Answer: 5040 7-digit numbers
Step-by-step explanation:
Permutations:
1: 1 ==> 1 permutation ==> 1 ==> 1!
12: 12, 21 ==> 2 permutations ==> 1*2 ==> 2!
123: 123, 132, 213, 231, 312, 321 ==> 6 permutations ==> 1*2*3 ==> 3!
7-digits: 7!=
1*2*3*4*5*6*7=5040 7-digit numbers
Answer:
Arc length MK = 15.45 units (nearest hundredth)
Arc measure = 58.24°
Step-by-step explanation:
Calculate the measure of the angle KLN (as this equals m∠KLM which is the measure of arc MK)
ΔKNL is a right triangle, so we can use the cos trig ratio to find ∠KLM:

where:
is the angle- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
Given:
= ∠KLM- A = LN = 8
- H = KL = 15.2



Therefore, the measure of arc MK = 58.24° (nearest hundredth)

Given:
- r = 15.2
- ∠KLM = 58.24313614°


Annie's total earnings from her initial savings, $12, and from babysitting should be equal or more than 30. Annie's total earnings from babysitting may be expressed as $6n. The inequality should be,
12 + 6n <span>≥ 30
Solving for x,
6n </span><span>≥ 30 - 12
</span><span>
6n </span>≥ 18 ; n <span>≥ 3
</span><span>
Thus, the answer is the second among the choices.
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