34.56%. This is a binomial probability that can efficiently be calculated using the following formula: Here, n signifies the total number of trials (in this case, 4), x denotes the number of "successes" (which is 3), p is the success probability (60% or 0.6), and q indicates the failure rate (1 - p, thus 0.4). Plugging these values into the formula yields the solution: in percentage form, the probability is found to be 34.56%.
Begin by disregarding the inequality symbol and substituting it with an '=' sign. After that, determine the x- and y-intercepts.
15x + 10y = 1,100
x-intercept:
15x + 0 = 1,100
x = 1,100/15 = 73.33
y-intercept:
0 + 10y = 1,100
y = 1,100/10 = 110
Now, plot the points (73.33,0) and (0,110). Given that the inequality symbol is ≥, representing equality, connect these points using a solid line.
Next, let's identify a point on the graph, for instance, the origin (0,0). Use this point in the equation.
15x + 10y ≥ 1,100
15(0) + 10(0)? 1,100
0? 1,100
0 < 1,100
This makes the ≥ statement false. As a result, the alternate area defined by the line is the solution. Consequently, shade that region. The resulting graph is displayed in the attached image.
In this scenario, the first step is to assign variables.
We define:
x: time measured in minutes
y: distance covered.
The equations formulated are as follows:
For Kathleen:

For Arnob:

At the moment Arnob meets Kathleen, we have:

Next, we isolate x.
We now have:


Answer:
Arnob takes a total of 75 minutes to catch up to Kathleen:
d. 75
Answer:
The initial goal was $25019.154.
Step by step Explanation:
Assuming the original goal is denoted as x.
As stated
Another Kickstarter initiative for an iPad stylus secured 1,253% of its target, accumulating a total of $313,490.
1253% can be expressed as a decimal.

= 12.53
Thus, the equation is rearranged to
12.53 × x = 313490
12.53x = 313490

x = $ 25019.154
This means the initial goal stands at $25019.154.