Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, 1), hence
y = a(x - 3)² + 1
To find a substitute (- 2, - 4) into the equation
- 4 = a(- 2 - 3)² + 1
- 4 = 25a + 1 ( subtract 1 from both sides )
25a = - 5 ( divide both sides by 25 )
a = - = -
y = - (x - 3)² + 1 ← in vertex form
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:
ABC is not a right angled triangle
<em><u>Solution:</u></em>
Given that, Triangle ABC has perimeter 18 cm
AB = 7 cm
BC = 3 cm
We have to find whether ABC is a right angled triangle
Let the sides of triangle be AB, BC, AC
<em><u>Perimeter of triangle is given by formula:</u></em>
perimeter = sum of length of all three sides of triangle
18 = AB + BC + AC
18 = 7 + 3 + AC
AC = 18 - 10
AC = 8
Thus the length of sides of triangle are:
AB = 7 cm
BC = 3 cm
AC = 8 cm
For a triangle to be right angle, it must satisfy the pythagoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
The longest side of triangle is hypotenuse
Therefore, AC = 8 cm is the hypotenuse
Thus by above theorem we get,
Substituting the values we get,
Thus the pythagoras theorem is not satisfied
Thus ABC is not a right angled triangle
