After 3 hours of of driving, Paul had gone 183 miles. What was his average rate of speed? Explain your answer.

The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.

To find the expected number of visits to 0 before reaching 4, analyze two cases:

By the given data, the probabilities of two cases are:

P(success) p = 1/4,

P(failure)=3/4.

The expected count of failures, X, can be found in terms of success probability p as

[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]

On substituting p = 1/4 gives:

[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]

On taking (1/4) gives

[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]

Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]

This forms a geometric series tends to infinity and the sum is given by :

[tex]S_\infty = a/(1-r)[/tex]

Here: a= 3/4

r = 3/4

Plugging these values into formula gives:

[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]

[tex]S_\infty= 3/4/(1-3/4)[/tex]

On subtracting the denominator gives:

= 3/4/(1/4)

On taking reciprocal gives:

= 3/4 * 4

On simplifying gives:

= 3

Substituting these value into given equation 1 gives:

E(X) = 1/4*[3]

On multiplying gives:

E(X) = 3/4.

Therefore, the  expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

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Answer:

4 x 10⁵

so that i think will be OD)

Answer:

r = 4

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define equation

-5 + 22 = r - 4 + 3r + 5

Step 2: Solve for r

Step 3: Check

Plug in r to verify it's a solution.

Answer: 80

Step-by-step explanation:

First you split the shape into simple parts, and think about the measurements when you do so. Although you can't see my work, the way I split it is a rectangle that measures 8 by 4, and a rectangle that measures 8 by 6. You find the answer to these separately (32 and 48) and add them together (80).

Answer:

8 feet

Step-by-step explanation:

All you have to do is find the area of one box and find the root to find the cube edge, as it says they have the same volume.

Lets find the volume of the rectangular box.

8 x 4 x 16 =

32 x 16 =

512.

The volume of the cube is 512 feet cubed, but you are looking for the edge.

The edge cubed should be equal to 512 feet cubed.

So 512 cube root is 8, because 8 x 8 x 8 is 512.

8 feet.

Hope this helps!

Answer:

The answer to your question is 2744 ft³

Step-by-step explanation:

Data

length = 14 ft

width = 14 ft

height = 14 ft

- Volume of a Cube

Volume = length x width x height

-Substitution

Volume = 14 x 14 x 14

-Simplification

Volume = 2744 ft³

Conclusion

The volume of this cube is 2744 ft³

Answer:

y = 3x + 7.

To graph the line mark off the 2 points and draw a line through them.

Step-by-step explanation:

The slope = (-2-7) / (-3-0)

= -9/-3

= 3.

The value of b is found using the point-slope form of a line:

y - y1 = m(x - x1)

using m = 3, (x1, y1) = (0, 7):

y - 7 = 3(x - 0)

y = 3x + 7.

Answer:

Step-by-step explanation:

Grove City = 45,032

Franklin = 41,064

Franklin < Grove City

5 thousands > 1 thousand

Answer:

8

Step-by-step explanation:

we can say that AD is congruent to DC

so your equation for x is: 4x - 1 = 2x

solve this to get x = 0.5

plug x into and equation and multiply you answer by 2 to find the hypotenuse of triangle ABC and DEF

4(0.5) - 1 = 1

hypotenuse: 1 x 2 = 2

since we know x is 0.5, plug this into 4x + 1 to find the length of the leg FE,

4(0.5) + 1 = 3

In the diagram, it shows that the legs of triangle are congruent

this means that FE, ED, BA, and BC are all congruent

since we know FE is 3, we know that all the other sides are 3 as well

this means that the perimeter of the triangle is: leg + leg + hypotenuse

so 3 + 3 + 2

the perimeter is 8

Answer: 7 x 10 + 2 x 1 + 6 x 1/10+ 3 x 1/1000

Step-by-step explanation: just had this question on the test

Answer:

1/3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

let the number of songs Byron have be s songs.

s + 26 = 75

Answer:

D

Step-by-step explanation:

s= number of songs played.

s+26=75

s-26=75-26

s=49

Answer:

good luck tho oh and dont forget to tell me the answer

Step-by-step explanation:

Answer:

2x(9x - 8)(x - 1)

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]X + Y \geq 15\\\\10X + 5Y \leq 100[/tex]

we want to put it into terms of Y

[tex]y \geq 15 - x\\and\\5y \leq 100 - 10x\\y \leq 20 - 2x[/tex]

the graph is in the attached image. Any point in the shaded overlap region where x is greater than or equal to 0 (assuming you cannot have negative coins) works, e.g. (2, 14)

The solution of the inequalities is required.

One of the solutions is [tex](5,10)[/tex]

Number of dimes is [tex]x[/tex]

Number of nickels is [tex]y[/tex]

Minimum number of coins is 15.

So, [tex]x+y\geq 15[/tex]

Maximum total value of the coins is $1

So, [tex]0.1x+0.05\leq 1[/tex]

The equations are

[tex]x+y=15[/tex]

[tex]0.1x+0.05y=1[/tex]

Points of the first equation

[tex](0,15)[/tex] and [tex](15,0)[/tex]

Graph the points and draw a line through them.

Points of the second equation

[tex]x=0[/tex]

[tex]y=\dfrac{1}{0.05}=20[/tex]

[tex]y=0[/tex]

[tex]x=\dfrac{1}{0.1}=10[/tex]

[tex](0,20)[/tex] and [tex](10,0)[/tex]

Graph the points and draw a line through them.

The shaded regions can be determined by substituting the point in the equations.

One of the solutions is [tex](5,10)[/tex]

This means there are 5 dimes and 10 nickels.

[tex]5+10=15\geq 15[/tex]

[tex]0.1\times 5+0.05\times 10=1\leq 1[/tex]

Hence, one of the solutions is [tex](5,10)[/tex].

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Answer:

X=17

Step-by-step explanation:

73+x=90 90-73=17

Answer:

(4,3)

Step-by-step explanation:

2y = x + 2

x - 3y = -5

Rearrange the second equation to equal y.

x - 3y = -5

x + 5 = 3y

(x+5)/3 = y

Substitute into the first equation.

2y = x +2

2[(x+5)/3] = x + 2

(2x + 10)/3 = x + 2

2x + 10 = 3(x + 2)

2x + 10 = 3x + 6

10 - 6 = 3x - 2x

4 = x

Therefore, the correct ordered pair is (4,3) since x is equal to 4.

Answer:

x = ± [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]|a|= \left \{ {a,if{a\geq 0} \atop-a, if {a<0}} \right.[/tex]

~~~~~~~~~~~~

7 | 3x | + 2 = 16

7 | 3x | = 14

| 3x | = 2

1). 3x = 2

x = [tex]\frac{2}{3}[/tex]

2). - 3x = 2

x = - [tex]\frac{2}{3}[/tex]

Answer:

i believe its the rise and the run of the slope.

Step-by-step explanation:

i believe its something similar to this photo

Answer:

3.5

Step-by-step explanation:

 3.5 inches would represent 350 feet.

Relationship between inches and feet is that one inch is equal to [tex]\boldsymbol{100}[/tex] feets as per the map.

So,[tex]350[/tex] feet represent [tex]\frac{350}{100}=3.5[/tex] inches.

Therefore, [tex]\boldsymbol{3.5}[/tex] inches would represent [tex]350[/tex] feet in decimal.

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Answer:

c = 6P

Step-by-step explanation:

equation format: c = mP

c = the total cost Donna pays

m = the cost per pound of chocolate(6)

P = the amount of pounds Donna buys

Since we know the cost per pound is $6, we can input it into the equation format:

c = 6P

Now we have an equation that represents the total cost (c) that Donna pays for P pounds.

Let C = total cost that Donna pays.

Donna buys P pound at $6 per pound tells me to multiply.

C = 6P.

Understand?

Answer:

Number of stock A = 200

Number of stock B = 300

Step-by-step explanation:

Let :

Number of stock A shares = a

Number of stock B shares = b

Worth of stock A = 50 * a = 50a

Worth of stock B = 60 * b = 60b

50a + 60b = 28000 - - - (1)

Triple the value of stock B:

3 * 60 = 180

Value of stock A goes up by 50%

(100 + 50)% * 50 = 1.5 * 50 = 75

75a + 180b = 69000 - - - (2)

50a + 60b = 28000

75a + 180b = 69000

Multiply equation 1 by 3 and subtract

150a + 180b = 84000

75a + 180b = 69000

75a = 15000

a = 15000/75

a = 200

75(200) + 180b = 69000

15000 + 180b = 69000

180b = 69000 - 15000

180b = 54000

b = 300

Answer:

ACD

Step-by-step explanation:

VNQLW3M2L,Q;KJ52KQ

Answer:

Associative Property

Step-by-step explanation:

:)

9514 1404 393

Answer:

  k = -50

Step-by-step explanation:

The fraction denominators are 5 and 10. The least common multiple of those values is 10. This means we can eliminate fractions by multiplying both sides of the equation by 10:

  6k -50 = 7k

Subtracting 6k from both sides of the equation leaves you with the solution:

  -50 = k

Answer:

It depends on what x is

Step-by-step explanation:

I cant help

Answer:

0

Step-by-step explanation:

well if its just 4, then that means it doesnt have a y value

Answer:

The solutions to the system of equations will be:

[tex]y=6,\:x=0[/tex]

Step-by-step explanation:

Given the equation

[tex]-6y+11x=-36[/tex]

[tex]-4y+7x=-24[/tex]

solving the system of equations

[tex]\begin{bmatrix}-6y+11x=-36\\ -4y+7x=-24\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}-6y+11x=-36\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-12y+22x=-72[/tex]

[tex]\mathrm{Multiply\:}-4y+7x=-24\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:-12y+21x=-72[/tex]

[tex]\begin{bmatrix}-12y+22x=-72\\ -12y+21x=-72\end{bmatrix}[/tex]

[tex]-12y+21x=-72[/tex]

[tex]-[/tex]

[tex]\underline{-12y+22x=-72}[/tex]

[tex]-x=0[/tex]

[tex]\begin{bmatrix}-12y+22x=-72\\ -x=0\end{bmatrix}[/tex]

solving for x

[tex]-x=0[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]

[tex]\frac{-x}{-1}=\frac{0}{-1}[/tex]

[tex]x=0[/tex]

[tex]\mathrm{For\:}-12y+22x=-72\mathrm{\:plug\:in\:}x=0[/tex]

[tex]-12y+22\cdot \:0=-72[/tex]

[tex]-12y+0=-72[/tex]

[tex]-12y=-72[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-12[/tex]

[tex]\frac{-12y}{-12}=\frac{-72}{-12}[/tex]

[tex]y=6[/tex]

Therefore, the solutions to the system of equations will be:

[tex]y=6,\:x=0[/tex]