At a skills competition, a target is being lifted into the air by a cable at a constant speed. An archer standing on the ground

Answer:

89

Step-by-step explanation:

Given that

2 O, 2 T and 1 M

Now based on this, the following arrangements exist  

1

Three arrangements i.e. {M,T,O}

2

XX or XY

XX in 2C1 = two arrangements i.e. {OO or TT}

XY in 3C2 × 2! = six arrangements

3

XXY or XYZ

XXY in 2C1 × 2C1 × 3! ÷ 2! = twelve arrangements

XYZ in 3C3 × 3! = six arrangements

4

XXYY or XXYZ

XXYY = 4! ÷ (2! × 2!) = six arrangements

XXYZ in 2C1 ×  4! ÷ 2! = twenty four arrangements

5

= 5! ÷ (2! ×2!)

= 120 ÷ 4

= 30

Thus, the overall total is

= 3 + (2 +6)+ (12 +6) + (6 +24) + 30

= 89

Answer:

Steven is mistaken.

Step-by-step explanation:

Steven has

• 9 unique shirts
• 5 unique hats
• 4 unique scarves.

He selects only two out of the three types of clothing. The combinations can be calculated as

• options to select a shirt and a hat;
• options to select a hat and a scarf;
• options to select a shirt and a scarf.

In total, there are

different methods to choose just two out of the three clothing items.

As a result, Steven is not correct.

Response: The properties of mathematical operations assist in solving integer-related problems as they provide various methods to arrive at the solution.

Step-by-step explanation:

The arrow reaches a height of 48 feet at about 0.55 seconds and again at approximately 5.45 seconds.

Explanation

The formula provided is:

Given the initial velocity as 96 ft/s, we have

To determine when the arrow attains a height of 48 feet, substitute into the formula:

Therefore, the arrow is at 48 feet height at roughly 0.55 seconds and again at 5.45 seconds.