x-intercept is 6, coordinates (6,0)
y-intercept -4, coordinates (0,-4)
gradient= y1-y2/x1-x2= 0-(-4)/6-0= 4/6= 2/3 or 0.667 (3.s.f.)
Answer:
P(X ≥ 1) = 0.50
Step-by-step explanation:
Given that:
The word "supercalifragilisticexpialidocious" has 34 letters in which 'i' appears 7 times in the word.
Then; the probability of success = 7/34 = 0.20588
Using Binomial distribution to determine the probability; we have:
where;
x = 0,1,2,...n and 0 < β < 1
and x represents the number of successes.
However; since the letter is drawn thrice; the probability that the letter "i" is drawn at least once can be computed as:
P(X ≥ 1) = 1 - P(X< 1)
P(X ≥ 1) = 1 - P(X =0)
![P(X \ge 1) = 1 - \bigg [ {^3C__0} (0.21)^0 (1-0.21)^{3-0} \bigg]](https://tex.z-dn.net/?f=P%28X%20%5Cge%201%29%20%3D%20%201%20-%20%5Cbigg%20%5B%20%7B%5E3C__0%7D%20%280.21%29%5E0%20%281-0.21%29%5E%7B3-0%7D%20%5Cbigg%5D)
![P(X \ge 1) = 1 - \bigg [ 1 \times 1 (0.79)^{3} \bigg]](https://tex.z-dn.net/?f=P%28X%20%5Cge%201%29%20%3D%20%201%20-%20%5Cbigg%20%5B%201%20%5Ctimes%201%20%280.79%29%5E%7B3%7D%20%5Cbigg%5D)
P(X ≥ 1) = 1 - 0.50
P(X ≥ 1) = 0.50
Dilation is the process in which the dimensions of a given shape is increased or decreased by a scale factor. Therefore the answers to the questions are:
A. Since the dilation of triangle XYZ do not affect the measure of its internal angles, then the trigonometric ratios of respective internal angles are the same.
B. segment CB = 10
ii. segment AB = 11.18
From the given information in the question, triangle XYZ is an image of triangle ACB. In triangle XYZ, given that Sin X = ; it implies that its hypotenuse is 5.59, and the opposite side as 5. So that;
Sin X =
X = 0.8945
X =
Thus,
<X + <Y + <Z =
+ + <Z =
<Z = -
=
<Z =
So then, the third side can be determined by applying the Pythagoras theorem.
= +
= +
= -
= 6.2481
x =
= 2.49962
x = 2.5
Thus,
Cos X =
=
Cos X =
Tan X =
=
Tan X =
Therefore:
A. Considering triangles XYZ and ACB, the measure of their respective internal angles are the same.
i.e <X ≅ <A
<B ≅ <Z
<C ≅ <Y
So that the trigonometric ratios of respective internal angles are the same.
B. Given that triangle XYZ was dilated by a scale factor of 2, then the respective length of each sides of triangle ACB is twice that of XYZ.
Then,
i. segment CB = 2 x segment YZ
= 2 x 5
segment CB = 10
ii. segment AB = 2 x segment XZ
= 2 x 5.59
segment AB = 11.18
Answer:
4 is the absolute value of -4
Step-by-step explanation:
absolute value is basically how many units from 0 the number is.
