A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.
2 answers:
Answer:
Option A is correct
4.8 in
Step-by-step explanation:
Definition:
If the centers of two circle radius r and r' are d units apart, then the length of the direct common tangent between them is:
....[1]
As per the statement:
A chain fits tightly around two gears as shown.
Let r' be the radius of the smaller gear.
The radius of lager gear(r) = 14 in
The distance between the centers(d) = 22 in.
Direct common tangent = 20 in.
Substitute in [1] we have;
Squaring both sides we have;
⇒
Taking square root both sides we have;
⇒
Subtract 14 from both sides we have;
Divide both sides by -1 we have;
inches
Therefore, the radius of the smaller gear to the nearest tenth is, 4.8 inches
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Answer:
0.0588 = 5.88% probability that a middle-aged man with diabetes is very active
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Has diabetes.
Event B: Is very active.
Probability of having diabetes:
To find this probability, we take in consideration that:
It also found that men who were very active (burning about 3,500 calories daily) were a fourth as likely to develop diabetes compared with men who were sedentary. Assume that one-fifth of all middle-aged men are very active, and the rest are classified as sedentary.
So the probability of developing diabetes is:
x of 4/5 = x of 0.8(not active)
x/4 = 0.25x of 1/5 = 0.2(very active). So
Probability of developing diabetes while being very active:
0.25x of 0.2. So
What is the probability that a middle-aged man with diabetes is very active?
0.0588 = 5.88% probability that a middle-aged man with diabetes is very active
Answer:
- The sphere has a diameter of 32 in. CORRECT: the diameter of a sphere doubles its radio, so if the radio equals 16,the diameter measures the double, in this case, 32.
- The radius' lenght is one half the length of the diameter. CORRECT: , by definition, the diameter is the maximum distance between two opposite points on the surface of the sphere, and its lenght equals twice the radius because the radius is the distance between the center of the sphere and any point of the frontier of the sphere (then, one colud imagine that the distance between two opposite points in a sphere can be united by two radius, or a diameter).
- The volume (V) of a sphere can be calculated as
, where r is the radio. In this case, the volume of the sphere will be
, which is also equal to
.
Chebyshev's theorem in statistics states that for many probability distributions, no more than 1/k² of measured values will be k standard deviations away from the mean.
Because the area under the probability distribution curve is equal to 1, Chebyshev's theorem means that the shaded area shown in the figure is equal to 1 - 1/k².
When k = 1.75, the shaded area is
1 - 1/1.75² = 0.7635 = 67.35%
Therefore the percent of the area within +/- 1.75 standard deviations from the mean is
67.35/2 = 33.7%, which is at least 33% of the observations.
Answer:
According to the Chebyshev theorem, at least 33% of the observations lie within +/- standard deviations from the mean.
Because the area under the probability distribution curve is equal to 1, Chebyshev's theorem means that the shaded area shown in the figure is equal to 1 - 1/k².
When k = 1.75, the shaded area is
1 - 1/1.75² = 0.7635 = 67.35%
Therefore the percent of the area within +/- 1.75 standard deviations from the mean is
67.35/2 = 33.7%, which is at least 33% of the observations.
Answer:
According to the Chebyshev theorem, at least 33% of the observations lie within +/- standard deviations from the mean.