MATHEMATICS HIGH SCHOOL

Janene is solving the equation log3x324=2. Which exponential equation can she use to solve the problem?A. 324^2=3x
B. 334^x=2/3
C. (3x)^2=324
D. 3x^2=324

Answers

Answer 1

Answer:

Answer:

Option C: (3*x)^2 = 324

Step-by-step explanation:

Janene is solving the equation:

Log₃ₓ(324) = 2

First, some rules we need to remember:

Logₙ(x) = Ln(x)/Ln(n)

and:

Ln(x^b) = b*Ln(x)

So we can rewrite our expression as:

Log₃ₓ(324) = Ln(324)/Ln(3*x) = 2

Ln(324) = 2*Ln(3*x)

Now we can use the second property:

Ln(324) = 2*Ln(3*x) = Ln( (3*x)^2 )

The arguments in both sides must be the same thing, then:

324 = (3*x)^2

This is the exponential equation she needs to solve.

Then the correct option is C.

Related Questions

Brittany has a gift box in the shape of a cube. Each side of the box measures 15 cm. what is the volume of the gift box?
Divide 36 by the difference of 16 and 4
What is the length of leg y of the right triangle?A right triangle with hypotenuse 26 and legs 24 and y10142426
Solve for x. 8(x + 1) - 3(x + 4) = 7(2 - x) 41/3
The weights (to the nearest pound) of some boxes to be shipped are found to be: Weight 65 68 69 70 71 72 90 95 frequency 1 2 5 8 7 3 2 2 Explain why or why not this could be represented by a bell curve (a normal distribution).

What is the answer for. What is hg = 45g

Answers

To solve hg = 45g

Apply Multiplication Property of Equality which is to multiply both sides of the equation with 1/g.

hg (1/g) = 45g (1/g)
   h = 45

Or you can divide both sides with the equation with g.

   hg / g = 45g / g

You can cancel g to both sides.
Then,
   h = 45

a scale drawing of a building needs to be made using the scale 1 in=170 ft.how tall will the building in the scale be if the building is 680 ft.tall?

Answers

Hi there! The answer is 4 inches.

If 1 inch on scale equals 170 feet in reality, 680 feet in reality equals 680 / 170 = 4 inches on scale (since the proportions don't change).

Describe the range of a square root function

Answers

It really depends on the function.

If it's:
sqrt(x^3 - 3x + 47), or something similar,
The RANGE will be ALL REAL NUMBERS.

Most of the time the range of a square root function (provided all of the function is inside the square root) will be all reals. This is because all positive integers have a positive and negative square root.

A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 69 customers. The dealer will be fined if the number of customers who report favorably is between 40 and 46. The dealership will be dissolved if fewer than 40 customers report favorably. It is known that 73% of the dealer’s customers report favorably on satisfaction surveys. a. What is the probability that the dealer will be fined? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)b. What is the probability that the dealership will be dissolved? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

Answers

Step-by-step explanation:

The probability that the dealer will be fined is 0.0948

To find p(a <= Z <= b) = F(b) - F(a)

P(X < 20) = (20 - 30.5)/3.4489

= -10.5/3.4489

= -3.0444

= P(Z < -3.0444) from standard normal table

= 0.00117

P(X < 26) = (26 - 30.5)/3.4489

= -4.5/3.4489 = -1.3048

= P(Z < -1.3048) From standard normal table

= 0.09599

P(20 < x < 26) = 0.09599 - 0.00117 = 0.0948

The answer in this question is 0.0948

Final answer:

To determine the probabilities requested, the normal distribution model is employed. The number of favorable reports follows a normal distribution with mean μ = 0.73 * 69 and standard deviation σ. The probabilities are then calculated from the z-scores corresponding to the given ranges, using standard normal distribution tables or calculators.

Explanation:

To calculate the probability that the dealership will be fined or dissolved, we use the normal distribution model because the sample size is large enough, and the variable (the number of customers who report favorably) can be approximated by a normal distribution. Given that 73% of the dealer's customers report favorably, and we have a sample size of 69 customers, we can find the mean (μ) and the standard deviation (σ) of the distribution. The mean (μ) is 0.73 * 69, and the standard deviation (σ) is $√((0.73 * 0.27 * 69))$ .

To find the z-score for the number of favorable reports between 40 and 46, we use the formula z = (x - μ) / σ. Then we find the corresponding probabilities using the standard normal distribution table or a calculator providing such functionalities. To find the probability that the dealer will be fined, we subtract the cumulative probability at the lower boundary from that at the upper boundary. Similarly, to find the probability that the dealership will be dissolved (fewer than 40 favorable reports), we find the cumulative probability at 39 (since it's fewer than 40) and use it directly because it represents all values below that number.