Answer:
0.205 ; 0.117 ; 0.999
Step-by-step explanation:
Using binomial probability distribution :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
Probability of success, p = 0.5
P(x = 4) = 10C4 * 0.5^4 * 0.5^6
P(X = 4) = 0.205078125
B.) 3 heads and 7 tails
P(X = 7) = 10C7 * 0.5^7 * 0.5^3
P(X = 7) = 120 * 0.0009765625
P(X = 7) = 0.117
P(atleast one head)
P(x greater than equal to 1) = p(x =1) +... P(x = 10)
Using a binomial probability calculator :
P(x greater than equal to 1) = 0.999
Answer: estimate 7
exact: 6 7/15
Step-by-step explanation: for the estimate round 3 4/5 to 4 and 2 2/3 to 3 and 4 + 3 = 7
for the exact number convert 3 4/5 to 3 12/15
and convert 2 2/3 to 2 10 /15
then add 3 + 2 = 5
and 12/15 + 10/15 = 22/15
convert 22/15 to a mixed number which is 1 7/15
then 5 + 1 7/15
answer 6 7/15
hope this helps mark me brainliest if it helped
Answer:
7.5 miles per hour.
Step-by-step explanation:
We have been given that Mr. Ward runs a lot. He ran 45 minutes each day, 5 days each week, for 16 weeks.
First of all, we will find time for that Mr. Ward ran in 16 weeks.
We will multiply 5 by 16 to find number of days for that Mr. Ward ran and then we will multiply the result by 45 minutes to find the time.
Now, we will divide 3600 minutes by 60 minutes to convert time into hours as:
Now, we will divide 450 miles by 60 hours to find Mr. Ward's average speed as:
Therefore, Mr. Ward's average speed in 7.5 miles per hour.
y-intercept: Let x = 0 and solve for y:
(x-1)^2 + (y-2)^2 = 10 => (-1)^2 + y^2 - 4y + 4) = 10
=> 1 + y^2 - 4y + 4 = 10, or y^2 - 4y -5 = 0
The solutions of this quadratic are y = 5 and y = -1.
Thus, the y-intercepts are (0, 5) and (0, -1).
Now find the x-intercepts: Let y = 0 and solve the resulting equation for x:
(x-1)^2 = 10 - (-2)^2, or (x-1)^2 = 10 - 4 = 6.
Taking the sqrt of both sides, x - 1 = plus or minus sqrt(6), or:
x = 1 +√6 and x = 1 - √6, so that the x-intercepts
are (1+√6, 0) and (1-√6, 0).
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
