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Your boss asks you to design a Boolean circuit that verifies whether a given integer 0 < x < 16 is divisible by 5.

Every such number is represented in binary using four bits, say b₃b₂b₁b₀, and so your Boolean circuit will have four inputs. For instance, the number 13 is written in binary as 1101 and so to test its divisibility by 5 a user would feed the values b₀ = 1, b₁ = 0, b₂ = 1, and b₃ = 1 into the inputs of your circuit.

The Boolean circuit will have a single output, which should deliver the value 1 if the iput values represent a number that is divisible by 5 and 0 otherwise.

a) write down the truth table of the Boolean function F(b₀,b₁,b₂b₃) that implements this "divisible by 5" operation

b) construct a Boolean expression in disjunctive normal form that implements the Boolean function yo wrote down in a)

Answer:

Given that;

integer range = 0≤ x ≤ 16

within 4bits, we can represnt each number

(0,5,10,15)

a)  

Truth table for function that implements  divisible by 5

Integer    B3    B2    B1    B0     Y

0              0       0      0      0      1

1              0       0      0       1      0

2              0       0      1        0     0

3              0       0      1        1      0

4              0       1       0       0     0

5              0       1       0       1      1

6              0       1       1        0     0

7              0       1       1        1       0

8              1       0      0        0      0

9              1       0      0        1       0

10             1       0      1         0      1

11              1       0      1          1      0

12             1        1      0         0     0

13             1         1     0          1      0

14             1         1       1         0     0

15            1         1        1        1       1

b)

Boolean expression that implements the Boolean function from a)

from the truth table;

Boolean expression Y is;

Y = b⁻₃b⁻₂b⁻₁b⁻₀ / y₁   +   b⁻₃b₂b⁻₁b₀ / y₂   +   b₃b⁻₂b₁b⁻₀ / y₃   +   b₃b₂b₁b₀ / y₄

Answer:

  circuit is in the second attachment

Step-by-step explanation:

Attached is a truth table for the desired circuit, where b3–b0 are the input bits, MSB–LSB. We notice that the output is true whenever b3=b1 and b2=b0. This can be written in DNF as ...

  [tex]Y=b_3'b_2'b_1'b_0'+b_3b_2'b_1b_0'+b_3'b_2b_1'b_0+b_3b_2b_1b_0[/tex]

More compactly, it can be written in terms of the exclusive-nor function as ...

  [tex]y=(b_3\odot b_1)\wedge(b_2\odot b_0)[/tex]

A circuit diagram showing this circuit is the second attachment. (A–D are the input bits, in order MSB–LSB (or its reverse)).

Answer:

A

[tex]f(x + h) = 21x -x^2 -2xh+ 21h+h^2[/tex]

B

[tex]f(x-h)-f(x) = 21h+h^2 -2xh[/tex]

C

[tex]\frac{f(x-h)-f(x)}{h} = 21+h -2x[/tex]

Step-by-step explanation:

From the question we are told that

   The equation given is

                    [tex]f(x) = x (21 - x )[/tex]

Considering  A

      [tex]f(x + h) = (x + h) (21 - (x + h))[/tex]

      [tex]f(x + h) = (x + h) (21 - x - h)[/tex]

      [tex]f(x + h) = 21x -x^2 -2xh+ 21h+h^2[/tex]

Considering B

       [tex]f(x + h)-f(x) = 21x -x^2 -2xh+ 21h+h^2 -[ x(21 -x)][/tex]

        [tex]f(x + h)-f(x) = 21x -x^2 -2xh+ 21h+h^2 -21x + x^2[/tex]

       [tex]f(x-h)-f(x) = 21h+h^2 -2xh[/tex]

Considering C

       [tex]\frac{f(x-h)-f(x)}{h} = \frac{21h+h^2 -2xh}{h}[/tex]  

       [tex]\frac{f(x-h)-f(x)}{h} = \frac{h(21+h -2x)}{h}[/tex]

       [tex]\frac{f(x-h)-f(x)}{h} = 21+h -2x[/tex]

Answer:

D. 30.5

Step-by-step explanation:

Given that A, B, C, D, and E are collinear,

AE = 38,

BD = 15, since segment BC = CD = DE, therefore

BD = ⅔ of BE

15 = ⅔*BE (substitution)

Solve for BE

Multiply each side by 3

15*3 = ⅔*BE*3

45 = 2*BE

Divide both sides by 2

45/2 = BE

22.5 = BE

BE = 22.5

Find AB:

AB + BE = AE (segment addition postulate)

AB + 22.5 = 38 (Substitution)

AB = 38 - 22.5 (Subtracting 22.5 from each side)

AB = 15.5

Find length of segment AD:

AB + BD = AD (segment addition postulate)

15.5 + 15 = AD (Substitution)

30.5 = AD

AD = 30.5

Answer:

yes totally

Step-by-step explanation:

5a+5b=5a+5b

Answer:

36 9/16 ft^3

Step-by-step explanation:

volume = length * width * height

volume = 3 3/4 ft * 3 ft * 3 1/4 ft

Change all mixed numerals to fractions.

volume = 15/4 * 3/1 * 13/4 ft^3

volume = 585/16 ft^3

volume = 36 9/16 ft^3

Answer:

16. 200+3

17. 30+4+0.1+0.02+0.007

18. 200+70+6+0.1+0.03

19. 30000000+4000000+100000+20000+3000+6

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

(3-2i)(3+2i)

as (a+b)(a-b) =a²-b²

3²-(2i)²

=9-(4*-1)

=9-(-4)

=9+4

=13

Hope this helps you!

Answer:

13

Step-by-step explanation:

3^2=9, 2i*(-2i)=-4i^2=4

the 6i and -6i cancel leaving the positive 9 and 4

9+4=13

Answer:

the contribution margin per composite unit is $365

Step-by-step explanation:

The computation of the contribution margin per composite unit is shown below:

= Contribution margin per unit for product A × ratio of A + Contribution margin per unit for product B × ratio of B

= ($86 - $45) × 5 + ($124 - $49) × 2

= $205 + $160

= $365

Hence the contribution margin per composite unit is $365

Answer:

200 is the maximum amount

Step-by-step explanation:

94x100=9400

9400/47=200

can i have brainliest?

Answer:

because angles on a straight line add up to 180 degrees substract (180-110), step 2; you will get 70 degrees afterwards the angle y is perpendicular it's 90 degrees.step 3;add (90+70) you get 160 .step 4;then substract (180-160) you get your answer as 20 degrees

Answer:

x = 20º

Step-by-step explanation:

Since it is a triangle, the sum of the internal angles is 180º.

We know that y = 90º, because 110º + 70º = 180º, and the line intercepts it, splitting the larger triangle into 2.

Since, y = 90º, and the other angle is 70º, we add those together to 160º.

Then, we take 180º - 160º = 20º.

x = 20º

Hope this helps.

:)

Answer:

[tex]-\frac{15}{16}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4} ^{2}[/tex]= [tex]\frac{1}{16}[/tex]

2*(pq)= 2([tex]\frac{1}{6}[/tex])= [tex]\frac{1}{3}[/tex]

-3[tex]q^{2}[/tex]= -3[tex](\frac{4}{9} )[/tex]= [tex]-\frac{4}{3}[/tex]

[tex]\frac{1}{16} +\frac{1}{3}-\frac{4}{3}[/tex]=

[tex]\frac{1}{16} -1[/tex]=

[tex]-\frac{15}{16}[/tex]

Answer:

P ($)=70-5(t)

Where p = price at t days

t = number of days

Step-by-step explanation:

The product price initially = $70

Now, every day , it reduces $5

The rate=$5 per day reduction

The price in the days will be determined by the formula below

P ($)=70-5(t)

Where p = price at t days

t = number of days

So let's assume it's on the second day

The price after the second day

P($) = 70-5(2)

P($) = 70-10

P($)= $60

The price after two days will be reduced to $60

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²               ------------------(i)

From the question:

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

Open the brackets and have the following:

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [equation has already been normalized since the coefficient of x² is 1]

Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [subtract 25 from both sides]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

Answer:

The area should be 56.4

Step-by-step explanation:

When you try to find the area of a triangle you have to multiply the base and height, which was 12km and 9.4 km,and you divide it by 2.

Answer:

See below.

Step-by-step explanation:

Rule:

[tex] a^m \times a^n = a^{m + n} [/tex]

Explanation:

When multiplying monomials with the same base, write the same base and add the exponents.

Answer:

[tex]R(200) = 6200[/tex]

[tex]R(3000) = 93000[/tex]

Step-by-step explanation:

Given

[tex]R(x) = 31x[/tex]

Solving (a): R(200)

[tex]R(x) = 31x[/tex]

Substitute 200 for x

[tex]R(200) = 31 * 200[/tex]

[tex]R(200) = 6200[/tex]

This means that the revenue from 200 hats is 6200

Solving (b): Revenue from 3000 hats

[tex]R(x) = 31x[/tex]

Substitute 3000 for x

[tex]R(3000) = 31 * 3000[/tex]

[tex]R(3000) = 93000[/tex]

The above represents the functional notation and the revenue sale is 93000

Answer:the answer is 1, b option i just take the tes

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

the answer is one

Answer:

5u - 23

Step-by-step explanation:

Answer:

4( 2u - 2) - 3(u + 5)​

(4*2u + 4*-2)-(3*u + 3*5)

8u-8-3u+15

8u-3u-8+15

5u+7

Step-by-step explanation:

I hope this helped you.

Please mark Brainliest.

Have a great day!!!!!!!!!

Answer:

Radius= 11

Circumference= 69.12

Area= 380.133

Step-by-step explanation:

Radius is half of the diameter.

Circumference is 2[tex]\pi[/tex]r.

Area is [tex]\pi r^2[/tex].

Step-by-step explanation:

A straight line graph is of the form:

y = mx+b

So we get our equation in this form:

9=2x+3y

or, 9-2x=3y

or, -2x+9 = 3y

or, y= (-2x+9)/3

or, y = -2/3x + 3

So,

Slope(m)=−2/3

y-intercept (b) = 3

Therefore, slope(m) is -2/3x and y-intercept(b) is 3.

Answer:

Area of drawing= 0.315 m²

Step-by-step explanation:

Base = 6m

Height = 4.2 m

Area = height* base

Area= 4.2*6

Area= 25.2 m²

The scale is 10 cm on the drawing for every 8 meters on the sculpture.

Which is 10 cm to 800 cm

Or

0.1m to 8m

Arra of sculpture= 25.2 m²

area of drawing= (25.2*0.1)/8

Area of drawing= 0.315 m²

Answer:

X = m - 2w

Step-by-step explanation:

just isolate the variable.

Answer:

x=m-2w

Step-by-step explanation:

Just take the +2w to the other side where it becomes negative.

Step-by-step explanation:

N(t) is continuous at t = 6, so f(6) = 25(6) + 150 = 300.

f(0) = 80.

f(t) is continuous, so by Intermediate Value Theorem, f(t) must equal 250 at some point between t=0 and t=6.

Answer:

75%

Step-by-step explanation:

Total = 21 + 7

         = 28 cupcakes

Vanilla cupcakes = 21 / 28 x 100

                             = 0.75 x 100

                             = 75%

Answer:

75%

Step-by-step explanation:

21+7=28

21 divided by 28 is equal to 0.75. 0.75 x 100 = 75%

Please choose my answer as the brainliest. It gets me to the next level!

Answer:

A;C;E

Step-by-step explanation:

Let cost of almond per pound be X

Cost of 3 pounds of almonds=3X

cost of pistachios per pound = X+4

Cost of 2 pounds of pistachios=2X+8

Total cost=5X+8=48

5X+8=48

5X=40

X=8

cost of one pound almond is $8

cost of one pound pistachios is $12

Please mark it brainly

Simplify the Integer part of the SQRT

Step-by-step explanation:

Factor 200 into its prime factors

           200 = 23 • 52 

Answer:

Step-by-step explanation:205

The sample space for first tossing a coin and then rolling a number cube is (T, 2).

An outcome is a possible result of an experiment or trial in probability theory. Each experiment's possible outcomes are distinct, and alternative outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment).

As, the outcomes for tossing a coin is Head (H) and Tail (T).

and, the outcome for rolling a die

{1, 2, 3, 4, 5, 6}.

So, the sample space for first tossing a coin and then rolling a number cube

= ( T, 2)

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Answer:

x=7

Step-by-step explanation:

[tex]1 + 3x = - 13 + 5x[/tex]

Collect like terms and simplify

[tex]3x - 5x = - 13 - 1 \\ - 2x = - 14[/tex]

Divide both sides of the equation by -2

[tex] \frac{ - 2x}{ - 2} = \frac{ - 14}{ - 2} [/tex]

Simplify

[tex]x = 7[/tex]

Answer:

Step-by-step explanation:

1 + 3x = 5x - 13

-2x + 1 = -13

-2x = -14

x = 7

A sequence is defined as an arrangement of numbers in a particular order.

The number of Band members in the year 2018 is expected to be 76.

A sequence is defined as an arrangement of numbers in a particular order.

We have,

Year         Number of Band members

2014        40

2015        46

2016        54

2017         64

We can make a sequence with the number of band members that increases each year.

i.e

40  46  54  64

We see that,

46 - 40 = 6

54 - 46 = 8

64 - 54 = 10

We see that the difference between the consecutive terms is increasing by 2.

So, the next term in the sequence will be 64 + 12 = 76.

Thus the number of band members in the year 2018 is expected to be 76.

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