Answer:
Step-by-step explanation:
In the first part the given polynomial is 
, we have to divide this polynomial by (x-1) using synthetic division.
Here are the steps of synthetic division
Step 1: Set up the synthetic division table in which the coefficients are written in descending power of x.
Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.
Step 3: Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient. Here, a is 1(taken from divisor)
Step 4: Add the column made in step 3. Repeat these steps until the last column reached.
In the second part,
It is given that divisor polynomial is the factor of given polynomial then we have to tell the remainder which is 0 because if divisor polynomial is the factor the it will completely divide the given polynomial which gives remainder 0.
In the third part,
Given when one uses the synthetic division to divide by (x-3) then what number is used to multiply each term that is dropped down or added.
As explained the steps of synthetic division in first part
x-3=0 ⇒ x=3 which is a
In step 3, Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient. So, 3 is multiplied.
As explained in Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.
The columns which is formed by above steps are added.
Since we have that the volume of a sphere is given by:
And we have that the diameter equals 3.6ft, we then will have a volume of:
Since we have that the volume is approximately 13.74 ft^3, then the best approximation in the problem is A. 13.6 ft^3.
The solution for P is P = A / (1 + r)^t, the initial deposit is $1,510, and I agree that A is always greater than P when given the conditions stated.
<h3>How do we calculate the initial deposit?</h3>
The correct formula in the question is provided as follows:
A = P(1 + r)^t ........................ (1)
a. P can be solved for and the amount of Patricia's initial deposit can be found from equation (1) as follows:
P = A / (1 + r)^t ................................. (2)
Where:
A = $1839.79
r = 2.5% = 0.025
t = 8
Substituting all the relevant values into equation (2), we have:
P = $1839.79 / (1 + 0.025)^8
P = $1,510
b. Yes, I agree.
The reason is that interest at the rate of 2.5% will be earned yearly on P and added to A making A always greater than P.
Learn more about initial deposits here: brainly.com/question/21845455.
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Using it's concept, there is a 0.125 = 12.5% probability that Craig will pitch it between 70 and 75 mph.
<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
From the histogram, the number of pitches is given by:
1 + 5 + 3 + 4 + 1 + 2 = 16.
Of those, 2 were between 70 and 75 mph, hence the probability is given by:
p = 2/16 = 1/8 = 0.125.
There is a 0.125 = 12.5% probability that Craig will pitch it between 70 and 75 mph.
More can be learned about probabilities at brainly.com/question/14398287
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