Answer:
x<1 or x>5
Step-by-step explanation:
2x -3< -1 or -3x < -15
Solve them separately then put them back together
2x-3 < -1
Add 3 to each side
2x-3+3<-1+3
2x<2
Divide by 2
2x/2 <2/2
x<1
-3x < -15
Divide each side by -3, remembering to flip the inequality
-3x/3 > -15/-3
x>5
Put them back together
x<1 or x>5
The information given is sufficient for this proof .
Slope of a line passing through x1 ,y1) and ( x2,y2) is given by the formula :
M = ( y2 - y1)/ ( x2-x1)
________________________________
Let us start finding the slope of line PQ
the given points are ( a,b) and ( c,d)
using the slope formula we get :
slope of line PQ = m= ( d-b) /( c-a)
Let us now try finidng slope of the another line P'Q'
It is passing through ( -b ,a) and (-d,c)
using the formula we get slope of P'Q' = m' = ( c-a) /( -d - -b)
m'= ( c-a) /( -d+b)
m'= ( c-a) / -( b-d Let us find the product of m and m' :
( d-b ) * ( c-a)
----------- ------------ = -1
(c-a) - ( b-d)
Because we got product of m and m' = -1 hence proved product of perpendicular lines are negative reciprocal of each other .
y = mx+b
(5-8)/(9-0) = -1/3 which is m
solve point slope to find slope intercept by using one of the points (0,8)
y-y1=m(x-x1)
y-8 = -1/3(x-0)
y-8 = -1/3x
Answer: y = -1/3x + 8
Answer:
a) 229 and 305 days
b) 229 days or less
c) 305 days or more
Step-by-step explanation:
The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 267
Standard deviation = 19
(a) Between what values do the lengths of the middle 95% of all pregnancies fall?_____________and___________days
By the Empirical rule, 95% of all pregnancies fall within 2 standard deviations of the mean.
So
267 - 2*19 = 229 days
to
267 + 2*19 = 305 days
(b) How short are the shortest 2.5% of all pregnancies?______days or less
95% of all pregnancies fall within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. Since the distribution is symmetric, 2.5% is more than 2 standard deviations below the mean(shortest 2.5%) and 2.5% is more than 2 standard deviations above the mean(longest 2.5%). So
267 - 2*19 = 229 days
c) How long do the longest 2.5% of pregnancies last?________days or more
Explanation in b)
267 + 2*19 = 305 days
Answer:
1 in 12 chance of landing on 3
1 in 12 chance of landing on 4
1 in 6 chance of landing on either 3 or 4
Step-by-step explanation:
12 equal sections means probability is 1 in 12 of landing on any one numbered section.
2 in 12 or 1 in 6 chance of landing on either of two numbered sections in one attempt.
