a is the one in which every two pairs of vertices are connected. a. directed graph b. weighted graph c. complete graph d. connected graph

Answer:

Step-by-step explanation:

Answer:

a. parameter

Step-by-step explanation:

A parameter is any descriptive measure of a population characteristic.

The equation of a line perpendicular to p(t) = 3t + 4 and passing through the point (3, 1) is: P(t) = -1/3 + 1

Given:

p(t) = 3t + 4

point (3,1)

To find this out, we must use the slope perpendicular to 3

perpendicular slopes are the slope's reciprocal's negative, which in this case it is -1/3

to find the line with the points (3,1), we simply use the equation y = -1/3x + b and then plug them in

1 = -1/3(3) + b

1 = -1 + b

b = 2

the y intercept is 2 and so we can write the equation like this:

P(t) = -1/3t + 2

Hence we get the required equation of a line.

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Answer:

The answer is b

Step-by-step explanation:

Applying the distance formula, the length of the bike path as shown in the coordinate plane is approximately 28 feet.

To find the distance between two points that are on a coordinate plane, the formula used is the distance formula which is given as:

d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

Point G on the coordinate plane is at (20, 20), while point E is at (0, 0):

Therefore:

E (0, 0) = [tex](x_1, y_1)[/tex]

G (20, 20) = [tex](x_2, y_2)[/tex]

Plug in the values into the distance formula:

EG = √[(20 − 0)² + (20 − 0)²]

EG √[(20)² + (20)²]

EG = √(400 + 400)

EG = √800

EG ≈ 28 feet

The length of the bike path would be approximately 28 feet.

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If the is lets say 5 years old, in 2 years, she will be 5 + 2 = 7 years old, and in 10 years 5 + 10 = 15 years old

so age in the future is the present age + how many years from now she will be

in this example the present age is 5 years old , if you replace that 5 with an x, the age in 10 years will be x + 10

The next step of marshall should be divide both sides of the equation by 5.

Given:

Marshall is writing an equivalent equation to solve for x. what should be his next step.

5 + 4 y = 8.

5+4y-4y = 8-4y

5x = 8 - 4y

To solve for x:

The correct step is:

divide by 5 on both sides

5x/5 = 8-4y / 5

x = 8/5 - 4y/5

x = 1/5(8-4y).

Therefore The next step of marshall should be divide both sides of the equation by 5.

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The nearest foot, on the building does the ladder reach is 7.1 ft

Because of Pythagorean Theorem.

Since the ladder is leaning against a building it makes 10ft the hypotenuse, (c).

Additionally, they give you one of the bases = 7ft, (a)

So in order to find the other base you must plug in what you already know.

= [tex]10^{2} = 7^{2} + b^{2}[/tex]

Which equals to 100= 49 + [tex]b^{2}[/tex]

Then you have to subtract 49 on both sides ending up with

[tex]b^{2}[/tex] = 51.

Then you have to square root on both sides and we will get [tex]\sqrt{51}[/tex].

Which is around 7.1 ft.

Hence the answer is the nearest foot, on the building does the ladder reach is 7.1 ft

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The five rules of congruence theorem are described below.

The sign for congruence is ≅ and we compose △ABC≅△DEF. ∠A relates to ∠D, ∠B compares to ∠E, and ∠C relates to ∠F. Side Stomach muscle relates to DE,BC compares to EF, and AC relates to DF.

Side-Side-Side(SSS):Corresponding sides of two triangles are equal, then triangles are congruent.

Side-Angle-Sid(SAS):Corresponding two sides and one angle are equal, then triangles are congruent.

Angle-Side- Angle(ASA):One side and two angles are equal, then triangles are congruent.

Angle-Angle-Side(AAS):Corresponding conductive two angles and one side are equal, then triangles are congruent.

Right angle- Hypotenuse-Side(RHS): assuming the hypotenuse and side of one right-calculated triangle are equivalent to the hypotenuse and the comparing side of another right-calculated triangle, the two triangles are consistent.

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The table which shows probability distribution is ,

X    P(X)

0    0.25

1      0.05

2     0.7

What is probability distribution?

   In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Utilizing graphs or probability tables, probability distributions are frequently represented. For a specific data generation process, a probability distribution shows the anticipated results of potential values. According to the mean, standard deviation, skewness, and kurtosis, probability distributions can take many different forms and exhibit a variety of properties.

A= Older eaglet survive

B = Younger eaglet survive

Given the older eaglet has 50% of survival ,

P(A) = 50% = 50/100 = 0.5

Now the older eaglet survive , the younger eaglet have only 10% of survival chance,

=> P(B/A)=10% = 10/100 = 0.1

Here P(B/A) = P(B∩A)/P(A)

=> 0.1 = P(B∩A) ×0.5

=> P(B∩A) = 0.05.

Both eaglet survives is P(B∩A) = 0.05. -------> 1

Now if the older eaglet does not have survive , the younger eaglet has 30% of survival chance,

=>P(B/A') = 30% = 0.3

Here P(B/A') = P(B∩A')/P(A')

Here P(A') = 1-P(A) = 1-0.50 = 0.50.

=> P(B∩A') = P(B/A')*P(A')

=> P(B∩A') = 0.3*05

=> P(B∩A') = 0.15

Now P(B) = P(B∩A)+P(B∩A')

=> P(B) = 0.05+0.15

=> P(B) = 0.20

P(only one eaglet survive) = P(A)+P(B)

=> 0.5+0.2 = 0.7 .-------> 2

Let x be the number of eaglet that survive,

Here x takes value of 0,1,2.

P(both eaglet survive ) = 0.05 ( from equation 1)=P(X=2)

P(only one eaglet survive) = 0.7 (from equation 2) =P(x=1)

As we know x takes only 3 values and we want to find probability distribution of x,

=> P(X=0) = 1-P(X=1)-P(x=2)

=> P(X=0) = 1-0.7-0.05

=> P(X=0) = 0.25 .

Therefore the table which shows probability distribution ,

X    P(X)

0    0.25

1      0.05

2     0.7

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The probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999

1) Using by the central limiting theorem:

We know the formula for the z-score for the normal distribution is given by:

z = (x - μ) /( ρ√n)  

Follows normal distribution with mean 0 and the variance of 1.

Where

x is the  sample mean,

μ is the  population mean,

ρ denotes population standard deviation

n = sample size

The required probability is

P(z < 0.5/[0.4/√ 10])

= P(z < 3.95)

P = 0.9999

Therefore the probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999 .

Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.

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Answer:

[tex]\sqrt{178}[/tex] or 13.3 rounded to the nearest tenth

Step-by-step explanation:

The height of the tree to the nearest centimeter is 613 centimeters

A proportion can be described as an equation having two ratios set equal to each other.

It is also seen as the mathematical comparison of two elements, numbers of ratios.

From the information given, we have that;

If 57 centimeters = 161 centimeters

Then 217 centimeters = x

cross multiply

x = 161(217)/57

multiply the values

x = 34, 937/57

x = 613 centimeters

Hence, the value is 613 centimeters

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Natural numbers known as prime numbers can only be divided by one (1) and by the number itself.

In the given question we have to explain about the prime number.

Natural numbers known as prime numbers can only be divided by one (1) and by the number itself. In other terms, prime numbers are positive integers greater than one that only have the number itself and the number's first digit as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are only a few examples.

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take any negative value of x suppose x= -1,-2 ....etc then it makes sence and it is valid cube

What are types of expressions?

There are three kinds of expressions: An arithmetic expression evaluates to a single arithmetic value. A character expression evaluates to a single value of type character. A logical or relational expression evaluates to a single logical value.

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The expected value of this game is $20.The typical net gain or loss that we would anticipate from playing a game of chance several times is known as the anticipated value.

Simply multiply each value of the discrete random variable by the probability associated with that value to obtain the expected value, E(X), or mean. E (X) = = x P (x) is the formula that is given.

The typical net gain or loss that we would anticipate from playing a game of chance several times is known as the anticipated value. By dividing the value of each outcome by the likelihood that it will occur, we can calculate the expected value. Then, we total up all the results.

The formula is given as E ( X ) = μ = ∑ x P ( x ) .

                                                         = $5 * $4

                                                          = $20.    

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Answer:

an obtuse angle are angles that are greater than 90 degrees

Step-by-step explanation:

an obtuse angle are angles that are greater than 90 degrees

Answer:

a function is like f(X)=2x+6 where X can be anything , you just substitute in the number u have been given

Step-by-step explanation:

other examples could include

f(X)=X+1

or they can start with

g(X)=3x+7

h(X)=4-3x

and there are inverse functions witch can be found be rearranging the function

example if substituteing a function

if

f(X)= 2x+1

f(3)=2(3)+1

f(3)=6+1=7

Hope this helps

Yes, the given curves are orthogonal.

In mathematics, an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally.

Given equation is,

x²+y²=ax

Differentiating,

2x+2yy'=a

y' = (a-2x)/2y = m1

Again,

x²+y²=by

Differentiating,

2x+2yy'=by'

y' = -2x/(2y-b) = m2

For both curves are orthogonal, we have

m1*m2 = -1

(a-2x)/2y*-2x/(2y-b)  = -1

-2ax+4x² = -4y²+2yb

4(x²+y²) = 2ax+2yb

Since, ax = (x²+y²)

by = (x²+y²)

Then,

4(x²+y²) = 2(x²+y²) +2(x²+y²)

4(x²+y²) = 4(x²+y²)      (true)

Hence, the above response is appropriate.

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Answer:

A

Step-by-step explanation:

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 3, 6 ) and r = 2 , then

(x - (- 3) )² + (y - 6)² = 2² , that is

(x + 3)² + (y - 6)² = 4

The correct option b. 0.004629 for  the probability of observing a 1 three times in a row.

Probability of an event = (Number of favorable events) /   (total number of event).

P(B) = (Event B) / (total number of event).

The number of times the dice are rolled has no bearing on the outcome of the roll.

The likelihood of receiving 1 is 1/6.

The likelihood of obtaining 1 three times in a row is equal to the likelihood of getting 1 the first time, the second time, and the third time.

Receiving 1 three times in succession has a probability;

= 1/6 x 1/6 x 1/6

= 1/216.

As a result, there is a 0.463% chance that you'll get 1 three times in a row.

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The probability of all 3 selected were rated excellent is 1/114 and the probability of one from each category was selected, is 7/114.

In the given question,

In a certain department, 5 employees received excellent ratings, 14 received good ratings, and 1 received a marginal rating.

So total number of employees = 5+14+1 = 20

If 3 employees in this department are randomly selected to complete a form for an internal study of the firm, then we have to find the probability that the following occurs.

The following occurs given below:

(a) We have to find the probability of all 3 selected were rated excellent.

5 employees who got excellent rating. So the selection of 3 employees from 5 employees who got excellent rating is:

selection of 3 employees from 5 employees = [tex]^5C_{3}[/tex]

Using, [tex]^nC_{r}=\frac{n!}{r!(n-r)!}[/tex]

selection of 3 employees from 5 employees = [tex]\frac{5!}{3!(5-3)!}[/tex]

selection of 3 employees from 5 employees = [tex]\frac{5!}{3!2!}[/tex]

selection of 3 employees from 5 employees = [tex]\frac{5\times4\times3!}{3!\times2\times1}[/tex]

selection of 3 employees from 5 employees = 5×2

selection of 3 employees from 5 employees = 10

Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140

Probability of 3 employees who got excellent rating

P(E) = 10/1140

P(E) = 1/114

(b) We have to find the probability of one from each category was selected.

One candidate selected from excellent category = [tex]^5C_{1}[/tex] = 5

One candidate selected from marginal category = [tex]^1C_{1}[/tex] = 1

One candidate selected from good category = [tex]^{14}C_{1}[/tex] = 14

Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140

The probabilty of one from each category = (5*1*14)/1140

The probabilty of one from each category = 70/1140

The probabilty of one from each category = 7/117

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A polynomial is a function with two or more terms that have positive integer exponents. The terms can be constants and/or have variables. They are separated by either addition or subtraction signs.

fundamental coefficients are the numbers written in front of the variable with the maximum important exponent. just like ordinary coefficients, they may be fine, terrible, real, or imaginary further to whole numbers, fractions, or decimals. for instance, inside the equation [tex]-7x^4[/tex] +[tex]2x^(3-11)[/tex], the very satisfactory exponent is four.

The degree of the polynomial is the best strength of the variable that takes location in the polynomial. the number one time period is the time period containing the very high-quality energy of the variable: the term with the very wonderful degree.

In a polynomial, the principal term is the term with the very first-rate electricity of x. for instance, the principal term of 7+x−3x² is −3x². the principal coefficient of a polynomial is the coefficient of the primary term. within the above instance, the primary coefficient is −3.

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By using the formula for mean and variance, it can be calculated that

Mean of X = 25

Variance of X = 51.67

What is mean and variance?

Suppose there is a data set. Mean gives the average of the values of the data set

Variance is the square of the sum of deviation from mean.

Let x be the total; of the numbers on the two card

Possible values of X= 15, 20, 25, 30, 35

P(X = 15) = [tex]\frac{2}{12}[/tex]

P(X = 20) = [tex]\frac{2}{12}[/tex]

P(X = 25) = [tex]\frac{4}{12}[/tex]

P(X= 30) = [tex]\frac{2}{12}[/tex]

P(X = 35) = [tex]\frac{2}{12}[/tex]

Mean of X =

[tex]15 \times \frac{2}{12} + 20 \times \frac{2}{12} +25 \times \frac{4}{12} + 30 \times \frac{2}{12} + 35 \times \frac{2}{12}\\\\\frac{300}{12}\\\\25[/tex]

Variance of X =

= [tex](225 \times \frac{2}{12} + 400 \times \frac{2}{12}+625 \times \frac{4}{12}+900 \times \frac{2}{12}+1225 \times \frac{2}{12}) - (25)^2\\\\\frac{8000}{12} - 625}\\\\666.67 - 625\\\\51.67[/tex]

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Complete Question

In a box are four cards numbered 5, 10, 15, 20. two cards are taken out at random without replacement, and X is the total; of the numbers on the two card. Find the mean and variance of X .

The way fuel consumption of a car change as its speed increases represents a relationship that is curved with higher at extremes when scatter plot is constructed. It shows fuel efficiency is high at moderate speeds.

What is scatter plot?

A scatter plot is a type of mathematical diagram using Cartesian coordinates to demonstrate values for typically two variables for a set of data.

Main body:

In the given case, the scatter plot shows a relationship between the speeds of a car and fuel consumption.

The curved relationship which is high on extreme and low in the middle. As the car speed increases from 10km/h to 60 km/h, the fuel consumption decreases. As the car speed increases from 60km/h to 150khm/h, the fuel consumption increases. Hence, the fuel consumption is lowest at 60km/h and its generally low for moderate speeds – 40 km/hr to 100 km/h. It can be deduced that fuel efficiency (which pertains to how well a vehicle uses fuel) is high for moderate speeds.

Hence, at moderate speeds best performance is achieved.

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An writing format called R Markdown (. Rmd) makes it simple to create dynamic documents, presentations, and reports with R.

It mixes R code chunks that are embedded and run so that their result can be included in the final document with the basic grammar of R markdown, a simple plain text format. The following are some benefits of utilizing R markdown: explicitly connects your data, R code, and output to produce a workflow that is completely reproducible. You can include ALL of the R code that was used to explore, summarize, and analyze your data in a single, simple-to-read document.

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Applying the given exponential function  y = 7.1(1.03)ˣ, the amount produced in 2006 was approximately 7.8 billion pounds and the estimated amount in 2014 will be approximately 9.8 billion pounds

An exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

In the function given;

y = 7.1(1.03)ˣ

a) What is the estimated number in 2006

The value of x in 2006 is

x = 3

Plug the values into the formula above;

y = 7.1(1.03)³

y = 7.76 ≅ 7.8 billion pounds

b)

The cheese produced in 2014

The value of x in 2014 = 11

Plug in the value

y = 7.1(1.03)¹¹

y = 9.83 ≅ 9.8 billion pounds

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Answer:

A triangle in which each angle is less than 90 degrees is called an acute angled triangle.

Step-by-step explanation:

The ordered pair (4, 0) makes both inequalities true.

What is inequality equation?

The mathematical expressions in which both sides are not equal are called inequalities.

Main body:

In inequality, unlike in equations, we compare two values.

The equal to sign in between is replaced by less than, greater than or not equal to sign.

It is given that

y < 3x -1 …. (1)

y > -x + 4 …. (2)

Let us take the point (4, 0)

In inequality (1)

y < 3x-1

0 < 3 (4) - 1

0 < 12 - 1

0 < 11 which is true

In inequality (2)

y ≥ - x + 4

0 ≥ -4 + 4

0 ≥ 0 …. Which is true

Therefore, the ordered pair (4, 0) makes both inequalities true.

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