All categories

3 years ago

Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places.

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

4 0

Answer:

3.4594

Step-by-step explanation:

To change the base of a logarithm

• $log_{b}$ x = $\frac{log_{c}x }{log_{c}b }$

where c represents the new base

Changing the base from 2 to 10

$log_{2}$ 11 = $\frac{log_{10}11 }{log_{10}2 }$ ≈ 3.4594

You might be interested in

Si 46 x + 322 = 1242 cual es el valor de x?

erma4kov [3.2K]

Answer:

x = 20

Step-by-step explanation:

46 x + 322 = 1242

46x = 920

x = 20

8 0

3 years ago

Find all the solutions of sin x + cos x = 1 in the interval [0, 2pie).

Mashcka [7]

Answer:

X = 0, π/2 in the interval [0, 2pi).

Step-by-step explanation:

Use the auxiliary angle method:

R sin(x + a) = Rsin x cos a + Rcos x sin a = 1

sin x + cos x = 1

Comparing coefficients:

R cos a = 1 and R sin a = 1, so

tan a = R sin a / R cos a = 1

So a = π/4 radians.

Also R^2(sin^2 a + cos^2 a) = 1^2 + 1^2 = 2

Therefore R = √2.

So √2 sin (x +π/4 = 1

sin x + π/4 = 1/√2

x + π/4 = π/4

x = 0 radians

Also

x = 0 + π/2 = π/2.

8 0

3 years ago

Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Write a probability model for this ex

allsm [11]

Answer:

We estimate to have 8.33 times the number 6 in 50 trials.

Step-by-step explanation:

Let us consider a success to get a 6. In this case, note that the probability of having a 6 in one spin is 1/6. We can consider the number of 6's in 50 spins to be a binomial random variable. Then, let X to be the number of trials we get a 6 out of 50 trials. Then, we have the following model.

$P(X=k) = \binom{50}{k}(\frac{1}{6})^k(\frac{5}{6})^{50-k}$

We will estimate the number of times that she spins a 6 as the expected value of this random variable.

Recall that if we have X as a binomial random variable of n trials with a probability of success of p, then it's expected value is np.

Then , in this case, with n=50 and p=1/6 we expect to have $\frac{50}{6}$ number of times of having a 6, which is 8.33.

6 0

3 years ago

Read 2 more answers

HELPPPPP MATCH the graph with the situation. I WILL GIVE BRAINLIEST!

netineya [11]

Answer:

1) c

2) D

3) H

Step-by-step explanation:

Just follow the graph as shown

8 0

3 years ago

What is the slope intercept form of 6x + 2y = 24?

dsp73

6x + 2y = 24....subtract 6x from both sides
2y = -6x + 24...now divide both sides by 2
y = -6/2x + 24/2...now reduce
y = -3x + 12 <=== slope intercept form of y = mx + b

7 0

3 years ago