Answer:
![(-\infty, 0)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%200%29)
Step-by-step explanation:
(w circle r) (x) is the composite function(w of r(x)), that is, w(r(x))[/tex]
We have that:
![r(x) = 2 - x^{2}](https://tex.z-dn.net/?f=r%28x%29%20%3D%202%20-%20x%5E%7B2%7D)
![w(x) = x - 2](https://tex.z-dn.net/?f=w%28x%29%20%3D%20x%20-%202)
Composite function:
![w(r(x)) = w(2 - x^{2}} = 2 - x^{2} - 2 = -x^{2}](https://tex.z-dn.net/?f=w%28r%28x%29%29%20%3D%20w%282%20-%20x%5E%7B2%7D%7D%20%3D%202%20-%20x%5E%7B2%7D%20-%202%20%3D%20-x%5E%7B2%7D)
is a negative parabola with vertex at the original.
So the range(the values that y assumes), is:
![(-\infty, 0)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%200%29)
Answer:
=![\frac{5}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B13%7D)
Step-by-step explanation:
Total Number of Cards=52
Number of Cards having a point value of 10=16
Number of Aces=4
We want to determine the probability that both cards dealt are aces or 10-point cards.
P(Aces) = ![\frac{4}{52}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B52%7D)
P(10 point cards)=![\frac{16}{52}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B52%7D)
Definition
If A and B are mutually exclusive events,
Probability (A OR B) = P(A)+P(B)
P(both cards dealt are aces or 10-point cards) = P(Aces) + P(10 point cards)
=![\frac{4}{52}+\frac{16}{52}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B52%7D%2B%5Cfrac%7B16%7D%7B52%7D)
=![\frac{20}{52}= \frac{5}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7B52%7D%3D%20%5Cfrac%7B5%7D%7B13%7D)
Answer:
![h = 3.214\,m](https://tex.z-dn.net/?f=h%20%3D%203.214%5C%2Cm)
Step-by-step explanation:
El área total del camino es el producto del perímetro del jardín y el ancho del camino:
![A = 2\cdot (w + l) \cdot h](https://tex.z-dn.net/?f=A%20%3D%202%5Ccdot%20%28w%20%2B%20l%29%20%5Ccdot%20h)
Donde:
- El ancho del jardín, en metros.
- El largo del jardín, en metros.
- El ancho del camino, en metros.
El ancho del camino es:
![h = \frac{A}{2\cdot (w+l)}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7BA%7D%7B2%5Ccdot%20%28w%2Bl%29%7D)
![h = \frac{540\,m^{2}}{2\cdot (50\,m + 34\,m)}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B540%5C%2Cm%5E%7B2%7D%7D%7B2%5Ccdot%20%2850%5C%2Cm%20%2B%2034%5C%2Cm%29%7D)
![h = 3.214\,m](https://tex.z-dn.net/?f=h%20%3D%203.214%5C%2Cm)
Ben's age in x yeears=30+x
daniel's age in x years is 2+x
when will ben's age in x years be 3 times of daniel's age in x years
30+x=3(2+x)
30+x=6+3x
minus x both sides
30=6+2x
minus 6 both sides
24=2x
divide by 2 both sides
12=x
answer is in 12 years
I think he bought 14 meduim pumpkins and six large pumpkins.