Only 20 percent of the spectators left the contest discontented. If 6000 spectators left the contest contented,
how many left discontented?

Answer:

Step-by-step explanation:

A perpendicular line will have a sope that is the negative inverse of the reference line.  The reference line is y = -3 + 4, with a slope of -3.  The negative inverse would be -(-1/3) or (1/3).

The new line will take the form of y = (1/3)x + b, where b is the y-intercept (the value of y when x=0).  We want the new line to go through point (-3,-7).  We;ll need a value of b that will make that happen.  To find b, enter the given data point and solve for b:

y = (1/3)x + b for (-3,-7).

-7 = (1/3)(-3) + b

-7 = -1 + b

b = -6

The new equation is y = (1/3)x - 6

See the attached graph.

since z=6, so z+15 is equal to 21

or a+k+z=21

Answer:

angle 4 and 5 are interior angles, and 3 and 6 as well

Answer:

1/26

Step-by-step explanation:

If the cards are all there, you can count there are 2 red threes. And there are 52 cards. The fraction is 2/52 or 1/26

The triangle ABC is an equilateral triangle. This means that each angle equals 60°. Hence, the angle at B is 60°.

The length of each side of ABC is given to be 3 cm long.

We can get the length of side AD by solving the triangle ABD using the Cosine Rule given to be:

Since we're considering triangle ABD, and we have the measure of angle B, we can use the relationship:

Note that a, b, and d are the sides, such that:

Substituting these values, we have:

The length of AD is 6.08 cm to 2 decimal places.

Answer:

Domain: -6,-1,4,6,7

Range: -5,3,6,8,9

Step-by-step explanation:

The domain is the first element in each ordered pair.  It is the x value.  The range is the second element in each ordered pair.  It is the y values.

89 degrees

The sum of an angle and its complement is equal to 90 degrees.

Let the measure of the complement be "x"

Given the information below:

Angle = 1 degrees

Taking the sum of the angle and its complement will give:

Subtract 1 from both sides

Therefore the measure of the complement for the angle given is 89 degrees

The simplest form of the ratios are:

So, the ratios in the simplest form are:

We can observe that the simplest form of all the ratios is similar which is 3.

Therefore, the simplest form of the ratios are:

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The most appropriate choice for domain of a  functions will be given by -

What is a domain of a function

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

The set of values for which the function is defined is called domain of the function.

Here, from the graph, the set of values of x axis for which the graph is drawn is [tex]-6\leq x \leq 6[/tex].

And values of x - axis represents the domain.

So domain of function is {x ∈ [tex]\mathbb{R}[/tex], [tex]-6 \leq x \leq 6[/tex]}

Third option is correct.

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To solve this question, you have to look for the answers in the table.

Let's analise each part of the question to solve it:

(a) f(1) =

f(1) means the output of the function [f(x)] when x = 1.

Looking for x =1 in the table, you can see that f(x) = 0.

f(1) = 0.

(b) f(x) = 3, x =

Now, you have to find the input (x) when the outpout [f(x)] is 3.

Looking for f(x) = 3, you can see that x = 7.

f(x) = 3, x = 7.

(c) f⁻¹(0) =

Now, you have to evaluate the inverse function.

To look for the values of the inverse function, x will be the output and f⁻¹ will be the input.

To look for f⁻¹(0), look for f(x) = 0 (input) and the output will be 1

f⁻¹(0) = 1.

(d) f⁻¹(x) = 7; x =

Again, you have an inverse function. So, 7 will be the input in the table (x). x is 7 (output).

f⁻¹(x) = 7; x = 3.

Answer:

9 terms

Step-by-step explanation:

The sequence given is a geometric sequence

In a geometric sequence, the nth term of the sequence can be found by the formula

[tex]a_n = a_1r^{n-1}[/tex]

[tex]\text{where }\\\\ a_n = \text {nth term}\\\\\text{$a_1 = $ first term}\\\\\text{$r = $ common ratio}[/tex]

In the given sequence,

a₁ = 1

r = -4

aₙ = 65536

So we get the relation:
65536 =  1·  (-4)ⁿ⁻¹

65536  = (-4)ⁿ⁻¹

It is clear that n-1 has to be even so that the power of 4  is positive.
Substituting x = n -1 where x is even gives us
4ˣ = 65536

If we take logarithms to the base 4 on both sides we get

=> x = [tex]\log_465536 = 8\\\\[/tex]

Since x = n - 1 and x = 8, n = 9

So the 9th term in the series is 65536

Answer:

12

Step-by-step explanation:

Answer:

A) there are no outliers in this distribution.

Let the total number students be s. Then

s = 3 + 5 + 2= 10

x | Number of students(n) | Pr(x) | xPr(x)

---------------------------------------------------------------------------------

76 | 3 | 0.3 | 22.8

---------------------------------------------------------------------------------

79 | 5 | 0.5 | 39.5

--------------------------------------------------------------------------------

175 | 2 | 0.2 | 35

--------------------------------------------------------------------------------

Therefore, the expected value of x is 97.3

Step-by-step explanation:

You would start off with solving inside, the parenthesis, and you would get -8/27.

Then, your would solve the 1 1/4 - 3/4 and get 1/2.

You then have to multiply -8/27*1/2, which is -4/27.

Lastly, you divide by negative 4.

-4/27 divided by -4.

You have to flip it to multiply the reciprocal, and you get -4/27*-1/4.

Since negative times negative is positive, the answer would be 1/27.

Answer:

1/27

Hope this helped! :)

Answer:

The slope is undefined

Step-by-step explanation:

Answer: [tex]x^4 - 12x^3 - 27x^2 +486x[/tex]

Step-by-step explanation:

[tex](f \cdot g)(x)=f(x)g(x)\\\\=(x^2 -3x-54)(x-9)\\\\=x^3 - 9x^2 - 3x^2 + 27x - 54x + 486\\\\=x^3 -12x^2 -27x+486\\\\\therefore x(f \cdot g)(x)=x(x^3 -12x^2 -27x+486)\\\\=x^4 - 12x^3 - 27x^2 +486x[/tex]

Answer:

[tex]45120 in^2[/tex]

Step-by-step explanation:

Area of Taylor's Banner (AT): [tex]A_T = 8*564=4512 in^2[/tex]

Area of Emily's Banner (AE): [tex]A_E=10*A_T[/tex]

Plugging in AT: [tex]A_E = 10 * 4512 = 45120 in^2[/tex]

The Area of Emily's Banner is 45120 inch²

The Area of rectangle is the product of its length to its width.

i.e., Area of rectangle= length x width

Given:

Taylor’s banner : 8 inches tall and 564 inches wide.

Area of Taylor's Banner= l x w

                                       = 8 x 564

                                       = 4512 inch²

and, area of Emily’s banner is 10 times as large as the area of Taylor’s banner.

So, Area of Emil's Banner= 10 x 4512

                                          = 45120 inch²

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Answer:

665

Step-by-step explanation:

the reasoning is because you divide 525/15 and you get 35 with that you multiply by 19 because you are seeing how far you can get with 19 gallons of gas .

665 miles Santiago can travel on 19 gallons of fuel.

A ratio in mathematics demonstrates how many times one number is present in another.

Given, Santiago's car used 15 gallons to travel 525 miles. Since,

Santiago travels in 15 gallons  = 525 miles

Santiago travels in 1 gallons = 525/ 15 = 35

Santiago travels in 19 gallons = 35* 19 = 665

Therefore,  Santiago can travel 665 miles on 19 gallons of fuel.

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The result of the expression given as 6x/(-2) is -3x

From the question, the expression is given as

6x/(-2)

The above expression is a quotient expression

So, we start by rewritting it as a product

This is represented as

6x/(-2) = 6x * 1/(-2)

Remove the bracket

So, we have the following equation

6x/(-2) = 6x * 1/-2

Evaluate the product

6x/(-2) = -3x

Hence, the value of the expression is -3x

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The sampling strategy used in this problem is an example of:

Sampling is when a subset of an entire population is studied, to verify whether characteristics of the sample can be expanded to the entire population.

The sample has to be representative of the population, that is, large enough, hence it should contain all the subsets of the population.;

In the context of this problem, the chain sees about 500 customers a week and they receive the responses from 50 of them. This is a not large enough sample size, hence it could cause biased results, meaning that the perspective of the entire population will not be considered.

In the context of this problem, the survey are anonymous, and the objective of a survey is generally not to reward the participants, hence the last two options are false.

The options are given as follows:

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Answer:

Yes 12 is an Integer

Step-by-step explanation:

12 is a whole number that can be written without a fractional component, thus 12 is an integer.

Answer:

Step-by-step explanation:

We have to calculate the area and perimeter of ABC.

Area:

We can calculate the area by substracting from the area of the big triangle ABD the area of the little triangle BCD. Both are right triangles.

The area of ABD is:

The area of BCD is:

Then, the area of ABC is:

The area of ABC is 90 cm^2.

Perimeter:

We calculate the perimeter by adding the length of the three sides. We know only 2 of the sides, so we have to calculate the other one (BC).

The length of BC can be calculated using Pythagorean theorem for the triangle BCD, so we can write:

Now, we can calculate the perimeter as:

The perimeter is 53 cm.

The length of the arc of the circle is 19.6 inches

We can find the length of the arc using the formula;

where ;

Substituting these values;

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. For illustration: If we take 45 into account. Here, the fourth digit is in the tens column.

Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.

X has a value of 3. The following is a list of the arguments made for each step.

Adding more line segments

Rule of substitution (b)

c) Simplifying by incorporating related terms

d) Compiling terms for lies

e) Multiplying each side by 8

AB = 2x

BC = 6x + 8

AC = 32

AB plus BC equals AC. (Extension rule)

addition of a line's individual segments

2x + 6x + 8 = 32 (Substitution rule) (Substitution rule)

replacing AB, BC, and AC in the formula AB + BC = AC

8x + 8 = 32 (Simplification) (Simplification)

2x + 6x + 8 = 32, simplified adding comparable terms

8x = 24 (Assembling similar terms)

8x = 32 - 8

8x = 24

x = 3 (Divide both sides by 8) (Divide both sides by 8)

8x / 8 = 24/8

x = 3

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Answer:

  sum = -15/2

Step-by-step explanation:

Given the formula for the n-th term of a sequence is n(n-8)/√(n+3), you want the sum of the 1st and 6th terms.

The first term is found by substituting 1 for n:

  1(1 -8)/√(1 +3) = 1(-7)/√4 = -7/2

The sixth term is found by substituting 6 for n:

  6(6 -8)/√(6 +3) = 6(-2)/√9 = -12/3 = -4

The sum of the first and sixth terms is ...

  -7/2 +(-4) = -(7/2 +8/2) = -15/2

  sum = -7 1/2

we have

1/2 +1/3

Remember that

1/2=0.5

1/3=0.33 -----> rounded 0.3

so

0.5+0.3=0.80

Answer: please help

Step-by-step explanation: I don’t know what the answer is I need help

Answer:175/48

Step-by-step explanation:

A Communication system consists of n components.

a) Binomial distribution,

P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾

b) For 5-component system,

P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5

c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.

Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .

(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.

(b) Now , 5-component system is function . That is n=5

Probability that 5-components system will function is P(X= 5)

= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)

(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is

⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵

Whereas the corresponding probability for a 3-components system

³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3

³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³

5-Component system is better than 3-Components system if

10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³

=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²

Which reduce to

3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0

either p> ½ or p <1

=> p belongs to ( 0.5, 1)

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