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Mrac [35]
2 years ago
12

A library has six identical copies of a certain book. At any given time, some of these copies are at the library and some are ch

ecked out. How many different ways are there for some of the books to be in the library and the rest to be checked out if at least one book is in the library and at least one is checked out? (The books should be considered indistinguishable.)
Mathematics
1 answer:
lions [1.4K]2 years ago
4 0
5 different ways I believe
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Write a function rule to calculate the cost of buying bananas at $.39 a pound
QveST [7]
$.39 times x=cost
x=pounds
6 0
2 years ago
The hypotenuse of a 45°-45°-90° triangle measures 10 StartRoot 5 EndRoot in. A right triangle is shown. The hypotenuse has a len
suter [353]

Answer:

5\sqrt{10}\ units

5 StartRoot 10 EndRoot

Step-by-step explanation:

we know that

The legs of a 45°-45°-90° triangle are congruent

Let

x ---->  the length of one leg of the triangle

Applying the Pythagorean Theorem

c^2=a^2+b^2

where

c is the hypotenuse

a and b are the legs

we have

c=10\sqrt{5}\ units

a=b=x\ units

substitute

(10\sqrt{5})^2=x^2+x^2

500=2x^2\\x^2=250\\x=\sqrt{250}\ units

Simplify

x=5\sqrt{10}\ units

5 StartRoot 10 EndRoot

4 0
2 years ago
Read 2 more answers
The width of a rectangle is the length minus 3 units. The area of the rectangle is 54 units. What is the width, in units, of a r
saul85 [17]

Width of the rectangle is 9 units

Step-by-step explanation:

  • Step 1: Let the width of the rectangle be x. Then the length = x - 3. Find dimensions of the rectangle if its area = 54 sq. units

Area of the rectangle = length × width

54 = x (x - 3)

54 = x² - 3x

x² - 3x - 54 = 0

x² + 6x - 9x - 54 = 0 (Using Product Sum rule to factorize)

x(x + 6) - 9(x + 6) = 0

(x + 6)(x - 9) = 0

x = -6, 9 (negative value is neglected)

x = 9 units

4 0
2 years ago
The price of an article is Rs 1200 and a customer pays Rs 1380 with VAT. Find the rate of VAT​
garik1379 [7]

Answer:

15%

Step-by-step explanation:

vat amount

= 1380 - 1200

=180

finding the rate of vat

= 1380/1200 *100

= 115%

NB : the 115% shows that 1200 8 115% = 1380 , this give total amount including vat , we only want vat hence we have to deduct the 100% which indicates the amount of article)

hence 115 - 100 = <u>15%</u>

15% * 1200= 180

8 0
2 years ago
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that th
Sergeeva-Olga [200]

Answer:

Step-by-step explanation:

(a)

The bid should be greater than $10,000 to get accepted by the seller. Let bid x be a continuous random variable that is uniformly distributed between

$10,000 and $15,000

The interval of the accepted bidding is [ {\rm{\$ 10,000 , \$ 15,000}], where b = $15000 and a = $10000.

The interval of the provided bidding is [$10,000,$12,000]. The probability is calculated as,

\begin{array}{c}\\P\left( {X{\rm{ < 12,000}}} \right){\rm{ = }}1 - P\left( {X > 12000} \right)\\\\ = 1 - \int\limits_{12000}^{15000} {\frac{1}{{15000 - 10000}}} dx\\\\ = 1 - \int\limits_{12000}^{15000} {\frac{1}{{5000}}} dx\\\\ = 1 - \frac{1}{{5000}}\left[ x \right]_{12000}^{15000}\\\end{array}

=1- \frac{[15000-12000]}{5000}\\\\=1-0.6\\\\=0.4

(b)  The interval of the accepted bidding is [$10,000,$15,000], where b = $15,000 and a =$10,000. The interval of the given bidding is [$10,000,$14,000].

\begin{array}{c}\\P\left( {X{\rm{ < 14,000}}} \right){\rm{ = }}1 - P\left( {X > 14000} \right)\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{15000 - 10000}}} dx\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{5000}}} dx\\\\ = 1 - \frac{1}{{5000}}\left[ x \right]_{14000}^{15000}\\\end{array} P(X14000)

=1- \frac{[15000-14000]}{5000}\\\\=1-0.2\\\\=0.8

(c)

The amount that the customer bid to maximize the probability that the customer is getting the property is calculated as,  

The interval of the accepted bidding is [$10,000,$15,000],

where b = $15,000 and a = $10,000. The interval of the given bidding is [$10,000,$15,000].

\begin{array}{c}\\f\left( {X = {\rm{15,000}}} \right){\rm{ = }}\frac{{{\rm{15000}} - {\rm{10000}}}}{{{\rm{15000}} - {\rm{10000}}}}\\\\{\rm{ = }}\frac{{{\rm{5000}}}}{{{\rm{5000}}}}\\\\{\rm{ = 1}}\\\end{array}

(d)  The amount that the customer bid to maximize the probability that the customer is getting the property is $15,000, set by the seller. Another customer is willing to buy the property at $16,000.The bidding less than $16,000 getting considered as the minimum amount to get the property is $10,000.

The bidding amount less than $16,000 considered by the customers as the minimum amount to get the property is $10,000, and greater than $16,000 will depend on how useful the property is for the customer.

5 0
2 years ago
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