Using the special right triangle shortcuts, what is the length of the hypotenuse of a 45-45-90 triangle with a leg length of 8?

The length of the guy wire, to the nearest foot is 23 feet.

Based on the information provided, we can logically deduce that triangle ABE (ΔABE) is similar to triangle (ΔCDE) and the following parameters about the geometric figures;

Additionally, the corresponding sides of similar triangles are equal;

AB/CD = BE/DE

AB/6 = (9 + 4)/4

AB/6 = 13/4

AB = 19.5 feet.

By applying Pythagorean' theorem, side AE is given by:

AE = √(AB² + BE²)

AE = √(19.5² + 13²)

AE = 23.44 ≈ 23 feet.

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The point (if it exists) at which the following plane and line intersect: x=11;r(t)==11; for −[infinity] will be (11, t, 11)

We are given the equation of a plane and a line, but we need more information to determine if and where they intersect. Specifically, we need the equation of the plane in the form Ax + By + Cz = D, and we need the parametric equation of the line in the form x = x0 + at, y = y0 + bt, z = z0 + ct, where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector of the line.

Assuming that the equation of the plane is of the form Ax + By + Cz = D and the parametric equation of the line is of the form x = 11, y = t, z = 11 for all real numbers t, we can proceed as follows:

1. Substitute the parametric equation of the line into the equation of the plane to get an equation in t:

A(11) + B(t) + C(11) = D

2. Solve for t:

t = (D - A(11) - C(11)) / B

3. Substitute the value of t into the parametric equation of the line to get the point of intersection:

(11, t, 11)

This calculation assumes that the line and plane intersect at a single point. If the line is parallel to the plane, it may not intersect at all, or it may intersect in a line or a plane.

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In length 5.4 feet is equivalent to 164.592 centimeters.

Firstly, it is important to understand that length is a physical quantity that describes the size or distance of an object. The unit of length can vary depending on the system of measurement used. The Imperial system, which is commonly used in the United States, measures length in feet, whereas the metric system, which is used worldwide, measures length in centimeters.

Now, to convert 5.4 feet into centimeters, we need to use a conversion factor. One foot is equivalent to 30.48 centimeters, so we can multiply 5.4 feet by 30.48 to get the equivalent length in centimeters.

5.4 feet x 30.48 cm/1 foot = 164.592 cm

It is important to note that when dealing with measurements, it is crucial to use the appropriate unit of length to ensure accuracy and consistency.

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Answer:

Step-by-step explanation:

The sequence is in AP

a=-12, d= -4

Nth term is given by [tex]T_{n}=a+(n-1)d\\[/tex]

[tex]T_{n}=-12+(n-1)(-4) = -12-4n+4 = -4n-8[/tex]

[tex]T_{n}= -4n-8[/tex]

The output the last three characters of a string, we need to create a variable to store the string, assign the string to the variable, and use the string slicing method to extract the last three characters

To start, we need to create a variable to store our string. We can name this variable "str". Next, we need to assign our string to the variable. We can do this by using the assignment operator "=".

Now, we can begin manipulating the string to output the last three characters. To do this, we can use the string slicing method. This method allows us to extract a portion of the string by specifying the start and end indices. In this case, we want to start at the third-last character, so our start index will be -3. Since we want the last three characters, our end index will be -1. We can use this information to create the following code:

str = "hello"

last_three_characters = str[-3:-1]

Now, when we print the variable last_three_characters, it should output "lo". This is because the slicing method extracts the characters from the start index up to, but not including, the end index.

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Complete Question:

Write a program to the postfix of 3 is the last 3 characters of a string. Given a string input, output the last three characters of that string. Assume the string will always have at least three characters

(a) 27 outcomes in the sample space are : (1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3), (2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3), (3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) All outcomes in the event that all three members go to the same station are : (1,1,1), (2,2,2), (3,3,3)

(a) The 27 outcomes in the sample space can be represented as ordered triples, where each element corresponds to the station that each family member is assigned to. The possible values for each element are 1, 2, and 3. Therefore, the sample space consists of the following 27 outcomes:

(1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3),

(2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3),

(3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) The outcomes in the event that all three members go to the same station can be found by examining the 27 outcomes in the sample space and selecting those outcomes where all three elements are the same. Therefore, the outcomes in the event that all three members go to the same station are:

(1,1,1), (2,2,2), (3,3,3)

In these outcomes, all three family members are assigned to the same station. There are three such outcomes, since each family member can be assigned to any one of the three stations.

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The requried length of the segment CE in the given figure is 16 centimeters.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
From the given figure,
Applying the trig ratios in triangle ABC to evaluate BC,
tan60 = 12/BC
BC = 12/√3
BC = 4√3

Now,
BC = AD and ∠EAD = 90 - ∠ABC  [∠ABC = ∠ADC]
So ∠EAD = 90 - 60 = 30

Again in triangle ADE,
tan60 = ED/AD
ED = AD/√3
ED = 4√3/√√3
ED = 4

SO, the required length CE
= ED + DC
= 4 + 12
= 16 cm

Thus, the requried length of the segment CE in the given figure is 16 centimeters.

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The conversion method from milimeter to nanometer is Quantity in nanometer = quantity in milimeter × 10⁶.

In the question, the two short forms mm and nm are representative of milimeter and nanometer. As per the known information, the milimeter represents 1/10³ meters and nanometer represents 1/10⁹ meters. So, we see that the difference between the exponents of 10 is 6 (as 9 - 3 = 6).

Therefore, the conversion of milimeter to nanometer will be through the mentioned formula -

Quantity in nanometer = quantity in milimeter × 10⁶

For instance, the quantity 3 mili meters in nanometer will be calculated as follows.

Quantity in nanometer = 3 × 10⁶ nanometer

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Answer:

The probability of drawing a red marble then a yellow marble out of the bag is probably 0.48(Decimal) or 12/25(Fraction).

The expected population size after two generations is 216.

To calculate the expected population size after two generations using the given value of λ, we can use the formula:

[tex]Nt = N0 * lemda ^{t}[/tex]

where Nt is expected population size after t generations,

N0 is the initial population size, and lemda (λ) is the geometric growth rate.

Here, initial population size is N0 = 150, and the growth rate is λ = 1.2. We want to find the expected population size after two generations, so t = 2.

Putting these values into the formula, we get:

[tex]Nt = 150 * (1.2)^{2} \\Nt = 150 * 1.44\\Nt = 216[/tex]

Therefore, the expected population size after two generations is 216.

So, the correct answer is option (d) 216.

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The conversion of 750ml in oz is equal to 25.36 fluid ounces.

One- thousandth of a liter is a substitute to one milliliter.

Milliliters denoted by ml.

Ounces and fluid ounces are two unlike units.

1 fluid ounce is equal to the 1.04 oz weight.

US fluid ounce contain 29.6 milliliters and British fluid ounce contain 28.4 milliliters.

Ounce expressed by notation oz.

We can use the following formula to convert milliliters (ml) to fluid ounces (oz):

1 ml = 0.033814 oz

Here we want to convert the  750ml into oz

So, to convert 750 ml to oz,

We can multiply 750 by 0.033814:

750 ml × 0.033814 oz/ml

= 25.36 oz (rounded to two decimal places)

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An online calculator of simplifying fractions is a tool that can be used to reduce a fraction to its simplest form or lowest terms.

These calculators are easily accessible on the internet and are designed to make it easy for users to simplify fractions quickly and accurately. To use the calculator, users simply input the numerator and denominator of the fraction they wish to simplify.

The calculator then performs the necessary calculations to find the greatest common factor of the numerator and denominator and divides both by this factor to provide the simplified fraction. These calculators can be especially helpful for students and professionals who need to simplify a large number of fractions or who are learning how to simplify fractions for the first time.

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The result of the multiplication of -5.6 and -4/2 is given as follows:

11.2.

The multiplication operation for this problem is defined as follows:

-5.6 x -4/2.

A multiplication operation and a division operation have the same precedence, hence we can simplify the division as follows:

-4/2 = -2. (fraction is equivalent to a division operation).

Considering the simplified quotient, the multiplication is given as follows:

-5.6 x (-2)

As two terms with the same signal are multiplied, the product is positive, 5.6 x 2 = 11.2, hence the product is given as follows:

-5.6 x (-2) = 11.2.

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Answer:

11/20

Step-by-step explanation:

3/4 - 1/5

= 15/20 - 4/20

= 11/20

So, the answer is 11/20

Answer:

Plug in the variable (x) in the equation.

Step-by-step explanation:

once you plug it in, multiplied by two, and subtract by 3, and it should equal your y input

We can solve the given problem using conversion of Binomial to Normal distribution.

(The binomial distribution is defined as the discrete probability distribution which can only give two possible results in an experiment, that is either success or failure.)

The binomial distribution is converted to Normal distribution  when the number of total trial, denoted as n is sufficiently large and the probability of success ( or failure), represented as p is small.

Mean , E(x)= np

Variance, V(x) = npq

where  V(x) and E(x) are variance and mean of normal distribution.

Given,

n= 4590, p=  35%= 0.35, q= 0.65

Thus, E(x) = 4590 * 0.35 = 1606.5

V(x) = 4590 * 0.35* 0.65= 1044.225

Thus,  the probability the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35% is,

P( x > 1606.5)= P( x<= 1606.5)

                    = P( z= x-1606.5 / 1044.225)

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With the help of expression 6*33 we found that Mike took a total of 198 baseballs.

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.

Now,

Given that Total baseballs=363

Total trash bin=11

baseballs in one trash bin =363/11

=33

Mike took 6 trash bins

then baseballs in 6 trash bins are =6*33

=198

hence,

            Mike took a total of 198 baseballs.

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With the help of linear equation 3 3/5+x=7 1/5, Elana ran 3 3/5 miles.

What exactly is a linear equation?

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0, for example, x-10=0. In this equation, x is a variable, A is a coefficient, and B is constant.

A linear equation in two variables has the conventional form Ax + By = C, for example, 2x-4y=10. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.

Now,

Given that Emily ran 3 3/5 miles.

and Emily and Elana together ran 7 1/5 miles

i.e. 3 3/5+x=7 1/5

where x= Miles Elana ran

then x=7 1/5 - 3 3/5

=3 3/5

hence,

      The  linear equation will be 3 3/5+x=7 1/5 and Elana ran 3 3/5 miles.

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The answers are :- 1) Δ ABC ~ Δ DEF, by AA rule and 2) Δ RTS and Δ MQP are not similar.

Similar triangles are the triangles that look similar to each other, but their sizes might not be exactly the same.

Given are two pairs of triangles, we need to determine if they are similar or not,

1) Δ ABC and Δ DEF :-

We know that, the sum of the interior angles of a triangle is 180°,

Therefore,

∠ A + ∠ B + ∠ C = 180°

60° + ∠ B + 79° = 180°

∠ B = 180°-139°

∠ B = 41°

In Δ DEF,

∠ F = 79° and ∠ E = 60°

That means,

∠ B ≅ ∠ F and ∠ E ≅ ∠ C

Since, we get two corresponding angles congruent,

Therefore, by the definition of similar triangles,

Δ ABC ~ Δ DEF, By AA rule.

2) Δ RTS and Δ MQP :-

∠ R ≅ ∠ M

RT / MQ = TS / QP = 4 / 5

RS / MP = 20 /26 = 10 / 13

That means,

RT / MQ = TS / QP ≠ RS / MP

Since, we have a condition in similarity, that if, in two triangles two corresponding sides are in equal ratio, and an angle between these sides are congruent then the triangle are similar by SAS rule,

But the angle R and angle M is not in between the sides having equal ratio,

Therefore, Δ RTS and Δ MQP are not similar.

Hence, the answers are :- 1) Δ ABC ~ Δ DEF, by AA rule and 2) Δ RTS and Δ MQP are not similar.

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The probability that someone would have done at least as well as the man with no ESP is 0.077, or 7.7%.

The probability that someone would have done at least as well as the man with no ESP is calculated by the binomial probability formula. This formula takes into account the number of trials, the number of successes, and the probability of success in each trial. In this case, the number of trials is 22, the number of successes is 16, and the probability of success in each trial is 50% (0.5). The binomial probability formula states that the probability of success given this information is 0.077. This means that the probability that someone would have done at least as well as the man with no ESP is 0.077, or 7.7%.

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Answer:90

Step-by-step explanation:

The result of multiplcation of two positive numbers that is 18 and 5 or 18× 5 is equals to the ninty.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number. How to calculate 18 multiplied by 5 using long multiplication : we have one is two digits number,i.e, 18 and other one is 5.

1 8

x 5

______

Step 2: Multiply, 5 x 8 = 40. Put 0 below the line and 4 as a reminder on top:

4

1 8

x 5

_______

0

Step 3: Multiply 5 x 1 = 5. Take 5 and add 4 from the previous step to get 9. Enter 9 at the bottom:

1 8

x 5

_______

9 0

So, required value is 90.

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heres a photo of the graph to that equation

230 lbs is approximately equal to 104.3260 kg  ( rounded to four decimal places )

The conversion factor to convert lbs to kilogram is 0.453592

1 lbs = 0.453592 kg

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in kg = The mass in lbs × conversion factor

Substitute the values in the equation

1 lbs = 0.453592 kg

230 lbs =  0.453592 × 230

Multiply the numbers

= 104.3260 kg ( rounded to four decimal places )

Therefore, 230 lbs is 104.3260 kg

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In the case of converting 3cm to mm, we find that there are 30mm in 3cm.

Understanding how to convert measurements is a fundamental skill that will serve you well in many areas of study. In this case, we'll focus on how to convert 3cm to mm.

First, it's important to understand that cm and mm are both units of measurement for length or distance. The abbreviation cm stands for centimeters, while mm stands for millimeters. A centimeter is larger than a millimeter, with 1cm equaling 10mm.

To convert 3cm to mm, we need to use this relationship between the two units of measurement. We know that 1cm is equal to 10mm, so we can use multiplication to find out how many millimeters are in 3cm.

We can start by writing out the equation:

3cm x 10mm/1cm

In this equation, we're multiplying 3cm by the conversion factor of 10mm/1cm. This conversion factor tells us that there are 10mm in 1cm. When we multiply 3cm by this conversion factor, we get:

3cm x 10mm/1cm = 30mm

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The height of the tree in the given situation , by using similar triangles property , we have y = 19.54 ft.

Two figures are said to be similar if they have the same shape. Congruent objects are those that are exactly the same size and shape. . The objects with similar shapes, however, varied in size despite having the same shape.

If Susan , mirror and bottom of tree are points on the ground all on one line, then the two right triangle are these:

LEFT: y and 34 as the legs and unknown hypotenuse.

RIGHT: 5 and 8.7 as legs and unknown hypotenuse.

The two angles at the mirror are of same measure; that is, the 34 and the hypotenuse of LEFT triangle makes same angle measure as the 8.7 and the hypotenuse of the RIGHT triangle.

Then the ratio of corresponding sides ,

y / 34 = 5 / 8.7

y = 19 .54 ft

The tree is 19.54 ft tall.

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From the Venn diagram , the value of  required probability P(A∪B) is given by :

Option a). 0.6 . The probability that students  takes both Spanish and Chemistry.

Let us consider 'A' be the probability of the students who takes Chemistry.

And 'B' be the probability of the students who takes Spanish.

From the Venn diagram we have,

Probability of A 'P(A) ' = 0.2 + 0.1

                                    = 0.3

Probability of B 'P(B)' = 0.3 + 0.1

                                   = 0.4

Probability of A∩B 'P(A∩B)' = 0.1

Probability of A∪B is given by :

P(A∪B) = P(A) + P(B) - P(A∩B)

Substitute the value we get ,

⇒ P(A∪B) = 0.3 + 0.4 - 0.1

⇒ P(A∪B) =  0.6

P(A∪B) represents the probability of the students that takes both Chemistry and Spanish.

Therefore, the value and explanation of P(A∪B)  is equal to :

Option a). 0.6 , the probability of the students that takes both Chemistry and Spanish.

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The above question is incomplete , the complete question is:

The - Venn diagram below describes the probability of students who will take Chemistry and Spanish at Jefferson High School next year, where A Student takes chemistry and B Students takes Spanish. Suppose one student is chosen at random Use the attached Venn diagram .

Find the value of P(A∪B) and describe in words.

a.) 0.6; The probability that the student takes both chemistry and Spanish.

b.) 0.1; The probability that the student takes both chemistry and Spanish.

c.) 0.1; The probability that the student takes either chemistry or Spanish; but not both.

d.)0.6; The probability that the student takes either chemistry or Spanish, or both.

Venn diagram is attached.

Therefore, there are 21 possible selections of two individuals from a group of seven people.

In mathematics, a combination is a way of selecting a subset of objects from a larger set, where the order of selection does not matter. Combinations are also known as unordered selections or combinations without repetition. The number of combinations of k objects that can be selected from a set of n distinct objects is denoted by "n choose k" and is given by the formula: n choose k = n! / (k! (n - k)!) where n! is the factorial of n, defined as the product of all positive integers up to and including n, and k! and (n-k)! are the factorials of k and n-k, respectively. In words, this formula says that the number of combinations of k objects that can be selected from a set of n objects is equal to the number of ways to arrange k objects out of n, divided by the number of ways to arrange the remaining n-k objects.

Here,

To determine the number of possible selections of two individuals from a group of seven people, we can use the formula for combinations:

nCk = n! / (k! (n - k)!)

where n is the total number of individuals in the group, and k is the number of individuals to be selected. In this case, we want to select 2 individuals from a group of 7, so we have:

n = 7

k = 2

Substituting these values into the formula, we get:

7C2 = 7! / (2! (7 - 2)!)

= 7! / (2! 5!)

= (7 x 6 x 5!) / (2 x 1 x 5!)

= (7 x 6) / (2 x 1)

= 21

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Answer:

Step-by-step explanation:

Firgure is out your self

From the given data, the answer is option B, 22 cans. Larissa should purchase minimum 22 cans of sport drink.

First, we need to calculate the volume of each cone-shaped cup using the given dimensions:

Radius of the cone = diameter / 2 = 7 cm / 2 = 3.5 cm

Height of the cone = 10 cm

Using the formula for the volume of a cone, we get:

Volume of each cone-shaped cup = (1/3) x π x radius² x height

Volume of each cone-shaped cup = (1/3) x π x (3.5 cm)² x 10 cm

Volume of each cone-shaped cup ≈ 128.68 cm³

Next, we need to calculate the total volume of sports drink needed for 900 servings:

Total volume of sports drink needed = 900 x 128.68 cm³

Total volume of sports drink needed ≈ 115811.2 cm³

Now, we need to calculate the volume of one economy can of sports drink using the given dimensions:

Radius of the can = diameter / 2 = 15 cm / 2 = 7.5 cm

Height of the can = 30 cm

Using the formula for the volume of a cylinder, we get:

Volume of one can of sports drink = π x radius² x height

Volume of one can of sports drink = π x (7.5 cm)² x 30 cm

Volume of one can of sports drink ≈ 5309.73 cm³

Finally, we can divide the total volume of sports drink needed by the volume of one can of sports drink to find the minimum number of cans Larissa should purchase:

Minimum number of cans of sports drink = Total volume of sports drink needed / Volume of one can of sports drink

Minimum number of cans of sports drink = 115811.2 cm³ / 5309.73 cm³ = 21.83

Since we need to purchase whole cans, the minimum number of cans Larissa should purchase is 22.

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The value of the original price is $185

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

Sales price = $222.00

Percent of markup = 20%​

The original price is calculated as

Original=  Sales Price/(1 + Markup)

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

Original = 222/(1 + 20%)

Evaluate

Original = 185

Hence, the original price is $185

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Complete question

Diane wants to buy a leather chair at 20% markup. The sale price is $222. What was the original price?