Answer: 
<u>Step-by-step explanation:</u>
Parabola Skate Rental: 4.50x + 35
Arc Hawk Skate Rental: 5.25x + 25
If you want to know when their cost will be the same, set the equations equal to each other.
5.25x + 25 = 4.50x + 35
0.75x + 25 = 35 <em>subtracted 4.50x from both sides</em>
0.75x = 10 <em>subtracted 25 from both sides</em>
<em>divided both sides by 0.75</em>
x = 
<em>simplified the fraction</em>
Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - <em>α</em>)% confidence interval for population mean μ is:
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
<em>n</em>₁ = 25
<em>n</em>₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
![\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]](https://tex.z-dn.net/?f=%5Ctext%7BWidth%7D%3D2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7B25%7D%7D%3D%5Cfrac%7B1%7D%7B5%7D%5Ccdot%20%5B2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Csigma%5D)
Width for n = 64:
![\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]](https://tex.z-dn.net/?f=%5Ctext%7BWidth%7D%3D2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7B64%7D%7D%3D%5Cfrac%7B1%7D%7B8%7D%5Ccdot%20%5B2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Csigma%5D)
Thus, the sample consisting of 64 data values would give a greater precision
<span>8x3(3x2)=24x6 = True
</span><span>4x3(6x2)=24x6 = True
</span><span>6b^3(−2b3)=−12b^6 = Ture
</span><span>3a^3(−3a^4)=−9a^7 = True
They are all correct</span>
You haven't provided the series, therefore, I can only help with the concept.
<u><em>For an infinite geometric series, we have two possibilities for the common ratio (r):</em></u>for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series
<u><em>In an infinite series with r < 1, the summation can be found using the following rule:</em></u>sum =
where:
a₁ is the first term in the series
r is the common ratio
<u>Example:</u>
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum =
Hope this helps :)
Answer:
- circumscribed circle
- The center of a circle circumscribing the triangle connecting the 3 cities will be equidistant from all three cities.
Step-by-step explanation:
The circumscribed circle or <em>circumcircle</em> of a polygon is a circle that passes through all the vertices of the polygon. The center of the circle, the circumcenter, is equidistant from all of the polygon's vertices.
The center is found at the point of intersection between the perpendicular bisectors of any two (non-parallel) chords of the circle. That is, <em>the perpendicular bisectors of any two of the sides of the triangle joining the cities will intersect at the circumcenter</em>.
The method of locating the center of the circle this way is simple and effective.
