Answer:
Step-by-step explanation:
Hope this helped!
<h3>~AH1807</h3>
What is 4.1363636… as a fraction?
2 answers:
Answer:
x = .
Step-by-step explanation:
Given : 4.1363636…
To find : Convert it as fraction .
Solution : We have given 4.1363636…
Let x = 4.1363636…
On multiplying both sides by 100
100 x = 100 * 4.1363636…
100 x = 413 .63636...
We can convert it in term of x
100 x = 409 .5 + 4.1363636...
100 x = 409.5 + x
On subtracting both sides by x
100 x -x = 409.5
99 x = 409. 5
On dividing both sides by 99
x = .
x = .
On dividing both sides by 5
x = .
Therefore, x = .
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Answer:
3.)
2.)
1.)
Step-by-step explanation:
3.) By the Rational Root Theorem, we would take the Least Common Divisor [LCD] between the leading coefficient of 1, and the initial value of −16, which is 1, but we will take 2 since it is the <em>fourth root</em> of 16; so this automatically makes our first factor of Next, since the factor\divisor is in the form of
, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
2| 1 2 −6 4 −16
↓ 2 8 4 16
__________________
1 4 2 8 0 →
You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [x⁴ + 2x³ - 6x² + 4x - 16]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x³, the 4x² follows right behind it, bringing 2x right up against it, and bringing up the rear, 8, giving you the quotient of
However, we are not finished yet. This is our first quotient. The next step, while still using the Rational Root Theorem with our first quotient, is to take the Least Common Divisor [LCD] of the leading coefficient of 1, and the initial value of 8, which is −4, so this makes our next factor of Then again, we use Synthetic Division because
is in the form of
:
−4| 1 4 2 8
↓ −4 0 −8
_____________
1 0 2 0 →
So altogether, we have our four factors of
__________________________________________________________
2.) By the Rational Root Theorem again, this time, we will take −1, since the leading coefficient & variable\degree and the initial value do not share any common divisors other than the <em>special</em><em> </em><em>number</em> of 1, and it does not matter which integer of 1 you take first. This gives a factor of Then start up Synthetic Division again:
−1| 1 3 5 −3 −6
↓ −1 −2 −3 6
__________________
1 2 3 −6 0 →
Now we take the other integer of 1 to get the other factor of then repeat the process of Synthetic Division:
1| 1 2 3 −6
↓ 1 3 6
_____________
1 3 6 0 →
So altogether, we have our three factors of
Hold it now! Notice that is unfactorable. Therefore, we have to apply the Quadratic Formula to get our two complex solutions,
[or zeros in this matter]:
__________________________________________________________
1.) By the Rational Root Theorem one more time, this time, we will take 4 since the initial value is 48 and that 4 is the root of the polynomial. This gives our automatic factor of Then start up Synthetic Division again:
4| 1 −1 −16 4 48
↓ 4 12 −16 −48
___________________
1 3 −4 −12 0 →
We can then take −3 since it is a root of this polynomial, giving us the factor of
−3| 1 3 −4 −12
↓ −3 0 12
_______________
1 0 −4 0 →
So altogether, we have our four factors of and when set to equal zero, you will get
I am delighted to assist you anytime.
Answer:
Step-by-step explanation:
If you want to factor
, you could throw that into the quadratic formula with a = 1, b = 11 and c = 0, but the easier thing to do is to factor out what's common in those 2 terms. m is common, so when we factor it out:
That's the factored form.
By the Zero Product Property, either
m = 0 or m + 11 = 0.
So the 2 solutions to this are
m = 0 or m = -11
Not sure how far you need to go with this.
Answer:
The value of P-value is 0.0472.
Step-by-step explanation:
We are given that you take a simple random sample of 12 apartments in town A and calculate the average price of these apartments. You repeat this for 15 apartments in town B.
Let = <u><em>true average price of apartments in town A</em></u>
= <u><em>true average price of apartments in town B</em></u>
So, Null Hypothesis, :
Alternate Hypothesis, :
The test statistics that have been used here is <u>two-sample t-test statistics</u>, i.e;
The test statistics given to us is 2.1
Now, the P-value of the test statistics is given by the following formula;
P-value = P( > 2.1)
= P( > 2.1) = 0.0236
In two-tailed test, P-value is calculated as = 2 0.0236 = <u>0.0472</u>
Hence, the value of the p-value is 0.0472.