Martin charges $10 for every 5 bags of leaves he rakes. Last weekend, he raked 28 bags of leaves. How much money did he earn?
2 answers:
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Answer:
a) Between 39 and 40 rods can be expected to have a strength less than 39.4 kpsi.
b) 260 rods are expected to have a strength between 39.4 and 60 kpsi
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
(a) Assuming a normal distribution, how many rods can be expected to have a strength less than 39.4 kpsi?
The percentage of rods with a stength less than 39.4 is the pvalue of Z when X = 39.4. So
has a pvalue of 0.1314
13.14% of rods have a strength less than 39.4 kpsi.
Out of 300
0.1314*300 = 39.42
Between 39 and 40 rods can be expected to have a strength less than 39.4 kpsi.
(b) How many are expected to have a strength between 39.4 and 60 kpsi?
The percentage of rods with a stength in this interval is the pvalue of Z when X = 60 subtracted by the pvalue of Z when X = 39.4. So
X = 60
has a pvalue of 0.9987
X = 39.4
has a pvalue of 0.1314
0.9987 - 0.1314 = 0.8673
86.73% of the rods are expected to have a strength between 39.4 and 60 kpsi
Out of 300
0.8673*300 = 260
260 rods are expected to have a strength between 39.4 and 60 kpsi
Answer:
1. a. Please find attached, the diagram for the first circle with radius = 3 cm
b. Please find attached, the diagram for the second circle with diameter = 3 cm
2. The similarities are;
a) Both circles can be described by a point and a radius or a diameter
The differences are;
a) The length of the radiuses are different for the two circles (3 cm and 1.5 cm)
b) The circumferences of the two circles are different
c) The area covered by the two circles are different
3. The circumference of the circle with radius equal to 3 cm is larger than the circumference of the circle with diameter equal to 3 cm
4. The circumference to diameter ratio of the circle with radius = 3 cm is π
The circumference to diameter ratio of the circle with diameter = 3 cm is π
Both circles have equal circumference to diameter ratio given that the circumference = π × The diameter
Step-by-step explanation:
1. a. The radius length of the first circle = 3 cm
The diagram for the first circle with radius 3 cm is attached
b. The diameter length of the second circle = 3 cm
The diagram for the second circle with diameter 3 cm is attached
2. The similarities are;
a) Both circles can be described by a point and a radius or a diameter
The differences are;
a) The length of the radiuses are different for the two circles (3 cm and 1.5 cm)
b) The circumferences of the two circles are different
c) The area covered by the two circles are different
3. The circumference of the circle with radius equal to 3 cm is 2 × π × 3 = 6·π cm
The circumference of the circle with diameter equal to 3 cm is π × 3 = 3·π cm
Therefore, the circumference of the circle with radius equal to 3 cm is larger than the circumference of the circle with diameter equal to 3 cm
4. The circumference to diameter ratio of the circle with radius = 3 cm is 6·π cm/(2 × 3 cm) = π
The circumference to diameter ratio of the circle with diameter = 3 cm is 3·π cm/(3 cm) = π.
Both circles have equal circumference to diameter ratio given that the circumference = π × The diameter.
