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1 year ago

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Which function represents a vertical stretch of an exponential function? A. f(x)=3(1/2)^x B. f(x)=1/2(3)^x C. f(x)=(3)^2x D. f(x

)=3^(1/2x)

2 answers:

Dimas [21]1 year ago

6 0

Answer:

A. f(x) = 3*(1/2)^x

Step-by-step explanation:

We know that, a function can be stretched or shrinked both horizontally and vertically.

Now, according to our question we are required to look at the vertical stretch of an exponential function.

The general form for a vertical stretch of a function f(x) is k*f(x) where k>1.

So, we compare this form with the options provided.

We see that in option A the exponential function is multiplied by 3 and so the function will be stretched vertically.

Hence, option A is correct.

il63 [147K]1 year ago

5 0

Selection A seems appropriate.

It is of the form k*f(x), where f(x) is an exponential function and k > 1.

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What is the sum of all positive integers smaller than $1000$ that can be written in the form $100\cdot 2^n$, where $n$ is an int

netineya [11]

Answer:

The sum is 1575.

Step-by-step explanation:

Consider the provided information.

It is given that positive integers smaller than 1000 and that can be written in the form $100\cdot 2^n$

Where n is integer that means the value of n can be a positive number or a negative number.

For n = 0

$100\cdot 2^{0}=100$

For n=-1

$100\cdot 2^{-1}=50$

For n=-2

$100\cdot 2^{-2}=25$

For n = -3 the obtained number is not an integer.

Now consider the positive value of n.

For n=1

$100\cdot2^1 = 200$

For n=2

$100\cdot2^2 = 400$

For n=3

$100\cdot2^3 = 800$

For n=4 the obtained number is greater than 1000.

Now add all the numbers.

$100+50+25+200+400+800=1575$

Hence, the sum is 1575.

6 0

1 year ago

-3^(-x)-6=-3^x+10<br><br>Solve the equation below for x by graphing plz

vitfil [10]

To graph it, just graph $y=-3^{-x}-6$ and $y=-3^x+10$ and see where they intersect

I would like to solve it by using math and not graphing
if you don't want to see the math, just don't scroll down
the graphical meathod is above, first line, just read it

hmm
multiply both sides by -1
$3^{-x}+6=3^x-10$
multiply both sides by $3^x$
$3^0+6(3^x)=3^{2x}-10(3^x)$
$1+6(3^x)=3^{2x}-10(3^x)$
minus 1 from both sides and minus 6(3^x) from both sides
$0=3^{2x}-16(3^x)-1$
use u subsitution
$u=3^x$
we can rewrite it as
$0=u^2-16u-1$
now factor
I mean use quadratic formula
for $ax^2+bx+c=0$ $x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}$
so for 0=u^2-16u-1, a=1, b=-16, c=-1
$u=\frac{-(-16)+/-\sqrt{(-16)^2-4(1)(-1)}{2(1)}$
$u=8+/-\sqrt{65}$
remember that u=3^x so u>0
if we have u=8+√65, it's fine, but u=8-√65 is negative and not allowed
so therfor
$u=8+\sqrt{65}=3^x$
$8+\sqrt{65}=3^x$
if you take the log base 3 of both sides you get
$log_3(8+\sqrt{65})=x$
if you use ln then
$ln(8+\sqrt{65})=xln(3)$
then
$\frac{ln(8+\sqrt{65})}{ln(3)}=x$

8 0

2 years ago

Read 2 more answers

The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

Step-by-step explanation:

Previous concepts

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".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

5 0

2 years ago

PLEASE HELP, I’ve been stuck on this question for a whileIn the diagram, AB is divided into equal parts. The coordinates of poin

castortr0y [4]

AB is divided into 8 equal parts and point C is 1 part FROM A TO B, so the ratio is 1:7, with C being 1/7 of the way. The ratio is k, found by writing the numerator of the ratio (1) over the sum of the numerator and denominator (1+7). So our k value is 1/8. Now we need to find the rise and the run (slope) of the points A and B. $m= \frac{5-9}{9-(-3)}$ . That gives us a rise of -4 and a run of 12. The coordinates of C are found in this formula: $C(x,y)=[ x_{1} +k(run), y_{1} +k(rise)]$ . Filling in accordingly, we have $C(x,y)=[-3+ \frac{1}{8}(12),9+ \frac{1}{8}(-4)]$ which simplifies a bit to $C(x,y)=(-3+ \frac{3}{2},9- \frac{1}{2})$ . Finding common denominators and doing the math gives us that the coordinates of point C are $(- \frac{3}{2}, \frac{17}{2})$ . There you go!

3 0

2 years ago

Read 2 more answers

Colin leaves school to go home. He walks 3 blocks south and then 9 blocks west. If Colin could walk in a straight line to the sc

White raven [17]

Answer:

9.48*

Step-by-step explanation:

This is a right triangle. The formula for solving the Hypotenuse, or the longest side of the right triangle is A^2 + B^2 = C^2. If we put the numbers from the problem into the formula this is what we get :

3^2 + 9^2 = C^2

9 + 81 = C^2

90 = C^2

9.48 = C

* This is rounded, the exact number is closer to 9.486832980505138. Your class should tell you what to round to.

5 0

2 years ago