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Variable y varies directly with variable x, and y = 45 when x = 9.

Alenkasestr [34]

Direct variation means their ratio is a constant
x/y is 9/45=1/5
so when x=2, y=5*2=10

4 0

3 years ago

I need three dollars seventy-eight cents more to buy a pair of tennis shoes. The tennis shoes cost eight dollars less the one hu

aleksandrvk [35]

Answer:

$118.22

Step-by-step explanation:

Subtract $130.00-$8.00= $122.00

Then subtract $122.00- $3.78 = $118.22

7 0

3 years ago

Read 2 more answers

Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 8 liters of

Sloan [31]

9514 1404 393

Answer:

340

Step-by-step explanation:

The ratio of natural to synthetic is give as ...

5 : 8

Then the ratio of natural to total would be ...

5 : (5+8) = 5 : 13

The amount of natural oil in 884 total liters of oil will be ...

(5/13)(884 L) = 340 L

884 liters of Petrolyn oil will contain 340 liters of natural oil.

4 0

2 years ago

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In a certain region, about 6% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban po

Sedbober [7]

Answer:

City @ 2017 = 8,920,800

Suburbs @ 2017 = 1, 897, 200

Step-by-step explanation:

Solution:

- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:

0.94*p_c + 0.04*p_s = p_c'

0.06*p_c + 0.96*p_s = p_s'

- Assuming 6% moved while remaining 94% remained settled at the time of migrations.

- The matrix representation is as follows:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}p_c\\p_s\end{array}\right] = \left[\begin{array}{c}p_c'\\p_s'\end{array}\right]$

- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_k = x_k_+_1$

- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o = x_1$

- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.

$x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o$

- Where,

$x_o = \left[\begin{array}{c}10,000,000\\800,000\end{array}\right]$

- The population in 2017 x_2 would be:

$x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}10,000,000\\800,000\end{array}\right] \\\\\\x_2 = \left[\begin{array}{c}8,920,800\\1,879,200\end{array}\right]$

5 0

3 years ago

Consider an algorithm that uses only assignment statements that replaces the quadruple (w, x, y, z) with (x, y, z, w). What is t

Likurg_2 [28]

Answer:

The minimum number of assignment statements needed is 5

Step-by-step explanation:

To write the algorithm, we apply the strategy of interchanging the values of variables in the assignment statements.

Assume "tmp" is the new variable, let assign tmp to w

The algorithm is:

Procedure exchange (w,x,y,z: integers)

tmp := w

w := x

x := y

y := z

z := tmp

return (w,x,y,z)

end

From the algorithm, it is obvious that there will be a minimum of 5 assignment statements needed.

6 0

3 years ago