Answer: A
Step-by-step explanation:
To find the inner product of two vectors (a,b) and (c,d) you would use the equation (a * c) + (b * d)
So for (7,2) and (0,-2) the inner product would be
(7 * 0) + (2 * -2)
= 4
The vectors are only perpendicular when the inner product is equal to 0. Since it is equal to -4 in this case, the vectors are not perpendicular.
A -4; no
Answer:
(b) ![\frac{7}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B30%7D)
Step-by-step explanation:
When two p and q events are independent then, by definition:
P (p and q) = P (p) * P (q)
Then, if q and r are independent events then:
P(q and r) = P(q)*P(r) = 1/4*1/5
P(q and r) = 1/20
P(q and r) = 0.05
In the question that is shown in the attached image, we have two separate urns. The amount of white balls that we take in the first urn does not affect the amount of white balls we could get in the second urn. This means that both events are independent.
In the first ballot box there are 9 balls, 3 white and 6 yellow.
Then the probability of obtaining a white ball from the first ballot box is:
![P (W_{u_1}) = \frac{3}{9} = \frac{1}{3}](https://tex.z-dn.net/?f=P%20%28W_%7Bu_1%7D%29%20%3D%20%5Cfrac%7B3%7D%7B9%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
In the second ballot box there are 10 balls, 7 white and 3 yellow.
Then the probability of obtaining a white ball from the second ballot box is:
![P (W_{u_2}) = \frac{7}{10}](https://tex.z-dn.net/?f=P%20%28W_%7Bu_2%7D%29%20%3D%20%5Cfrac%7B7%7D%7B10%7D)
We want to know the probability of obtaining a white ball in both urns. This is: P(
and
)
As the events are independent:
P(
and
) = P (
) * P (
)
P(
and
) = ![\frac{1}{3}* \frac{7}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%2A%20%5Cfrac%7B7%7D%7B10%7D)
P(
and
) = ![\frac{7}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B30%7D)
Finally the correct option is (b) ![\frac{7}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B30%7D)
When a quadratic equation ax^2+bx+c has a double root, the discriminant,
D=b^2-4ac=0
Here
a=2,
b=b,
c=18
and
D=b^2-4ac=b^2-4*2*18=0
solve for b
b^2-144=0
=> b= ± sqrt(144)= ± 12
So in order that the given equation has double roots, the possible values of b are ± 12.
Answer:
5.48 or 5.477225575 hope this helps
Step-by-step explanation:
F(x) = <span>x^2+3x+8
now, the pending of the tangent line is d/dx f(x)
f'(x) = 2x + 3
now, we need know when the pending is increasing.
so
</span>2x + 3> 0
solving
x>-3/2
The interval over which the function f(x)= x^2+3x+8 is <span>increasing is (-3/2,+</span>∞<span>)</span><span>
</span>