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2 years ago

A salad bar offers nine choices of toppings for lettuce and how many ways can you choose five toppings

Mathematics

2 answers:

MaRussiya [10]2 years ago

8 0

$\displaystyle \binom{9}{5}=\dfrac{9!}{5!4!}=\dfrac{6\cdot7\cdot8\cdot9}{2\cdot3\cdot4}=126$

Lera25 [3.4K]2 years ago

7 0

Since, a salad bar offers nine choices of toppings for lettuce.

We have to determine the number of ways in which we can choose five toppings from nine toppings.

We will use the combination formula, which states that

"
It is a formula for the number of possible combinations of r objects from a set of n objects", which is given by the formula as:

$^nC_{r}=\frac{n!}{r!(n-r)!}$

So, $^9C_{5}=\frac{9!}{5!(9-5)!}$

$^9C_{5}=\frac{9!}{5!4!}$

$^9C_{5}=\frac{9 \times 8 \times 7 \times 6 \times 5!}{5!4!}$

$^9C_{5}=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2}$

$= 18 \times 7$

= 126

Therefore, in 126 ways, we can choose five toppings from nine toppings for lettuce.

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Step-by-step explanation:

Part 1

For this case we know the following info: The length, l cm, of a simple pendulum is directly proportional to the square of its period (time taken to complete one oscillation), T seconds.

$L \propto T^2$

Using the condition given:

$2.205 m = K (3)^2$

$K = 0.245 \approx \frac{g}{4\pi^2}$

So then if we want to create an equation we need to do this:

$L = K T^2$

With K a constant. For this case the period of a pendulumn is given by this general expression:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where L is the length in m and g the gravity $g = 9.8 \frac{m}{s^2}$ .

Part 2

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

If we square both sides of the equation we got:

$T^2 = 4 \pi^2 \frac{L}{g}$

And solving for L we got:

$L = \frac{g T^2}{4 \pi^2}$

Replacing we got:

$L =\frac{9.8 \frac{m}{s^2} (5s)^2}{4 \pi^2} = 6.206m$

Part 3

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

Replacing we got:

$T = 2\pi \sqrt{\frac{0.98m}{9.8\frac{m}{s^2}}}= 1.987 s$

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