Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map f: X --> X such that f(x) = x- 1 is an example of continuous map is one to one and honto but is not a homemorphism .
What is a bijective function?A function f: A --> B is said to be bijective or bijection if it satisfies both injective (one-to-one function) and surjective (over-function) properties. Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map
f : X--> X such that f(x) = x- 1 ; x∈X (domain)
Now, we show that it is bijective, so
One to One : let x₁ and x₂ belongs to X such that f(x₁) = f(x₂) we have to show x₁= x₂
f(x₁) = f(x₂) => x₁ - 1 = x₂ - 1
=> x₁ = x₂ -1 + 1
=> x₁ = x₂
So, f(x) is one to one.
Onto : let y be a element of X ( co-domain) We can show that there exists x∈A such that f(x)=y. Choose x= f⁻¹(y) and so f(f⁻¹(y))=y. So for all y∈B, there exists an x∈A such that f(x)=y. Therefore, it is onto. Thus, f(x) is one to one and onto and continus( due to polynomial nature) i.e it is a continuous bijection from X to itself, but it is not a
homeomorphism, since the image of N is not open.
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Can anyone pls help me find the answer to this problem. I will give brainliest
Answer:
[tex]\log_{10}\sqrt{a} -\dfrac{3}{4}=\dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]
Step-by-step explanation:
Given:
[tex]x=\dfrac{\sqrt{10a\sqrt{0.1}}}{10}[/tex]
Therefore:
[tex]\implies \log_{10}x=\log_{10}\left(\dfrac{\sqrt{10a\sqrt{0.1}}}{10} \right)[/tex]
[tex]\textsf{Apply the log quotient law}: \quad \log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay[/tex]
[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-\log_{10}10[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-1[/tex]
[tex]\textsf{Apply radical rule: $\sqrt{ab}=\sqrt{a}\sqrt{b}$, \quad assuming $a \geq 0,\;b\geq 0$}[/tex]
[tex]\implies \log_{10}\left(\sqrt{10}\sqrt{a}\sqrt{\sqrt{0.1}}}\right)-1[/tex]
[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \log_{10}\sqrt{10} + \log_{10}\sqrt{a} + \log_{10}\sqrt{\sqrt{0.1}}}\right)-1[/tex]
Rewrite the radicals:
[tex]\implies \log_{10} \left(10\right)^{\frac{1}{2}} + \log_{10}\sqrt{a} + \log_{10}\left(0.1\right)^{\frac{1}{4}\right)-1[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \dfrac{1}{2}\log_{10} 10 + \log_{10}\sqrt{a} + \dfrac{1}{4}\log_{10}0.1-1[/tex]
[tex]\textsf{Apply log laws}: \quad \log_aa=1 \quad \textsf{and} \quad \log_a\dfrac{1}{a}=-1[/tex]
[tex]\implies \dfrac{1}{2}(1) + \log_{10}\sqrt{a} + \dfrac{1}{4}(-1)-1[/tex]
[tex]\implies \dfrac{1}{2}+ \log_{10}\sqrt{a} -\dfrac{1}{4}-1[/tex]
[tex]\implies \log_{10}\sqrt{a} -\dfrac{3}{4}[/tex]
If you want to simplify further:
[tex]\implies \log_{10}\left(a\right)^{\frac{1}{2}} -\dfrac{3}{4}[/tex]
[tex]\implies \dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]
Answer:
56
Step-by-step explanation: 10a+10 0.1 -=
I need help with this question
The equation has one repeated irrational number solution. thus Option A is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given equation is the quadratic equation by
[tex]-4x^2+ 24x-36=0[/tex]
We need to determine the number and type of solutions.
Noted that If the discriminant equals zero, the equation has one repeated rational number solution.
Since we know that If the discriminant is positive, then the equation has two real solutions.
And If the discriminant is negative, then the equation has two imaginary solutions.
To Calculate the discriminant of the equation [tex]-4x^2+ 24x-36=0[/tex] by substituting a= -4, b= 24 and c= -36 into the discriminant formula:
Since the discriminant equals zero, it follows that the equation has one repeated irrational number solution x = 3
The equation has one repeated irrational number solution.
Option A is correct.
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Correct 45.7395 to 3 decimal places
To correct a number to 3 decimal places, we need to round it to the nearest thousandth. The number 45.7395 is already very close to 45.740, which is the nearest thousandth. Therefore, we can round 45.7395 to 45.740, which is the correct answer to 3 decimal places.
Please help will mark Brainly
The equation of the line that includes CD, in slope-intercept form, is: B. y = -4/3x + 2.
How to Write the Equations of Parallel Lines and Perpendicular Lines?To write the equations of two lines that are parallel or perpendicular to each other, recall that parallel lines have the same slope (m), while perpendicular lines have slopes that are negative reciprocals.
The slope of y = 3/4x - 11 is 3/4. The negative reciprocal of 3/4 is -4/3. Therefore, the slope of AB that is perpendicular to the graph of y = 3/4x - 11 is, m = -4/3.
Since the CD is parallel to AB, then CD will have the same slope of, m = -4/3.
To write the equation of the line that includes CD, substitute m = -4/3 and (a, b) = (-6, 10) into y - b = m(x - a):
y - 10 = -4/3(x + 6)
Rewrite in slope-intercept form:
y - 10 = -4/3x - 8
y = -4/3x - 8 + 10
y = -4/3x + 2
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3. Find the composition (fog)(-2) for the functions f(x) = 2x+1 and g(x)=x²-3
Answer:
3
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=2x+1\\g(x)=x^2-3\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
The given composite function f o g(-2) means to substitute the function g(-2) in place of the x in function f(x):
[tex]\begin{aligned}(f \circ g)(-2)&=f[g(-2)]\\&=2[g(-2)]+1\\&=2(2^2-3)+1\\&=2(4-3)+1\\&=2(1)+1\\&=2+1\\&=3\end{aligned}[/tex]
find -7x3x(-2)x(-5)x(-1) how do i simplify this?
Answer:
42
Step-by-step explanation:
To simplify the expression -7x3x(-2)x(-5)x(-1), we need to apply the rules of exponentiation and multiplication.
First, we note that the terms -7, -2, -5, and -1 are all negative numbers, which means that they will be multiplied together to give a positive result.
Next, we apply the rule that says that any term raised to the power of 0 is equal to 1. Since -1 raised to the 0 power is 1, this means that the expression -7x3x(-2)x(-5)x(-1) is equivalent to -7x3x(-2)x(-5)x1.
Next, we apply the rule that says that any term raised to the power of 1 is equal to itself. Since 3 raised to the 1 power is 3, and 5 raised to the 1 power is 5, this means that the expression -7x3x(-2)x(-5)x1 is equivalent to -7x3x(-2)x5x1.
Finally, we apply the rule that says that the product of any number and its multiplicative inverse (or reciprocal) is equal to 1. Since the reciprocal of 5 is 1/5, this means that the expression -7x3x(-2)x5x1 is equivalent to -7x3x(-2)x(1/5)x1.
We can now use the rules of multiplication to simplify the expression further. Since any number multiplied by 1 is equal to itself, this means that the expression -7x3x(-2)x(1/5)x1 is equivalent to -7x3x(-2)x(1/5).
Next, we use the rule that says that the product of two negative numbers is a positive number. This means that the expression -7x3x(-2)x(1/5) is equivalent to 7x3x2x(1/5).
Finally, we can apply the rules of exponentiation and multiplication to evaluate the expression. Since any number raised to the power of 1 is equal to itself, this means that the expression 7x3x2x(1/5) is equivalent to 7x3x2. We can then multiply these terms together to get the final result:
7x3x2 = 42
Therefore, the simplified expression is equal to 42.
PLEASE HELP WILL MARK BARINLIEST
Answer:
<CYZ = 60 degrees
Step-by-step explanation:
CY = CZ ==> both segments are radiuses of the circle since they both have
a CenterPoint at Point C and a point touching the edge of the
circle
CY = YZ ==> Since CY=CZ and YZ=CZ, CY also equal YZ. In addition, this
means that CY, YZ, and CZ are all radiuses of the circle
Hence, CY = YZ = CZ.
Since all sides of the triangle are equal, that means that all angles of the triangle are equal as well:
<CYZ + <CZY + <YCZ = 180 ==> 180 is the total degrees in a triangle
<CYZ + <CYZ + <CYZ = 180 ==> all angles have the same measure
3 * <CYZ = 180 ==> solve for <CYZ
(3 * <CYZ)/3 = 180/3 ==> divide by 3 on both sides to isolate <CYZ
<CYZ = 60 degrees
Answer: [tex]\angle CYZ=60^{\circ}[/tex]
Step-by-step explanation:
[tex]\overline{CZ}=\overline{CY}[/tex] (radii of a circle)
[tex]\implies \overline{YZ}=\overline{CZ}=\overline{CY}[/tex]
[tex]\therefore \angle CYZ=60^{\circ}[/tex] (equilateral triangle)
16.13- cerebral tumors and cell phone use. in a case-controlled study on cerebral tumors and cell phone use, tumors occurred more frequently on the same side of the head where cellular telephones had been used in 26 of 41 cases. test the hypothesis that there is an equal distribution of contralaterial and ipsilateral tumors in the population. use a two-sided alternative.
Null Hypothesis: H0: There is an equal distribution of contralateral and ipsilateral tumors in the population.Ha: There is not an equal distribution of contralateral and ipsilateral tumors in the population.
1) Calculate the observed value:
The observed value is 26 out of 41 cases.
2) Calculate the expected value:
The expected value is 20.5 out of 41 cases.
3) Calculate the test statistic:
The test statistic is (26-20.5)/sqrt(20.5) = 2.44
4) State the critical value:
The critical value for a two-sided test with a significance level of 0.05 is 1.96.
5) The test statistic (2.44) is greater than the critical value (1.96), so we reject the null hypothesis and conclude that there is not an equal distribution of contralateral and ipsilateral tumors in the population.
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of 649 adults selected randomly from one town, 54 of them smoke. construct a 92.5 percent n interval for the true percentage of all adults in the town that smoke.
The 92.5% of confidence interval for the percentage of adults is
(-1.176 , 1.342).
as per given in the question,
The total number of adults (n) is 649
The number of smokers (x) = 54
the probability of getting a smoker is P =x/n
=> P = 54/649
=> 0.083
not getting a smoker is
1 - P = 1-0.083
=> 0.916
At 92.5% confidence level the Z critical value is ,
[tex]\alpha[/tex] = 1 - 92.5%
=> 1 - 0.925
=> 0.075
[tex]\alpha[/tex] / 2 = 0.075/ 2
=> 0.0375
now,
for the two tail test
Z[tex]\alpha[/tex]/2
= Z(0.0375)
= 1.7805
Margin of error
E = [tex]Z\alpha / 2 * \sqrt{( p * (1 - p) / n)}[/tex]
= 1.780 [tex]\times (\sqrt{((0.083 \times 0.916 ) / 649)}[/tex]
= 1.2596
A 92.5 % confidence interval for population proportion p is ,
P- E < P < P + E
0.083- 1.259 < P < 0.083 + 1.259
-1.176 < p < 1.342
(-1.176 , 1.342) is the interval
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According to a recent poll the percentage of Americans who would vote for the incumbent president is 53%. If a random sample of 100 people in New York results in 45% who would vote for the incumbent, test the claim that the percentage of people in New York who would vote for the incumbent president is different from 53%. Use a 0.10 significance level.
H0: p = 0.53. Ha: p ≠ 0.53.
α = 0.10
Test statistic: z = -1.60. P-Value = 0.1090
State your conclusion about H0.
Draw a new sample.
Do not reject H0
Reject H0
Reject Ha
Do not reject Ha
We cannot conclude that the percentage of people in New York who would vote for the incumbent president is different from 53%.
The correct answer is B) Do not reject H0.
What is a null hypothesis in probability?
The null hypothesis is a typical statistical theory that suggests that no statistical relationship and significance exists in a set of given single observed variables, between two sets of observed data and measured phenomena.
In this situation, the null hypothesis H0 is that the percentage of people in New York who would vote for the incumbent president is equal to 53%. The alternative hypothesis Ha is that the percentage of people in New York who would vote for the incumbent president is different from 53%.
The test statistic for this hypothesis test is z = -1.60. This means that the sample result of 45% is 1.60 standard deviations away from the hypothesized value of 53%.
The p-value is the probability of observing a test statistic as extreme as or more extreme than the one observed, given that the null hypothesis is true. In this case, the p-value is 0.1090, which is greater than the significance level of 0.10.
Since the p-value is greater than the significance level, we do not have sufficient evidence to reject the null hypothesis.
Hence, we cannot conclude that the percentage of people in New York who would vote for the incumbent president is different from 53%.
The correct answer is B) Do not reject H0.
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PLEASE HELP
find the sum of ( 2.25 x 10^19) and ( 6.7 x 10^17) Write the answer using proper scientific notation.
A) 231.7 X 10^15
B) 2.317 X10^19
C) 231.7 X 10^17
D) 2.317 X 10^15
Answer:
Step-by-step explanation:
The sum of (2.25 x 10^19) and (6.7 x 10^17) is (2.317 x 10^19).
To find the sum of these two numbers, we first need to line up the decimal points and add the numbers as we would with any other addition problem:
2.25 x 10^19
+ 6.7 x 10^17
Then, we can carry the 1 and add the numbers:
2.25 x 10^19
6.7 x 10^17
2.317 x 10^19
The sum of these two numbers is 2.317 x 10^19, which is equal to choice B.
One leg of a right triangle is 2 feet longer than the other leg. The hypotenuse is 10 feet long. Find the length of the legs of the triangle?
The lengths of the right-angled triangle are 6 and 8.
What is a right triangle?A right-angled triangled is a triangle that has one of its angles equal to 90°. The sum of the other two interior angles is also equal to 90°.
What is Pythagoras theorem?The Pythagoras theorem relates the three sides of a right-angled triangle through a simple equation. According to the Pythagoras theorem,
hypotenuse^2 = base^2 + opposite^2
Let base = b, so opposite = b + 2
So,
10^2 = b^2 + (b+2)^2
100 = b^2 + b^2 + 4b + 4
100 = 2b^2 + 4b + 4
50 = b^2 + 2b + 2
b^2 + 2b - 48 = 0
solving this quadratic equation gives, b = 6 and b = -8. Since length cannot be negative, the base is 6 feet and the opposite is 8 feet.
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Show that the plane and line with the given equations intersect, and then find the acute angle of intersection between them. (Give the angle in degrees and round to one decimal place.) The plane given by x + y + 2z = 0 and the line given by x = 2 + t y = 1 - 2t z = 3 + t. Substituting the parametric equations for the line into the equation for the plane and solving for t gives t = so that the plane and the line intersect at the point (x, y, z) = (). What is the acute angle of intersection? theta = degree
The acute angle of intersection is 5.2°.
What is acute angle?
Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.
The direction vector normal to the plane is ...
n = (1, 1, 3)
The direction vector of the line is ...
m = (1, -3, 1)
Then the angle θ between them can be found from the dot product:
n•m = |n|·|m|·cos(θ)
(1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)
1 = 11·cos(θ)
θ = arccos(1/11) ≈ 84.8°
This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, the line and plane must intersect.
acute angle = 90° -84.8° = 5.2°
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yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $70 and costs and costs and additional $0.30 per mile driven. The second plane has no initial fee but costs $0.80 per mile driven. How many miles would Yolanda need to drive for the two plans to cost the same?
The two plans will cost the same when Yolanda has driven 233 miles distance. That is, $70 + (0.30 x 233) = $233 = 0.80 x 233.
To find out how many miles Yolanda needs to drive for the two plans to cost the same, we need to set up an equation. The equation should calculate the total cost of each plan. For the first plan, the total cost is the initial fee plus the cost of the miles driven. For the second plan, the total cost is just the cost of the miles driven. We can then set the two equations equal to each other and solve for the number of miles distance driven. The final result is that Yolanda needs to drive 233 miles for the two plans to cost the same.
Plan 1: C = F + (D × CPM)
Plan 2: C = (D × CPM)
Plan 1 = Plan 2
F + (D × CPM) = (D × CPM)
F = 0
D × CPM = D × CPM
D = 233
Therefore, Yolanda needs to drive 233 miles for the two plans to cost the same.
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A rectangle has length that is 4 inches greater than twice its width. The perimeter of the rectangle is 26 inches. What is the area?
Gerolamo Cardano in his book, The Gambling Scholar, written in the early
1500s, considers the following carnival game. There are six dice. Each of the
dice has ve blank sides. The sixth side has a number between 1 and 6|a
dierent number on each die. The six dice are rolled and the player wins a
prize depending on the total of the numbers which turn up.
(a) Find, as Cardano did, the expected total without nding its distribution.
(b) Large prizes were given for large totals with a modest fee to play the
game. Explain why this could be done.
Therefore , [tex](\frac{1}{6})^{2}[/tex] is the probability of getting 5 of same number on all the dice.
what is probability?The probability of winning is actually closer to 1/3 (25/72). Carnival game operators want you to think that a game is fair like I did, so that you will play. If you knew that the probability of winning a game was only about 1/3, most likely you would not waste your money.
Mathematical descriptions of the likelihood that an event will occur or that a claim will be true are called probabilities.
Here,
[tex](\frac{1}{6})^{2}[/tex] is the probability of getting 5 of same number on all the dice.
Therefore , [tex](\frac{1}{6})^{2}[/tex] is the probability of getting 5 of same number on all the dice.
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The lifetime X of a certain brand of sixty-watt light bulb is exponentially distributed with population mean 1000 hours, that is, 5.23 1 e/1000 1000 f(x) x > 0. If 30 light bulbs having this lifetime distribution are placed on test, find the probability that 10 or fewer of these light bulbs survive to time 1200 by (a) writing a mathematical expression, (b) giving an R statement that will compute the probability.
The function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.
Given, the lifetime X of a certain brand of sixty-watt light bulb is exponentially distributed with population mean 1000 hours.
That is, 5.231(e/1000)f(x) x > 0. I
f 30 light bulbs having this lifetime distribution are placed on test.
we have to find the probability that 10 or fewer of these light bulbs survive to time 1200.
as, we have to find the expression for the function f(x) so that 10 or fewer of the given light bulbs survive to time 1200.
f(x) = 1/1000×e^(-x/1000)
So, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.
Hence, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.
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help me find the slope
Answer: Rise over Run
Step-by-step explanation: Take the change in the x coordinates, and divide by the change in y coordinates.
For example, to find slope when given 2 coordinates:
(2,5) (5, 10)
The change in the x coordinates is 3, because from 2-->5 it moves 3 places to the right. (run)
The change in the y coordinates is 5, because from 5-->10 it moves 5 places upwards. (rise)
Use rise/run.
Rise= 5 (change in y coordinate)
Run = 3 (change in x coordinate)
5/3 is the slope.
On questions like #6, the slope is -3. That is because the equation for slope is y=mx+b.
m is the coefficient of the x, so -3 is the slope.
Likewise, the slope of #2 is 7. The slope of #10 is 3/4.
The ticket sales at a movie theater were $3,402. Adult tickets are $11, and senior tickets are $8. The number of senior tickets sold was 27 less than twice the number of adult tickets. Determine the number of adult tickets and senior tickets sold.
Answer:
Adults: 134
Senior: 241
Step-by-step explanation:
Known
Number of adult tickets sold: x
Revenue from adult tickets: $11x
Number of senior tickets sold: y
Revenue from senior tickets: $8y
From the problem, we found the equation [tex]y = 2x - 27[/tex] and 3,402 = 11x + 8y
Combining the two equation:
[tex]3,402 = 11x + 8(2x-27)\\3,402 = 11x + 16x - 216\\3,402 + 216 = 27x\\27x = 3,618[/tex]
Divided both side by 27
[tex]x = 134[/tex]
Since
[tex]y = 2x - 27[/tex]
Inserting the value of x,
[tex]y = 2(134) -27\\y = 268 - 27\\y = 241[/tex]
So, there are 134 adult tickets sold and 241 senior tickets sold.
It takes Christina 2 minutes to read one page of her 250 page book. Which of the following represents the appropriate domain and range for a function relating the total time she has spent reading the book, x, and the number of pages she has read, y?
Answer:
Domain: 0<=x<=500
Range: 0<=y<=250
Step-by-step explanation:
I'm not sure if this is what you asked for. She spend 2 minutes reading 1 page, there are 250 pages, therefore: 250*2=500
the range is simply the total pages
Hope this help!
consider the equation 6y+13=____+8
which value or expression can you write in the blank so the equation has no solution
0, 13, 5y, or 6y
Answer:
6y
Step-by-step explanation:
What can you remove form the left side that makes this a false equation?
It's 6y. So place 6y on the right side.
6y + 13 = 6y + 8
Subtract 6y from both sides.
13 = 8
Since 13 = 8 is a false statement, the equation 6y + 13 = 6y + 8 has no solution.
Answer: 6y
Step-by-step explanation:
i did the iready and got it right
its 6y
Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are rolled. Find P(X = 4). (Round your answer to two decimal places.)
The likelihood or the probability is 121, or 8.33%.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
We must make a table for easier comprehension in order to determine the P(x=4);
Refer to the attachment for table:
There are three different ways that P(x=4) can occur based on the table. Out of 36 possible results (6 x 6 = 36), they are (1,3), (2,2), and (3,1). As a result, the chance of the event is 363; it is then reduced to 121, or 8.33%.
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24. The average price of a new car is a function of the year it was purchased. In 1994.
the average price of a new car was $16.930. In 2002, the average price was
$19.126. Find the rate of change of the average price of a new car. Include units
in your answer.
please help me i’m struggling
The rate of change of the average price of the new car is $274.50 per year.
What is the rate of change?The rate of change of the average price of the new car is a function of the change in average price over the years and the change in the number of years.
Rate of change = change in the average price / change in the number of years
Rate of change = (price in 2002 - price in 1994) / difference in the number of years
Rate of change = (19,126 - 16,930) / (2002 - 1994)
Rate of change = 2196 / 8
Rate of change = $274.50
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start by thinking of the number 22 as divided into 22 individual items and the variables x1, x2, and x3 as three categories into which these items are placed. since each xi is a positive correct: your answer is correct. integer, start by placing one item in each category and distribute the remaining items among the categories. the number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. thus, the answer is 20 incorrect: your answer is incorrect. .
If the number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Then, the answer is 210 .
In the question ,
it is given that ,
number 22 is divided into 22 individual items ,
the three categories in which these items are placed are x₁, x₂ and x₃ .
x₁ + x₂ + x₃ = 22 .....equation(1)
(x₁ - 1) + (x₂ - 1) + (x₃ - 1) = 22 - 3 = 19
let a = x₁ - 1 , b = x₂ - 1 and c = x₃ - 1 .
Hence , a + b + c = 19 ....equation(2)
Now , because the number of solution of equation(1) excluding zero will be equal to the number of solutions of equation(2) including the zero .
So , we subtracted 1 from x₁, x₂ and x₃ respectively .
Now , we have to divide 19 into 3 parts where any part can be zero also or any part is a whole number .
For Example : let us have 19 apples , which must be divided into 3 parts by placing 2 J's among 19 A's .
Now we have reduced the problem to such that we have to find the permutation of 19 A's and 2 J's that is 21 characters in which every permutation is a solution .
So , the number of ways of arranging 21 characters in which 19 are same(A) and 2 are same (J)
= 21!/(2! * 19!)
= 21*10 = 210
It means there are 210 non negative integral solutions of a+b+c = 19 .
It means total positive solutions of x₁ + x₂ + x₃ = 22 is 210 .
Therefore , the number of solution to the equation is 210 .
The given question is incomplete , the complete question is
Start by thinking of the number 22 as divided into 22 individual items and the variables x₁, x₂, and x₃ as three categories into which these items are placed. since each [tex]x_{i}[/tex] is a positive integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is ______ .
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Given inputs A, B, C, D, E, design a CMOS circuit to implement the logic function: Y(not) = A(B+C) + D + E
Given inputs A, B, C, D, E, design a CMOS circuit to implement the logic function: Y(not) = A(B+C) + D + E has 5-c-mos, 5-pmos total 10 mos transistors
this can be realize by takeing three c-mos in parallel which gives ABC ,two c-mos are series which is in serires with
another c-mos whic gives D(A+B), now connect ABC and D(A+B) in series
the out put will be (ABC + D(A+B) )'
so we require total 6-mos and 6-pmos total 12mos transistors
F = AC + BD
pull down
this can be realize by takeing two c-mos in series which gives AB ,two cmos are in series
which whic gives BD, now connect AC and BD in parallel
pull up
this can be realize by takeing two c-mos in parallel which gives Ac ,two c-mos are in parallel
which whic gives BD, now connect AC and BD in series
the output is (AC+BD)'
to avoid the complement we have to connect the output to c-mos inverter then we get AC+BD
so we require 5-nmos, 5-pmos total 10 mos transistors
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Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
What is the probability that a randomly selected bike is green given that the bike has bike tires?
Simplify any fractions.
The probability that a randomly selected bike is green given that the bike has road bike tires is 0.66
Given :
Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event .
From the table given :
Total number of 6 road bikes = 4
Total road bikes = 2 + 4 = 6
Probability = 4 / 6
= 2 / 3
= 0.66
Hence the probability that a randomly selected bike is green given that the bike has road bike tires is 0.66 .
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show two examples of the associative property
Kiran was running around the track. The graph shows the time, t, he took to run various distances, d. The table shows his time in seconds after every three meters.
How long did it take Kiran to run 6 meters?
The time that it will take for Kiran to run 6 meters is; 2 seconds
How to interpret Function Tables?A function table is defined as a visual table that has columns and rows that display the function with regards to the input and output.
Now, the coordinates of the function table are given as;
(0, 0), (3, 1), (6, 2), (9, 3.2), (12, 3.8), (15, 4.6), (18, 6), (21, 6.9), (24, 8.09), (27, 9)
Now, the graph shows that the y-axis represents the time, t, he took to run various distances, d which is represented on the x-axis.
Now, we want to find the time that it takes Kiran to run 6 meters. From the graph and table attached, it is seen to be 2 seconds.
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Your goal here is to find the least squares line y(x) = mx + b for the following data: (-2, 1), (2, 1), (-1,-1), (0, -2), (2,-2), and (-2, 1) Feel free to use a calculator! The normal equation for determining the approximating parameters ħ and în are: Then the least squares line is: y(x) = = number + number
The least squares line , y = mx + b form from given data is y = ( -32/100 )x + ( -39/100).
We have an equation of line is
y(x) = mx + b --(1)
given data, (-2, 1), (2, 1),(-1,-1), (0,-2), (2,-2) and (-2, 1)
plugging each point on above equation we get, 1 = -2m + b ; 1 = 2m + b ; -1 = -m + b ; -2 = 0m + b ;
-2 = 2m +b ; 1 = -2m + b
The above equations can be written in matrix form as,
[ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] [ m ; b]
= [ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
AX = B
X = (Aᵀ A)⁻¹ AᵀB where Aᵀ is transpose of matrix A and (Aᵀ A)⁻¹ is inverse of (Aᵀ A).
AᵀA = [ -2 2 -1 0 2 -2 ; 1 1 1 1 1] [ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] = [ 17 -1 ; -1 6 ]
so, X = [ 17 -1 ; -1 6 ] ^-1 [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
let [ 17 -1 ; -1 6 ] = P
[ 17 -1 ; -1 6 ]⁻¹ = adj.P/det P
det P = 17×6 - 1 = 101
P⁻¹ = 1/101 [ 6 1 ; 1 17 ]
Now, X = 1/101 [ 6 1 ; 1 17 ] [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
=> X = 1/101[ 6 1 ; 1 17 ] [ -5 ; -2 ]
=> X = 1/101 [ -32 ; -39] = [ -32/100 ; -39/100 ]
=> [ m ; b ] = [ -32/100 ; -39/100 ]
=> m = -32/100 , b = -39/100
then, y = mx + b
=> y = ( -32/100 )x + ( -39/100)
Hence, the required equation is
y = ( -32/100 )x + ( -39/100).
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you are given a rectangular matrix m. your goal is to write a program that, if an element of m is equal to 0, sets that element's entire row and column to 0.
The program for a given rectangular matrix m, if an element of m is equal to 0, sets that element's entire row and column to 0
def zeroify_matrix(m):
rows = len(m)
cols = len(m[0])
rows_to_zeroify = []
cols_to_zeroify = []
for i in range(rows):
for j in range(cols):
if m[i][j] == 0:
rows_to_zeroify.append(i)
cols_to_zeroify.append(j)
for i in range(rows):
for j in range(cols):
if i in rows_to_zeroify or j in cols_to_zeroify:
m[i][j] = 0
return m
It is coded in python for the given problem of recreating a rectangular matrix, for a single element to be 0, the whole row nad column will contain zero elements.
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