Answer:
19.47
Step-by-step explanation:
Use the law of sines.
sin(90)/6 = sin(x)/2
Multiply both sides by 2
2 * sin(90)/6 = sin(x)
Use a calculator
0.33333 = sin(x)
sin^-1 0.3333 = 19.47
<span>1220
Subtracting the lower boundary of 1492 grams from the mean of 3234 gives you 1742 grams below the mean. Dividing 1742 by the standard deviation of 871 gives you 2 standard deviations below the curve. Now doing the same with the upper limit of 4976 grams also gives you 2 standard deviations above the mean (4976-3234)/871 = 2
So you now look for what percentage of the population lies within 2 standard deviations of the mean. Standard lookup tables will indicate that 95.4499736% of the population will be within 2Ď of the mean. So multiply 1278 by 0.954499736 giving 1219.851. Then round to the nearest whole number and you have an estimated 1220 babies that weigh between 1492 grams and 4976 grams.</span>
The mid-point for given endpoints is (4,3)
Step-by-step explanation:
a mid-point is the point on a line segment that divides it into two equal portions.
If (x1,y1) and (x2,y2) are the coordinates of vertices of a line segment, then mid-point is given by:
given
(x1,y1) = (9,9)
(x2,y2) = (-1,-3)
The mid-point for given endpoints is (4,3)
Keywords: Coordinate Geometry, Mid-point
Learn more about coordinate geometry at:
#LearnwithBrainly
Complete the square:
F(x) = -3x² - 6x - 5
F(x) = -3 (x² + 2x) - 5
F(x) = -3 (x² + 2x + 1 - 1) - 5
F(x) = -3 ((x + 1)² - 1) - 5
F(x) = -3 (x + 1)² + 3 - 5
F(x) = -3 (x + 1)² - 2
The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :
F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5
The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.
The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from
(x + 1)² ≥ 0 ⇒ -3 (x + 1)² ≤ 0 ⇒ -3 (x + 1)² - 2 ≤ -2
This is to say, every point on the parabola has a y-coordinate no greater than -2.
As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.
-2x^2 + 5x -3 =0
Find the discriminate:
In the given formula a = -2, b = 5 and c = -3
The discriminate is found using the formula b^2 - 4(ac)
Replace the letters with their values:
5^2 - 4(-2*-3)
25 - 4*6
25-24 = 1
When the discriminate is greater than or equal to 0, there are two real solutions.
The answer is c) 2
