1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nekit [7.7K]
2 years ago
14

What is the solution to the equation 9^(x - 2) = 27 ?

Mathematics
2 answers:
larisa [96]2 years ago
4 0
  As we are given the equation
<span> 9^(x - 2)=27
solving
 =</span><span>3^2(x-2)=3^3
 just equal the basis 
2(x-2)= 3 

x=7/2=3.5
so correct option is D
hope it helps</span>
ASHA 777 [7]2 years ago
3 0
9^{x-2}=27\\\\(3^2)^{x-2}=3^3\\\\3^{2(x-2)}=3^3\\\\3^{2x-4}=3^3\iff2x-4=3\ \ \ |add\ 4\ to\ both\ sides\\\\2x=7\ \ \ \ |divide\ both\ sides\ by\ 2\\\\\boxed{x=3.5}
You might be interested in
Jose left the white house and drove toward the recycling plant at an average of 40km/h. Rob left some time later driving in the
tiny-mole [99]
I would think it would be 200km before rob caught up with him?
6 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Cfrac%7B33%7D%7B4-%5Csqrt%7B5%7D%20%7D" id="TexFormula1" title="\frac{33}{4-\sqrt{5} }" alt=
kvv77 [185]
The answer I got was: 12 + 3/5

Sorry I didn’t have that symbol thing on my phone so i had to use a slash.
Hope this helps :)
7 0
2 years ago
A Math professor scores all tests with a maximum of 100 points. A student must have an average of 90 on six tests to receive an
nignag [31]

Answer:

No, he cannot

Step-by-step explanation:

Lets say the student takes the maximum socre on his last test, so he gets 100. Now, his average on the six texts will be:

(75+85+90+95+94+100)/6 = 89.83

So, if taking 100 is not enough to get to the average of 90, this means he would need a score greater than 100, which is impossible as 100 is the maximum. So, the student CAN'T get an A

3 0
3 years ago
27. Morgan scored 41 points in 3 games. How many points would you expect him to make in an
kondaur [170]
I think there would be 150 points in 11 games
5 0
3 years ago
Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample
lana [24]

Answer:

z=\frac{0.579 -0.67}{\sqrt{\frac{0.67(1-0.67)}{38}}}=-1.193  

p_v =P(z  

So the p value obtained was a very high value and using the significance level given \alpha=0.1 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can conclude that  the proportion of women athletes graduated is not significantly lower than 0.67 or 67% at 10% of significance

Step-by-step explanation:

Data given and notation

n=38 represent the random sample taken

X=22 represent the number of women athletes graduated

\hat p=\frac{22}{38}=0.579 estimated proportion of women athletes graduated

p_o=0.67 is the value that we want to test

\alpha=0.1 represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.67 or no:  

Null hypothesis:p \geq 0.67  

Alternative hypothesis:p < 0.67  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.579 -0.67}{\sqrt{\frac{0.67(1-0.67)}{38}}}=-1.193  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.1. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(z  

So the p value obtained was a very high value and using the significance level given \alpha=0.1 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can conclude that  the proportion of women athletes graduated is not significantly lower than 0.67 or 67% at 10% of significance

3 0
2 years ago
Other questions:
  • Which triangle is similar to △ABC if sin(A) = One-fourth, cos(A) = StartFraction StartRoot 15 EndRoot Over 4 EndFraction, and ta
    5·2 answers
  • The graph of f(x)=4x^3-13x+9x+2 is shown below. How many roots of f(x) are rational numbers? Quick Please!!!!
    14·1 answer
  • How can you find the area of a two-dimensional composite figure, or the surface area of a three-dimensional composite figure?
    15·1 answer
  • Which number line model of the sum of 8 + -12 correctly ​
    11·2 answers
  • Help asap plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
    10·1 answer
  • What did I do wrong in notes, and why is the answer what it shows on screenshot
    15·1 answer
  • Is the relation a function? Explain your reasoning. <br><br><br> Plz help will give brainliest
    12·1 answer
  • A 14.5-gallon gasoline tank is $\frac{3}{4}$
    14·1 answer
  • URGENT
    9·1 answer
  • shawn is shoppping for a rug for his dinning room. the rectangular sug he likes measures 5 feat by 7 feet. what is the area of t
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!