Answer:
Step-by-step explanation:
Given that a soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.1 inch.
a) sigma = 0.25
Since population std dev is known we can use Z critical value i.e. 2.58
![2.58(\sigma/\sqrt{n} )25.8*\sigma\\i.e. n>665.64 \sigma^2](https://tex.z-dn.net/?f=2.58%28%5Csigma%2F%5Csqrt%7Bn%7D%20%29%3C0.1%5C%5C%5Csqrt%7Bn%7D%20%3E25.8%2A%5Csigma%5C%5Ci.e.%20n%3E665.64%20%5Csigma%5E2)
Hence when sigma =0.25
we get n should be atleast = 41.6025 or 42
b) when sigma = 0.3 we get
n >59.390=60
c) Big std deviation requires larger sample size.
The question is asking for an absolute value inequality that represents all real numbers less than
![4](https://tex.z-dn.net/?f=4)
units from
![6](https://tex.z-dn.net/?f=6)
in any direction on the number line.
This can be written as
![2 \ \textless \ |x| \ \textless \ 10](https://tex.z-dn.net/?f=2%20%5C%20%5Ctextless%20%5C%20%7Cx%7C%20%5C%20%5Ctextless%20%5C%2010)
.
![4](https://tex.z-dn.net/?f=4)
numbers from
![6](https://tex.z-dn.net/?f=6)
to the left is or
![6-2](https://tex.z-dn.net/?f=6-2)
, or
![4](https://tex.z-dn.net/?f=4)
.
![4](https://tex.z-dn.net/?f=4)
numbers to the right of
![6](https://tex.z-dn.net/?f=6)
is
![6+4](https://tex.z-dn.net/?f=6%2B4)
, or
![10](https://tex.z-dn.net/?f=10)
. Therefore, the inequality can only allow real numbers whose absolute values fall between
![2](https://tex.z-dn.net/?f=2)
and
![10](https://tex.z-dn.net/?f=10)
.
Answer:
-6, 9, and 81
Step-by-step explanation:
Answer:
![\large \boxed{\$98.16}](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5C%2498.16%7D)
Step-by-step explanation:
Assume that your map looks like the one below.
1. Calculate the distance
It looks like the distance on the map is 12 cm.
![\text{Distance} = \text{12 cm} \times \dfrac{\text{30 mi}}{\text{1 cm}} = \text{ 360 mi}](https://tex.z-dn.net/?f=%5Ctext%7BDistance%7D%20%3D%20%5Ctext%7B12%20cm%7D%20%5Ctimes%20%5Cdfrac%7B%5Ctext%7B30%20mi%7D%7D%7B%5Ctext%7B1%20cm%7D%7D%20%20%3D%20%5Ctext%7B%20360%20mi%7D)
2. Calculate the volume of gasoline
![\text{Volume} = \text{ 360 mi} \times \dfrac{\text{1 gal}}{\text{15 mi}} = \text{24 gal}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%7D%20%3D%20%5Ctext%7B%20360%20mi%7D%20%5Ctimes%20%5Cdfrac%7B%5Ctext%7B1%20gal%7D%7D%7B%5Ctext%7B15%20mi%7D%7D%20%3D%20%5Ctext%7B24%20gal%7D)
3. Calculate the cost of the gasoline
![\text{Cost} = \text{24 gal} \times \dfrac{\$4.09}{\text{1 gal}} = \mathbf{\$98.16}\\\\\text{It will cost $\large \boxed{\mathbf{\$98.16}}$ to drive to the ski lodge.}](https://tex.z-dn.net/?f=%5Ctext%7BCost%7D%20%3D%20%5Ctext%7B24%20gal%7D%20%5Ctimes%20%5Cdfrac%7B%5C%244.09%7D%7B%5Ctext%7B1%20gal%7D%7D%20%3D%20%5Cmathbf%7B%5C%2498.16%7D%5C%5C%5C%5C%5Ctext%7BIt%20will%20cost%20%24%5Clarge%20%5Cboxed%7B%5Cmathbf%7B%5C%2498.16%7D%7D%24%20to%20drive%20to%20the%20ski%20lodge.%7D)