Nick spent 1 3/4 hours doing homework. Of that time, 2/3 was spent on a social studies project. How many hours did Nick spend working on the project?

Answers

Answer 1
Answer: 1 3/4 hours spent on homework

2/3 of that 1 3/4 hours spent on the project...

2/3 x 1 3/4 =
2/3 x 7/4 = 14/12 = 1 2/12 = 1 1/6

Nick spent 1 1/6 hours (or 1 hour and 10 minutes) on the project.

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How do you solve
216^x-1=6

Answers

216^(x-1)=6 \n(6^3)^(x-1)=6 \n6^(3(x-1))=6 \n6^(3x-3)=6^1 \n3x-3=1 \n3x=4 \nx=(4)/(3)
216^(x-1)=6\nln(216^(x-1))=ln(6)\n(x-1)ln(216)=ln(6)\nxln(216)-ln(216)=ln(6)\nxln(216)=ln(6)+ln(216)\nx= (ln(6)+ln(216))/(ln(216)) \approx  1,333

In an experiment, Plant 1 receives 10 grams less food than Plant 2. Plant 2 receives 3/5 the amount that Plant 3 receives. If Plant 3 receives 30 grams of food, how many grams of food does Plant 1 receive?

Answers

Well if plant 2 receives 3/5 of plant 3, which is 30 grams. You multiply 3/5 by 30 and you should get 18 grams. Now that is plant 2, and since plant one receives 10 grams less you just subtract 10 from 18 and you get 8.
Plant 1 receives 8 grams of food.

Final answer:

To determine the food received by Plant 1, first calculate Plant 2's food based on Plant 3's amount (30 grams * 3/5), yielding 18 grams. Then, subtract 10 grams (because Plant 1 gets 10 grams less than Plant 2) to find that Plant 1 gets 8 grams of food.

Explanation:

To solve this problem, we start by finding out how much food Plant 2 receives. Since Plant 2 gets 3/5 of the food that Plant 3 receives, and we know that Plant 3 gets 30 grams, we find out Plant 2's food amount by doing a multiplication of 30*(3/5), giving us 18 grams.

Next, we need to consider how much Plant 1 receives in comparison to Plant 2. The problem states Plant 1 gets 10 grams less than Plant 2. So, if Plant 2 receives 18 grams, then Plant 1 must receive 18 - 10 = 8 grams.

In summary

Plant 1 receives 8 grams of food based on the data provided in the problem.

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A chemist needs to mix an 20% acid solution with a 50% acid solution to obtain 15 liters of a 34% acid solution. How many liters of each of the acid solutions must be used?

Answers

This question is based on the system of equation. Therefore, the 8 litres of the 20%  and  7 liters of the 50% solution.

Given:

A chemist needs to mix an 20% acid solution with a 50% acid solution to obtain 15 liters of a 34% acid solution.

We need to determined the numbers of liters of each of the acid solutions must be used.

According to the question,

Let the number of liters  be x for 20% and y for the 50% solution.

Then,

0.2x + 0.5y = 15 * 0.34

⇒ 0.2x + 0.5y = 5.1        

Also we have:

Multiply the first equation by -2:

⇒ x    +  y  =  15            

Adding these last 2 equations:

⇒ -0.4x - y = -10.2    

⇒ 0.6x = 4.8

⇒ x = 4.8 / 0.6

⇒ x = 8 and y = 15 - 8 = 7 .

Therefore, the 8 liters of the 20%  and  7 liters of the 50% solution  acid solutions must be used.

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Answer:

8 litres of the 20%  and

7 litres of the 50% solution.

Step-by-step explanation:

Let the number of litres  be x for 20% and y for the 50% solution. Then

0.2x + 0.5y = 15*0.34

0.2x + 0.5y = 5.1         Also we have:

x      +  y  =  15             Multiply the first equation by -2:

-0.4x - y = -10.2           Adding these last 2 equations:

0.6x = 4.8

x = 4.8 / 0.6

x = 8.

and y = 15 - 8 = 7 .

Our school swimming pool is 25 m long if our coach wants us to swim 3 km how many lengths of food will we need to swim ?

Answers

So,

We will have to divide the length the coach wants you to swim by the length of your pool to find how many laps you must swim.  However, we need to first convert 3 km to meters by multiplying by 1000 (because 1 km = 1000 m).

3 * 1000 = 3000 m

Now we can divide.

(3000)/(25) = (600)/(5)= 120

You will need to swim 120 laps (not a realistic number).

The fastest texter in the world is Ben Cook who typed a 160-letter messge in about 40 seconds. How many letters can Ben text in a second? How many lettersin a minute.

Answers

4 in a second and 240 in a minute

Answer:

Wow that's impressive he can type 4 letters a second and 240 a minute

1. The velocity "v" in feet per second of a freely falling object that has fallen h feet can be represented by v = 8h^1/2. Find the distance that an object has fallen if its velocity is 96 feet per second.2. The relationship of the current, the power, and the resistance in an appliance can be modeled by IR^1/2 = √P, where I is the current in amperes, P is the power in watts, and R is the resistance in ohms. Find the power that an appliance is using if the current is 2.5 amps and the resistance is 16 ohms.

In your answer, please explain and show your work to the best of your ability. I want to know how you got your answer. It will help me a lot! :)

Note: These questions are from 7-3 Practice: Rational Exponents from Glencoe Algebra 1.

Good luck! :)

Answers

We isolate the variables that we wish the values determined in the given problems above.

(1) To solve for h, we manipulate the variable such that it becomes,
                                h = √(v / 8)
Substituting the given,
                                h = √ (96 / 8) = √12 ft

(2) To solve for P in this problem, we raise both sides of the equation to exponent 2,
                                P = I²R
Substituting,
                                P = (2.5 amps)² x (16 ohms)
                                P = 100 watts

Final answer:

To find the distance fallen, substitute the given velocity into the equation and solve for h. To find the power being used, substitute the given current and resistance into the equation and solve for P.

Explanation:

1. To find the distance that an object has fallen if its velocity is 96 feet per second, we need to use the given equation v = 8h^(1/2). We'll substitute 96 for v in the equation and solve for h:

96 = 8h^(1/2)

To isolate h, we'll divide both sides of the equation by 8:

12 = h^(1/2)

To get rid of the exponent, we'll square both sides of the equation:

144 = h

Therefore, the object has fallen a distance of 144 feet.

2. The equation IR^(1/2) = √P represents the relationship between current (I), power (P), and resistance (R). We're given that I = 2.5 amps and R = 16 ohms. We'll substitute these values into the equation and solve for P:

(2.5)(16)^(1/2) = √P

(2.5)(4) = √P

10 = √P

To isolate P, we'll square both sides of the equation:

100 = P

Therefore, the appliance is using 100 watts of power.

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