Answer: D. 45 inches, 75 inches
Step-by-step explanation:
To resolve this inquiry, we first need to divide the board's total length by the number of segments forming the two sections.
Given the ratio of 3:5, one section consists of 3 segments and the other of 5, making a total of 8 segments.
120 divided by 8 equals 15 inches for each segment.
Next, we multiply the length of each segment by how many segments each section has (3 and 5).
15 times 3 equals 45 inches.
15 times 5 equals 75 inches.
The piece-wise function can be expressed as follows: The base charge for renting the vehicle is $35 per day. If the car is rented for three days or fewer, there’s an insurance surcharge of $10 per day. For rentals over three days, the daily insurance cost drops to $5. Let’s denote the number of days as x. Accordingly, we have: For x ≤ 3, f(x) = 35 × x + 10 × x = x × (45) For x > 3, f(x) = 35 × x + 5 × x = x × (40). Therefore, the charge for renting the vehicle for three days or less is 45·x, and for rentals longer than three days is 40·x.
Finding a solution to an equation entails determining the value of x that renders the equation valid.
We must reverse the operations applied to x to isolate it.
Final Note:
The resulting equation is false, indicating that there is NO solution. Graphically, both equations will be represented as parallel lines that do not intersect.
The likelihood of selecting a girl first is 5/10.
The chance that the second pick is a boy is 5/9.
(As there are now 9 students remaining after a girl was chosen)
The probability of the third student being a girl stands at 4/8
(after one girl has been picked, 4 girls and 8 students total remain).
Hence, the overall probability is (5/10)(5/9)(4/8)=0.139
Answer: 0.139
Ho ho ho, let’s kick off this party!
I’m super excited to apply what I’ve just learned!
So
multiplicities
When a root or zero features an even multiplicity, the graph bounces off that root. However, if it has an odd multiplicity, the graph intersects that root.
So
The roots are:
-1
2
4
The multiplicity indicates how many times a root occurs. Since 2 has an even multiplicity, we have 2 as odd and 1 as even.
For the roots, r1 and r2, the factors would be
(x-r1)(x-r2)
Therefore,
(x-(-1))^1(x-2)^2(x-4)
(x+1)(x-2)^2(x-4)
This represents a 4th degree polynomial.
Typically, it runs from the upper right to the upper left but is upside down.
Thus, it has a negative leading coefficient.
y=-k(x+1)(x-4)(x-2)^2
