Answer: There is a difference between rote counting and rational counting. Rote counting involves the memorization of numbers. Rational counting tells children "how many there are." For children to count rationally, they need to demonstrate one-to-one correspondence.
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
<u><em>Answer:</em></u>
A. (3x²-4x-5)(2x⁶-5)
<u><em>Explanation:</em></u>
<u>The fundamental theorem of Algebra states that:</u>
"A polynomial of degree 'n' will have exactly 'n' number of roots"
We know that the degree of the polynomial is given by the highest power of the polynomial.
Applying the above theorem on the given question, we can deduce that the polynomial that has exactly 8 roots is the polynomial of the 8th degree
<u>Now, let's check the choices:</u>
<u>A. (3x²-4x-5)(2x⁶-5)</u>
The term with the highest power will be (3x²)(2x⁶) = 6x⁸
Therefore, the polynomial is of 8th degree which means it has exactly 8 roots. This option is correct.
<u>B. (3x⁴+2x)⁴</u>
The term with the highest power will be (3x⁴)⁴ = 81x¹⁶
Therefore, the polynomial is of 16th degree which means it has exactly 16 roots. This option is incorrect.
<u>C. (4x²-7)³</u>
The term with the highest power will be (4x²)³ = 64x⁶
Therefore, the polynomial is of 6th degree which means that it has exactly 6 roots. This option is incorrect
<u>D. (6x⁸-4x⁵-1)(3x²-4)</u>
The term with the highest power will be (6x⁸)(3x²) = 18x¹⁰
Therefore, the polynomial is of 10th degree which means that it has exactly 10 roots. This option is incorrect
Hope this helps :)
If each lap in a pool is 100 meters long,how many laps equal one mile
Round to the nearest tenth.(Hint:1 foot=0.3048 meter)
1 mile = 5280 ft
lets do a ratio: 1ft/.3034m = x ft/100m
the ft and meters sybols cancel, so 1/.3048 =x/100
so 100/.3038 = x = 329.164
so there are 329.164 ft for every 100 meters
to find the number of laps to get to a mile which is 5280, do another ratio
329.164ft/100 m =5280 ft/xm
the left side reduces to 3.29164 =5280/x
you can compute this and see that 5280/3.29164 = 1604.064 meters
1604.064 meters *1 lap / 100m = 16.04064 laps are required to make a mile
If the acceptable percent error is 2.5%, then the amount it can be over or under 16 oz is 0.4oz.
16 + 0.4
16 - 0.4
16.4 is the greatest, 15.6 is the least
