Answer:
![m](https://tex.z-dn.net/?f=m%3C49%2F12)
Step-by-step explanation:
we are given
![y = 3x^2+7x+m](https://tex.z-dn.net/?f=y%20%3D%203x%5E2%2B7x%2Bm)
To find x-intercept means we have to find zeros
and for finding zeros , we will use quadratic formula
and we have it has two x-intercepts
so, it's discriminant must be greater than 0
so, we will find discriminant
![D = \sqrt{b^2-4ac}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7Bb%5E2-4ac%7D)
now, we can compare with
![y=ax^2+bx+c\\y=3x^2+7x+m](https://tex.z-dn.net/?f=y%3Dax%5E2%2Bbx%2Bc%5C%5Cy%3D3x%5E2%2B7x%2Bm)
and then we can find a , b and c
a = 3, b = 7, c = m
now, we can find D
![D = \sqrt{7^2-4*3*m} \\D=\sqrt{49-12m}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B7%5E2-4%2A3%2Am%7D%20%5C%5CD%3D%5Csqrt%7B49-12m%7D)
It has two x-intercepts
so,
![D = \sqrt{49-12m}>0](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B49-12m%7D%3E0)
now, we can solve for m
![49-12m>0\\12m](https://tex.z-dn.net/?f=49-12m%3E0%5C%5C12m%3C49%5C%5Cm%3C49%2F12)
Answer:
13sqrt(2) units
Step-by-step explanation:
LM² = 7² + 17²
LM² = 338
LM = sqrt(338)
LM = 13sqrt(2)
sqrt: square root
Answer:
a) z = -1.645
b) z = 0.674
Step-by-step explanation:
We have to find the value of z of a standard normal variable Z that satisfies each of the following conditions.
a) 5% of the observations fall below z
Calculation the value from standard normal z table, we have,
![P(Z](https://tex.z-dn.net/?f=P%28Z%3C-1.645%29%20%3D%200.05%5C%5Cz%20%3D%20-1.645)
b) 25% of the observations fall above z
![P(Z > z) = 0.25\\\Rightarrow P(Zz) = 1 - 0.25 = 0.75](https://tex.z-dn.net/?f=P%28Z%20%3E%20z%29%20%3D%200.25%5C%5C%5CRightarrow%20P%28Z%3Cz%29%20%3D%201%20-%20P%28Z%3Ez%29%20%3D%201%20-%200.25%20%3D%200.75)
Calculation the value from standard normal z table, we have,
![P(Z](https://tex.z-dn.net/?f=P%28Z%3C0.674%29%20%3D%200.75%5C%5Cz%20%3D%200.674)
1.414 x 10 to the 7th power.