312 is the LCM for this set
Answer:
=900
Step-by-step explanation:
Answer:
the rate at which the height of the box is decreasing is -0.0593 cm/s
Step-by-step explanation:
Given the data in the question;
Constant Volume of a rectangular box with a square base = 500 cm³
area of the base increases at a rate of 6 cm²/sec
so change in the area of the base with respect to time dA/dt = 6 cm²/sec
each side of the base is 15 cm long
so Area of the base = 15 cm × 15 cm = 225 cm²
the rate at which the height of the box is decreasing = ?
Now,
V = Ah
dv/dt = 0 ⇒ Adh/dt + hdA/DT = 0
⇒ dh/dt = -hdA/dt / A
we substitute
dh/dt = [ -( 500 / 225 ) × 6 ] / 225
dh/dt = [ -(2.22222 × 6) ] / 225
dh/dt = [ -13.3333 ] / 225
dh/dt = -0.0593 cm/s
Therefore, the rate at which the height of the box is decreasing is -0.0593 cm/s
Answer:
d. Approximate the standard normal distribution with the Student's t distribution
(0.2199 ; 0.2327)
Step-by-step explanation:
Given that :
Sample size, n = 31
Sample mean, xbar = 0.2258
Sample standard deviation, s = 0.0188
Confidence interval (C. I) :
xbar ± margin of error
Margin of Error : Tcritical * s/sqrt(n)
Degree of freedom, df = n - 1 = 31 - 1 = 30
Tcritical value :
T0.05/2, 30 = 2.042
Margin of Error = 2.042 * 0.0188/sqrt(31)
Margin of Error = 0.0068949
C. I = 0.2258 ± 0.0068949
Lower boundary : (0.2258 - 0.006895) = 0.2189
Upper boundary : (0.2258 - 0.006895) = 0.2327
(0.2199 ; 0.2327)
A is the only number line that correctly shows the locations of all given values.
Answer=A
***EDIT***
Okay, so if you look at the number line, you notice that the distance between one line and the next is equal to 1/4. When we move to the left, we decrease in value. When we move to the right, we increase in value.
So, knowing that, lets look at A and see if all of the numbers are correctly placed.
1/2 should be two lines to the right of 0 (since distance between one line and the next is equal to 1/4, and 1/4+1/4=2/4 or 1/2)
-4 is a relatively easy value to find, since its line is labeled.
-2 3/4 should be three lines to the right of -2 (since distance between one line and the next is equal to 1/4, and 1/4+1/4+1/4=3/4 and if you go 3/4 to the left of -2 u get -2 3/4)
(-2-3/4=-2 3/4)
1 1/4 should be three lines behind 2 (since distance between one line and the next is equal to 1/4, and 1/4+1/4+1/4=3/4 and if you go 3/4 to the left of 2 you get 1 1/4)
(2-3/4=1 1/4)
