500 = 625 wolves

FLOORING miguel is putting hardwood flooring in a hallway that measures 5 feet by 18 feet. The wood he has chosen is $5.48 per square foot. What is the range of the actual cost of putting the flooring in the hallway

Answers

Answer:

The cost of putting in the flooring is $493.20

Step-by-step explanation:

First you have to find the area

area = length times width

area = 5 x  18

a = 90 feet

The cost will be 90 x 5.48 = 493.20

Helping in the name of Jesus.

A 3-pack of baseball caps costs $4.93. What is the unit price, rounded to the nearest cent?

Answers

Answer:

$1.64

Step-by-step explanation:

To find the unit price, we need to divide the total cost by the number of units. In this case, we have 3 caps in a pack, so the unit price is:

$4.93 / 3 = $1.64333333...

Rounding to the nearest cent, the unit price is $1.64.

What is wrong with step 3 and 6?

Answers

Step 3 is incorrect because it states that if all the sides of two figures are proportional then those two figures are similar.

Step 6 is incorrect because it states that if needed, we should reflect A B C D over segment WX. This is incorrect because reflection is not required to prove two figures are similar.

What is a segment?

A segment is part of a market that is specifically targeted for a product or service. It is defined by characteristics such as demographics, geography, buying behavior, and interests. Segmentation helps companies to identify their target market and direct their marketing activities accordingly.

We can prove two figures are similar using a sequence of transformations that includes translations, rotations, and dilations, but not reflections. Reflection may be used to help visualize similar figures, but it is not necessary to prove that they are similar.

from the question:

Step 3 is erroneous since it implies that two figures are identical if all of their sides are proportionate. This isn't always the case because two figures can resemble one another without having sides that are proportional. When two figures of the same shape, such as two squares or two circles, proportional sides can only ensure that the two figures are identical.

Step 6 is erroneous because it instructs us to reflect A, B, C, and D over segment WX if necessary. This is false since the similarity between two figures can be established without thought. Using a series of transformations that includes translations, rotations, and dilations but not reflections, we may demonstrate the similarity of the two figures. Reflection may be employed to aid in seeing related figures, but it is not required to establish their similarity.

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Help with all please

Answers

A scatter plot of the data is shown below.

An equation of a reasonable trend line is y = x - 0.1.

The arm span of someone who is 1.6 m tall is 1.5 meter.

The arm span of someone who is 2.2 m tall is 2.1 meters.

How to write an equation of the line of best fit for the data?

In order to write a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the heights would be plotted on the x-axis of the scatter plot while the arm span would be plotted on the y-axis of the scatter plot.

At point (2.0, 1.9), an equation of this line can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 1.9 = (2.0 - 1.9)/(2.1 - 2.0)(x - 2.0)

y - 1.9 = (x - 2.0)

y = x - 0.1.

For someone who is 1.6 m tall, their arm span is given by;

y = x - 0.1

y = 1.6 - 0.1.

x = 1.5 meter.

For someone who is 2.2 m tall, their arm span is given by;

y = x - 0.1

y = 2.2 - 0.1.

x = 2.1 meters.

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please help!! answers needed now-- work only NEEDS to be shown for question 3

use the triangle to answer the questions:

1. What is the exact length of the base of the triangle, y?

2. What is the exact height of the triangle, x?

3. What is the exact area of the triangle? Leave your answer in radical terms.
Show your work

4. What is the area of the triangle to the nearest hundredth of a square in?

Answers

Answer:

1. y = 5

2. x = 8√11

3. A = 20√11

4. 20√11 = 66.33

Step-by-step explanation:

1. sin(30) = y/10

=> 1/2 = y/10

y = 5

2. Pythagorean theorem: c^2 = a^2 + b^2

10^2 = x^2 + y^2

10^2 = x^2 + 5^2

x^2 = 100 - 25

x^2 = 75

x = √75 = 8√11

3. Are of right △: A=ab/2 = xy/2 = 5 x 8√11 x 1/2 = 20√11

4. 20√11 = 66.33

pressure=Force/area A brake pad has an area of 0.35m² and has a force of 140 N applied to it. Calculate the pressure on the brake pad in N/m². If you answer is a decimal, give it to 1 d.p.​

Answers

Answer:

Step-by-step explanation:

140/0.35squared

=1142.857142

to 1 d,p=1142.9

a local university reports that 3% of their students take their general education courses on a pass/fail basis. assume that fifty students are registered for a general education course. what is the expected number of students who have registered on a pass/fail basis?

Answers

The expected number of students who have registered for the course on a pass/fail basis is 1.5.

To answer the given question, we can use the formula for expected value:
Expected Value = (Probability of Event Occurring) x (Number of Trials)
Here, the event is students taking the course on a pass/fail basis, and the number of trials is the total number of students registered for the course.

We are given that the probability of a student taking the course on a pass/fail basis is 3%, or 0.03.
Using this information,

we can substitute the values into the formula and calculate the expected number of students taking the course on a pass/fail basis:
Expected Value = (0.03) x (50)
Expected Value = 1.5.

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Alonzo is sitting in a movie theater, 21 meters from the screen. The angle of elevation from his line of sight to the top of the screen is 17°, and the angle of
depression from his line of sight to the bottom of the screen is 38°. Find the height of the entire screen.
Do not round any intermediate computations. Round your answer to the nearest tenth.
Note that the figure below is not drawn to scale.

Answers

The access to a full is [tex]23[/tex] m in height.

What kind of height is that?

Height is a measurement of vertical distance, or how high or some someone is (how tall they were) "The altitude of an aircraft in flight is around 10,000 m," for instance.

How can I determine my height?

Ensure that your shoulders are level, arms are at your sides, and legs are straight. The youngster or adolescent should maintain a straight gaze that is parallel to the ground. Measure the kid or adolescent when they are standing with their head, shoulders, buttocks, & heels on a flat surface.

The calculation of the total screen height is displayed below;

[tex]= a + b[/tex]

where

[tex]a = 21 * tan 17[/tex] degrees

[tex]= 21 * 0.305[/tex]

[tex]= 6.4 m[/tex]

And

[tex]b = 21 * tan 38[/tex] degree

[tex]= 21 * 0.781[/tex]

[tex]= 16.4 m[/tex]

So, the height of the entire screen is

[tex]= 6.4 m + 16.4 m[/tex]

[tex]= 22.8 m[/tex]

[tex]= 23 m[/tex]

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6. Provide FOUR ways a positive attitude could help you to avoid interpersonal conflict (4 x 2) (8) between you and people you may meet after school.​

Answers

Being Respectful, Practicing Empathy, Being Open-Minded, Remaining Patient

What is attitude?

Attitude is an individual's way of perceiving and responding to their environment. It is a state of mind that influences how people think, feel, and behave. Attitudes are shaped by experiences, beliefs, and values, and they can be positive or negative, depending on the situation.

1. Being Respectful: A positive attitude helps to foster respect between yourself and those you meet. Respect is the foundation of any successful relationship, and having a positive attitude can help ensure that respect is maintained in the face of any potential conflicts.

2. Practicing Empathy: Having a positive attitude allows you to practice empathy and understanding of the people around you. Taking the time to understand the perspectives of others can help to prevent misunderstandings and conflicts.

3. Being Open-Minded: A positive attitude allows you to remain open-minded and flexible in any situation. This can help to stave off interpersonal conflicts by allowing you to better understand the needs and wants of those around you.

4. Remaining Patient: A positive attitude can help you remain patient and understanding of people in your life. Being patient in the face of any potential conflicts can help to resolve issues in a peaceful manner and prevent them from escalating.

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The historical returns on a portfolio had an average return of 12 percent and a standard deviation of 18 percent. Assume that returns on this portfolio follow a bell-shaped distribution. a. What percentage of returns were greater than 30 percent? Percentage of returns 16 b. What percentage of returns were below -24 percent?

Answers

The percentage of returns that were greater than 30 percent is 16% and the percentage of returns that were below -24 percent is 2.5%..

The historical returns on a portfolio had an average return of 12 percent and a standard deviation of 18 percent. We can use the Empirical Rule to answer the questions about the percentage of returns that were greater than 30 percent and below -24 percent. The Empirical Rule states that for a bell-shaped distribution:

- 68% of the data falls within 1 standard deviation of the mean
- 95% of the data falls within 2 standard deviations of the mean
- 99.7% of the data falls within 3 standard deviations of the mean

a. What percentage of returns were greater than 30 percent?

30 percent is 1 standard deviation above the mean (12 percent + 18 percent = 30 percent). Therefore, according to the Empirical Rule, 68% of the data falls within 1 standard deviation of the mean, or between -6 percent and 30 percent.

This means that 32% of the data falls outside of this range, with 16% above 30 percent and 16% below -6 percent. So the percentage of returns that were greater than 30 percent is 16%.

b. What percentage of returns were below -24 percent?

-24 percent is 2 standard deviations below the mean (12 percent - 2*18 percent = -24 percent). Therefore, according to the Empirical Rule, 95% of the data falls within 2 standard deviations of the mean, or between -24 percent and 48 percent.

This means that 5% of the data falls outside of this range, with 2.5% above 48 percent and 2.5% below -24 percent. So the percentage of returns that were below -24 percent is 2.5%.

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The sides of a triangle are 54, 31, and 69. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.

Answers

The triangle is acute since a² + b² < c² ( 2916 + 961  < 4761.

Is the triangle is right, acute, or obtuse?

To determine whether the triangle is right, acute, or obtuse, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

We can start by finding the longest side of the triangle, which is the hypotenuse.

hypotenuse = 69

Now we can use the Pythagorean Theorem to check whether the triangle is right:

a² + b² = c²

where a and b are the lengths of the other two sides of the triangle.

Plugging in the values we know, we get:

54² + 31² = 69²

Simplifying, we get:

2916 + 961 = 4761

3877 = 4761

Since this equation is not true, we know that the triangle is not a right triangle.

To determine whether the triangle is acute or obtuse, we need to compare the sum of the squares of the lengths of the shorter sides to the square of the length of the longest side:

a² + b² < c² => the triangle is acute

a² + b² > c² => the triangle is obtuse

c² = 69² = 4761

Plugging in the values we know, we get:

54² + 31² = 2916 + 961 = 3877

Since 3877 < 4761, we can conclude that the triangle is acute.

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