In the function, Three of the factors are (x + 1).
We have to given that,
The function for the graph is,
⇒ f (x) = x⁴ + x³ - 3x² - 5x - 2
Now, We can find the factor as,
⇒ f (x) = x⁴ + x³ - 3x² - 5x - 2
Plug x = - 1;
⇒ f (- 1) = (-1)⁴ + (-1)³ - 3(-1)² - 5(-1) - 2
⇒ f(- 1 ) = 1 - 1 - 3 + 5 - 2
⇒ f (- 1) = 0
Hence, One factor of function is,
⇒ x = - 1
⇒ ( x + 1)
(x + 1) ) x⁴ + x³ - 3x² - 5x - 2 ( x³ - 3x - 2
x⁴ + x³
-------------
- 3x² - 5x
- 3x² - 3x
---------------
- 2x - 2
- 2x - 2
--------------
0
Hence, We get;
x⁴ + x³ - 3x² - 5x - 2 = (x + 1) (x³ - 3x - 2)
= (x + 1) (x³ - 2x - x - 2)
= (x + 1) (x + 1) (x + 1) (x - 2)
Thus, Three of the factors are (x + 1).
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Select the correct answer. If function f has zeros at -3 and 4, which graph could represent function f?
Answer:
first one
Step-by-step explanation:
The graph intersects x-axis at (4,0) and (-3,0)
If function f has zeros at -3 and 4 then the first graph represents the function f.
When a function has zeros at -3 and 4, it means that the function's value is equal to zero at those x-values.
In other words, when x = -3 and x = 4, the function f(x) becomes 0.
To represent this on a graph, you should look for two points where the graph intersects the x-axis at -3 and 4.
When the graph crosses the x-axis at these points, it indicates that the function has zeros at those x-values.
When we observe the graphs, the first graph has zeros at -3 and 4.
Hence, the first graph could represent the function f with zeros at -3 and 4.
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statistical process control tools are used most frequently because
Statistical process control (SPC) tools are used most frequently because they provide a systematic and data-driven approach to monitor and improve processes.
The main advantage of using SPC tools is that they enable organizations to detect and respond to variations in their processes. By collecting and analyzing data over time, SPC tools help identify patterns, trends, and abnormalities in the process performance.
This allows for timely intervention and corrective actions to be taken, reducing the likelihood of defects, errors, and inefficiencies. SPC tools provide a proactive approach to quality management, helping organizations maintain consistency and meet customer requirements.
Furthermore, SPC tools provide objective and quantitative measures of process performance. They use statistical techniques to measure process capability, control limits, and performance indicators such as mean, standard deviation, and control charts.
This allows organizations to make data-driven decisions and prioritize improvement efforts based on reliable information rather than subjective assessments.
SPC tools also provide a common language and framework for quality improvement efforts, facilitating communication and collaboration among team members.
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Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'. On a coordinate plane, 2 parallelograms are shown. Parallelogram M N P Q has points (2, negative 2), (4, negative 2), (3, negative 3), and (1, negative 3). Parallelogram M prime N prime P prime Q prime has points (5, negative 5), (10, negative 5), (8, negative 7), and (3, negative 7). Which statements are true about the parallelograms?
Which statements are true about the parallelograms? Check all that apply.
The length of side MN is 2 units.
The length of side M'N' is 5 units.
The image is smaller than the pre-image.
Sides MQ and M'Q' both have the same slope, 1.
The scale factor is 2/5
Parallelogram M'N'P'Q' is larger than parallelogram MNPQ because MN and M'N' have lengths of 2 and 5 respectively, and parallelogram MNPQ is dilated by a factor of 5/2 to give parallelogram M'N'P'Q'.
What is parallelograms?A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.
To make parallelogram M'N'P'Q, parallelogram MNPQ was enlarged.
Points include M(2, 2), N(4, 2), P(3, 3), and Q. (1,-3)
M'(5, 5), N'(10, 5), P'(8, 7), and Q' (3,-7)
A) First, determine Minnesota's length:
|MN| = 2
|M'N'| = 4
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4. A car is priced at $7200. The car dealer allows a customer to
pay a one-third deposit and 12 payments of $420 per month.
How much extra does it cost the customer?
Answer:
$240 extra
Step-by-step explanation:
1/3(7200) + 12(420) = 2400 + 5040 = 7440
7440 - 7200 = 240
The customer had to pay 1720 extra.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A car is priced at $7200.
If the deposit is one third = 7200/3
= 240
The amount after 12 payments will be
= 240 x 12
= 2880
total cost will be
= 2880 + 2400
= 5280
and, The customer had to pay extra amount
= 7200 - 5280
= 1720
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5. Write two expressions for the area of the big rectangle.
Answer:
Two expressions for the area are;
i) x/3 + 2·y + 6
ii) (1/3) × (x + 6·y + 18)
Step-by-step explanation:
The given dimension of the rectangle are;
The height of the rectangle, h = 1/3
The width of the smallest rectangle, w₁ = x
The width of the med sized rectangle, w₂ = 6·y
The width the large rectangle, w₃ = 18
The area, 'A', of the entire rectangular figure, the big rectangle, can be expressed as follows;
A = A₁ + A₂ + A₃
Where;
A₁ = The area of the smallest rectangle
A₂ = The area of the mid sized rectangle
A₃ = The area of the large rectangle
∴ A = (1/3) × x + (1/3) × 6·y + (1/3) × 18 = x/3 + 2·y + 6
The area of the big rectangle. 'A', can also be found as follows;
A = (1/3) × (x + 6·y + 18)
Therefore, two expressions for the area of the big rectangle are;
x/3 + 2·y + 6 and (1/3) × (x + 6·y + 18).
The Mona Lisa, shipped in a private cabin and received
by important dignitaries, was treated more like -------
than a painting upon its arrival in the United States.
(A) a perfectionist (B) a maverick (C) a potentate
(D) an ascetic (E) an interloper
The correct answer is option c) a potentate.
The Mona Lisa, shipped in a private cabin and received by important dignitaries, was treated more like a potentate than a painting upon its arrival in the United States.
As a monarch, ruler, king, or queen is what is meant by the term "potentate," option C is the correct response.
Because of this, the correct response is C because the Mona Lisa was a monarchical figure.
In addition, there are An unconventional or independent person is referred to as a maverick. Living a simple life is what an ascetic does.
Trespassers are those who break in. Potentate is the best option, taking into account all of the definitions of the other choices.
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calculate the coefficient of variation for a sample of cereal boxes with a mean weight of 340 grams and a standard deviation of 5.2 grams.? 0.15% A
1.53% B
15.29% C
0.65% D
The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.
In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.
CV = (Standard Deviation / Mean) * 100
CV = (5.2 / 340) * 100
CV ≈ 1.53%
Therefore, the correct answer is option B: 1.53%.
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If the length of a rectangle is four less than twice its width and the perimeter is
220 inches, what is the width of the rectangle?
The width of the rectangle with a perimeter of 220 inches is 38 inches.
What is the width of the given rectangle?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The perimeter of a rectangle is expressed as;
P = 2( length + width )
Given the data in the question;
Let x represent the width of the rectangle.
Width of the rectangle = xLength = 2x - 4Perimeter = 220 inchesTo solve for the width ( x ), plug the given values into the perimeter formula above and solve for x.
P = 2( length + width )
220 = 2( (2x - 4 ) + x )
220 = 2( 2x - 4 + x )
220 = 2( 3x - 4 )
220 = 6x - 8
6x = 220 + 8
6x = 228
x = 228/6
x = 38
Therefore, the width of the rectangle x is 38 inches.
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solve the equation 5(3x-1)=4(3x-2)
Answer:
x=-1
Step-by-step explanation:
15x-5=12x-8 Simplify Parentheses
3x=-3 Isolate the variable
x=-1 Divide by 3 on both sides
Answer:
\(x=-1\)
Step-by-step explanation:
Our equation is
\(5\left(3x-1\right)=4\left(3x-2\right)\)
First, we distribute
Now we have
\(15x-5=12x-8\)
Subtract \(12x\) from both sides
\(3x-5=-8\)
add \(5\) to both sides
\(3x=-3\\\)
Divide both sides by 3
\(x=-1\)
Brainliest please
Can someone answer this question i am having an issue to how to figure it out
Answer:
explanation below
Step-by-step explanation:
f(x) = 3x + 2
f(8) : replace x with 8 f(8) = 3 * 8 + 2 = 26
g(x) = 5x
g(a+2) : replace x with a+2 g(a+2) = 5 (a+2) or 5a + 10
Which of the data sets below has a total of 7 data points (observations)? A) 18, 91, 93, 55, 57, 18 B) 25, 26, 28, 91, 18 C) 9, 12, 8, 5, 12, 9,7 D) 7,5, 9, 11, 13, 4, 9, 18 E) 95, 91, 87, 99, 95, 84, 77
To know the number of data points, simply count the number of values in the data, these values are separated by a comma
Option A: 18, 91, 93, 55, 57, 18. is not correct (it has 6 data points)
Option B: 25, 26, 28, 91, 18, is not correct ( it has 5 data points)
Option C: 9, 12, 8,5, 12, 9, 7. is correct (it has 7 data points)
Option D: 7,5, 9, 11, 13, 4, 9, 18. is not correct ( it has 8 data points)
Option E: 95, 91, 87, 99, 95, 84, 77. is correct (it has 7 data points)
Options C and E are correct
Your new hot tub is being filled with water at a rate of r(t) gallons per minute, where t is the time in minutes. Explain the meaning of the expression. t Srce)dt = 3
The integral ∫t S(r(t)) dt calculates the total amount of water that has been filled into the hot tub from the initial time (t = 0) up to time t. It represents the accumulated water volume over the interval [0, t].
The expression ∫t S(r(t)) dt = 3 represents the definite integral of the rate function r(t) over a specific time interval [t1, t2], where t1 and t2 are the limits of integration. In this case, the limits are not provided, so we'll consider it as a general integral.
To understand the meaning of this expression, let's break it down:
r(t): This represents the rate at which water is being filled into the hot tub at time t. The rate function r(t) gives the instantaneous rate of change of the water level with respect to time. It is measured in gallons per minute.
S(r(t)): This indicates the amount of water being filled into the hot tub per unit of time. It is obtained by multiplying the rate r(t) by a small time increment Δt. As Δt approaches zero, S(r(t)) represents the infinitesimal amount of water being filled in during that very small time interval.
dt: This represents the infinitesimal change in time. It is the differential of the independent variable t.
∫: This symbol denotes the integral operation, which is used to find the accumulated or total amount of something over a given interval.
t: This variable represents the time.
In this case, the given expression ∫t S(r(t)) dt = 3 indicates that after a certain amount of time t, the total volume of water in the hot tub is 3 gallons. This means that the integral of the rate function r(t) from the initial time to the given time t has resulted in a total volume of 3 gallons in the hot tub.
It's important to note that the specific limits of integration are not provided in the given expression. Therefore, the exact meaning of this expression may vary depending on the specific time interval considered.
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Evaluate the expression when a=6 and b=4. b - 3a
-14 is the value of the expression b - 3a at a =6 and b = 4.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression b - 3a
For this expression given,
a = 6 and b = 4
Thus the value of expression at given values
=> b - 3a
=> 4 - 3 * 6
=>4 - 18
=> -14
Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.
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which of the following method returns the sine of 90 degree?
The correct method to return the sine of 90 degrees is Math.sin(90). The Math.sin() method accepts the angle in radians as its parameter and returns the sine value of that angle. Thus, option B is correct.
In Java, the Math class provides various mathematical functions, including trigonometric functions like sine (sin). Option A, Math.sine(90), is incorrect because there is no method named "sine" in the Math class. The correct name is "sin".
Option C, Math.sin(PI), is incorrect because the constant PI is the value of pi in radians, not in degrees. Since the parameter of the Math.sin() method should be in radians, passing PI as the argument will give the sine of pi radians, not 90 degrees.
Option D, Math.sin(Math.toRadians(90)), is incorrect because the radians () method converts an angle in degrees to radians. So, Math.toRadians(90) would give the value of pi/2 in radians, not 90 degrees.
Option E, Math.sin(Math.PI), is also incorrect for the same reason as option C. Math.PI represents the value of pi in radians, not in degrees.
In conclusion, the correct method to return the sine of 90 degrees in Java is Math.sin(90), which takes the angle in degrees as its parameter. Thus, option B is correct.
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Complete Question:
Which of the following method returns the sine of 90 degree?
A. Math.sine(90)
B. Math.sin(90)
C. Math.sin(PI)
D. Math.sin(Math.toRadian(90))
E. Math.sin(Math.PI)
escribe how relative frequencies of past events are used to predict future events. (for example, if a student passed seven out of ten assignments in a course, what do you think is the probability that this student will pass the next assignment in the course? how did you calculate this probability?)
Relative frequencies of past events can be used to predict future events by using probability theory. Probability theory is a branch of mathematics that deals with the study of random phenomena.
In the given example, if a student passed seven out of ten assignments in a course, the probability that the student will pass the next assignment in the course can be calculated by using relative frequency. We can use the formula of probability to calculate the probability of the student passing the next assignment. Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, the number of favorable outcomes is seven because the student passed seven out of ten assignments. The total number of possible outcomes is ten because the student attempted ten assignments. Therefore, the probability of the student passing the next assignment is 7/10 or 0.7. This means that there is a 70% chance that the student will pass the next assignment.
In conclusion, the relative frequency of past events can be used to predict future events. Probability theory can be used to calculate the probability of an event occurring in future events. By using the formula of probability, we can calculate the probability of an event occurring based on the relative frequency of past events. In the given example, the probability of the student passing the next assignment is calculated as 0.7 or 70%.
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How is field data aggregated? Number of failed parts Number of failures Hours of operation Maintenance time Mark for follow up Question 3 of \( 7 . \) Data collection extends over a large number of it
Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,
such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.
Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,
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7(n – 1) = -2(3 + n) solve for n
For every 15 students on a field trip, there needs to be one teacher. What is minimum number of teachers needed for a group of 100 students? Write your answer as an inequality, then explain in words why you know your answer is correct.
Answer:
7 teachers
Step-by-step explanation:
you decide 100 by 15 which equals 6.7 since you can't have half a teacher you round it to 7 teachers.
Answer:
The minimum number of teachers needed is 6
Step-by-step explanation:
To find minimum number of teachers we have to divide 100 and 15 so the answer is 6.666.....but if we
multiply 6 and 15 we get 90 , so it means that 6 teachers can only provide for 90 students , unfortunately there are 100
students , so we need 1 more teacher for the rest ten students that's why the answer came in decimal point . so the answer could be 6.66 or 7 .
Which of the following statements is not true?
A. the adjusted r-squared value is always smaller than the r-squared value
B. the adjusted r-squared value will always decrease with the addition of another variable
C. the r-squared value cannot decrease when a new variable is added to the regression
D. the adjusted r-squared, more so than the r-squared, is more useful for comparing different regression models
E. all of the above
Therefore ,a result, the answer to the variable problem (B) is incorrect because, even though the adjusted R-square has a lower value .
Variable : What is it ?A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.
Here,
Given : The adjusted r-squared number is always lower than the s n value The added variable always causes the modified r-squared value to fall.
If a new variable is included to the regression, the r-squared result cannot drop.
. When comparing several regression models, the adjusted r-squared is more helpful than the r-squared.
Therefore ,a result, the answer to the variable problem (B) is incorrect because, even though the adjusted R-square has a lower value than the R-square, it might not drop as you add more variables.
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brian and summer took a 12-mile canoe ride down a river in two hours. after stopping for lunch, they returned back up the river in three hours. find the rate of the canoe in still water and the rate of the current.
The rate of the canoe in still water is 5 miles per hour, and the rate of the current is 1 mile per hour.
Let's use the letters "c" for the canoe's speed in still water and "r" for the current's speed. The formula is as follows:
Rate times distance
establishing two equations, one for the upstream trip and one for the downstream trip.
Trip downstream:
12 miles is the distance.
rate = c plus r. (since the current is helping them)
t = two hours
We thus have:
12 = (c + r) × 2
When we simplify this equation, we obtain:
6 = c + r
Trip upstream:
12 miles is the distance.
rate equals c-r (since they are now going against the current)
three hours.
We thus have:
12 = (c - r) × 3
When we simplify this equation, we obtain:
4 = c - r
There are now two equations:
6 = c + r
4 = c - r
By combining the two equations, we may find the value of one of the variables:
6 + 4 = 2c
If we simplify, we get:
10 = 2c
When you divide both sides by 2, you get:
c = 5
To solve for the other variable, we may now re-insert this value into one of the equations. Let's apply the formula:
6 = c + r
With c = 5, we obtain:
6 = 5 + r
5 is subtracted from both sides to yield:
r = 1
In still water, the canoe moves at a rate of 5 miles per hour, while the current moves at a rate of 1 mile per hour.
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HELP MATH AHH URGENT PLS
Answer:
Step-by-step explanation:
Area of a triangle: .5(b*h)
which means that
.5(4(x-1)*(2x+5))=30
mulitply the two equations
(4x-4)(2x+5) = 8x²+12x-20
distribute the 1/2
.5(8x²+12x-20)
4x²+6x-10 = 30
divide both sides by 2
2x²+3x-5= 15
move everything to one side
2x²+3x-20=0
not sure if you need to solve it but x= 2.5 or x= -4
The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. What is the probability that the cycle time exceeds 60 minutes if it is known that the cycle time exceeds 55 minutes
The probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes is 2/1 or simply 1, which means it is certain that the cycle time exceeds 60 minutes if it exceeds 55 minutes.
Given that the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes, we know that the probability density function is:
f(x) = 1 / (70 - 50) = 1/20, for 50 <= x <= 70
To find the probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes, we need to use conditional probability:
P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)
We can simplify this by noticing that if X is greater than 55, then it must be between 55 and 70, and therefore:
P(X > 55) = P(55 <= X <= 70) = (70 - 55) / (70 - 50) = 1/4
Similarly, we can rewrite the numerator as:
P(X > 60 and X > 55) = P(X > 60)
since if X is greater than 60, it is also greater than 55.
Now, to find P(X > 60), we integrate the density function from 60 to 70:
P(X > 60) = ∫60^70 (1/20) dx = (1/20) × (70 - 60) = 1/2
Putting it all together:
P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)
= P(X > 60) / P(X > 55)
= (1/2) / (1/4)
= 2
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a cone has a volume of 1,570in3. If the height of the cone is 15 inches. Calculate the radius of the cone?
Answer:
approximately 10
Step-by-step explanation:
Volume = 1/3h times \(\pi\) times radius square
1570 = 1/3 x 15 x 22/7 x \(r^{2}\)
1570 = 5 times \(\frac{22}{7}\) times \(r^{2}\)
1570 = 15.71\(r^{2}\)
\(\frac{1570}{15.71}\) = \(\frac{15.71 r^{2}}{15.71}\)
99.9 = r^2
\(\sqrt{99.9}\) = r
≅10
PLZ HELP It’s due soon
Answer:
30
Step-by-step explanation:
Answer:
Oh thats easy its $30
Step-by-step explanation:
so for 2 icecreams it costs $6
so if u divide them it would become 1 icecream for $3 so
10 times 3 will be $30
Use the given graph to determine the limit, if it exists. (4 points)
A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3.
Find limit as x approaches three from the right of f of x. .
Explanation:
Refer to the graph below. It should be similar to what your teacher gave you, based off the description.
Since we're approaching 3 from the right side, this means we'll be working with the horizontal line portion. We could start at something like x = 3.2 and move closer to 3 by getting to x = 3.1 then x = 3.01 then x = 3.001 and so on. We never actually get to 3 itself.
As x gets closer to 3 from this direction, the y values are approaching 3 since every point on this horizontal line has the same y coordinate. Technically the y value is already at 3, but it's the same idea.
In terms of notation, we can write \(\displaystyle \lim_{x\to3^{+}}f(x) = 3\)
The portion \(x \to 3^{+}\) means we're approaching 3 from the positive side, aka the right hand side on the number line.
GIVING BRAINLIEST! HELP
Answer:
Below
Step-by-step explanation:
125 kg * 2.204 pound/kg = 275.5 pounds
Answer:
D. 275.5 pounds
Step-by-step explanation:
1 kg = 2.204 lbs
=> 125 kg = (125 kg)(2.204 lbs/1 kg) = 275.5 lbs
Write the following sets using the "roster method". That is, write the sets in list form. (a) A = {: is a natural number and x appears in the decimal expansion of 313/999} (b) B = {x:x is an odd integer smaller than 1} 2. List the next element in each of the following sets. (a) {1,1/4,1/16,1/64,...} (b) (3,3,6,9,15,24,...} 3. Answer either TRUE or FALSE to each of the statements (a) through (d). A = {3,6,9, ..., 96, 99} B = {1,0, 1, 2, 3, 4, 5, 6} (a) 66 € A ___
(b) 0 € C ___ (c) {4} € B ___ (d) C C A ___
66 € A is true as 66 is a multiple of 3, which is a member of A. Therefore, 66 € A is True. 0 € C (FALSE). The set C is not given. Therefore, it is not possible to say whether 0 belongs to C or not. Hence, 0 € C is false.
A. A = {0.313, 0.626, 0.939} B. B = {-1}
A set in mathematics is a collection of distinct objects called elements of the set. These elements could be numbers, letters, or any other kind of object. Here, we are going to use the roster method to represent the sets in list form.
The roster method is the method of representing a set by listing its elements within braces {}. A. Set A comprises all the natural numbers (x) that appear in the decimal expansion of 313/999. Now, let's solve the problem using the roster method: A = {0.313, 0.626, 0.939}. Set A comprises all the natural numbers (x) that appear in the decimal expansion of 313/999.
The roster method is the method of representing a set by listing its elements within braces {}. The set A can be represented in list form as A = {0.313, 0.626, 0.939}. B. The set B comprises all odd integers smaller than 1. The set B comprises all odd integers smaller than 1. The roster method is the method of representing a set by listing its elements within braces {}. The set B can be represented in list form as B = {-1}.2.
a) {1,1/4,1/16,1/64,...}
Notice that each term is of the form 1/4ⁿ. The next element in the set is 1/256.2.b) {3,3,6,9,15,24,...}
Notice that the differences between consecutive terms in the sequence are 0, 3, 3, 6, 9,.... The next term would be obtained by adding 12 to 24. Therefore, the next term is 36.3. a) 66 € A (TRUE) as 66 is a multiple of 3, which is a member of A. Therefore, 66 € A is True.
3. b) 0 € C (FALSE). The set C is not given. Therefore, it is not possible to say whether 0 belongs to C or not. Hence, 0 € C is False.
3. c) {4} € B (FALSE)The set B has only odd integers, and 4 is an even integer. Therefore, {4} € B is False. 3. d) C C A (FALSE)Since 0 € C is False, C € A is False.
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Suppose we roll a fair six-sided die and sum the values obtained on each roll, stopping once our sum exceeds 354. Approximate the probability that at least 94 rolls are needed to get this sum
The approximate probability that at least 94 rolls are needed to get a sum greater than 354 is 0.852.
X be the number of rolls needed to obtain a sum greater than 354. We are interested in finding P(X ≥ 94).
We can use the fact that the sum of two fair six-sided dice is uniformly distributed between 2 and 12. Thus, the sum of n rolls of a fair six-sided die is uniformly distributed between n and 6n.
Let Yn be the sum of the first n rolls of the die. Then Yn is uniformly distributed between n and 6n, and we have:
P(Yn > 354) = P(Yn - n > 354 - n) = P((Yn - n)/5 > (354 - n)/5)
Now, (Yn - n)/5 is uniformly distributed between 1 and 6, and (354 - n)/5 is between 1 and 70. So we have:
P(Yn > 354) = P((Yn - n)/5 > (354 - n)/5) = P(U > (354 - n)/5)
where U is a uniform random variable on [1,6].
We want to find P(X ≥ 94) = P(Y94 ≤ 354) = 1 - P(Y94 > 354) = 1 - P(U > (354 - 94)/470) = 1 - (70/471) = 0.852.
Therefore, the approximate probability that at least 94 rolls are needed to get a sum greater than 354 is 0.852.
Probability is the likelihood or chance of an event. Occurring for example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .
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Hello I need help on this math questionBRAINLIEST For the fastest correct answer
The level of significance in hypothesis testing is the probability of:A. Accepting a true null hypothesisB. Accepting a false null hypothesisC. Rejecting a true null hypothesisD. None of these alternatives is correct
The correct option C. Rejecting a true null hypothesis, is the probability in significance level in hypothesis testing.
Explain about the null hypothesis significance testing?By testing an experimental component against a no effect or even no relationship hypothesis based on a specific observation, NHST is a statistical inference technique.
The idea that there is no influence on the population is known as the null hypothesis. We may refuse the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect with in population (p ).In the biological, biomedical, and social sciences, null hypothesis significance testing (NHST) continues to be the statistical technique of choice for presenting evidence of an effect.Thus, the likelihood of rejecting a valid null hypothesis determines the significance level in hypothesis testing.
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