Given that the sides of the acute triangle are as follows:
21 cm
x cm
2x cm
Stated that 21 cm is one of the shorter sides of the triangle2x is greater than x, so it follows that 2x MUST be the longest side
For acute triangles, the longest side must be less than the sum of the 2 shorter sides
Therefore, 2x < x + 21cm
2x – x < 21cm
x < 21cm
If x < 21cm, then 2x < 42cm
Therefore, the longest possible length for the longest side is 42cm
Answer:
$675.00
Step-by-step explanation:
4500 x 0.05 x 3 = 675
Answer:
The standard deviation of weight for this species of cockroaches is 4.62.
Step-by-step explanation:
Given : A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
To find : What is the approximate standard deviation of weight for this species of cockroaches?
Solution :
We have given,
Mean 
The sample mean x=55
A lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
i.e. P(X>55)=14%=0.14
The total probability needs to sum up to 1,



The z-score value of 0.86 using z-score table is z=1.08.
Applying z-score formula,

Where,
is standard deviation
Substitute the values,





The standard deviation of weight for this species of cockroaches is 4.62.
Answer:
The function is defined when x > 0
Step-by-step explanation:
Functions with radicals are only undefined when the value in the radical is negative, because the root of a negative number is imaginary.
We know the function is undefined when the denominator is equal to zero.
is equal to zero when x=0.
We also know that functions with radicals are undefined when the value in the radicals are negative, because the root of a negative number is imaginary. .
will always be positive, but
is negative when x < 0.
So the function is undefined when x = 0, and when x < 0.
Therefore it is defined when x > 0