How to write 8/12 as a product of a whole number and a unit fraction

The speed of the plane in still air is 605 miles per hour and the wind speed is 55 miles per hour. This is found through solving simultaneous equations derived from the given distance, and time taken both with and against the wind.

In this problem, the plane's speed in still air can be denoted as 'p' and the wind speed as 'w'. Given the total distance of the trip as 3300 miles, the total time with the wind as 5 hours, and the total time against the wind as 6 hours, we can create two equations: p + w = 3300/5 = 660 miles/hour (with the wind) and p - w = 3300/6 = 550 miles/hour (against the wind).

These equations can be solved simultaneously to get the values of 'p' and 'w'. By adding the two equations, we get 2p = 660 + 550 = 1210. Dividing by 2 gives p = 605 miles/hour. With the value of 'p' we can find 'w' by substituting p = 605 into either of the original equations (let's use p - w = 550): 605 - w = 550, which leads to w = 55 miles/hour.

So, the speed of the plane in still air is 605 miles per hour and the speed of the wind is 55 miles per hour.

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Answer:

First choice is cheaper.

Step-by-step explanation:

Joel could pay $50 per month for unlimited use or he could pay $12 per month plus $4 per visit.

Let the monthly visits be x

We can define this as :

[tex]12+4x> 50[/tex]

[tex]4x >50-12[/tex]

[tex]4x >38[/tex]

[tex]x> 9.5[/tex]

So, x can be greater than 9.5 means 10.

[tex]4(10)+12>50[/tex]

[tex]52 > 50[/tex]

Comparing both we can say that the first choice is cheaper.

Answer:

B: (4, –1)

Step-by-step explanation:

The original weight of the crackers in the box is 15/16 pound.

The question asks us to determine the original weight of a box of crackers, given that 5/8 pound of crackers was served, which was 2/3 of the entire box.

We can set up the proportion by stating that 5/8 pound represents 2/3 of the whole, so let's represent the total weight of the crackers with the variable 'w'. The equation to represent this situation is (5/8) pound = (2/3) * w.

To solve for 'w', we'll multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:

(5/8) * (3/2) = w

Simplifying this equation gives us the total weight:

(5 * 3) / (8 * 2) = w

15 / 16 = w

w = 15/16 pound, which is the original weight of the crackers in the box.

Answer: The answer is b) 77.5

Step-by-step explanation:

hope i helped

Madeline has approximately $400 after rounding her garage sale earnings and paycheck to the nearest ten and adding them together.

The question involves estimating the total amount of money Madeline has after selling items at a garage sale and receiving her paycheck. To estimate the total amount, we need to round each amount to the nearest ten and then add the rounded numbers together.

First, round $167 to the nearest ten, which is $170.

Next, round $232 to the nearest ten, which is $230.

Finally, add the rounded numbers: $170 + $230 = $400.

The current population of Australia is 24 million.

It is given to us that the initial population was 23.13 million and the population 5 year later has grown by 870000 or 0.87 million. Thus to find the current population we simply need to add the initial population and the growth that has happened in 5 years. This gives us:

[tex]Current\ population = 23.13\ million + 0.87\ million = 24\ million[/tex]

Thus, the current population of Australia is 24 million.

3/6 should b you answer answer

Final answer:

The  volume will be of 6.3 for the second model.

Explanation:

The student is asked to calculate the volume of the second model pyramid, Khafre's pyramid, which is 9/10 the volume of the first model, Khufu's pyramid. The student has already calculated that, for Khufu's pyramid, S = √3*73.5​/4.5=7. To find the volume Kristina should make the second model, we simply multiply the volume of the first model by 9/10.

Although the question does not provide the exact volume of the first model, we will assume the value of S given is the volume of Khufu's pyramid model. Therefore, the volume of Khafre's pyramid model should be 7 * (9/10) = 6.3.

This result is based on the proportion given between the two pyramids' volumes and is a straightforward calculation of this proportion.

The patient's weight is first converted from lbs to kg, resulting in 100 kg. The dosage in micrograms per hour is then found to be 42000 mcg/hour. Lastly, this is converted to milligrams to give a final dosage of 42 mg/hour.

This is a question pertaining to medical dosage calculations. First, we need to convert the patient's weight from pounds to kilograms since our dosage is based on that unit. We know that 1 kg equates to approximately 2.2 lbs. So, the patient's weight in kilograms would be 220 lbs/2.2 = 100 kg.

Now, we can use the patient's weight to find the dosage per minute: 7 mcg/kg/min * 100 kg = 700 mcg/min. But the question asks for the dosage per hour, so we must convert minutes to hours: 700 mcg/min * 60 min/hour = 42000 mcg/hour. Finally, we need convert from mcg to mg as the question asked for the amount in milligrams. Since there are 1000 mcg in 1 mg, the dosage becomes: 42000 mcg/hour / 1000 = 42 mg/hour.

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