An ice cream shop has 15 different toppings for sundaes, and it is running a special for 3 free toppings. How many 3-topping sundaes can be made, assuming all 3 toppings chosen are different?

455

Step-by-step explanation:

This is a combination problem: we need to create groups of 3 elements from the pool of 15 options, and the order of the elements in the group doesn't matter.

So, to solve the problem, we need to find the combination of 15 choose 3:

C(15,3) = 15! / (3! * 12!) = (15*14*13)/(3*2) = 455

We can make 455 different 3-topping sundaes.

146%

step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).