1. The direction of the vector relative to the positive x-axis satisfies
2. A vector with magnitude and direction has component form
We have , but "angle of 60 degrees with the negative x-axis" is a bit ambiguous. I would take it to mean "60 degrees counterclockwise relative to the negative x-axis", so that the direction is . Then
But this doesn't match any of the options, so more likely it means the angle is 60 degrees clockwise relative to the negative x-axis, in which case and we'd get
3. Same as question 2, but now we're using notation. The vector has magnitude and its direction is . So the vector is
4. The velocity of the plane relative to the air, is 175 mph at 40 degrees above the positive x-axis. The velocity of the air relative to the ground, , is 35 mph at 60 degrees above the positive x-axis. We want to know the velocity of the plane relative to the ground, .
We use the relationship
Translating the known vectors into component form, we have
This vector has magnitude and direction
(or 43 degrees NE)
Answer:
4618.1 ft³
Step-by-step explanation:
Volume of the cone:
Volume of the cilinder:
Total volume is 2*Vcone + Vcilinder = 1470π ≈ 4618.1 ft³
Exponential growth will be seen with exponentiated values that are themselves >1 and, for decay, < 1.
So going from left to right and top down:
first function is G(rowth)
2nd D(ecay)
3rd is G
4th is G
5th is D
6th is D
Answer:
D. The z- score of the bags is equal to a value of 0.
Step-by-step explanation:
The probability that a normally distributed data with statndard deviation σ and a mean, μ,exceeds a value x, is given by
P(X > x)=1-p(X < x)= 1- P(z<
Now,
Given:
weight of corn chips dispensed into a 14-ounce bag by the dispensing machine is a normal distribution with
mean = 14.5 ounces
standard deviation =0.2 ounce.
So,
If 100 bags of chips are randomly selected the probability that the mean weight of these 100 bags exceeds 14.6 ounces is given by:
⇒ P(X> 14.6)= 1- P(z<
⇒ 1- P(z< 5)=
⇒ 1 - 1 = 0.
Therefore,
The z score of the bags is equal to a value of zero.
Answer:
c = 3
Step-by-step explanation:
Let's solve the problem,
→ -40 = -5c - 25
→ -5c = -40 + 25
→ -5c = -15
→ c = -15/-5
→ [ c = 3 ]
Hence, the value of c is 3.