Consider a political discussion group consisting of 6 ​Democrats, 6 ​Republicans, and 4 Independents. Suppose that two group members are randomly​ selected, in​ succession, to attend a political convention. Find the probability of selecting an Independent and then a Republican.

___.
(Type an integer or a simplified​ fraction.)

Answer:

a^ 8 / b^12

Step-by-step explanation:

We know that x^y / x^z = x^ (y-z)

a^-5 b^-4

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

a^ -13 b^8

a^ (-5 - -13) b ^ (-4 -8)

a^ (-5+13) b^ (-4-8)

a^ 8 b^ (-12)

We know that x ^ - y = 1/ x^y

a^ 8 / b^12

Answer:

2.1n-2.1

Step-by-step explanation:

The increase is

1.10 (n-1)= 1.1n -1.1

Add this to the original amount

(n-1) + 1.1n - 1.1

2.1n-2.1

9514 1404 393

Answer:

  (b)  f(x) = (-x)^(1/2)

Step-by-step explanation:

The square root is only defined for argument values that are non-negative. Hence the domain of ...

  f(x) = (-x)^(1/2)

is all values of x less than or equal to zero. This is not "all values of x."

Answer:

[tex]\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}[/tex]

Step-by-step explanation:

A quadratic function is given to us . And we need to fill out the table by using the function . The given function is ,

[tex]\rm\implies y = x^2+x - 6 [/tex]

Here we need to substitute the different values of x , to get the different values of y.

Put x = -3 :-

[tex]\rm\implies y = 3^2-3-6\\ [/tex]

[tex]\rm\implies y = 9 - 3 - 6 \\[/tex]

[tex]\rm\implies y = 0 [/tex]

Put x = -2 :-

[tex]\rm\implies y = 2^2-2-6\\ [/tex]

[tex]\rm\implies y = 4 -2-6\\[/tex]

[tex]\rm\implies y = -4 [/tex]

Put x = -1 :-

[tex]\rm\implies y = -1^2-1-6\\[/tex]

[tex]\rm\implies y = 1 -1-6 \\[/tex]

[tex]\rm\implies y = -6 [/tex]

Put x = 1 :-

[tex]\rm\implies y = 1^2+1-6\\ [/tex]

[tex]\rm\implies y = 2 -6[/tex]

[tex]\rm\implies y = -4[/tex]

Put x = 2 :-

[tex]\rm\implies y = 2^2+2-6\\ [/tex]

[tex]\rm\implies y = 4 +2-6\\ [/tex]

[tex]\rm\implies y = 2[/tex]

Put x = 3 :-

[tex]\rm\implies y = 3^2+3-6\\ [/tex]

[tex]\rm\implies y = 9 +3-6\\ [/tex]

[tex]\rm\implies y = 6 [/tex]

Final table :-

[tex]\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}[/tex]

9514 1404 393

Answer:

  105 ft

Step-by-step explanation:

Let x represent the height of the pole. Then (x -49) is the distance from the pole to the anchor point, and (x+14) is the length of the wire from the top of the pole to the anchor point.

The Pythagorean theorem gives us the relation ...

  (x +14)² = x² +(x -49)²

  x² +28x +196 = x² +x² -98x +2401 . . . . eliminate parentheses

  x² -126x +2205 = 0 . . . . . . . . put in standard form

  x² -126x +3969 -1764 = 0 . . . . "complete the square)

  (x -63) = ±√1764 . . . . . . add 1764, take the square root

  x = 63 +42 = 105 . . . . . . highest value root. The pole must be higher than 49 feet

The height of the pole is 105 feet.

Answer:

can you please send me another one

Answer:

There are two intersections.

(-3,1) and (-1,-3)

Step-by-step explanation:

Answer:

They intersect at (-3,1), and also (-1,-3)

Step-by-step explanation:

Graph:

Answer:

22.5

Step-by-step explanation:

 percent is any number over 100, so 25% is 25 over 100, this means that 25% can be written as:

25100

Now, any number in fractional form (a number over a number) is the same as division so 25% can also be written as a decimal, we just move the decimal point 2 places to the right of 25, like this:

25100=0.25

Now we have two ways that we can solve this problem! I'll start with the fractional method of solving.

Answer:

I don't know, because i really don't know

Answer:

Volume = 204 m³

Step-by-step explanation:

The figure is a triangular prism

Volume of the triangular prism = ½ × a × c × h

Where,

a = 8 m

c = 5.1 m

h = 10 m

Plug in the known values and solve

Volume = ½ × 8 × 5.1 × 10

Volume = 4 × 5.1 × 10

Volume = 204 m³

Answer:

C. 58ft

Step-by-step explanation:

An imaginary triangle is described here. The hypotenuse is 60, and one of the other sides is 15.

60*60=3600

15*15=225

3600-225=3375

sqrt3375=58.09

round that to get 58ft

First take a time derivative of a function describing motion,

[tex]\frac{d}{dt}h(t)=\frac{d}{dt}-4.9t^2+19.6t-14.6=-9.8t+19.6[/tex].

Finding the maxima of the function is obtained by determining where the critical points are. You can find the critical points by equating the derivative with 0 and solving for t,

[tex]\frac{d}{dt}h(t)=0[/tex]

[tex]-9.8t+19.6=0\implies t=\frac{19.6}{9.8}=\boxed{2}[/tex].

So at 2 seconds the ball peaks in height.

To find out the height feed 2 to the function h.

[tex]h(2)=-4.9\cdot2^2+19.6\cdot2-14.6=\boxed{5}[/tex].

So at 2 seconds the ball reaches maximum height of 5 meters.

Hope this helps :)

Answer:

D) 13

[tex]\sqrt{169} = 13[/tex]

Step-by-step explanation:

We have that the Fuction's result for the given values are

From the Question we are told that

Function

[tex]f(x) = 7x^2 -2x + 5.[/tex]

Generally

For -2

[tex]f(-2) = 7(-2)^2 − 2(-2) + 5.[/tex]

f(-2) =37

For -1

[tex]f(-1) = 7(-1)^2 − 2(-1) + 5.[/tex]

f(-1) =14

For 0

[tex]f(0) = 7(0)^2 − 2(0) + 5.[/tex]

f(0) =5

For 0

[tex]f(1) = 7(1)^2 − 2(1) + 5.[/tex]

f(1) =10

For 2

[tex]f(2) = 7(2)^2 − 2(2) + 5.[/tex]

f(2) =29

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Answer:

C. The graph of f(x) is shifted 11 units up.

Step-by-step explanation:

Given

[tex]g(x) = f(x) + 11[/tex]

Required

Interpret g(x)

When a function is shifted up in b units, the rule is:

[tex](x,y) \to (x,y+b)[/tex]

Replace b with 11

[tex](x,y) \to (x,y+11)[/tex]

Replace y with f(x)

[tex](x,f(x)) \to (x,f(x)+11)[/tex]

So, we have:

[tex]g(x) = f(x) + 11[/tex]

Hence; f(x) is shifted 11 units up.

Answer:

10.5

Step-by-step explanation:

In the picture if you think about it, it has to be a number less than 15 since CB is 15. I picked 12.3 and got it wrong therefore it has to be 10.5.

Answer:

A) 10.5

Step-by-step explanation:

Answer:

4,00 pounds

Step-by-step explanation:

Answer:

4,800 pounds

Step-by-step explanation:

2 tons = 4,000 pounds

800 pounds

4,000 + 800 =

4,800 pounds

9514 1404 393

Answer:

  2,664,118.8 cm³/min

Step-by-step explanation:

The diameter at the water level of 5 m is (5/8)(6 m) = 3.75 m, so the area of the water surface is ...

  A = (π/4)d² = (π/4)(3.75 m)² ≈ 11.044662 m²

When rising at the rate of 24 cm/min, the volume is increasing at the rate ...

  (110,446.62 cm²)(24 cm/min = 2,650718.8 cm³/min

The input volume must be sufficient to accommodate this increase as well as the leakage. Then the input volume is ...

  2,650718.8 cm³/min + 13,400 cm³/min = 2,664,118.8 cm³/min

Answer:

x = 0 or x = 3

Step-by-step explanation:

-3x(x-3)(x^2+16)=0

3x = 0

x-3 = 0

x^2+16 =0 (not possible with real numbers)

x = 0, x= 3

Hence,

x = 0 or x =3

Feel free to mark this as brainliest :D

Answer:

4a+12b-20c

Step-by-step explanation:

Use the distributive property, multiply the number on the outside to everythign on the inside.

4*a=4a

4*3b=12b

-5c*4=-20c

Answer:

C. definition

Step-by-step explanation:

A precise statement of the qualities of an idea, object, or process is called a definition. Hence, option (C) is answer.

Answer:

A

Step-by-step explanation:

The correct answer is A

Answer: [tex]y^\frac{1}{8}[/tex]

Step-by-step explanation:

Ok so when taking roots the number in the little corner at the left of the radical sign (if there is one) is the root you take. It could be the 4th root, 6th root, or the x root. You don't have to use the radical sign though, you can use an exponent to write it. All you have to do is take the reciprocal of the number to find what to write for the exponent. So for those examples it would be [tex]\frac{1}{4}, \frac{1}{6} ,\frac{1}{x}[/tex]. The number in the top left of the radical sign is 8 so the answer would be [tex]y^\frac{1}{8}[/tex]

Answer:  Choice A.   [tex]-x^2+2x+8[/tex]

Work Shown:

[tex](f - g)(x) = f(x) - g(x)\\\\(f - g)(x) = (2x+1) - (x^2-7)\\\\(f - g)(x) = 2x+1 - x^2+7\\\\(f - g)(x) = -x^2+2x+(1+7)\\\\(f - g)(x) = -x^2+2x+8\\\\[/tex]

which shows the answer is choice A.

Side note: be sure to distribute the negative to every term inside the second set of parenthesis. So you wouldn't say -(x^2-7) = -x^2-7. If you did this error, then you'd get to the wrong answer choice C.

Answer:

hope it helps u plz mark me brainliest mate

Step-by-step explanation:

(f-g)(x)=2x+1-(x^2-7)

(f-g)(x)=2x+1-x^2+7

(f-g)(x)= -x^2+2x+8

this is the correct answer

Answer:

Step-by-step explanation:

To begin with the answer. This is very personal, but I would choose D. I think you have to relate things to what you know. How do other people live through the same problem? Does the author believe that the best path has been chosen, or does he/she believe that the central character is doomed to failure? And how do these comments relate to me. You are going to get the most out of any novel when you can relate to the central character or any of the characters for that matter.

I'm not concerned with C. You can read trash and what they say is likely consistent but that only means that trash is pandering to a clientele that does not want to think much. Whatever spin you put on C, agreement is not a terrific thing. It does not make you think.

I suppose B is important if you are reading non fiction. I'm not answering it that way.

A: not the answer. This is a very remote connection. Most of the time symbolism is not the main attraction of any novel nor especially of any non fiction writing.  Moby D*ick is not a great novel because of its symbolism of which there is a huge amount. It is a great novel because the conflict is between man and nature and although that is symbolic, it is not as important as the character study of Ahab (who is himself a symbol). Nor or Ishmael for that matter. I will admit you have to have a Bible in one hand and Moby Di*ck in the other, but it is not critical. The theme is.

Answer:

Option B

Step-by-step explanation:

Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

Slope (m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through (-5, -2) and (3, -1) will be,

m = [tex]\frac{-1+2}{3+5}[/tex]

m = [tex]\frac{1}{8}[/tex]

Equation of the line passing through (h, k) and slope 'm' is given by,

y - k = m(x - h)

Therefore, equation of the line passing through (3, -1) and slope = [tex]\frac{1}{8}[/tex] will be,

[tex]y+1=\frac{1}{8}(x-3)[/tex]

[tex]y=\frac{1}{8}x-\frac{3}{8}-1[/tex]

[tex]y=\frac{1}{8}x-\frac{11}{8}[/tex]

Option B will be the answer.

Answer:

The probability that they purchased a green or a gray sweater is [tex]\frac{12}{31}[/tex]

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

[tex]P(A)=\frac{number of favorable cases}{number of possible cases}[/tex]

The addition rule is used when you want to know the probability that 2 or more events will occur. The addition rule or addition rule states that if we have an event A and an event B, the probability of event A or event B occurring is calculated as follows:

P(A∪B)= P(A) + P(B) - P(A∩B)

Where:

P (A): probability of event A occurring.

P (B): probability that event B occurs.

P (A⋃B): probability that event A or event B occurs.

P (A⋂B): probability of event A and event B occurring at the same time.

Mutually exclusive events are things that cannot happen at the same time. Then P (A⋂B) = 0. So, P(A∪B)= P(A) + P(B)

In this case, being:

You know:

So:

Then:

P(A∪B)= P(A) + P(B)

P(A∪B)= [tex]\frac{8}{31}+ \frac{4}{31}[/tex]

P(A∪B)= [tex]\frac{12}{31}[/tex]

The probability that they purchased a green or a gray sweater is [tex]\frac{12}{31}[/tex]

Answer:

Speed of canoiest is 10 miles/hour.

Speed of current is 2 miles/hour.

Step-by-step explanation:

Let the speed of canoiest is v and the speed of current is u.

distance = speed x time

24 = (v + u ) x 2

v + u = 12 ..... (1)

Now

24 = (v- u) x 3

v - u = 8 .... (2)

By solving (1) and (2)

2 v = 20

v = 10 miles/hour

u = 2 miles/hour