To find the inflection points the first step we have to follow is to find the second and third derivatives of the function:
[tex]\begin{gathered} f\mleft(x\mright)=x^3-9x^2+10 \\ f^{\prime}\left(x\right)=3x^2-18x \\ f^{\prime}^{\prime}\left(x\right)=6x-18 \\ f^{\prime}^{\prime}^{\prime}\left(x\right)=6 \end{gathered}[/tex]Now, find the values of x for which the second derivative is 0:
[tex]\begin{gathered} 0=6x-18 \\ 18=6x \\ x=\frac{18}{6} \\ x=3 \end{gathered}[/tex]Evaluate the third derivative at this values of x, if the third derivative is different from 0, then that value is an inflection point:
[tex]f^{\prime}^{\prime}^{\prime}\left(3\right)=6[/tex]It means that there is an inflection point at x=3.
What is the solution to the following system of equations. Enter your answer as an ordered pair.3x+2y=17and4x+6y=26As an ordered pairHelp me pls
The system of equation are:
[tex]\begin{gathered} 3x+2y=17 \\ 4x+6y=26 \end{gathered}[/tex]to solve this problem we can solve the second equation for x so:
[tex]\begin{gathered} 4x=26-6y \\ x=6.5-1.5y \end{gathered}[/tex]Now we can replace x in the firt equation so:
[tex]3(6.5-1.5y)+2y=17[/tex]and we can solve for y so:
[tex]\begin{gathered} 19.5-4.5y+2y=17 \\ 19.5-17=2.5y \\ 2.5=2.5y \\ \frac{2.5}{2.5}=1=y \end{gathered}[/tex]Now we replace the value of y in the secon equation so:
[tex]\begin{gathered} x=6.5-1.5(1) \\ x=5 \end{gathered}[/tex]So the solution as a ordered pair is:
[tex](x,y)\to(5,1)[/tex]I need help with this practice problem solving It is trigonometry I will send another picture with the graph that is included in the problem, it asks to use the graph to solve
Given the function
[tex]f(x)=\sin (\pi x+\frac{\pi}{2})[/tex]The graph of the function is as shown below:
Which inequality is represented by the graph?
Answer:
A. x > -1
Step-by-step explanation:
x > -1
-------------->
<----0------------->
-1
x < -1
<-------
<------0------------>
-1
x ≥ -1
---------->
<---------|---------->
-1
x ≤ -1
<----------
<---------|---------->
-1
< and > represent an open circle
≤ and ≥ represent a closed circle
I hope this helps!
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 149 millimeters, and a standard deviation of 8 millimeters.
If a random sample of 50 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 3.3 millimeters? Round your answer to four decimal places.
The probability that the sample mean will differ from the population mean by more than 1.8 mm = 0.9949
Given,
In the question:
According to the given problem the mean diameter μ= 149 mm (population mean) and the standard deviation is σ = 8mm
random sample size, n= 50 steel bolts is selected
Let the random variable that represents the diameter of steel bolts be denoted by x and from the problem we have x = 3.3mm
Let z = (x-μ) / (σ/√n ) ....(1)
using formula (1) and when the sample mean differs from the population mean by more than 1.8mm
z = (3.3 - 149) /(8/√50 )
⇒z = -2.575
The probability that the sample mean will differ from the population mean by more than 1.8 mm
P( z > -2575) = 1 - P(z< -2.575) = 1 - 0.0051 = 0.9949
Hence, The probability that the sample mean will differ from the population mean by more than 1.8 mm = 0.9949.
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may ou solve the system of linear equations by substitution
y= 11 + 4x
3x +2y = 0
Put the first equation into the second one. (replace the value of y)
3x +2 (11 + 4x) = 0
Solve for x:
3x + 22 + 8x = 0
3x+8x = -22
11x = -22
x = -22/11
x = -2
Replace x=-2 in the first equation and solve for y
y= 11 + 4 (-2)
y= 11-8
y= 3
Solution:
x= -2 , y=3
Fill in the blank with a number to make the expression of perfect square.x^2-18x t
Answer:
[tex]81[/tex]Explanation:
Here, we want to write a figure that would make the given expression a perfect square
As a perfect square, we mean that:
[tex]ax^2+bx+c=(x+d)(x+d)=(x+d)^2[/tex]In this case, what we have to do is to divide the coefficient of x by 2, square it and write it
The coefficient of x is the number before x (we must consider its sign however)
Thus, we have the coefficient in this case as -18
Dividing this by 2 and squaring, we have:
[tex]\frac{-18}{2}=(-9)^2\text{ = 81}[/tex]Thus, we have:
[tex]x^2-18x+81=(x-9)(x-9)=(x-9)^2[/tex]
A body is moving in simple harmonic motion with position function
s(t) =2 + 2 cos t
where s is in meters and t is in seconds. Find the at time t.
The velocity of the body under simple harmonic motion (SHM) at time t is equal to -2sint. (Option D)
A type of self-sustaining periodic motion known as simple harmonic motion.
It is observed by the formula:
y = y' + Δy · cos ωt ....1.
Where,
y' = Initial position
Δy = Amplitude
ω = Angular frequency.
t = Time
To find the equation for the velocity of the body in simple harmonic motion differentiating equation w.r.t time (1),
then we get
v = - ω · Δy · sin ωt ....2.
If we know that ω = 1, t = t and Δt = 2, then the velocity of the body is:
v = - 1 · 2 · sin t
v = -2sint
The velocity is equal to -2sint
The velocity of the body under simple harmonic motion (SHM) at time t is equal to -2sint. (Option D)
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Can I get help, the last tutor didn't help me that much.
We know that
• The volume of one ball is 221 cubic centimeters.
Since the ball is spherical, we can find its radius with the following formula.
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ 221\cdot\frac{3}{4\pi}=r^3 \\ r^3=\frac{663}{4\pi} \\ r=\sqrt[3]{\frac{663}{4\pi}}\approx3.75 \end{gathered}[/tex]The diameter would be double than the radius, by definition.
[tex]d=2(3.75)=7.5[/tex]Since there are three balls in the cylinder, the height would be
[tex]h=3(7.5)=22.5[/tex]Now, we find the volume of the cylindrical package.
[tex]V=\pi r^2h=\pi(3.75)^2(22.5)\approx993.52[/tex]Therefore, the volume of the cylindrical package is 993.52, approximately.If the coordinates of a are (3,4) and the coordinates of b are (-3,3) then the length of an is
The length of the line segment from a to b is 6.08 units or [tex]\sqrt{37}[/tex] units.
What is the length of a line segment and what is the role of coordinates?The length is described as the distance between the two points in a line. The coordinate usually refers to the dimensions of the point with respect to the two dimension graph.
Relation between the coordinates and length: [tex]\sqrt{(x_{1} -x_{2}) ^{2} +(y_{1} -y_{2} )^{2} }[/tex]
Now let point a be ([tex]x_{1},y_{1}[/tex]) and point b be ([tex]x_{2},y_{2}[/tex])
Thus putting values,
length = [tex]\sqrt{(3-(-3))^{2}+(4-3)^{2} }[/tex]
length = [tex]\sqrt{36+1}[/tex]
length = [tex]\sqrt{37}[/tex]
Hence the length of ab is [tex]\sqrt{37}[/tex] or 6.08 units.
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Given the focus and directrix shown on the graph, what is the vertex form of the equation of the parabola?
[tex]x\ =\ \frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]x\ =\ 10(y\ +\ 3)^2\ +\ \frac{3}{2}[/tex]
[tex]x\ =\ \textrm{-}\frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]y\ =\ \frac{1}{10}(x\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
The vertex-form equation of the parabola is given as follows:
y = 1/10(y - 3)² - 3/2.
What is the equation of a horizontal parabola?An horizontal parabola of vertex (h,k) is modeled as follows:
x = (1/4p)(y - k)² + h.
In which:
The directrix is x = h - p.The focus is (h + p, k).In the context of this problem, we have that:
The directrix is x = -4.The focus is: (1,3), hence k = 3.A system of equations is built for h and p as follows:
h - p = -4.h + p = 1.Hence:
2h = -3
h = -3/2.
p = 1 + 3/2 = 2.5.
Then the equation is:
y = 1/10(y - 3)² - 3/2. (first option).
Missing informationThe graph is given by the image at the end of the answer.
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A cone has a base radius of length r, and an perpendicular height length h. If the height remains the same, and the radius is multiplied by 3, then the volume is multiplied by:A. 27B. 2C. 9D. 4/3
ANSWER
C. 9
EXPLANATION
The volume of a cone is:
[tex]undefined[/tex]Referring to the table in question 14, how would you graph the solution set representing students that do not receive a note sent home to parents?Draw points on the integers to the left of, and including, 0.Draw points on the integers to the right of, and including, 0.Draw points on the integers to the left of 0.Draw points on the integers to the right of 0.
According to the table, the statement "note sent to parents" is represented by the following inequality:
[tex]points\text{ < 0}[/tex]this can be represented as all integers less than zero. That is all integers to the left of 0.
We can conclude that the correct answer is:
Answer:Draw points on the integers to the left of 0.
What is The volume of a cylinder 7 in height and 3 radius and a cone of 7 height and 3 radius together? So what is The volume of both together?
In this case r =3, h= 7
[tex]\Rightarrow V_{cy}=\pi\times3^2\times7=63\pi=197.92unit^3[/tex][tex]\begin{gathered} \text{The Volume V}_{co\text{ }}of\text{ a cone with base radius r and height h is given by:} \\ V_{co}=\frac{1}{3}\times\pi\times r^2\times h \end{gathered}[/tex]In this case,
r=3, h=7
[tex]V_{co}=\frac{1}{3}\times\pi\times(3)^2\times7=21\pi=65.97unit^3[/tex][tex]\begin{gathered} \text{Therefore} \\ V_{cy}+V_{co}=63\pi+21\pi=84\pi=263.89unit^3 \end{gathered}[/tex]Hence
volume of cone + volume of cylinder = 263.89 cube units
In a class of 10 boys and 12 girls, a committee of 4 members is to be formed. What is the probability to form a committee consisting of 2 boys and 2 girls?A. 0.3040B. 0.4060C. 0.5060D. 0.2060
Given:
Number of boys=10
Number of girls=12
Out of 22 members, 4 members is need to be selected.
To find probability to form a committee consisting of 2 boys and 2 girls:
So, we get
[tex]\begin{gathered} \frac{^{10}C_2\times^{12}C_2}{^{22}C_4}=\frac{\frac{10\times9}{2\times1}\times\frac{12\times11}{2\times1}}{\frac{22\times21\times20\times19}{4\times3\times2\times1}} \\ =\frac{5\times9\times6\times11}{11\times7\times5\times19} \\ =\frac{9\times6}{7\times19} \\ =\frac{54}{133} \\ =0.4060 \end{gathered}[/tex]Hence, the correct option is B.
Is (x + 3) a factor of 7x4 + 25x³ + 13x² - 2x - 23?
According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0. Finding the polynomials' n roots and factoring them are two of their principal applications.
What is the remainder and factor theorem's formula?When p(x) is divided by xc, the result is p if p(x) is a polynomial of degree 1 or higher and c is a real number (c). For some polynomial q, p(x)=(xc)q(x) if xc is a factor of polynomial p. The factor theorem in algebra connects a polynomial's components and zeros. The polynomial remainder theorem has a specific instance in this situation. According to the factor theorem, f(x) has a factor if and only if f=0.The remainder will be 0 if the polynomial (x h) is a factor. In contrast, (x h) is a factor if the remainder is zero.The factor theorem is mostly used to factor polynomials and determine their n roots. Factoring is helpful in real life for comparing costs, splitting any amount into equal parts, exchanging money, and comprehending time.To learn more about Factor theorem refer to:
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Maggie has $30 in an account. The interest rate is 10% compounded annually.To the nearest cent, how much will she have in 1 year?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Solution:
Using the formula;
[tex]\begin{gathered} B=p(1+r)^t \\ \\ \text{ Where }B=balance,p=principal,r=rate,t=time \end{gathered}[/tex][tex]p=30,r=10\text{ \%}=0.1,t=1[/tex]Thus;
[tex]\begin{gathered} B=30(1+0.1)^1 \\ \\ B=33 \end{gathered}[/tex]ANSWER: $33
Enter a range of values for x.1416202x+109/15-5
26
Here, we want to write a range of values for x.
The shape we have is not a parallelogram but we have two equal sides
If it was a complete parallelogram, the two marked angles will be equal
But since what we have is not a complete parallelogram,
then;
[tex]\begin{gathered} 2x\text{ + 10 < 62 } \\ 2x\text{ < 62 - 10} \\ \\ 2x\text{ < 52} \\ \\ x\text{ < }\frac{52}{2} \\ \\ x\text{ < 26} \end{gathered}[/tex]3. What is the slope of a line that is parallel to the line that contains these
two points: (-2,5) and (-3,1).
Answer:
4
Step-by-step explanation:
The slope of the line through the points is
[tex]\frac{1-5}{-3-(-2)}=4[/tex]
Parallel lines have the same slope, so the answer is 4.
This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
A line graph measuring time and amount of rain. The horizontal axis is labeled Time, hours, in intervals of 1 hour. The vertical axis is labeled Amount of rain, millimeters, in intervals of 1 millimeter. A line runs through coordinates 2 comma 5 and 4 comma 10.
It is to be noted that the slope of the line is 5/2. This means that 5 mm of rain falls every 2 hours. See the calculation below.
What is a slope in math?In general, the slope of a line indicates its gradient and direction. The slope of a straight line between two locations, say (x₁,y₁) and (x₂,y₂), may be simply calculated by subtracting the coordinates of the places. The slope is often denoted by the letter 'm.'
To find the slope of the line in the graph, we use the following equation:
m = [y₂ - y₁]/[x₂-x₁]
Where (x1,y1) = coordinates of the first point in the line; and
(x₂,y₂) = coordinates of the second point in the line
Given that the points (2, 5) from the graph is (x₁, y₁) and the point on graph (4, 10) are (x₂,y₂) Hence,
m = [10-5]/[4-2]
The slope (m) = 5/2
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Full Question:
This is the complete question and the described graph is attached
This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement
The slope of the line is ___
This means that ___ mm of rain falls every ___
Add or subtract the fractions. Write the answer in simplified form.-2/13+(-1/13)
1) To add or subtract fractions, let's firstly check the denominators
In this case, the denominator is the same.
The plus before the bracket does not change the sign.
[tex]\begin{gathered} -\frac{2}{13}+(-\frac{1}{13}) \\ \frac{-2-1}{13} \\ \\ \frac{-3}{13} \end{gathered}[/tex]That is why we get to -3/13 as a result.
Match each piece of the function with its domain.(6, oo)(-00, 1)(1,00)(-oo, -2)(-00, 6)(-2, 6)(3,00)(1, 4)
Explanation
The question wants us to select all the domains in the set of functions graphed.
The domain of a function is the set of all possible inputs for the function.
To do so, we have to be aware that there are 3 pieces of functions
These are shown below
These are
[tex]\begin{gathered} (-\infty,-2) \\ \\ (-2,6) \\ \\ (6,\infty) \end{gathered}[/tex]
The figure is not drawn to scale. Find the unknown angle.
ThereforeGiven the image, we can find the missing angle using the sum of angles at a point rule.
The sum of angles at a point is known to be 360 degrees.
Therfore,
[tex]\begin{gathered} a^0+315^0=360^0 \\ a^0=360^0-315^0 \\ a^0=45 \end{gathered}[/tex]Therefore, the measure of "a" is
Answer:
[tex]45^0^{}[/tex]Which number is not a solution to3(x+4)−2≥7?-2-12 1
The inequality is:
[tex]3(x+4)-2\ge7[/tex]now we solve the inequality for x
[tex]\begin{gathered} 3(x+4)\ge7+2 \\ 3(x+4)\ge9 \\ x+4\ge\frac{9}{3} \\ x+4\ge3 \\ x\ge3-4 \\ x\ge-1 \end{gathered}[/tex]This means that all the number, from -1 to infinit are solution of the inequality, and the only option that is not a solution is a) -2
RATIONAL FUNCTIONSSynthetic divisiontable buand write your answer in the following form: Quotient *
The given polynomial is:
[tex]\frac{2x^4+4x^3-6x^2+3x+8}{x\text{ + 3}}[/tex]Using the long division method:
The equattion can be written in the form:
Quotient + Remainder / Divisor
[tex](2x^3-2x^2\text{ + 3) +}\frac{-1}{x+3}[/tex]11) a- 15 > 40-6 +3a) 12) 366b-1) > 18 - 3b a-151-46-67+1-useBay 9-15 124-12a atiza324+15 13a339 ay/9 13) 26 + m 2 5(-6 +3m) 14) 20-2p>-2lp
Answer
11) a > 3
12) b > (2/3)
Explanation
11) a - 15 > -4 (-6 + 3a)
a - 15 > 24 - 12a
a + 12a > 24 + 15
13a > 39
Divide both sides by 13
(13a/13) > (39/13)
a > 3
In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.
But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.
Then, the direction of the graph depends on the direction of the inequality sign, for example, the answer here says a is greater than 3. So, the graph will start with an unshaded circle and cover the numbers greater than 3.
12) 3 (6b - 2) > (8 - 3b)
18b - 6 > 8 - 3b
18b + 3b > 8 + 6
21b > 14
Divide both sides by 21
(21b/21) > (14/21)
b > (2/3)
This answer is similar to that of number 11. For the graph, it will start with an unshaded circle and move towards the numbers greater than (2/3)
Hope this Helps!!!
A. Write an exponential function to model with population Y of bacteria X hours after 2 PM
B. How many bacteria were there at 7 PM that day
In this problem, we have an exponential growth function of the form
[tex]y=a(b)^x[/tex]where
a=10 bacteria (initial value at 2 pm)
b is the base of the exponential function
[tex]y=10(b)^x[/tex]Find out the value of b
we know that
For x=0 (2 pm), y=10 bacteria
At 5 pm
y=33,750 bacteria
x=(5 pm-2 pm)=3 hours
substitute in the exponential equation
[tex]33,750=10(b)^3[/tex]Solve for b
[tex]b^3=\frac{33,750}{10}[/tex][tex]\begin{gathered} b=\sqrt[3]{\frac{33,750}{10}} \\ b=15 \end{gathered}[/tex]the equation is
[tex]y=10(15)^x[/tex]Part B
At 7 pm
x=(7 pm-2 pm)=5 hours
substitute
[tex]\begin{gathered} y=10(15)^5 \\ y=7,593,750\text{ bacteria} \end{gathered}[/tex]Applying the product rule to expression \left(3^3\div 3^4\right)^5gives us Answer raised to the power of Answerdivided by Answer raised to the power of AnswerSimplify that into a reduced fraction.The numerator is AnswerThe denominator is Answer
Given the expression
[tex](3^3\div3^4)^5[/tex]Using product rule
[tex]\begin{gathered} (3^3\div3^4)^5=(\frac{3^3}{3^4})^5 \\ =(3^{3-4})^5=(3^{-1})^5 \\ =3^{-1\times5}=3^{-5} \end{gathered}[/tex]Where
[tex]3^{-5}=\frac{1}{3^5}=\frac{1}{243}[/tex]Hence, answer is 1/243
[tex](3^3\div3^4)^5=\frac{1}{243}[/tex]The numerator is 1
The denominator is 243
The frequency distribution of blood groups of a sample of patients was found to be as follows:A 14B 6AB 3O 17The relative frequency of AB in this data is:Group of answer choices7.5%30.033%
we have that
the number of patients is (14+6+3+17)=40
patients AB=3
so
40 -----> 100%
applying proportion
100/40=x/3
x=3*100/40
x=7.5%Iq scores were gathered for group of college students at a local university. What is the level of measurement of dataNominal, ordinal, interval, ratio
Nominal data refers to non numerical data, for example categories, colors, etc...
Ordinal data refers to numerical data with a natural order, it comprehends real numbers.
Intervals comprehends data with equal distance between the values and no meaningful zero
Ratios comprehends data with equal distance between the values and a meaningul zero value.
With this in mind, the IQ scores of the college students represent numerical data, with a natural order, and the distance between the values is not equal, so you can classify the data as "ordinal"
In ACDE, m/C= (5x+18), m/D= (3x+2), and m/B= (2+16)°.
Angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.CDE provides the following: 3. angles
m<C=(5x+18),m<D=(3x+2), andm<E=(x+16)degree.The total of the angles in a triangle is 180 degrees, so:
"mC + mD + mE = 180°"(5x+18)° + (3x+2)° + (x+16)° = 180°5x + 18 + 3x + 2 + x + 16 = 180°5x + 3x + x + 18 + 2 + 16 = 180°9x +36= 180°From both sides, deduct 36 as follows:
9x + 36 - 36 = 180° - 36°9x = 144°x = 144°/9x = 16From the aforementioned query, we are requested to determine:
angular D (m<D)Hence:
m∠D=(3x+2)°m∠D=( 3 × 16 + 2)°m∠D=(48 + 2)°m∠D= 50°Therefore, angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°To learn more about angles, refer to:
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