if f (x) = x³-2 x²- 75, prove that: 5 is one of zeros of the function f
Answers
Since f(5) = 0, we have shown that 5 is one of the zeros of the function f(x).
What is function zero?
A function zero (also known as a root or a solution) is a value of the independent variable in a function that makes the function equal to zero. In other words, a function zero is a value of x for which f(x) = 0.
To prove that 5 is one of the zeros of the function f(x) = x³ - 2x² - 75, we need to show that f(5) = 0.
Substituting x = 5 into the function, we get:
f(5) = 5³ - 2(5)² - 75
= 125 - 50 - 75
= 0
Since f(5) = 0, we have shown that 5 is one of the zeros of the function f(x).
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Related Questions
What is the value of x?
Answers
Answer:
4x= 40
Step-by-step explanation:
40/4 = 10
suppose that when a transistor of a certain type is subjected to an accelerated life test, the lifetime x (in weeks) has a gamma distribution with mean 24 weeks and standard deviation 12 weeks. (a) what is the probability that a transistor will last between 12 and 24 weeks? (b) what is the probability that a transistor will last at most 24 weeks? (c) is the median of the lifetime distribution less than 24? why or why not?
Answers
The probability that the transistor will last between 12 and 24 weeks is 0.424
the probability that a transistor will last at most 24 weeks is 0.567
The median of the lifetime distribution is less than 24
X= lifetime of the transistor in weeks E(X)= 24 weeks
O,= 12 weeks
The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.
a) X~gamma(\(\alpha , \beta\))
E(X)= \(\alpha \beta\) \(\beta\) =\(12^{2}/24\) =6 weeks
V(x)=\(\alpha \beta ^{2}\) \(\alpha\)=24/6= 4
Now we can find the solutions:
The excel formula used to create Figure one is as follows:
=gammadist(X,\(\alpha\) ,\(\beta\) , False)
P(\(12\leq X\leq 24\))
P(\(12/6 \leq X\leq 24/6\))
P(\(2\leq X\leq 4\))
P= 0.424
Therefore, the probability that the transistor will last between 12 and 24 weeks is 0.424
b) For this case we want this probability:
\(P(X\geq 24)=1-P(X\leq 24)\)
In order to find this probability we can use excel with the following code:
=1-GAMMA.DIST(24,4,6,TRUE)
And we got:
\(P(X\geq 24)=P(1-X\leq 24)= 0.567\)
c) For this case the median of the lifetime distribution is less than 24
\(P(X\leq \alpha )\) = 0.5 (by definition) So \(\alpha\)< 24 because P(\(X\leq 24\))=0.567 which is greater than 0.5
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Help please I’ll mark brainliest
Answers
Answer:
- \(\frac{1}{2}\)
Step-by-step explanation:
One cubic down and 2 cubics to the right
joe wants to find all the four-letter words that begin and end with the same letter. how many combinations of letters satisfy this property?
Answers
Answer: There are $26$ choices for the first letter, $26$ for the second, and $26$ for the third. The last letter is determined by the first letter. Thus, there are $26^3 = \boxed{17576}$ such combinations.
Step-by-step explanation:
This means that picking a four-letter word that follows this rule is just like picking any 3 letter word (pick a 3 letter word and then add a "copy" of the first letter as a fourth letter)
so there's a total of 263 =17,576 combinations- 26 options for the first letter, 26 options for the second letter, and 26 options for the third letter.
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The top of a ladder is 10 meters from the ground when the ladder leans against the wall at an angle of 35. 5° with respect to the ground. If the ladder is moved by x meters toward the wall, it makes an angle of 54. 5° with the ground, and its top is 14 meters above the ground. What is x rounded to the nearest meter?.
Answers
Answer:
Step-by-step explanation:
Find the missing factor
Answers
Answer:
\((x^4y^5)(x^2y^4)\)
Step-by-step explanation:
Keep these things in mind:
\(x^3\times x^3=x^{3+3}=x^6\\\\(x^3)^3=x^{3\times3}=x^9\)
Using those, simplify the left side of this equation:
\((x^2y^3)^3\\x^6y^9\)
Now we know what the exponents need to become, so we can find the difference between those and what we have on the right:
\(6-4=2\\9-5=4\)
We need to add a 2 to the x, and add a 4 to the y.
\((x^4y^5)(x^2y^4)\)
a bag contains 5 blue ribbons, 7 white ribbons, and 3 red ribbons, . Find the probability of getting a red ribbons (suppose you pick red ribbons 5 times and you repeat thaprocess 10 times)
Answers
the probability of getting at least one red ribbon in each set of 5 draws, repeated 10 times, is approximately 0.000657.
Given that the bag contains 5 blue ribbons, 7 white ribbons, and 3 red ribbons, we first need to determine the probability of picking a red ribbon in a single draw. There are a total of 5 + 7 + 3 = 15 ribbons in the bag, so the probability of picking a red ribbon is 3/15 (3 red ribbons out of 15 total ribbons).
Next, we will consider the scenario where you pick ribbons 5 times and repeat this process 10 times. Since the question doesn't mention whether the ribbons are replaced after each draw, I will assume that they are not replaced.
1. Calculate the probability of getting a red ribbon in the first 5 draws:
P(Red in 5 draws) = 1 - P(Not getting Red in 5 draws)
P(Not getting Red in 5 draws) = (12/15) * (11/14) * (10/13) * (9/12) * (8/11)
P(Not getting Red in 5 draws) = 0.3916
P(Red in 5 draws) = 1 - 0.3916 = 0.6084
2. Determine the probability of getting at least one red ribbon in each set of 5 draws, repeating this process 10 times:
P(At least 1 Red in each set of 5 draws)^10 = (0.6084)^10 = 0.000657
So, the probability of getting at least one red ribbon in each set of 5 draws, repeated 10 times, is approximately 0.000657.
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solve for y on this shape
Answers
The sum of all of the angles in a pentagon is 540 degrees
A graph shows time (minutes) on the horizontal axis and speed (miles per hour) on the vertical axis. Both axes are unnumbered. An orange line is in four sections, labeled A, B, C, D. A starts near the top of the vertical axis and goes down as time increases. B levels out as time continues. C moves up the vertical axis as time continues. D levels out as time continues.
Use the drop-down menus to complete each sentence.
In section A, speed is
as time is increasing.
In section B, speed is
as time is increasing.
In section C, speed is
as time is increasing.
In section D, speed is
as time is increasing.
Answers
Section A shows a decreasing speed, section B and D exhibit a constant speed, and section C displays an increasing speed as time continues. By analyzing the movements of the orange line on the graph.
In section A of the graph, the speed is decreasing as time is increasing. The description mentions that the orange line starts near the top of the vertical axis and goes down as time increases.
This downward movement indicates a decrease in speed. As time progresses, the speed is getting slower, resulting in a negative slope for section A of the graph.
In section B, the speed levels out as time continues. This implies that there is no significant change in speed as time increases. The orange line remains relatively constant, indicating a constant speed. This section is characterized by a horizontal line on the graph.
Moving on to section C, the speed is increasing as time continues. The description mentions that the orange line moves up the vertical axis as time increases. This upward movement signifies an increase in speed. As time progresses, the speed is getting faster, resulting in a positive slope for section C of the graph.
Finally, in section D, the speed levels out as time continues. Similar to section B, there is no significant change in speed as time increases. The orange line remains relatively constant, indicating a constant speed. This section is also characterized by a horizontal line on the graph.
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if x/ 3=3/x then what is the value of x
1.-3
2.3
3.+-3
Answers
Answer:
x = ±3 (Option 3)
Step-by-step explanation:
\(\frac{x}{3} = \frac{3}{x}\)
Multiply both the sides with 3.\(=> \frac{x}{3} \times 3 = \frac{3}{x} \times 3\)
\(=> x = \frac{9}{x}\)
Multiply both the sides with 'x'.\(=> x \times x = \frac{9}{x} \times x\)
\(=> x^2 = 9\)
Root-square both the sides.\(=> \sqrt{x^2} = \sqrt{9}\)
\(=> x = (+3) \: or \: (-3)\)
∴ x = ±3
select all the correct answers. jim writes down a large number. the number is 543 followed by 12 zeroes. how would jim express this number in scientific notation?
Answers
40 points
hey whats the answer
pls show step explanation
Answers
Answer:.
Answer:1.we have dividend =divisor*quotient+remainder=
(x²+2x-1)(x²-2x+1)+(-4x+1)
=x²(x²-2x+1)+2x(x²-2x+1)-1(x²-2x+1)-4x+1
=x⁴-2x³+x²+2x³-4x²+2x-x²+2x-1-4x+1
=x⁴-4x²
Dividend is x⁴-4x².
2.
Multiplier is a-a²+1.
Answer:
\(i \: hope \: the \: above \: picture \\ helps\)
\(have \: a \: nice \: day \: \)
\(#Liliflim\)
The function,y=−16x2+32x+48, represents the height, in feet, of a firework x seconds after it is launched.
After how many seconds does the firework hit the ground?
Enter your answer in the blank.
x=□seconds
Answers
The number of seconds does the firework hit the ground is 3 seconds
How to determine the valueFrom the information given, we have the quadratic function;
y = -16x² + 32x + 48
To determine the value of x , let's reduce the expression, we get;
-2x² + 4x + 6
Now, let's factorize the terms
Multiply the coefficient by the constant and find the pair factors
-2x² + 6x - 2x + 6
Factorize in pairs, we get;
-2x(x -3) - 2(x -3)
Then, we have the expressions
-2x - 2 = 0
solve for x
x = -1
x - 3 = 0
x = 3
Hence, the value is 3 seconds
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Answer:
3
Step-by-step explanation:
i took the test
Math is dumb and i can't do it
Answers
Answer:
B
Step-by-step explanation:
its a graph and I agree math is dumb
Answer:
agreed
Step-by-step explanation:
Solve this system of linear equations. Separatethe x- and y-values with a comma.- 17x = -37 - 7y10x = 16 + 7y
Answers
- 17x = -37 - 7y
10x = 16 + 7y
then now add both equations , to eliminate y
(-17x + 10x) = -37 + 16 + (-7y+7y)
then
-7x = -21 + 0
. x = -21/-7
. x = 3
Now find y = ?
y = (10x - 16)/7
. = (10•3 - 16)/7
. = (30-16)/7
. = 14/7 = 2
Then, answers are
x= 3
y= 2
What is the value of the missing angle in this quadrilateral?
56
67
304
360
Answers
Answer:
Hello There!!
Step-by-step explanation:
The answer is 56.
hope this helps,have a great day!!
~Pinky~
Find the scale length of 15cm and 3cm.
Please help if you can thank youuu
Answers
Answer: 5
the scale length of 15cm and 3cm is 15/3 = 5
Step-by-step explanation:
The Brennan Aircraft Division of TLN Enterprises operates a large number of computerized plotting machines. For the most part, the plotting devices are used to create line drawings of complex wing airfoils and fuselage part dimensions. The engineers operating the automated plotters are called loft lines engineers. The computerized plotters consist of a minicomputer system connected to a 4- by 5-foot flat table with a series of ink pens suspended above it When a sheet of clear plastic or paper is properly placed on the table, the computer directs a series of horizontal and vertical pen movements until the desired figure is drawn. The plotting machines are highly reliable, with the exception of the four sophisticated ink pens that are built in. The pens constantly clog and jam in a raised or lowered position. When this occurs, the plotter is unusable. Currently, Brennan Aircraft replaces each pen as it fails. The service manager has, however, proposed replacing all four pens every time one fails. This should cut down the frequency of plotter failures. At present, it takes one hour to replace one pen. All four pens could be replaced in two hours. The total cost of a plotter being unusable is $50 per hour. Each pen costs $8. If only one pen is replaced each time a clog or jam occurs, the following breakdown data are thought to be valid: Hours between plotter failures if one pen is replaced during a repair Probability 10 0.05 20 0.15 30 0.15 40 0.20 50 0.20 60 0.15 70 0.10 Based on the service manager’s estimates, if all four pens are replaced each time one pen fails, the probability distribution between failures is as follows: Hours between plotter failures if four pens are replaced during a repair Probability 100 0.15 110 0.25 120 0.35 130 0.20 140 0.00 (a) Simulate Brennan Aircraft’s problem and determine the best policy. Should the firm replace one pen or all four pens on a plotter each time a failure occurs?
Answers
To determine the best policy for Brennan Aircraft's plotter pen replacement, we can simulate the problem and compare the expected costs for both scenarios: replacing one pen or replacing all four pens each time a failure occurs.
Let's calculate the expected costs for each scenario:
Replacing one pen:
We'll calculate the expected cost per hour of plotter failure by multiplying the probability of each failure duration by the corresponding cost per hour, and then summing up the results.
Expected cost per hour = Σ(Probability * Cost per hour)
Expected cost per hour = (10 * 0.05 + 20 * 0.15 + 30 * 0.15 + 40 * 0.20 + 50 * 0.20 + 60 * 0.15 + 70 * 0.10) * $50
Expected cost per hour = $39.50
Replacing all four pens:
We'll calculate the expected cost per hour using the same method as above, but using the probability distribution for the scenario of replacing all four pens.
Expected cost per hour = (100 * 0.15 + 110 * 0.25 + 120 * 0.35 + 130 * 0.20 + 140 * 0.00) * $50
Expected cost per hour = $112.50
Comparing the expected costs, we can see that replacing one pen each time a failure occurs results in a lower expected cost per hour ($39.50) compared to replacing all four pens ($112.50). Therefore, the best policy for Brennan Aircraft would be to replace one pen each time a failure occurs.
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with a reserve requirement of 5% and an initial deposit of $400, what is the maximum total amount of money that will be in the money supply? assume that all currency is deposited in a bank 7 banks hold no excess reserves (rr=.05)
Answers
The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.
How to find maximum money?To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.
The money multiplier is given by the formula: MM = 1 / reserve requirement.
Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.
The initial deposit is $400.
To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:
Maximum Money Supply = Initial Deposit * Money Multiplier
= $400 * 20
= $8,000.
Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.
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In a class of 22 students, 7 are female and 17 have an A in the class. There are 3 students who are male and do not have an A in the class. What is the probability that a student who has an Ais a male?
Answers
Answer:
Step-by-step explanation:
total number of students=22
number of female students=7
number of male students=22-7=15
number of male students not having A=3
Number of male students having A=15-3=12
P(male student having A)=12/22=6/11
The probability that a student who has an A is male is approximately 0.632
What is probability?We can use the formula for conditional probability:
P(Male | A) = P(Male and A) / P(A)
We are given that there are 3 male students who do not have an A, so there are 22 - 3 = 19 students who have an A. Of these 19, we do not know how many are male. However, we do know that there are 7 female students, so the number of male students who have an A is:
19 - 7 = 12
Therefore, the probability that a student who has an A is male is:
P(Male | A) = 12 / 19
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor (which is 1 in this case):
P(Male | A) = 12 / 19
So the probability that a student who has an A is male is approximately 0.632.
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There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 people use the gym and the pool. 9 people use the pool and the track. 16 people use the gym and the track. 4 people use all three facilities. How many people didn't use any facilities?
Answers
Answer:
24 people
Step-by-step explanation:
((The numbers are up there, so I am not going to define each variable.))
For starters, there is no overlap between the double facilities groups, except the triple facility users, so:
19 + 9 + 16 - 4 = 40 people
Since there is overlap between single and double groups, you will need to subtract, so:
Gym: 73 - 19 - 16 = 38
Pool: 59 - 19 - 9 = 31
Track: 31 - 9 - 16 = 6
Total for 1 facility: 38 + 31 + 6 - 4 = 71 people
((Minus 4 because the 4 triple facility users overlap the double facility users (problem is in layers: layer 1 minus layer 2, then minus layer 3).))
Next, add the totals:
71 + 40 = 111 people (using facilities)
135 - 111 = 24 people (who didn't use any)
(((I'm not 100% sure on this answer, so if someone could check my work, that would be much appreciated.)))
a new oven is $1,500. the sales tax is 6.2%. what is the total cost of the oven including sales tax.
a.1500
b.1593
c.1693
d.1893
Answers
Answer:
B
Step-by-step explanation:
Answer:
B.1593
Step-by-step explanation:
I NEED HELP, Look at the picture for question
Answers
Answer:
A, C, D, E
Step-by-step explanation:
Input your equations and tables into Desmos graphing to get your answers.
19. 16+ [(21-13)33] is hard for me
Answers
Answer: 280
Step-by-step explanation:
because of PEMDAS, you start with the parenthesis, so 21-13=8. Next, you do the brackets, so 8 x 33=264. Lastly just add 16 to 264, so 16+264=280
Name two lines in the diagram.
B.
S
A
D
E
line A
line B
BC
point a
Answers
Answer:
Options (3) and (6)
Step-by-step explanation:
"A straight line is a set of all points between two points and extending beyond these points."
Therefore, from the given diagram,
Arrows connecting set of two points B and C and D and E will be straight lines.
Geometrically we denote them with an arrow over the line.
\(\overleftrightarrow {BC}\) and \(\overleftrightarrow {DE}\)
Therefore, Options (3) and (6) will be the answer.
In which quadrant on a graph will (-5, -7) be found? *
Quadrant 1
Quadrant II
Quadrant III
Quadrant IV
Answers
Answer:
on a graph will (-5, -7) be found Quadrant III.
If tan m = one-half and tan n = â€"6, what is the exact value of tan(m n)?
Answers
Since tan m = 1/2 and tan n = -6, the precise value of tan (m+n) will be 3.51.
What is tangent?The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle. The law of tangent is another name for tan. The ratio of a triangle's opposing side to its adjacent side is known as the tangent formula for a right-angled triangle. The angle's sine to cosine ratio can also be used to represent the angle.
Here,
tan m= 1/2
tan n= -6
m=tan inverse(1/2)
n=tan inverse(-6)
m=26.565 degrees
n= -80.537 degrees
n=360-80.537
n=279.463 degree
tan (m+n)=tan(26.565+279.463)
tan 306.028=3.51
The exact value of tan (m+n) will be 3.51 as the value of tan m= 1/2 and tan n= -6.
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Popular wisdom is that eating presweetened cereal tends to increase the number of dental caries (cavities) in children A sample of children was (with parental consent) entered into a study and followed for several years. Each child was classified as a sweetened-cereal lover or a unsweetened cereal lover. At the end of the study, the amount of tooth damage was measured. Here are the summary data: 10 15 Mean 6.41 5.20 Std Dev 5.0 15.0 225 Sweetened Unsweetened Assuming the necessary conditions for inference are met, which of the following an approximate 95% confidence interval for the difference in the mean tooth damage?
O (6.41 -5.20) + 2.145 3+
O (6.41 - 6:20) +1.96 Vi+
O (6.41 -- 5.20) +1,96/13 + 38
O (6.41 -5.20) +2.202/33+
O (6.41 - 5:20): 2.2821+13 228 X
Answers
An approximate 95% confidence interval for the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26\(\sqrt{\frac{25}{10}+\frac{225}{15} }\)
For sweetened samples
The value of n = 10
The mean of the samples = 6.14
The standard deviation of the sample = 5.0
For unsweetened samples
The value of n = 15
The mean of the sample = 5.20
The standard deviation of the sample = 15.0
We have to assume that necessary conditions for inference are met
The confidence interval = 95%
The equation will be
(6.41 - 5.20) ± 2.26\(\sqrt{\frac{25}{10}+\frac{225}{15} }\)
Therefore, the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26\(\sqrt{\frac{25}{10}+\frac{225}{15} }\)
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Your answer should be at 50 or more words. You imagine that your tutor is asked to record the \D, student name, date of birth, home address and phone number of every student in your tutorial and then email the spreadsheet to the unit convenor. What problems might arise? Note: there are around 120 students in this, unit and several tutors. You must start a thread before you can read and reply to other threads
Answers
There are several potential problems that might arise if a tutor is asked to record personal information such as student names, dates of birth, home addresses, and phone numbers for a large number of students and then email the spreadsheet to the unit convenor.
One major concern is the security and privacy of the students' personal information.
There are logistical challenges involved in managing and organizing the large amount of data.
One major concern is the security and privacy of the students' personal information. Emailing a spreadsheet containing sensitive data poses a risk of unauthorized access, interception, or data breaches. If the spreadsheet falls into the wrong hands, it could lead to identity theft, privacy violations, or misuse of personal information. Additionally, there is the issue of compliance with data protection regulations, such as the General Data Protection Regulation (GDPR), which requires the protection of personal data and imposes strict guidelines on its handling.
Moreover, there are logistical challenges involved in managing and organizing the large amount of data. Ensuring accuracy and maintaining data integrity becomes increasingly difficult with a higher number of students and multiple tutors. There may be instances of data entry errors, missing information, or duplication, which can lead to confusion and inaccuracies in student records.
To address these problems, it is important to establish secure data management protocols, such as using encrypted file transfer methods or secure file sharing platforms. Implementing strict access controls and limiting the number of individuals handling and transmitting the data can help mitigate the risks. It is also essential to comply with relevant privacy laws and regulations and provide clear guidelines to tutors on data protection and confidentiality. Regular data audits and reviews can help identify and rectify any potential issues in the data management process.
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congruent equilateral tringales are used to tesselate the plane. how many tringals share a common vertex
Answers
In a tesselation of the plane with congruent equilateral triangles, each vertex is shared by six triangles.
This can be visualized by imagining a single equilateral triangle as the center, surrounded by six other equilateral triangles that share a common vertex with the central triangle. Therefore, in this type of tesselation, each vertex is surrounded by six neighboring triangles.
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