A triangle PQR has vertices P(2, 1, -2), Q(1, 2, 2), R(3, 0, 2). Use the distance formula to decide which one of the following properties the triangle has.
1. isoceles with |QP| = |QR|
2. not isoceles
3. isoceles with |P Q| = |P R|
4. isoceles with |RP| = |RQ|

Probability that Margie's first serve will be good at least four of the next six times she serves is 0.68

What is Binomial Distribution in Probability?

Assume that n independent replications of a random experiment with exactly two outcomes are performed. Success has a probability of [tex]p[/tex], while failure has a probability of [tex]q[/tex]. Assume that out of these n times, we will experience success [tex]x[/tex] times and failure [tex]n-x[/tex] times. There are [tex]^nC_x[/tex] different ways in which we can succeed. If, [tex]X[/tex] has a binomial distribution, then,

[tex]P(X=x)=p(x)[/tex]

                  [tex]=[/tex] [tex]^nC_xp^xq^{n-x}[/tex]

for [tex]x[/tex] = 0, 1,..., n. Here,  [tex]q=1-p[/tex]. A binomial variate is any such random variable [tex]X[/tex]. A group of n separate Bernoullian trials is known as a binomial trial. Binomial distribution requirements:

For each trial, the odds of success [tex]p[/tex], or failure [tex]q[/tex], remain constant.

Given,

Probability of good serves = Success

⇒ [tex]p=\frac{20}{30}[/tex]

⇒[tex]p=\frac{2}{3}[/tex]

Failure = [tex]q[/tex]

⇒ [tex]q=1-p[/tex]

⇒ [tex]q=1-\frac{2}{3}[/tex]

⇒ [tex]q=\frac{1}{3}[/tex]

Number of trials [tex]= n[/tex]

[tex]n=6[/tex]

Probability of at least four good serve = [tex]P(4 < X < 6)[/tex]

According to the binomial distribution,

Therefore,

[tex]P(4 \leq X \leq 6)=P(X=4)+P(X=5)+P(X=6)[/tex]

                      [tex]=[/tex] [tex]^6C_4(\frac{2}{3}) ^4(\frac{1}{3})^2+ ^6C_5(\frac{2}{3}) ^5(\frac{1}{3})^1+^6C_6(\frac{2}{3}) ^6(\frac{1}{3})^0[/tex]

                      [tex]=[/tex] [tex]15\times\frac{16}{729} +6\times\frac{32}{729} +1\times\frac{64}{729}[/tex]

                      [tex]=[/tex] [tex]\frac{496}{729}[/tex]

                      [tex]= 0.68[/tex]

To know more about Binomial distribution..........

https://brainly.com/question/9325204

#SPJ4

Answer:

corresponding, supplementary, alternate interior, same side interior, vertical, alternate exterior, corresponding, alternate exterior, vertical, and alternate interior

In the figure 10, the pair of angles are alternate interior angles.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

From the given figure,

1) corresponding angles

2) Adjacent angles (Supplementary)

3) Alternate interior angles

4) Allied angles (Same side interior)

5) Vertically opposite angles

6) Alternate exterior angles

7) corresponding angles

8) Alternate exterior angles

9) Vertically opposite angles

10) Alternate interior angles

Therefore, in the figure 10, the pair of angles are alternate interior angles.

Learn more about the parallel line angles here:

https://brainly.com/question/17237586.

#SPJ2

Calculate the total amount invested by summing up all the values of the investment.

Total = 50,000

Calculate the weight of each investment. For WOOPS, weight = 5000 / 50000 = 10% and so on.

Now, Expected Return = sum of weight x Returns = 10% x 0.14 + 20% x 0.16 + ... + 18%x 0.18 = 16.01%

b) Similarly,

Beta of the portfolio = sum of weight x beta = 10% x 0.6 + 20% x 0.8 + ... + 18% x 0.18 = 0.7605

c) Portfolio has less systematic risk as the beta for the average market is 1, which is above the portfolio

d) Using CAPM, Return = Rf + beta x (Rm - Rf) = 4% + 0.7605 x (14% - 4%) = 11.605%

To calculate the expected return of a portfolio, the investor needs to know the expected return of each security in the portfolio and the total weight of each security in the portfolio. This means that investors need to sum the weighted averages of the expected returns (RoRs) of each security.

Investors are based on estimates of the expected rate of return on securities, assuming that what has proven to be true in the past will be true in the future. Investors do not use the structural view of the market to calculate the expected return. Instead, it determines the weight of each security in the portfolio by dividing the value of each security by the total value of the security.

Learn more about Percentage here: https://brainly.com/question/843074

#SPJ4

Answer:

This is your answer.

Step-by-step explanation:

There are different kinds of angles:

Angles below 90= Acute

90= Right

91–179= Obtuse

180= Straight Angle

181–359= Reflex Angle

360= Complete Angle or Circle.

Because 80 degrees is less than 90 degrees, Angle ABC is an acute angle.

Answer:

[tex]x=-1,\frac{5}{7}[/tex]

Step-by-step explanation:

1) Split the second term in [tex]7{x}^{2}+2x-5[/tex] into two terms.

1 - Multiply the coefficient of the first term by the constant term.

[tex]7\times -5=-35[/tex]

2 - Ask: Which two numbers add up to 2 and multiply to -35?

7 and -5.

3 - Split 2x as the sum of 7x and -5x.

[tex]7x^2+7x-5x-5[/tex]

2)  Factor out common terms in the first two terms, then in the last two terms.

[tex]7x(x+1)-5(x+1)=0[/tex]

3) Factor out the common term x+1.

[tex](x+1)(7x-5)=0[/tex]

4) Solve for x.

1 - Ask: When will (x+1)(7x-5) equal zero?

When x + 1 0 or 7x-5=0

2 - Solve each of the 2 equations above.

[tex]x=-1,\frac{5}{7}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What are the quadratic formulas?}[/tex]

[tex]\bullet\rm{\ \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

[tex]\bullet\rm{\ ax^2 + bx + c = 0}[/tex]

[tex]\huge\textbf{What are we solving for?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{What do we have to do?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{Factor the LEFT side of the given}\\\\\huge\textbf{equation:}[/tex]

[tex]\rm{(7x - 5)(x + 1) = 0}[/tex]

[tex]\rm{(7x - 5) \times (x + 1) = 0}[/tex]

[tex]\huge\textbf{Set 0 to the factors:}[/tex]

[tex]\rm{7x - 5 = 0\ or\ x + 1 = 0}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x = \dfrac{5}{7}\ or\ x = -1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\mathsf x = \dfrac{5}{7}\ or\ \mathsf{x} = -1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

-16t^2 represent the position on the graph on the negative side.

According to the statement

we have given equation is h(t)=5+100t-16t^2 -(1)

And we have to find representation of -16t^2

we know that the equation number (1) represent the Quadratic Equation

And in this we have to solve the Quadratic Equation and find the representation of the given terms. then

h(t)=5+100t-16t^2

5+100t-16t^2 = 0

16t^2 -100t-5 = 0

In this equation 16t^2 represent the equation on the graph.

It means that it shows the position on the graph.

Overall, -16t^2 represent the position on the graph on the negative side.

Learn more about GRAPH here https://brainly.com/question/4025726

#SPJ1

Answer:

the answer is 17y 3y+6y is 9y plus 8y is 17y

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Simplifying it:}[/tex]

[tex]\mathsf{3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathsf{(3y + 6y + 8y)}[/tex]

[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]

[tex]\mathsf{\rightarrow 9y + 8y}[/tex]

[tex]\mathsf{\rightarrow 17y}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{17}\mathsf{y}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

1:3.

Step-by-step explanation:

Probability(getting > 3 on one roll) = 3/6 = 1/2.

So on 2 cubes rolled the probability   of getting > 3 is 1/2 * 1/2 = 1/4.

As a ratio this is 1:3.

The table represents an exponential function:

[tex]f(x) = 3^x[/tex]

Then the correct option is B.

Here we have the table:

x       y

1       3

2      9

3      27

4      81

5      243

You can see that each time that x increases by one unit, the value of is multiplied by 3. This is clearly an exponential function.

The function actually is:

[tex]f(x) = 3^x[/tex]

Evaluating it we get:

[tex]f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\...[/tex]

So the correct option is B, exponential.

If you want to learn more about exponential functions:

https://brainly.com/question/11464095

#SPJ1

The surface area of the composite figure shown in the figure attached is 233.6 cm²

An equation is an expression that shows the relationship between two or more numbers and variables.

The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²

The surface area of the composite figure shown in the figure attached is 233.6 cm²

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The value of x is 6 and the measure of ∠C is 86 degrees

The complete question is added as an attachment

Given that:

ABCDE ~ LMNOP

It means that we have the following equivalent ratio

ED : BC = PO : MN

This gives

8 : 6 = 12 : x

Express as fraction

6/8 = x/12

Multiply both sides by 12

12 *  6/8 = x

Evaluate

9 = x

Rewrite as

x = 9

Also

ABCDE ~ LMNOP implies that the corresponding angles are equal

The corresponding angle of C is N

And, we  have:

N = 86

This implies that

C = 86

Hence, the value of x is 6 and the measure of ∠C is 86 degrees

Read more about similar shapes at:

https://brainly.com/question/14285697

#SPJ1

The ratio of all the corresponding sides of the triangle are equal to each other.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two triangles are said to be similar if they have the same shape and the same corresponding angles.

Also, the ratio of all the corresponding sides of the triangle are equal to each other.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The trigonometric values are:

[tex]cos(\frac{3\pi}{4})=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=\frac{1}{\sqrt{2} }[/tex]

The given trigonometric identities are:

[tex]cos(\frac{3\pi}{4} )\\\\sin(\frac{3\pi}{4})[/tex]

Note that:

[tex]\pi=180^o\\\\\frac{3\pi}{4}=135^0[/tex]

Therefore, using the calculator for the given expressions:

[tex]cos(\frac{3\pi}{4})=cos135^0=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=sin135^0=\frac{1}{\sqrt{2} }[/tex]

Learn more on exact values of trigonometric expressions here: https://brainly.com/question/11907145

#SPJ1

The x-coordinate of the point is -2

The points are given as:

J = (-6, -2)

K = (8, -9)

m : n = 2 : 5

The x-coordinates of the point is calculated as:

[tex]jk = \frac{m}{m+n} *(x_2 -x_1) +x_1[/tex]

So, we have:

[tex]jk = \frac{2}{2+5} *(8+6) -6[/tex]

This gives

[tex]jk = \frac{2}{7} *14 -6[/tex]

So, we have:

jk = 4 - 6

Evaluate

jk = -2

Hence, the x-coordinate of the point is -2

Read more about line segment ratio at:

https://brainly.com/question/15895161

#SPJ1

Answer:

[tex]y = \frac{1}{4} x + 9[/tex]

Step-by-step explanation:

All lines take the form

[tex]y = mx + c[/tex]

Where m is the gradient (or slope), and c is the y-intercept. To find the gradient if a line perpendicular to another, we must find the negative reciprocal of the other line. The gradient of the line given is -4, so our negative reciprocal is 1/4.

To find our y-intercept, we must find the point where the line crosses the y-axis (in other words, when the X coordinate is 0). Helpfully, the coordinate given is already at this point, so we can simply take the y coordinate from here, and we know our y-intercept is 9. Putting this altogether, our equation is:

[tex]y = \frac{1}{4} x + 9[/tex]

Answer:

B.) 54π units²

Step-by-step explanation:

First, we need to find the height of the cone. We can do this using the Pythagreom Theorem.

a² + b² = c²                              <----- Pythagreom Theorem

3² + b² = 15²                            <----- Insert side lengths

9 + b² = 225                            <----- Solve 3² and 15²

b² = 216                                   <----- Subtract 9 from both sides

b = 14.7 units                          <---- Take square root of 216

Now, we can use the surface area of a right cone equation to find the final answer.

r = 3 units

h = 14.7 units

SA = πr(r + √(h² + r²))                              <----- Surface Area equation

SA = π(3)(3 + √(14.7² + 3²))                     <----- Insert values

SA = π(3)(3 + √(216 + 9))                         <----- Solve 14.7² and 3²

SA = π(3)(3 + √225)                                <----- Add 216 and 9

SA = π(3)(3 + 15)                                     <----- Take square root of 225

SA = π(3)(18)                                            <----- Add 3 and 15

SA = 54π units²                                     <----- Multiply 3 and 18

The slope of both lines is mathematically equivalent to

[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]i

Generally, the equation for Slope is  mathematically given as

[tex]S= dy / dx[/tex]

Therefore

[tex]Slope of PQ = \frac{(z - v)}{(x - w)}[/tex]

[tex]S of P'Q' =\frac{ (z + b - (v + b))}{((x + a) - (w + a))}\\\\S of P'Q' =\frac{ (z - v)}{(x - w)}[/tex]

The slopes of both lines are equivalent to

[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]

In conclusion, The slope of both lines is equivalent to

[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]

Read more about slope

https://brainly.com/question/3605446

#SPJ1

Answer:

A: z - v | x - w

Step-by-step explanation:

Answer:

The scale factor from the original triangle to the image is 1/2.  The scale factor from the image to the original is 2.

Step-by-step explanation:

I make a sketch of the information.  Look at the corresponding sides.  Side AC on the big triangle is 8 and A'C' is 4.  It is half of the size of the large triangle.  That is true for each pair of sides.

If I went the other way, the original sides are twice as big as the images sides.

x + 3, x > -3 is the piece which will be included in the given function          f(x) = [ x + 3 ]. This can be obtained by removing modulus and finding the value for x.

Given that,  

f(x) = [ x + 3 ] which is an absolute value function.

Therefore,

| x+3 | > 0

By removing the modulus,

x+3 > 0

x > - 3

Hence x + 3, x > -3 is the piece which will be included in the given function          f(x) = [ x + 3 ].

Learn more about absolute value function here:

brainly.com/question/10538556

#SPJ4

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Consider this absolute value function.

f(x) = [ x + 3 ]

If function f is written as a piecewise function, which piece will it include?

A. x + 3, x > 3

B. x + 3, x > -3

C. -x + 3, x < -3

D. -x - 3, x < 3

Answer:

The Answer is C. X+3, x > -3

for edmentum users

Step-by-step explanation:

The expressions that have a sum of 6 are Options C and D

In this case, we use the following rules

(-) + (-) = -

(+) + (+) = +

(+) + (-) = -

(-) + (+) = -

From the first case

8 + 2 = 10

(-4) + (-2) = -4 + -2 = -6

(-3) + 9 = -3 + 9 = 6

7 + (-1) = 7 - 1 = 6

Thus, the expressions that have a sum of 6 are Options C and D

Learn more about mathematical signs here:

https://brainly.com/question/25421984

#SPJ1

Answer:

60 degrees

Step-by-step explanation:

The sum of the interior angles of a triangle are 180.  The bottom triangle give you two of the angle measurements (43 and 35)  Take 180 - 43 -35 = 102.  Angle E is 102.  Vertical angles are congruent so that mean that we can use that to find angle a.  Again, the sum of the interior angles adds up to 180.  180 - 102 - 18 gives us the measurement of angle a (60)

Hello, the solution is in this photo.

The correct answer is 300

Answer:

300cm^2

Step-by-step explanation:

Replace pie by 3. 3(10)^2 which equals to 300cm^2. 10 is radius.

Resolviendo un sistema de ecuaciones, veremos que se vendieron 250 boletos de adulto.

Definamos las variables:

Se vendieron un total de 430 boletos, entonces:

x + y = 430

Y se vendieron 70 boletos de estudiante menos que boletos de adulto:

y = x - 70

Tenemos el sistema de ecuaciones:

x + y = 430

y = x - 70

Para resolverlo, podemos reemplazar la segunda ecuación en la primera:

x + y = 430

x + (x - 70) = 430

2x = 430 + 70 = 500

x = 500/2 = 250

Se vendieron 250 boletos de adulto.

Sí quieres aprender más sobre sistemas de ecuaciones:

https://brainly.com/question/13729904

#SPJ1

Intermediaries who are independent, but agree to cooperate have likely formed a(n) contractual distribution system.

The most commonplace form of Contractual VMS is Franchising. In franchising, the manufacturer authorizes the distributor to promote its product below the producer's call against some annual license rate. For example, McDonald's, Dominos, Pizza Hut, etc. are all styles of a franchise that might be operating on a contractual foundation.

A form of vertical advertising machine in which unbiased firms at unique degrees of distribution are tied together by using contracts to achieve economies of scale and more income impact.

A vertical advertising system refers to a marketing system that aims to draw and attain organizations running inside the same industry. then again, horizontal advertising and marketing device refers to an advertising and marketing system whereby corporations which can be on equal degree join collectively to advantage economies of scale.

Learn more about the distribution system here: https://brainly.com/question/1001771

#SPJ4

Answer:

multiply x and y coordinates by 2 since its a whole number dilation (make bigger basically) ... (-8,6)

Step-by-step explanation:

Answer:

D. (4,0) and (-4,0)

C. there is one discontinuity at x=3

Step-by-step explanation:

Roots can be found by setting f(x)=0:

f(x)=(x^2-16)/(x^2-2x-3)

0=(x^2-16)/(x^2-2x-3), multiply both sides by x^2-2x-3 to get rid of the denominator

0=x^2-16, use difference of squares to factor it

0=(x+4)(x-4)

x=4,-4

Therefore the roots are (4,0) and (-4,0)

Discontinuities are when f(x) is undefined, and f(x) is undefined when something is divided by 0

Set the denominator equal to 0:

0=x^2-6x+9, use the form a^2 - 2ab + b^2 to factor

0=(x-3)^2

x=3

Therefore, there is a discontinuity at x=3

Answer: The lowest common multiple of 12, 18, and 56 would be 504. Why? Well, see below for an explanation!

Step-by-step explanation: What is the lcm? Well, the lcm of two or more numbers is the lowest possible number that each number has in common as a multiple. Because we are dealing with large numbers, we can tell that the lcm will be a multiple of these numbers times at least 5. I multiplied all the numbers by 10, and it was too large and did not work. However, I backed up and tried 9.

56 x 9 = 504.

Why is this acceptable? Well, this is acceptable because I found that 504 can be divided by 12 and 18 both to get a whole number.

504 divided by 18 equals 28.

504 divided by 12 equals 42.

Using this principle, we will find that 504 is the lowest number that 12, 18, and 56 have in common.

Your final answer: 504 is the lowest common denominator. If you need extra help, let me know and I will gladly assist you.

To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.

This method consist of extracting the common and uncommon prime factors, then

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 18 \ \ \ 56}\\ \ 6 \ \ \ \ 9 \ \ \ \ 28\\ \ 3 \ \ \ \ 9 \ \ \ \ 14\\ \ 3 \ \ \ \ 9 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 3 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 1 \ \ \ \ \ 7\\ \ 1 \ \ \ \ 1 \ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 3\\ 3\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]

                        [tex]\sf{L.c.m.(12,18,56)=2\times2\times2\times3\times3\times7}[/tex]

                                        [tex]\sf{L.c.m.(12,18,56)=2^{3}\times3^{2}\times7 }[/tex]

                                            [tex]\boxed{\boxed{\sf{L.c.m.(12,18,56)=504}}}[/tex]

The lowest common multiple of 12, 18, and 56 is 504.

Patrick has an absolute advantage in playing quarterback.

Given a table containing touchdowns and field goals by Partrik and Field goals as under:

Person                       Touchdowns                         Field goals

Patrik                              39                                            13

Jimmy                             25                                            5

We are required to find a person who has an absolute advantage in playing quarterback.

Absolute advantage is the ability of an individual, company to produce greater advantage of good or service than the individual.

Total of touchdowns and field goals by Patrik=39+13=52

Total of touchdowns and field goals by Jimmy=25+5=30

We can see that total of touchdowns and field goals by Patrik is greater than total of touchdowns and field goals by Jimmy. So Patrik has an absolute advantage playing quarterback.

Hence Patrick has an absolute advantage in playing quarterback.

Learn more about competitive advantage at https://brainly.com/question/26356446

#SPJ4

Question is incomplete as it should include the following table:

Person                       Touchdowns                         Field goals

Patrik                              39                                            13

Jimmy                             25                                            5

The probability in all given conditions is 1/4.

According to the statement

Number of coin tossed = 3

Total outcomes = 8

Now, we have to find the probabilities on different conditions.

Probability = A head on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

Probability = alternating tale and head / total outcomes

Probability = 2/8

Probability = 1/4.

Probability = A No tails on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

So, The probability in all given conditions is 1/4.

Learn more about PROBABILITY here https://brainly.com/question/25870256

#SPJ1