The scatter plot has been attached
Answer:
Options C, D & E are true
Step-by-step explanation:
Option A is wrong because from the scatter plot, only four athletes were faster in the second race than in the first one.
Option B is wrong because only 1 athlete had his second race time differing from the first race time by exactly 2 seconds.
Option C is true because exactly 9 of the times for the first race were at least 16 seconds
Option D is true because there are exactly 3 athletes who had the same time in both races
Option E is true because 8 of the times for the second race were less than 17 seconds
Answer:
31.
Step-by-step explanation:
The mode is the value which occurs the most.
Stem = 3 and leaf = 1, 1,6 so that is 2 31's.
Answer:
Step-by-step explanation:
Since the cube fits perfectly in the sphere, it means that the diagonal of the cube will form the diameter of the sphere. In a cube, all sides are equal. To determine the length of its diagonal, d, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
d² = 10² + 10² = 200
d = √200 = 14.14cm
Formula for finding the volume of a sphere is expressed as
Volume = 4/3 × π × r³
Radius of sphere = diameter/2 = 14.14/2 = 7.07cm
Volume = 4/3 × π × 7.07³ = 471.19π cm³
Answer:
Hope it helps....!!!!!
Step-by-step explanation:
AB = c = 38
BC = a = 29
AC = b
Angle ABC = 63 degrees
Solving for AC "b":
Cosine rule: c^2 = a^2 * b^2 -2ab * cos C
38^2 = 29^2 * b^2 - (2* 29) * b * (cos 38)
1444 = 841 * b^2 - 58 * b * 0.955
(1444 + 58)/0.955 = b^2 * b
1572.77486911 = b^3
11.62935 = b
11.63 = b (rounded to two decimal places)
Now solving for angle A:
Sine rule: a/sinA = b/sinB
29/sinA = 11.63/sin(63)
sinA/29 = sin(63)/11.63
sin A = (sin(63)/11.63) * 29
sin A = 0.41731
A = sin^-1 (0.41731)
A = 24 degrees 39 minutes 53 seconds
Now solving for angle C:
Sine rule: c/sinC = b/sinB
38/sinC = 11.63/sin(63)
sinC/38 = sin(63)/11.63
sin C = (sin(63)/11.63) * 38
sin C = 0.54682
C = sin^-1 (0.54682)
C = 33 degrees 8 minutes 56 seconds
Answer: f(x)/g(x) = 3x^2 + 6x - 2 - 12/3x+1
Step-by-step explanation:
The first function is f(x) = 9x^3+21x^2-14
The second function is g(x) = 3x+1
f(x)/g(x = 9x^3+21x^2-14/3x+1
We perform the long division as shown in the attachment to obtain the quotient as: Q(x) = 3x^2+6x - 2 and remainder R = -12
Therefore f(x)/g(x) = 3x^2 + 6x - 2 - 12/3x-1
Where x does not = -1/3
