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
Answer:
The distance between the points is 5 units
Step-by-step explanation:
I used distance formula for the question using two points
I
Answer:
ok here we go
Step-by-step explanation:
So this is a function because it's x-axis has only one solution.
Using the z-distribution, the confidence interval is given by: (11.95, 12.65).
<h3>What is a z-distribution confidence interval?</h3>
The confidence interval is:
![\overline{x} \pm z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%5Cpm%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which:
is the sample mean.
is the standard deviation for the population.
In this problem, we have a 90% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.645.
The other parameters are given as follows:
![\overline{x} = 12.3, \sigma = 1.5, n = 50](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%3D%2012.3%2C%20%5Csigma%20%3D%201.5%2C%20n%20%3D%2050)
Hence the bounds of the interval are:
![\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20-%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%2012.3%20-%201.645%5Cfrac%7B1.5%7D%7B%5Csqrt%7B50%7D%7D%20%3D%2011.95)
![\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20-%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%2012.3%20%2B%201.645%5Cfrac%7B1.5%7D%7B%5Csqrt%7B50%7D%7D%20%3D%2012.65)
More can be learned about the z-distribution at brainly.com/question/25890103
#SPJ1
Answer:
60
Step-by-step explanation:
Area of trapezoid:
![\frac{1}{2}(b1+b2) * h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28b1%2Bb2%29%20%2A%20h)
The top base of the trapezoid is given as 7 cm. The bottom base of the trapezoid can be found with 7+5+5 = 17 cm. The height is given as 5 cm. Then, plug these values into the formula.
![\frac{1}{2} (7+17) * 5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%287%2B17%29%20%2A%205)
= ![\frac{1}{2} (24) *5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2824%29%20%2A5)
= ![12*5](https://tex.z-dn.net/?f=12%2A5)
= 60