Answer:
B. (1,5) and (5.25, 3.94)
Step-by-step explanation:
The answer is where the 2 equations intersect.
We need to solve the following system of equations:
y = -x^2 + 6x
4y = 21 - x
From the second equation:
x = 21 - 4y
Plug this into the first equation:
y = -(21 - 4y)^2 + 6(21 - 4y)
y = -(441 - 168y + 16y^2)+ 126 - 24y
y = -441 + 168y - 16y^2 + 126 - 24y
16y^2 + y - 168y + 24y + 441 - 126 = 0
16y^2 - 143y + 315 = 0
y = [-(-143) +/- sqrt ((-143)^2 - 4 * 16 * 315)]/ (2*16)
y = 5, 3.938
When y = 5:
x = 21 - 4(5) = 1
When y = 3.938
x = 21 - 4(3.938) = 5.25.
Answer: 64 cups
Step-by-step explanation:
Each gallon has 16 cups so you multiply 16 by 4 because there are 4 gallons and you get 64. Hope that helped. :)
Answer: One sample z test for means
Step-by-step explanation:
From the information given, the sample size is large. It is greater than 30. Again, the population standard deviation is given. This means that the test statistic would be the z score which is determined by the formula
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = population standard deviation
The probability value would be determined from the normal distribution table.
Therefore, the hypothesis test that should be used is
One sample z test for means
Answer:
V= 14.13
Step-by-step explanation:
Information needed:
V= 4/3
r^3
= 3.14
r= 3/2
Solve:
V= 4/3r^3
V= 4/3(3.14)(3/2)^3
V= 4/3(3.14)(27/8)
V= 14.13
Answer:
1.6x10^-18 gram
Step-by-step explanation:
(5.3 x 10⁻²³ gram/molecule) x (20,000 molecule)
= (5.3 x 10⁻²³ x 2 x 10⁴) gram
= (10.6 x 10⁻²³⁺⁴) gram
= (1.06 x 10⁻²³⁺⁵) gram
= 1.06 x 10⁻¹⁸ gram
We need to find the mass of 20,000 molecules of oxygen. It can be calculated using unitary method. Here, we can multiply 20,000 molecules by the mass of one oxygen molecule.
