Every line from the tangent to the centre is 90°. This is said in the circle theorems.
So angle OBC and ODC are 90°.
angle O is twice the size of angle F. This is another circle theorem.
Therefore angle O is 152°.
The quadrilateral of ODBC would equal to 360°. Which means 90° + 90° + 152° = 332°
360° - 332° = 28°.
The answer is 28°
Answer :
taxable income is $30,300
Step-by-step explanation:
Given
The combine income of the husband and wife = $62,000
Number of children the couple has = 3
In order to find out the taxable income for an U.S. family, the following formula is used
taxable income = total income - exemption deduction - standard deduction
We know the exemption deduction for a married couple with three kids fixed according to the U.S. government is $19,500.
And the standard deduction for a married couple with three kids fixed according to the U.S. government is $12,200.
Therefore,
taxable income = total income - exemption deduction - standard deduction
= $62,000 - $19,500 - $12,200
= $30,300
Thus the taxable income is $30,300.
Answer:
16% probability that a randomly chosen U.S. adult sleeps more than 8.7 hours per night
Step-by-step explanation:
The Empirical Rule(Standard Deviation) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 7.5
Standard deviation = 1.2
Using the Standard Deviation Rule, what is the probability that a randomly chosen U.S. adult sleeps more than 8.7 hours per night?
8.7 = 7.5 + 1.2
So 8.7 is one standard deviation above the mean.
By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% are more than one standard deviation from the mean. Since the normal probability distribution is symmetric, 16% are more than one standard deviation below the mean and 16% are more than one standard deviation above the mean(above 8.7 hours)
So, 16% probability that a randomly chosen U.S. adult sleeps more than 8.7 hours per night
