Answer:
Please check the explanation.
Step-by-step explanation:
As the given graph includes distance 'd' at the y-axis and time 't' at the x-axis.
so from the distance-time graph, it is clear that the graph includes 5 chunks.
The first chunk of the graph indicates that the object has started traveling. And the distance 'd' is being covered in time 't', as the slope is upward, hence the speed of the object is increasing.
- Please note that speed is basically the distance covered per unit time.
The second chunk of the graph indicates the no distance is being covered. It means the object is at rest.
The third chunk of the graph indicates that the distance 'd' is being covered in time 't', as the slope is again upward, hence the speed of the object is increasing and the object has started traveling.
The fourth chunk of the graph indicates that the slope is downward, and the object has started traveling to get back to the destination, and eventually, the object has reached the starting point.
Answer:
Tom drank 1/6 glasses of water.
Step-by-step explanation:
1/12 + 1/12 = 1/6
Answer:
![\large\boxed{x=\dfrac{5-\sqrt5}{4},\ x=\dfrac{5+\sqrt5}{4}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bx%3D%5Cdfrac%7B5-%5Csqrt5%7D%7B4%7D%2C%5C%20x%3D%5Cdfrac%7B5%2B%5Csqrt5%7D%7B4%7D%7D)
Step-by-step explanation:
![\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac](https://tex.z-dn.net/?f=%5Ctext%7BThe%20quadratic%20formula%20for%7D%5C%20ax%5E2%2Bbx%2Bc%3D0%5C%5C%5C%5C%5Ctext%7Bif%7D%5C%20b%5E2-4ac%3C0%2C%5C%20%5Ctext%7Bthen%20the%20equation%20has%20no%20real%20solution%7D%5C%5C%5C%5C%5Ctext%7Bif%7D%5C%20b%5E2-4ac%3D0%2C%5C%20%5Ctext%7Bthen%20the%20equation%20has%20one%20solution%3A%7D%5C%20x%3D%5Cdfrac%7B-b%7D%7B2a%7D%5C%5C%5C%5C%5Ctext%7Bif%7D%5C%20b%5E2-4ac%2C%5C%20%2C%5C%20%5Ctext%7Bthen%20the%20equation%20has%20two%20solutions%3A%7D%5C%20x%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D)
![\text{We have the equation:}\ 4x^2-10x+5=0\\\\a=4,\ b=-10,\ c=5\\\\b^2-4ac=(-10)^2-4(4)(5)=100-80=20>0\\\\x=\dfrac{-(-10)\pm\sqrt{20}}{2(4)}=\dfrac{10\pm\sqrt{4\cdot5}}{8}=\dfrac{10\pm\sqrt4\cdot\sqrt5}{8}=\dfrac{10\pm2\sqrt5}{8}\\\\=\dfrac{2(5\pm\sqrt5)}{8}=\dfrac{5\pm\sqrt5}{4}](https://tex.z-dn.net/?f=%5Ctext%7BWe%20have%20the%20equation%3A%7D%5C%204x%5E2-10x%2B5%3D0%5C%5C%5C%5Ca%3D4%2C%5C%20b%3D-10%2C%5C%20c%3D5%5C%5C%5C%5Cb%5E2-4ac%3D%28-10%29%5E2-4%284%29%285%29%3D100-80%3D20%3E0%5C%5C%5C%5Cx%3D%5Cdfrac%7B-%28-10%29%5Cpm%5Csqrt%7B20%7D%7D%7B2%284%29%7D%3D%5Cdfrac%7B10%5Cpm%5Csqrt%7B4%5Ccdot5%7D%7D%7B8%7D%3D%5Cdfrac%7B10%5Cpm%5Csqrt4%5Ccdot%5Csqrt5%7D%7B8%7D%3D%5Cdfrac%7B10%5Cpm2%5Csqrt5%7D%7B8%7D%5C%5C%5C%5C%3D%5Cdfrac%7B2%285%5Cpm%5Csqrt5%29%7D%7B8%7D%3D%5Cdfrac%7B5%5Cpm%5Csqrt5%7D%7B4%7D)
2 because 93 only goes in to 100 once and you only have 253
Answer:
C. H0 : p = 0.8 H 1 : p ≠ 0.8
The test is:_____.
c. two-tailed
The test statistic is:______p ± z (base alpha by 2) ![\sqrt{\frac{pq}{n} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D)
The p-value is:_____. 0.09887
Based on this we:_____.
B. Reject the null hypothesis.
Step-by-step explanation:
We formulate null and alternative hypotheses as proportion of people who own cats is significantly different than 80%.
H0 : p = 0.8 H 1 : p ≠ 0.8
The alternative hypothesis H1 is that the 80% of the proportion is different and null hypothesis is , it is same.
For a two tailed test for significance level = 0.2 we have critical value ± 1.28.
We have alpha equal to 0.2 for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28
The test statistic is
p ± z (base alpha by 2) ![\sqrt{\frac{pq}{n} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D)
Where p = 0.8 , q = 1-p= 1-0.8= 0.2
n= 200
Putting the values
0.8 ± 1.28 ![\sqrt{\frac{0.8*0.2}{200} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B0.8%2A0.2%7D%7B200%7D%20%7D)
0.8 ± 0.03620
0.8362, 0.7638
As the calculated value of z lies within the critical region we reject the null hypothesis.