the length of a rectangle is six feet less than twice the width. if the perimeter of the rectangle is 48, find both lengths

The number of subscribers to a streaming video service doubles each week.

Ilya [14]

Answer:

Step-by-step explanation:

This is an exponential equation that is solved by taking the natural log of both sides. The equation is

$f(x)=2^x$

If we are looking for x when f(x) = 64, then

$64=2^x$

Take the natural log of both sides:

$ln(64)=ln(2^x)$

The rules of logs allows us to bring the x down in front:

$ln(64)=xln(2)$

Divide both sides by ln(2) to get:

$\frac{ln(64)}{ln(2)}=x$

Do this on your calculator to get that x = 6.

You could also have just gone right to your calculator and started raising 2 to consecutive powers starting at like 3 or 4 to eventually get that 2 to the 6th power is equal to 64, but for the basics of solving log equations, you need to know how to do this.

5 0

3 years ago

Read 2 more answers

Plz help

kvv77 [185]

Option C: $5 x(4 x+7)(3 x+2)$ is the possible expressions for length, width and height of the prism.

Explanation:

The volume of the rectangular prism is $60 x^{3}+145 x^{2}+70 x$

To determine the length, width and height of the rectangular prism, let us factor the expression.

Thus, factoring 5x from the expression, we have,

$5 x\left(12 x^{2}+29 x+14\right)$

Let us break the expression $12 x^{2}+29 x+14$ into two groups, we get,

$5x[\left(12 x^{2}+8 x\right)+(21 x+14)]$

Factoring 4x from the term $12 x^{2}+8 x$ , we get,

$5x[4 x(3 x+2)+(21x+14)]$

Similarly, factoring 7x from the term $21 x+14$ , we get,

$5x[4 x(3 x+2)+7(3x+2)]$

Now, let us factor out $3x+2$ , we get,

$5 x(4 x+7)(3 x+2)$

Hence, the possible expressions for length, width and height of the prism is $5 x(4 x+7)(3 x+2)$

Therefore, Option C is the correct answer.

8 0

2 years ago

Zach paid $56.50 including sales tax for a book priced at $45. What was the sales tax rate?

kondaur [170]

Answer:

25.56% or $11.50

Step-by-step explanation:

I took it and put it in a sales tax calc.

3 0

2 years ago

Ryan needs $100 for a new bike. He already has $28 and will make $12 per day working for his grandfather. Write an inequality to

bezimeni [28]

Answer:

100 ≥ 12x + 28

Step-by-step explanation:

He needs $100 for the new bike but already has the $28 so you also have to add 12x because thats what you need to find. X represents the amount of days he has to work.

3 0

2 years ago

You are a waterman daily plying the waters of Chesapeake Bay for blue crabs (Callinectes sapidus), the best-tasting crustacean i

notsponge [240]

The question given is incomplete, I googled and got the complete question as below:

You are a waterman daily plying the waters of Chesapeake Bay for blue crabs (Callinectes sapidus), the best-tasting crustacean in the world. Crab populations and commercial catch rates are highly variable, but the fishery is under constant pressure from over-fishing, habitat destruction, and pollution. These days, you tend to pull crab pots containing an average of 2.4 crabs per pot. Given that you are economically challenged as most commercial fishermen are, and have an expensive boat to pay off, you’re always interested in projecting your income for the day. At the end of one day, you calculate that you’ll need 7 legal-sized crabs in your last pot in order to break even for the day. Use these data to address the following questions. Show your work.

a. What is the probability that your last pot will have the necessary 7 crabs?

b. What is the probability that your last pot will be empty?

Answer:

a. Probability = 0.0083

b. Probability = 0.0907

Step-by-step explanation:

This is Poisson distribution with parameter λ=2.4

a)

The probability that your last pot will have the necessary 7 crabs is calculated below:

P(X=7)= {e-2.4*2.47/7!} = 0.0083

b)

The probability that your last pot will be empty is calculated as:

P(X=0)= {e-2.4*2.40/0!} = 0.0907

8 0

2 years ago