A two digit number less than 30 is written down at random. What is the probability that it Will be a prime number?
1 answer:
You might be interested in
9514 1404 393
Answer:
1.05 × 1.05 × 1.05 × 1.05 × 1.05 = 1.2762815625
Step-by-step explanation:
An exponent indicates how many times the base is a factor in the product. That is, 1.05 to the 5th power means ...
1.05⁵ = 1.05 × 1.05 × 1.05 × 1.05 × 1.05
This multiplication expression is evaluated in the usual way.
= 1.1025 × 1.05 × 1.05 × 1.05
= 1.157625 × 1.05 × 1.05
= 1.21550625 × 1.05
= 1.2762815625
__
All scientific and graphing calculators have a button for computing the power of a number. On my calculator its label is . The particulars of the function of this button can be found in the manual for your calculator.
For on-line calculators, such as the go.ogle calculator, or the Desmos graphing calculator, the caret (^) is used to signify an exponent. (See the input line in the first attachment for an example.)
You are correct. The answer is choice D
The only way for g(x) to be differentiable at x = 0 is for two things to happen
(1) g(x) is continuous at x = 0
(2) g ' (x) is continuous at x = 0
To satisfy property (1) above, the value of b must be 1. This can be found by plugging x = 0 into each piece of the piecewise function and solving for b.
So the piecewise function becomes
after plugging in b = 1
--------------------------------
Now differentiate each piece with respect to x to get
The first piece of g ' (x) is always going to be equal to 1. The second piece is equal to zero when x = 0
Because -sin(x) = -sin(0) = 0
So there's this disconnect on g ' (x) meaning its not continuous
Therefore, the value b = 1 will not work.
So there are no values of b that work to satisfy property (1) and property (2) mentioned at the top.
The only way for g(x) to be differentiable at x = 0 is for two things to happen
(1) g(x) is continuous at x = 0
(2) g ' (x) is continuous at x = 0
To satisfy property (1) above, the value of b must be 1. This can be found by plugging x = 0 into each piece of the piecewise function and solving for b.
So the piecewise function becomes
after plugging in b = 1
--------------------------------
Now differentiate each piece with respect to x to get
The first piece of g ' (x) is always going to be equal to 1. The second piece is equal to zero when x = 0
Because -sin(x) = -sin(0) = 0
So there's this disconnect on g ' (x) meaning its not continuous
Therefore, the value b = 1 will not work.
So there are no values of b that work to satisfy property (1) and property (2) mentioned at the top.