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snow_lady [41]
3 years ago
10

For each of the following pairs of signed integers (2’s complement), subtract the second from the first. Show the decimal equiva

lents of each operand and the difference, Indicate overflow where appropriate
a) 111010 001111
b) 000100 011000
c) 010001 011010
d) 010000 100100
Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
3 0

Answer:

The answers are

a)111010 - 001111 = 101011 = 43

b) 000100 - 011000 = 111111111 (overflow) = -20

c) 010001 - 011010 = 11111111 (overflow) = -9

d) 010000 - 100100 = 1111111 (overflow) = -20

Step-by-step explanation:

a)111010 = 1×2⁵+1×2⁴+1×2³+0×2²+1×2¹+0×2⁰ = 32+16+8+0+2+0= 58

001111 = 0×2⁵+0×2⁴+1×2³+1×2²+1×2¹+1×2⁰ = 8+4+2+1=15

111010 - 001111 = 101011 = 43

b) 000100 = 0×2⁵+0×2⁴+0×2³+1×2²+0×2¹+0×2⁰ = 4

011000 = 0×2⁵+1×2⁴+1×2³+0×2²+0×2¹+0×2⁰  = 24

000100 - 011000 = 1111111111 (overflow), 4 - 24 =-20

c)  010001 = 1×2⁴+1×2⁰ = 17

011010 = 1×2⁴+1×2³+1×2¹ = 26

010001 - 011010 = 11111111 (overflow) 17-26=-9

d) 010000 = 1×2⁴ = 16

100100 = 1×2⁵+1×2² = 36

010000 - 100100 = 1111111 (overflow) 16-36=-20

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Answer:

(a)D(x)=-2,500x+60,000

(b)R(x)=60,000x-2500x^2

(c) x=12

(d)Optimal ticket price: $12

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Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500

Therefore, we have:

y=-2500x+b

At point (12,30000)

30000=-2500(12)+b\\b=30000+30000\\b=60000

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D(x)=-2,500x+60,000

(b)Revenue

R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0

Therefore:

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Step-by-step explanation:

We know that 1 ton = 2000 pound

Then , \text{1 pound}=\dfrac{1}{2000}\text{ ton}

Given : Mustafa’s horse ate 6,400 pounds of hay last year.

Then, the number of tons of hay his horse ate last year is given by :-

6400\times\dfrac{1}{2000}\ \ \text{ tons}\\\\=3.2 \text{ tons}

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From the information given

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