Given:
The given digits are 1,2,3,4,5, and 6.
To find:
The number of 5-digit even numbers that can be formed by using the given digits (if repetition is allowed).
Solution:
To form an even number, we need multiples of 2 at ones place.
In the given digits 2,4,6 are even number. So, the possible ways for the ones place is 3.
We have six given digits and repetition is allowed. So, the number of possible ways for each of the remaining four places is 6.
Total number of ways to form a 5 digit even number is:
![Total=6\times 6\times 6\times 6\times 3](https://tex.z-dn.net/?f=Total%3D6%5Ctimes%206%5Ctimes%206%5Ctimes%206%5Ctimes%203)
![Total=3888](https://tex.z-dn.net/?f=Total%3D3888)
Therefore, total 3888 five-digit even numbers can be formed by using the given digits if repetition is allowed.
Answer:
BBBBBBBBBBBBBBBBBBBBBBBBBBBB
Answer:
Step-by-step explanation:
Simplify expression with rational exponents can look like a huge thing when you first see them with those fractions sitting up there in the exponent but let's remember our properties for dealing with exponents. We can apply those with fractions as well.
Examples
(a) ![(p^4)^{\dfrac{3}{2}}](https://tex.z-dn.net/?f=%28p%5E4%29%5E%7B%5Cdfrac%7B3%7D%7B2%7D%7D)
From above, we have a power to a power, so, we can think of multiplying the exponents.
i.e.
![(p^{^ {\dfrac{4}{1}}})^{\dfrac{3}{2}}](https://tex.z-dn.net/?f=%28p%5E%7B%5E%20%7B%5Cdfrac%7B4%7D%7B1%7D%7D%7D%29%5E%7B%5Cdfrac%7B3%7D%7B2%7D%7D)
![(p^{^ {\dfrac{12}{2}}})](https://tex.z-dn.net/?f=%28p%5E%7B%5E%20%7B%5Cdfrac%7B12%7D%7B2%7D%7D%7D%29)
Let's recall that when we are dealing with exponents that are fractions, we can simplify them just like normal fractions.
SO;
![(p^{^ {\dfrac{12}{2}}})](https://tex.z-dn.net/?f=%28p%5E%7B%5E%20%7B%5Cdfrac%7B12%7D%7B2%7D%7D%7D%29)
![= (p^{ 6})](https://tex.z-dn.net/?f=%3D%20%28p%5E%7B%206%7D%29)
Let's take a look at another example
![\Bigg (27x^{^\Big{6}} \Bigg) ^{{\dfrac{5}{3}}}](https://tex.z-dn.net/?f=%5CBigg%20%2827x%5E%7B%5E%5CBig%7B6%7D%7D%20%5CBigg%29%20%5E%7B%7B%5Cdfrac%7B5%7D%7B3%7D%7D%7D)
Here, we apply the
to both 27 and ![x^6](https://tex.z-dn.net/?f=x%5E6)
![= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{6}{1}\times {{\dfrac{5}{3}}} }\Bigg)](https://tex.z-dn.net/?f=%3D%20%5CBigg%20%2827%5E%7B%7B%5Cdfrac%7B5%7D%7B3%7D%7D%7D%20%5Ctimes%20x%5E%5CBig%7B%5Cdfrac%7B6%7D%7B1%7D%5Ctimes%20%7B%7B%5Cdfrac%7B5%7D%7B3%7D%7D%7D%20%7D%5CBigg%29)
![= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{2}{1}\times {{\dfrac{5}{1}}} }\Bigg)](https://tex.z-dn.net/?f=%3D%20%5CBigg%20%2827%5E%7B%7B%5Cdfrac%7B5%7D%7B3%7D%7D%7D%20%5Ctimes%20x%5E%5CBig%7B%5Cdfrac%7B2%7D%7B1%7D%5Ctimes%20%7B%7B%5Cdfrac%7B5%7D%7B1%7D%7D%7D%20%7D%5CBigg%29)
Let us recall that in the rational exponent, the denominator is the root and the numerator is the exponent of such a particular number.
∴
![= \Bigg (\sqrt[3]{27}^{5} \times x^{10} }\Bigg)](https://tex.z-dn.net/?f=%3D%20%5CBigg%20%28%5Csqrt%5B3%5D%7B27%7D%5E%7B5%7D%20%5Ctimes%20x%5E%7B10%7D%20%7D%5CBigg%29)
![= \Bigg (3^{5} \times x^{10} }\Bigg)](https://tex.z-dn.net/?f=%3D%20%5CBigg%20%283%5E%7B5%7D%20%5Ctimes%20x%5E%7B10%7D%20%7D%5CBigg%29)
![= 249x^{10}](https://tex.z-dn.net/?f=%3D%20249x%5E%7B10%7D)
Answer:
Your answer would be D: isometry
Step-by-step explanation:
Diameter of semicircle is 4 cm
so cicumference of circle is 4pi
since there are 4 semicircles, they add up to 2 circles
so total perimeter is 8pi
which when rounded off is 25.13 cm (2d. p.)