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ra1l [238]
3 years ago
15

ome pleated draperies must be twice as wide as the window they cover. How many square yards of material are needed to cover this

kind of window 2 ft. wide and 3 ft. long? 12 4 1
Mathematics
1 answer:
Burka [1]3 years ago
6 0
It would be 12 bc you need to find the area of the curtain--to double the width of the curtain you multiply 2x2, which equals 4.  then to get the area you multiply by the length, 4x3, which equals 12.
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Topic: Recognizing Linear and Exponential and Quadratic Functions.
BigorU [14]

Answer:

  Recursive: f(1) = 1; f(n) = f(n-1)/3

  Equation: f(x) = 5/3·(1/3)^(x-1)

Step-by-step explanation:

You know this is an exponential function because sequential lines in the table have a common ratio of f(x) values:

  f(2)/f(1) = (5/9)/(5/3) = 3/9 = 1/3

  f(3)/f(2) = (5/27)/(5/9) = 9/27 = 1/3

and it continues like that.

Besides telling you the function is exponential, it also tells you that each term is 1/3 of the previous term.

<h3>Recursive formula</h3>

The value of f(1) is read from the table. For x = 1, that value is ...

  f(1) = 5/3

As we noticed above, each term is 1/3 the previous term, so the recursive relation is ...

  f(n) = (1/3)·f(n-1)

<h3>Equation</h3>

The general form of the equation for a geometric (exponential) relation is ...

  f(x) = f(1)·r^(x-1) . . . . . . where f(1) is the first term, and r is the common ratio

For this function, we have f(1) = 5/3 and r = 1/3, so the equation is ...

  f(x) = 5/3·(1/3)^(x-1)

__

<em>Additional comment</em>

When given values of x that count from 1, we often express the equation in terms of (x-1). That equation can be simplified so the exponent is x.

  f(x) = 5·(1/3)^x

5 0
1 year ago
Let f(x) = cxe−x2 if x ≥ 0 and f(x) = 0 if x &lt; 0.
sergij07 [2.7K]

(a) If <em>f(x)</em> is to be a proper density function, then its integral over the given support must evaulate to 1:

\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx = \int_0^\infty cxe^{-x^2}\,\mathrm dx=1

For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em>. Then as <em>x</em> → 0, <em>u</em> → 0; as <em>x</em> → ∞, <em>u</em> → ∞:

\displaystyle\frac12\int_0^\infty ce^{-u}\,\mathrm du=\frac c2\left(\lim_{u\to\infty}(-e^{-u})-(-1)\right)=1

which reduces to

<em>c</em> / 2 (0 + 1) = 1   →   <em>c</em> = 2

(b) Find the probability P(1 < <em>X </em>< 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):

\displaystyle\int_1^3 2xe^{-x^2}\,\mathrm dx = \boxed{\frac{e^8-1}{e^9}} \approx 0.3678

5 0
2 years ago
It costs $2.80 to make a sandwich at the local deli shop. To make a profit, the deli sells it at a price that is 170% of the cos
Svetlanka [38]

Answer:

Sandwich sells for  $4.76  .

Step-by-step explanation:

As given

It costs $2.80 to make a sandwich at the local deli shop.

To make a profit, the deli sells it at a price that is 170% of the cost.

170% is written in the decimal form

= \frac{170}{100}

= 1.7

Thus

Sandwich selling cost = 1.7 × Cost of making

Put all the values in the above

Sandwich selling cost = 1.7 × $ 2.80

                                    = $4.76

Therefore the Sandwich sells for  $4.76  .

7 0
3 years ago
Read 2 more answers
Write an equation for a line parallel to y=−4x+5 and passing through the point (4,-21)
Sindrei [870]

Answer:

Y=-4x-5

Step-by-step explanation:

-21=-4(4)+b

-21=-16+b

b=-5

y=-4x-5

3 0
3 years ago
Read 2 more answers
What is the product of 5 and 2/3
alukav5142 [94]
The product of 5 and 2/3 is 5.6666
5 0
2 years ago
Read 2 more answers
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