A. The critical points of the function are (1, -1) and (-1, -3).
B. The function is increasing on the intervals (-∞, -1) and (1, ∞), and decreasing on the interval (-1, 1). Test points are used to determine the intervals.
C. The relative maximum occurs at (-1, -3), and there is no relative minimum.
D. The function is concave up on the intervals (-∞, -1) and (1, ∞), and concave down on the interval (-1, 1). Test points are used to determine the intervals.
E. The point(s) of inflection are not provided.
F. The graph will have a relative maximum at (-1, -3), and concave up intervals on (-∞, -1) and (1, ∞), with a concave down interval on (-1, 1).
A. To find the critical points, we take the derivative of the function and set it equal to zero. The derivative of f(x) = x^3 - 3x + 1 is f'(x) = 3x^2 - 3. Solving 3x^2 - 3 = 0 gives x = ±1. Plugging these values back into the original function, we find the critical points as (1, -1) and (-1, -3).
B. To determine where the function is increasing or decreasing, we evaluate the derivative at test points within each interval. Choosing x = 0 as a test point, f'(0) = -3, indicating the function is decreasing on the interval (-1, 1). For x < -1, say x = -2, f'(-2) = 9, indicating the function is increasing. For x > 1, say x = 2, f'(2) = 9, indicating the function is increasing. Hence, the function is increasing on the intervals (-∞, -1) and (1, ∞), and decreasing on the interval (-1, 1).
C. To find the relative extrema, we evaluate the function at the critical points. Plugging x = -1 into f(x) gives f(-1) = -3, which corresponds to the relative maximum. There is no relative minimum.
D. To determine the intervals of concavity, we evaluate the second derivative of the function. The second derivative of f(x) is f''(x) = 6x. Evaluating test points within each interval, we find that f''(-2) = -12, f''(0) = 0, and f''(2) = 12. This indicates concave down on (-1, 1) and concave up on (-∞, -1) and (1, ∞).
E. The point of inflection are not provided, so we cannot determine their coordinates.
F. Based on the information obtained, we can sketch the graph of the function. It will have a relative maximum at (-1, -3), be concave up on (-∞, -1) and (1, ∞), and concave down on (-1, 1).
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Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 20 (newly deceased) adults, the mean failure strain (%) was 26.0, and the standard deviation was 3.4. (a) Assuming a normal distribution for failure strain, estimate true average strain in a way that conveys information about precision and reliability. (Use a 95% confidence interval. Round your answers to two decimal places.)
The true average strain in a way that conveys information about precision and reliability is 27.314.
Given that sample size is 20, mean is 26%, standard deviation is 3.4, confidence level is 95%.
We have to calculate the true average strain in a way that conveys information about precision and reliability.
We have to use t test in our problem because sample size is less than 30.
Weknow that,
t=x bar-μ/s[tex]\sqrt{n}[/tex]
where μ is sample mean,
s is sample standard deviation.
Degree of freedom=n-1
=20-1
=19
T value at 95% confidence interval=1.7281
put the values in the formula of t given above.
1.7291=x bar-26/3.4/[tex]\sqrt{20}[/tex]
1.7291=xbar-26/3.4/4.47
1.7291= x bar-26/0.76
1.7291*0.76=x bar-26
1.314=x bar-26
x bar=26+1.314
x bar=27.314
After rounding it will be 27.31
Hence the true average strain in a way that conveys information about precision and reliability is 27.31%.
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the diffrence of 3-7p^2+11(4+n)
The expression 3 - 7p² + 11(4 + n) to find an example of each kind of expression is;
The first value is a number, 3 = constantThe second value, -7p² = factorThe third value, 11(4 + n) = binomial and monomial valuesExpression3 - 7p² + 11(4 + n)
The expression has 3 parts
3-7p²11(4 + n)3 - 7p² + 11(4 + n)
= 3 - 7p² + 44 + 11n
= 47 + 7p² + 11n
Complete question:
Use the expression 3 — 7p2 + 11(4 + n ) to find an example of each kind of expression
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I need help someone with graphs
Answer:
B.) The graph of g(x) is shifted 4 units up
Step-by-step explanation:
In a linear function in slope-intercept form, b, or 4 in this case, represents the y-intercept which technically acts as a vertical shift
write 75 as a product of prime use index notation when giving your answer
What is the equation of a circle whose center at (-5, -2) and radius is 2?
The equation of a circle whose centre ([tex]-5,-2[/tex]) and radius [tex]2[/tex] is [tex]x^{2}+y^{2}+10x+4y+25=0[/tex]
What is equation of a circle?
A circle is a closed curve drawn from a fixed point called centre of the circle. The distance between the centre of the circle and the arc of the circle is called the radius of the circle.
The equation of a circle with centre [tex](h, k)[/tex] radius [tex]r[/tex] is
[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]
Given center = [tex](-5,-2)[/tex] and Radius = [tex]2[/tex]
Put the Given value in the equation:
= [tex](x-(-5))^{2} +(y-(-2))^{2} = 2^{2}[/tex]
= [tex](x+5)^{2} +(y+2)^{2}=2^{2}[/tex]
= [tex](x^{2} +10x+25)+(y^{2}+4y+4)= 4[/tex]
= [tex]x^{2} +y^{2}+10x+ 4y+ 29 = 4[/tex]
= [tex]x^{2} +y^{2}+10x +4y+ 29-4=0[/tex]
= [tex]x^{2} +y^{2}+10x+4y+25=0[/tex]
So, the equation of the circle whose centre is [tex](-5,-2)[/tex] and Radius [tex]2[/tex] is
[tex]x^{2}+y^{2}+10x+4y+25=0[/tex]
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PLEASE HELP FAST!!! Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
Using the surface area formula for rectangular and triangular prism, the surface area of the composite figure is: 444 m².
What is the Surface Area of the Composite Figure?Total surface area = surface area of the top triangular prism + surface area of the bottom rectangular prism - area of the surface both share together.
Surface area of the top triangular prism = (S1 + S2+ S3)L + bh = (10 + 10 + 16)5 + (16)(6) = 276 m².
Surface area of the bottom rectangular prism = 2(wl + hl + hw) = 2·(5·16+4·16+4·5) = 328 m²
Area of the surface both share together = 2(16)(5) = 160 m²
Total surface area = 276 + 328 - 160 = 444 m².
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Identify the scale of measurement for the following variable: The weight of a group of dieters. Group of answer choices nominal ratio ordinal interval
Ratio scale of measurement for the following variable, The weight of a group of dieters.
What scale of measurement is the variable of weight?Ratio measurement scale of ratio variables include height, weight, and distance. The ratio scale allows for the addition, subtraction, division, and multiplication of data. Additionally, ratio scales have a "real zero," which sets them apart from interval scales. The ratio scale is used to determine weight. The ratio is identical to the interval scale, with the exception that 0 on the scale denotes the absence of anything. serval scales can depict values lower than zero and do not hold a true zero. For instance, you can gauge temperatures as low as -10 degrees Celsius. Contrarily, ratio variables are always greater than zero. Height and weight are measured starting at 0 and never below it. Because they are numbers as we typically think of them, ratio scales are the simplest to comprehend. On a ratio scale, the distance between consecutive numbers is equal, and a score of zero indicates that there is no presence of the thing being measured. The majority of ratio scales are counts of items.
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If f(x)=2x-6, which of these is the inverse of f(x)?
○ A. f-¹(x) = 1 +6
X-6
○ B. f-¹(x) = x=6
2
○ C. f-¹(x) = X+6
2
○ D. f¹(x) = -6
Answer:
f-¹(x) = (x + 6)/2
Step-by-step explanation:
Replace f(x) with y.
y = 2x – 6
Interchange x and y.
x = 2y – 6
Solve for y.
y = (x + 6)/2
Replace y with f-¹(x)
f-¹(x) = (x + 6)/2
The padlock for your gym locker uses a 3 number sequence to open the lock. If
the numbers go from 1 to 22, how many different sequences are there on the dial
without repeating a number?
Answer:
9,240
Step-by-step explanation:
For the first number, there are 22 numbers available to choose from. For the second number, there are 21 numbers available, since the first number cannot be the same as the second number. And for the last number, there are 20 remaining numbers to choose from. So, there are 22*21*20=9240 possible sequences.
Sonji bought a combination lock that opens with four-digit number created using the digits 0 through 9. The same
digit cannot be used more than once in the combination.
If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be
chosen?
O 84
• 504
• 3,024
• 60,480
Answer:
Step-by-step explanation:
This is what I am thinking. - ,- ,- , - I number goes in each space. There are 10 numbers to choose from and I cannot use a digit more than once. I only have 1 choice for last slot and that is the number 7. I have 9 numbers left . I could put any one of the 9 numbers in the first spot, then there are only 8 numbers to choose from, so I will put 8 in the second spot. I now have only 7 numbers that are left for the third spot.
If I multiple this together 9x8x7x1 = 504
A 4-column table with 3 rows. The first column has no label with entries students, teachers, total. The second column is labeled wear glasses with entries 32, 4, 36. The third column is labeled do not wear glasses with entries 97, 2, 99. The fourth column is labeled total with entries 129, 6, 135.
Which statements are correct about the two-way frequency table? Check all that apply.
The correct statements about the two-way frequency table are:
Option C, and Option E.
According to the statement
we have to check that the given statement is applicable or not on the given conditions.
So, For this purpose
The two-way frequency table is
In Mathematics and statistics, A two-way frequency table is a tabular method for displaying relative data for two categories of variables. (See the attached).
the given options are:
Option A the row categories are "wears glasses"
Option B and "do not wear glasses."
Option C two teachers do not wear glasses.
Option D thirty-six students wear glasses.
Option E a total of 6 teachers were polled.
So, The correct statements about the two-way frequency table are:
Option C, and Option E.
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Answer: the corret answer is A, C and E
if 3n+2 is an odd number which of the following is an even number
A. 3n
B. 3n + 4
C. 3n + 3
D. (3n)²
Answer: 3n+3
Step-by-step explanation:
Adding 1 to an odd number results in an even number.
An urn contains 11 balls, 3 white, 3 red, and 5 blue balls. Take out two balls at random, without replacement. You win $1 for each red ball you select and lose a $1 for each white ball you select. Let X be the random variable that notes the amount you win. Find the probability mass function (pmf) of X.
Let X be the number of times you win.
The total number of ways to select 2 balls (order does not matter) =>
The number of ways so that two balls are white:
= 3/55
The number of ways so that two balls are red:
= 3/55
The number of ways so that one ball is red, one is white:
= 9
The number of ways so that two balls are blue:
= 10
i.e. p = 10+9/55 = 19/55
The number of ways so that one ball is blue, one is white:
p = 15/55 = 3/11
The number of ways so that one ball is blue, one is red:
15/55 = 3/11
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The numerator in the fixed asset turnover ratio is:_______
The numerator in the fixed asset turnover ratio is sales.
To determine the fixed Asset Turnover ratio, the subsequent components are used: fixed Asset Turnover = sales / common fixed property.
The fixed asset turnover ratio exhibits how green an employer is at generating sales from its current fixed assets. A higher ratio implies that control is the usage of its fixed property extra efficiently.
Within the retail region, an asset turnover ratio of 2.5 or greater can be considered good, even as a business enterprise in the software region is much more likely to intention an asset turnover ratio it is among zero.25 and 0.5.
We can now calculate the constant asset turnover ratio by dividing the internet revenue for the yr through the average constant asset balance, which is equal to the sum of the modern-day and earlier duration balance divided through two.
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am bad at this type of geomtry
pls haIp
x =x=x, equals
^\circ
∘
degrees
Answer:
15
Step-by-step explanation:
The blue angle and the yellow angle form a linear pair, so they are supplementary (angle measures add up to 180).
180 - 165 = 15
PLEASE HELP HURRYYYYY
Answer:
See below
Step-by-step explanation:
Looks like positive linear to me....slope is up and to the right (positive) and the line drawn shows it ot be approx linear
rewrite each expression without using absolute value notation |x-y| if x>y
Answer: x-y
Step-by-step explanation:
If x>y, then [tex]x-y > 0[/tex].
So, [tex]|x-y|=x-y[/tex]
The solution of the expression |x-y| if x>y without using absolute value notation is (x - y).
A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression
Example = 4y, 3x+4
The absolute value of any number or expression is always positive.
An expression that is either less than or greater than is called as inequality.
Given expression, |x-y| and the given inequality is x>y.
When x is greater than y, the difference between x and y is already positive.
So, the expression will be (x-y).
So, if x > y, then |x - y| = (x - y).
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HELP ASAP
You work at a canning factory that's producing cans for a new brand of soup. You need to decide what size the cans should be. The soup cans can have a radius of either 2 in, 2.5 in, 3 in, or 3.5 in. The cans need to hold a volume of exactly 90 in3. The company wants the cans to be no more than 5 inches tall, and it wants the cans to have the greatest lateral surface area possible so it can print more information on the side of the cans.
To solve this problem, you will fill in this table with the surface area and volume of each cylinder:
a. First, calculate the height each can must be, given the radius and volume.
b. Now calculate the lateral surface area for each possible can.
c. Based on the requirements for the can, which can should you make?
Answer:
The answers are in the image
Step-by-step explanation:
The solution is in the attached image
Which expressions are equivalent to 2(4f+2g)-
choose three answers
A. 8f+2g
B. 2f(4 + 2g)
C. 8f+4g
D. 4(2f+g)
E. 4f+4f+4g
help me w this pls thanks
Answer:
Perimeter: 4+[tex]\pi \\[/tex] mm
Area: [tex]\pi[/tex] mm^2
Step-by-step explanation:
Perimeter:
90/360 * 4[tex]\pi \\[/tex] +2 + 2 = 4+ [tex]\pi \\[/tex]
Area:
90/360 * 4[tex]\pi[/tex] = [tex]\pi[/tex]
Answer: 7.14 mm and 3.14 mm²
Step-by-step explanation:
The perimeter of a figure is the total length on the outside of the figure. A regular circle has a perimeter of [tex]2\pi r[/tex], where r is the radius and [tex]\pi[/tex] is an irrational constant, approximately 3.14.
Due to the right angle, we know that this is a quarter circle, as it is a quarter of 360°, or a full circle. Hence, the curved portion of the quarter circle is [tex]\frac{1}{4}* 2\pi r[/tex] or [tex]\frac{1}{2} \pi r[/tex]. The radius is 2 mm, so this value is
[tex]\frac{1}{2} \pi*2=\pi[/tex]
However, this isn't the total perimeter, as there are straight edges in the figure too. Both edges are radii of the whole circle, so both would be 2mm. Their total is
[tex]2+2=4[/tex]
By adding [tex]\pi[/tex] to 4 we get [tex]\pi +4[/tex] or 7.14 mm.
The area is the total space enclosed by a figure. The total area of a whole circle is [tex]\pi r^2[/tex], where r is still the radius. Since this is a quarter circle, it would take up a quarter of the area, or [tex]\frac{1}{4} \pi r^2[/tex]. We can plug in 2 for r and solve to get the area.
[tex]\frac{1}{4}\pi*2^2\\\frac{1}{4}\pi*4\\\pi[/tex]
Hence, the area is [tex]\pi[/tex], or around 3.14 mm².
Find the interval in which the function is positive.
f(x)=x²-7x + 10
1. (-∞0, 2)
II. (2,5)
III. (5,00)
O I, II
O I, III
O II, III
O II only
Answer:
(b) I, III
Step-by-step explanation:
The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).
General shapeThe leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.
If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.
Specific shapeThe answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).
f(2) = 2² -7·2 +10 = 4 -14 +10 = 0
f(5) = 5² -7·5 +10 = 25 -35 +10 = 0
This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.
in this triangle, cosA/cosB =
AB = 4.24
BC= 3
AC = 3
<C 90deg.
Answer:
1
Step-by-step explanation:
[tex]\cos A=\frac{3}{4.24} \\ \\ \cos B=\frac{3}{4.24} \\ \\ \frac{\cos A}{\cos B}=1[/tex]
Write the standard form of the equation of the line trough the given point with the given slope.
Step-by-step explanation:
we use the point-slope approach :
y - y1 = m(x - x1)
m is the slope, and (x1, y1) is a point on the line.
so,
1.
y - 2 = 7(x - 1) = 7x - 7
y = 7x - 5
2.
y - -1 = -1×(x - 3) = -x + 3
y + 1 = -x + 3
y = -x + 2
3.
y - 5 = -4(x - -2) = -4x - 8 (3x a "-" is a "-" for 8)
y = -4x - 3
4.
y - 5 = 5/3 × (x - 3) = 5x/3 - 5
y = 5x/3 or 5/3 × x
Answer:
1. [tex]7x-y=5[/tex]
2. [tex]x+y=2[/tex]
3. [tex]4x+y=-3[/tex]
4. [tex]5x-3y=0[/tex]
Step-by-step explanation:
Since we already know the slope and the coordinates of one point, first use the point-slope form to create an equation.
[tex]y-k=m(x-h)[/tex]
[tex]y-2=7(x-1)[/tex]
[tex]y-2=7x-7[/tex]
[tex]7x-y=5[/tex]
[tex]y+1=-1(x-3)[/tex]
[tex]y+1=-x+3[/tex]
[tex]x+y=2[/tex]
[tex]y-5=-4(x+2)[/tex]
[tex]y-5=-4x-8[/tex]
[tex]4x+y=-3[/tex]
[tex]y-5=\frac{5}{3} (x-3)[/tex]
[tex]y-5=\frac{5}{3}x-5[/tex]
[tex]3y-15=5x-15[/tex]
[tex]5x-3y=0[/tex]
A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft3/min. How fast is the diameter of the balloon increasing when the radius is 1 ft
When an spherical balloon volume is increasing at the rate of [tex]3ft^3/min[/tex] then the diameter of the balloon is increasing [tex]\frac{3}{2\pi }ft /min[/tex]
How can we find the rate of change of balloon's diameter ?
The volume of a spherical balloon is [tex]v=\frac{4}{3} \pi r^3[/tex]
In form of diameter we can write as
[tex]v=\frac{4}{3} \pi (\frac{D}{2} )^3\\=\frac{1}{6} \pi D^3[/tex]
Now we will differentiate both sides wrt to [tex]t[/tex] we get
[tex]\frac{dv}{dt} =\frac{1}{6} \pi 3D^2 \frac{dD}{dt} \\\frac{dD}{dt} =\frac{2}{\pi D^2} \frac{dv}{dt} \\\\when r=1\\D=2ft[/tex]
Given in the question [tex]\frac{dv}{dt} =3ft^3/min[/tex]
thus when we substitute the values we get
[tex]\frac{dD}{dt} =\frac{2}{\pi *2^2} (3)\\\frac{dD}{dt}=\frac{3}{2\pi } ft/min[/tex]
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PLEASE HELP FAST!!! Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
The surface area of the composite figure is 524 square meters
Surface area of a figureThe given composite figure is made up of a triangular prism and a rectangular prism. The surface area of the figure is given as:
Surface area = 2(16*5+5*4+16*4) + (16*6) + 2(50)
Take the sum
Surface area = 2(80+20+64) + 96 + 100
Surface area = 2(164) +196
Surface area = 328 + 196
Surface area = 524 square meters
Hence the surface area of the composite figure is 524 square meters
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Help with this!! Thank you
Answer:
Step-by-step explanation:
1) The equation of circle having center at origin:
x² + y² = r²
Where 'r' is the radius.
diameter = 36
r = 36 ÷ 2 = 18
Equation of circle :
x² + y² = 18²
x² + y² = 324
Option d.
2) Find the discriminant D.
If D > 0, then the quadratic equation has two distinct real roots.
If D= 0, then the quadratic equation has two identical real roots.
If D < 0, then the quadratic equation has no real roots.
D = b² - 4ac
x² - 6x + 9 = 0
a = 1 ; b = -6 ; c = 9
D = (-6)² - 4*1*9
= 36 - 36
D = 0
As D = 0, the quadratic equation has two identical real roots
Option a.
3) The axis of symmetry of a parabola is the vertical line passing through the vertex. It will be middle of the x-intercepts.
X- intercepts are -8 , 2
( -8 + 2 ) ÷ 2 = -6 ÷ 2 = -3
x = - 3
Option d.
Brett had 3/4 of a family sized pizza. he gave each of his brothers half of this. what fraction of the pizza was each brother given?
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] * [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]
There are 5,280 feet in a mile. Gary walked 220 feet to the bus stop, and the bus took him a quarter of a mile to school. What is the ratio of his distance walking to.the distance he rode the bus
The ratio of distance travelled by walking to distance travelled by bus is 1 : 6.
What is ratio?When two quantities of the same units are compared, the ratio is what shows how much of one quantity is included in the other.
Total no. of Feet in a Mile = 5280
Distance Gary walked to the bus stop = 220 feet
Distance travelled by bus = 1/4 mile = (1 / 4)*5280 = 1320 feet
Ratio of distance walking to distance by bus = 220 / 1320 = 1 : 6
Hence, the ratio of distance travelled by walking to distance travelled by bus is 1 : 6.
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A wall is in the shape of a trapezoid. The lengths of the parallel bases are 8 feet and 20 feet. The height of the room is 8 feet. How much paint is needed to cover the wall? 80 ft2 112 ft2 160 ft2 224 ft2
The amount of paint needed to cover the wall is 112 square feet
How to determine the amount of paint?The given parameters are:
Parallel bases = 8 feet and 20 feet
Height = 8 feet
The area is calculated as:
Area = 0.5 * (Sum of parallel bases) * Height
So, we have;
Area = 0.5 * (8 + 20) * 8
Evaluate
Area = 112
Hence, the amount of paint needed to cover the wall is 112 square feet
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PLEASE I NEED HELP SO BADLY
Answer:
[tex]3y^{2} -3y-5[/tex]