Answer:
The percent of these mothers are between the ages 30-35 is 36.53%
Step-by-step explanation:
we are given
mean of age =31.7 years
standard deviation of 5.2 years
For age=30 years:
x=30
we can find z-score
we can plug values
For age=35 years:
x=35
we can find z-score
we can plug values
now, we can use normal distribution table
now, we can find percentage
=36.53%
Answer:
the value of h on the diagram is 9cm
Step-by-step explanation:
area = 1/2 * base * height
a = 1/2*b*h
36=1/2*8*h
36=4h
since the 1/2 will multiply the 8
36=4h
multiply both sides by 4
h=9cm.
Answer: 1, 3, both show a change in temp
<h3>
Answer: Largest value is a = 9</h3>
===================================================
Work Shown:
b = 5
(2b)^2 = (2*5)^2 = 100
So we want the expression a^2+3b to be less than (2b)^2 = 100
We need to solve a^2 + 3b < 100 which turns into
a^2 + 3b < 100
a^2 + 3(5) < 100
a^2 + 15 < 100
after substituting in b = 5.
------------------
Let's isolate 'a'
a^2 + 15 < 100
a^2 < 100-15
a^2 < 85
a < sqrt(85)
a < 9.2195
'a' is an integer, so we round down to the nearest whole number to get
So the greatest integer possible for 'a' is a = 9.
------------------
Check:
plug in a = 9 and b = 5
a^2 + 3b < 100
9^2 + 3(5) < 100
81 + 15 < 100
96 < 100 .... true statement
now try a = 10 and b = 5
a^2 + 3b < 100
10^2 + 3(5) < 100
100 + 15 < 100 ... you can probably already see the issue
115 < 100 ... this is false, so a = 10 doesn't work
Taking
and differentiating both sides with respect to
yields
Solving for the first derivative, we have
Differentiating again gives
Solving for the second derivative, we have
Now, when
and
, we have