Answer:
= - 536
Step-by-step explanation:
The n th term of an arithmetic series is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 10 and
= - 144 , thus
10 + (n - 1)d = - 144 ( subtract 10 from both sides )
(n - 1)d = - 154
The sum to n terms of an arithmetic series is
=
[ 2a₁ + (n - 1)d ] , thus
=
[ (2 × 10) + (- 154) ]
= 4(20 - 154)
= 4 × - 134
= - 536
The approximate value of log b to the nearest hundredth using the logarithm property is 1.23. The correct option is B.
<h3>What is a logarithm?</h3>
Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.
The two expressions below have the same value when rounded to the nearest hundredth.
![\rm Log_ 5 b \ \ and \ \ Log _ 9 48](https://tex.z-dn.net/?f=%5Crm%20%20Log_%205%20%20b%20%5C%20%5C%20and%20%5C%20%5C%20%20Log%20_%209%20%2048)
We know that the formula
![\rm log_ab = \dfrac{log\ b}{log\ a}](https://tex.z-dn.net/?f=%5Crm%20log_ab%20%3D%20%5Cdfrac%7Blog%5C%20b%7D%7Blog%5C%20a%7D)
Then we have
![\rm log_ 5\ b = log _ 9 48\\\\\\ \dfrac{log \ b}{log\ 5} = \dfrac{log\ 48}{log \ 9}\\\\\\log \ b = log \ 5 * \dfrac{log\ 48}{log \ 9}\\\\\\log \ b = 1.2315](https://tex.z-dn.net/?f=%5Crm%20%20log_%205%5C%20%20b%20%3D%20%20log%20_%209%20%2048%5C%5C%5C%5C%5C%5C%20%5Cdfrac%7Blog%20%5C%20b%7D%7Blog%5C%205%7D%20%3D%20%5Cdfrac%7Blog%5C%2048%7D%7Blog%20%5C%209%7D%5C%5C%5C%5C%5C%5Clog%20%5C%20b%20%3D%20log%20%5C%205%20%2A%20%20%5Cdfrac%7Blog%5C%2048%7D%7Blog%20%5C%209%7D%5C%5C%5C%5C%5C%5Clog%20%5C%20b%20%3D%201.2315)
Thus, the value of log b is 1.23.
More about the logarithm link is given below.
brainly.com/question/7302008
Answer:
2
Step-by-step explanation:
The equation whit the largest outcome is 5*103=515
The absolutely positively most area that the picture could possibly have is
<em>25.783 square feet</em> (rounded). That would happen if the picture is circular
and the 18-ft goes around its circumference. Then its diameter is 18/pi =
about 5.73 ft and its radius is about 2.865 ft.
If the picture has straight sides, then its greatest possible area is <em>20.25 square ft</em>.
That happens if the picture is square and the 18-ft goes around its perimeter.
Then each side is 4.5-ft.
The area can be as <em><u>small</u></em> as you want, with no limit.
For example,
-- if the picture is 1-ft high and 7-ft wide, and the 18-ft goes
around its perimeter, then its area is <em>7</em> square feet;
-- if the picture is 6-in high and 7-1/2 ft wide, and the 18-ft goes
around its perimeter, then its area is <em>3.75 </em>square feet;
-- if the picture is 1-in high and 8-ft 11-in wide, and the 18-ft goes
around its perimeter, then its area is <em>0.743</em> of a square foot.