Step-by-step explanation:
Using similar triangles, the height and width of the water is proportional to the height and width of the trough.
w / h = 5 / 1
w = 5h
The volume of the water is:
V = AL
V = (½ wh) (14)
V = 7wh
Substituting:
V = 7(5h)h
V = 35h²
Take derivative with respect to time:
dV/dt = 70h dh/dt
Given that dV/dt = 15 and h = ⅓:
15 = 70 (⅓) dh/dt
dh/dt = 9/14
dh/dt ≈ 0.643 ft/min
Here we shall use the binomial distribution formula to evaluate the probability:
let the probability that the temp will be above 80 be P(F)=2/3;
Probability that the temp will be below 80 be P(F')=1/3
thus,
The probability that the temp will be above 80 for 20 days for the month of June will be:
P(F)=n!/((n-x)!x!)p^xq^(n-x)
p=2/3 and q=1/3, n=30, x=20
plugging the values in the equation we obtain:
P(F)=30!/(10!*20!)*(2/3)^20*(1/3)^(30-20)
P(F)=0.153
Answer:
|−70 − 15| = |−85| = 85 units - B
Step-by-step explanation:
In this item, it can be seen that from an expression of,
(4 + 5i) + (-3 + 7i)
Aiko transformed the equation by factoring out the i's from the expression and wrote it as,
(4 + 5)i + (-3 + 7)i
Now this is wrong because i there is not a variable but a notation that 5 and 7 are imaginary numbers. In fact, she cannot factor out the i's because it is not present in both -3 and 4. The answer therefore to this item is the last sentence, "Aiko incorrectly used the distributive property by combining ..."
Answer:
-5
negative nine-halves
Step-by-step explanation:
we know that
In the quadratic equation
If
then
The system has no real numbers solutions
we have
so
substitute
<u><em>Verify each case</em></u>
case 1) -5
For c=-5
substitute
------> is true
therefore
The value of c=-5 will cause the quadratic equation to have no real number solutions
case 2) negative nine-halves
For c=-9/2
substitute
------> is true
therefore
The value of c=-9/2 will cause the quadratic equation to have no real number solutions
case 3) negative one-quarter
For c=-1/4
substitute
------> is not true
therefore
The value of c=-1/4 will not cause the quadratic equation to have no real number solutions
case 4) 1
For c=1
substitute
------> is not true
therefore
The value of c=1 will not cause the quadratic equation to have no real number solutions
case 5) 9 Over 4
For c=9/4
substitute
------> is not true
therefore
The value of c=9/4 will not cause the quadratic equation to have no real number solutions