Answer: The cube root of 10 is 2.1544, using an initial value of -0.003723.
Step-by-step explanation: The Newton-Raphson method is utilized for root finding, and its formula is NR: X=Xo-(f(x)/f'(x)). Before applying this formula, the derivative of the equation must be determined. Given that X =10, this method was implemented to identify the best root to ascertain the cube root of 10 to 5 significant figures. Utilizing software like Excel for quicker iteration calculations is advisable. The found root in this instance was -0.003723.
Answer:
Step-by-step explanation:
Delivery charge = $7.50
Cost per pizza = $14
Budgeted total = $60
7.50 + 14p < 60
First, subtract 7.50 from both sides
14p < 60 - 7.50
14p < 52.50
Now divide both sides by 14
p < 52.50 / 14
p < 3.75
Each pizza consists of 8 slices
Therefore, the total number of slices she can buy = 3.75 × 8
= 30 slices
Answer:
Yes, the cost 
in dollars and the quantity of yogurt 
are indeed proportional.
The relationship can be expressed as: 
Step-by-step explanation:
1. If varies directly with , it can be represented as:
Here, 
represents the constant of proportionality.
2. We'll calculate the proportionality constant. Given that 
and 
, we have:
3. Thus, the equation becomes:
4. Now, we need to verify proportionality. Substituting 
, which is the quantity of yogurt purchased by Jonah, we should arrive at $0.48:
5. They are indeed directly proportional.
Answer:
Step-by-step explanation:
Player A has a red marble and a blue marble, while Player B also has a red marble and a blue marble.
Therefore, the probability of selecting one marble is equal, at 0.5.
Due to the independence of A and B's choices, the joint event is calculated by multiplying the probabilities.
Let A represent the amount that player A wins.
If both players select one marble, the sample space can be considered as
(R,R) (R,B) (B,R) (B,B)
Probability 0.25 0.25 0.25 0.25
A's winnings 3 -2 -2 1
E(A) 0.75 -0.5 -0.5 0.25 = 0
Thus, the game is even, offering equal expected values for both A and B.
It does not influence the outcome whether you are A or B.
Answer:
(B) There is a single solution: x = 0.
Step-by-step explanation:
The equation that Kate is attempting to solve is: 
Consequently, this equation results in one solution: x = 0.
