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iren [92.7K]
3 years ago
13

To obtain the sequence 1, 1/3, 1/9, 1/27,..., what domain should be applied to the exponential function shown here?

Mathematics
1 answer:
Gnesinka [82]3 years ago
7 0

Consider the exponential function

y=\left(\dfrac{1}{3}\right)^x.

  • At x=0, y=\left(\dfrac{1}{3}\right)^0=1;
  • At x=1, y=\left(\dfrac{1}{3}\right)^1=\dfrac{1}{3};
  • At x=2, y=\left(\dfrac{1}{3}\right)^2=\dfrac{1}{9};
  • At x=3, y=\left(\dfrac{1}{3}\right)^3=\dfrac{1}{27};
  • and so on.

Thus, the domain is {0, 1, 2, 3, ...}

Answer: option D.

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One method for estimating abundance of animals is known as line-intercept sampling. The theory of this method, when applied to A
Kruka [31]

Answer:

0.6848

Step-by-step explanation:

Mean of \hat{p} = 0.453

Answer = 0.453

Standard deviation of \hat{p} :

= \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = \sqrt{\frac{0.453(1-0.453)}{100}} = 0.0498

Answer = 0.0498

P(0.0453 - 0.05 < p < 0.0453 + 0.05)

On standardising,

= P(\frac{0.0453-0.05-0.0453}{0.0498} <Z<\frac{0.0453+0.05-0.0453}{0.0498})

= P(-1.0044 < Z < 1.0044) = 0.6848

Answer = 0.6848

3 0
3 years ago
Write this equation in standard form<br> y + 4 = 2/3 (x+7)
Karo-lina-s [1.5K]

Answer:

y=\frac{2}{3}x+\frac{2}{3}

Step-by-step explanation:

The standard equation of a straight line is of the form:

y=mx+c

We have to convert the given equation into above form.

Simplifying the given equation:

y=\frac{2}{3}x+\frac{14}{3}-4

         =\frac{2}{3}x+\frac{(14-12)}{3}

        =\frac{2}{3}x+\frac{2}{3}.- This is in standard form

where m=c=\frac{2}{3}

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3 years ago
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On a number line, point D is at -6, and point E is at 8. Point F lies between points D and E. If DF: FEis 3: 1, where does point
Vadim26 [7]

F is located on the numbe<u>r 4.5</u><u> </u>on the number line.

<h3></h3><h3>Where does point F lie on the number line?</h3>

We know that point D is at -6

Point E is at 8.

Point F is between D and E, such that the ratio:

DF:FE is 3:1

So if we divide the distance between D and E in 4 parts, 3 of these parts are DF, and one of these parts is FE.

First, the distance between E and D is:

distance = 8 - (-6) = 14 units.

Now, if we divide that by 4, we get:

14/4 = 3.5

Then we have:

DF = 3*(3.5) = 10.5

This means that F is at 10.5 units to the right of D, then:

F = D + 10.5 = -6 + 10.5 = 4.5

F is located on the numbe<u>r 4.5</u><u> </u>on the number line.

If you want to learn more about ratios:

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7 0
1 year ago
In the equation <img src="https://tex.z-dn.net/?f=y%20%3D%20ax%5E%7B2%7D%20%2Bk" id="TexFormula1" title="y = ax^{2} +k" alt="y =
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2 years ago
One number i ix le than a econd number. Four time the firt i 2 more than 6 time the econd. Find the number
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When the difference between one and two numbers is two, the two numbers are -10 and -12.

Given that,

The difference between one and two numbers is two. Twelve more than six times the second is four times the first.

We have to find the number.

We know that,

The system of equation we get

x=y-2 ----->equation(1)

4x=12+6y ----->equation(2)

Substitute for x in the equation(2)

4(y-2)=12+6y

4y-8=12+6y

4y-6y=12+8

-2y=20

y=-10

Substitute y=-10 in equation(1)

x=-10-2

x=-12

Therefore, The two numbers area -10 and -12 when the difference between one and two numbers is two.

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9 months ago
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