Can someone please help me with these questions.
1 answer:
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Answer:
To purchase 700 business cards, Jamie needs to pay $43.
Step-by-step explanation:
We are given that Jamie ordered 200 business cards and paid $23 in total.
We are also given that Jamie ordered 500 business cards and paid $35.
We can use the rate of change formula to find the average change.
This can also be represented with:
Therefore, we need to identify our variables.
In every relationship, there is a <u>dependent variable</u> and an <u>independent variable</u>.
- The independent variable is the variable that an experimenter adjusts in order to receive an altered effect from an output.
- The dependent variable is the variable that adjusts based on the changes made to the independent variable.
We change the amount of business cards that are purchased, which in turn, changes the price.
The y-variable is assigned to the dependent variable and the x-variable is assigned to the dependent variable.
Therefore, if we use the coordinate system:
- (200, 23)
- (500, 35)
Now, we can name our coordinates. We use this system:
- (x₁, y₁)
- (x₂, y₂)
This means that we can name our points:
- x₁ = 200
- y₁ = 23
- x₂ = 500
- y₂ = 35
Revisiting the rate of change formula, we can insert these values.
Next, we need to find the y-intercept of our line. We can do this by using one coordinate pair from above and our slope.
The slope-intercept equation is:
We already know m:
We also know x and y (we take them from of the coordinate pairs):
Now, we can substitute these values into the equation and solve for b.
Now, we can set up our linear equation.
Therefore, in order to find the price of 700 business cards, we make x in the equation equal 700 and then solve.
Therefore, the price of 700 business cards is equal to $43.
The interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
<h3>What is convergent of a series?</h3>A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.
We can find the interval for the convergent by root test.
Like the Ratio Test, the root Test is used to determine absolute convergence (or not) with factorials, the ratio test is useful.
For the given series:
As the series goes infinitely, we can use root test.
By the root test, the convergence interval will be;
The interval of convergence is:
x < -3 or x > 3 we can write this as:
|x| < 3
Thus, the interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
Learn more about the convergent of a series here:
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