What is the least common denominator for the fractions below? (Round the answer to the nearest integer.)

1/2, 2/3, 4/5

The most likely weight of pencil is 25 g, because a pencil is a lighter object which is measured in grams.

To find the circumference of the flower bed (which is a circle), you use the formula π×diameter\pi \times \text{diameter}π×diameter. With a diameter of 5 feet and using π≈3.14\pi \approx. 3.14π≈3.14, the calculation is 3.14×5=15.73.14 \times 5 = 15.73.14×5=15.7 feet, which is the required length of the barrier.

We use the relation 1 kg =1000 g to convert 3.193 kg to g

To calculate the average rate of change per month, we first determine the total change in the account balance and then divide that by the number of months over which the change occurred.

The change in the balance from March 15 to August 15 is:

Changeinbalance=1450−1140=310

Now, we calculate the number of months between March 15 and August 15:

Numberofmonths=5months

Next, we find the average rate of change per month:

Averagerateofchangepermonth = = 62

To solve this problem, we need to find the mean, mode and median of the above data set.

From the data set, the mode of the data is 2 and 8. They are the most occurring elements in the data set.

Mean of data is total divided by number of elements

Total=1+ 1 + 2+ 2+ 2+ 2+ 3 +3+ 7+ 7+8+8+ 8+ 8+ 9+9=80

Number of elements=16

Mean=80/16=5

Median will fall in between the (N/2)th and (N/2+1)th position

(N/2)th =16/2 =8th position and (16/2+1)th =9th position

Since the data is arranged in ascending order as below

1, 1, 2, 2, 2, 2, 3, 3, 7, 7, 8, 8, 8, 8, 9, 9

Element in 8th position = 3

Element in 9th position =7

So median average of the two elements=(3+7)/2=5

Now the data could be presents as follows in the distribution curve

This is because the data set has two modes, meaning the data is bimodal.

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

The constant of proportionality is the distance traveled divided by gallons of gas consumed

Constant of proportionality=386.4 miles/14 gallons= 27.6 miles per gallon.

The dimension of the field is shown below.

Area of rectangle =length * width

Area of rectangle =100 m *75 m= 7500 m2

Area of rectangle in hectares =

Change in weight of client=new -old=1072-841= 231

Percent change=change/old*100%=231/841*100%=27.47%

The percentage change increase is about 27%

Rounded to the nearest dollar, the original price of the recliner is approximately $451.