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puteri [66]
2 years ago
14

Solve 2 log(x) + log(5) = log (80) using the one-to-one property.

Mathematics
1 answer:
vodomira [7]2 years ago
5 0

x=4

Step-by-step explanation:

2log(x)+log(5)=log(80)

log(x^2)+log(5)=log(80)

log(5x^2)=log(80)

5x^2 =80

x^2 =80/5

x^2=16 , taking square root both sides

x=√16

=4

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1/4 i hope this helps u
6 0
3 years ago
In a random sample of 5 residents of the state of Texas, the mean waste recycled per person per day was 1.9 pounds with a standa
sammy [17]
<h2>Answer with explanation:</h2><h2 />

The confidence interval for population mean is given by :-

\overline{x} \pm\ t_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

Given : Sample size : n= 5, since n<30 , so the test we use here is t-test.

Sample mean : \overline{x}=1.9\text{ pounds}

Standard deviation: \sigma=0.89\text{ pounds}

Significance level : 1-\alpha:1-0.99=0.01

By using the standard normal distribution table , the critical value corresponds to the given significance level will be :-

t_{n-1,\alpha/2}=t_{5-1,0.01/2}=t_{4,0.005}=4.604

Now, the 99% confidence interval for the mean waste recycled per person per day for the population of Texas will be :-

1.9\pm\ (4.604)\dfrac{0.89}{\sqrt{5}}\\\\\approx1.9\pm1.832\\\\=(1.9-1.832,1.9+1.832)=(0.068,\ 3.732)

Hence, the 99% confidence interval for the mean waste recycled per person per day for the population of Texas  = (0.068, 3.732)

5 0
3 years ago
The first- and second-year enrollment values for a technical school are shown in the table below: Enrollment at a Technical Scho
lyudmila [28]

Answer:

  • <u><em>The solution to f(x) = s(x) is x = 2012. </em></u>

Explanation:

<u>Rewrite the table and the choices for better understanding:</u>

<em>Enrollment at a Technical School </em>

Year (x)       First Year f(x)      Second Year s(x)

2009                  785                        756

2010                   740                        785

2011                    690                        710

2012                   732                         732

2013                   781                          755

Which of the following statements is true based on the data in the table?

  • The solution to f(x) = s(x) is x = 2012.
  • The solution to f(x) = s(x) is x = 732.
  • The solution to f(x) = s(x) is x = 2011.
  • The solution to f(x) = s(x) is x = 710.

<h2>Solution</h2>

The question requires to find which of the options represents the solution to f(x) = s(x).

That means that you must find the year (value of x) for which the two functions, the enrollment the first year, f(x), and the enrollment the second year s(x), are equal.

The table shows that the values of f(x) and s(x) are equal to 732 (students enrolled) in the year 2012,<em> x = 2012. </em>

Thus, the correct choice is the third one:

  • The solution to f(x) = s(x) is x = 2012.
5 0
3 years ago
Help, I need somebody to help me out with this question.
Rama09 [41]
The first one is 4•7 I believe
4 0
3 years ago
AB is tangent to circle O. If AO=24 and BC=50, what is AB? <br> The diagram is not to scale.
Oksana_A [137]

Answer:

The correct option is 70

Step-by-step explanation:

It is a right triangle so we will use Pythagorean theorem to find AB:

We have One side = 24 and hypotenuse = 24+50 which is 74

Now apply Pythagorean theorem:

AB = √(74)²-(24)²

AB = √5476-576

AB= √4900

Take the square root of 4900.

AB= 70

Thus the correct option is 70....

8 0
3 years ago
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