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Katena32 [7]
1 year ago
6

There are 520 marbles in a jar. The ratio of red to yellow marbles is 3:4 and the ratio of yellow to blue marbles is 2:3. What i

s the total number of yellow and blue marbles?
Mathematics
1 answer:
frutty [35]1 year ago
7 0

Answer:

Step-by-step explanation:

Change the 2/3 to 4/6

Now the ratio becomes 3:4:6

So the number of each is

3x + 4x + 6x = 520

13x = 520

x = 40

Red = 3*40 =      120

Yellow = 4*40 = 160

Blue = 6 * 40  = 240

Total =               520

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By definition the area of a rectangle is:
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 w: width
 So we have to clear the width:
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 Substituting the values:
 w = (234) / (18) = 13
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 answer
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Bill, George, and Ross, in order, roll a die. The first one to roll an even number wins and the game is ended. What is the proba
hram777 [196]

Answer:0.5714\frac{1}{15}

Step-by-step explanation:

Given that Bill, George, and Ross, in order, roll a die.

The first one to roll an even number wins and the game is ended.

Since Bill starts the game he can win by throwing even number or lose by throwing odd number

P(win) = 0.5, otherwise, the die will go to George.  For Bill to win, both George and Ross should throw an odd number so that Bill again gets the chance with game non ending.

Thus we have Prob of Bill winning =P of Bill winning in I throw +P of Bill winning in his II chance of throw +....infinitely

To get back the dice once he loses probability

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= 0.5+0.25(0.5)^2+0.25(0.5)^3(0.25)+...

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4 0
1 year ago
Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be
Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of t=0.6482

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

h(t)=-16t^2 +v_{o}t+s       Eqn(1).

Where:

h(t) : is the height range as a function of time

v_{o}   : is the initial velocity

s     : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

h(t)=-16t^2 + v_{o}t + 40        Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

<u>Ben:</u>

We know that v_{o}=60ft/s

Thus Eqn. (2) becomes:

h(t)=-16t^2+60t+40        Eqn.(3)

<u>Josh:</u>

We know that v_{o}=48ft/s

Thus Eqn. (2) becomes:

h(t)=-16t^2+48t+40       Eqn. (4).

<em><u>Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at </u></em>h(t)=0<em><u>. Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one. </u></em>

Thus we have for Ben, Eqn. (3) gives:

h(t)=0-16t^2+60t+40=0

Using the quadratic expression to find the roots of the quadratic we have:

t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec

Since time can only be positive we reject the t_{2} solution and we keep that Ben's book took t=4.3276 seconds to reach the ground.

Similarly solving for Josh we obtain

t_{1}=3.6794sec\\t_{2}=-0.6794sec

Thus again we reject the negative and keep the positive solution, so Josh's book took t=3.6794 seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482

So to answer the original question:

<em>Whose textbook reaches the ground first and by how many seconds?</em>

  • Josh's textbook reached the ground first
  • Josh's textbook reached the ground first by a difference of t=0.6482

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Answer:

IMPOSSIBLE

Step-by-step explanation:

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