PLEASE HELP AND SHOW WORK! EXPLAIN HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST!!!!
Answers
The time it will take to fill the pool at the given rate would be = 8 mins.
How to calculate the volume of the cylindrical swimming pool?To calculate the volume of the cylindrical swimming pool the formula for the volume of the cylinder should be used which is = πr²h
where r = 5ft
h = 8ft
volume = π×5×5×8 = 200πft³
If 25πft³ = 1 minute
200πft³ = X
Make X the subject of formula;
X = 200/25 = 8mins
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Related Questions
I NEED HELP ON THIS ASAP!!!
Answers
The horizontal asymptote of the function f(x) = 2ˣ is y = 0.
What is a horizontal asymptote?In Mathematics and Geometry, a horizontal asymptote can be defined as a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).
In this context, the line passing through the ordered pair (0, 1) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 0, as shown in the image attached above.
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answer the last one plss i give brain
Answers
The complete sequence are 2, 3, 5, 8, 12, 17, 23, 30 38, 47, 1024, 512, 256, 128, 64 and 32.
How do we get the last numbers?Looking at the pattern, we can find the next two numbers in the sequence. All we need to do is notice that each term in the sequence is obtained by dividing the previous term by 2.
To get term after 128, we cam divide 128 by 2 which will give us:
= 128 / 2
= 64
To get term after 64, we divide 64 by 2 which give us:
= 64 / 2
= 32
Therefore, the last two numbers in the sequence are 64 and 32.
Full question: Find the last 2 numbers after the sequence of "2, 3, 5, 8, 12, 17, 23, 30 38, 47, 1024, 512, 256, 128, __ and ___.
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Use the image to determine the type of transformation shown.
Reflection across the x-axis
90' clockwise rotation
Horizontal translation
Vertical translation
C
B
Answers
Explanation: the figure moved left to right and did not flip or rotate or move up or down. The points all stayed in the same location.
It simply moved horizontally to the right.
How to do substitution
Answers
Step Two→ Substitute the expression from step one into the 2nd equation.
Step Three→ Solve the second equation for the given variable.
Step Four→ Plug you solution back into the first equation.
Step Five→ Write your solution as a point.
Two amateur marathoners were running a marathon. The first marathoner kept a steady pace and was able to finish in four hours. The second marathoner was keeping 4 the speed of the speed of the first runner. Then he was tired and his speed for the 3
second half of the distance was only 3 4 the speed of the first runner. How much did it
take the second runner to finish the distance?
Answers
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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A grocery store finds that the number of boxes of new cereal sold increases each week. In the 1st week, 24
boxes of cereal were sold. In the 2nd week, 39 boxes of cereal were sold and in the 3rd week 54 boxes of
cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.
A) Write the explicit rule in simplified form for the arithmetic sequence that defines the number of boxes
of cereal sold in week n. Make sure to show all steps
B) Use this rule to calculate how many boxes of cereal will be sold during the 10th week.
Answers
Answer: a)159 boxes of cereal will be sold during the 10th week, b) an = 15n + 9
Step-by-step explanation:
Boyle's Law states that the pressure exerted by a gas held at a constant temperature varies inversely with the volume of the gas. At a volume of 4 L the pressure of a gas is 112 kPa. If the volume of the gas is 16 Lwhat would be the pressure of the gas in kPa? (Write your answer as a whole number)
Answers
Answer:
the pressure of the gas at a volume of 16 L would be 28 kPa.
Step-by-step explanation:
Using Boyle's Law:
P1V1 = P2V2
Where:
P1 = 112 kPa (initial pressure)
V1 = 4 L (initial volume)
V2 = 16 L (final volume)
Solving for P2:
P2 = (P1 x V1) / V2
P2 = (112 kPa x 4 L) / 16 L
P2 = 28 kPa
Therefore, the pressure of the gas at a volume of 16 L would be 28 kPa.
a threat to internal validity occurs only if a potential design confound varies _________with the independent variable. group of answer choices spontaneously especially systematically haphazardly
Answers
A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable.
In experimental research, an independent variable is a variable that the researcher manipulates or systematically varies in order to study its effect on the dependent variable. It is called "independent" because it is not influenced by any other variables in the experiment, and its effects on the dependent variable can be observed and measured independently of any other factors.
Only when a possible design confound fluctuates systematically with the independent variable does internal validity come under threat. In other words, it might be challenging to distinguish between the effects seen on the dependent variable and the independent variable if there is a component that fluctuates consistently or predictably with changes in the independent variable. Internal validity is less likely to be threatened by random or unplanned variation.
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A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable. This means that if the confound varies randomly or haphazardly, it is less likely to affect the results of the study.
This means that the confound is consistently related to the independent variable, making it difficult to determine if the observed effects are due to the independent variable or the confound. If the confound varies spontaneously or haphazardly, it is less likely to pose a threat to internal validity, as it would not be consistently associated with the independent variable.
However, if the confound is related to the independent variable in a consistent and predictable way, it can introduce bias and undermine the internal validity of the study. It is important for researchers to carefully control for potential confounds and ensure that any observed effects are truly due to the independent variable and not some other factor.
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what is the number of permutations of the letters in the word indis- tinguishable such that the strings git, tin, and nab do not appear in the permutation?
Answers
The number of permutations of the letters in the word indistinguishable such that the strings git, tin, and nab do not appear in the permutation is
3,172,973,824,000
Let A be the set of stages that contain the string "git",
B be the set of changes that contain the string "tin", and
C be the set of stages that contain the string "nab".
We need to discover the number of stages that don't contain any of these strings, which is the same as finding the measure of the set (A∪B∪C)'.
Utilizing the guideline of inclusion-exclusion, we have:
|A∪B∪C| = |A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|
We need to discover |(A∪B∪C)'|, which is the complement of the set A∪B∪C. In this manner:
|(A∪B∪C)'| = n! - |A∪B∪C|
Now we have to discover the measure of the sets A, B, and C, and their convergences.
For set A, able to settle the string "git" in its put in 3! ways, and after that permute the remaining 14 letters in 14! ways. In this manner, |A| = 3!×14!.
Essentially, we will discover |B| = 3!×14! and |C| = 3!×14!.
For the convergences, we are able to settle the comparing strings in their places and permute the remaining 11 letters in 11! ways. In this manner,
|A∩B| = 2!×11!,
|A∩C| = 2!×11!,
and |B∩C| = 2!×11!.
At long last, we have |A∩B∩C| = 1!×11! since we are able to settle all three strings in their places and permute the remaining 11 letters in 11! ways.
Substituting these values into the inclusion-exclusion equation, we get:
|A∪B∪C| = 3(3!×14!) - 3(2!×11!) + 1!×11!
|A∪B∪C| = 13608000
Subsequently:
|(A∪B∪C)'| = 17! - 13608000
|(A∪B∪C)'| = 3172973824000
So there are 3,172,973,824,000 permutations of the letters within the word "indistinguishable" such that the strings "git", "tin", and "nab" don't show up within the stage.
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a=
B=
C=
what is A,B and C
Answers
A. (-1, A)
B. (2, infinite)
C: (-infinite, - 1)
(pls let me know if I'm wrong and if I am I'm very sorry.)
How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen's d?
A) Larger variance increases both the standard error and measures of effect size.
B) Larger variance increases the standard error but decreases measures of effect size.
C) Larger variance decreases the standard error but increases measures of effect size.
D) Larger variance decreases both the standard error and measures of effect size.
Answers
The estimated standard error and measures of effect size such as r2 and Cohen's d larger variance increases the standard error but decreases measures of effect size. B.
Larger variance increases the standard error but decreases measures of effect size.
The standard error is a measure of how much the sample mean is likely to vary from the true population mean.
It is calculated as the standard deviation of the sample divided by the square root of the sample size.
If the sample variance is large, the standard deviation of the sample will also be large, resulting in a larger standard error.
Measures of effect size, such as r2 and Cohen's d, indicate the strength of the relationship between variables or the size of the difference between groups, respectively.
Larger sample variances indicate greater variability in the data, which can make it more difficult to detect significant effects.
This can result in smaller effect sizes, as the magnitude of the effect is reduced relative to the variability in the data.
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suppose that 8% of the patients tested in a clinic are infected with hiv. furthermore, suppose that when a blood test for hiv is given, 97% of the patients infected with hiv test positive and that 4% of the patients not infected with hiv test positive. what is the probability that a patient testing positive for hiv with this test is infected with hiv? (enter the value of the probability in decimal format and round the final answer to three decimal places.)
Answers
The likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4%
To illuminate this issue, we will utilize Bayes' hypothesis. Let's characterize the taking after occasions:
A: the persistent is contaminated with HIV
B: the persistent tests positive for HIV
We need to calculate P(A|B), the likelihood that an understanding is contaminated with HIV given that they tried positive for HIV.
By Bayes' hypothesis:
P(A|B) = P(B|A) * P(A) / P(B)
where
1. P(B|A) is the likelihood of testing positive for HIV given that the persistent is tainted with HIV (97%)
2. P(A) is the predominance of HIV within the clinic (8%)
3. P(B) is the likelihood of testing positive for HIV, which can be calculated utilizing the law of adding up to likelihood:
P(B) = P(B|A) * P(A) + P(B|A') * P(A')
where
1. P(B|A') is the likelihood of testing positive for HIV given that the persistent isn't tainted with HIV (4%)
2. P(A') is the complement of A, i.e., the likelihood of a quiet not being tainted with HIV (1 - 8% = 92%)
Substituting the values we have:
P(B) = 0.97 * 0.08 + 0.04 * 0.92 = 0.0736
P(B) = 0.0736
Hence,
P(A|B) = 0.97 * 0.08 / 0.0736 ≈ 0.104
P(A|B) = 0.104
So the likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4% (adjusted to three decimal places).
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A cylinder has a volume of 490 pi inches squared and a height of 10 inches what is the length of the radius
Answers
The length of the radius of the cylinder with a volume of 490π cubic inches and a height of 10 inches is 7 inches.
The formula for the volume of a cylinder is V = πr²h,in which r= radius , h= cylinder height. Now we can rearrange formula by equating for r which gives the following formula:
V = πr²h
r² = V/(πh)
r = √(V/(πh))
By putting the values in the formula we can get:
r = √(490π/(π*10))
r = √49
r = 7
Therefore, the length of the radius is 7 inches.
Cylinder's volume can be viewed as the area that it takes up. It is computed by dividing the cylinder's height by the base's area, which is a circle. In this instance, we are informed that the height is 10 inches and the capacity is 490 cubic inches.
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What is the value of the expression below?
(31½ - 93) ÷ (-2.5)
A - 2.5
B-2.3
C 2.3
D 2.5
Answers
Answer: the value of the expression is 24.6, which corresponds to option C.
Step-by-step explanation: In order to assess the expression, we must adhere to the sequence of operations (PEMDAS) and execute the computations in the subsequent manner:
Begin by calculating the expression in the parentheses as a priority: (31.5 squared minus 93) equals negative 61.5.
Next, perform the operation of dividing -61.5 by -2.5 which results in 24.6.
If the area of a triangle is 72 square inches and the height is 6 inches, what is the length of the base
Answers
Answer: 24 inches.
Step-by-step explanation:
We can use the formula for the area of a triangle to solve for the length of the base:
A = (1/2)bh
where:
A = the area of the triangle (in this case, 72 square inches)
b = the length of the base (what we're trying to find)
h = the height of the triangle (in this case, 6 inches)
Plugging in the values we know, we get:
72 = (1/2)b(6)
72 = 3b
b = 24
Therefore, the length of the base of the triangle is 24 inches.
Last year Liz bought a book for $10. This year the same book is on sale for $5. What was the percent of change?
Answers
The percent of change in the price of the book is 50%.
To calculate the percent of change, we first need to find the difference between the original price and the new price. In this case, the original price of the book was $10, and the new price is $5. To find the difference, we can subtract the new price from the original price, which is:
$10 - $5 = $5
Now, we need to express this difference as a percentage of the original price. To do this, we divide the difference by the original price and then multiply by 100. In other words, we need to find the percentage that the original price has changed by. This can be represented mathematically as:
Percent of change = (Difference / Original price) x 100
Plugging in the values we found earlier, we get:
Percent of change = ($5 / $10) x 100
Percent of change = 0.5 x 100
Percent of change = 50%
This means that the price of the book has decreased by 50% from the original price of $10 to the sale price of $5.
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The tables represent the points earned in each game for a season by two football teams.
Panthers
14 10 10
10 17 3
28 13 17
32 16 10
14 7 21
Saints
21 12 3
3 10 10
14 3 12
28 40 10
17 20 7
Which team had the best overall record for the season? Determine the best measure of center to compare and explain your answer.
Saints; they have a larger mean value of about 14 points
Panthers; they have a larger mean value of about 14.8 points
Saints; they have a larger median value of 12 points
Panthers; they have a larger median value of 14 points
Answers
The team that had the best overall record for the season is Panthers. Therefore the best way to explain the answer B. Panthers; they have a larger mean value of about 14.8 points.
What are the mean values of the score of both team?For panthers, we calculate their mean values by totaling all their scores.
14+10+10+10+17+3+28+13+17+32+16+10+14+7+21 = 222
222/15 scores = 14.8
For Saints, 21+12+3+3+10+10+14+3+12+28+40+10+17+20+7 = 210
210/15 score = 14
This shows that Panthers have a larger mean value. Also, Panthers have a larger median value than saints. We find the median by arranging the scores from small to large and picking the number in between.
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1. Complete the table and determine the rule for this transformation.
Answers
Answer:
the table is analysis swap around
Step-by-step explanation:
like if the input is (3,1) the output will be (1,3)
A rectangle has a length of 9 cm and width of (3x-y)cm the area of the rectangle is 72cm^2
PQRS is a kite where PQ = 4xcm and QR = ycm
The perimeter of the kite PQRS IS 33cm
Calculate the values of x and y
You must show your working
Do not use a trial and improvement method.
Answers
Answer:
the value of x ia 7/2 and y is 5/2
QUICK QUICKQUICK QUICKQUICK QUICKQUICK QUICKPLEASE PELASE QUICK QUICKQUICK QUICKQUICK QUICKQUICK QUICKQUICK QUICKQUICK QUICK
Answers
Answer:
x ∈ {6, 7, 8, 9, 10}
Step-by-step explanation:
You want possible values of whole number x such that ...
4 ≤ √3 +√x < 5
SolutionWe can solve this inequality by first subtracting √3 from all sides:
4 -√3 < √x < 5 -√3
Squaring these positive numbers does not change their order:
19 -8√3 < x < 28 -10√3
5.14 < x < 10.67
The value of x may be any whole number in the range 6–10, inclusive.
what two numbers multiply to 21 and add to -10
Answers
Answer: brainliest ?
-3 and -7
Step-by-step explanation:
Which of the following is not an equation?
Answers
Answer:
Option (3)
Step-by-step explanation:
Option (3) is not an equation. It is an expression. An equation is a mathematical statement where two expressions are equal to each other connected by an equal sign. In option (1), 3+1 is equal to 4+0 so it is an equation. In option (2), x2-2x is equal to 8, so it is also an equation. In option (4), 1+3 is equal to 6, so it is an equation, though it is not a true statement. However, in option (3), there is no equal sign, so it is not an equation. It is an expression that simplifies to 8x+2.
Andre, Bilal, Glenna, and Juanita are all friends. They have given each other nicknames as well. The four nicknames are Boss, Buzz, Cosmo, and Tiger. The following clues, determine the nickname of each of the friends. friends are competing in the track and field day at their school. Using the Clues: 1. Juanita beat Tiger in the 400 m race, but Juanita lost to Buzz in the high jump. 2. Glenna and Tiger tied in the long jump, but Boss beat Glenna in the 1500 m 3. Cosmo, Tiger and Andre found the water station together after the first event. 4. Cosmo and Juanita ran separate legs on the relay race. race. Problem A Track and Field be helpful in solving this problem. The table below, with a column for each name and a row for each nickname, may Boss Buzz Cosmo Tiger Andre Bilal Glenna Juanita
Answers
Answer:vvv
Step-by-step explanation:
Boss's nickname is Boss because they beat Glenna in the 1500m race.
Buzz's nickname is Buzz because they beat Juanita in the high jump.
Cosmo's nickname is Cosmo because they were with Tiger and Andre at the water station.
Tiger's nickname is Tiger because they lost to Juanita in the 400m race and tied with Glenna in the long jump.
Andre's nickname is not given, but we know they ran a leg of the relay race with Bilal.
Bilal's nickname is not given, but we know they ran a leg of the relay race with Andre.
Glenna's nickname is not given, but we know they tied with Tiger in the long jump.
Juanita's nickname is not given, but we know they lost to Buzz in the high jump and beat Tiger in the 400m race, and ran a leg of the relay race with Cosmo.
A large Ferris wheel has a diameter of 90 meters and the top of the wheel is 102 meters above the ground. The Ferris wheel has 36 passenger capsules spaced evenly along the wheel. The diagram below shows 10 of the Ferris wheel capsules arranged such that the center of the wheel is at point C, the capsule at point M is at the same height as the center of the wheel, and the capsule at point T is at the very top of the wheel.
Answers
The height of the center of the Ferris wheel 51 m.
The height of capsule M is 51 m and the height of capsule T is 102 m.
What is the height of the wheel?
Using this information, we can calculate the height of the center of the Ferris wheel, the height of capsule M, and the height of capsule T.
Height of the center of the Ferris wheel:
The center of the Ferris wheel is the midpoint of its diameter. Therefore, the height of the center of the Ferris wheel is half of the height of the top of the wheel above the ground.
Height of center of Ferris wheel = 102 meters / 2 = 51 meters.
Height of capsule M:
Since capsule M is at the same height as the center of the Ferris wheel, the height of capsule M is also 51 meters.
Height of capsule T:
Since capsule T is at the very top of the Ferris wheel, its height above the ground is equal to the height of the top of the Ferris wheel above the ground.
Height of capsule T = 102 meters.
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Trend component is easy to identify by using
A. Moving average
B. Exponential smoothing
C. Regression analysis
D. Delphi approach
Answers
Trend component is easy to identify by using Moving average, Exponential smoothing, Regression analysis. So, correct options are A, B and C.
The trend component of a time series is a long-term movement in the data that represents a gradual increase or decrease over time. It is an important component of time series analysis because it can provide insights into the overall direction of the data and help forecast future trends.
One of the easiest ways to identify the trend component of a time series is by using a moving average. A moving average is a statistical method that calculates the average of a set of data over a specified period of time. By calculating the moving average, we can smooth out the short-term fluctuations in the data and identify the underlying trend.
Exponential smoothing is another method that can be used to identify the trend component of a time series. It is a forecasting technique that assigns exponentially decreasing weights to older observations, which places greater emphasis on more recent data.
This approach can help identify the trend by smoothing out the data and highlighting the underlying pattern.
Regression analysis can also be used to identify the trend component of a time series. It involves fitting a mathematical model to the data and identifying the relationship between the independent and dependent variables.
If the independent variable represents time and the dependent variable represents the data being analyzed, then regression analysis can help identify the trend component.
The Delphi approach is not typically used to identify the trend component of a time series. It is a forecasting technique that involves gathering expert opinions and using them to make predictions about future events.
In conclusion, the methods that are most commonly used to identify the trend component of a time series are moving average and exponential smoothing. Regression analysis can also be used in certain situations.
So, correct options are A, B and C.
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Which trapezoid is not isosceles
Answers
Answer:
D) a trapezoid with congruent diagnols
Explanation:
When none of the sides of a trapezoid are congruent, then it is a non isosceles trapezoid or a scalene trapezoid.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Factor completely and then place the factors in the proper location on the grid.
20y 2 + 3y - 2
Answers
The complete factorization of the quadratic equation, would lead to the factor being (5y + 1)(4y - 1).
How to factor completely ?To factor the quadratic expression 20y² + 3y - 2 completely, we can use the "ac method" (product-sum method).
Rewrite the quadratic expression using these two numbers:
20y² - 5y + 8y - 2
Now, factor by grouping:
5y(4y - 1) + (4y - 1)
Now, we can see that there is a common factor of (4y - 1) in both terms:
(5y + 1)(4y - 1)
So, the factored form of the quadratic expression 20y² + 3y - 2 is (5y + 1)(4y - 1).
In conclusion, the factored form of the quadratic expression 20y² + 3y - 2 is (5y + 1)(4y - 1).
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a person who works from home in sales earned an average of $2,350 per month over the past 12 months with a standard deviation of 175. calculate 90% confidence interval for the true mean income per month. round to 2 decimal places.
Answers
After calculating the 90% confident true mean income per month of a person who works from home in sales falls between $2146.47 and $2553.53.
To calculate the 90% confidence interval for the true mean income per month of a person who works from home in sales, we can use the following formula:
[tex]CI = X' ± Z\frac{a}{2}[/tex] * (σ/√n)
here:
X' = sample mean
Zα/2 = z-score that corresponds to the desired level of confidence (in this case, 90%)
σ = population standard deviation
n = sample size
Placing the values
CI = 2350 ± 1.645 * (175 / √12)
= [2146.47, 2553.53]
After calculating the 90% confident true mean income per month of a person who works from home in sales falls between $2146.47 and $2553.53.
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A polynomial p(x) has a relative maximum at (-2, 4), a relative minimum at (1,1), and a relative maximum at (5,7) and no other critical points. How many real zeros does p(x) have?a) oneb) twoc) threed) foure) five
Answers
The polynomial p(x) has option (c) three real zeros because it has a relative maximum at (-2, 4), a relative minimum at (1,1), a relative maximum at (5,7), and a negative leading coefficient.
Since p(x) has a relative maximum at (-2, 4), a relative minimum at (1,1), and a relative maximum at (5,7), it means that the degree of the polynomial must be odd and at least three.
Moreover, we know that p(x) has no other critical points. This means that p(x) does not change sign between these relative extrema, which in turn implies that there are no real zeros between these extrema.
Therefore, the number of real zeros of p(x) is either one or three. To determine the answer, we need to consider the leading coefficient of p(x).
If the leading coefficient is positive, then p(x) must eventually increase on both ends, since the degree is odd. This means that there is exactly one real zero.
If the leading coefficient is negative, then p(x) must eventually decrease on both ends. In this case, since there are three relative extrema, there must be three real zeros.
Thus, we need to find the sign of the leading coefficient of p(x). This can be done by looking at the relative extrema.
Since p(x) has a relative maximum at (-2, 4), we know that the leading coefficient is negative.
Therefore, the correct option is (c) three.
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A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.
A polynomial p(x) has a relative maximum at (-2, 4), a relative minimum at (1, 1), and a relative maximum at (5, 7), with no other critical points. This means there are turning points at these coordinates. Since there are two relative maxima and one relative minimum, the polynomial must have at least 3 turning points.
A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.
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solve cos^2x = (power reducing formula)
Answers
[tex]cos^2(x) = cos^2(x)[/tex].
This equation is true for all values of x, so the solution is:
x ∈ ℝ (x is any real number).
To solve the equation[tex]cos^2(x)[/tex]= (power reducing formula),
we need to replace [tex]cos^2(x)[/tex] with the power reducing formula.
The power reducing formula for [tex]cos^2(x)[/tex] is:
[tex]cos^2(x) = (1 + cos(2x)) / 2[/tex]
Now, let's solve the equation:
[tex](1 + cos(2x)) / 2 = cos^2(x)[/tex]
We want to find x when this equation is true.
Since the left side is the power reducing formula for [tex]cos^2(x)[/tex],
we can simply write:
[tex]cos^2(x) = cos^2(x)[/tex].
The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.
It is most commonly used for reducing the power of the sine and cosine functions.
The power reducing formula for cosine is:
[tex]cos^2(x) = (1 + cos(2x))/2[/tex]
The power reducing formula for sine is:
[tex]sin^2(x) = (1 - cos(2x))/2[/tex]
These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]
By solving for either [tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine [tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex]we can arrive at the power reducing formulas.
The power reducing formulas can be used to simplify trigonometric expressions and make them easier to work with.
For example, if you have an expression such as [tex]sin^4(x)[/tex], you can use the power reducing formula for sine to express [tex]sin^4(x)[/tex] in terms of [tex]sin^2(x),[/tex]and then use the power reducing formula for cosine to express [tex]sin^2(x)[/tex]in terms of cos(2x).
This can make the expression simpler and easier to integrate or differentiate.
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