Whats the smallest natural number that has exactly 6 factors and isn't divisible by 2,3 or both
1 answer:
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Answer:
The equation does not have a real root in the interval
Step-by-step explanation:
We can make use of the intermediate value theorem.
The theorem states that if is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:
- If a continuous function has values of opposite sign inside an interval, then it has a root in that interval. This is also known as Bolzano's theorem.
- The image of a continuous function over an interval is itself an interval.
Of course, in our case, we will make use of the first one.
First, we need to proof that our function is continues in , which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval
, which means to evaluate the equation in 0 and 1:
Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval . I attached a plot of the equation in the interval
where you can clearly observe how the graph does not cross the x-axis in the interval.
Answer:
14.
15. This is not possible since p(yellow)=0.10 which is less than the stated 0.35
Step-by-step explanation:
13 a. -A goal-scoring statistic is the probability of a player scoring one goal in any given game played.
-A 0.36 goal scoring statistic means that the player has a 0.36 or 36% chance of scoring a goal in any game that he is involved in.
b. To determine the number of games it takes to score a whole goal, we divide the probability by 1 goal:
Hence, it takes approximately 3 games to score a full goal.
14.-The cost of a GCSE retake is £600 and attracts a 15% deposit
#The 15% equivalent in actual pounds is calculated by multiplying the percentage by the total cost as:
Hence, the 15% deposit amount equals £90
b.#The student pays the balance in a £20 per week scheme,the total number of weeks is calculated as:
Hence, it takes 26 weeks to clear the balance.
c. Given that 10% is the equivalent of £450
-We divide this amount by 10% to get the 100% equivalent
#We know that 10%=0.10
#Alternatively, 100% divided by 10% is 10. Multiply this value by £540:
We subtract the discount amount for the per-discount price:
Hence, it will cost £4,860 without the discount.
15. Since we are not given the proportion of colors in the bag, we assume that all the 10 beads have different colors.
-As such, the sample space is 10 and each color has an equal chance of being picked:
Hence, this is impossible since 0.10<0.35