You will use the word absolute value. The absolute value describes a distance from zero. Here is how you would write this in math terms and symbols:
|9|
Answer:
$104.19
Step-by-step explanation:
We will use the compound interest formula to solve this:

<em>P = initial balance</em>
<em>r = interest rate (decimal)</em>
<em>n = number of times compounded annually</em>
<em>t = time</em>
<em />
First, lets change 5% into a decimal:
5% ->
-> 0.05
Now, plug the values into the equation:


After 3 years, Maria will have $104.19
Answer: 11x + 11
Step-by-step explanation:
This is two points equation. It could be done in various ways depending on the level of understanding of the topics. The formula goes thus
y - y₁ y₂ ₋ y₁ y₂ ₋ y₁
------ = ---------- or y ₋ y₁ = --------- ˣ ( x - x₁ )
x - x₁ x₂ ₋ x₁ x₂ ₋ x₁
Where x₁ = -1, x₂ = -1, y₁ = 6, y₂ = -5. Now substitute for the values in the formula above and solve.
y - 6 -5 - 6 -11 -11
------ = -------- = ---- = -----
x - (-1) -1 - (-1) -1 + 1 0
y - 6 -11
------ = -----
x + 1 0 ,
Now we cross multiply to have a linear equation
0( y - 6 ) = -11( x + 1 )
0 = -11x - 11, now multiply by -1
The equation now becomes
11x + 11
Answer:

Step-by-step explanation:
We can use the definition of inverse functions. Recall that if two functions, <em>f</em> and <em>g</em> are inverses, then:

So, we can let <em>j</em> be the inverse function of <em>h</em>.
Function <em>h</em> is given by:

Find its inverse. Flip variables:

Solve for <em>y. </em>Add:

Hence:

Therefore, <em>a</em> = 1/3 and <em>b</em> = 2/3.
We can verify our solution:

And:

Answer:
Step-by-step explanation:
We are given the following in the question:
The needle size should not be too big and too small.
The diameter of the needle should be 1.65 mm.
We design the null and the alternate hypothesis

Sample size, n = 35
Sample mean,
= 1.64 mm
Sample standard deviation, s = 0.07 mm
Type I error:
- It is the error of rejecting the null hypothesis when it is true.
- It is also known as false positive error.
- It is the rejecting of a true null hypothesis.
Thus, type I error in this study would mean we reject the null hypothesis that the average diameter is 1.65 mm but actually the average diameters of the needle is 1.65 mm.
Thus, average diameter is 1.65 mm and we decide that it is not 1.65 mm.