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3 years ago

3/4 times what equals 12

Mathematics

2 answers:

Dmitrij [34]3 years ago

7 0

Answer: The required number is 16.

Step-by-step explanation: We are given to find the number such that $\dfrac{3}{4}$ times of that number is equal to 12.

Let the required number be represented by x.

Then, according to the given information, we have

$\dfrac{3}{4}\times x=12\\\\\Rightarrow 3x=48\\\\\Rightarrow x=\dfrac{48}{3}\\\\\Rightarrow x=16.$

Thus, the required number is 16.

Tema [17]3 years ago

6 0

What is 12/3? 4.
What is 4x4? 16
So 3/4 x 16 = 12 because 12 is 3/4 of 16

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What are the square roots of 1?

Marta_Voda [28]

Answer:

Step-by-step explanation:

1^2=1

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2 years ago

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A single story house is to be built on a rectangular lot 70 feet wide by 100 feet deep. The shorter side of the lot is along the

dedylja [7]

Answer:

250 sq ft

Step-by-step explanation:

Since the shorter side is along the street and the setback is 10ft from each side, the house is 50 ft wide

and 100 -20 -30 = 50 ft long

50 x 50 = 250 sq ft

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3 years ago

Find dy/dx if f(x) = (x + 8)^3x.

vlabodo [156]

This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...

Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.

Let y = (x+8)^(3x)

Take the natural log of both sides:

ln(y) = ln((x+8)^(3x))

By laws of logarithms, this can be rearranged:

ln(y) = 3xln(x+8)

Next, differentiate both sides. By implicit differentiation:

d/dx(ln(y)) = 1/y dy/dx

The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):

d/dx(3xln(x+8)) = d/dx(uv)

du/dx = 3

Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:

v = ln(a)
da/dx = 1
dv/da = 1/a

By chain rule:

dv/dx = dv/da * da/dx = 1/a = 1/(x+8)

Finally, use the product rule:

d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)

This overall produces the equation:

1/y * dy/dx = 3x/(x+8) + 3ln(x+8)

We want to solve for dy/dx, achievable by multiplying both sides by y:

dy/dx = y(3x/(x+8) + 3ln(x+8))

Since we know y = (x+8)^(3x):

dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))

Neatening this up a bit, we factorise out 3/(x+8):

dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))

Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.

I hope this helped you :)

8 0

3 years ago

So far this year, the average monthly revenue at Lexington Times is 50,711. That is 5% less than the monthly average was last ye

SOVA2 [1]

53,380 was the average last year .

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

Here we have , So far this year, the average monthly revenue at Lexington Times is 50,711. That is 5% less than the monthly average was last year. We need to find that What was the average last year . Let's find out:

Let the monthly average was last year be x , According to question the average monthly revenue at Lexington Times is 50,711 but , That is 5% less than the monthly average was last year . Following equation for above scenario is :

⇒ $x-\frac{5(x)}{100}=50711$

⇒ $\frac{100x-5x}{100}=50711$

⇒ $\frac{95x}{100}=50711$

⇒ $\frac{95x(100)}{100(95)}=\frac{50711(100)}{95}$

⇒ $x=\frac{50711(100)}{95}$

⇒ $x=53380$

Therefore , 53,380 was the average last year .

7 0

3 years ago

Consider an experiment where we ask what type of car – either domestic (e.g., Chevrolet, Ford, Chrysler, etc.), foreign built ab

Nostrana [21]

Answer:

$12^{20}$ outcomes for this sample space (under some considerations)

Step-by-step explanation:

Let's define the multiplication principle.

If a first part of an experiment can happen in n1 ways, a second part of an experiment can happen in n2 ways , . . . , a i - part of an experiment can happen in ni ways, then the total outcomes for the all the experiment are

(n1) x (n2) x ... x (ni)

In this exercise n1 = domestic

n1 is the total classes for domestic category

(Let's suppose n1 = 3 because of Chevrolet, Ford and Chrysler)

n2 = 1 (Also supposing we only have ''a Toyota built in Japan'' category for n2)

n3 = 1 (Also supposing we only have ''A Toyota built in Kentucky'' category for n3)

n4 = 4 (Also supposing we only have ''sedan,hatchback, truck or SUV'' category for n4

The possible outcomes for one person in the experiment are

$(Domestic).(ForeignBuiltAbrod).(ForeignBuiltInTheU.S).(Style)$

Where what it is brackets are the possible categories for that classification.

$n1.n2.n3.n4=3.1.1.4=12$

We have 20 different people then $12^{20}$ are the possible outcomes sample space

In the sample space there are $12^{20}$ outcomes if we consider that we have 3 types of domestic car, 1 type of foreign car built abroad,1 type of foreign car built in the U.S and 4 differents styles for this 20 different people.

7 0

3 years ago