Final answer:
There are 108 students in the class, calculated using the data from the class survey with the principle of inclusion-exclusion.
Explanation:
To find out how many students are in the class, we should analyze the survey data provided. We know that:
29 students watched TV on Monday.
24 students watched TV on Tuesday.
25 students watched TV on Wednesday.
13 students watched TV on only Monday.
9 students watched TV on only Tuesday.
10 students watched TV on only Wednesday.
12 students watched TV on all three days.
14 students watched TV on both Monday and Tuesday.
Since 14 watched on both Monday and Tuesday, and 12 of those also watched on Wednesday, there are 14 - 12 = 2 who watched on Monday and Tuesday but not Wednesday.
We can now calculate the total number of students using the principle of inclusion-exclusion:
Start with the total number of students who watched TV each day: 29 + 24 + 25 = 78.
Subtract the students who were counted twice because they watched on two different days: 78 - 2 (from Monday and Tuesday) = 76.
Subtract the students who watched on all three days, as they have been counted three times: 76 - 12 = 64.
Add back the number of students who watched TV on all three days to account for their previous subtraction: 64 + 12 = 76.
Add the students who watched TV on only one specific day to avoid double-counting those who were included in the two and three days' viewership: 76 + 13 (Monday only) + 9 (Tuesday only) + 10 (Wednesday only) = 108.
Therefore, there are 108 students in the class.
The line contains the point (9,-9) and has the same y-intercept as y + 1 = 4 (x - 2). Write the equation of this line in slope-intercept form.
Answer:
The equation for this line, in slope-intercept form, is given by:
[tex]y = - 9[/tex]
Step-by-step explanation:
The equation of a line in the slope-intercept form has the following format:
[tex]y = ax + b[/tex]
In which a is the slope of the line and b is the y intercept.
Solution:
The line has the same y-intercept as [tex]y + 1 = 4 (x - 2)[/tex].
So, we have to find the y-intercept of this equation
[tex]y + 1 = 4 (x - 2)[/tex]
[tex]y = 4x - 8 - 1[/tex]
[tex]y = 4x - 9[/tex]
This equation, has the y-intercept = -9. Since this line has the same intercept, we have that [tex]b=-9[/tex].
Fow now, the equation of this line is
[tex]y = ax - 9[/tex]
The line contains the point [tex](9,-9)[/tex]
This means that when [tex]x = 9, y = -9[/tex]. We replace this in the equation and find a
[tex]y = ax - 9[/tex]
[tex]-9 = 9a - 9[/tex]
[tex]9a = 0[/tex]
[tex]a = \frac{0}{9}[/tex]
[tex]a = 0[/tex]
The equation for this line, in slope-intercept form, is given by:
[tex]y = - 9[/tex]
Plato math help please
Answer: option (C)
Step-by-step explanation: The slope of a linear function is undetermined when the line is parallel respect to the y-axis. In the current problem there is no way to observe such geometrical issue, but if we consider how to derive the slope using the following expression; [tex]m=\frac{\Delta y}{\Delta x}= \frac{y_{2}-y_{1}}{x_2-x_{1}}[/tex].
With the previous equation, we have
[tex]a) for P_{1}(-1,1), P_{2}(1,-1) m=\frac{\Delta y}{\Delta x}= \frac{-1-1}{1-(1)}=\frac{-2}{2}=1\\[/tex], therefore the slope is defined
[tex]b) for P_{1}(-2,2), P_{2}(2,2) m=\frac{\Delta y}{\Delta x}= \frac{2-2}{2-(2)}=\frac{0}{4}=0\\[/tex], therefore the slope is defined
[tex]c) for P_{1}(-3,3), P_{2}(-3,3) m=\frac{\Delta y}{\Delta x}= \frac{3-(-3)}{-3-(-3)}=\frac{6}{0}=undetermined\\[/tex]
[tex]d) for P_{1}(-4,4), P_{2}(4,4) m=\frac{\Delta y}{\Delta x}= \frac{4-(-4)}{4-(-4)}=\frac{8}{8}=1\\[/tex]
In this case, the option (C) shows that is not possible to divide over zero. Given such issue, the slope is undetermined and therefore it is a vertical line parallel to y-axis.
Estimate the number of steps you would have to take to walk a distance equal to the circumference of the Earth. (We estimate that the length of a step for an average person is about 18 inches, or roughly 0.5 m. The radius of the Earth is 6.38 ✕ 106 m.)
Answer:
8771408311 steps ( approx )
Step-by-step explanation:
Given,
The radius of the earth,
[tex]r=6.38\times 10^6[/tex]
So, the circumference of the earth,
[tex]S=2\pi (r)[/tex]
[tex]=2\times \frac{22}{7}\times (6.38\times 10^8)[/tex]
[tex]=4.0102857143\times 10^9\text{ meters}[/tex]
∵ 1 meter = 39.3701 inches
[tex]\implies S =1.578853496\times 10^{11}\text{ inches }[/tex]
Also, the length of one step = 18 inches
Hence, the total number of steps = [tex]\frac{1.578853496\times 10^{11}}{18}[/tex]
[tex]= 8.7714083111\times 10^9[/tex]
[tex]\approx 8771408311[/tex]
April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 11 feet high. The height of the arrow is given by the function h(t) = -16t2 + 64t + 11, where t is the time is seconds. What is the maximum height of the arrow?
Answer:
Maximum height of the arrow is 203 feets
Step-by-step explanation:
It is given that,
The height of the arrow as a function of time t is given by :
[tex]h(t)=-16t^2+64t+11[/tex]..........(1)
t is in seconds
We need to find the maximum height of the arrow. For maximum height differentiating equation (1) wrt t as :
[tex]\dfrac{dh(t)}{dt}=0[/tex]
[tex]\dfrac{d(-16t^2+64t+11)}{dt}=0[/tex]
[tex]-32t+64=0[/tex]
t = 2 seconds
Put the value of t in equation (1) as :
[tex]h(t)=-16(2)^2+64(2)+11[/tex]
h(t) = 203 feet
So, the maximum height reached by the arrow is 203 feet. Hence, this is the required solution.
1/4÷(-2/3) =3/8 she is right now did she get the answer
Answer:
see below for the working
Step-by-step explanation:
Dividing by a number is the same as multiplying by the inverse of that number.
[tex]\displaystyle\frac{\left(\frac{1}{4}\right)}{\left(-\frac{2}{3}\right)}=-\frac{1}{4}\cdot\frac{3}{2}=-\frac{3}{4\cdot 2}=-\frac{3}{8}[/tex]
Select the best answer that defines the radius of a circle.
The radius is a line segment joining two distinct points on the circle.
The radius is a line segment that starts at the center of the circle and ends at a point on the circle.
The radius is the boundary of a circle.
The radius is a line segment that starts at one point on the circle, passes through the center of the circle, and ends at another point on the circle.
Answer:
The radius is a line segment that starts at the center of the circle and ends at a point on the circle.
Step-by-step explanation:
The radius is half of the diameter. The diameter is one line going across the whole, through the midpoint. The radius starts at the midpoint and that's why it's only half of the diameter.
Answer: The radius is a line segment that starts at the center of the circle and ends at a point on the circle.
Step-by-step explanation:
The radius of a circle is the distance from the center of the circle to any point on it.Let's check all the options.
The radius is a line segment joining two distinct points on the circle. → Wrong.
Reason :- Radius joins center and any point on circle not any two points.
The radius is the boundary of a circle. → Wrong.
Reason :- Circumference is the boundary of circle ,
Formula for circumference C= 2π r , where r is radius .
The radius is a line segment that starts at one point on the circle, passes through the center of the circle, and ends at another point on the circle.→ Wrong.
Reason :- Its diameter that starts at one point on the circle, passes through the center of the circle, and ends at another point on the circle and it is twice of radius.
So , the best answer that defines the radius of a circle is The radius is a line segment that starts at the center of the circle and ends at a point on the circle.
Use the variation of parameters method to solve the DE y"+y'- 2y=1
Answer:
[tex]y(t)\ =\ C_1.e^{-2t}+C_2e^t-\ t.\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given differential equation is,
y"+y'-2y=1
[tex]=>\ (D^2+D-2D)y\ =\ 1[/tex]
To find the complementary function we will write,
[tex]D^2+D-2=0[/tex]
[tex]=>\ D\ =\ \dfrac{-1+\sqrt{1^2+4\times 2\times 1}}{2\times 1}\ or\ \dfrac{-1-\sqrt{1^2+4\times 2\times 1}}{2\times 1}[/tex]
[tex]=>\ D\ =\ -2\ or\ 1[/tex]
Hence, the complementary function can be given by
[tex]y(t)\ =\ C_1e^{-2t}\ +\ C_2e^t[/tex]
Let's say,
[tex]y_1(t)\ =\ e^{-2t}\ \ =>y'_1(t)\ =\ -2e^{-2t}[/tex]
[tex]y_2(t)\ =\ e^{t}\ \ =>y'_2(t)\ =\ e^{t}[/tex]
[tex]g(t)\ =\ 1[/tex]
Wronskian can be given by,
[tex]W\ =\ y_1(t).y'_2(t)\ -\ y_2(t).y'_1(t)[/tex]
[tex]=\ e^{-2t}.e^{t}\ -\ e^{t}.(-2e^{-2t})[/tex]
[tex]=\ e^{-t}\ +\ 2e^{-t}[/tex]
[tex]=\ 3.e^{-t}[/tex]
Now, the particular integral can be given by
[tex]y_p(t)=\ -y_1(t)\int\dfrac{y_2(t).g(t)}{W}dt\ +\ y_2(t)\int\dfrac{y_1(t).g(t)}{W}dt[/tex]
[tex]=\ -e^{-2t}\int\dfrac{e^t.1}{3.e^{-t}}+e^t\int\dfrac{e^{-2t}.1}{3.e^{-t}}dt[/tex]
[tex]=\ -e^{-2t}\int\dfrac{1}{3}dt+\dfrac{e^t}{3}\int e^{-t}dt[/tex]
[tex]=\ \dfrac{-e^{-2t}}{3}.t\ -\ \dfrac{e^t}{3}.e^{-t}[/tex]
[tex]=\ -t.\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]
Hence, the complete solution can be given by
[tex]y(t)\ =\ C_1.e^{-2t}+C_2e^t-\ t.\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]
3. You have decided to wallpaper your rectangular bedroom. The dimensions are 12 feet 6 inches by 10 feet 6 inches by 8 feet 0 inches high. The room has two windows, each 4 feet by 3 feet and a door 7 feet by 3 feet. Determine how many rolls of wallpaper are needed to cover the walls, allowing 10% for waste and matching. Each roll of wallpaper is 30 inches wide and 30 feet long. How many rolls of wallpaper should be purchased? * OA. 4 rolls OB. 5 rolls OC. 6 rolls OD. 7 rolls OE. 8 rolls
Answer:
B. 5 rolls
Step-by-step explanation:
The areas of the room, not including the ceiling, are discriminated as follows:
Longer walls: [tex](12.5\times8)\times2=200ft^2[/tex] (6 inches equals one foot)
Shorter walls: [tex](10.5\times8)\times2 = 168ft ^ 2[/tex] (6 inches equals one foot)
Window area: [tex](4\times3)\times2 = 24ft ^ 2[/tex]
Door area: [tex](7\times3) = 21ft ^ 2[/tex]
Area that will be effectively covered:
Total area to wallpaper: [tex]200 + 168 -24 -21 = 323ft ^ 2[/tex]
Amount of paper needed: [tex]323\times1.1 = 355.3ft ^ 2[/tex]
[tex]30in = 24in + 6in = 2ft + 0.5ft = 2.5ft.[/tex] That is, the area of a roll of paper is [tex]2.5\times30 = 75ft ^ 2[/tex]
Number of rolls needed:
[tex]\frac{355.3}{75} = 4.73[/tex] rolls
Answer:
Correct answer is B. 5Rolls
Step-by-step explanation:
First you have to put all values in same unit of measurement, knowing that 1 foot=12 inches, we apply 3 rule:12 inches is 1 feet
6 inches is 6/12 feet= 0,5 feet.
12 inches is 1 foot
30 inches is 30/12 feet=2,5feet.
2. Second,you have to calculate the total surface where you will wallpaper.
So you have to calculate the dimension of 2 different rectangles and substract the surfaces that you don't have to wallppaper (door and windows).
Let's calculate the surface of the rectancles. Let's put all units in feets.[tex]Area rectangle 1 =10.5feet*8feet=84ft^{2} \\Area rectangle2=12.5feet*8feet=100ft^{2}\\Total Area of walls=(Area rectangle 1 *2) + (Area rectangle2*2)\\Total Area of walls=(84ft^{2} *2)+(100ft^{2})\\\\Total Area of walls=368ft^{2}[/tex]
3. Now we have to calculate the area to substract from the total area, since you will not wallpaper the door and windows:
[tex]Windows=4feet*3feet*2=24ft^{2} \\Door=7feet*3feet=21ft^{2}[/tex]
4. Total area to wallpaper is Total surface of the room minus door and windows surface:
[tex]wallpaperArea=368ft^{2} -45ft^{2}\\wallpaperArea=323ft^{2}[/tex]
5. Now you have to add 10% waste to the calculated surface:
[tex]323ft^{2} +(323*0.10)=355.3ft^{2}[/tex]
6. So, you have the real area that will wallpaper considering 10% waste, it is 326.23 square feet. To calculate how many rolls you will need, you have to calculate the surface that each roll covers and then divide total surface by roll surface.
[tex]Roll surface=2,5feet*30feet=75feet^{2}[/tex]
[tex]Rolls needed=355.3ft^{2}/75ft^{2}=4.73[/tex]
7. As the number of rolls is not integer you have to round, then the answer is you will need 5 rolls of wallpaper.
A batch contains 37 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Six cells are selected at random, without replacement, to be checked for replication. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that all six cells of the selected cells are able to replicate? (b) What is the probability that at least one of the selected cells is not capable of replication?
The probability that all six cells are able to replicate is approximately 0.0051, while the probability that at least one cell is not capable of replication is approximately 0.9949.
Explanation:To solve this problem, we need to use the concept of probability and combinations.
(a) Probability that all six cells are able to replicate:There are 37 - 12 = 25 cells capable of replication. Out of these, we need to select 6 cells. The probability of selecting a cell capable of replication is 25/37 for the first selection, multiplied by 24/36 for the second selection, and so on, until 20/32 for the sixth selection. So, the probability is:
P(all 6 cells able to replicate) = (25/37) * (24/36) * (23/35) * (22/34) * (21/33) * (20/32) ≈ 0.0051
(b) Probability that at least one cell is not capable of replication:The probability that at least one cell is not capable of replication is equal to 1 minus the probability that all six cells are able to replicate. So, the probability is:
P(at least one cell not able to replicate) = 1 - P(all 6 cells able to replicate) ≈ 0.9949
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What is the probability of selecting a brown marble from a jar of marbles?
Seven of the marbles are brown, two of the marbles are white, and one of the marbles is green.
9/10
1/10
3/10
7/10
Answer:
Quality A is greater
Step-by-step explanation:
Answer:
7/10
Step-by-step explanation:
The total number of marbles is 7 + 2 + 1 = 10. So the probability of selecting a brown marble is 7/10
The opposite process rule says to solve for ________. a known variable by replicating the process used to form the original equation an unknown variable by reversing the process used to form the original equation an unknown variable by replicating the process used to form the original equation a known variable by reversing the process used to form the original equation
Answer:
An unknown variable by reversing the process used to form the original equation.
Step-by-step explanation:
The opposite process rule says to solve for - an unknown variable by reversing the process used to form the original equation.
If an equation indicates an operation such as addition, subtraction, multiplication, or division, solve for the unknown variable by using the opposite process.
For example:
Lets say we have to find [tex]x+25=35[/tex]
Here 25 is subtracted from both sides of the equation to isolate x.
[tex]x+25-25=35-25[/tex]
we get x = 10
Check this : [tex]10+25=35[/tex]
Final answer:
The opposite process rule is a technique used to solve for an unknown variable by reversing the operations that were used to create the equation. It is a key concept in algebra for finding values of unknown variables.
Explanation:
The opposite process rule refers to solving for an unknown variable by reversing the process used to form the original equation. This is a fundamental technique in solving algebraic equations, necessary for determining the value of the unknown.
To solve for an unknown variable, you follow several steps. Initially, identify the unknowns and known variables. Then, find an equation that expresses the unknown in terms of the knowns. If more than one unknown is present, multiple equations may be needed.
To find the numerical value of the unknown, substitute known values, including their units, into the equation and solve. In algebra, this could mean performing operations such as addition, subtraction, multiplication, or division inversely to isolate the variable.
find m angle A
A
10
B
20
C
16
D
14
Answer:
D. 14°
Step-by-step explanation:
The Law of Sines tells you sides are in proportion to the sine of the opposite angle:
sin(A)/BC = sin(B)/AC
sin(A) = BC/AC·sin(B)
A = arcsin(BC/AC·sin(B)) = arcsin(7/28·sin(75°)) ≈ 13.974° ≈ 14°
In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are three machine tools, four polishing tools, and three painting tools, how many different routings (consisting of machining, followed by polishing, and followed by painting) for a part are possible?
Answer:
36Step-by-step explanation:
As per the given question,
In a manufacturing operation, a part is produced by machining, polishing, and painting.
Number of machine tools = 3
Number of polishing tools = 4
Number of painting tools = 3
Now,
For finding the different routing consisting of machining, followed by polishing, and followed by painting, we have to simply multiply the number of machine tools, polishing tools and painting tools.
Therefore,
The different routing (consisting of machining, followed by polishing, and followed by painting) for a part are possible = 3 × 4 × 3 = 36.
Hence, the required answer is 36.
Number of ways a process can be done is the count of total distinguished ways that process can be done. The count of different routings possible for a part is 36
In how many ways, two things with a and b choices be done sequentially?Suppose that a process A can be done in 'a' different ways.
And there is a process following A, call it B, can be done in 'b' different ways. Then, the process A then B can be done in a×b different ways.
This is called rule of product in combinatorics.
Since there are 3 processes to be done subsequently(machining, polishing, then painting), and each of them can be done in 3, 4, and 3 ways respectively, thus,
Total number of routings possible for a part is [tex]3 \times 4 \times 3 = 36[/tex] ways.
Thus, The count of different routings possible for a part is 36
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c) Use the Bisection method to find a solution accurate to within 10^-2 for x^4 − 2x^3 − 4x^2 + 4x + 4 = 0 on [0, 2].
Answer:
x ≈ 181/128 ≈ 1.41406
Step-by-step explanation:
The attached table shows the iterations. At each step, the interval containing the root is bisected and the function value at the midpoint of the interval is found. The sign of it relative to the signs of the function values at the ends of the interval tell which half interval contains the root. The process is repeated until the interval width is less than 10^-2.
Interval: [0, 2], signs [+, -], midpoint: 1; sign at midpoint: +
[1, 2] 3/2 -
[1, 3/2] 5/4 +
...
the rest is in the attachment. The listed table values are the successive interval midpoints.
The final midpoint is 181/128 ≈ 1.41406. This is within 0.0002 of the actual root.
_____
The actual solution in the interval [0, 2] is √2 ≈ 1.41421.
To find a solution utilizing the Bisection Method, one needs to establish the function and verify it satisfies the bisection condition. The process is iteratively repeated by adjusting the interval to the midpoint until the error tolerance is reached or the function value of the midpoint is within the desired accuracy.
Explanation:The subject of your question concerns utilizing the Bisection method to solve a certain polynomial equation from a given interval [0, 2] with an accuracy of within 10^-2. The Bisection Method is a root-finding method in numerical analysis to solve for roots in given intervals.
First, establish the function f(x) = x^4 − 2x^3 − 4x^2 + 4x + 4 and set the interval a = 0 and b = 2. The midpoint c = (0 + 2) / 2 = 1.Check whether the configuration of f(0), f(1), and f(2) satisfies the bisection condition. The bisection condition states that the product of function at the end points should be negative i.e., f(a)*f(b) < 0. If it does, the root lies between a and b.Find f(1) and check its product with the values at the end points. If f(a)*f(c) < 0, then the root lies in the first subinterval so b is updated to be c. If not, then root is in the other interval, so a = c.We repeat this process until we get a c value that yields a function value within our desired accuracy or till we reach a point where (b-a)/2 < error tolerance, in this case, 10^-2 .This is an example of how the Bisection Method would be applied in solving for roots of polynomial equations. Do take note that this method only provides approximate solutions and it can be a lengthy process for equations with multiple roots.
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A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 282 businesses at random. Of these, 69 return the questionnaire mailed by the committee. The population for this study is
A. the 282 businesses chosen.
B. all businesses in the college town.
C. the 69 businesses that returned the questionnaire.
D. None of the above.
Answer:
option C the 69 businesses that returned the questionnaire.
Step-by-step explanation:
It is given in the question that only 69 businesses out of all 282 randomly chosen businesses have returned the questionnaire mailed by the committee.
Therefore,
The data available for the study by the committee is of only 69 businesses that have replied to the committee. So the study is based on this population of 69 businesses only.
Hence, option c is the correct answer.
The American Sugar Producers Association wants to estimate
themean yearly sugar consumption. A sample of n = 12 people
revealsthe mean yearly consuption to be 55 pounds with a
standarddeviation of 20 pounds. Find the lower bound for the 98%
confidenceinterval for the mean yearly sugar consumption. Assume
thepopulation is normal.
Answer: 39.308 pounds
Step-by-step explanation:
We assume that the given population is normally distributed.
Given : Significance level : [tex]\alpha: 1-0.98=0.02[/tex]
Sample size : n= 12, which is small sample (n<30), so we use t-test.
Critical value (by using the t-value table)=[tex]t_{n-1, \alpha/2}=t_{11,0.01}=2.718[/tex]
Sample mean : [tex]\overline{x}=50[/tex]
Standard deviation : [tex]\sigma= 20[/tex]
The lower bound of confidence interval is given by :-
[tex]\overline{x}-t_{(n-1,\alpha/2)}\dfrac{\sigma}{\sqrt{n}}[/tex]
i.e. [tex]55-(2.718)\dfrac{20}{\sqrt{12}}[/tex]
[tex]=55-15.6923803166\approx55-15.692=39.308[/tex]
Hence, the lower bound for the 98% confidence interval for the mean yearly sugar consumption= 39.308 pounds
A certain chalkboard manufacturer determines that their largest blackboard model has a mean length of 5.00 m and a standard deviation of 1.0 cm. A certain school district orders 1000 of these chalkboards. How many are likely to have lengths of under 4.98 m?
Answer:
23 chalkboards
Step-by-step explanation:
Given:
Mean length = 5 m
Standard deviation = 0.01
Number of units ordered = 1000
Now,
The z factor = [tex]\frac{\textup{x - Mean}}{\textup{standard deviation}}[/tex]
or
The z factor = [tex]\frac{\textup{4.98 - 5}}{\textup{0.01}}[/tex]
or
Z = - 2
Now, the Probability P( length < 4.98 )
Also, From z table the p-value = 0.0228
therefore,
P( length < 4.98 ) = 0.0228
Hence, out of 1000 chalkboard ordered (0.0228 × 1000) = 23 chalkboard are likely to have lengths of under 4.98 m.
1000.0 cm3 of a metallic cylinder has a mass of 556 gram. Calculate the density of the cylinder.
Answer:
[tex]\text{Density}=\frac{0.556\text{ Grams}}{\text{ cm}^3}[/tex]
Step-by-step explanation:
We are asked to find the density of a cylinder whose volume is 1000.0 cubic cm and mass is 556 grams.
[tex]\text{Density}=\frac{\text{Mass}}{\text{Volume}}[/tex]
Substitute the given values:
[tex]\text{Density}=\frac{556\text{ Grams}}{1000.0\text{ cm}^3}[/tex]
[tex]\text{Density}=\frac{0.556\text{ Grams}}{\text{ cm}^3}[/tex]
Therefore, the density of the metallic cylinder is 0.556 grams per cubic centimeter.
Dan worked three hours for eight days.how many hours did he work in total
An urn contains three red balls, five white balls, and two black balls. Four balls are drawn from the urn at random without replacement. For each red ball drawn, you win $6, and for each black ball drawn, you lose $9. Let X represent your net winnings Compute E(X), your expected net winnings E(x)
Answer:
0
Step-by-step explanation:
total number of balls = 3+5+2= 10
Probability of getting red P(R) = 3/10
Probability of getting white P(W) = 5/10
Probability of getting black P(B) = 2/10
for each red ball drawn you win $6 and for each black ball drawn you loose $9 dollars
E(X)= 6×3/10 +0×5/10 -9×2/10= 0
E(X)= 0
Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 3y 6212 3x + (x, y. z)
Answer:
The solution of the system of linear equations is [tex]x=3, y=4, z=1[/tex]
Step-by-step explanation:
We have the system of linear equations:
[tex]2x+3y-6z=12\\x-2y+3z=-2\\3x+y=13[/tex]
Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.
The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).
From the system of linear equations that we have, the coefficient matrix is
[tex]\left[\begin{array}{ccc}2&3&-6\\1&-2&3\\3&1&0\end{array}\right][/tex]
the variable matrix is
[tex]\left[\begin{array}{c}x&y&z\end{array}\right][/tex]
and the constant matrix is
[tex]\left[\begin{array}{c}12&-2&13\end{array}\right][/tex]
We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so
[tex]\left[\begin{array}{ccc|c}2&3&-6&12\\1&-2&3&-2\\3&1&0&13\end{array}\right][/tex]
To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:
multiply the 1st row by 1/2[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\1&-2&3&-2\\3&1&0&13\end{array}\right][/tex]
add -1 times the 1st row to the 2nd row[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\3&1&0&13\end{array}\right][/tex]
add -3 times the 1st row to the 3rd row[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\0&-7/2&9&-5\end{array}\right][/tex]
multiply the 2nd row by -2/7[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&-7/2&9&-5\end{array}\right][/tex]
add 7/2 times the 2nd row to the 3rd row[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&3&3\end{array}\right][/tex]
multiply the 3rd row by 1/3[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&1&1\end{array}\right][/tex]
add 12/7 times the 3rd row to the 2nd row[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&0&4\\0&0&1&1\end{array}\right][/tex]
add 3 times the 3rd row to the 1st row[tex]\left[\begin{array}{ccc|c}1&3/2&0&9\\0&1&0&4\\0&0&1&1\end{array}\right][/tex]
add -3/2 times the 2nd row to the 1st row[tex]\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&4\\0&0&1&1\end{array}\right][/tex]
From the reduced row echelon form we have that
[tex]x=3\\y=4\\z=1[/tex]
Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.
Answer the following true or false. Justify your answer.
(a) If A is a subset of B, and x∈B, then x∈A.
(b) The set {(x,y) ∈ R2 | x > 0 and x < 0} is empty.
(c) If A and B are square matrices, then AB is also square.
(d) A and B are subsets of a set S, then A∩B and A∪B are also subsets of S.
(e) For a matrix A, we define A^2 = AA.
Answer:
a) False b) False c) True d) True e) True
Step-by-step explanation:
a) If A is a subset of B, and x∈B, then x∈A. False
Suppose A is Z (Set of Integers), and B is R (Set of Real Numbers). Then A is a subset of B. x ∈ B, let's say x equals π. If x ∈ B (B = Real Numbers) and x=π then x ∉ A (Z).
We could call A, any other subset of Real numbers (Q, I,..) and we both would come up to the same conclusion when it comes to Real numbers the Set.
So this conclusion is False. Not always an element of a subset is an element of a set.
b) False
For this one, I've drawn some lines, and it is useful to work with them.
Given the set {(x,y) ∈ R²| 0<x<0} then all negative and positive numbers but zero belong to this set.
c) If A and B are square matrices, then AB is also square. True
Taking into account the rules for multiplying matrices. The number of columns of A must be the same number of lines of B to there can be a matrix product.
Whenever we multiply square matrices, we'll always get square matrices. Then this conclusion is true.
d) A and B are subsets of a set S, then A∩B and A∪B are also subsets of S. True
Suppose A= Z (Integer Numbers) and B=Q (Rational Numbers) and S= R (Real Numbers)
A∩B = Z∩Q=∅ and A∪B =Z∪Q = subset
Since the ∅ empty set ⊂ in every set and ZUQ is another Subset of R this is a True conclusion.
e) True. For a matrix A, we define A²= AA
For any Power of Matrices, all we have to do is multiply any given matrix by itself for a given number of times.
M²=M*M
M³=M*M*M
Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous or neither. You order a pizza. The kind of pizza you order is recorded by entering the appropriate number on an order form. The numbers used are given below. 1) Pepperoni 2) Mushroom 3) Black Olive 4) Sausage
Answer:
Qualitative and Neither
Step-by-step explanation:
Quantitative data is such a data which can be measured or calculated i.e. which is defined only in terms of numbers. In simple words we can say that numeric data is the Quantitative data.
On the other hand, qualitative data describes the characteristics, attribute or quality of the objects. This type of data is not measured or calculated.
The data which we are dealing with is "Kind of pizza". The kind/flavor of pizza is an attribute or characteristic of pizza. So from here it is clear that the data is Qualitative. Though numbers are assigned to different flavors, these numbers are just for identification of the flavor on the order form.
The terms discrete and continuous can only be used when the data is Quantitative. Qualitative data cannot be referred to as discrete or continuous data, even if some numbers are assigned to data.
Therefore, the answers are: Qualitative and Neither
Graph each point on a coordinate plane. Name the quadrant in which each is located
14. D(1, -5)
13. C(-4,3)
12. B(-2, -3)
11. A(3,5)
Given f(x) = 4x - 1, evaluate each of the following:
15. f(-4)
16. f(0)
17. f(2)
Answer:
14. Quadrant IV
13. Quadrant II
12. Quadrant III
11. Quadrant I
15. -17
16. -1
17. 7
Step-by-step explanation:
52.25 is ___% of 1,1050.00
Answer: 0.4729%
Step-by-step explanation:
The formula to find the percent of a part in total amount :-
[tex]\%=\dfrac{\text{Part}}{\text{Total}}\times100[/tex]
Given : Total amount = 1,1050.00
Part of total amount = 52.25
Now, substitute all the values in the formula , we get
[tex]\%=\dfrac{52.25}{11050}\times100\\\\\Rightarrow\ \%=\dfrac{5225}{1105000}\times100=\dfrac{5225}{11050}=0.472850678733\approx0.4729\%[/tex]
Hence, 52.25 is 0.4729% of 1,1050.00.
kendra remembered glue.
ally remembered an eraser
sarah remembered scissors
please be more specific
Write the equation in the slope-intercept form and then find the slope m and y-intercept b of the corresponding line.
4x + 7y + 4 = 7
Answer:
[tex]m=-\frac{4}{7}[/tex]
[tex]b=\frac{3}{7}[/tex]
Step-by-step explanation:
Slope intercept form of a line is
[tex]y=mx+b[/tex] ... (1)
where, m is slope and b is y-intercept.
The given equation is
[tex]4x+7y+4=7[/tex]
We need to find the slope intercept form of given line.
Subtract 4 from both sides.
[tex]4x+7y=7-4[/tex]
[tex]4x+7y=3[/tex]
Subtract 4x from both sides.
[tex]7y=3-4x[/tex]
Divide both sides by 7.
[tex]y=\frac{3-4x}{7}[/tex]
[tex]y=\frac{3}{7}-\frac{4}{7}x[/tex]
Arrange the terms.
[tex]y=-\frac{4}{7}x+\frac{3}{7}[/tex] .... (2)
Form (1) and (2) we get
[tex]m=-\frac{4}{7}[/tex]
[tex]b=\frac{3}{7}[/tex]
Therefore, the slope of the line is -4/7 and y-intercept is 3/7.
An election for a new treasurer was held at a recent trade conference. In the election, Jamal received 40% of the votes, and his only opponent, Tran, received 4,320 votes. How many people voted for Jamal in the election?
Answer:
Jamal received 2,880 votes
Step-by-step explanation:
In the election,
Jamal received 40% of all votes
Tran received 100% - 40% = 60% that is 4,320 votes
Let x be the number of votes Jamal received. Then
x - 40%
4,320 - 60%
Write a proportion:
[tex]\dfrac{x}{4,320}=\dfrac{40}{60}\\ \\\text{Cross multiply}\\ \\60\cdot x=40\cdot 4,320\\ \\x=\dfrac{40\cdot 4,320}{60}=\dfrac{2\cdot 4,320}{3}=\dfrac{2\cdot 1,440}{1}=2,880[/tex]
What is the probability of selecting a red queen from a deck of cards?
2/26
3/52
1/52
1/26
Y=∛x -8 inverse of the function
Answer:
The inverse function of [tex]\sqrt{3]{x} - 8[/tex] is [tex](x+8)^{3}[/tex]
Step-by-step explanation:
Inverse of a function:
To find the inverse of a function [tex]y = f(x)[/tex], basically, we have to reverse r. We exchange y and x in their positions, and then we have to isolate y.
In your exercise:
[tex]y = \sqrt[3]{x} - 8[/tex]
Exchanging x and y, we have:
[tex]x = \sqrt[3]{y} - 8[/tex]
[tex]x + 8 = \sqrt[3]{y}[/tex]
Now we have to write y in function of x
[tex](x+8)^{3} = (\sqrt[3]{y})^{3}[/tex]
[tex]y = (x+8)^{3}[/tex]
So, the inverse function of [tex]\sqrt{3]{x} - 8[/tex] is [tex](x+8)^{3}[/tex]