discr etemathematics deals with objects that can assume only distinct, separate values like integers. information technology needs separate values so as to be accepted
Final answer:
Discrete mathematics is crucial in Information Technology for creating efficient algorithms in cryptography, network communication, and software development, as well as for driving insights from data analysis.
Explanation:
The importance of discrete mathematics in Information Technology cannot be understated, particularly due to its fundamental role in various IT applications. Discrete mathematics provides the theoretical underpinning for computer science and information technology, where discontinuous structures are observed, such as computer algorithms, software development, and data structures. It allows IT professionals to design efficient algorithms for data encryption, network communication, and software development.In cryptography, discrete mathematics helps in securing online transactions by creating algorithms that are easy to compute in one direction (like multiplying large numbers) but challenging to reverse (like factoring into primes). Moreover, discrete mathematics is central to understanding and working with concepts such as recursion, combinatorics, and graph theory which are essential in programming and data analysis.Its principles also facilitate the quantification of information as noted by C. Shannon, aiding in the differentiation between mere data and valuable information that can drive insights and business decisions. Discrete mathematics also provides the tools for approximating continuous mathematical operations, which is vital in scientific computing and the practical implementation of IT solutions.(6-3(cube root of 6)/(cube root of 9)
For this case we must simplify the following expression:
[tex]\frac {6-3 \sqrt [3] {6}} {\sqrt [3] {9}}[/tex]
Multiplying the numerator and denominator by[tex](\sqrt [3] {9}) ^ 2[/tex]
[tex]\frac {6-3 \sqrt [3] {6}} {\sqrt [3] {9}} * \frac {(\sqrt [3] {9}) ^ 2} {(\sqrt [3] { 9}) ^ 2} =[/tex]
We rewrite:
[tex]\frac {\frac {6-3 \sqrt [3] {6}} * (\sqrt [3] {9}) ^ 2} {\sqrt [3] {9} * (\sqrt [3] {9 }) ^ 2} =[/tex]
By properties of powers we have that:
[tex]a ^ m * a ^ n = a ^ {m + n}\\\frac {(6-3 \sqrt [3] {6}) * (\sqrt [3] {9}) ^ 2} {(\sqrt [3] {9}) ^ 3} =\\\frac {(6-3 \sqrt [3] {6}) * (\sqrt [3] {9}) ^ 2} {9} =[/tex]
We rewrite, moving the exponent within the radical:
[tex]\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {9 ^ 2}} {9} =\\\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {81}} {9} =[/tex]
We can rewrite[tex]3 * 3 ^ 3 = 81[/tex]
[tex]\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {3 * 3 ^ 3}} {9} =[/tex]
We simplify:
[tex]\frac {(6-3 \sqrt [3] {6}) * 3 \sqrt [3] {3}} {9} =[/tex]
We apply distributive property:
[tex]\frac {18 \sqrt [3] {3} -9 \sqrt [3] {18}} {9} =[/tex]
Simplifying we finally have:
[tex]2 \sqrt [3] {3} - \sqrt [3] {18}[/tex]
Answer:
[tex]2 \sqrt [3] {3} - \sqrt [3] {18}[/tex]
Destiny bought 10 1/2 yards of material for costumes for the city pageant she will use one and 140 yards of the material to make each costume how many costumes can destiny complete
Answer:
She can complete 8 costumes
Step-by-step explanation:
Answer:
8 costumes
Step-by-step explanation:
Suppose that 7% of the general population has a disease and that the test for the disease is accurate 70% of the time. What is the probability of testing positive for the disease.
Answer:
0.049
4.9 % of probability
Step-by-step explanation:
The probability of having the disease is equal to 7%
The probability of testing positive, having the disease is equal to 70%
We are looking for the probability of testing positive.
For that, we need to multiply the probabilities to find the result
P = (0.07)*(0.7)
P = 0.049
P = 4.9%
PLEASE HELP ME i'm struggling in math what is x? if i carry the 3 over does that mean i add or multiply? Brainliest answer!!!! 30 points
Answer:
carry over the three means to add i hope you are happy
Step-by-step explanation:
Answer: Usually you have to find the value of X, for example if 9 - x = 5, then you have to subtract 5 from the nine and you get 4, and when you carry three over that means you have to regroup, for example
902 +
459
so 9+2=11, so you put 1 right there
902 +
459
.....1
and you carry the other 1 next to the 0, then it will become 10 + 5,
hope this helps, if you still don't get it tell me
Step-by-step explanation:
+
A can contains 24 fluid ounces of juice. How many pints of fruit juice does the can contain?
Answer:
The can contains 1.5 pints of fruit juice.
Step-by-step explanation:
A can contains 24 fluid ounces of juice.
We have to convert the amount of juice from ounce to pints.
As we know that 1 fluid ounces = [tex]\frac{1}{16}[/tex] pints or 0.0624 pints.
So 24 fluid ounces = 0.0625 × 24 = 1.5 pints.
Therefore, The can contains 1.5 pints of fruit juice.
The can contain 1.5 pints of fruit juice
How many pints of fruit juice does the can contain?A pint is equal to 16 fluid ounces. That is:
1 pint = 16 fluid ounces
To find out how many pints of juice the can contains, we need to divide the number of fluid ounces by the number of fluid ounces in a pint.
Thus, 24 fluid ounces of juice in pint will be:
24/ 16 = 1.5 pints
Therefore, the can contains 1.5 pints of fruit juice.
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Find the area of the shape shown below. (Please try to break down.)
The answer is:
The area of the shape is: [tex]10units^{2}[/tex]
[tex]TotalArea=10units^{2}[/tex]
Why?To solve the problem, we must consider that the shape is formed by two right triangles and a square, so, to calculate its area, we need to calculate the areas of the two triangles and square, and then, add them.
So, we are given the following information:
Smallest triangle:
[tex]base=2units\\height=2units[/tex]
Square:
[tex]base=2units\\height=2units[/tex]
Largest triangle:
[tex]base=4\\height=2[/tex]
CalculationsSmallest triangle:
We can calculate the area of a triangle using the following formula:
[tex]A=\frac{base*height}{2}[/tex]
So, substituting, we have:
[tex]A=\frac{2units*2units}{2}=2units^{2}[/tex]
Square:
We can calculate the area of a square using the following formula:
[tex]A=base*height[/tex]
So, substituting, we have:
[tex]A=2units*2units=4units^{2}[/tex]
Largest triangle:
We can calculate the area of a triangle using the following formula:
[tex]A=\frac{base*height}{2}[/tex]
So, substituting, we have:
[tex]A=\frac{4units*2units}{2}=4units^{2}[/tex]
Now, calculating the area of the entire shape, we have:
[tex]TotalArea=SmallestTriangleArea+SquareArea+LargestTriangleArea\\\\TotalArea=2units^{2} +4units^{2} +4units^{2} =10units^{2}[/tex]
Hence, the area of the shape is: [tex]10units^{2}[/tex]
[tex]TotalArea=10units^{2}[/tex]
Have a nice day!
Answer:56
Step-by-step explanation:
What is the hypothesis of the given statement? If pigs had wings, you could fly.
The hypothesis of the given statement is that if pigs had wings, you could fly.
Explanation:The hypothesis of the given statement is that if pigs had wings, you could fly.
This statement is an example of a hypothetical scenario, as pigs do not actually have wings. The hypothesis implies that if pigs did have wings, it would enable flight for humans.
It is important to note that this statement is purely hypothetical and does not reflect the reality of pigs having wings.
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[(8 x 7)] - 35 divided by 3 + 2
[tex]\frac{21}{5}[/tex]
Start with your equation: [tex]\frac{(8 * 7) - 35}{3 + 2}[/tex]
Now, simplify the multiplication: [tex]\frac{56 - 35}{3 + 2}[/tex]
Then, simplify the addition and subtraction: [tex]\frac{21}{5}[/tex]
This fraction cannot be simplified further, so it is the answer.
Answer:
[tex]\frac{\left(\left(8x\cdot \:7\right)\right)-35}{3+2}=\frac{56x-35}{5}[/tex]
[tex]\frac{8x\cdot \:7-35}{3+2}\\\mathrm{Multiply\:the\:numbers:}\:8\cdot \:7=56; =\frac{56x-35}{3+2}\\\mathrm{Add\:the\:numbers:}\:3+2=5; =\frac{56x-35}{5}[/tex]
Hope this helps and have a great day!!!
[tex]Sofia[/tex]
What is 1 hundreth + 3 tenths
Answer: 0.31
Step-by-step explanation:
For a certain spinner, if we expect to win a prize four times in sixty tries, what is the theoretical probability of winning a prize?
A) 1/30
B) 1/20
C) 1/15
D) 1/5
Answer:
C
Step-by-step explanation:
60 divided by 4, is fifteen, and 1/15 is 4/60 simplified.
Answer: A is maybe the answer.
Step-by-step explanation:
The expression -3m - [2m + (5 - m)] + 7 was simplified as 2 - 4m. Without simplifying, explain how you can show that it has been simplified correctly.
Answer: It is correctly simplified form.
Step-by-step explanation:
Since we have given that
[tex]-3m-[2x+(5-m)]+7[/tex]
We need to simplify the above expression:
[tex]-3m-2m-5+m+7\\\\=-5m+m+2(\text{gather the like terms})\\\\=-4m+2\\\\=2-4m[/tex]
So, [tex]-3m-[2x+(5-m)]+7=2-4m[/tex]
Hence, it is correctly simplified form.
find the value of x 5x+6-2=9
A.1
B.5
C.3/7 fraction
D. 5/7 fraction
Answer:
A
Step-by-step explanation:
Given
5x + 6 - 2 = 9, that is
5x + 4 = 9 ( subtract 4 from both sides )
5x = 5 ( divide both sides by 5 )
x = 1 → A
Which is the best estimate for the percent that is represented by the shaded portion of the diagram? 30% 36% 38% 40%
Answer:
Three of the boxes out of the eight are shaded.
So, 3/8 is .375 which is around 38%.
Hello there!
In this diagram, there are a total of 8 squares, and 3 of them are shaded. This means that 3/8 of them are shaded, and to find what percent this is, divide 3 by 8 and multiply what you get by 100.
3 divided by 8 = 0.375
0.375 x 100 = 37.5%.
37.5% is closest to 38%, so that is your answer!
I hope this helps and have a great rest of your day!
Which of the following equations corresponds to the graph below
the answer would be d because it goes down 2 and over 1
The answer is d because of the y intercept is -1 and the slope is -2 according to y=mx+b
A state park had a population of 330 rabbits. The population grew, with continuous compounding at a rate of 15% per year for 12years. How many rabbits were in the park after the 12 years?
330(1.15)^12=1765.58
The population of rabbits grew continuous compounding so formula for continuously compounded will apply.
The rabbits were in the park after 12 years is 1,996 rabbits.
Given:
The population of rabbit is [tex]P=330[/tex].
The rabbit increasing rate is [tex]r=15\%[/tex].
Time is [tex]t=12\:\rm year[/tex].
Apply the formula for continuously compounded to calculate the number of rabbit after 12 year.
[tex]A=Pe^{rt}[/tex]
Substitute the value.
[tex]A=330.00(2.71828)^{(0.15)(12)}\\A=1,996.38 \\A\approx1996[/tex]
Thus, the rabbits were in the park after 12 years is 1,996 rabbits.
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answer for a math problem i am stuck on
Answer:
m = 116 and a = 105
Step-by-step explanation:
The angle m and 64 are supplementary angles because line of a straight line separated by another straight line. This means that m + 64 = 180, or m = 116.
The sum of all the angles in a quadralateral like this one is 360. So angle a = 360 - 89 - 50 - 116, or a =105.
Answer:
m=116 a=105
Step-by-step explanation:
there is 360 degrees inside a square, i found M by subtracting 180 - 64, because there is a 180 degree angle on a flat line and it showed the other side has 64 degrees, and since we know that m is 180-64=116, we can find A. take the total of degree of the inside of the square which is 360, and subtract all the other angle degrees from it to find the missing number. 360-89-50-116=A. A= 105 degrees.
im sorry if this made your problem more confusing, its hard to explain with words alone
What is 9 +[(4.2- 3.3)+(6.4/0.8)] x 3
answer. 35.7
explanation: bedmas is important in this question. subtract and divide in the brackets first. add the two numbers in the brackets second. multiply the 8.9 by the 3. then add the 9 to the 26.7
Answer:
35.7
Step-by-step explanation:
9 +[(4.2- 3.3)+(6.4/0.8)] x 3
(4.2- 3.3) = 0.9
(6.4/0.8) = 8
9 + (0.9 +80) × 3 = 9 + 8.9 × 3
= 9+26.7
= 35.7
Solve the proportion 15t/5=(2t+3)/6.
[tex] \frac{15t}{5} = \frac{2t + 3}{6} \\ 90t = 10t + 15 \\ 80t = 15 \\ t = 0.1875[/tex]
How many solutions exist for the given equation 0.75(x+40)=0.35(x+20)+(x+20)
Answer: Wow! That's a tough one, but x = 5 is the only possibility
Step-by-step explanation:
What is the probability of flipping a coin 10 times and getting tails 7 times ? Round your answer to the nearest tenth of a percent.
Answer:
Option C: 11.7%
Step-by-step explanation:
The number of elements in sample space when a coin is flipped 10 times will be:
[tex]n(S) = 2^{10} \\= 1024[/tex]
Let A be the event that the tails appear 7 times:
Then,
[tex]C_{(n,k)}=\frac{n!}{(k!)(n-k)!} \\where\\n=population\\k=picks\\In our case, k =7\\and\\n=10\\C_{(10,7)}= \frac{10!}{(7!)(10-3)!}\\= 120\\So, \\P(A) = \frac{n(A)}{n(S)} \\P(A) = \frac{120}{1024} \\= 0.1171\\[/tex]
Converting into percentage:
[tex]P(A) = 0.1171*100=11.7%[/tex]
So, option C is correct ..
Answer:4.4%
Step-by-step explanation:just took it
Factor the following polynomial 14c^2+15c
Answer:
c • (15c2 + 14)
Step-by-step explanation:
14c + (3•5c3)
3.1 Pull out like factors :
15c3 + 14c = c • (15c2 + 14)
Answer:
c ( 1 4 c + 1 5 )
Step-by-step explanation:
1 4 c ² + 1 5 c
Factor out c
c ( 1 4 c + 1 5 )
Which best explains or justifies step 2
Answer B
Step-by-step explanation:
The equation of a parabola is given. y=1/4x^2−3x+18 What are the coordinates of the focus of the parabola?
Answer:
(6,10)
Step-by-step explanation:
Used a calculator
What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?
7ab3
6a4b
42a5b4
77a8b7
7ab3
To find the GCF, find the number(s) that that have the highest multiple factor in common. The first numbers can all be divided by 7, there's 1 a in common, and 3 b's in common. Combine them since you have variables and numerical values to get 7ab3 .
The greatest common factor of 42a⁵b³, 35a³b⁴, and 42ab⁴ is,
⇒ 7ab³
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
We have to given that;
The numbers are,
⇒ 42a⁵b³, 35a³b⁴, and 42ab⁴
Now, We can formulate;
⇒ GCD {42, 35, 42 } = 7
⇒ GCD {a⁵, a³, a } = a
⇒ GCD {b³ , b⁴, b⁴} = b³
Thus, The greatest common factor of 42a⁵b³, 35a³b⁴, and 42ab⁴ is,
⇒ 7ab³
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Complete the table, and make a graph showing the relationship between quarts and pints
Step-by-step explanation:
One quart equals to Two pints.
As a result to find the number of quarts that equal a certain number of pints you multiply number of quarts by 2
FORMULA= (P=Q×2)
1Q=2P
2Q=4P
3Q=6P
4Q=8P
if amanda got on the bus at 2:40 and got off the bus at 3:15. how long was amanda on the bus
Answer:
35 minutes
Step-by-step explanation:
Answer:
35 minutes
Step-by-step explanation:
She was on the bus for :20 before 3:00 and for :15 after 3:00, for a total of ...
:20 +:15 = :35
That is, 35 minutes.
___
There are 60 minutes in an hour. If you like, you can change an hour to 60 minutes and write the exit time as 3:15 = 2:75. Then you can perform the subtraction
2:75 -2:40 = 0:35
Six less than what number is eighteen?
3
12
24
108
Answer:
24
Step-by-step explanation:
X - 6 = 18
Add 6 to both sides
x = 24
Answer:
the answer is 24
Step-by-step explanation:
You are to demonstrate that you understand what represents a function and what does not represent a function. You may do this by either writing a paragraph using complete sentences or drawing pictures with labels.
we are required to demonstrate that we understand what represents a function and what does not represent a function by writing a paragraph which can be given as:
We know that functions are mathematical entities that assign unique outputs to given inputs. In other words, a function can't have repeated values in the input repeated x-value.
For example consider the relation {(1,4), (1,5), (2,6), (3,7), (4,8), (5,9)}.
We see that above relation has repeated x-value "1" which is assigned to two different output values 4 and 5. So by definition of function, above relation can't be a function.
8 less than the product of a number n and 1/5 is no more than 95
Answer:
(n/5)-8≤95
Step-by-step explanation:
The solution for the given problem is : [tex]\( n \leq 515 \)[/tex].
Sure, let's solve the problem step by step.
Given: [tex]\( \frac{1}{5}n - 8 \leq 95 \)[/tex]
To solve for [tex]\( n \),[/tex] we'll first add 8 to both sides of the inequality:
[tex]\( \frac{1}{5}n \leq 95 + 8 \)[/tex]
[tex]\( \frac{1}{5}n \leq 103 \)[/tex]
Now, we'll multiply both sides by 5 to isolate[tex]\( n \)[/tex]:
[tex]\( 5 \times \frac{1}{5}n \leq 5 \times 103 \)[/tex]
[tex]\( n \leq 515 \)[/tex]
So, the solution is[tex]\( n \leq 515 \)[/tex]
In conclusion, the solution to the problem is [tex]\( n \leq 515 \)[/tex]. We reached this conclusion by carefully manipulating the inequality step by step to isolate [tex]\( n \).[/tex] This process ensures that our solution is accurate and follows the rules of algebra.
Complete question:
8 less than the product of a number n and 1/5 is no more than 95
What is the main purpose of the reproductive system in organisms on Earth?
A.
to enable an organism to make more of its kind
B.
to control the level of various hormones in the organism
C.
to allow an organism to move through contractile forces
D.
to provide leverage for movement and organ protection
Answer:
A.
Step-by-step explanation:
That's what I would say, at least.