Consider the function f(x)=x^3+16x
Find the intervals on which f is positive.
Answers
f(x) > 0 for x > 0. Based on the analysis above, we can conclude that the function f(x) = x^3 + 16x is positive for x > 0. In interval notation, the intervals on which f(x) is positive are (0, ∞).
To determine the intervals on which the function f(x) = x^3 + 16x is positive, we need to find the values of x for which f(x) > 0.
To do this, we can analyze the sign of the function for different intervals of x by considering the sign of each term separately.
Consider x < 0:
For x < 0, x^3 < 0 and 16x < 0.
Since both terms are negative, their sum (f(x)) will also be negative.
Therefore, f(x) < 0 for x < 0.
Consider x = 0:
When x = 0, f(x) = 0^3 + 16(0) = 0.
Therefore, f(x) = 0 at x = 0.
Consider x > 0:
For x > 0, x^3 > 0 and 16x > 0.
Since both terms are positive, their sum (f(x)) will also be positive.
Therefore, f(x) > 0 for x > 0.
Based on the analysis above, we can conclude that the function f(x) = x^3 + 16x is positive for x > 0.
In interval notation, the intervals on which f(x) is positive are (0, ∞).
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Related Questions
Kevin Horn is the national sales manager for National Textbooks Inc. He has a sales staff of 4040 who visit college professors all over the United States. Each Saturday morning he requires his sales staff to send him a report. This report includes, among other things, the number of professors visited during the previous week. Listed below, ordered from smallest to largest, are the number of visits last week.
38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57
59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79
a. Determine the median number of calls.
b. Determine the first and third quartiles. (Round Q1 to 2 decimal places and Q3 to nearest whole number.)
c. Determine the first decile and the ninth decile. (Round your answer to 1 decimal place.)
d. Determine the 33rd percentile. (Round your answer to 2 decimal places.)
Answers
a. The median number of calls = 55
b. The first and third quartiles, Q1 = 48 and Q3 = 66
c. The first decile and the ninth decile, D1 = 45 and D9 = 71.
d. The 33rd percentile = 52.5
To answer the questions, let's first organize the data in ascending order:
38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79
(a) The median is the middle value of a dataset when arranged in ascending order.
Since we have 40 observations, the median is the value at the 20th position.
In this case, the median is the 55th visit.
(b) The quartiles divide the data into four equal parts.
To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.
The first quartile is the value at the 10th position, which is 48.
To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.
The third quartile is the value at the 30th position, which is 66.
Therefore, Q1 = 48 and Q3 = 66.
(c) The deciles divide the data into ten equal parts.
To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.
The first decile is the value at the 4th position, which is 45.
To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.
The ninth decile is the value at the 36th position, which is 71.
Therefore, D1 = 45 and D9 = 71.
(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.
Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:
Lower value: 52
Upper value: 53
Position: 13
Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5
33rd percentile = Lower value + (Percentage * (Upper value - Lower value))
= 52 + (0.5 * (53 - 52))
= 52.5
Therefore, the 33rd percentile is 52.5.
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What property is “If AB=CD than CD=AB”
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The given property “If AB=CD then CD=AB” is known as the symmetric property. Symmetric property is a type of equivalence relation in mathematics that states that if the relation between two elements is in the form of "if A is related to B, then B is related to A," then this type of relation is symmetric.
The symmetric property states that if two objects are related to one another, then this relationship can be reversed. That is, if a=b, then b=a. The symmetric property applies to many different mathematical concepts and structures, including numbers, geometric figures, and functions.For example, if two angles are congruent, then they have the same measure. Using the symmetric property, we can say that if two angles have the same measure, then they are congruent. This property is important in proving theorems and solving problems in geometry, algebra, and other mathematical fields.For such more question on symmetric
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hhhhhjklllkbvcccccgghhhjjughujhbhj
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Step-by-step explanation:
give me brainly lsssssss
literally can no one help, i said id give brainliest and anything u need, i jst want all of it answered
Answers
B) $94.98
C) The equation is 394.94 = 59.99x + 34.99y, where x is the number of months she had membership and visited less than 12 times, and y it’s the number of months she had membership while going 12 or more times.
find difference between 2/3 53/300
Answers
Answer:
0.5 difference
Step-by-step explanation:
2/3=0.66666666666=0.7
53/300= 0.17666666666=0.2
0.7-0.2=0.5
Describe the likelihood of the situation. Use likely, unlikely, neither likely nor unlikely, certain, or impossible.
The next baby born at a hospital is a girl.
What best describes thelikelihood of the statement?
Please hurry
Giving BRAINLYest
Answers
It cannot be predicted, theres a 50/50 chance.
The cost of renting the Party Barn is $150 flat fee plus an additional $50 per hour. Manny can spend up to $325 to rent
the Party Barn for his birthday party. What are the possible hours that Manny could rent the Party Barn?
Answers
solve for x 2x-2+4x-5
Answers
Answer:
-40
Step-by-step explanation:
2 times negative 2 is 4 plus 4 is 8 times negative 5 is -40
Answer:
\(x=3/2=1.5\)
Step-by-step explanation:
So we have the equation:
\(2x-2=4x-5\)
And we want to solve for x. To do this, we need to first isolate the x-variable. So, start by adding 2 to both sides:
\((2x-2)+2=(4x-5)+2\)
The 2s on the left cancel:
\(2x=4x-3\)
Now, subtract 4x from both sides:
\((2x)-4x=(4x-3)-4x\)
The 4xson the right cancel:
\(-2x=-3\)
Now, divide both sides by -2.
\(\frac{(-2x)}{-2}=\frac{-3}{-2}\)
The negatives cancel. The 2s on the left cancel. Therefore:
\(x=3/2=1.5\)
how do you find the x for this and the angles, thanks in advance
Answers
HOPE THIS HELPS...
Hooke's law is a law of physics that states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram.[1][2] He published the solution of his anagram in 1678[3] as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the force"). Hooke states in the 1678 work that he was aware of the law since 1660.
Hooke's equation holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, and a musician plucking a string of a guitar. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean.
Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.
On the other hand, Hooke's law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. For this reason, Hooke's law is extensively used in all branches of science and engineering, and is the foundation of many disciplines such as seismology, molecular mechanics and acoustics. It is also the fundamental principle behind the spring scale, the manometer, and the balance wheel of the mechanical clock.
The modern theory of elasticity generalizes Hooke's law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers.
In this general form, Hooke's law makes it possible to deduce the relation between strain and stress for complex objects in terms of intrinsic properties of the materials it is made of. For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness k directly proportional to its cross-section area and inversely proportional to its length.
Step-by-step explanation:
2x + 15° + x = 180° { Being co-interior angles }
3x = 180°- 15°
3x = 165°
x = 165° / 3
x = 55°
2x + 15° = 2 *55° + 15° = 125°
Hope it will help :)❤
What percentage of newborn puppies should weigh between 7.5 and 13.5 ounces? b. What percentage of newborn puppies should weigh between 9 ounces and 10.5 ounces? c. What percentage of newborn puppies should weigh more than 15 ounces? d. If there are 120 newborn puppies in the shelter, how many are expected to weigh less than 12 ounces? puppies (rounded to the nearest puppy)
Answers
a. Approximately 84.13% of newborn puppies should weigh between 7.5 and 13.5 ounces. b. Approximately 34.13% of newborn puppies should weigh between 9 ounces and 10.5 ounces. c. Approximately 0.15% of newborn puppies should weigh more than 15 ounces. d. If there are 120 newborn puppies in the shelter, approximately 105 puppies are expected to weigh less than 12 ounces.
Given that the weights of newborn puppies follow a normal distribution with a mean of 10.5 ounces and a standard deviation of 1.5 ounces, we can use the properties of the normal distribution to determine the percentages and expected counts.
a. To find the percentage of puppies weighing between 7.5 and 13.5 ounces, we calculate the area under the normal curve between these two values. Using a standard normal distribution table or a calculator, we find that approximately 84.13% of the puppies fall within this range.
b. Similarly, to find the percentage of puppies weighing between 9 ounces and 10.5 ounces, we calculate the area under the curve between these two values. This is approximately 34.13% of the puppies.
c. To find the percentage of puppies weighing more than 15 ounces, we calculate the area under the curve beyond 15 ounces. This is approximately 0.15% of the puppies.
d. To estimate the number of puppies weighing less than 12 ounces out of the total 120 puppies, we use the properties of the normal distribution. We calculate the area under the curve to the left of 12 ounces and multiply it by the total number of puppies. This yields approximately 105 puppies expected to weigh less than 12 ounces.
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Complete the following conversions. i) 1 mm = m ii) mm = 1 m iii) 1 cm = m iv) cm = 1 m v) 1 km = m vi) km = 1 m vii) 1 cm = mm viii) cm = 1 mm
Answers
The unit conversion for the given values are explained below.
What is unit conversion?Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.
The following measurements: length, weight, capacity, temperature, and speed are all measured in units.
Some basic unit conversions are-
1 Km = 1000 m1 m = 100 cm1 m = 1000 mm1 cm = 10 mmThere are two methods to convert the units
To convert smaller unit into larger divide the number by conversion factor.To convert larger value into smaller value multiply by the conversion factor.The unit conversion for the following factors are-
i) 1 mm = _ m
Here, conversion is from smaller to larger. So, divide by conversion factor.
1 mm = (1/100)m
ii) _ mm = 1 m
Here, conversion is from larger to smaller. So, multiply with conversion factor.
1000 mm = 1 m
iii) 1 cm = _ m
Here, conversion is from smaller to larger. So, divide by conversion factor.
1 cm = (1/100)m
iv) _ cm = 1 m
Here, conversion is from larger to smaller. So, multiply with conversion factor.
100 cm = 1 m
v) 1 km = _m
Here, conversion is from larger to smaller. So, multiply with conversion factor.
1 km = 1000 m.
vi) _ km = 1 m
Here, conversion is from smaller to larger. So, divide by conversion factor.
(1/1000) km = 1 m.
vii) 1 cm = _mm
Here, conversion is from larger to smaller. So, multiply with conversion factor.
1 cm = 10 mm
viii) _cm = 1 mm
Here, conversion is from smaller to larger. So, divide by conversion factor.
(1/10) cm = 1 mm.
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A cube of side 3 inches has a cube of side 1 inch cut from each corner. A cube of side 2 inches is then inserted in each corner. What is the number of square inches in the surface area of the resulting solid
Answers
The total surface area of the resulting solid is \(6+96=\boxed{102}\) square inches.
The resulting solid after the described procedure consists of a central cube of side length 1 inch and 6 congruent smaller cubes, each of side length 2 inches. We can find the surface area of the resulting solid by adding up the surface area of each of these cubes.
The surface area of the central cube is simply \(6(1^2)=6\) square inches.
The surface area of each of the smaller cubes is \(6(2^2)=24\) square inches, but since each cube shares one face with the central cube and another face with its neighboring cube, we only count four of its faces, so the contribution of each smaller cube to the surface area of the resulting solid is 4(24/6)=16 square inches.
Since there are 6 smaller cubes in total, their contribution to the surface area of the resulting solid is \(6\times16=96\)square inches.
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What is the value of x to the nearest degree?
Answers
2nd tan = 13 / 6
x = 65.22
to the nearest degree, it would be 65°.
It has rained two out of the past nine days.
Based on this data, what is the probability
that it will not rain for the next four days?
Answers
Answer:
There is only a 25% of the probability
Please Help me to answerthe questions and options are in picture
Answers
Evelyn has initially $524.96, then she paid $32.50, so she will have less than $500. In order to have at least $500, she needs to deposit the value x.
So the initial value, minus the value paid, plus the deposit needs to be greater than or equal 500, so we have the inequality:
\(524.96-32.5+x\ge500\)Solving this inequality for x, we have:
\(\begin{gathered} 492.46+x\ge500 \\ x\ge500-492.46 \\ x\ge7.54 \end{gathered}\)Therefore the correct option is the first one (a).
Working on Scientific Notations please help
Answers
Answer: The answer is scientific notation
Step-by-step explanation:
is a fraction a term? If it's not a term, why is it that we can apply the distributive property to it? the distributive property only works for either terms, or addition and subtraction. a fraction is technically division, so why does it work? Please help!!!!!
Answers
No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.
A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.
The distributive property states that for any real numbers a, b, and c:
a × (b + c) = (a × b) + (a × c).
When working with fractions, we can apply the distributive property as follows:
Let's consider the expression: a × (b/c).
We can rewrite this as: (a × b)/c.
Now, let's distribute the 'a' to 'b' and 'c':
(a × b)/c = (a/c) × b.
In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.
Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.
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According to deterrence theory, if the probability of arrest, conviction, and sanctioning could be increased, crime rates should:
Answers
To deterrence theory, if the probability of arrest, conviction, and sanctioning could be increased, crime rates should go down.
Deterrence is one of the goals of sentencing, and it works to stop crime by setting an example for others by punishing offenders. While specific deterrence aims to stop a specific offender from committing more crimes, general deterrence is focused on preventing crime among the general populace.
According to deterrence theory, if the probability of arrest, conviction, and sanctioning could be increased
The prospect of punishment can persuade rational criminals that crime does not pay; methods of this notion include the death penalty, mandatory sentences, and vigorous police. Fear of the repercussions of crime will dissuade potential offenders.
Therefore, to deterrence theory, if the probability of arrest, conviction, and sanctioning could be increased, crime rates should go down.
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You invested $8000 in a savings bond. When you cash it in 5 years later, you received $9,250. Find the annual return.
Answers
We will find the return as follows:
\(AR=(\frac{\text{FVI}}{IVI})^{\frac{1}{n}}\)Here AR is the annual return, FVI is the final value of investment and IVI is the initial value of investment and n is the number of years. Now, we replace:
\(AR=(\frac{9250}{8000})^{\frac{1}{5}}\Rightarrow AR\approx1.029462068\)So, the annual return is approximately 1.03.
please help--
Area of triangle PQR = 10.2 square units
Area of triangle PRS = 11.5 square units
Area of triangle PST = 16.3 square units
The area of Figure PQRST is
square units. (Input whole number only.)
Answers
The area of \(PQRST\) equals to the sum of areas of the triangles it consists of. So,
\(A(\mathrm{PQRST})=A(\mathrm{PQR})+A(\mathrm{PRS})+A(\mathrm{PST})=10.2+11.5+16.3=\boxed{38}\)
40% of what number = 18
Answers
Answer:
The answer is 45
Step-by-step explanation:
Follow the steps:
set it up:
18/? = 40%/100%
18 x 100= 1800
1800 divided by 40 equals 45
Hope this helps! :)
find the midpoint of (-8,-9) and (-5,1)
Answers
Help me answer this please
Answers
Answer:
y=38 °
Step-by-step explanation:
Answer:38
Step-by-step explanation:
a matrix consisting entirely of zeros is called a
Answers
A matrix consisting entirely of zeros is called a zero matrix, or an all-zero matrix.
It is denoted with the symbol O and can be written in a matrix form, such as O = [0 0 0 0] where the number of columns and rows depends on the size of the matrix. A zero matrix is a matrix which has all its elements equal to zero. It has a number of special properties that make it useful in linear algebra. For instance, the sum of any two zero matrices is a zero matrix, and any scalar multiple of a zero matrix is a zero matrix. Additionally, the product of two zero matrices is a zero matrix, and the product of a zero matrix and an identity matrix is a zero matrix. These properties make it useful in solving systems of linear equations where all the coefficients are zero. Finally, the inverse of a zero matrix does not exist since its determinant is zero.
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perpendicular to y=2x+9 and has the point (4,-1)
Answers
Answer: y = \(-\frac{1}{2}\)x + 1
Step-by-step explanation:
First, we will find the slope. The slope of perpendicular lines are negative reciprocals.
In this case, the first slope is 2. The negative of 2 is -2, and the reciprocal of -2 is \(-\frac{1}{2}\).
Now, we will plug in this new slope, the point given, and solve for the b, or the y-intercept.
y = mx + b
(-1) = (\(-\frac{1}{2}\))(4) + b
-1 = -2 + b
1 = b
Lastly, we will write our equation.
y = mx + b
y = \(-\frac{1}{2}\)x + 1
The line is y = \(-\frac{1}{2}\)x + 1, or y = 1 - \(\frac{x}{2}\).
Answer:
\(\sf y=-\dfrac{1}{2}x+1\)
Step-by-step explanation:
Slope-intercept form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Given: y = 2x + 9
where:
2 is the slope(0, 9) is the y-interceptNote:
Perpendicular lines have slopes that are negative reciprocals of each other.
\(\sf \textsf{a slope of 2} \implies \textsf{would have a negative reciprocal of} -\dfrac{1}{2}\)
\(\textsf{Perpendicular line:}\ \sf y=-\dfrac{1}{2}x+b\)
Substitute the given point into the the equation to find the value of b:
\(\sf \sf y=-\dfrac{1}{2}x+1\\\\-1=-\dfrac{1}{2}(4)+b\\\\-1=-2+b\\\\-1+2=-2+2+b\\\\1=b\)
\(\textsf{Perpendicular line:}\ \sf y=-\dfrac{1}{2}x+1\)
slope of ½y-intercept of (0, 1)last years computer models are discounted 20% what is the original price to the nearest dollar of a computer that now costs 1,480
Answers
Answer:
$1850.
Step-by-step explanation:
If the original price was $ x, then
x - 0.20x = 1480
0.8x = 1480
x = 1480 / 0.8
x = 1850 dollars.
I need help with this
Answers
solve 13x+5=83 pleaseeee
Answers
13x=78
So x=6
Which of the following is a measure of the reliability of a statistical inference? Answer A descriptive statistic. A significance level. A sample statistic. A population parameter.
Answers
The measure of reliability of a statistical inference is the significance level. The significance level, also known as alpha, is the probability of rejecting the null hypothesis when it is actually true. It determines the threshold for accepting or rejecting a hypothesis.
A lower significance level indicates a higher level of confidence in the results. A descriptive statistic provides information about the data, but it does not directly measure the reliability of a statistical inference. It simply summarizes and describes the characteristics of the data.
A sample statistic is a numerical value calculated from a sample, such as the mean or standard deviation. While it can be used to make inferences about the population, it does not measure the reliability of those inferences.
A population parameter is a numerical value that describes a population, such as the population mean or proportion.
While it provides information about the population, it does not measure the reliability of inferences made from a sample. In conclusion, the significance level is the measure of reliability in a statistical inference as it determines the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.
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5 boxes of pencils whith ten pencils per box = what
Answers
Answer:
50 pencils in total
Step-by-step explanation:
5 boxes * 10 in each = 50 pencil in total