A new physician saw 841 clients during the first year of practice and 1,072 clients during the second year of practice. Which of the following represents the approximate percentage increase in client volume?

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)

Let's work step by step to find the original price of the recliner.

Let the original price of the recliner be x.

The recliner is on sale for 30% off the original price. So, the sale price is:

SalePrice = x−0.30x = 0.70x

The consumer has a coupon that saves an additional 25% off the sale price. So, the final price is:

FinalPrice = 0.70x − 0.25(0.70x)

= 0.75(0.70x)

= 0.525x

The consumer paid $237 for the recliner. Therefore, we have the equation:

0.525x = 237

Solving for x:

x =

​≈ 451.43

Rounding to the nearest dollar, the original price is approximately $451,

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

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

We know that the two people work on the same work but the time to complete the work differs. Thus, the rate of doing the work for each person is as follows:

Rate of work for person A = 1 /2 work per hr

Rate of work for person B=1/3 work per hour

If the person A and B wok together, the time of doing the same work will be less than the fastest person A. Thus, we combine the two rates of A and B

We have 1 work and time to complete by both A and B becomes

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%

Which of the following is the median of the data set below?

To find the number of calories from fat per tablespoon, follow these steps:

Calculate the total calories from fat in one serving (2 tablespoons):

87.5%×80=0.875×80=70caloriesfromfat

Determine the calories from fat per tablespoon: Since one serving is 2 tablespoons, divide the total calories from fat by 2:

=35caloriesfromfatpertablespoon