MATHEMATICS HIGH SCHOOL

A punch recipe that serves 24 calls for 1/3cup of lemon juice. If Mike plans to make only enough punch to serve 12 people, how much lemon juice will he need? Explain how you found your answer.

Answers

Answer 1

Answer:

Mike will need 1/6 cup of lemon juice to serve 12 people

Step-by-step explanation:

1/3 cup of lemon juice = 24 servings

x cups of lemon juice = 12 servings

Using ratio

1/3 : 24 = x : 12

1/3 ÷ 24 = x / 12

1/3 × 1/24 = x/12

1/72 = x/12

Cross product

1*12 = 72*x

12 = 72x

Divide both sides by 72

x= 12/72

= 1/6

x= 1/6

Mike will need 1/6 cup of lemon juice to serve 12 people

Answer 2

Answer:

Answer:

Mike needs 1/6 cup of lemon juice to serve 12 people.

Step-by-step explanation:

1/3 cup of lemon juice = 24 servings

x cups of lemon juice = 12 servings

1/3 : 24 = x : 12

1/3 ÷ 24 = x / 12

1/3 × 1/24 = x/12

1/72 = x/12

1/3 cup of lemon juice = 24 servings

x cups of lemon juice = 12 servings

Using ratio:

1/3 : 24 = x : 12

1/3 ÷ 24 = x / 12

1/3 × 1/24 = x/12

1/72 = x/12

Cross product:

1*12 = 72*x

12 = 72x

Divide both sides by 72:

x= 12/72

= 1/6

x= 1/6

Mike will need 1/6 cup of lemon juice to serve 12 people

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tyler mixed 1 1/2 cups of flour with 3/4 cup of sugar. What is the total amount of flour and sugar tyler mixed?

Answers

Hello! try simplifying those two numbers so that they have the same denominators. You can see that you can convert 11/2 of flour so that you can add it with 3/4 of sugar and get the total amount together.

To convert multiply the top and bottom by 2 $(11)/(2) &* (2)/(2) = (22)/(4)$ :

Now add across the top numbers $(3)/(4) + (22)/(4) = (25)/(4)$ :

And finally simplify the fraction to get your final answer. You can pull out 24 out of 25 as the common factor for 4 and 6 $(25)/(4)=6 (1)/(4)$ and the remainder will be in the numerator.

Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1.5 ft/s. When Graham’s arms are 18 ft above the ground, Hunter, who is standing directly underneath Graham, throws Graham a ball as the cable continues to lift him higher. Hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. Which system of equations can be used to model this situation?A) h=18+1.5t
h=5+24t-16t^2

B) h=18+1.5t
h=5+24t+16t^2

C) h=18+1.5t
h=5+24t

D) h=18t+1.5t-16t^2
h=5+24t-16t^2

Answers

Answer: Hello there!

this type of equations in one dimension (when all the factors are constants) are written as:

h = initial position + initial velocity*t + (acceleration/2)*t^2

First, let's describe the hunter's equation:

We know that Graham moves with a velocity of 1.5 ft/s, and when he is 18 ft above the ground, Hunter throws the ball, and because Graham is pulled with a cable, he is not affected by gravity.

If we define t= 0 when Graham is 18 ft above the ground, the equation for Graham height (in feet) is:

h = 18 + 1.5t

where t in seconds.

Now, the equation for the ball:

We know that at t= 0, the ball is thrown from an initial distance of 5ft, with an initial velocity of 24ft/s and is affected by gravity acceleration g, where g is equal to: 32.2 ft/s (notice that the gravity pulls the ball downwards, so it will have a negative sign)

the equation for the ball is:

h = 5 + 24t - (32.2/2)t^2 = 5 + 24t - 16.1t^2

So the system is:

h = 18 + 1.5t

h = 5 +24t - 16.1t^2

so the right answer is A

Answer:

Step-by-step explanation:

EDGE 2020

How to find simplify the ratio 25:35

Answers

5:7

Step-by-step explanation:

To simplify the ratio 25:35, you can divide both numbers by their greatest common divisor (GCD). In this case, the GCD of 25 and 35 is 5. So, dividing both numbers by 5 gives us the simplified ratio: 5:7.

Answer:

25:35 or 25/35 = 5/7 or 5:7

Step-by-step explanation:

1. Start with the ratio 25:35.

2. Find the HCF of 25 and 35. The HCFof 25 and 35 is 5.

3. Divide both numbers in the ratio by the HCF.

25 ÷ 5 = 5

35 ÷ 5 = 7

4. The simplified ratio is 5:7.

Therefore, the simplified form of the ratio 25:35 is 5:7.

Situation #3: Jamie can type 243 words in 3 minutes. How many words canshe type in 10 minutes?

Answers

Answer:

810 words

Step-by-step explanation:

243 words per 3 minutes

243/3 to get 81 words per minute

81 times 10 = 810

I ain’t never seen two pretty best friends

If it is 8:50 a.m., what will the time be 4 hours and 20 minutes later?1:20 a.m.
12:30 a.m.
1:10 p.m.
12:30 p.m.

Answers

Answer:

1:10 pm

Step-by-step explanation

it will be 1:10p.m.
8:50+4:20=12:70. (↪70=1h+10min)=1:10

Two lawn care companies are competing for a landscaping contract. Company A charges a $250 monthly consulting fee plus $10 per square foot, whereas Company B charges a $90 landscaping fee plus $12 per square foot. When will the two companies charge the same amount?