what is the following sum? assume x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0startroot x squared y cubed endroot 2 startroot x cubed y superscript 4 baseline endroot x y startroot y endrootx squared y squared startroot y endroot minus 2 x y squared startroot x endroot2 x y startroot y endroot 2 x y squared startroot x endroot4 x y startroot x superscript 5 baseline y superscript 8 baseline endroot2 x y startroot x y endroot

By using the concept of probability, it can be calculated that

a) State space S(x) = {-1, 0, 1, 2}

b) The required probability mass function is

    P(X = -1) = [tex]\frac{125}{216}[/tex]

    P(X = 0)  [tex]= \frac{25}{72}[/tex]

    P(X = 1)  [tex]= \frac{5}{72}[/tex]

    P(X = 2)  [tex]= \frac{1}{216}[/tex]

c) Expected value of X  = -0.5

d) the stake of the gambler in  order to make this a fair game is $0.5

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

a) Let a number n be chosen between 1 and 6

Three fair six sided dice are thrown

The following cases can occur

1) Number n occur on none of the three dice

2) Number n occur on one dice

3) Number n occur on two dice

4) Number n occur on three dice

Let X denote your net win after one round of gambling (i.e., the payment received from the casino minus your stake)

1) X = 0  -1 = -1

2) X = 1 - 1 = 0

3) X = 2 - 1 = 1

4) X = 3 - 1 = 2

State space S(x) = {-1, 0, 1, 2}

b) P(X = -1) = [tex]{3 \choose 0}(\frac{1}{6})^0(\frac{5}{6})^3 = (\frac{5}{6})^3 = \frac{125}{216}[/tex]

    P(X = 0) = [tex]{3 \choose 1})(\frac{1}{6})(\frac{5}{6})^2 = \frac{25}{72}[/tex]

    P(X = 1) = [tex]{3 \choose 2}(\frac{1}{6})^2\frac{5}{6} = \frac{5}{72}[/tex]

    P(X = 2) = [tex]{3 \choose 3}(\frac{1}{6})^3(\frac{5}{6})^0 = \frac{1}{216}[/tex]

    The required probability mass function is

    P(X = -1) = [tex]\frac{125}{216}[/tex]

    P(X = 0)  [tex]= \frac{25}{72}[/tex]

    P(X = 1)  [tex]= \frac{5}{72}[/tex]

    P(X = 2)  [tex]= \frac{1}{216}[/tex]

c) Expected value of X = [tex]-1 \times \frac{125}{216} + 0 \times \frac{25}{72} + 1 \times \frac{5}{72} + 2\times \frac{1}{216}[/tex]

                                      = [tex]\frac{-125 + 0 + 15 +2}{216}\\[/tex]

                                      = [tex]-\frac{108}{125}[/tex]

                                      = -0.5

d) The gambler looses $0.5 on a average

   So this is not a fair game

   Let the stake of the gambler in  order to make this a fair game be t

   By the problem,

   -0.5 + t = 0

     t = 0 + 0.5

     t = $0.5

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There are 5 1's in the given identity matrix of order 5.

Given, an identity matrix of order 5

we have to find the number of 1 in the given matrix

So, as the matrix is an identity matrix and the order of the matrix is 5

in an identity matrix, the entry is 1 when

i = j i.e. on the diagonal elements.

As, the order of the matrix is 5 then, the number of 1's in the matrix are 5.

Hence, there are 5 1's in the given identity matrix of order 5.

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Answer:

130 mi/ per quart

Step-by-step explanation:

260 mi/8 gallons =32.5 mi/gallon

1 gallon = 4 quarts, so 32.5 gallons is 130 quarts

Answer:

Step-by-step explanation:

8.5

Answer:

12.45, 0.25, -0.85, -12

Step-by-step explanation:

The larger the negative the lesser the value, opposite for positive numbers

The required radius of given circle is 30 units.

A circle is a shut two-layered figure wherein the arrangement of the multitude of focuses in the plane is equidistant from a given point called "focus". Each line that goes through the circle shapes the line of reflection evenness. Likewise, it has rotational evenness around the middle for each point.

Picture result for What is circle and region of its area?

The equation for the region of the area of a circle is(r2) /360where r is the span of the circle and is the point of the area.

Angle of sector = 100 degree, area= 250π

Let radius of circle be r

Then,

area of sector = (r^2) /360

250π =  (r2) 100/360

r^2 = 250×360/100

r = √25×36 = 30 units

Thus, radius of the circle is 30units.

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As a seismologist, Janet understands the devastating effects that earthquakes can have. so, she keeps her basement stocked with canned food, like chili. This table shows the relationship between the number of cans of chili Janet buys, x, and the total cost (in dollars), y.

[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]

According to the values in the table, x and y have not a proportional relationship.

Table

[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]

Specifies the gradient (m) in rows 1 and 2

m₁ = [tex]\displaystyle \frac{56.80 - 26.40}{44-12}[/tex]

m₁ = [tex]\displaystyle \frac{30.40}{32}[/tex]

m₁ = [tex]\displaystyle \frac{19}{20}[/tex]

Specifies the gradient (m) in rows 2 and 3

m₂ = [tex]\displaystyle \frac{77.70 - 56.80}{66-44}[/tex]

m₂ = [tex]\displaystyle \frac{20.9}{22}[/tex]

Because the values of m₁ and m₂ are not the same [tex]\displaystyle \frac{19}{20}[/tex] ≠ [tex]\displaystyle \frac{20.9}{22}[/tex], then x and y have not a proportional relationship.

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She needs to get her interest rate at will 5.592 %/year.

What is Compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest is applied per time period

t = number of time periods elapsed

Solving for rate r as a decimal

r = n[(A/P)1/nt - 1]

r = 12 × [(2,500.00/2,000.00)1/(12)(4) - 1]

r = 0.0559158

Then convert r to R as a percentage

R = r * 100

R = 0.0559158 * 100

R = 5.592%/year

Hence, she needs to get her interest rate at will 5.592 %/year.

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Point C - Tolerance values above 0.2 may indicate multi collinearity in the data is correct.

Given that

It must be below 0.2, along with VIF above 10.

The remaining options are not correct.

A. If the average variance inflation factor is greater than 1 then the regression model might be biased.

B. Multi collinearity in the data is shown by a VIF (variance inflation factor) greater than 10.

D. The tolerance is 1 divided by the VIF (variance inflation factor).

Hence the answer is Point C - Tolerance values above 0.2 may indicate multi collinearity in the data is correct.

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Chance is also referred to as probability and the probability that one is blue and one is red is 4/19

probability = Number of event/Total samples space

If there are 10 black socks,20 white socks,2 red socks, and 6 blue socks in a drawer, the total number of socks will be the sample space

Sample space = 10+20+2+6

Sample space = 38

Total number of blue and red socks is the event

Number of event one blue and one red = 8 blue socks

Chance that the socks is blue = n(E)/n(S)

Chance that the socks is one red and one blue  = 8/38

Chance that the socks is red and blue = 4/19

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Answer:

In explanation down below.

Step-by-step explanation:

So if the boat was able to travel 27 miles in 2 hours that means that it traveled 13.5 miles an hour. I think that you want to know how many miles the boat will travel in 1/2 an hour. Which is 6.75.  

1 hour: 13.5 miles

1/2 hour the boat has traveled 6.75 miles.

I hope this helps!!!

Please mark brainliest :)

Answer:

The function crosses the Y axis (the up down axis) at -1

Step-by-step explanation:

The domain of the function is 24.The collection of all potential inputs for a function is known as its domain.

Explanation:

F(x)= 12x-5 and G(x) = 2x²+3

Find (G-F) (-2) ,    put x = 0 ,   2+3-12-5 = -12.

-12 * -2 = 24.

The domain of the function is 24.    

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If this property is violated, the observations are said to be: autocorrelated

What is Random Series?

The results of an experiment are functions of an integer argument, and the results are described by a random series: U1, U2.. (or, simply, sequences of random values - 1st value, 2nd value, etc).

The term "time series" and, occasionally, "random processes with discrete time" are frequently used to describe random series. The Markov chain exemplifies a crucial category of random series.

In this question, it's asked when the property of independence is violated.

If the consecutive observations are correlated or linearly related, then they are said to be autocorrelated. This denotes that there will be an association of the current time period with the successive and preceding time periods. Violation of the autocorrelation assumption yields inaccurate results.

Hence, The observations are said to be: autocorrelated in the random series.

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The number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.

In the given question, if the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, then we have to find the collections of 30 coins can be chosen.

Number of coins only of quarters = 15

Number of coins only of dimes = 20

The number of ways to choosing coins with at least 15 quarters and 20 dimes= Total- [tex](^{18}C_{3}+^{13}C_{3})[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]^{33}C_{3}-(^{18}C_{3}+^{13}C_{3})[/tex]

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

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33!}{3!(33-3)!}-(\frac{18!}{3!(18-3)!}+\frac{13!}{3!(13-3)!})[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33!}{3!30!}-(\frac{18!}{3!15!}+\frac{13!}{3!10!})[/tex]

Simplifying

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33\times32\times31\times30!}{3\times2\times1\times30!}-(\frac{18\times17\times16\times15!}{3\times2\times1\times15!}+\frac{13\times12\times11\times10!}{3\times2\times1\times10!})[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 11×16×31-(3×17×16+13×2×11)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-(816+286)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-1102

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 4354

If the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, the number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.

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The expression that represents the total amount that can be raised from selling 50 tickets is -2t + 250 and the total amount that can be raised is $194.

What is total revenue?

Total revenue is the amount of money earned by a company from the sale of its goods and services. In other words, businesses use this metric to determine how well their core revenue-generating operations are performing. Total revenue is directly related to marginal revenue.

Number of tickets that will be sold = 50

Number of student tickets that will be sold = t

Number of adult tickets that will be sold = 50 - t

The total amount of money that can be raised from selling 50 tickets is the sum of the total amount raised from selling student tickets and adult tickets.

Total revenue = total amount raised from selling students tickets + total amount raised from selling adults tickets

Total revenue = [3 x t] + [(50 -t) x $5]

Total revenue = $3t + $250 - 5t

Total revenue = -2t + 250

Total revenue = -2(28) + 250

Total revenue = -56 + 250 = $194

Hence, the expression that represents the total amount that can be raised from selling 50 tickets is -2t + 250, and the total amount that can be raised is $194.

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The equation of a line that passes through points (a,b) and (c,d) is (c-a)y = (d-b)x+b(c-a)-a(d-b).

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Let the two points are (a,b) and (c, d)

To find the equation of line,

Use formula y- y₁ = (y₂-y₁/x₂-x₁) (x-x₁)

The equation of line,

y-b = (d-b/c-a)(x-a)

(c-a)(y-b) = (d-b)(x-a)

(c-a)y = (d-b)x+b(c-a)-a(d-b)

The required equation of the line is (c-a)y = (d-b)x+b(c-a)-a(d-b).

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f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

Given that the function g(x) is a transformation of the parent function f(x).

To Decide how f(x) was transformed to make g(x).

The reflection of the point (x,y) across the line y = 1/2 x is the point (y, x).

By the given tables we can see that;

g(x) = 1/2 f (x)

Therefore, f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.

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The direction of increase of the given objective functions is

(a) in the direction of x₁

(b) in the direction of x₂

(c) in the direction of x₂

In the question ,

three objective functions are given ,

we have to find the direction in which the given function increase ,

So ,

Part (a) ,

z = 4x₁ - x₂

According to the signs of the variables given ,

the function z will increase in the direction of x₁ , because x₁ has positive sign and it will decrease in the direction of x₂ as it has a negative sign .

Part(b) ,

z = -x₁ + 2x₂

According to the signs of the variables given ,

the function z will increase in the direction of x₂ , because x₂ has positive sign and it will decrease in the direction of x₁ as it has a negative sign .

Part(c) ,

z = -x₁ + 3x₂

According to the signs of the variables given ,

the function z will increase in the direction of x₂ , because x₂ has positive sign and it will decrease in the direction of x₁ as it has a negative sign .

Therefore , The direction of increase of the given objective functions is

(a) in the direction of x₁

(b) in the direction of x₂

(c) in the direction of x₂ .

The given question is incomplete , the complete question is

For each of the following, determine the direction in which the objective function increases:

(a) z = 4x₁ - x₂

(b) z = -x₁ + 2x₂

(c) z = -x₁ + 3x₂

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If the data collection contains the given following numbers: 1, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 87 , Here 1 and 87 represents the outlier.

The important characteristics of the Statistics that are given as follows:

Statistics have always been numerically expressed.

For instance, if the data collection contains the following numbers: 1, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 87

The display of all data and outliers

The numbers 1 and 87, which are at the extreme and are hence outliers in the number line above, may be seen to be at these extremes.

The group outliers are a part of it, but they are not always close to the other group members.

Outliers are a concern as they cause an imbalance in the data set, which is why they are typically eliminated. Furthermore, an error can sometimes cause an outlier to appear in a data collection.

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If no box has a card with the same letter as the box, then count the number of elements as 24 ways.

Given that,

Four randomly selected cards with the letters A, B, C, and D are placed in the corresponding boxes. There is exactly one card in each box.

We have to find If no box has a card with the same letter as the box, then count the number of elements.

We know that,

A permutation is a mathematical calculation that establishes the number of possible arrangements for a given set, taking into account the arrangement's order.

From the given information:

The permutation approach can be used to represent the four cards that are randomly placed in the four boxes and can be used to express the following:

=⁴P₄

Since no box contains a card that begins with the same letter as the box, it follows that

Card A can be inserted into a box four different ways,

Card B three different ways,

Card C two ways, and

Card D one way.

The four cards' permutation can then be calculated as follows:

⁴P₄=4!/0!=4×3×2×1/1=24.

Therefore, If no box has a card with the same letter as the box, then count the number of elements as 24 ways.

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Exactly one unique triangle exists with the given side lengths, option B is correct.

Here, we are given that the three sides of triangle are- 12, 15 and 18.

According to the triangle inequality theorem- “The sum of the length of any two sides of a triangle should be greater than the third side”. Let us see if this holds in this case-

(12 + 15) > 18

(15 + 18) > 12

(12 + 18) > 15

Thus, we see that the triangle inequality theorem is satisfied. So there is only one triangle possible with the sides of given lengths.

Hence, exactly one unique triangle exists with the given side lengths, option B is correct.

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Your question was incomplete. Check for full content below-

How many triangles exist with the given side lengths?

12 in, 15 in, 18 in

A) No triangle exists with the given side lengths.

B) Exactly one unique triangle exists with the given side lengths.

C) More than one triangle exists with the given side lengths.

The triangle with angles 44 degrees, 54 degrees, and 82 degrees will be a scalene triangle.

We are given the following:

The measures, in degrees, of the three angles of a triangle are x, x + 10, and 2x - 6.

We know from the triangle angle sum property that the sum of its internal angles is 180 degrees.

Let us find the given angles;

x + x + 10 + 2x - 6 = 180 degrees

4x + 4 = 180 degrees

4x = 180 - 4 degrees

x = 176 / 4 degrees

x = 44 degrees

So,

Angles will be;

x = 44 degrees

x + 10 = 44 + 10 = 54 degrees

2x - 6 = 2 * 44 - 6 = 88 - 6 = 82 degrees

All the angles are different.

Thus, the triangle with angles 44 degrees, 54 degrees, and 82 degrees will be a scalene triangle.

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Option (d)- No, because the events are not independent. Hence we can not conclude that because (0.26)(0.15) = 0.039 about 4% of the labor force are college-educated labors or operators.

We have given that government data show that 26% of the civilian labor force has at least 4 years of college and that 15% of the labor force works as laborers or operators of machine or vehicle.

So here,

event A = 26% of civilian labor force hast at least 4 years of college

event B = 15% of the labor force works as laborers or operators of machines or vehicles

Therefore it is observe that both the events are not independent.

Hence we cannot conclude that because (0.26)(0.15) = 0.039 about 4% of the labor force are college-educated laborers or operators.

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After doing a hypothesis test the conclusion is reject [tex]H_0[/tex] .

Given:

tom is a big green bay packers and aaron rodgers fan. he claims that aaron rodger's average number of touchdowns per game is 2.45. dave (a hardcore bears fan) believes that tom might be inflating rodgers's statistics. from his debut until november 18, 2019, aaron rodgers has played 175 games! dave does not want to look at all of them. he randomly selects 52 games that rodgers played and finds the sample average number of touchdowns to be 1.942 with a standard deviation of 1.42.

here n = 52

σ = 1.42

x = 1.942

μ = 2.45

z = x - μ / σ/√n

= 1.942 - 2.45 / 1.42/√52

= -2.58

p value = 0.0049

[tex]H_0:mean = 2.45[/tex]

[tex]H_a:mean < 2.45[/tex]

Rejection rule:Reject [tex]H_0[/tex] if p value < 0.05

Conclusion Reject [tex]H_0[/tex]

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The answer to the given question is 4096-fold. If it assumed that each cycle in the PCR process takes 5 minutes, then total 4096-fold amplification could be accomplished in an hour.

PCR is based on 3 simple steps needed for any DNA synthesis reaction. Those steps are: denaturation of the template to the single strands; annealing of the primers to every original strand for a new strand synthesis; and development of the new DNA strands from the primers.

In this case, each cycle takes 5 minutes and doubles the DNA.

Thus, in one hour, there would be 60 / 5 = 12 cycles.

So, the DNA would be amplified 212 = 4096-fold.

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Because EFGH is a rhombus, the distance from E to F is the same distance from E to H. Since E is the same distance from F as it is from H, it must lie on the perpendicular bisector of FH. By the same reasoning, G must lie on the perpendicular bisector of FH. Therefore, line EG is the perpendicular bisector of segment FH. So, reflecting rhombus EFGH across line FH will take E to G and G to E (because E and G are on the line of reflection) and F to H and H to F (since FH is perpendicular to the line of reflection, and R and H are the same distance from the line of reflection, on opposite sides). Since the image of rhombus EFGH reflected across EG is rhombus EHGF (the same rhombus), line EG must be a line of symmetry from rhombus EFGH.

The solution to the system of equation is [tex](\frac{14}{3},-\frac{16}{3})[/tex]

A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.

Differentiate between substitution and elimination method.

The major difference between the substitution and elimination method is that the substitution method is the process of replacing the variable with a value, whereas the elimination method is the process of removing the variable from the system of linear equations.

The system of equations are :

y = x - 10 and

2x + y = 4

On solving two equations by using substitution method ,we get

By substituting the value of y in another equation ,we obtain the equation in terms of one variable :

Now, according to the question

⇒ 2x + (x - 10) = 4

⇒ (2x + x) = (4 + 10)

⇒ 3x = 14

⇒ x = 14/3

Further for y ,we substitute obtained value of x in the equation

y = x - 10

Now,

[tex]y = \frac{14}{3}-10[/tex]

  [tex]=\frac{(14-30)}{3}[/tex]

  [tex]= (\frac{-16}{3})[/tex]

  [tex]= - (\frac{16}{3})[/tex]

Hence ,the solution is (x,y) : [tex](\frac{14}{3},-\frac{16}{3})[/tex]

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Answer:

[tex]3(4)^{23}[/tex]

Step-by-step explanation:

Let the first term be [tex]a[/tex] and the common ratio be [tex]r[/tex].

We know [tex]a=3[/tex] and [tex]ar=12[/tex], meaning [tex]r=4[/tex].

This means the 24th term is [tex]3(4)^{23}[/tex].