Draw and simplify the karnaugh maps of x,y,Z for (a)m0 +m1+ m5+m7. (b)F(1,3,5,4,7). (c)m0+m2+m4+m6. (d)F(0,2,4,6)
Answers
The simplified Karnaugh maps are F(A, B, C) = A’B’ + AC , F(A, B, C) = C + AB’, F(A, B, C) = C’.
What are Karnaugh Maps ?A Karnaugh map can be compared to a more advanced version of a truth table
In a K-map there are all the possible input variables and outcomes stored in cells.
It is a method to simplify and optimize Boolean expressions.
(a) m0 +m1+ m5+m7
Mapping the given function in a Karnaugh map,
The image is attached with the answer.
we can see two pairs
Pair-1 is m0 + m1
and Pair-2 is m5 + m7
= A’B’C’ + A’B’C + AB’C + ABC
= A’B’(C’ + C) + AC(B’ + B)
= A’B’ + AC
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = A’B’ + AC.
(b) F(1,3,5,4,7)
On Mapping the given function in a Karnaugh map, we will see
1 Pair and 1 Quad
Pair is m4 + m5
Quad is m1 + m3 + m5 + m7
= A’B’C + A’BC + AB’C + ABC + AB’C’ + AB’C
= A’C(B’ + B) + AC(B’ + B) + AB’(C’ + C)
(B +B' ) = 1 , (C’ + C) = 1
= A’C + AC + AB’
= C(A’ + A) + AB’
= C + AB’
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = C + AB’.
(c) m0+m2+m4+m6.
On Mapping the given function in a Karnaugh map, we will see
2 Pairs
Pair-1 is m0 + m4
Pair-2 is m2 + m6
= A’B’C’ + AB’C’ + A’BC’ + ABC’ = B’C’(A’ + A) + BC’(A’ + A)
= B’C’ + BC’
= C’(B’ + B)
= C’
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = C’.
(d) (0,2,4,6)
It will have the same expression as that of Option (c)
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Related Questions
Help me with the problem please!!
Answers
Step-by-step explanation:
Scale factor red to blue meaning 42 to 7
42÷7=6
Scale factor is 6
Perimeter of the blue quadrilateral = ?
If perimeter of red = 204
Then we use this following proportion
[tex]204 \div 42 = x \div 7[/tex]
[tex] \frac{204}{42} = \frac{x}{7} [/tex]
Then we cross multiply
42x=7×204
42x=1428
x=34
Area of the blue quadrilateral = ?
If area of the red quadrilateral = 2880
Then we use the following proportion
[tex]2880 \div 42 = x \div 7[/tex]
[tex] \frac{2880}{42} = \frac{x}{7} [/tex]
Then we cross multiply
42x=2880×7
42x=20160
x=480
Given that the triangle ABC is at A=(-1,5) B=(1, 1) C = (2, 3), and if the triangle is
reflected across the line x = 4, find the new position of point C'.
Answers
Answer: (6,3)
Step-by-step explanation:
Since C is 2 units from the line of reflection, and it lies on the left of the line of reflection, C' will lie 2 units to the right of the line of reflection.
Therefore, C'=(6,3).
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 3%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that:
a. None of the LED light bulbs are defective?
b. Exactly one of the LED light bulbs is defective?
c. Two or fewer of the LED light bulbs are defective?
d. What are the mean and standard deviation of the binomial distribution for the number of defective LED light bulbs?
Answers
Answer:
a) There is a 59.87% probability that none of the LED light bulbs are defective.
b) There is a 31.51% probability that exactly one of the light bulbs is defective.
c) There is a 98.84% probability that two or fewer of the LED light bulbs are defective.
d) There is a 100% probability that three or more of the LED light bulbs are not defective.Step-by-step
explanation:
For each light bulb, there are only two possible outcomes. Either it fails, or it does not. This means that we use the binomial probability distribution to solve this problem.
In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 < x < 68, where x represents height, can be used to represent the height range. Which is another way of writing the inequality?
x > 64 and x < 68
x > 64 or x < 68
x < 64 and x < 68
x < 64 or x < 68
Answers
Michael and Zach are hiking in the mountains. They left Michael’s car in the parking lot and walked northwest for 12.4 km to a campsite. Then they turned due south and walked another 7.0 km to a glacier lake. The weather was taking a turn for the worse, so they decided to plot a course directly back to the parking lot. Zach remembered, from the map in the parking lot, that the angle between the path to the campsite and the path to the glacier lake measures about 30°. What compass direction should they follow to return directly to the parking lot?
Answers
Answer:
about 101°
Step-by-step explanation:
The bearing back to the parking lot is the reverse of the bearing from the parking lot to the lake. That bearing can be found two ways. One of them uses the bearing and distance of each leg of the hike. The other uses what Zach remembers about the map.
__
sum of vectorsThe location of the lake from the parking lot can be found by adding the vectors to the campsite from the lot and to the lake from the campsite. That sum will be ...
12.4∠315° +7.0∠180° ≈ 8.94∠281.4°
A suitable calculator can be used to find this sum, as shown in the second attachment. (Angles are displayed by the calculator in the range (-180°, 180°].)
__
The direction of the parking lot from the lake will be the opposite direction. It can be found by subtracting 180° from the angle:
bearing to parking lot = 281.4° -180° = 101.4°
Michael and Zack should follow a compass direction of about 101°.
__
map memoryNorthwest is a compass bearing of 315°. Points south of that bearing will have a smaller angle. Zach remembers the direction of the lake to be about 30° less than that angle, so at 315° -30° = 285°.
The bearing back to the parking lot is the opposite direction, so ...
285° -180° = 105°
Based on Zack's memory, they should follow a compass direction of about 105°.
They will come within about 560 meters of the parking lot using this heading.
_____
Additional comments
When doing these vector calculations by hand, a couple of different methods can be used. One is to convert the vectors to component form, add the components, then convert back to polar form. The other is to make use of the Law of Cosines and the Law of Sines to solve the relevant triangles.
Here, the lake-lot distance is the third side of a triangle with two sides and the included angle known. The Law of Cosines applied to this situation is ...
c² = a² +b² -2ab·cos(C) . . . . . generic Law of Cosines equation
c² = 12.4² +7.0² -2(12.4)(7.0)cos(45°) ≈ 80.0063
c ≈ √80.0063 ≈ 8.9446
Using the Law of Sines, we find the obtuse angle of the triangle to be ...
sin(L)/12.4 = sin(C)/8.9446 . . . . . L and C are vertex angles in the diagram
L = 180° -arcsin(12.4/8.9446×sin(45°)) ≈ 101.4°
__
If translation to rectangular coordinates is used, this can be done using the usual translation ...
(x, y) = (r·cos(θ), r·sin(θ)) . . . . rectangular coordinates for r∠θ
The value of θ used can be the bearing angle (measured clockwise from north), or it can be the corresponding Cartesian plane angle (measured counterclockwise from +x). As long as the angles are consistently measured, the math works either way.
__
We have assumed that "northwest" is a bearing of 315°. If the compass rose is divided into 32 segments, the name "northwest" will be given to any bearing within 5° of this value. This makes our detailed vector calculations be somewhat approximate, and means that Zach's memory of the required bearing may be sufficiently accurate after all. Or not.
A group of researchers wants to develop an experiment to determine whether a new drug effectively treats hypothyroidism. The researchers want to inject the drug in rabbits first to determine whether there are any potential serious side effects.
Part A: What are some possible ethical issues to this type of testing? (5 points)
Part B: While conducting the experiment, the researchers find the thyroid begins functioning properly, and they declare the new drug is causing the change. Is this a good assumption? Explain. (5 points)
Answers
Some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.
What is experiment?Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a experiment. To avoid any ambiguity or surprise, a experiment must be properly defined.
A) Because human experimentation is immoral, animal research has been employed as a research approach.
However, using animals is unethical because they are subjected to unpleasant and hazardous procedures, as well as stress and injury. The use of non-animal methods to substitute animal methods as much as possible will provide both ethical and technical benefits. Researchers should make the use of non-animal methods for a top priority experiments.
B) Even though the purpose of an experiment is to ensure success in rabbits, this is incorrect in people because action is what will operate properly.
The absence of thyroid-stimulating hormone in rabbit serum is a mistaken notion. As a result, it is preferable to test the drug further, and it was a success. As a result, there will be no dysfunctionality for humans.
Thus, some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.
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Can somebody please help with Khan Academy? Thx :)
Answers
Answer:
x ≤ 0
Step-by-step explanation:
The number line's direction is left, any number that is left on a number line behind zero has a less value. Greater than or equal!
Solve for x and y.
7x-4
#
4y+8
24#
+
31
Answers
Answer:
7x-4 = -28
4y+8 = 4(y + 2)
Step-by-step explanation:
Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 14 and its height is 6?
Answers
The possible base and height of a second triangle are 12 and 7, respectively
How to determine the possible base and height of a second triangle?An inverse variation is represented as:
Base * Height = k
Where k is the constant of variation.
In this case, k is the area
So, we have:
Base * Height = Area
For the first triangle, we have:
14 * 6 = Area
Evaluate
Area = 84
Substitute Area = 84 in Base * Height = Area
Base * Height = 84
Express 84 as the product of two numbers
Base * Height = 12 * 7
By comparison;
Base =12 and Height = 7
Hence, the possible base and height of a second triangle are 12 and 7, respectively
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Which of the numbers below are whole numbers? Check all that apply.
A. 29
B. 367.53
C. 71.1
D. 6523
DE 1/2
F. 126
Answers
Answer:
A,D,F
Step-by-step explanation: Because it not a fraction or decimal in it its an whole number
What is the equation of the line that is perpendicular to the line and passes through the point (15,-5)?
Answers
The equation of the line that is perpendicular to the line and passes through the point (15,-5) is y = -x + 10
The complete question is
What is the y-intercept of the equation of the line that is perpendicular to the line y = x + 10 and passes through the point (15, –5)?
What is the meaning of Perpendicular ?A perpendicular means a line which intersects the other line at 90 degree.
Line given y = x+10
slope = 1
Slope of the line perpendicular to the above line = -1
and it passes through the point (15, –5)
The equation will become
y = mx +c
-5 = -1 * 15 + c
15-5 = c
c = 10
Therefore the equation is y = -x +10
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Answer: d
Step-by-step explanation:
Triangle ABC is translated 2 units to the right
on a coordinate plane to form triangle DEF.
The measure of AB= 6 units, BC = 5 units,
CA= 4 units, and m/ABC = 41°. Which of the
following is not a corresponding measure of
triangle DEF?
Answers
Answer:
56
Step-by-step explanation:
Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the
following is true.
P(-C≤Z≤c)=0.9715
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Answers
Using the normal distribution, considering it's symmetry, it is found that the value of C is of 2.19.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The standard normal distribution has mean and standard deviation given, respectively, by:
[tex]\mu = 0, \sigma = 1[/tex].
Hence, considering the symmetry of the normal distribution, the value of c is Z with a p-value of (1 + 0.9715)/2 = 0.98575, hence c = Z = 2.19.
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What are the domain and range of the function represented by the set of ordered pairs?
{(-6, 12), (-3, -2), (1, 0), (14, -4)}
A. Domain: {-6, -3, 1, 14}
Range: {-4, -2, 0, 12}
B. Domain: -6 ≤ x ≤ 14
Range: -4 ≤ y ≤ 12
C. Domain: {-4, -2, 0, 12}
Range: {-6, -3, 1, 14}
D. Domain: -4 ≤ x ≤ 12
Range: -6 ≤ y ≤ 14
Answers
Answer:
A
Step-by-step explanation:
the domain is the definition of the valid x (input) values.
the range is the definition of the valid y (result) values.
as the function is defined by listing the specific points, the function only consists of individual points and not of connecting lines.
therefore the domain and range cannot be continuous intervals (otherwise the function would suddenly also include points not in the original list).
so, B and D are wrong.
and A is right, because the domain contains the x values, and the range the y values.
Find sin A for the triangle below. Give the exact value as an expression and an approximation to the nearest ten-thousandth. Note: The triangle is not drawn to scale.
Answers
the exact value of sin A to the nearest ten- thousandth is 0. 6625
Using the pythagorean theorem
a² + b² = c²
The opposite side is unknown, so use the pythagorean theorem to find it
c = hypotenuse = 4
a= opposite site = ?
b= adjacent side = 3
Substitute into the formula
4² = a² + 3²
16 = a² + 9
a² = 16 -9 = 7
Find the square root
a =√7 = 2. 65
To find Sin A, use
Sin A = opposite side ÷ hypotenuse
Sin A = 2. 65 ÷ 4 = 0. 6625
Thus, the value of sin A is 0. 6625
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A company lost $5,676 over a year. How much money did they lose each month to split evenly?
Answers
Answer:
$473
Step-by-step explanation:
We divide 5676 by 12 and we get 473
$473 they lose each month (?)
Step-by-step explanation:
calculator
Expand and simplify: (-7y - 8) (y - 4)
Answers
Answer:
[tex] { - 7y}^{2} + 20y + 32[/tex]
Step-by-step explanation:
1.) -7y times y = -7y(squared)
2.) -7y times -4 = 28y
3.) -8 times y = -8y
4.) -8 times -4 = 32
5.) Combine like terms
[tex] { - 7y}^{2} + 28y - 8y + 32 = { - 7y}^{2} + 20y + 32[/tex]
function h is a transformation of the parents tangent function such that h(x)=-tan(1/2x). Which graph represents function h?
Answers
The graph that represents function h is the graph in; Option C
How to Interpret Graph Transformations?The parent function is; f(x) = tan (x)
The transformed function is; h(x) = -tan(¹/₂x)
Now, from general tangent function we know that; y = tan(Bx)
Thus, period = π/(¹/₂)
From the given transformation that produced the h(x) function and when we look at the given graphs, the one that represents the function h is Option C.
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For the data set represented on the box plot, which region contains the most dispersed data?
Answers
The region that contains the most dispersed data is between the upper quartile and the median.
Which region contains the most dispersed data?A box plot is used to study the distribution and level of a set of scores. The box plot consists of whiskers which measure the minimum and maximum numbers.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Difference between the lower quartile and the median : 300 - 275 = 25Difference between the upper quartile and the median : 340 - 300 = 40Difference between the upper quartile and the maximum : 355 - 340 = 15Difference between the minimum and the lower quartile : 275 - 250 = 25To learn more about box plots, please check: brainly.com/question/27215146
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4. Evaluate e^-2 to one decimal place
A) 0.7
B) -1.4
C) 0.1
D) 1.4
Answers
Which expression is a possible leading term for the polynomial function graphed below?
Answers
Like wise, option 2 is not the answer because it has a negative symbol.
This leaves us with option 4, 22x^9 as the right answer.
The population of Detroit, Michigan, decreased from 1,027,974 in 1990 to 688,701 in 2013 (Source: U.S. Census Bureau). Find the average rate of change in the population of Detroit, Michigan, over the 23-year period.
Answers
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, so let's use the ones provided in that
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{years}{x}&\stackrel{population}{y}\\ \cline{1-2} 1990&1027974\\ 2013&688701\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{1990}~,~\stackrel{y_1}{1027974})\qquad (\stackrel{x_2}{2013}~,~\stackrel{y_2}{688701}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{688701}-\stackrel{y1}{1027974}}}{\underset{run} {\underset{x_2}{2013}-\underset{x_1}{1990}}} \implies \cfrac{-339273}{23}\implies -14751\qquad \stackrel{rate~of}{change}[/tex]
let's notice, is negative since the population decreased.
If Toni wants to grow flowers in her garden, she will need a special type of top soil. If she wants the topsoil to be 1 foot deep, how much topsoil is needed? Remember, the length of the garden is 44 feet and the width is 2 feet.
Answers
Answer:
Depending on the unit your answer needs to be in, it would be 88 cubic feet or 3.25926 cubic yards
If your question asks you to round to the nearest hundredth it would be 3.26 cubic yards.
Step-by-step explanation:
To find the volume of soil:
Volume= Length x Width x Depth/Height
Volume= 44ft x 2ft x 1ft
Volume= 88 cubic feet or 3.25926 (there are 27 cubic feet in a cubic yard, 88/27=3.25926)
hope this helps! :)
find the
-2
-4
-3
-1
-9-8
determinant OF
-15
- 5
6
Answers
Determinants are defined only for square matrices, so I assume you are given the 3×3 matrix
[tex]A = \begin{bmatrix}-2 & -4 & -3 \\ -1 & -9 & -8 \\ -15 & -5 & 6 \end{bmatrix}[/tex]
Let's compute the determinant by taking the cofactor expansion along the first column:
[tex]\det A = -2 \det\begin{bmatrix}-9 & -8 \\ -5 & 6\end{bmatrix} + \det\begin{bmatrix}-4 & -3 \\ -5 & 6\end{bmatrix} - 15 \det \begin{bmatrix}-4 & -3 \\ -9 & -8\end{bmatrix}[/tex]
[tex]\det A = -2 ((-9)\times6-(-8)\times(-5)) + ((-4)\times6 - (-3)\times(-5)) \\ ~~~~~~~~~~~~~~~- 15 ((-4)\times(-8)-(-3)\times(-9))[/tex]
[tex]\det A = -2(-54-40) + (-24 - 15) - 15 (32 - 27)[/tex]
[tex]\det A = \boxed{74}[/tex]
Two triangles are similar. The base of one is 2 inches and the height is 5 inches. If the base of the other is 7 inches, what is the height?
Answers
Step-by-step explanation:
similar shapes means that they have the same angles, and there is one scale factor that applies to all sides and other lines in the shapes (like heights).
therefore the ratios between 2 correlated lines are all the same.
so,
2/7 = 5/height
2×height / 7 = 5
2×height = 7×5 = 35
height = 35/2 = 17.5 in
jackson bought 3 pounds of candy for $9.60.
What was the price of this candy in cents per once ?
Answers
Answer:
to find for one divide 9 dollars 60 pounds by 3 to get the coast of one candy
help please, i need to turn this in
Answers
Answer:
a = -3
b = 9
c = -3
Step-by-step explanation:
[tex]a. (2^{5} )(2)^{-8} =2^{a} \\2^{(5-8)} =2^{a} \\2^{-3}=2^{a}[/tex]
[tex]a=-3[/tex]
[tex]b.\frac{4^{7} }{4^{-2} } =4^{b} \\4^{(7-(-2))} } =4^{b} \\4^{(7+2)} =4^{b}[/tex]
[tex]4^{9} =4^{b}[/tex]
[tex]b=9[/tex]
[tex]c. \frac{7^{9} }{7^{c} } =7^{12}[/tex]
[tex]7^{9-c} =7^{12}[/tex]
[tex]9-c=12[/tex]
[tex]c=9-12[/tex]
[tex]c=-3[/tex]
Hope this helps
The measure of an exterior angle of a regular polygon is 45º. How many sides does the polygon have?
Answers
Answer:The answer is 8 sides
Step-by-step explanation:
What is the volume of a sphere with a radius of 5.9 in, rounded to the nearest tenth of a cubic inch?
Answers
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=5.9 \end{cases}\implies V=\cfrac{4\pi (5.9)^3}{3}\implies V\approx 860.3~in^3[/tex]
Two similar cylinders have surface areas of 24 cm² and 54 cm². The volume of the smaller cylinder is 167 cm³.
What is the volume of the larger cylinder?
O 367 cm³
46 cm³
O 48
cm³
O 54
cm³
Answers
The volume of the larger cylinder will be 36π cm³. Then the correct option is A.
The complete question is attached below.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
The ratio of the volume to surface area will be
V / SA = πr²h / 2πrh
Then we have
Two similar cylinders have surface areas of 24 cm² and 54 cm².
The volume of the smaller cylinder is 16π cm³.
Then the volume of the larger cylinder will be
Let x be the volume of the larger cylinder.
Then we have
x / 54 = 16π / 24
x = 36π cm³
Then the correct option is A.
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