Y=-0.005x^2+0.41x-5.1

A certain bookstore chain has two stores, one in San Francisco and one in Los Angeles. It stocks three kinds of books: hardcover

riadik2000 [5.3K]

Answer:

<h2>See the explanation.</h2>

Step-by-step explanation:

(a)

$\left[\begin{array}{cccc}T&H&S&P\\S&600&1300&2000\\L&400&300&400\end{array}\right]$ = A.

In the above matrix A, the columns refers the three type of books and the rows refers the from which stores the books are been sold.

The numbers represents the corresponding sales in the month of January.

The sale is same for the 6 months.

Hence, 6A = $\left[\begin{array}{cccc}T&H&S&P\\S&3600&7800&12000\\L&2400&1800&2400\end{array}\right]$ . This matrix 6A represents the total sales over the 6 months.

(b)

If we denote the books in stock at the starting of January by B, then

B = $\left[\begin{array}{cccc}T&H&S&P\\S&1000&3000&6000\\L&1000&6000&3000\end{array}\right]$ .

Each month, the chain restocked the stores from its warehouse by shipping 500 hardcover, 1,400 softcover, and 1,400 plastic books to San Francisco and 500 hardcover, 500 softcover, and 500 plastic books to Los Angeles.

If we represent the amount restocked books at the end of each month by another matrix C, then

C = $\left[\begin{array}{cccc}T&H&S&P\\S&500&1400&1400\\L&500&500&500\end{array}\right]$ .

This restocking will be done for 5 times before the end of June.

If there would be no sale, then the stock would be

B + 5C = $\left[\begin{array}{cccc}T&H&S&P\\S&1000+2500&3000+7000&6000+7000\\L&1000+2500&6000+2500&3000+2500\end{array}\right] \\= \left[\begin{array}{cccc}T&H&S&P\\S&3500&10000&13000\\L&3500&8500&5500\end{array}\right]$ .

Since, the total sale is given by 6A, at the end of June, the inventory in each store can be shown as following,

B+5C-6A $\left[\begin{array}{cccc}T&H&S&P\\S&3500&10000&13000\\L&3500&8500&5500\end{array}\right] - \left[\begin{array}{cccc}T&H&S&P\\S&3600&7800&12000\\L&2400&1800&2400\end{array}\right] \\= \left[\begin{array}{cccc}T&H&S&P\\S&-100&2200&1000\\L&1100&6700&3100\end{array}\right]$

6 0

3 years ago

Given that u =< 2,12 >, and z =< -7,5 >

swat32

Using the dot product:

For any vector x, we have

||x|| = √(x • x)

This means that

||w|| = √(w • w)

… = √((u + z) • (u + z))

… = √((u • u) + (u • z) + (z • u) + (z • z))

… = √(||u||² + 2 (u • z) + ||z||²)

We have

u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37

z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74

u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46

and so

||w|| = √((2√37)² + 2•46 + (√74)²)

… = √(4•37 + 2•46 + 74)

… = √314 ≈ 17.720

Alternatively, without mentioning the dot product,

w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩

and so

||w|| = √((-5)² + 17²) = √314 ≈ 17.720

7 0

2 years ago

397 students went on a field trip. Eight

lbvjy [14]

Answer:48

Step-by-step explanation:

Total number of students=397

Students that travelled in a car=29

Let the students that travelled in a bus be represented by y.

Since 8 buses were filled, it will be 8y for total students

8y + 29= 397

8y= 397-29

8y= 368

Divide both side by 8

8y/8=368/8

y = 46

Number of students in each bus is 46

8 0

3 years ago

Geoffrey is evaluating the expression (-3)^6(2^6)/(-3)^5(2^2) as shown below.

Alekssandra [29.7K]

Answer:

48.

Step-by-step explanation:

First you multiply the number by itself as many times as the number of the exponent is. In this case you multiply -3 to itself 6 times which makes -729, 2 to the 6th power is 64, -3 to the 5th power is -243, and 2 to the 2nd power is 4. Then you multiply -729 by 64 which makes -46656 and multiply -243 by 4 which makes -972, and then divide -972 from -46656 which makes 48.

3 0

2 years ago

Find the 52nd term of the following arithmetic sequence. 3, 9, 15, 21,

Alex Ar [27]

Answer:

309

Step-by-step explanation:

a = 3, d = 6, n 52

Nth term of an Arithmetic sequence is given as:

$t_n=a +(n-1)d \\ \therefore \: t_{52}=3 +(52-1) \times 6 \\ \therefore \: t_{52}=3 +51\times 6 \\ \therefore \: t_{52}=3 +306 \\ \huge \red{ \boxed{\therefore \: t_{52}=309 }}\\$

4 0

3 years ago