In order to solve for the variable in the equation 2 (4 x + 3) + 4 = 3 x minus (2 x + 4), Giovanni first applies the distributiv
e property. Which equation is a result of this step?
2 answers:
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Answer:
i) 60°
ii) 14.7 cm
Step-by-step explanation:
length of Arc BA = 8.4 cm
length of radius = 8 cm
angle AOC = 45°
BO = AO = CO = 8 cm
<u>i) What is the measure of Angle BOA </u>
= length of Arc BA / Radius
= 8.4 / 8 = 1.05 radians = 60.16° ≈ 60°
<u>ii) what is the length of arc BAC</u>
= radius * angle BAC *
angle BAC = angle AOC + angle BOA
= 45° + 60° = 105°
hence length of arc BAC
= 8 * 105 *
≈ 14.7 cm
Answer:
25 : 1
Step-by-step explanation:
The diameter of the football is 5 times the diameter of the cricket ball. This means that the radius of the football is also 5 times the radius of the cricket ball.
Let the radius of the football be R.
Let the radius of the cricket ball be r.
This implies that:
R = 5r
Both balls are spherical.
The surface area of the cricket ball is given as:
The surface area of the football is given as:
Therefore, the ratio of their surface areas is:
A : a
= 100 : 4
25 : 1
Answer:
Each adult male has a 5.05% probability of having a hip width greater than 16.2 inches.
There is a 0.01% probability that the 110 adult men will have an average hip width greater than 16.2 inches.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
In this problem
Assume that adult men have hip breadths that are normally distributed with a mean of 14.4 inches and a standard deviation of 1.1 inches. This means that .
What is the probability that any one of those adult male will have a hip width greater than 16.2 inches?
For each one of these adult males, the probability that they have a hip width greater than 16.2 inches is 1 subtracted by the pvalue of Z when X = 16.2. So:
has a pvalue of 0.9495.
This means that each male has a 1-0.9495 = 0.0505 = 5.05% probability of having a hip width greater than 16.2 inches.
For the average of the sample
What is the probability that the 110 adult men will have an average hip width greater than 16.2 inches?
Now, we need to find the standard deviation of the sample before using the zscore formula. That is:
.
Now
has a pvalue of 0.9999.
This means that there is a 1-0.9999 = 0.0001 = 0.01% probability that the 110 adult men will have an average hip width greater than 16.2 inches.