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vfiekz [6]
2 years ago
15

Solve the equation for x. show your work log(2x-6)=2

Mathematics
2 answers:
borishaifa [10]2 years ago
8 0

Answer:

x = e^2/2 + 3

Step-by-step explanation:

Solve for x:

log(2 x - 6) = 2

Hint: | Eliminate the logarithm from the left hand side.

Cancel logarithms by taking exp of both sides:

2 x - 6 = e^2

Hint: | Isolate terms with x to the left hand side.

Add 6 to both sides:

2 x = e^2 + 6

Hint: | Solve for x.

Divide both sides by 2:

Answer: x = e^2/2 + 3

Mrac [35]2 years ago
8 0

Answer:

x = 53

Step-by-step explanation:

Rewrite  log ( 2 x − 6 ) = 2  in exponential form using the definition of a logarithm. If  x  and  b  are positive real numbers and  b  ≠  1 , then  log  b ( x ) =  y  is equivalent to  b y  =  x .

10  =  x  −  6

Solve for  x .

Rewrite the equation as  

x  −  6  =  10 .

x  −  6  =  10

Raise  10  to the power of  2 .

x  −  6  =  100

Move all terms not containing  x  to the right side of the equation.

x  =  106

Divide each term by  2  and simplify.  x = 53

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An advertising executive claims that there is a difference in the mean household income for credit cardholders of Visa Gold and
Maslowich

Answer:

Null hypothesis:\mu_{Visa}=\mu_{Mastercard}

Alternative hypothesis:\mu_{Visa} \neq \mu_{Mastercard}

t=\frac{66970-59060}{\sqrt{\frac{9500^2}{11}+\frac{10000^2}{17}}}}=2.108  

p_v =2*P(t_{26}>2.108)=0.0448

Comparing the p value with the significance level given \alpha=0.1 we see that p_v so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the  in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .

Step-by-step explanation:

Data given and notation

\bar X_{Visa}=66970 represent the mean for Visa

\bar X_{Mastercard}=59060 represent the mean for the sample Mastercard

s_{Visa}=9500 represent the population standard deviation for Visa

s_{Mastercard}=10000 represent the population standard deviation for Mastercard

n_{Visa}=11 sample size for the group Visa

n_{Mastercard}=17 sample size for the group Mastercard

t would represent the statistic (variable of interest)

\alpha=0.1 significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:

Null hypothesis:\mu_{Visa}=\mu_{Mastercard}

Alternative hypothesis:\mu_{Visa} \neq \mu_{Mastercard}

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

z=\frac{\bar X_{Visa}-\bar X_{Masterdcard}}{\sqrt{\frac{s^2_{Visa}}{n_{Visa}}+\frac{s^2_{Mastercard}}{n_{Mastercard}}}} (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the value of the test statistic for this hypothesis testing.

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

t=\frac{66970-59060}{\sqrt{\frac{9500^2}{11}+\frac{10000^2}{17}}}}=2.108  

What is the p-value for this hypothesis test?

First we need to calculate the degrees of freedom given by:

df= n_{Visa}+n_{Mastercard}-2 = 11+17-2= 26

Since is a bilateral test the p value would be:

p_v =2*P(t_{26}>2.108)=0.0448

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given \alpha=0.1 we see that p_v so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the  in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .

4 0
3 years ago
Help~~~~~~~~~~~~~~~~~~~~~~~~~
igor_vitrenko [27]

Answer:

28.25 square units

Step-by-step explanation:

A circumference of the circle is

C=2\pi r,

where r is the radius of the circle.

So,

18.84=2\pi r\\ \\r=\dfrac{18.84}{2\pi}=\dfrac{9.42}{\pi}\ cm

The area of the circle is

A=\pi r^2

Substitute the value of the radius:

A=\pi \cdot \left(\dfrac{9.42}{\pi}\right)^2=\dfrac{9.42^2}{\pi}\approx 28.25\ un^2

8 0
3 years ago
Read 2 more answers
At the end of year 1, Boller Co. had an ending balance in allowance for uncollectible accounts of $30,000. During year 2, Boller
Masja [62]

Answer:

$34,000

Step-by-step explanation:

First they had 30,000

Then wrote off 40,000

So balance is 30,000 - 40,000 = -10,000

Now, they want 8% of 300,000 as uncollectible. So that would be

0.08 * 300,000 = 24,000

Thus, to bring the balance to 24,000 [balance is -10,000], how much would they need to add?? Let it be x:

-10,000 + x = 24,000

x = 24,000 + 10,000 = $34,000

8 0
3 years ago
The vertices of a triangle are A(7.5), B(4,2), and C19. 2). What is
geniusboy [140]

Answer- 45 degrees

Step-By-Step Explanation- You're welcome lol

3 0
3 years ago
The incenter is the center of the _______ circle of a triangle
blagie [28]

Answer:

In

Step-by-step explanation:

An incircle is a circle inside a triangle that touches all three sides of the triangle.

5 0
3 years ago
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