All categories

3 years ago

Solve the exponential equation 16 = 2^x − 2.

Mathematics

2 answers:

adell [148]3 years ago

6 0

There’s no answer to the question

Sholpan [36]3 years ago

3 0

2^x-2=16
+2 +2
——————
2^x=18

(Log)(2))=log (18)

X=log(18)
————-
Log(2)

X=4.169925

You might be interested in

The U.S. and many other countries have recently tightened airport security. A sociologist is interested in estimating the propor

melisa1 [442]

Answer:

0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.

Step-by-step explanation:

Conduct a test to determine whether the true proportion of interest is higher than 0.7.

This means that the null hypothesis is: $H_{0}: p = 0.7$

And the alternate hypothesis is: $H_{a}: p > 0.7$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that $\mu = 0.7, \sigma = \sqrt{0.7*0.3}$

The sociologist found that 375 of the 500 travelers randomly selected and interviewed indicated that the airports were safe.

This means that $n = 500, X = \frac{375}{500} = 0.75$

Value of the z-statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.75 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{350}}}$

$z = 2.44$

P-value of the test:

Probability of z being larger than 2.44, that is, a proportion larger than 0.75.

This is, looking at the z-table, 1 subtracted by the pvalue of Z = 2.44. S

Z = 2.44 has a pvalue of 0.9927

1 - 0.9927 = 0.0073

0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.

8 0

3 years ago

Calculate the area of the regular pentagon below: A regular pentagon with side length of 11.8 inches and dotted line from center

vlada-n [284]

Answer:

Area of regular pentagon is 238.95 square inches.

Step-by-step explanation:

Given a regular pentagon with side length of 11.8 inches and dotted line from center to middle of side of 8.1 inches.

we know a regular polygon divides into 5 congruent triangles.

Side of pentagon i.e base of one triangle is 11.8 inches.

Also, distance from center to middle of side which is height of triangle is 8.1 inches.

Area of 1 triangle= $\frac{1}{2}\times base\times height$

= $\frac{1}{2}\times 11.8\times 8.1$

= 47.79 sq inches.

Area of regular pentagon=area of 5 congruent triangles= $5\times 47.79$ =238.95 sq inches.

5 0

3 years ago

Mrs. Flores asked her students to write a number, its opposite, and its absolute value, in that order. Four of her students turn

oee [108]

Answer:

Sarah is correct

Step-by-step explanation:

Required

Which of the students is correct

Let a number be x,

Given what the teacher asked the students to do, the solution is:

$Number = x$

$Opposite = -x$

$Absolute = |x|$

Only Sarah got this correctly; others are incorrect.

The proof is as follows.

For Sarah

$Number = 1416$

$Opposite = -1416$

$Absolute =|1416| = 1416$

So, the numbers will be: 1416, -1416 and 1416

<em>Other students are incorrect</em>

4 0

3 years ago

Rewrite the equation by completing the square.<br> x^2+ 12x + 36 = 0

svetoff [14.1K]

Answer:

(x+6)^2 =0

Step-by-step explanation:

x^2+ 12x + 36 = 0

Subtract 36 from each side

x^2+ 12x + 36-36 = 0-36

x^2 +12x = -36

Take the coefficient of x

Divide by 2

12/2 =6

Square it

6^2 =36

Add this to each side

x^2+ 12x + 36 = -36+36

(x+12/2)^2 = 0

(x+6)^2 =0

4 0

3 years ago

Read 2 more answers

In the diagram below, what is the measure of the missing angle?

Neporo4naja [7]

Answer:

Answer is 62 degrees.

Step-by-step explanation:

The sum of all angles of a triangle is 180°

x + 70 + 48 = 180

x + 118 = 180

x = 180 - 118

x = 62

4 0

3 years ago