If f(x) =5x2 - 3x + 1, calculate the following

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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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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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.

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.

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! :)

Solution:

The spinner has a total of 8 sections.

There are two green sections and 4 four vowel sections where one of the vowels is also green.

Then, the probability of landing on green or a vowel is;

Using positive integers between 1 and 9 and each positive integer at most once,

2 x+ 9 < 3 x + 1

6x+ 4 > 5 x+ 8

To get two constraints so that x = 7 is the only integer that will satisfy both constraints at the same time. Upon analysing it can be seen that to the coefficients of x in eaxh equation shouch be two consecutive number. The coefficient on the lesser than side should be lower than the coeffiecient present on the greater than side.

To make the equation in such a way that only 7 satisfy it, the lesser than sides are added with numbers higher than 7 that is 8 and 9.

Therefore, Using positive integers between 1 and 9 and each positive integer at most once,

2 x+ 9 < 3 x + 1

6x+ 4 > 5 x+ 8

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The ordered pair which is a solution to the given linear equation is (-5, -4)

Linear equations are equations that has a leading degree of 1. The standard linear equation is given as Ax + By = C.

Given the linear equation below;

-2x+9y=-26

We need to determine the ordered pair that gives a solution to the linear expression.

For the coordinate point (4, 4)

-2(4) + 9y = -26

9y = -26 + 8

9y = -18

y = -18/9 = -2

This shows that (4, 4) is not a solution.

For the coordinate point (-4, -4)

-2(-4) + 9y = -26

9y = -26 - 8

9y = -34

y = -34/9

This shows that (-4, -4) is not a solution.

For the coordinate (-5, -4)

-2(-5) + 9y = -26

9y = -26 - 10

9y = -36

y = -4

This shows that (-5, -4) is a solution of the linear equation.

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Answer:

The equivalent expression is;

Explanation:

We want to simplify the expression;

we will first multiply the negative by every term in the bracket, then simplify by collecting the like terms.

Therefore, the equivalent expression is;

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:

  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

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

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

or a+k+z=21

Answer:

Step-by-step explanation:

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 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:

A) there are no outliers in this distribution.

Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:

We had 21 dollars and we spent 5x on the notebooks, this can be express as:

Finally we know that this is equal to the six dollars we had at the end, then we have the equations:

Solving for x we have:

Therefore each notebook cost $3

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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The demand function of  the number of sets sold will increase by 130 per week is p(x) = (-1 ÷ 13)x + 550.

Determine the coordinates of two points mostly online. Estimate the difference in y-coordinates between these two places. Estimate the difference in x-coordinates between these two places. Divide the y-coordinate difference by the x-coordinate difference.

Let p(x) denote the demand function, with x denoting the number of TV sets desired. As stated in the issue, a $10 decrease in p(x) causes a 130 rise in x. As a result, the slope of the demand function graph is -13 ÷ 130 = -1 ÷ 10.

Given p(1250) = 450,

-1 ÷ 10 = (p(x) - 450) ÷ (x - 1250)

p(x) = (-1 ÷ 13)x + 550

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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 volume of a cone is given as follows;

The volume of the cone with the given dimensions is

1,046,666.67 cubic feet (rounded to the nearest hundredth)

Without approximation, the answer would be,

1,046,666.6666 cubic feet

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:

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:

22

Step-by-step explanation:

Answer:

V

Step-by-step explanation:

Answer:

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

Standard deviation is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean.

What is measure of variability?

Measures of variability provide descriptive information about the dispersion of scores within data.

Standard deviation uses all the values in the distribution in it's calculation hence the standard deviation provides the most information.

Therefore standard deviation is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean.

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