Select the correct answer.

Which of the following represents the sum of the series? 6 8 10 12 14 16 18 20 22 24 26

stira [4]

The sum of the arithmetic series 6 8 10 12 14 16 18 20 22 24 26 is 176

<h3>How to determine the sum of the series?</h3>

The series is given as:

6 8 10 12 14 16 18 20 22 24 26

The above series is an arithmetic series with the following parameters:

First term, a = 6

Last term, L = 26

Number of terms, n = 11

The sum of the series is calculated using:

$S_n= \frac{n}{2} *(a + L)$

This gives

$S_n= \frac{11}{2} *(6 + 26)$

Evaluate

$S_{11} = 176$

Hence, the sum of the arithmetic series 6 8 10 12 14 16 18 20 22 24 26 is 176

Read more about arithmetic series at:

brainly.com/question/6561461

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7 0

2 years ago

each of the letters in the word SAMSUNG are on separate cards, face down on the table. If you pick a card at random, what is the

shutvik [7]

There are 7 cards. The number of possible correct picks is 2 (if you pick an 'S') plus 1 (if you pick the 'U') = 3 ways to succeed. So the probability of success is 3/7 ... about 43% .

8 0

3 years ago

Help please I’m not sure what the answer for this one is no need to explain

natka813 [3]

Answer:

b. e^9.45 = x

see last example and this explains whole numbers and decimals.

Step-by-step explanation:

Another example we can Solve 100=20e^2t .

Solution

100 = 20e^2t

5 = 20e ^2t

in 5 = 2t

Therefore t = in5/ 2

Step 1 was ; Divide by the coefficient of the power

Step 2 was ; Take ln of both sides. Use the fact that ln(x) and ex are inverse functions

Step 3 was; Divide by the coefficient of t

Another example;

Solve e^2x−e^x = 56 .

Solution

Analysis

When we plan to use factoring to solve a problem, we always get zero on one side of the equation, because zero has the unique property that when a product is zero, one or both of the factors must be zero. We reject the equation e^x=−7 because a positive number never equals a negative number. The solution ln(−7) is not a real number, and in the real number system this solution is rejected as an extraneous solution.

Another example is;

Solve e^2x=e^x+2 .

Answer

Q&A: Does every logarithmic equation have a solution?

No. Keep in mind that we can only apply the logarithm to a positive number. Always check for extraneous solutions.

Last example determines decimals ;

Solve lnx =3 .

Solution

lnx^x=3=e^3

Use the definition of the natural logarithm

Graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to 20 . In other words e^3≈20 . A calculator gives a better approximation: e^3≈20.0855 .

The graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to 20 . In other words e^3≈20 . A calculator gives a better approximation: e^3≈20.0855 .

It shows values of graphs of y=lnx and y=3 cross at the point (e^3,3) , which is approximately (20.0855,3) .

See graph below.

7 0

3 years ago

Help pleaseeee this is a final exam

Mandarinka [93]

Answer:

3x +89 + 8x + 58 =180 (they are supplementary angles, so added together they are equal to 180)

11x + 147= 180 (combine like terms on the left side of the = sign)

11x= 33 (subtract 147 from both sides and then divide by 11 to isolate x)

x= 3 (this is x)

3x +89 (this is the measure of angle MON, plug in x and solve)

3(3)+89

9+89

98 degrees (this is your answer)

Step-by-step explanation:

4 0

3 years ago

Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the

Lana71 [14]

There are 26 integers in the set $\{630,631,\ldots,655\}$ . If the wavelength of light is uniformly distributed, then the probability that it has a wavelength of any one of these integers is $\dfrac1{26}$ , so the distribution of wavelengths has probability mass function

$\mathbb P(X=x)=\begin{cases}\dfrac1{26}&\text{for }630\le x\le655,x\in\mathbb Z\\\\0&\text{otherwise}\end{cases}$

The mean (expected value) is given by

$\mathbb E(X)=\displaystyle\sum_xx\mathbb P(X=x)$

and the variance by

$\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2$

First, the mean:

$\mathbb E(X)=\displaystyle\sum_{x=630}^{655}x\mathbb P(X=x)=\frac1{26}\sum_{x=630}^{655}x$
$\mathbb E(X)=\dfrac{16705}{26}\approx643$

(rounded up from an exact value of 642.5)

Now for the variance:

$\mathbb E(X^2)=\displaystyle\sum_xx^2\mathbb P(X=x)=\frac1{26}\sum_{x=630}^{655}x^2$
$\mathbb E(X^2)=412862.5$

Meanwhile, $\mathbb E(X)^2=642.5^2=412806$ , which gives a total variance of

$\mathbb V(X)=412862.5-412806\approx57$

(rounded up from 56.5)

3 0

3 years ago