Answer:
The lower limit of 95% confidence interval is 99002.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = $100,000
Sample mean, 
= $111,000
Sample size, n = 36
Alpha, α = 0.05
Population standard deviation, σ = $36,730
First, we design the null and the alternate hypothesis
We have to find the lower limit of the 95% confidence interval.
95% Confidence interval:
Putting the values, we get,
The lower limit of 95% confidence interval is 99002.
Answer:
Wind
Step-by-step explanation:
The theorem that justifies why triangles ABC and DEF are congruent is: HL.
<h3>What is the Hypotenuse-Leg Congruence Theorem (HL)?</h3>
The hypotenuse-leg congruence theorem (HL) states that if two triangles that are right triangles have a pair of congruent hypotenuse and a pair of corresponding congruent legs, then both right triangles are proven to be congruent to each other. This means both right triangles are have the same shape and size.
Given that:
angle ABC = angle DEF = 90° (congruent right angles, this means both triangles are right triangles)
AC = FD (a pair of congruent hypotenuse)
AB = DE (a pair of congruent legs)
Thus, we can conclude that since triangle ABC and triangle DEF have a pair of congruent hypotenuses and a pair of congruent legs, therefore, the two right triangles, triangle ABC and triangle DEF are congruent to each other by the HL congruent theorem.
Thus, the theorem that justifies why both triangles are congruent is: HL.
Learn more about the HL congruence theorem on:
brainly.com/question/2102943
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Answer:
Fran's balance will be $866.73.
Step-by-step explanation:
She has an existing balance of $752.69
Her current card charges her a transfer fee of 12.5%, added to her balance, for transferring her debt.
This becomes: 
Total is : 
The new card has an opening fee of $50, which is also added to her balance.
This becomes now = 
She will also have to make an immediate minimum payment, which is 3.35% of her total balance.
This amount is = 
Now balance in her account is = 
So, Fran's balance will be $866.73.
Probability of 1st number being even : 3/7
probability of 2nd number being even : 2/6
probability of 3rd number being even : 1/5
probability of all 3 numbers being even : 3/7 * 2/6 * 1/5 = 6/210 = 1/35
