Which sets of side lengths could form a triangle?
1 answer:
Answer:
D. 4 centimeters, 6 centimeters, 9 centimeters
Step-by-step explanation:
Considering side length for forming a triangle, most of the time it is about Triangle Inequality Theorem, which for 3 sides length a,b,c, it must satisfy the following set of inequalities:
By checking each of them only D satisfy:
For simplicity you only have to check if the two shortest sides add up to be larger than the longest side:
You might be interested in
The farmers had to plough a total of 1,456 acres of land.
Step-by-step explanation:
Step 1; The group of farmers ploughed at a rate of 112 acres of land a day which was 8 acres more than schedule.
Scheduled rate = 112 acres per day - 8 acres = 104 acres per day.
So the farmers were supposed to plough 104 acres a day according to schedule.
Step 2; If the farmers finished a day earlier, it means they had to have completed ploughing 104 acres extra by doing an extra 8 acres a day.
So days took to complete ploughing = = 13 days.
So in 13 days, they should have ploughed 13 × 104 = 1,352 acres but due to their increased rate, they ploughed 13 × 112 = 1,456 acres in 13 days.
Difference in acres ploughed = 1,456 - 1,352 = 104 acres.
So the farmers ploughed 1,456 acres in 13 days.
Answer:
And we can use the z score formula given by:
And if we find the z score for 76 we got:
And if we use the complement rule and the normal standard distribution or excel we got:
And we can find this using the ti 84 with the following code:
1-normalcdf(-1000, 76, 75, 0.5 )
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
Let X the random variable who represent the score of golfers. We select a sampel size of 81.
From the central limit theorem we know that the distribution for the sample mean is given by:
And we want to find this probability:
And we can use the z score formula given by:
And if we find the z score for 76 we got:
And if we use the complement rule and the normal standard distribution or excel we got:
And we can find this using the ti 84 with the following code:
1-normalcdf(-1000, 76, 75, 0.5 )