Express the following relationship as a rate.

The Marshall Island goby, the world's smallest fish, measures .47 inch. The striped bass, an American sport fish, is about 25.5

OLEGan [10]

150 inches because i say it is because i just need the points to ask another question

6 0

3 years ago

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

Alenkasestr [34]

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.

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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."

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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.

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<em>Additional comment</em>

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).)

5 0

3 years ago

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Points M, N, and P are respectively the midpoints of sides AC , BC , and AB of △ABC. Prove that the area of △MNP is on fourth of

Hunter-Best [27]

Answer:

The area of △MNP is one fourth of the area of △ABC.

Step-by-step explanation:

It is given that the points M, N, and P are the midpoints of sides AC, BC and AB respectively. It means AC, BC and AB are median of the triangle ABC.

Median divides the area of a triangle in two equal parts.

Since the points M, N, and P are the midpoints of sides AC, BC and AB respectively, therefore MN, NP and MP are midsegments of the triangle.

Midsegments are the line segment which are connecting the midpoints of tro sides and parallel to third side. According to midpoint theorem the length of midsegment is half of length of third side.

Since MN, NP and MP are midsegments of the triangle, therefore the length of these sides are half of AB, AC and BC respectively. In triangle ABC and MNP corresponding side are proportional.

$\triangle ABC \sim \triangle NMP$

$MP\parallel BC$

$MP=\frac{BC}{2}$

By the property of similar triangles,

$\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{PM^2}{BC^2}$

$\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{(\frac{BC}{2})^2}{BC^2}$

$\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{1}{4}$

Hence proved.

5 0

3 years ago

What is the length of the side opposite the 45degree angle

Lemur [1.5K]

Answer:

In a 45 - 45 - 90 triangle, the legs are equal and the ratio of sides from shortest to longest is 1 : 1 : √2 where 1 are the legs and √2 is the hypotenuse. In this case the leg is 10 / √2 = 5√2.

5 0

3 years ago

What is fractions on a lineplot question 5

Ghella [55]

So, we know that

4/5n = 2/3

n = 2/3 x 5/4 . . . . .. if fraction is moved to other side of the equation the numerator and denominator will be swithced

n = 10/12 ......................... divide numerator and denominator by 2

n = 5/6

The answer is Fraction 5 over 6 hopes this help

7 0

2 years ago