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
inysia [295]
3 years ago
6

Solve: 9^2x + 1 = 9^3x – 2

Mathematics
2 answers:
nirvana33 [79]3 years ago
7 0

Answer:

1/216

Step-by-step explanation:

Move variables to one side and constants to the other

9^3x-9^2x=3

factor out 9^2x

(9^2x)(8)=3

9^2x=3/8

3^4x=3/8

3^3x=1/8

x=1/8 x 27

x=1/216

kipiarov [429]3 years ago
6 0

Answer:

x = 1/216

Step-by-step explanation:

Simplify the equation, like the powers.

81x + 1 = 729x - 2

Subtract 729x on both sides to balance the equation.

-648x + 1 = - 2

Then subtract 1 from both sides.

-648x = -3

Finally divide by -648, which then leaves x equal to 1/216

x = 1/216

You might be interested in
A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the fl
cricket20 [7]

Answer:

1) We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:  

Null hypothesis:\mu \leq 5  

Alternative hypothesis:\mu > 5  

2) df=n-1=8-1=7  

Since is a one sided test the p value would be:  

p_v =P(t_{(7)}>2.233)=0.0304  

3) For this case is we use a significance level of 1% or 99% of confidencewe see that p_v >\alpha and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance \alpha=0.05 or 95% of confidence we see that p_v and we have enough evidence to conclude that the specification is satisfied.

Step-by-step explanation:

Data given and notation  

\bar X=6.5 represent the sample mean

s=1.9 represent the sample standard deviation

n=8 sample size  

\mu_o =5 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

Part 1: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:  

Null hypothesis:\mu \leq 5  

Alternative hypothesis:\mu > 5  

If we analyze the size for the sample is <30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{6.5-5}{\frac{1.9}{\sqrt{8}}}=2.233    

Part 2: P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=8-1=7  

Since is a one sided test the p value would be:  

p_v =P(t_{(7)}>2.233)=0.0304  

Part d: Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant higher compared to the height of men in 1960 at 1% of signficance.  

Part 3

For this case is we use a significance level of 1% or 99% of confidencewe see that p_v >\alpha and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance \alpha=0.05 or 95% of confidence we see that p_v and we have enough evidence to conclude that the specification is satisfied.

4 0
3 years ago
An item has a listed price of $75. If the sales tax rate is 7%, how much is the sales tax (in dollars)
Arlecino [84]

Answer:

$69.75

Step-by-step explanation:

5 0
3 years ago
The calories per serving for three sports drinks are 60 cal, 42 cal, and 90 cal. The probability of choosing a 60 calorie drink
dsp73
The expected value is given by:
E(x)= ∑x*p(x)
thus the expected value of calories will be given by:
E(x)=1/6*60+1/2*42+1/3*90
E(x)=10+21+30
E(x)=61

the answer is 61
7 0
3 years ago
Consider the following pair of equations:
miv72 [106K]

3x + 3 = x - 1 \\ 3x - x =   - 1 - 3 \\ 2x =  - 4 \\ x =  \frac{ - 4}{2 }  =  - 2
Take X=-2 into y
y = x - 1 \\ y =  - 2 - 1 \\ y =  - 3
(x, y) =(-2,-3)
6 0
3 years ago
A ___________ is a line segment that has end points on a circle and passes through the center of the circle. radius regular poly
Kobotan [32]
A diameter is a line segment that has end points on a circle and passes through the centre of the circle.
7 0
3 years ago
Other questions:
  • The volume of a rectangular prism is (x3 – 3x2 + 5x – 3), and the area of its base is (x2 – 2). If the volume of a rectangular p
    8·2 answers
  • Can someone help me please
    12·2 answers
  • Solve the following equation<br> M-6 3<br> —— = —-<br> 8 2
    12·1 answer
  • For what value of x is the rational expression below equal to zero?<br> x-1<br> (x-3)(x + 1)
    9·1 answer
  • How to write 12 and a half trillion
    10·2 answers
  • Show two ways three people can share a 5 segment chewy fruit worm
    5·2 answers
  • What is the volume of the cylinder below?
    11·2 answers
  • URGENT WILL GIVE BRAINLIEST
    6·1 answer
  • 3) Solve the equation for x.<br> 10(4x + 4) = 400<br> A) 2<br> B) 4<br> C) 9<br> D) 18
    8·2 answers
  • 5 (- 9) + 12, t = 20
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!