Special right triangles

Total number of outcomes in rolling a die 3 times = [tex]6^3[/tex]  =216

What is outcome of an event?

Suppose an event is happening. The result of the event is called outcome of the event.

For example : let the event be throwing of a die. One of the outcome of the event is getting a 4 on the die

Number of outcomes of rolling a die first time = 6

Number of outcomes of rolling the die second time = 6

Number of outcomes in rolling a die third time = 6

Total number of outcomes in rolling a die 3 times = [tex]6 \times 6 \times 6[/tex]

                                                                                   = [tex]6^3[/tex]

                                                                                   = 216

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The simplified form of the expression 52 + 1/5(-1/2)  is [tex]\frac{519}{10}[/tex]

A fraction is a ratio of two integers.

The integers are always in two parts separated by a division line. the part above the division line is called the numerator and the part below the division line is called the denominator.

52 + 1/5(-1/2)

Multiply out the fraction

we have

52 + (-1/10)

52 - 1/10

to make 52 have the same denominator as 1/10 we multiply 52 by 10/10 so that it becomes

520/10 - 1/10

simplifying the numerator we have,

[tex]\frac{520 - 1}{10}[/tex] =  [tex]\frac{519}{10}[/tex]

In conclusion the solution to 52+1/5(-1/2) is  [tex]\frac{519}{10}[/tex]

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The probability that he gets four or fewer questions correct is 0.9984

Let p be probability of getting correct answer and q be probability of getting in correct answer.

Number of trails :  n = 6

Number of Successes : x = 4

By using binominal distribution ,

P(x≤4) = 1 - P(x>4)

= 1 - [P(x = 5) + P(x = 6)]

= 1 - [ ⁶C₅ p⁵ q +⁶C₆ p⁶ ]

solving combination ,

= 1 - [ 6 × 4/(5⁶) + 1 /(5⁶) ]

= 1 - (24 + 1 / 625)

= 1 - 25 / 625

= 624/625 = 0.9984

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La ecuación exponencial 9ˣ⁺¹ + 3 = 28.3ˣ tiene una solución en x ≈ 1.922.

Aquí tenemos una ecuación exponencial en forma implícita, esto es, que la variable x no está en términos implícitos de las constantes de la ecuación.

Esta forma se puede resolver mediante métodos gráficos, a partir de la graficación del siguiente sistema de ecuaciones:

f(x) = 9ˣ⁺¹ - 28.3ˣ - 3

g(x) = 0

La solución es todo punto tal que f(x) = g(x).

A continuación, se grafica cada ecuación en un plano cartesiano mediante una herramienta gráfica. De acuerdo con la imagen, la solución de la ecuación es x ≈ 1.922.

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According to the Pythagoras theorem, the value of x is 13.76

Pythagoras theorem:

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“ is known as Pythagoras theorem.

Given,

Here we have the triangle with the side values.

Now, we have to find the value of x through this given values.

In order to calculate the value of x,

First, we need the value of the side KM.

Let us consider the value of KM is y.

Then according to the concept of Pythagoras theorem,

The value of y is calculated as,

=> (12.3)² = y² + (5.4)²

=> 151.29 = y² + 29.16

=>  y² = 122.13

=> y = 11.05

Therefore, the value of the hypotenuse  x is calculated as,

=> x² = (11.05)² + (8.2)²

=> x² = 122.13 + 67.24

=> x² = 189.37

=> x = 13.76

Therefore, the value of x is 13.76.

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The equation to represent the cost is C =  8 + 1.50x + 0.75y.

To write an equation that represents the cost of a pizza.

An equation that represents the cost of a pizza will be

C = 9 + 1.75x + 0.50y

   Fixed cost = $9

   Cost of additional inch = 1.75x

   Cost of additional topping = 0.50y

Total cost (C) will then be:

= 9 + (1.75 × x) + (0.50 × y)

C = 9 + 1.75x + 0.50y

Hence the answer is, the equation to represent the cost is C =  8 + 1.50x + 0.75y.

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The points scored by Mrs. Dellett  on her 9th attempt is 210.

Given, Mrs. Dellett took up archery as a hobby.

On her first attempt she scored 18 points.

then every attempt after that, she increased her score by 24 points.

first attempt = 18 points

after this her score increased to 24 points on every attempt.

second attempt = 18+24 = 42

third attempt = 42+24 = 66

fourth attempt = 66+24 = 90

fifth attempt = 90 + 24 = 114

sixth attempt = 114 + 24 = 138

seventh attempt = 138 + 24 = 162

eight attempt = 162 + 24 = 186

ninth attempt = 186 + 24 = 210

Hence the option D is correct.

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Answer:

31. (25 - 8) x 3 = 51

32.  9 + 4 x (5 - 3) = 17

Step-by-step explanation:

grouping symbols

31.) 25 - 8 x 3 = 51

(25 - 8) x 3 = 51

Do the parentheses first

17 * 3 = 51

51=51

32.) 9 + 4 x 5 - 3 = 17

9 + 4 x (5 - 3) = 17

Parentheses first

9 + 4 * 2 = 17

Multiply

9+8 = 17

Add

17=17

The length of the third side of the triangle is 2x+13.

According to the question,

We have the following information:

A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.

We know that perimeter of triangle is the sum of all three sides of triangle.

Let's take its third side to be y.

So, we have the following expression:

3x+2x-5+y = 7x+8

5x-5+y = 7x+8

Adding 5 on both the sides:

5x+y = 7x+8+5

5x+y = 7x+13

Subtracting 5x from both the sides:

y = 7x-5x+13

y = 2x+13

Hence, the correct option is B.

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Answer:

B. 2x+13

Step-by-step explanation:

I got it right on the test

The percentage of items that have not been sold is: 60%

In mathematics, the percentage is calculated by dividing the given value by the total which is then multiplied by 100.

Percent in itself stands for out of 100.

Let the total number of items= i

Let the percentage be represented as= p

Then,

         i=100 (Given in the question)

Let the number of items sold in the first hour be= a

Let the number of items sold in the second-hour be= b

Since,

         p= Given Value/Total value x100

thus,

        a/100x100=30%

        The hundreds cancel out.

Thus, a=30 -(i)

The number of items sold in the second hour= b

b=10 (provided in the question) -(ii)

Let the total number of items sold be=T

The total number of items sold= a+b

From (i) and (ii)

Total number of items sold=30+10

Thus,

        Total number of items sold=40 -(iii)

Number of items that have not been sold(n)=100-(a+b)

                                                                        =100-T

                                                                        = 100-40

                                                       From (iii)

                                                                     n = 60 -(iv)

Then,

          Percentage of items that have not been sold = n/100x100

                                                                From -(iv)              

                                                                                      = 60/100x100

          Canceling hundred by hundred                      

                                                                                      = 60%

Thus,

          Answer: The percentage of items that have not been sold is: 60%

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According to the central limit theorem, given a population with mean μ and standard deviation σ, if a suitably large random sample (n ≥ 30) is drawn from the population with permutation, the distribution of the sample mean will be approximately normally distributed. Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.

Then the mean of the sample mean is given by

[tex]\mu_ {x} =\mu[/tex]

and the standard deviation of the sample mean is given by

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} }[/tex]

The standard deviation of the sample mean is inversely proportional to the sample size n

so if n increases, the standard deviation decreases and vice versa.

(a) Sample size increased from 64 to 196.

As mentioned above, the standard deviation decreases as the sample size increases.

Therefore, increasing the value of n from 64 to 196 reduces the standard deviation of the sample mean.

n = 64 sample mean standard deviation:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{64} } \\\\\sigma_{x} = 0.7[/tex]

n = 196 sample mean standard deviation:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{196} } \\\\\sigma_{x} = 0.4[/tex]

sample mean standard deviation decreased from 0.7 to 0.4 n was 64 When it increased to 196.

Therefore the variance is also decreases.

(b)

decreace the sample size, increase the standard deviation.

Therefore, as the value of n decreases from 784 to 49, the standard deviation of the sample mean increases.

Standard deviation of sample mean for n = 784:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{784} } \\\\\sigma_{x} = 0.2[/tex]

Standard deviation of sample mean for n = 49:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{49} } \\\\\sigma_{x} = 0.8[/tex]

Standard deviation of sample mean increased from 0.2 to 0.8 while, n increased from 784 Then 49 decreases.

Therefore, the variance is also increases.

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The possible outcomes must contain at least three tails, not 33 because a coin is flipped eight times. Then, the possible outcomes that contain at least three tails are 219.

The possible outcome is the possible result of an event. The possible outcomes that contain at least three tails mean the possible outcomes with exactly three tails and more than three. So, the calculation is:

Hence, the possible outcomes that contain at least three tails are 219.

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If she sold the gold bracelet at $2012, the profit would be $1212

Let  original price of the gold bracelet be x

Mrs Tan wanted to make a profit of 52%

The selling price would be $1216

Selling price = x + 52% of x

1216 = x + (52/100)x

1216 = 152/100x

x = 1216(100/152)

x = 800

The original price is $800

The price at which she sells the gold bracelet is 2012

Profit = selling price - original price

= 2012 - 800

= 1212

Therefore, if she sold the gold bracelet at $2012, the profit would be $1212

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Equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.

Total population in 2010 is equal to 470,000 people.

As given in the question,

Let 'p' represent the population in thousands of people.

Let x represents the number of years.

Population projected in 2005 = 450,000 people

                                                 = 450 ( in thousand people)

Population increases by 4000 people each year that is equal to 4 (in thousand of people)

Required equation to represent the population in x years ( in thousand of people ) is given by:

p = 4x + 450

Population in 2010 is equal to :

p = 4 ( 2010 - 2005) + 450

 = 4(5) + 450

= 20 + 450

= 470 ( in thousand of people)

= 470,000 people

Therefore, equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.

Total population in 2010 is equal to 470,000 people.

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Number of Atlantic cods caught in the year 2001 is; 40300 t

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. This is expressed as;

Percentage = (value / total value) * 100%

Now, we are told that;

Number of Atlantic cods caught in 1991 = 310000 t

We are told that in the year 2001, there were 87% less caught. Thus;

Number by which it was reduced = 310000 * 87% = 269700

Thus;

Number of Atlantic cods caught in the year 2001 = 310000 - 269700

Number of Atlantic cods caught in the year 2001 = 40300 t

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Check the picture below.

[tex]tan(x) =\cfrac{\stackrel{opposite}{10}}{\underset{adjacent}{4}}\implies tan(x)=\cfrac{5}{2}\implies x=tan^{-1}\left( \cfrac{5}{2} \right)\implies x\approx 68.20^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

Step-by-step explanation:

-2y = -x -1
2y = x+1
y = 1/2x+1/2

Answer:

Step-by-step explanation:

Ok:

1. First write as equation!

x/3=4.5

2. Isolate the variable on the left side. Remember if a variable or number goes over equal sign, it becomes opposite

x/3=4.5

x=4.5*3

x=13.5

3. Double Check as always!!

13.5/3= 4.5

TRUE

Answer: 13.5

Answer:

13.5 is the answer ..hopefully this helps

Answer:

  (s, f) = (4.5, 2.25)

Step-by-step explanation:

You want the solution to the simultaneous equations ...

Writing these in general form, we have ...

  3s +2f -18 = 0

  2s +3f -15.75 = 0

Using the "cross-multiplication method" for solution, we find ...

  ∆1 = (3)(3) -(2)(2) = 5

  ∆2 = (2)(-15.75) -(3)(-18) = 22.5

  ∆3 = (-18)(2) -(-15.75)(3) = 11.25

  s = ∆2/∆1 = 22.5/5 = 4.5

  f = ∆3/∆1 = 11.25/5 = 2.25

The solution is (s, f) = (4.5, 2.25).

__

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Answer:

k = 13

Hope this helps : )

Step-by-step explanation:

To solve the equation, we need to first isolate the variable by doing the inverse operation which in this case is dividing since 7 is being multiplied with the variable k.

1. Divide 7 on both sides of the equal sign.

7k = 91

7 7

2. Answer.

The 7 cancels out so we are left with k = 13 since

91 ÷ 7 = 13

k = 13

3. Check.

Plug in the variable "k."

7(13) = 91

91 = 91 ✓

The subtotal before the surcharge and the sales tax is $12.25   .

In the question ,

it is given that ,

the total amount paid for the taxi ride = $13.73

sales tax percent charged = 4%

amount of surcharge = $1 .

let the subtotal before the tax and surcharge be "x"

the amount paid by the customer can be represented by the equation ,

total amount = cost + 4% of cost + surcharge

Substituting the values from above , we get

13.73 = x + 4% of x  + 1

4% of x + x = 13.73 - 1

0.04x + x = 12.73

1.04x = 12.73

x = 12.73/1.04

x = 12.24038

x ≈ 12.25

Therefore , The subtotal before the surcharge and the sales tax is $12.25   .

The given question is incomplete , the complete question is

A taxi ride cost a customer a total of $13. 73, which included 4% , percent sales tax and then a $1dollar surcharge. What was the subtotal before the surcharge and sales tax ?

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Answer:

Step-by-step explanation:

d- down four then right three

Answer:

18 orders in 2 days 9 orders in 1 day

Answer:

Step-by-step explanation:

9x2=18 which is 2 days so 9x1= 9 which is one day

The unit rate of the number of cups of water per cup of lime juice are;

Jaylan;

Wanchen;

Unit rate indicates the rate of an item for a quantity of one of another item such that when the quantitative relationship is expressed as a ratio, the denominator will be one.

The content of limeade Jaylan makes are;

The ingredient of the limeade Wanchen makes are;

The unit rate of water (cups) per lime juice (cups) is therefore;

Jaylan; 34 cups of water for every 15 cups of lime juice

Therefore;

34/15 cups of water for 1 cup of lime juice

34/15 = 2.2[tex]\overline 6[/tex]

The unit rate of the drink Jaylen makes is 2.2[tex]\overline 6[/tex] cups of water per cup of lime juice

Wanchen; 35 cups of water per 12 cups of lime juice

Therefore;

35/12 cups of water per cup of lime juice

35/12 = 2.91[tex]\overline{6}[/tex]

The unit rate is 2.91[tex]\overline 6[/tex] cups of water per cup of lime juice

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The correct statement is that the value of n that make the relationship a function are any value except 1, 3, or 2

A function is a relationship that maps the elements of a set A to the elements of a set B, such that each element of A is mapped to exactly one element of the set B.

The ordered pair of known values are a function as the elements of the input variable are all different and the element of the output variable are also different, which indicates a 1 to 1 relationship.

The known elements of the set A in the question are; 2, 6, and 4

The elements of the set A are known as the domain of the function.

The known element of the set B are 8, 0, and 2

The fourth ordered pair (2·n, n), has a value similar to the pair (4, 2)

To prevent the presence of the elements 2,. 6, and 4, being assigned to other elements apart from 8, 0, and 2, the value of 2·n can be any value except 2, 6, 4

Therefore;

n can be any value except 2/2 = 1, 6/2 = 3, or 4/2 = 2

The correct statement is therefore;

n can be any value except 1, 3, or 2

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Answer:

31

Step-by-step explanation: