13 million<br> in scientific notation

Find the sum of the first 12 terms of the geometric sequence - 2,6,-18,54,-162....

nekit [7.7K]

Answer:

Sure, the common difference is -3, but like you have to multiple it and stuff, so it goes like this: -2,6,-18,54,-162,486,-1458,4374,-13122,39366,-118,098,354294.

So then, add all of the 12 terms I stated, and that will equal to 265,720

Therefore, the sum of the first 12 terms of that geometric sequence is 265,720.

Step-by-step explanation:

6 0

2 years ago

A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the number of shoppers is 10

Marta_Voda [28]

Answer:

1138

Step-by-step explanation:

From the information given:

We can represent it perfectly in an exponential form:

$m = p(q)^x$

where;

p = initial value = 120

q = base of the exponential form

q = 1 + r

here; r = rate in decimal = 10% = 0.1

Then q can now be = 1 + 0.1 = 1.1

Replacing it into the exponential form, we get:

$m = 120(1.1)^x$

where;

x = number of days and m = number of shoppers

Thus:

For the first day:

$m = 120(1.1)^x$

m = 120

For the second day:

$m = 120(1.1)^1$

m = 132

For the third day:

$m = 120(1.1)^2$

m = 145.2

For the fourth day

$m = 120(1.1)^3$

m = 159.72

For the fifth-day

$m = 120(1.1)^4$

m = 175.692

For the sixth-day

$m = 120(1.1)^5$

m = 193.2612

For the seventh-day

$m = 120(1.1)^6$

m = 212.58732

Thus; the total numbers of shoppers for the first 7 days is:

$= 120+ 132 + 145.2 + 159.72 + 175.692+193.2612+212.58732$

= 1138.46052

≅ 1138

6 0

2 years ago

Please help me!!!!! i need full answer.

salantis [7]

Answer:

see explanation

Step-by-step explanation:

Using the sum/ difference → product formula

cos x - cos y = - 2sin( $\frac{x+y}{2}$ )sin ( $\frac{x-y}{2}$ )

sin x - sin y = 2cos ( $\frac{x+y}{2}$ )sin ( $\frac{x-y}{2}$ )

Given

(cosA - cosB)² + (sinA - sinB )²

= [ - 2sin( $\frac{A+B}{2}$ )sin( $\frac{A-B}{2}$ ) ]² + [ 2cos( $\frac{A+B}{2}$ )sin( $\frac{A-B}{2}$ ) ]²

= 4sin² ( $\frac{A+B}{2}$ )sin² ( $\frac{A-B}{2}$ ) + 4cos² ( $\frac{A+B}{2}$ )sin² ( $\frac{A-B}{2}$ )

= 4sin² ( $\frac{A-B}{2}$ )[ sin² ( $\frac{A+B}{2}$ ) + cos² ( $\frac{A+B}{2}$ ) ← sin²x + cos²x = 1

= 4sin² ( $\frac{A-B}{2}$ ) × 1

= 4sin² ( $\frac{A-B}{2}$ ) = right side ⇒ proven

4 0

3 years ago

Julio purchased some power tools totaling $2174 using a six-month deferred payment plan with an interest rate of 28.19%. He did

quester [9]

I believe you have to do a cross product formula.

2174/x = 28.19/100

8 0

2 years ago

Read 2 more answers

Help it’s slope idk how to do it

Over [174]

a. $\boxed{y-602=\frac{2}{3}(x-3)}$

b. For every month the pine tree grows about 0.67 inches.

c. <em> </em>It represents the height of the tree at the moment Ariel started to record the heights.

<h2>Explanation:</h2>

In this exercise we have that in July Ariel recorded the height of a pine tree and how quickly it was expected to grow in next several months. From the Table, we can get the following points:

$P_{1}(3,602) \\ \\ P_{2}(6,604) \\ \\ P_{3}(q,606) \\ \\ P_{4}(12,608)$

It is obvious that this problem follows a linear equation, so our goal is to find the equation that matches the Table.

The point slope form of the equation of a line is:

$y-y_{1}=m(x-x_{1}) \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{1}, y_{1}):A \ point \ on \ the \ line$

Finding (m):

$Using: \\ \\ P_{1}(x_{1},y_{1}) \rightarrow P_{1}(3,602) \\ \\ P_{2}(x_{2}, y_{2}) \rightarrow P_{2}(6,604) \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{604-602}{6-3} \\ \\ m=\frac{2}{3}$

Finally, the equation of the line is:

$(x_{1}, y_{1}) \rightarrow (3,602) \\ \\ \boxed{y-602=\frac{2}{3}(x-3)}$

In this case, we have that:

The x-axis represents the <em>Number of Months </em>the pine tree was expected to grow.
The y-axis represents the <em>Height of the Tree </em>in inches.

Since the slope o a line is:

$Slope=\frac{Change \ in \ y}{Change \ in \ x}=\frac{2}{3}$

Then, this means that<em> every three months the pine tree grows two inches, </em><em>or </em><em>for every month the pine tree grows about 0.67 inches.</em>

The y-intercept can be found setting $x=0$ . So, from our equation:

$y-602=\frac{2}{3}(x-3)} \\ \\ \\ If \ x=0: \\ \\ y-602=\frac{2}{3}(0-3) \\ \\ y-602=-2 \\ \\ Solving \ for \ y: \\ \\ y=602-2 \\ \\ y=600$

So the y-intercept is $y=600$ and<em> represents the height of the tree at the moment Ariel started to record the heights.</em>

<h2>Learn more:</h2>

Slope Intercept form: brainly.com/question/4192440

#LearnWithBrainly

4 0

2 years ago

13 million in scientific notation