The force applied is directly proportional to the stretch of a coil. If a force of 132 Newtons stretches a coil 0.07 meters, what force would be needed to stretch a coil 0.1 meter? Round your answer to the nearest tenth.
A. 92.4 Newtons
B. 1885.7 Newtons
C. 188.6 Newtons
D. 136.0 Newtons
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
Therefore, the Correct Answer is C.
More Questions on TEAS 7 Math
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Q #1: A homeowner has hired two people to mow his lawn. If person A is able to mow the lawn in 2 hr by herself and person B is able to mow in lawn in 3 hr by himself. Which of the following is the amount of time it would take for both person A and B to mow the lawn together?
A. 5 hours
B. 2.5 hours
C. 1.2 hours
D. 1 hours
Answer Explanation
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 person A and B work 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
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Q #2: Which of the following is the total number of whole boxes that measure 2 ft * 2 ft * 2 ft that can be stored in a room that measures 9 ft * 9 ft * 9 ft, if the size of the boxes cannot not be altered?
A. 125
B. 64
C. 18
D. 92
Answer Explanation
Number of boxes in the room is equal to the volume of the room divided by the volume of one box
Volume of the room=9 ft*9 ft*9 ft= 729 ft3
Volume of one box = 2 ft* 2 ft * 2 ft= 8 ft3
Number of boxes= 729 ft3/ 8 ft3= 91.125 boxes
Thus, the room can store 91.125 boxes, which is about 92 boxes
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Q #3: Which of the following is the best description for the data set below? 1, 1, 2, 2, 2, 2, 3, 3, 7, 7, 8, 8, 8, 8, 9, 9
A. Uniform
B. Right-skewed
C. Bimodal
D. Left-skewed
Answer Explanation
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.
The mean of data is the total divided by the 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 the median average of the two elements=(3+7)/2=5
Now the data could be presented as follows in the distribution curve
This is because the data set has two modes, meaning the data is bimodal.
