Answer:
243 = 3⁵
Step-by-step explanation:
Firstly we will find the factors of 243. On calculating it see that the factors of 243 are 3 x 3 x 3 x 3 x 3.
or
243 = 9 x 9 x 3
We need to write 243 as the product of primes.
The number that divides itself or 1 are prime numbers.
3 is the only prime number here such that,
243 = 3⁵
Hence, this is the required solution.
The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.
<h3>What is a triangle?</h3>
A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
An equilateral triangle is a shape with three sides that have an equal measure of side length.
The 3 sides of triangle JKL are equal to each other, therefore we can equate any of the two sides together to find the unknown variable called x.
So, JK = KL
JK = 13x + 5
KL + 17x - 19
13x + 5 = 17x - 19
Collect like terms;
17x - 13x = 19 + 5
4x = 24
x = 24/4
x = 6
We can now proceed to find the sides;
JK = 13x + 5
13 x 6 + 5
= 78 + 5
= 83
JK = 83
KL = 17x - 19
= 17 x 6 - 19
= 102 - 19
= 83
KL = 83
JL= 8x + 35
= 8 x 6 + 35
= 48 + 35
= 83
JL = 83
Hence, The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.
Learn more about the triangles;
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Step-by-step explanation:
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Answer:
The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.
Step-by-step explanation:
What is Confidence Interval?
The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.
The confidence interval is given by

Where
is the mean weight
is the standard deviation
is the critical value from t-table and n is the sample size.
The term
is known as margin of error.
As the sample size is decreased the corresponding margin of error increases which results in wider confidence interval which means smaller precision.
The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.
We can say with 95% confidence that the true mean weight of the rock is within the interval of (25.2, 29.1).