If (D) is distance travelled and (R) is the rate of travel, which of the following represents the relationship between D and R for the equation D = 2R?

In direct proportion relation we utilize the relationship as:

Variable∝Variable 2

Thus from the given case,

Force∝stretch

We introduce a constant term, K to remove the sign of proportionality as

Force=K* stretch

Let’s find the value of K, using Force=132 N and stretch of 0.07 m

132 N=K*0.07 m

K=132 N/0.07 m=1885.7 N/m

Now substitute this value of K in the following equation

Force=1885.7 N/m * stretch

For a stretch of 0.1 m, the force needed is

Force=1885.7 N/m * 0.1 m=188.57 N=188.6 N

Given the equation D=2R means that the get the value of D, multiply the value of R by 2. That is D is two times the value of R.

Let two number be x and y. Then

Three time a number=3x

Eight times a different number=8y

Sum of the two is 3x+8y

The independent variable is the one that is changed or controlled in an experiment to test its effects on the dependent variables. Here, the number of hours worked is independent because it affects the other variables (taxes withheld, retirement savings, and sick leave), making it the cause rather than the effect.

Determine the number of blue and yellow gumballs as follows:

Percent of blue gumballs=100%-(20%+30%+5%+10%) =100%-65%=35%

Number of blue gumballs =35% of 120=0.55*120 = 42 blue gumballs [35%=35/100=0.35]

Number of yellow gumballs=5% of 120=0.05*120 = 6 yellow gumballs [5%=5/100=0.05]

Difference between number of blue and yellow gumballs=42-6= 36 balls

Therefore, there are 36 more blue gumballs than yellow gumballs.

In this case, we are measuring average weight of the babies with time. The weight of the babies will vary with time, meaning when we vary time, the average weight of the babies will be different. Here, time is independent while average weight is dependent variable.

Given the equation

(x/y)-z=rw

Subtract z on both sides of the equation

x/y=rw+z

multiply both sides by y

x=y(rw+z)

Now rearranging the fllowing equation

x=y(z+rw)

Yoghurt : toppings=4:3

Yoghurt: 4.5 oz =4:3

We convert the given ratio into a proportion equation as below

Multiply both sides by 4.5 oz

To find the average speed in miles per hour, we need to convert the time from minutes to hours and then use the formula for speed:

Speed =

The distance traveled is 7.125 miles.

The time was 10 minutes, which is equivalent to:hours

Now, we can calculate the speed:

Speed = 7.125 ÷ = 7.125×6 = 42.75mph