What is the sum of the geometric series 2^0 + 2^1 + 2^2 + 2^3 + 2^3 + 2^4 + … + 2^9?

Answers

Answer 1

Answer: sum is
$S_(n)=(a_(1)(1-r^(n)))/(1-r)$

r=common ratio
a1=first term
it looks like 2^0=1 is the first term aka a1
it goes to the 9th term (2^9)

sub
$S_(9)=(1(1-(2)^(9)))/(1-2)$
$S_(9)=(1-512)/(-1)$
$S_(9)=(-511)/(-1)$
$S_(9)=511$

Answer 2

Answer: so this one you don't multiply the base by the exponent. in this case its 2 times two how ever many time the exponent says.
2^0= 2
2^1= 2
2^2=4
2^3= 8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
So then you add all them up
2+2+4+8+16+32+64+128+256+512= 1024

so there is your answer 1024

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A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the Boulder, h, in feet after t seconds is given by te function h=-16t^2+112t+30. How long does it take the Boulder to reach its maximum height? What is the Boulder's maximum height ? Round to the nearest hundredth , if necessary . Please , help . I am really stuck here

Answers

Answer:

Boulder's maximum height is 226 ft.

It take 3.5 seconds the Boulder to reach its maximum height.

Step-by-step explanation:

Given :

A catapult launches a boulder with an upward velocity of 112 ft/s.

The height of the Boulder, h, in feet

After t seconds is given by the function :

$h = -16t^(2) +112t+30$ --(a)

A quadratic function can be graphed using a table of values. The graph creates a parabola.

If the coefficient of the squared term is positive then the parabola opens up and The vertex of this parabola is known as the minimum point.

If the coefficient of the squared term is negative then the parabola opens down and The vertex of this parabola is known as the maximum point.

Now we will use vertex formula to calculate t

When $f(x)= ax^(2) +bx+c$

then vertex will be

$x=(-b)/(2a)$

Now consider the given function:

$h = -16t^(2) +112t+30$

where a = -16

b=112

so using vertex formula :

$t=(-112)/(2*(-16))$

$t=3.5$

Thus, it take 3.5 seconds the Boulder to reach its maximum height.

Now to calculate the Boulder's maximum height . Put value of t = 3.5 in given function (a)

$h = -16(3.5)^(2) +112(3.5)+30$

$h = -196 +392+30$

$h = 226$

Thus, Boulder's maximum height is 226 ft.

Well we first need to do the math problem

-b/2a = -112/2(16) = 3.5 s t= 3.5s h = -16t^2 + 112t + 30 h = -16(3.5)^2 +122(3.5) +30 h = 226

adjust the windows to y=300

3.5 s; 226 ft

PLEASE HELPPPPPPP!!!!!! For accounting purposes, the value of assets (land, buildings, equipment) in a business are depreciated at a set rate per year. The value, V(t) of $408,000 worth of assets after t years, that depreciate at 18% per year, is given by the formula V(t) = Vo(b)t. What is the value of Vo and b, and when rounded to the nearest cent, what are the assets valued at after 8 years?

Answers

Vt=408000(1-0.18)^8=??

CAN SOMEONE PLEASE HELP I AM ALSO BEGGING! Probability theory predicts that there is a 76% chance of a water polo team winning any particular match. If the water polo team playing two matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?

Answers

In each of the two match simulations, the order in which one match is won and one match is lost does not matter. The probability of winning any particular match is 0.76 and the probability of losing any particular match is 1.00 - 0.76 = 0.24.
In each simulation the probability of winning exactly one match is:
$P(win\ exactly\ one)=2C1*0.76*0.24=0.3648$
Therefore in 10,000 simulations the expected number of times that exactly one match is won = 10,000 * 0.3648 = 3648 times.

Answer:

3648

Step-by-step explanation:

A research firm wants to compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour?

Answers

Answer:

n=97

Step-by-step explanation:

1) Notation and definitions

$\sigma=3$ population standard deviation known

Confidence=90% or 0.9

n sample size required (variable of interest)

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The sample mean have the following distribution

$\bar X \sim N(\mu, (\sigma)/(√(n)))$

2) Calculation for the sample size required

In order to find the critical value we need to take in count that we are finding the interval for the mean with the population deviation known, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_(\alpha/2)=-1.64, t_(1-\alpha/2)=1.64$

The margin of error for the sample mean interval is given by this formula:

$ME=z_(\alpha/2)(\sigma)/(√(n))$ (a)

And on this case we have that $ME =\pm 0.5$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=((z_(\alpha/2) \sigma)/(ME))^2$ (b)

And replacing into equation (b) the values from part a we got:

$n=((1.64(3))/(0.5))^2 =96.83$

And rounded up we have that n=97

Find three consecutive even numbers whose sum is 96?

Answers

so consectuve even numbers

we know that one even number plus 2= another even number so we want to find 3 consecutive even numbers that add up to 96 or
x is the first number
x+2 is the second number
x+4 is the third number

x+x+2+x+4=96
3x+6=96
subtract 6 from both sides
3x=90
divide both sides by 3
x=30

the first number is 30
x+2=32=second number
x+4=34=third number

the numbers are 30,32,34

Let me show you how I like to do problems like this:

-- If I just needed three numbers that add up to 96, the easiest way
to do it would be to find 1/3 of 96 . That's 32, so the three numbers
could be 32, 32, and 32.

-- If you want three consecutive even numbers, just take 2 away from
one of those numbers, and add it on to a different one.

Now you have 30, 32, and 34, and you haven't changed their sum.

Which of the following statements contain a variable? A. The time it takes to wash the dishes plus 30 minutes.

B. The age of my friend.

C. The number of kittens in a litter.

D. There are 24 hours in a day.

Answers

Answer:

Thetimeittakestowashthedishesplus30minutes

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