Answer:
Angle ACD = 38°
Step-by-step explanation:
The full, correct question is presented the attached image to this solution.
Given
Point O is the centre if the circle
Points A, B, C and D are points on the circle
Angle AOB = 140°
Angle OAC = 14°
Angle AOB = 2 × (Angle ACB) [angle subtended at the centre of the circle is twice the angle subtended at the circumference of the circle)
140° = 2 × (Angle ACB)
Angle ACB = (140°/2) = 70°
(Angle AOB) + (Angle OAB) + (Angle ABO) = 180° [sun of angles in a triangle is 180°]
But Angle OAB = Angle ABO = a [base angles of an iscosceles triangle are equal since OA and OB are both radii for the circle O)
(Angle AOB) + (Angle OAB) + (Angle ABO) = 180°
140° + a + a = 180°
2a = 40°
a = (40/2) = 20°
Angle OAB = Angle ABO = 20°
Angle CAB = (Angle OAC) + (Angle OAB) = 14° + 20° = 34°
Triangle ADC is an iscosceles triangle, hence,
Angle DAC = Angle ACD = x [base angles of an iscosceles triangle are equal]
But
(Angle DCB) + (Angle DAB) = 180° [Opposite angles of a cyclic quadilateral (a quadilateral inscribed in a circle) sum up to give 180°]
Angle DCB = (Angle DCA) + (Angle ACB) = (x + 70°)
Angle DAB = (Angle DAC) + (Angle CAB) = (x + 34°)
(Angle DCB) + (Angle DAB) = 180°
(x + 70°) + (x + 34°) = 180°
2x + 104° = 180°
2x = 180° - 104° = 76°
x = (76°/2) = 38°
Angle DAC = Angle ACD = 38°
Angle ACD = 38°
Hope this Helps!!!
Answer:
Step-by-step explanation:
b/c we can substructure 5cd and 3dc b/c it doesn't matter if the place of cd and dc change. what I mean if 5 ×3=15 and it is the same with 3×5=15 both of the product are the same but, if it is - and ÷ it wil be wrong for example 5-3=2 but 3-5= -2
if is helpful ❤❤
THANK YOU
Answer:
0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
18% of residents in Minneapolis, Minnesota, are African Americans. Suppose a local court will randomly sample 100 state residents and will then observe the proportion in the sample who are African American.
This means that
So, by the Central Limit Theorem:
How likely is the resulting sample proportion to be between 0.066 and 0.294?
This is the pvalue of Z when X = 0.294 subtracted by the pvalue of Z when X = 0.066. So
X = 0.294
By the Central Limit Theorem
has a pvalue of 0.9985
X = 0.066
has a pvalue of 0.0015
0.9985 - 0.0015 = 0.997
0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294