All categories

3 years ago

A. What formula will be use to relate the data? Explain the part of the formula?

Mathematics

2 answers:

Alenkasestr [34]3 years ago

5 0

9514 1404 393

Answer:

2.5 miles

Step-by-step explanation:

1A. The formula that applies to time/speed/distance problems is ...

distance = speed × time

The units of the numbers involved need to be compatible, which is to say the speed units need to be the ratio of distance units to time units.

The other applicable relationship is that the resultant speed in a body of water is the sum of the boat speed and the water speed. When they are in the same direction, the speeds add; when they are in the opposite direction, the net speed is their difference.

1B, C. Since Tom is traveling upstream, his net speed is the difference between his paddling speed (8 mph) and the current (3 mph). That is, he makes headway upstream at the rate of 8-3=5 mph. This difference is the "speed" in the formula.

Note that the time is given in minutes, but the units of speed have time units of hours. It is easiest in this problem to translate the time in minutes to a time in hours. (30 min = 1/2 h) This is the "time" in the formula.

We can "let 'distance' represent the distance we're being asked to find in the problem statement."

1D. Using the formula, we find ...

distance = (5 mi/h)(1/2 h)

This is the "formula" equation of part A with speed and time values filled in.

The solution to the equation is simply a matter of performing the indicated arithmetic.

distance = 2.5 mi

Tom would travel 2.5 miles in 30 minutes.

_____

Additional comment

You may see the above formula written a number of ways. Using single-letter variables, it is often written as ...

d = rt

where d represents distance, r represents speed, and t represents time. By using whole words for the variable names, I find less explanation is necessary.

By using units along with the numbers in the formula, the units of the answer "fall out". If they don't, then there has been a mistake. For example, if you use 30 minutes instead of 1/2 hour, your answer would be ...

(5 mi/h)(30 min) = 150 mi·min/h

These units are not distance units, so you know a mistake has been made. (The units multiply and/or cancel the same as any variable(s).)

Pachacha [2.7K]3 years ago

5 0

Answer:

1. Tom's paddles his kayak at a rate of 8 mph in still water. If Tom is traveling upstream in a river with a current of 3 mph, how far would Tom travel in 30 minutes?

You might be interested in

At Hogwarts School of Witchcraft and Wizardry, Professor Snape was concerned about grade inflation, and suggested that the schoo

ExtremeBDS [4]

Answers:

The z scores are approximately:

Care of Magical Creatures: z = 0.333
Defense Against the Dark Arts: z = 0.583
Transfiguration: z = -0.263
Potions: z = -0.533

From those scores, we can say:

Best grade = Defense Against the Dark Arts
Worst grade = Potions

=====================================================

Further Explanation:

We'll need to convert each given score to a corresponding standardized z score.

The formula to use is

z = (x - mu)/sigma

where,

x = given grade for each class
mu = mean
sigma = standard deviation

Let's find the z score for the Care of Magical Creatures class

z = (x - mu)/sigma

z = (3.80 - 3.75)/(0.15)

z = 0.333 approximately

Repeat this process for the Defense Against the Dark Arts score.

z = (x - mu)/sigma

z = (3.60 - 3.25)/(0.60)

z = 0.583 approximately

And for the Transfiguration class as well

z = (x - mu)/sigma

z = (3.10 - 3.20)/(0.38)

z = -0.263 approximately

The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.

Now do the final class (Potions) to get this z score

z = (x - mu)/sigma

z = (2.50 - 2.90)/(0.75)

z = -0.533 approximately

This grade is below average as well.

----------------------------

To summarize, we have these z scores

Care of Magical Creatures: z = 0.333
Defense Against the Dark Arts: z = 0.583
Transfiguration: z = -0.263
Potions: z = -0.533

Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.

3 0

2 years ago

Estimate the measure of the angle ? 85 70 235 310

alex41 [277]

Answer: 235 would be the estimate

5 0

3 years ago

A company uses the declining-balance method of calculating depreciation expense. On January 1, the company buys machinery for $7

NeX [460]

Answer:

$516,000

Step-by-step explanation:

Given:

- Beginning boo value of asset A = $750,000

- The salvage value of the asset B = $100,000

- The estimated life of asset t = 10 years

Find:

What is the book value in year 3?

Solution:

- Under the declining balance method, double declining method depreciation rate (R) is calculated by:

R = 1 / t

R = 1 / 10 = 10%

- The accumulated depreciation for 3 years is as follows:

Depreciation: ( A - B ) * R * 2

Year 1: DDB = ( 750,000 - 100,000 ) * 0.2 = $130,000

Year 2: DDB = ( 620,000 - 100,000)*0.2 = $104,000

- The book value in year 3 is:

$ 620,000 - $104,200 = $516,000

7 0

3 years ago

What is the range of the exponential function f(x)=2•7x

sergeinik [125]

f(x) cannot be 0 or less than zero, but can approach+ infinity

Answer is (0, ∞)

5 0

3 years ago

The formula for the rate at which water is flowing is R=v/t, where

Anarel [89]

The answer is b I hope I could help

3 0

3 years ago