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son4ous [18]
3 years ago
5

Simplify the expression.

Mathematics
2 answers:
astra-53 [7]3 years ago
8 0

a^{\log_a b}=b\\\\12^{\log_{12}24}=24

Pachacha [2.7K]3 years ago
8 0

<u>Answer:</u>

The correct answer option is A) 24.

<u>Step-by-step explanation:</u>

We are given the following log expression and we are to simplify it:

1 2 ^ { log _ { 1 2 } } ^ { 2 4 }

Here, we are going to apply the rule for solving a log problem:

a^{log_a^{(b)} = b

So if 1 2 ^ { log _ { 1 2 } } ^ { 2 4 }, then it would be equal to 24.

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A bag contains white marbles and red marbles, 20 in total. The number of white marbles is 5 more than 2 times the number of red
Nitella [24]

Answer:

15

Step-by-step explanation:

let r represent red marbles then white = 2r + 5 and total is 20, thus

r + 2r + 5 = 20 ( subtract 5 from both sides )

3r = 15 ( divide both sides by 3 )

r = 5 ← number of red marbles

Thus number of white = 20 - 5 = 15

7 0
3 years ago
A literature professor decides to give a 10-questiontrue-false quiz to determine who has read an as-signed novel. She wants to c
Darya [45]

Answer:

The teacher should set the score 7 as the lowest passing grade.

Step-by-step explanation:

Let <em>X</em> = number of correct guesses.

All the questions are of true-false format.

The probability of getting a correct answer is, <em>p</em> = 0.50.

The total number of questions is, <em>n</em> = 10.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 10 and <em>p </em>= 0.50.

The probability mass function of <em>X</em> is:

P(X=x)={10\chose x}0.50^{x}(1-0.50)^{10-x};\ x=0,1,2,3...

Now the teaches chose the grading scheme such that the probability of passing a student who guesses on every question is less than 0.05.

Then the probability of failing such a students is at least 1 - 0.05 = 0.95.

Compute the probability distribution of <em>X</em>.

Consider the probability distribution attached below.

The value of <em>x</em> for which P (X ≤ x) is at least 0.95 is, <em>x</em> = 7.

So the teacher should set the score 7 as the lowest passing grade.

7 0
3 years ago
Please solve thanks lovee
Bumek [7]

Answer:

m∠1 = 93.5°

Step-by-step explanation:

By theorem of intersecting chords inside a circle,

If two chords intersect inside a circle, angle formed between the chords measure half the sum of the measures of the intercepted arcs.

m∠1 = \frac{1}{2}(92+95)

       = \frac{187}{2}

       = 93.5°

Therefore, measure of angle 1 is 93.5°.

4 0
3 years ago
In the figure below, find the value of cose:
MariettaO [177]

Answer:

D

Step-by-step explanation:

cosΘ = \frac{adjacent}{hypotenuse} = \frac{x}{r}

4 0
2 years ago
A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t = 0 seconds. when the weight it rele
zhannawk [14.2K]

The equation which models the distance (d) of the weight from its equilibrium after time (t) is equal to d = -9cos(2π/3)t.

<h3>What is the period of a cosine function?</h3>

The period of a cosine function simply means the total length (distance) of the interval of values on the x-axis over which a graph lies and it's repeated.

Since the weight attached is at its lowest point at time (t = 0), therefore, the amplitude of equation will be negative nine (-9)

For the angular velocity at time period (t = 3s), we have:

ω = 2π/T

ω = 2π/3

Mathematically, the standard equation of a cosine function is given by:

y = Acos(ω)t

Substituting the given parameters into the formula, we have;

d = -9cos(2π/3)t.

Read more on cosine function here: brainly.com/question/4599903

6 0
2 years ago
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