Which expression is equivalent to (f g) (5)?

The ratio of total members in the group stands at 5:7, meaning that among every 7 members, there are 5 men and 2 women. We can set it up as a proportion: 5:7 = x:735, leading to the equation 5/7 = x / 735. By cross-multiplying, we get 7*x = 5 * 735, simplifying to 7*x = 3675. Dividing this by 7 results in x = 525. Therefore, there will be 525 men in total.

<span>Which formula can be applied to find the side length of the rhombus?

 The correct answer is the first choice: 10/Cos(30°)

 Explanation:

 1. The figure shows a right triangle, where the hypotenuse is denoted by "x," and this is the length you are solving for. Therefore, you have:

 Cos(</span>α)=Adjacent side/Hypotenuse
<span>
 </span>α=30°
<span> Adjacent side=(20 in)/2=10 in
 Hypotenuse=x

 2. Inputting these numbers into the equation yields:
</span>
 Cos(α)=Adjacent side/Hypotenuse
<span> Cos(30°)=10/x

 3. Hence, by isolating the hypotenuse "x," you arrive at the expression to find the side length of the rhombus, as shown below:

 x=10/Cos(30°)
</span>

Answer:

Approximately 59 stacked cups.

Step-by-step explanation:

We have the following measurements:

Height of one cup = 12.5 cm,

Height of two cups stacked = 14 cm,

Height of three cups stacked = 15.5 cm,

...and so on.

This situation can be described by an arithmetic sequence,

12.5, 14, 15.5,....

The first term is defined as a = 12.5,

with a common difference of d = 1.5 cm.

Thus, the height of x stacked cups is given by

As per the problem,

h(x) = 200

⇒ 1.5x + 11 = 200

⇒ 1.5x = 189

⇒ x = 59.3333333333 ≈ 59.

Therefore, you will need approximately 59 stacked cups.

6 × 10 × 10 × 10 × 10 = Step-by-step breakdown: The exponent of any number reveals how many times that number is multiplied. It signifies the power applied to a number indicating how often that number is multiplied. Here, 10 is used four times, indicating an exponent of 4 for 10. Therefore, the expression can be represented as: