Answer:
Step-by-step explanation:
Step 1:
Step 2:
Step 3:
Step 4:
To complete the square, add to both sides.
Step 5:
Step 6:
Taking square roots on both sides.
Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purc
2 answers:
Answer:
$110.
Step-by-step explanation:
Let x represent the cost of the item that Carmen bought from the department store.
Carmen possesses $30 in store bucks along with a 25% discount coupon for a local department store. Our goal is to determine the maximum cost for Carmen's purchase such that after applying her store bucks and discount, her total remains at or below $60 before sales tax.
Since the $30 in store bucks is deducted prior to applying the 25% discount, we need to find x such that x - 30 minus 25% of (x - 30) must be less than or equal to 60. This can be set up as an equation:
Thus, Carmen's purchases should total no more than $110 before sales tax.
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Answer:
i) A total of 40320 different arrangements
ii) For the initial 3 spots, there are 336 different combinations.
Step-by-step explanation:
Given: The total finalists = 8
The count of boys = 3
The count of girls = 5
To determine the number of sample point in the sample space S for possible arrangements, we calculate the factorial of 8!
The number of possible arrangements equals 8!
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
= 40320
ii) Among the 8 finalists, we must select the first 3 spots. The sequence matters, hence we utilize permutation.
nPr =
Here n = 8 and r = 3
Substituting n = 8 and r = 3 into the formula, we arrive at
8P3 =
=
= 6.7.8
= 336
Thus, there are 336 different arrangements for the first 3 spots.
Response:
Regarding this scenario, we have the following details about the timeframe to organize a return
And we select a sample size =49>30, and we aim to find the standard deviation for the sample mean. Based on the central limit theorem, we understand that the sample mean distribution is represented by:
The standard deviation would then be:
Therefore, the most accurate response would be
b. 2 minutes
Step-by-step explanation:
Prior concepts
Normal distribution, defines a probability distribution that is symmetric around the mean, showing that occurrences near the mean are more frequent than those that are further away.
The central limit theorem states that "when we have a population with mean μ and standard deviation σ and draw sufficiently large random samples from the population with replacement, then the distribution of the sample means will resemble a normal distribution. This applies regardless of whether the original population is normal or skewed, given that the sample size is large enough".
Solution to the problem
For this case, we have the following information about the time to prepare a return
A sample size =49>30 also indicates that we are focused on determining the standard deviation for the sample mean. Based on the central limit theorem, we recognize that the sample mean distribution is described by:
Hence, the most accurate answer would be
b. 2 minutes