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3 years ago

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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?

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