It takes the second marathoner 4 hours and 40 minutes to complete the marathon.
Let's assume the distance of the marathon is "d" miles.
The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:
speed = distance / time = d / 4
The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:
speed = 4(d / 4) = d
For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:
d / 2 = (3/4)(d / 4)(t)
Simplifying this equation, we get:
t = (2/3) hours
So the total time it takes the second marathoner to finish the race is:
4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.
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each unit square of a $3\times 3$ grid of unit squares is to be colored either blue or red. for each square, either color is equally likely to be used. find the probability of obtaining a grid that does not have a $2\times 2$ red square.
The probability of obtaining a grid that does not have a 2 × 2 red square is 127/128 and the value of (p + q + 1) / 310 is 0.82.
Total number of outcomes = [tex]2^9[/tex] = 512
We will subtract the outcomes of obtaining a grid that does not have a
2 × 2 red squares from the total outcomes.
Favorable outcomes = Total outcomes - outcomes having [tex]2[/tex] × [tex]2[/tex] red squares
= [tex]2 ^3 - 4[/tex]
= 508
So favorable outcomes are 508.
Probability calculates the chances of experiments occurring. It is obtained by the ratio between favorable outcomes and total outcomes. It is basically how likely something is to happen.
Probability = Favorable outcomes / Total no. of outcomes
= 508 / 512
= p/q
= 127/128
So, the probability of obtaining a grid that does not have a 2 × 2 red square is 127/128.
Now, the value of (p + q + 1)/310
= (127 + 128 + 1)/310
= 256/310
= 0.82
Therefore, the value of (p + q + 1) / 310 is 0.82.
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The complete question is -
"Each unit square of a 3 * 3 square grid is to be colored either blue or red for each square, either color is equally likely. The probability of obtaining a grid that does not have a 2 * 2 red square is CHCF(p,q) is 1). Find this probability and then find the value of (p + q + 1) / 310 ?"
Carol was packing up some of her old stuff into a box. A box can hold 2 pounds, but she only filled it up 1/2 full How much weight was in the box?
Answer:
1 pound
Step-by-step explanation:
If a box can hold 2 pounds but is only filled up 1/2 full, then there is only 1 pound of weight in the box.
To see why, consider that if the box was completely full, it would hold 2 pounds. But if it is only half full, it can only hold half of that amount, or 1 pound. Thus, the weight in the box is 1 pound.
A laptop computer sells for $2,149.99 and has a mail-in rebate for $200. What is
the cost after the rebate if an envelope costs 15¢ and a stamp costs 39¢?
The cost of the envelope and stamp may vary depending on the location and the method of delivery. In this example, we assumed that the cost of the envelope is $0.15 and the cost of the stamp is $0.39, but these values may change based on the specific circumstances.
What is cost?
Cost" is the amount of money or resources that are required to produce, acquire, or obtain something. In other words, cost refers to the expenses that are incurred in the process of acquiring or producing a good or service.
For example, the cost of producing a product may include the cost of raw materials, labor, overhead expenses, and other related costs. Similarly, the cost of acquiring a product may include the purchase price, taxes, shipping costs, and any other fees or expenses associated with the purchase. Overall, cost is a crucial factor in business and economics, as it determines the profitability of a venture and helps to make informed decisions regarding investments and pricing strategies
To find the cost of the laptop after the mail-in rebate and the cost of the envelope and stamp, we can follow these steps:
Subtract the mail-in rebate from the original price of the laptop:
$2,149.99 - $200 = $1,949.99
Add the cost of the envelope and stamp to the cost of the laptop after the mail-in rebate:
$1,949.99 + $0.15 + $0.39 = $2,090.53
Therefore, the cost of the laptop after the mail-in rebate and the cost of the envelope and stamp is $2,090.53.
To explain this calculation, we first subtract the mail-in rebate of $200 from the original price of the laptop, which gives us the price of the laptop after the rebate. Then, we add the cost of the envelope and the stamp to this price to get the total cost of the laptop after the rebate and the cost of the envelope and stamp.
Therefore, The cost of the envelope and stamp may vary depending on the location and the method of delivery. In this example, we assumed that the cost of the envelope is $0.15 and the cost of the stamp is $0.39, but these values may change based on the specific circumstances.
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SOMEONE PLS HELP ASAP
Answer:
10.12
Step-by-step explanation:
440=(x)(4x+3)
=10.11979...
What is the radius of the circle if it has a circumference of 153. 86153. 86153, point, 86 units
If the circumference of the circle is 153.86 units, then the radius of that circle is 24.5 units.
The "Circum-ference" of circle is defined as "total-length" of boundary of the circle. The formula for circumference is = 2 × π × Radius,
The "Radius" of circle is the distance from center of circle to its outer edge. It is half of "diameter" of circle, and it is a measure of size of circle.
We know that, circumference of circle is 153.86 units,
So, the circumference equation becomes,
⇒ 2 × 3.14 × Radius = 153.86,
⇒ 153.86/(2 × 3.14) = Radius,
⇒ Radius ≈ 24.5
So, the radius of the circle is approximately 24.5 units.
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The given question is incomplete, the complete question is
What is the radius of the circle if it has a circumference of 153.86 units?
In 1995, 57. 5% of students at Gardiner university graduated in 4 or fewer years of study. In 2009, that number had fallen to 52. 8%. What was the rate of change for percent of students graduating within 4 years from 1995 to 2009.
The percent rate of change of students graduating within 4 years from 1995 to 2009 = 8.17%
Here, the percent of studenst graduated in 1995 = 57. 5%
and the percent of studenst graduated in 2009 = 52. 8%
First we find the relative change.
Let a represents the initial value and b represents the findal value
a = 57.5 and b = 52.8
so, the relative rate of change of students would be,
r = (b - a)/a
r = |(52.8 - 57.5)| / 57.5
r = 0.0817
And the percent rate of change of students graduating within 4 years from 1995 to 2009 would be,
p = r × 100
p = 0.0817 × 100
p = 8.17%
Therefore, the required percent is 8.17%
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A(n) method is like a blueprint, or template, for all the objects within a class. true or false?
The statement " A(n) method is like a blueprint, or template, for all the objects within a class" is true because methods define the behavior or operations that an object can perform and are defined within a class, acting as a blueprint or template for creating objects in object-oriented programming.
A method in object-oriented programming is a set of instructions that defines the behavior or operations that an object can perform. It is a part of a class, which acts as a blueprint or template for creating objects. When an object is created from a class, it can access and use the methods defined within that class.
Methods can be used to perform tasks, manipulate data, or interact with other objects. They are an essential aspect of encapsulation in object-oriented programming, as they allow for data to be accessed and manipulated in a controlled manner. Overall, methods are a crucial tool for developers to create robust and scalable applications.
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the population of a town is 1,800 and is decreasing at a rate of 3.8% per year what will their population be after 6 years
Step-by-step explanation:
DECREASING 3.8% means 96.2 % is left each year ( .962 in decimal)
1800 (.962) ^6 =~ 1427 population
Answer:
1389.6
explamation
1500 of 3.8% is 68.4
68.4*6=410.4
1800-410.4=139.6
abag contains 8 green balls and 5 red balls. the following events occur in sequence: i aball is randomly drawn and its color is recorded. then, it is returned to the bag. ii 3 balls of the opposite color recorded in step (i) are added to the bag. (for example, if a red ball was drawn in step (i), 3 green balls would be added to the bag) iii a ball is randomly drawn from the bag. what is the probability that the second ball drawn is red?
A bag contains 8 green balls and 5 red balls. Then the probability that the moment ball is drawn is ruddy is 23.1%.To fathom this issue, able to utilize the law of adding up to likelihood and consider:
A ruddy ball is drawn in step (i)The likelihood of drawing a ruddy ball in step (i) is 5/13, as there are 5 ruddy balls out of 13 adding up to balls within the pack.
After step (ii), there will be 5 ruddy balls (unique) + 3 green balls (inverse color) = 8 ruddy balls within the pack. So, the likelihood of drawing a ruddy ball in step (iii) given that a ruddy ball was drawn in step (i) is 8/11.
Presently, we will apply the law of adding up to likelihood to discover the general likelihood of drawing a ruddy ball in step (iii):
P(Red ball in step iii) = P(Green ball in step i) x P(Red ball in step iii | Green ball in step i)
P(Red ball in step i) x P(Red ball in step iii | Ruddy ball in step i)
= (8/13) x (3/11) + (5/13) x (8/11)
= 0.231 or roughly 23.1%.
thus, the likelihood that the moment ball is drawn is ruddy is 23.1%
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The weight of 4 hummingbirds is recorded below. The weight of each hummingbird has been rounded to the nearest 1 /2 1 dot above two and one-half; 1 dot above three; 1 dot above four and one-half, and 1 dot above five. A line plot labeled weights of birds in grams shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, and five. Dots are plotted as follows: 1 dot above two and one-half; 1 dot above three; 1 dot above four and one-half, and 1 dot above five. What is the weight of all 4 hummingbirds combined? grams
Answer:
5
Step-by-step explanation:
Answer:
15 grams
Step-by-step explanation:
Based on the information provided, the weight of each hummingbird is 2.5 grams, 3 grams, 4.5 grams, and 5 grams. To find the total weight of all 4 hummingbirds combined, we can add up their individual weights: 2.5 + 3 + 4.5 + 5 = 15 grams. So, the total weight of all 4 hummingbirds combined is 15 grams.
Geometric constructions requires what tools
Compass and straightedge are the two tools you'll need to create geometric constructions.
Explain about the tools for Geometric constructions:Without using numbers, geometric building enables the creation of precise drawings and models. The term "geometric building" refers to the act of precisely drawing something without the aid of numbers.
Your compass and the straightedge are the two tools. You have three tools if you count a pencil as one, the straightedge. As a ruler has numbers, this is the case. There are no numbers involved in proper geometric building. The compass I referenced isn't the kind you is using to draw circles; rather, it's the one with a needle that never points north. This particular compass has a pencil point on one end and a sharp tip on the other. By placing the pointed end down and turning the compass, you may use this tool to draw an arc.know more about the Geometric constructions
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Simplify the expression.
−7+11+ (−3) + 9 =
Answer:
10
Step-by-step explanation:
Answer: Simple. The answer is 10.
I will be giving brainliest plis help me!!!??!!?!??
Answer:sine
Step-by-step explanation:
Find the exact value of tan P in simplest radical form. √85 2 N √89
Answer:
We can start by using the tangent formula:
tan(P) = sin(P) / cos(P)
We are not given the values of sin(P) and cos(P) directly, but we can use the Pythagorean identity to relate them:
sin^2(P) + cos^2(P) = 1
We can rearrange this expression to solve for sin(P) in terms of cos(P):
sin^2(P) = 1 - cos^2(P)
sin(P) = ±√(1 - cos^2(P))
Now we can substitute this expression into the tangent formula:
tan(P) = ±√(1 - cos^2(P)) / cos(P)
Substituting the given values and simplifying:
tan(P) = ±√(1 - (2/√85)^2) / (1/√89)
tan(P) = ±√(1 - 4/85) * √89
tan(P) = ±√(81/85) * √89 / 1
We want to express tan P in simplest radical form, so we can simplify the square root by factoring out the greatest perfect square factor of the numerator:
tan(P) = ±(√9/√85) * (√89/1)
tan(P) = ±(3/√85) * (√89/1)
Therefore, the exact value of tan P in simplest radical form is ±(3/√85) * (√89/1).
Can you pls help? This is geometry
The equation of the circle with a center at the origin and a diameter of 8 is x² + y² = 16
Define circleA circle is a two-dimensional shape that is defined as a set of points that are equidistant from a fixed point called the center. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points (locus) at a certain radius from the centre.
If the center of the circle is at the origin, then the equation of the circle can be written in the form of:
x² + y² = r²
where r denotes the circle's radius.
Since the diameter of the circle is 8, the radius is half of that, or 4. Consequently, the circle's equation is as follows:
x² + y² = 4²
x² + y² = 16
So the equation of the circle with a center at the origin and a diameter of 8 is x² + y² = 16.
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Rewrite the expression as a product of four linear factors:
(12x² – 19x)² – 13(12x² – 19x) – 90
Answer:
(4x - 9)(3x + 2)(4x - 5)(3x - 1).
Step-by-step explanation:
Let's substitute y = (12x² - 19x):
So we have y² - 13y - 90, which can be factored as:
y² - 13y - 90 = (y - 18)(y + 5)
Substituting y back:
(12x² - 19x)² - 13(12x² - 19x) - 90 = [(12x² - 19x) - 18][(12x² - 19x) + 5]
= (12x² - 19x - 18)(12x² - 19x + 5)
= (4x - 9)(3x + 2)(4x - 5)(3x - 1)
What do (180 degrees)/pi and pi/(180 degrees) equal?
Pi/(180 degrees) equals 1 degree in radians.
What is radian?Radians are a unit of measurement for angles, just like degrees. The radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
To visualize this, imagine taking a circle with a radius of r and drawing an arc on the circle that is the same length as the radius. The angle subtended by this arc at the center of the circle is one radian. Since the circumference of a circle is 2pir, there are always 2*pi b in a full circle.
(180 degrees)/pi is equivalent to the value of 180 degrees in radians. To convert from degrees to radians, we multiply the degree value by (pi/180). So:
(180 degrees)/pi = (180 degrees) * (pi/180) = pi radians
Therefore, (180 degrees)/pi equals pi in radians.
On the other hand, pi/(180 degrees) is equivalent to the value of 1 degree in radians. To convert from radians to degrees, we multiply the radian value by (180/pi). So:
pi/(180 degrees) = pi * (180/pi) = 180 degrees
Therefore, pi/(180 degrees) equals 1 degree in radians.
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What is the most common type of employee benefit?
O retirement
O disability insurance
O life insurance
O healthcare
Answer:
life insurance is the most common type of employee benefit
What are 2 questions that would require an interpretation of the table?
1. What is the relationship between education level and income in this population? 2. How does the popularity of different music genres vary across different age groups?
What do you mean by an interpretation?An interpretation is a way of understanding or explaining something. Interpretation often involves making connections between different elements or pieces of information to create a coherent understanding. It can also involve applying theories, frameworks, or methods to analyze or explain a particular subject. Ultimately, interpretations are subjective and may vary based on individual experiences and perspectives, making it important to consider multiple interpretations when analyzing a particular subject.
Here is two example questions:
1. What is the relationship between education level and income in this population?
Interpretation: To answer this question, you would need to examine a table that includes columns for education level and income, such as a cross-tabulation or a summary statistics table. You could look for patterns or trends in the data, such as higher incomes being associated with higher levels of education. You might also look for any outliers or anomalies in the data that could be affecting the overall relationship between education level and income.
2. How does the popularity of different music genres vary across different age groups?
Interpretation: To answer this question, you would need to examine a table that includes rows for different age groups and columns for different music genres, such as a frequency table or a bar chart. You could look for patterns or trends in the data, such as certain music genres being more popular among younger age groups or older age groups. You might also look for any outliers or anomalies in the data that could be affecting the overall relationship between age and music genre popularity.
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7. Julie had a balance of $1,189.17 in her checking account. She wrote checks for $62.41, $224.14, $12.92, and $357.16. Her deposits were $197.34 and $879.13. What was Julie's new bank balance?
According to the given information, Julie's new bank balance was $1,609.01
To calculate Julie's new bank balance, we need to subtract the total amount of checks she wrote from her initial balance, and then add the total amount of deposits she made.
Total amount of checks = $62.41 + $224.14 + $12.92 + $357.16 = $656.63
Total amount of deposits = $197.34 + $879.13 = $1,076.47
New bank balance = Initial balance - Total amount of checks + Total amount of deposits
New bank balance = $1,189.17 - $656.63 + $1,076.47
New bank balance = $1,609.01
Therefore, Julie's new bank balance was $1,609.01.
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It is recommended that a ramp have at least 5 feet of horizontal distance for every 1 foot of horizontal rise along an incline. The ramp shown has a vertical rise of 3 feet. Does the ramp shown match the recommended specifications? Explain.
Yes ,inclination in between 4in / 15 in < 4in / 18 in
What is incline?An inclined plane, also known as a ramp, is a flat supporting surface that is tilted at an angle from the vertical direction with one end higher than the other. It can be used to lift or lower a load.
What is horizontal and vertical?The horizontal line in coordinate geometry is the line perpendicular to the x-axis, and the vertical line is the line perpendicular to the y-axis. Horizontal lines and vertical lines will be parallel to the x-axis and the y-axis, respectively. As a result, lines that share at least one point are perpendicular to one another when they are drawn.
6 feet of horizontal distance for every 1 foot,
ramp shown has a vertical rise of 5 feet.
Therefore
M ≤ 1foot / 6 feet
Converting both to a single units of ( inches )
M ≤ 12 inches / 72 inches
Dividing by 4
M ≤ 4 inches / 18 inches
Where 5 feet = 60 inches
12 inches / 60 inches
= 4 inches / 15 inches
Therefore:
4in / 15 in < 4inch / 18 inch
The condition states the ramp has to be at least 6feet, what this means is it has to be between 0-6 so since it is lesser. Yes it meets the recommendations.
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Yes, inclination in between 4in / 15 in < 4in / 18 in
What is incline?A flat supporting surface that is inclined at an angle from the vertical direction with one end higher than the other is referred to as an inclined plane or a ramp. A load may be raised or lowered using it.
What is horizontal and vertical?In coordinate geometry, the horizontal line is the line parallel to the x-axis, while the vertical line is the line parallel to the y-axis. Vertical and horizontal lines will be perpendicular to the x- and y-axes, respectively. As a result, when lines are drawn, they are perpendicular to one another if they share at least one point.
6 feet of horizontal distance for every 1 foot,
ramp shown has a vertical rise of 5 feet.
Therefore
M ≤ 1foot / 6 feet
Converting both to a single units of ( inches )
M ≤ 12 inches / 72 inches
Dividing by 4
M ≤ 4 inches / 18 inches
Where 5 feet = 60 inches
12 inches / 60 inches
= 4 inches / 15 inches
Therefore:
4in / 15 in < 4inch / 18 inch
The condition states the ramp has to be at least 6 feet, what this means is it has to be between 0-6 so since it is lesser. Yes it meets the recommendations.
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What is the ¨length of a soccer field¨ unit of measurement
A - Square meters
B - Yards
C - Cubic inches
D - Cubic feet
E - Square centimeters
The unit of measurement "length of a soccer field" is in yards
What is the ¨length of a soccer field¨ unit of measurementThe unit of measurement "length of a soccer field" is typically measured in yards, which is option B.
A standard soccer field is rectangular, with a length ranging from 100 to 130 yards and a width ranging from 50 to 100 yards.
The measurement of the length of a soccer field is based on the distance between the goal lines, which is equivalent to the length of the field.
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since critical values of t vary by sample size, before using the t table we must first calculate
Critical values of t, which are used for hypothesis testing and confidence interval calculations, vary depending on the sample size and the degrees of freedom.
b) degrees of freedom.
Degrees of freedom (df) are calculated based on the sample size and represent the number of independent pieces of information available in the data. It is an important parameter in determining the appropriate critical value to use from the t-distribution table. Therefore, before using the t-table, it is essential to calculate the degrees of freedom of the data set in question.
Options a, c, and d are not correct answers as they do not pertain to the calculation needed before using the t-table.
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Complete Question
Since critical values of t vary by sample size, before using the t table we must first calculate:
a) the Z score.
b) degrees of freedom.
c) the population standard deviation.
d) the sample size.
The degrees of freedom will then determine the critical values of t that should be used in calculating confidence intervals or conducting hypothesis tests. Therefore, it is important to consider the sample size when working with t statistics and using the t table.
To answer your question, before using the t-table, you must first calculate the degrees of freedom. The degrees of freedom are important as they determine the critical values of t based on your sample size. Here's a step-by-step explanation:
1. Obtain your sample data.
2. Determine the sample size (n) by counting the number of data points in your sample.
3. Calculate the degrees of freedom (df) by subtracting 1 from the sample size: df = n - 1.
4. Refer to the t-table with the calculated degrees of freedom to find the critical values of t for your desired level of confidence or significance.
By following these steps, you'll be able to find the appropriate critical values of t based on your sample size before using the t-table.
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Animal Pens
The animal shelter is building new animal playpens. They
use fencing to enclose an area shaped like a rectangle.
The design for one of the playpens is shown below. What
other playpens could be made with the same amount of
fencing?
8 ft
10 ft
80
10 ft
2. Be Efficient How much fencing is used for
the playpen design shown above? How do
you know? 20.2.2. MAI
Ion
3. Explain Leah says that a square playpen with sides that are 9 feet uses
the same amount of fencing. Is Leah's statement correct? Explain your thinking. 2022
4. Make Sense Describe one other playpen that could be made.
The total fencing used is 36 ft and the playpen would look like a square rather than a rectangle.
1) The given design uses 36 feet of fencing. Other playpens that could be made with the same amount of fencing are:
A square playpen with sides of length 9 feet (since 4 x 9 = 36)
A rectangular playpen with length 12 feet and width 6 feet (since 2 x (12 + 6) = 36)
2) The fencing used for the given design is the sum of the lengths of all four sides. From the diagram, we can see that the two shorter sides have a length of 8 feet each, and the two longer sides have a length of 10 feet each. Therefore, the total fencing used is:
2(8 ft) + 2(10 ft) = 16 ft + 20 ft = 36 ft
3) Leah's statement is not correct. A square playpen with sides of length 9 feet would require a perimeter of 4 x 9 = 36 feet, which is the same amount of fencing used for the given design. However, the shape of the playpen would be different, since the sides would all be equal in length. The playpen would look like a square rather than a rectangle.
4) Another playpen that could be made with the same amount of fencing is a rectangular playpen with length 18 feet and width 0 feet (i.e., a straight line). The perimeter would be:
2(18 ft) + 2(0 ft) = 36 ft
This playpen may not be practical for animals, but it satisfies the requirement of using 36 feet of fencing.
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Suppose there is a regular polygon that can be decomposed into 46
triangles. The measure of one of its interior angles is (9.5x+26.2)
.
What is the value of x
?
The value of x in the regular polygon is 15.4.
What is the value of x?The value of x is calculated as follows;
The sum of the interior angles of a polygon with n sides is given by the formula;
(n-2) x 180
Since the regular polygon in question can be decomposed into 46 triangles, it has 46 x 3 = 138 sides.
The value of each interior angle is calculated as;
= (n - 2) x 180 / n
= (138 - 2) x 180 / 138
= 169.6⁰
9.5x + 26.2 = 169.6
9.5x = 143.4
x = 15.1
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Solve for the value of X 130 degrees X+134
Answer:
-4. my answers need to be 20 characters+ soooo
Choose the graph that correctly represents the equation 3x + 9y = −18
What is 6w-w to the cube root when w=288
The absolute maximum value of f(x)= x^3 -3x^2 +12 on the closed interval [-2,4] occurs at x=a) 4b) 2c) 1d) 0e) -2
The absolute maximum value of f(x) on the closed interval [-2, 4] occurs at x = -2 and x = 0, and the maximum value is 16. So the answer is option (e) -2.
To find the absolute maximum value of the function f(x) = x³ - 3x² + 12 on the closed interval [-2, 4], we need to evaluate the function at the critical points and at the endpoints of the interval, and then choose the largest value.
To find the critical points, we take the derivative of the function and set it equal to zero
f'(x) = 3x² - 6x = 3x(x - 2)
Setting f'(x) = 0 gives x = 0 and x = 2 as critical points.
Next, we evaluate the function at the critical points and at the endpoints of the interval
f(-2) = (-2)³ - 3(-2)² + 12 = 16
f(0) = (0)³ - 3(0)² + 12 = 12
f(2) = (2)³ - 3(2)² + 12 = 4
f(4) = (4)³ - 3(4)² + 12 = 4
Therefore, the correct option is (e) -2
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The absolute maximum value occurs at x = 4, with a value of 28. So, the answer is a) 4.
We occasionally encounter operations with hills and valleys. Hill and valley points in polynomial functions typically have many locations. We are aware that these places, which can be categorized as maxima or minima, are the function's critical points. The valley points are referred to as minimal and the hill points are as maxima. We must determine the locations of the function's global maxima and global minima, which are known as the minimum and maximum values, respectively, due to the fact that there are several maxima and minima.
To find the absolute maximum value of the function [tex]f(x) = x^3 - 3x^2 + 12[/tex] on the closed interval [-2, 4], we need to examine the critical points and the endpoints of the interval.
First, find the critical points by taking the derivative of f(x) and setting it equal to 0:
[tex]f'(x) = 3x^2 - 6x\\0 = 3x^2 - 6x\\0 = 3x(x - 2)[/tex]
The critical points are x = 0 and x = 2.
Next, evaluate the function at the critical points and the interval endpoints:
[tex]f(-2) = (-2)^3 - 3(-2)^2 + 12 = -8 - 12 + 12 = -8\\f(0) = 0^3 - 3(0)^2 + 12 = 12\\f(2) = 2^3 - 3(2)^2 + 12 = 8 - 12 + 12 = 8\\f(4) = 4^3 - 3(4)^2 + 12 = 64 - 48 + 12 = 28[/tex]
The absolute maximum value occurs at x = 4, with a value of 28. So, the answer is a) 4.
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A letter is chosen randomly from the word CANDLESTICK.
Find each probability.
4. P(a vowel)
5. P(N or S)
6. P(not C)
The probabilities for the given events are:
P(a vowel) = 3/11
P(N or S) = 2/11
P(not C) = 9/11
How to find the probabilities?The probability is given by the quotient between the outcomes that meet the event and the total possible outcomes.
In Candlestick there are 11 letters.
4) There are 3 vowels, then this probability is:
P(a vowel) = 3/11
5) The letters N and S appear 2 times, then the probability is:
P(N or S) = 2/11
6) The letter C appears 2 times, then the other 9 letters are not C, so the probability is:
P(not C) = 9/11
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