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3 years ago

Habib wants to cover a kitchen wall in ceramic tile. The wall is 42 feet by 10 feet.

Mathematics

1 answer:

Slav-nsk [51]3 years ago

7 0

Answer: Side of largest square tile will be 105 feet.

Explanation:

Since we have given that

dimensions of the wall is 42 feet by 10 feet

So,

Length of wall = 42 feet

Breadth of wall = 10 feet

First we calculate the H.C.F. of 42 and 10,

which is 2 only.

The largest square tile side would be 2 feet.

Now, we find the number of tiles used,

Number of tiles =

$\frac{\text{Area of wall}}{\text{H.C.F. of }42\text{ and }11\times\text{ H.C.F. of }42\text{ and } 11}}\\\\=\frac{42\times 10}{2\times 2}\\\\=\frac{420}{4}\\\\=105$

We get integer value of number of tiles.

Therefore, Side of largest square tile will be 2 feet.

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The area of a square is 64 n Superscript 36square units. What is the side length of one side of the square?

arsen [322]

The correct answer is option D which is the side length will be (64n)¹⁸.

<h3>What is the area of the square?</h3>

The square is defined as a quadrilateral having all four sides equal to each other and the area of the square is the product of its sides.

Given that:-

The area of the square is given as- A = (64n)³⁶.

The sides of the square will be calculated as follows:-

A = (64n)³⁶

a² = (64n)³⁶ Here a = Side of the square.

a = √ (64n)³⁶

a = 64n¹⁸

Therefore the correct answer is option D which is the side length will be (64n)¹⁸.

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2 years ago

2x3 + 5x2 + 6x + 15

iren [92.7K]

Answer:

Step-by-step explanation:

Distribute x^2 to 2x and 5, you’ll get 2x^3+5x^2.

The distribute 3 to 2x and 5, you’ll get 6x+15.

You’ll get what the question is asking for.

7 0

3 years ago

Let X ~ N(0, 1) and Y = eX. Y is called a log-normal random variable.

Cloud [144]

If $F_Y(y)$ is the cumulative distribution function for $Y$ , then

$F_Y(y)=P(Y\le y)=P(e^X\le y)=P(X\le\ln y)=F_X(\ln y)$

Then the probability density function for $Y$ is $f_Y(y)={F_Y}'(y)$ :

$f_Y(y)=\dfrac{\mathrm d}{\mathrm dy}F_X(\ln y)=\dfrac1yf_X(\ln y)=\begin{cases}\frac1{y\sqrt{2\pi}}e^{-\frac12(\ln y)^2}&\text{for }y>0\\0&\text{otherwise}\end{cases}$

The $n$ th moment of $Y$ is

$E[Y^n]=\displaystyle\int_{-\infty}^\infty y^nf_Y(y)\,\mathrm dy=\frac1{\sqrt{2\pi}}\int_0^\infty y^{n-1}e^{-\frac12(\ln y)^2}\,\mathrm dy$

Let $u=\ln y$ , so that $\mathrm du=\frac{\mathrm dy}y$ and $y^n=e^{nu}$ :

$E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu}e^{-\frac12u^2}\,\mathrm du=\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu-\frac12u^2}\,\mathrm du$

Complete the square in the exponent:

$nu-\dfrac12u^2=-\dfrac12(u^2-2nu+n^2-n^2)=\dfrac12n^2-\dfrac12(u-n)^2$

$E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{\frac12(n^2-(u-n)^2)}\,\mathrm du=\frac{e^{\frac12n^2}}{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du$

But $\frac1{\sqrt{2\pi}}e^{-\frac12(u-n)^2}$ is exactly the PDF of a normal distribution with mean $n$ and variance 1; in other words, the 0th moment of a random variable $U\sim N(n,1)$ :

$E[U^0]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du=1$

so we end up with

$E[Y^n]=e^{\frac12n^2}$

3 0

3 years ago

A regular octagon with side length a cm can be made by cutting off

Ksivusya [100]

Answer:

one side = $\frac{a\sqrt{2}}{2}$

Step-by-step explanation:

if you draw an octagon on a piece of paper, you can draw a square around it, you should be able to see a diagram of this attached, ignore the 6.

Let's say TP = a

since it's a regular octagon, TP = HT

and using the Pythagoras Theorem, we know a² + b² = c² and thus:

√(AT² + HA²) = HT

and since AT = HA which we will call x, the equation becomes:

√(2x²) = HT = a

rearrange the equation to solve for x and you get:

2x² = a²

x² = $\frac{a^{2} }{2}$

x = $\frac{a}{\sqrt{2}}$

which, if you rationalise the denominator, you get:

x = $\frac{a\sqrt{2}}{2}$

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3 years ago

I really don’t get it!!

AleksAgata [21]

Answer:

The answer is b.

Step-by-step explanation:

Square root 124, you'll get 29.10, after that once you simplify it, you will get the answer and you will have to do the formula, a^2 + b^2 = c^2 since it is a triangle.

8 0

3 years ago

Read 2 more answers