Each equation form a straight slanting line. For the first equation, it is slanting towards the right which denotes that it has a positive slope. For the the second equation, its plot is slanting towards the left denoting that its slope is negative. Common to both equation is the point (-1.25, 2.75). At this point, the two lines intersect.
Answer:
1) C
2) B
3) D
4) B
5) C
6) B
7) F
8) B
9) B
10) B
11) D
Step-by-step explanation:
1) The restaurants were measured for each restaurant to give ratings as observations is being carried out on restaurants
2) The percentage of customers was measured to determine ratings. The food and decor can't be measured. Seating capacity is not a measurement variable.
3) The date of measurement is not mentioned
4) The measurement would have to be taken at restaurant obviously.
5) The measurments were taken to determine the ratings and decide the best restaurant
6) Since percentage of customers was measured, the customers had to be surveyed.
7) There are no categorical variables. All variables were measured on the scale of 30
8) Quantitative variable under investigation is number of customers who returned.
9) This is a survey not a design experiment. In design experiment, somethig is put on a test.
10) This is a cross-sectional data. nothing is being measurd over a period of time
11) There are no specific ocncerns since no data is mentioned in the question.
The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
Learn more about prime numbers here:
brainly.com/question/145452
#SPJ1
Answer:
Full packs = 8
Left over = 6 pencils
Step-by-step explanation:
102 divided by 12 = 8
with a remainder of 6
