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jeka57 [31]
3 years ago
14

What is the shape of the graph of the function? g(x)= 3/2 (2/3) ^x

Mathematics
1 answer:
Andrew [12]3 years ago
5 0

Answer:

Please check the attached graph.

From the graph, it is clear that option B is the correct option.

Step-by-step explanation:

Given the function

g\left(x\right)=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^x

Determining the y-intercept

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

so

substituting x = 0 in the fuction

y=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^x

y=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^0

Apply rule:  a^0=1,\:a\ne \:0

y=1\cdot \frac{3}{2}

y=\frac{3}{2}

y = 1.5

Therefore, the point representing the y-intercept is:

  • (0, 1.5)

Determining the x-intercept

We know that the value of the x-intercept can be determined by setting y = 0, and determining the corresponding value of x.

so

substituting y = 0 in the function

0=\frac{3}{2}\left(\frac{2}{3}\right)^x

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

\left(\frac{2}{3}\right)^x=0

We know that a^{f\left(x\right)} can not be zero or negative for x ∈ R

Thus, NONE represents the x-intercept.

Please check the attached graph.

From the graph, it is clear that option B is the correct option.

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║a+9║/7=5
you multiply 7 on both sides which cancel out 7.
now it ║a=9║=35
and now it would be a+9=35 and a+9=-35 then solve it.
35-9 and 9-(-35)= 26 and -44
hope this helped!
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If there is a 4:6 ratio of dogs to cats in the store. What percentage of the store are dogs?
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What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories?
9966 [12]

Answer:

The goodness of fitness test χ²with significance of level ∝= 0.05 and 5 degrees of freedom is 11.07  (One tailed test )

Step-by-step explanation:

For n=6  the degrees of freedom will be n-1 = 5 .

The goodness of fitness test χ²with significance of level ∝= 0.05 and 5 degrees of freedom is 11.07  (One tailed test )

The critical region depends on ∝ and the alternative hypothesis

a) When Ha is σ²≠σ² the critical region is

χ²  < χ²(1-∝/2)(n-1) and  χ² > χ²(1-∝/2)(n-1)   Two tailed test

( χ²  < 0.83) and ( χ²  > 0.83)

b) When Ha is σ²> σ² the critical region falls in the right tail and its value is

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c) When Ha is σ² <σ² the critical region will be entirely in the left tail with critical value  

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Answer:

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Step-by-step explanation:

<u>Find the first implicit derivative using implicit differentiation</u>

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<u>Use the substitution of dy/dx to find the second derivative (d²y/dx²)</u>

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Select the correct location on the image.
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Answer:

Step 4

Step-by-step explanation:

Given: Steps used by Shelly to evaluate the expression

To find: step that includes Shelly's mistake

Solution:

According to PEMDAS,

P denotes Parentheses

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M denotes Multiplication

D denotes Division

A denotes Addition

S denotes subtraction

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In step 4, first subtraction operation has been applied before the division operation.

There is a mistake in step 4 as according to PEMDAS, first -20 should be divided by 5 then 1 should be subtracted from the resultant number.

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