The image of the question is attached below.
Given:
m∠DAC = 20° and m∠BCA = 30°
m∠ABC = 90° and m∠CDA = 90°
To find:
The value of x and y.
Solution:
In right triangle ABC,
m∠BAC = x° + 20°
Sum of the interior angles of a triangle = 180°
m∠BAC +m∠ABC + m∠BCA = 180°
x° + 20° + 90° + 30° = 180°
x° + 140° = 180°
Subtract 140° from both sides.
x° + 140° - 140° = 180° - 140°
x° = 40°
In right triangle ADC,
m∠ACD = y° + 30°
Sum of the interior angles of a triangle = 180°
m∠ACD +m∠CDA + m∠DAC = 180°
y° + 30° + 90° + 20° = 180°
y° + 140° = 180°
Subtract 140° from both sides.
y° + 140° - 140° = 180° - 140°
y° = 40°
The value of x is 40 and y is 40.
Answer:
And using a calculator, excel ir the normal standard table we have that:
And we can calculate the probability like this:
Step-by-step explanation:
A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval 47<=X<53. Is the assumption of normality important. Why?
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where 
and 
Since the distribution for X is normal then we know that the distribution for the sample mean 
is given by:
We can find the probability required like this:
And using a calculator, excel ir the normal standard table we have that:
And we can calculate the probability like this:
Plug -8 in for x:
4(-8) + 5
solve:
-32 + 5
-27
Answer:
The domain is (-∞ , ∞)
The domain is continuous
Step-by-step explanation:
Here, we want to identify the domain of the linear function
The domain in this case can be represented by the set of all real numbers.
When we talk of the domain of a function, we are simply referring to the the range of values between the smallest value on the x-axis and the largest number on the x-axis
Hence, mathematically, we are simply considering the smallest value of b up to the largest value of b in this case. Where b simply represents the number of books
Thus, the domain here will be (-∞ , ∞)
On if the domain is discrete or continuous, we can see that the domain is continuous.
The domain is continuous simply because, the domain we have contains all the values and not some in the set of real numbers. If it had contain only some, then it would have been discrete. But since it contains all, it is continuous
Answer:
The probability of hitting the bullseye at least once in 6 attempts is 0.469.
Step-by-step explanation:
It is given that a mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt.
The probability of hitting bullseye in each attempt, p = 0.10
The probability of not hitting bullseye in each attempt, q = 1-p = 1-0.10 = 0.90
Let x be the event of hitting the bullseye.
We need to find the probability of hitting the bullseye at least once in 6 attempts.
.... (1)
According to binomial expression
where, n is total attempts, r is number of outcomes, p is probability of success and q is probability of failure.
The probability that the dart thrower not hits the bullseye in 6 attempts is
Substitute the value of P(x=0) in (1).
Therefore the probability of hitting the bullseye at least once in 6 attempts is 0.469.
