Answer:
The answer to the first question is (5,1).
Answer: The 95% confidence interval is approximately (55.57, 58.43)
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Explanation:
At 95% confidence, the z critical value is about z = 1.960 which you find using a table or a calculator.
The sample size is n = 17
The sample mean is xbar = 57
The population standard deviation is sigma = 3
The lower bound of the confidence interval is
L = xbar - z*sigma/sqrt(n)
L = 57 - 1.960*3/sqrt(17)
L = 55.5738905247863
L = 55.57
The upper bound is
U = xbar + z*sigma/sqrt(n)
U = 57 + 1.960*3/sqrt(17)
U = 58.4261094752137
U = 58.43
Therefore the confidence interval (L, U) turns into (55.57, 58.43) which is approximate.
Answer: L = V/bh
b= V/Lh and h= V/Lb
Step-by-step explanation: V = Lbh or V= lwh is also used for the Basic form for the Volume of a cube or rectangular prism is
Volume = Length × breadth × height
The volume will be expressed as cubic units such as cubic meters cubic feet. Sometimes abbreviations are used like cm^3 for cubic centimeters.
When you know the Volume, and you need to find a missing dimension, just make a fraction with the V in the numerator and the dimensions you know in the denominator. This means you are dividing the Volume by the area of the dimensions you have been given to find the missing dimension.
Answer:
x = 12
prism's length = 36 centimeters
Prisms width = 25 centimeters
Step-by-step explanation:
volume of a rectangular prism, V = length × width × height
volume = 10,800 cubic centimeters
prism's length = 3x
Prisms height = 12 centimeters
Prisms width = (2x + 1)
volume of a rectangular prism, V = length × width × height
10,800 = 3x * 2x + 1 * 12
10,800 = 6x² + 3x * 12
10,800 = 72x² + 36x
72x² + 36x - 10,800 = 0
2x² + x - 300 = 0
Using quadratic formula
x = -b ± √b² - 4ac / 2a
= -1 ± √1² - 4*2*-300 / 2*2
= -1 ± √1 - (-2400) / 4
= -1 ± √1 + 2400 / 4
= -1 ± √2401 / 4
= -1 ± 49 / 4
x = (-1 + 49)/4 or (-1 - 49)/4
= 48/4 or -50/4
x = 12 or -12.5
x cannot be a negative value
Therefore, x = 12
prism's length = 3x
= 3(12)
= 36 centimeters
prism's length = 36 centimeters
Prisms width = (2x + 1)
= 2(12) + 1
= 24 + 1
= 25 centimeters
Prisms width = 25 centimeters
You can use this ratio:
1hour/60minutes=0.73hours/Xminutes
and cross multiply
so x= 43.8 minutes
