Answer:
1. 23
2. 8
Step-by-step explanation:
☆Cross multiply.
![\frac{2}{10} = \frac{4}{a - 3} \\ \\ 40 = 2(a - 3) \\ 40 = 2a - 6 \\ \frac{ + 6 = \: \: \: \: \: \: \: \: + 6}{ \frac{46}{2} = \frac{2a}{2} } \\ \\ 23 = a](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B10%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7Ba%20-%203%7D%20%20%5C%5C%20%20%5C%5C%2040%20%3D%202%28a%20-%203%29%20%5C%5C%2040%20%3D%202a%20-%206%20%5C%5C%20%20%20%5Cfrac%7B%20%2B%206%20%20%3D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%2B%206%7D%7B%20%5Cfrac%7B46%7D%7B2%7D%20%3D%20%20%5Cfrac%7B2a%7D%7B2%7D%20%20%7D%20%20%5C%5C%20%20%5C%5C%2023%20%3D%20a)
--------
![\frac{k}{6} = \frac{4}{3} \\ \\ \frac{24}{ 3} = \frac{3k}{3} \\ \\ 8 = k](https://tex.z-dn.net/?f=%20%5Cfrac%7Bk%7D%7B6%7D%20%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B24%7D%7B%203%7D%20%20%3D%20%20%5Cfrac%7B3k%7D%7B3%7D%20%20%5C%5C%20%20%5C%5C%208%20%3D%20k)
I think is
15 y = 50
y = 50/15
y = 3.3
or i think you
5y + 10x = 50
5y = -10x + 50
y = -2x + 10
<span>Number line refers to a mathematical process of
solving the equation with the use of lines.
=> 235 + 123
Starting from 0 you count 1 up to 235. Then starting from 235 you additionally
count another 123.
Then from zero start counting the total number to the line you stopped when
adding 123 to 235.
This simply equals to
=> 235 + 123
=> 358.
Pls. see attached image for illustration of number line.</span>Answer here
Answer:
1. D
2. C
3. A
4. B
Step-by-step explanation:
________________
Answer:
d) The difference exists due to chance since the test statistic is small
Step-by-step explanation:
From the given information:
Population mean = 178 cm
the sample mean = 177.5 cm
the standard deviation = 2
the sample size = 25
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis:
![H_o: \mu = 178](https://tex.z-dn.net/?f=H_o%3A%20%5Cmu%20%3D%20178)
Alternative hypothesis:
![H_1: \mu \neq 178](https://tex.z-dn.net/?f=H_1%3A%20%5Cmu%20%5Cneq%20178)
The t-test statistics is determined by using the formula:
![t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7BX%20-%20%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t = \dfrac{177.5 - 178}{\dfrac{2}{\sqrt{25}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7B177.5%20-%20178%7D%7B%5Cdfrac%7B2%7D%7B%5Csqrt%7B25%7D%7D%7D)
![t = \dfrac{-0.5}{\dfrac{2}{5}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7B-0.5%7D%7B%5Cdfrac%7B2%7D%7B5%7D%7D%7D)
![\mathbf{t= -1.25}](https://tex.z-dn.net/?f=%5Cmathbf%7Bt%3D%20-1.25%7D)
Degree of freedom df = n- 1
Degree of freedom df = 25 - 1
Degree of freedom df = 24
At the level of significance ∝ = 0.05, the critical value = 2.064
Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance
Conclusion: We fail to reject the null hypothesis since the test statistics is lesser than the critical value and we conclude that the difference exists due to chance since the test statistic is small