9514 1404 393
Answer:
- 2x
- 2
- 128x +640
Step-by-step explanation:
1.
![\displaystyle\frac{8x^2-4x}{4x-2}=\frac{4x(2x-1)}{2(2x-1)}=\boxed{2x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B8x%5E2-4x%7D%7B4x-2%7D%3D%5Cfrac%7B4x%282x-1%29%7D%7B2%282x-1%29%7D%3D%5Cboxed%7B2x%7D)
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2.
![\displaystyle\frac{8x-4}{x+3}-\frac{12x-20}{2x+6}=\frac{8x-4}{x+3}-\frac{4(3x-5)}{2(x+3)}=\frac{8x-4-2(3x-5)}{x+3}\\\\=\frac{8x-4-6x+10}{x+3}=\frac{2x+6}{x+3}=\frac{2(x+3)}{x+3}=\boxed{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B8x-4%7D%7Bx%2B3%7D-%5Cfrac%7B12x-20%7D%7B2x%2B6%7D%3D%5Cfrac%7B8x-4%7D%7Bx%2B3%7D-%5Cfrac%7B4%283x-5%29%7D%7B2%28x%2B3%29%7D%3D%5Cfrac%7B8x-4-2%283x-5%29%7D%7Bx%2B3%7D%5C%5C%5C%5C%3D%5Cfrac%7B8x-4-6x%2B10%7D%7Bx%2B3%7D%3D%5Cfrac%7B2x%2B6%7D%7Bx%2B3%7D%3D%5Cfrac%7B2%28x%2B3%29%7D%7Bx%2B3%7D%3D%5Cboxed%7B2%7D)
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3.
![\displaystyle\frac{(2x+10)^7}{(x+5)^6}=\frac{(2(x+5))^7}{(x+5)^6}=2^7(x+5)^{7-6}=128(x+5)\\\\=\boxed{128x+640}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B%282x%2B10%29%5E7%7D%7B%28x%2B5%29%5E6%7D%3D%5Cfrac%7B%282%28x%2B5%29%29%5E7%7D%7B%28x%2B5%29%5E6%7D%3D2%5E7%28x%2B5%29%5E%7B7-6%7D%3D128%28x%2B5%29%5C%5C%5C%5C%3D%5Cboxed%7B128x%2B640%7D)
Answer:
Just use long subtraction by expanding the decimal places of the whole number. This is done by adding a point, and enough zeros to it to match the number of decimal digits in the other number (digits after the decimal point).
12345678
i.e: 5 - 2.48374827, 2.48374827 has 8 decimal digits, so add 8 zeros after the point.
=
1 1 1 1 1 1 1
5.00000000
-
2.48374827
_______________
2.51625173
7 + 3 = <u>1</u>0, 7 + 2 + <u>1</u> = <u>1</u>0, 8 + 1 + <u>1</u>= <u>1</u>0, 5 + 4 + <u>1</u> = <u>1</u>0, 2 + 7 + <u>1</u> = <u>1</u>0, 3 + 6 + <u>1</u> = <u>1</u>0, 1 + 8 + <u>1</u> = <u>1</u>0, 5 + 4 + <u>1</u> = <u>1</u>0, 2 + 2 + <u>1</u> = <u>5</u><u> </u><u>:</u><u> </u>5.00000000
This is basically borrowing a group of 10s which are the same as 1s in the next decimal place up.
For each digit except the first to the right, let 10 subtract that number from it and minus 1 since the 1 is carried over.
Answer:
32.6
Step-by-step explanation:
Look at the decimal in the hundredths place in 32.62
If the number is 0-4, round down. If the number is 5-9, round up.
In 32.62, the number in the hundredths place is 2. So, we round down to 32.6
Uranus = 530.4
Neptune = 509.6
Saturn = 126
Answer: The value of test statistic is 2.442.
Step-by-step explanation:
Since we have given that
n = 238
Sample mean = 23.2 minutes
Standard deviation = 20.26 minutes
Hypothesis :
![H_0:\mu=20\\H_a:\mu\neq 20](https://tex.z-dn.net/?f=H_0%3A%5Cmu%3D20%5C%5CH_a%3A%5Cmu%5Cneq%2020)
So, the test statistic value would be
![z=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{23.2-20}{\dfrac{20.26}{\sqrt{236}}}\\\\z=2.442](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Cbar%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%5C%5C%5C%5Cz%3D%5Cdfrac%7B23.2-20%7D%7B%5Cdfrac%7B20.26%7D%7B%5Csqrt%7B236%7D%7D%7D%5C%5C%5C%5Cz%3D2.442)
Hence, the value of test statistic is 2.442.