explain how complex fractions can be used to solve problems involving ratios

Answer:

Option D. 20 minutes.

Step-by-step explanation:

It has been given in the question that distance between the shore of a lake is 3 miles.

Speed of Jim is 4 mph and speed of John is 5 mph.

Let they meet after time t hours.

Therefore distance traveled by Jim in t hours = 4×t miles

and distance traveled by John in t hours = 5×t miles

Total distance they cover = 3 miles.

Now 4t + 5t = 3

9t = 3

t = 3/9 hours.

t = (3×60)/9 minutes.

t = 20 minutes.

Answer is they will meet after 20 minutes.

Answer:

All boys in each grade.

Step-by-step explanation:

The teacher wants to know specifically about whether the boys in the entire school prefer watching television or playing outdoor games after school. The teacher does not include girls, or specifically people on the football team. The teacher also only wants to know about boy students not teachers.

he needs  1/4 gallon total

4 walls so need to divide 1/4 x 4

1/4 / 4/1 = 1/4 * 1/4 = 1/16 gallon on each wall

Answer:

He needs [tex]\frac{1}{16}[/tex] of gallon to paint each wall.

Step-by-step explanation:

Given :  He needs 1/4 of a gallon to paint all four walls .

To Find : How much paint will he need for each of his 4 walls if he uses the same amount of paint on each .

Solution:

He needs 1/4 of a gallon to paint all four walls .

He need paint to color 1 wall = [tex]\frac{\frac{1}{4}}{4}[/tex]

                                               = [tex]\frac{1}{16}[/tex]

Hence he needs [tex]\frac{1}{16}[/tex] of gallon to paint each wall.

The probability of getting the desired outcome is 5/12.

Like "point" and "time," the concept of "the likelihood of anything" is one of those concepts that we can't precisely describe but that are nevertheless helpful. The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.

Given flip a coin and roll a 6-sided die. to find the probability that you will flip a head and roll less than a 6. since there are two events that are separated from each other hence we need to find out the probability of both P(a∪b). hence,

probability of getting head on a coin flip P(a) = 1/2

probability of getting less than 6 on dice roll P(b) = 5/6

Probability of getting both the vent simultaneously = P(a) * P(b)

Therefore, the Probability of getting flipped a head and rolling less than a 6 is 5/12.

Learn more about probability here:

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If I am understanding you correctly,  first solve for the whole sector, which you can use this formula. 

[tex] \frac{\Theta}{360} \pi r^2[/tex] 

Once you find the area of the sector, all you have to do is get the area of the triangle and then subtract the area of the triangle from the sector and that will tell you the area of CFD and CED and let you know which one is greater.

For instance, Lets find A

sector area = [tex] \frac{90}{360} \pi 10^2 = 25\pi [/tex] 

Now lets get the area of the triangle, which is 

area triangle = [tex] \frac{1}{2} bh\sin C[/tex]

area triangle = [tex] \frac{1}{2} \times 10 \times 10 \times sin 90 = 50m^2[/tex]

CED =  sector area - area of triangle = [tex] 25\pi - 50 = 28.53m^2[/tex]

Now lets find B

sector area = [tex] \frac{60}{360} \pi 12^2 = 24\pi [/tex] 

Now lets get the area of the triangle, which is 

area triangle = [tex] \frac{1}{2} bh\sin C[/tex]

area triangle = [tex] \frac{1}{2} \times 12 \times 12 \times \sin 60 = 36\sqrt(3)[/tex]

CFD = sector area - area of triangle = [tex] 24\pi - 36\sqrt(3) = 13.04m^2[/tex]

So A has the greater area base.

Jacqueline's car gets 12 km per liter of gasoline. Therefore, on a full 50 L tank, she would be able to drive 600 km.

To solve this problem, we need to determine Jacqueline's rate of distance traveled per liter of fuel consumed, then scale this up to find out how far she could theoretically drive on a full tank of 50 liters of gasoline. Jacqueline drove 72 km on 6 L of gasoline, so she is driving at a rate of 72 km / 6 L = 12 km/L.

To find out how far she could drive on a full tank of 50 L of gasoline, we can multiply this rate (12 km/L) by the total volume of the tank. This gives us 12 km/L * 50 L = 600 km.

So using this rate, Jacqueline would be able to drive 600 km on a full 50 L tank of gasoline, assuming that her car’s fuel efficiency stays consistent.

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Jacqueline can travel 600 km on a full tank of 50 L.

First, set up the proportion based on the given information,

Distance travelled / Gasoline used = Unknown distance / Full tank

This gives us:

72 km / 6 L = X km / 50 L

Now, solve for X by cross-multiplying and then dividing,

72 km * 50 L = 6 L * X km

3600 kmL = 6X kmL

3600 kmL / 6 = X km

X = 600 km

Therefore, Jacqueline can travel 600 km on a full tank of 50 L of gasoline.

Final answer:

To solve 3/4x = 1/5, cross multiply and simplify to get 15 = 4x. Divide both sides by 4 to find x = 3.75 or 15/4.

Explanation:

To solve the equation 3/4x = 1/5, we need to find the value of x that makes the equation true. First, we will cross multiply to get rid of the fractions. We multiply both sides of the equation by 4x and by 5, resulting in 5 × 3 = 4x × 1, which simplifies to 15 = 4x.

To find the value of x, we then divide both sides of the equation by 4, yielding x = 15/4. Therefore, the solution to x is 3.75 or ⅔.

Answer: 0.1

Step-by-step explanation:

Given : The number of Democrats : 4

The number of Republicans : 6

The total number of group members =[tex]4+6+6=16[/tex]

The probability that the first member selected is Democrat :-

[tex]\dfrac{4}{16}=\dfrac{1}{4}[/tex]

Now, the total number of group members left = 15

The probability that the second member selected is Republican  :-

[tex]\dfrac{6}{15}=\dfrac{2}{5}[/tex]

Now, the required probability will be :_

[tex]\dfrac{1}{4}\times\dfrac{2}{5}=\dfrac{1}{10}=0.1[/tex]

x+y =44

x-y=22

x = 22+y

22+y +y =44

22+2y =44

2y=22

y=11

x=22+11=33

check:

11 +33 = 44

33-11=22

 so the numbers are 11 and 33

i checked the answer he had he is right :>

The probability that the first winner is from Pike and the second from Wells is 1/6, found by multiplying the individual probabilities of each event happening in sequence.

The question asks for the probability that the first winner comes from Pike and the second from Wells in a random drawing. With 10 customers in total, 3 from Pike and 5 from Wells, the probability of drawing a Pike resident first is 3/10. If that happens, one less customer is available, leaving 9, with 5 still from Wells.

So, the probability for the second draw is 5/9. Multiplying these probabilities gives the combined probability for both events happening in sequence. Therefore, the required probability is (3/10) * (5/9), which simplifies to 1/6.

The probability that both customers selected are Pike residents is [tex]{\frac{28}{153}}[/tex]

To find the probability that both customers selected are Pike residents, follow these steps:

1. Calculate the probability that the first customer is a Pike resident:

  - There are 18 customers in total.

  - There are 8 Pike residents.

  - So, the probability that the first customer is a Pike resident is:

  [tex]\[ \frac{8}{18} = \frac{4}{9} \][/tex]

2. Calculate the probability that the second customer is also a Pike resident, given that the first one was a Pike resident:

  - After selecting the first Pike resident, there are now 17 customers left.

  - There are now 7 Pike residents remaining.

  - So, the probability that the second customer is a Pike resident, given the first was a Pike resident, is:

  [tex]\[ \frac{7}{17} \][/tex]

3. Calculate the combined probability:

  - Since the selections are dependent events (one customer is selected after another without replacement), multiply the probabilities of each step:

  [tex]\[ \left( \frac{4}{9} \right) \times \left( \frac{7}{17} \right) \][/tex]

4. Simplify the multiplication:

  - Multiply the numerators: [tex]\(4 \times 7 = 28\)[/tex]

  - Multiply the denominators: [tex]\(9 \times 17 = 153\)[/tex]

  - So, the combined probability is:

    [tex]\[ \frac{28}{153} \][/tex]