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Which equation has x = –6 as the solution?

olya-2409 [2.1K]

Answer:

The equation 'log Subscript 3 Baseline (negative 2 x minus 3) = 2' i.e. $\log _3\left(-2x-3\right)=2$ has x = –6 as the solution.

Step-by-step explanation:

<u>Checking the equation</u>

log Subscript 3 Baseline (negative 2 x minus 3) = 2

Writing in algebraic expression

$\log _3\left(-2x-3\right)=2$

Use the logarithmic definition

$\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c$

$\log _3\left(-2x-3\right)=2\quad \Rightarrow \quad \:-2x-3=3^2$

$-2x-3=3^2$

$-2x-3=9$

$-2x=12$

$\mathrm{Divide\:both\:sides\:by\:}-2$

$\frac{-2x}{-2}=\frac{12}{-2}$

$x=-6$

Therefore, the equation 'log Subscript 3 Baseline (negative 2 x minus 3) = 2' i.e. $\log _3\left(-2x-3\right)=2$ has x = –6 as the solution.

3 0

3 years ago

Read 2 more answers

A group of five people are all working on the same mathematics problem. On the night before it is due, they call each other to d

UkoKoshka [18]

Answer:

Minimum number of calls = 10

Step-by-step explanation:

Lets name the five people as A,B,C,D and E.

<u>On the night before ,each person talks to every other person atleast once that means A would talk to B,C,D and E atleast once.</u>

Lets start with A. He would talk to other 4 people which means there would be 4 phone calls made.

Now lets take B. He can talk to A,C,D and E. But A has already talked to C therefore to get minimum number of phone calls , B need not call A again. So he calls only C,D and E.

In case of C using similar logic he need to talk to only D and E.

For D , he talks to E alone.

E does not have to talk to anyone as he has already talked to everyone atleast once.

Total calls = 4 + 3 + 2 + 1

= 10

5 0

3 years ago

How do you find the area of a rectangle

REY [17]

Answer: multiple the length vu the width

Step-by-step explanation:

5 0

3 years ago

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GRE Test: The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Student’s scores o

Zepler [3.9K]

Answer:

a) $\bar X=144.3$

b) The 95% confidence interval would be given by (138.846;149.754)

c) n=34

d) n=298

e) n=1190

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean with this formula:

$\bar X = \frac{\sum_{i=1}^n x_i}{n}$

$\bar X=144.3$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=8.8$ represent the population standard deviation

n=10 represent the sample size

a) Find a point estimate of the population mean

We can calculate the sample mean with this formula:

$\bar X = \frac{\sum_{i=1}^n x_i}{n}$

$\bar X=144.3$

b) Construct a 95% confidence interval for the true mean score for this population.

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$144.3-1.96\frac{8.8}{\sqrt{10}}=138.846$

$144.3+1.96\frac{8.8}{\sqrt{10}}=149.754$

So on this case the 95% confidence interval would be given by (138.846;149.754)

Part c

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =+20 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (5) we got: