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worty [1.4K]
3 years ago
9

The distance from Clarion to DuBois is 2 1/2 inches on the map. the actual distance is 40 miles. The distance from DuBois to Rid

geway is 1 1/2 inches on the map. What is the actual distance, in miles, from DuBois to Ridgeway?
Mathematics
1 answer:
lisov135 [29]3 years ago
4 0
Hello!

You have to find how many miles is 1 inch on the map

We can do this by doing 40 / 2 1/2 = 16

16 miles is equal to one inch

So we multiply this by 1 1/2

16 * 1 1/2 = 24

The answer is 24 miles

Hope this helps!
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A turtle and a rabbit engage in a footrace over a distance of 4.00 km. The rabbit runs 0.500 km and then stops for a 90.0-min na
Oxana [17]

Answer:

(a) 2.29 km/h

(b) 9 km/h

Step-by-step explanation:

For part (a) you have to apply<em> the average speed formula</em>, which is defined by:

v=\frac{d}{t}

where d is the total distance traveled and t is the total time needed.

d=\frac{4.00}{1.75}=2.29 km/h

For part (b) you have to calculate the running time (T) , which is the total time of the race minus the nap time:

The nap time in hours is:

90/60 = 1.5 h (because there are 60 minutes in one hour)

The running time is:

T= 1.75 - 1.5 = 0.25 h

Let t1 represent the time before the nap and t2 the time after the nap:

t1+t2 = T

t1+t2 = 0.25

You have to apply the formula d=vt before and after the nap:

-Before the nap, the distance traveled was 0.50 km

0.50 = v1t1

-Afer the nap, the distance traveled was 3.50 km

3.50=v2t2

But v2=2v1 (because after the nap the rabbit runs twice as fast)

You have to solve the system of equations:

t1=0.25-t2 (I)

v1t1=0.50 (II)

2v1t2=3.50 (III)

Replacing (I) in (II)

v1(0.25-t2)=0.50

Applying distributive property and solving:

0.25v1-v1t2=.050

For (III) you have that v1t2=3.50/2=1.75. Hence:

0.25v1-1.75=0.50

Solving for v1:

v1 = 9 km/h

7 0
3 years ago
When temperature is zero degree Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the correspondin
7nadin3 [17]

Answer:

\\ y = 1.8(x) + 32 or \\ y = \frac{9}{5}(x) + 32

or equivalently:

\\ F = 1.8(C) + 32 or \\ F = \frac{9}{5}(C) + 32

Step-by-step explanation:

To express the Fahrenheit temperature <em>as a linear function of the Celsius temperature</em>, F(c), we can proceed as follows.

We can use here <em>the two-point form</em> <em>equation</em> of a line:

\\ y-y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x-x_1) [1]

We are asked to express the <em>Fahrenheit temperature</em> as a function of <em>Celsius temperature</em>, so the independent variable, in this case, is <em>x</em> (Celsius temperature) and the dependent variable is <em>y</em> (Fahrenheit temperature).

When temperature is zero degree Celsius (\\x_1 = 0), the Fahrenheit temperature is 32 (\\y_1 = 32).

When the Celsius temperature is 100 (\\x_2 = 100), the corresponding Fahrenheit temperature is 212 (\\y_2 = 212).

Then, using [1], we have:

\\ y-32 = \frac{212 - 32}{100 - 0}(x-0)

\\ y-32 = \frac{180}{100}(x)

\\ y-32 = 1.8(x).

It could be also be written as:

\\ y-32 = \frac{18}{10}(x) = \\ y-32 = \frac{9}{5}(x), as it commonly appears in books.

Then <em>the Fahrenheit temperature express as a linear function of the Celsius temperature, F(c</em>) is ( solving the equation for <em>y </em>) :

\\ y = 1.8(x) + 32 or \\ y = \frac{9}{5}(x) + 32.

Or equivalently:

\\ F = 1.8(C) + 32 or \\ F = \frac{9}{5}(C) + 32

We can check this using the given values from the question:

For 0 Celsius degrees, the Fahrenheit temperature is:

\\ y = 1.8(0) + 32 = 32 Fahrenheit degrees.

For 100 Celsius degrees, the Fahrenheit temperature is:

\\ y = 1.8(100) + 32 = 180 + 32 = 212 Fahrenheit degrees.

5 0
3 years ago
if You flip an coin 200 times about how many times would you expect the coin to labd on tails what is the probality
inysia [295]

Answer:

100;200

There are 200 total flips and to find probability we would have to divide it by two. Doing so, should give you something like this 100;200.

4 0
3 years ago
A spinner is broken into section labeled 1 to 38. What is the probability that.On your next spin, that you will spin a 1?
VashaNatasha [74]

Answer:

1/38

Step-by-step explanation:

Given :

Probability = required outcome / Total possible outcomes

Total possible outcomes = total Numbe rod sections = 38

Required outcome = number of 1's on the entire section = 1

Hence, the probability of spinning a one equals :

P(spinning a 1) = 1 / 38

8 0
3 years ago
Plot two points that are 777 units from Point \blueD{D}Dstart color #11accd, D, end color #11accd and also share the same xxx-co
Karolina [17]

Right format of question:

Plot two points that are 7 units from Point D and also share the same x-coordinate as Point D.

Answer:

D' = (-4,-6) and D' = (-4,8)

Step-by-step explanation:

Given

D(x,y) = (-4,1)

Required

Determine a point 7 points from D and in the same x coordinate

Represent this point with D'.

From the requirement of the question, D' has two possible values and these values are:

D' = D(x,y-7) ----> 7 units down and

D' = D(x,y+7) ----> 7 units up

Substitute values for x and y in D' = D(x,y-7) and D' = D(x,y+7)

So, we have:

D' = D(x,y-7)

D' = (-4,1 - 7)

D' = (-4,-6)

D' = D(x,y+7)

D' = (-4,1+7)

D' = (-4,8)

3 0
3 years ago
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