Answer:
± 27.33 ft
Step-by-step explanation:
For the given problem, we can estimate the initial and final coordinates of the line of the ball path as (-40,-50) and (0,0). Therefore, the slope is:
(-50-0)/(-40-0) = 50/40 = 1.25
Similarly, we can estimate the slope of a perpendicular line to the line of the ball path as: -1*(1/1.25) = -0.8.
Therefore, using (0,0) and the slope -0.8, the equation of the perpendicular line is: -0.8 = (y-0)/(x-0);
-0.8 = y/x
y = -0.8x
Furthermore, we are given the circle radius as 35 ft and we can use the distance formula to find the two points 35 ft far from the origin:
35^2 = x^2 + y^2
y = -0.8x
35^2 = x^2 + (-0.8x)^2
1225 = (x^2 + 0.64x^2)
1225 = 1.64x^2
x^2 = 1225/1.64 = 746.95
x = sqrt(746.95) = ± 27.33 ft
Just times 16 and 5 ft. together to get your answer which is 80
There are two congruent triangles that are being formed from the lamppost, the light, the ground and the man. Always try to draw a picture for these types of problems. It helps a lot when solving. Your answer should be about 4.3ft
10a + 8b = 230
a + b = (2 + 2 + 13 + 10)...a + b = 27 (this is the number of gifts to buy)
a = 27 - b
10(27 - b) + 8b = 230
270 - 10b + 8b = 230
-10b + 8b = 230 - 270
-2b = -40
b = -40/-2
b = 20 <=== she bought 20 eight dollar gifts
a = 27 - b
a = 27 - 20
a = 7 <=== she bought 7 ten dollar gifts
Answer:
<em>84%</em><em> of the wage earners earn less than $14,000 each. </em>
Step-by-step explanation:
The Empirical Rule (68-95-99.7%)-
According to this around 95% of the data will fall within two standard deviations of the mean.
As the bell curve is symmetrical, so the remaining 5% will be divided into 2 equal parts. So 2.5% will be above 2 standard deviation and 2.5% will be below 2 standard deviation.
As it is given that, the top 2.5% of the wage earners earn $18,000 or more, so 18,000 is 2 standard deviation away from the mean 10,000.
i.e 

We know that,

where,
X = raw score = 14,000
μ = 10,000
σ = 4,000
Putting the values,

Now, calculating the value from the z score table,

As the probability at
is the area below that, so 84% of the wage earners earn less than $14,000 each.