Answer:
Lines a and b are considered parallel due to their corresponding angles being equal.
Step-by-step explanation:
The corresponding angle postulate states that two lines are parallel when a transversal intersects them and their corresponding angles are congruent.
In this case, line a and line b are intersected by transversal e, with both corresponding angles measuring 110 (which are congruent), hence, according to the corresponding angle postulate, we can conclude that line a and line b are indeed parallel to each other.
Cost function: Revenue function: Profit function: Dozens required for a specific profit P. If 150 dozen cookies are sold, the profit is negative, resulting in a loss of $322. Step-by-step explanation: We can enumerate the costs as follows: - Fixed monthly cost of $790. - Variable costs of $0.24 per cookie, equating to (12*0.24) = $2.88 per dozen. We can then construct the cost function C(x) considering C(x) represents the monthly cost and x denotes the number of dozens produced each month. Revenue can be calculated as the price ($6 per dozen) multiplied by the quantity sold, x. The profit is calculated by subtracting the total cost C(x) from the revenue R(x). The required number of dozens for a monthly profit can be derived from the preceding equation for P(x). To achieve a monthly profit P, a certain number of dozens must be sold. When selling 150 dozen cookies, the profit recorded is negative, indicating a loss of $322.
The average will increase by 5 points, therefore, option c is correct!
Answer:
When x = 72, the z score is:
The average is 58
This z-score indicates that x= 72 is 1.273 standard deviations above the mean.
Step-by-step explanation:
Let’s consider the following details for this question: John's typing speed on a test is assumed to follow a normal distribution. Let X denote the number of words he can type in a minute. Hence, X ~ N(58, 11). It’s important to round the result to three decimal points if needed.
Provide your response below for words per minute on a typing test conducted on Sunday. The z score when x = 72 is
In this scenario, we acknowledge that the variable under consideration is represented by a normal distribution:
The formula for the z score is as follows:
By substituting values, we derive:
The mean is 58
This z-score indicates that x= 72 is 1.273 standard deviations higher than the mean.
All prime numbers are odd with the exception of two. Hence, if we consider the sum of the first million primes, it consists of one even number combined with 999,999 odd numbers. Since the product of an odd number multiplied by another odd number results in an odd number, we conclude that the sum must be an odd number, being even + odd = odd.
It's clear that an odd number ends with an odd digit, so the only digit that can be eliminated is b (an even digit).
