The relative maxima and minima of the function g(x) are at the point (-4, 22) at the local maxima and at point (4,-124) at the local minima.
Given:
Function g(x) = x^3 - 48x + 4
Take the derivative and set it equal to zero
3x^2 - 48 = 0
x^2 = 48/3 = 16
x = sqr16 = ±4
At x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124
Point (4,-124) is a local or relative minimum
At x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122
The point (-4, 22) is a local or relative maximum
Refer to this complete question:
Find the relative maxima and minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =?
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a special window has the shape of a rectangle surmounted by an equilateral triangle. see the figure. if the perimeter of the window is 16 feet, what dimensions will admit the most light?
A triangle whose sides are all equal is called an equilateral triangle and its area is given by A=[tex]\frac{\sqrt{3} }{4}[/tex] [tex]x^{2}[/tex], where x is the side of the triangle.
The area of a rectangle is found by using the formula
A=lw, where l is the length and w is the width.
The given figure can be split into two shapes: a rectangle and an equilateral triangle as shown in the diagram. Let l be the length of the rectangle.
Add all of the sides of the window and equate their result to 16. Then solve for l.
x + x + l + x + l = 16
3x + 2l = 16
2l = 16 - 3x
l = [tex]\frac{16-3x}{2}[/tex]
The total area of the window will be the sum of the area of the equilateral triangle ABE and the area of rectangle BCDE.
A = [tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + lx
Subsitute [tex]\frac{16-3x}{2}[/tex] for l into the obtained equation and simplify.
A =[tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + ( [tex]\frac{16-3x}{2}[/tex])x
A = [tex]\frac{\sqrt{3} }{4} x^{2}[/tex] + 8x - [tex]\frac{3}{2} x^{2}[/tex]
Differentiate the obtained equation with respect to x and equate the first derivative to 0 to calculate the critical point x .
[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{4}[/tex] (2x) + 8 - [tex]\frac{3}{2}[/tex] (2x)
0 = [tex]\frac{\sqrt{3} }{2}[/tex] x - 3x + 8
x (3 - [tex]\frac{\sqrt{3} }{2}[/tex]) = 8
x = [tex]\frac{16}{6-\sqrt{3} }[/tex]≈3.74887
Again, differentiate the equation
[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]x - 3x + 8 with respect to x.
[tex]\frac{d^{2}A }{dx^{2} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] - 3
The value of the second derivative is [tex]\frac{\sqrt{3} }{2}[/tex]−3, which is negative. This implies that the area will be maximum at the critical point.
Subsitute x = 3.74887 into the equation
l = [tex]\frac{16-3x}{2}[/tex] and simplify
l = [tex]\frac{16-(3)(.74887)}{2}[/tex] ≈ 2.3767
The maximum light will enter through the window when the triangular portion will have the side length of 3.74887 feet and the dimensions of the rectangular portion will be 3.74887-ft-by-2.3767-ft.
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Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
Answer: h = 92
Step-by-step explanation:
148 - 180 = 32
32 + 56 = 88
88 - 180 = 92
Please help soon, functions problem! Thanks!
Answer:
5
Step-by-step explanation:
x=-1 doesn't fit in the range -1<x<2 since x>-1, not x=-1.
Hence, x=-1 fits in the range x<=-1 since (x<-1 or x=-1) which is true.
Hence, the expression -x+4 should be used
g(-1) =
-x + 4 =
-(-1) + 4 = ==> plugin -1 for x
1 + 4 = 5 ==> Negating a negative number is equal to taking a positive
number
to estimate the average cost of flowers for summer weddings in a certain region, a journalist selected a random sample of 15 summer weddings that were held in the state. a graph of the sample data showed an approximately symmetric distribution with no outliers. the sample mean and standard deviation were $734 and $102, respectively. the journalist will create a 95 percent confidence interval to estimate the population mean. have all conditions for inference been met?
No, it is not safe to assume that the sampling distribution of the sample means is about normal given the sample size.
Based on the information provided, it was reported that a journalist chose a random sample of 15 summer weddings that were hosted in the state in order to determine the average cost of flowers for summer weddings in a particular region.Note that the Z test usually includes more than 30 samples. 15 samples were used in this instance.Because of this, it is not possible to assume the sampling distribution from the sample size.Learn more about sampling on:
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In a company, 85% of the workers are men. If 405 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answer:
2700
Step-by-step explanation:
1st method:
let x be the number of all workers in the company
then, the number of female workers will be x-0.85x = 0.15x
0.15x = 405
x = 405/0.15 = 2700
2nd method
we know that the 405 people who aren't men make 15% (100%-85%) of the whole number of workers, by using proportions:
15% - 405
100% - X
X = (100% * 405 )/15% = 2700
distance formula definition
The distance formula is a mathematical equation that can be used to calculate the distance between two points in a coordinate system. It is typically expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) and (x2,y2)
The distance formula is an equation used to calculate the distance between two points in a coordinate system. To use it, you must know the x- and y-coordinates of each point. The equation is expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) are the x- and y-coordinates of the first point, and (x2,y2) are the x- and y-coordinates of the second point. The result, d, is the distance between the two points. To calculate the distance, you must first subtract the x-coordinate of the first point from the x-coordinate of the second point, then square the result. Next, subtract the y-coordinate of the first point from the y-coordinate of the second point and square the result. Finally, add the two squared numbers and take the square root of the sum. The result is the distance between the two points.
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5pages in a book have pictures and if there are 40pages in the book what percent of the book has pictures
Answer:
12.5%
Step-by-step explanation:
First,
take 5 page and divide by total amount in book 40 pages.
5/40 = 0.125.
Second,
To get percent multiply by 100.
0.125*100 = 12.5%
Can anyone solve these 2 questions they are very easy but i want to double check
Answer:
Corresponding angels:
a,f
h,b
e,d
c,g
y = 80 Vertical angles are congruent
x = 50 Sum of the interior angles of a triangle is 180
180 - 80 -50 = 50
Step-by-step explanation:
Find the missing power in the following calculation: 51/3⋅5□=5.
Based on the product of powers rule, the missing power in the given calculation is 2/3.
The product of powers rule is used in simplifying exponents. In a given term a^x, a number or variable raised to a power is called the base, while the superscript number is called the exponent, or power. According to the rule, if the bases are the same in the multiplication problem, it can be simplified by adding the exponents. Hence, for any number a and all integers m and n:
a^m * a^n = a^(m+n)
The given calculation is:
5^1/3*5^□ = 5
5^1/3*5^□ = 5^1
Hence, the sum of the powers would be one. Let the missing power be x. Therefore,
1/3 + x = 1
x = 1 - 1/3
x = 2/3
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sine rule find the length of ac
The length AC of the triangle ABC is approximately 12.083 centimeters.
How to use the law of sine
The law of sine is a relationship between the sides and the angles of the triangle, which is defined below:
AB / sin C = AC / sin B = BC / sin A
Where:
AB, AC, BC - SidesA, B, C - AnglesFirst, determine the measure of angle C:
AB / sin C = BC / sin A
sin C = (AB / BC) · sin A
sin C = (8.2 / 13.5) · sin 81°
C ≈ 36.865°
Second, determine the measure of angle B:
B = 180° - A - C
B = 180° - 81° - 36.865°
B = 62.135°
Third, determine the length of side AC:
AC / sin B = BC / sin A
AC = BC · (sin B / sin A)
AC = 13.5 · (sin 62.135° / sin 81°)
AC ≈ 12.083 cm
The length AC is approximately equal to 12.083 centimeters.
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What statistical technique is used to make predictions of future outcomes based on present data? Analysis of variance Repeated measures Linear regression Correlational analysis
To be able to make predictions for future outcomes based on present data, a statistical technique called regression analysis is used .
It helps in developing prediction models.
Regression analysis is basically a tool to show a relationship between two or more variables. Usually expressed in a graph, the method tests the relationship between a dependent variable against independent variables.
It is a quantative method wherein the basic form of regression models includes unknown parameters (β), independent variables (X), and the dependent variable (Y). Regression allows researchers to predict or explain the variation in one variable (called the dependent variable) based on another variable( known as the independent variable).
The most common and simple form of regression is the Linear Regression model.
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suppose steph curry is fouled while shooting a three-point goal and misses his shot. the probability of steph curry making a free throw is 90%. what is the probability that he makes the first and second free throw, but misses the third free throw?
The probability that he makes the first and second free throw, but misses the third free throw is 7.7 %.
Given :
suppose steph curry is fouled while shooting a three-point goal and misses his shot. the probability of steph curry making a free throw is 90%.
probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
P ( makes 2 then misses 1 ) = P ( make 1st ) and P ( make 2nd ) and P ( miss 3rd )
= 0.906 *0.906 * 0.094
= 0.077
= 7.7 %
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Of the markets in a certain city, 43/50 offered customers a salad bar in 1997
The given fraction in percentage is 86%.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
percentage, a relative value indicating the hundredth parts of any quantity. We must divide the amount by the sum to get the percentage, then multiply the result by 100.
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 of 100 questions correctly on a test (75/100).
To get the percentage, multiply the given fraction by 100.
(43/50)*100= 86%
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Question: Rewrite the fraction in the sentence below as a percentage.
The girls' soccer team wants to raise at least $2000 to buy new goals. If
they make $1.00 from each hot dog and $1.25 from each soda, how many of each item
do they need to sell?
a. Write an inequality to represent the situation.
b. Graph an inequality to represent the situation.
c. Plot at least 5 possible solutions on your graph.
The inequality to represent the problem is x + 1.25y ≥ 2000 and it's graph is attached below
Linear InequalityLinear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in mathematics. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).
Let;
x = number of hot dogy = number of sodaa) The inequality to represent the situation can be expressed as
1x + 1.25y ≥ 2000
This is further expressed as;
x + 1.25y ≥ 2000
b) The graph of the inequality x + 1.25y ≥ 2000 is attached below.
c) The possible solutions are at (2000, 0) and (0, 1600)
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100 POINTS + BRAINLIEST!!!
How does the graph of g(x) = (x - 4)^3 + 5 compare to its parent function f(x) = x^3?
g(x) is shifted 4 units to the right and 5 units up
g(x) is shifted 5 units to the right and 4 units up
g(x) is shifted 4 units to the left and 5 units up
g(x) is shifted 5 units to the right and 4 units down
The required choice for transformation is Option 1.
What is transformation?
When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects."
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift.
g(x) = (x - 4)^3 + 5 and f(x) = x^3
Then we get, g(x) is shifted 4 units to the right and 5 units up
Hence, the required answer for transformation is Option 1.
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Answer:
A) g(x) is shifted 4 units to the right and 5 units up-----------------------------
If original function is f(x), translated function is g(x) and
g(x) = f(x + h) + k,Then:
if h is negative, it indicates a shift to the right, if h is positive it indicates a shift to the left,if k is positive it indicates a shift up,if k is negative it indicates a shift down.Looking at the given functions we see that:
h = - 4 < 0, it is a shift to the right,k = 5 > 0, it is a shift up.This is reflected in the answer choice A.
Find the Amount (A) (Principal Rs 50000 Time = 7 years interest = 3%.
Answer: Rs 60500
Step-by-step explanation:
Principal = Rs 50000 = p
Time = 7 years = t
Simple interest rate = 3% = r
Interest = p*t*r/100
using above formula,
50000*7*3/100=10500
So, final amount = principal + interest = 50000+10500 = Rs 60500
Which is greater 30% of 105 or 32% 98
Answer: 30% of 105 (= 31.5)
Step-by-step explanation:
30% of 105 is 31.5 and
32% of 98 is 31.36
Kenneth drove 187.6 miles in 1.85 hours. What was his average speed?
Carlos earns 44.55 in 9 hours. Maggie earns 51 in 12 hours
By taking some products, we can see that if both of them work for 20 hours each, they will earn a total of 184 dollars.
How much do Carlos and Maggie earn if they work for 20 hours?After a small search online I found that we want to find how much will they earn (together) if both of them work for 20 hours.
We know that Carlos earns $44.55 in 9 hours, then the amount that he wins per hour is:
C = $44.55/9h
In 20 hours he will earn 20 times that, so the amount that Carlos earns in 20 hours is given by the product:
Carlos = 20h*($44.55/9h )
Similarly, Maggie earns per hour:
M = ($51/12h)
And in 20 hours, she will win:
Maggie = 20h*($51/12h)
The total amount that they earn together is:
20h*($44.55/9h ) + 20h*($51/12h) = $184.
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Shuja conducted a series of surveys asking respondents about the amount of time they spend cleaning their homes each week. Each sample contains 40 responses, and the standard error of the mean is 1.36. What is the standard deviation? Round your answer to the nearest hundredth.
The standard deviation of the distribution is 8.60
How to determine the standard deviation?From the question, we have the following parameters that can be used in our computation:
Sample size = 40
Standard error of the mean = 1.36
These parameters mean that
n = 40
SE = 1.36
The standard deviation is then calculated as
SE = σ/√n
Where
σ = standard deviation
Make σ the subject
σ = SE * √n
So, we have
σ = 1.36 * √40
Evaluate
σ = 8.60
Hence, the standard deviation is 8.60
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As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 58% in 1997 to only 38% in 2003. Each household, of course, is independent of the others. Using the cooperation rate from 2003, a) what is the probability that the next household on the list will be contacted but will refuse to cooperate? b) what is the probability of failing to contact a house hold or of contacting the household but
a)The probability that the next household on the list will be contacted but will refuse to cooperate will be 0.38
b)The probability of failing to contact a household or of contacting the household but will refuse to cooperate is 0.62.
We are given the information that interviewers can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 58% in 1997 to only 38% in 2003. To calculate these probabilities, we use the cooperation rate from 2003. Since the cooperation rate is 38%, this means that 38% of the people will cooperate and 62% will not cooperate. Therefore, the probability of the next household on the list not cooperating is 0.62 and the probability of the next household on the list cooperating is 0.38.
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As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 58% in 1997 to only 38% in 2003. Each household, of course, is independent of the others. Using the cooperation rate from 2003, a) what is the probability that the next household on the list will be contacted but will refuse to cooperate? b) what is the probability of failing to contact a house hold or of contacting the household but will refuse to cooperate
3x + 1.5 = 2.5x + 4.7
Answer:
x = 6.4
Step-by-step explanation:
Answer: x=6.4
Step-by-step explanation:
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.
$8
$9
$11
$13
$14
The stated inequality, x < 9 or x >=14, indicates that the two potential values for x are $8 and $14.
what is inequality in equation ?The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >,,, or are used to denote an inequality, when the two expressions aren't always equal.
x < 9 or x ≥ 14
This indicates that x must be more than 9 but not equal to 14.
In the choices
All values below nine are
$8
There are no values larger than or equal to 14.
$14
The stated inequality, x < 9 or x >=14, indicates that the two potential values for x are $8 and $14.
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what beat frequencies are possible with tuning forks of frequencies 254, 257, and 262
The three beat frequencies possible with tuning forks are-
f1 = 9 Hz; f2 = 3Hz; f3 = 5Hz
Explain the term beat frequencies?Whenever two waves of similar frequencies travel along the same path and superimpose, a beat is created. The resulting wave's intensity changes as a result on a regular basis.The quantity of beats generated each second is known as the beat frequency.The absolute value of a difference in frequency between the two waves determines the beat frequency. The uses of beats, which developed from basic interference, are incredibly diverse. Show. Two-tone wave envelopeThe beat frequency occurs when two sound waves of different frequencies cross paths and, for a predetermined amount of time, their amplitudes are alternately added and subtracted. This causes the sound to get louder and weaker over time.The three beat frequencies are -
f1= 262 - 254 = 9 Hz
f2 = 257 - 254 = 3Hz
f3 = 262 - 257 = 5Hz
Thus, the possible beat frequencies of the turning fork are found.
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What is the measure of angle B in this triangle?
Enter your answer in the box.
m∠B=
By using the fact that the sum of all internal angles must be equal to 180°, we will see that the measure of angle B is 70°.
How to find the measure of angle B?Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write the linear equation:
40° + (2x - 30°) + (x + 20°) = 180°
(2x - 30°) + (x + 20°) = 180° - 40°
2x + x - 30° + 20° = 140°
3x = 140° + 30° - 20°
3x = 150°
x = 150°/3
x = 50°
Then the measure of angle B is (2x - 30°) = (2*50° - 30°) = 70°.
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The correct answer is 70
Gravitational potential energy depends on which two of the following
Gravitational potential energy depends on which two of the following weight and height.
What is Gravitational potential energy ?The energy that an object can possess or acquire when its position changes as a result of a gravitational field is known as gravitational potential energy. The energy connected to gravity or gravity is what is known as gravitational potential energy.
What exactly does GCSE Gravitational Potential Energy mean?The motion, position, and deformation of an object can all contribute to its energy storage. Gravity affects you constantly on Earth. There is a latent (stored) energy present in everyone on Earth's surface. the gravitational potential energy of this.
Answer is - The gravitational potential energy of an object depends upon its weight and height.
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The correct question is -
What two things does gravitational potential energy depend on?
Solve |2 +1| = 10x
{-9/2, 9/2}
{-11/2, 9/2}
{9/2, 11/2}
The solution to the equation |2 +1| = 10x is x = 3/10
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
|2 +1| = 10x
Evaluate the sum in the above equation
So, we have the following representation
|3| = 10x
Remove the absolute bracket in the above equation
So, we have the following representation
3 = 10x
Divide both sides by 10
This gives
3/10 = x
Rewrite as
x = 3/10
Hence, the solution is 3/10
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Y=-3x²+26x–46
x+y = 8
Answer:
-3x^2--20x+(y-8)=0
Angel Sum Theorem PLEASE HELP with explanation if possible
Answer:
y = 90°
Step-by-step explanation:
You want the value of y in the diagram showing y as the angle at the base where the isosceles triangle a.pex angle bisector meets the base.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
Consider the large outside triangle. The sum of its angles is ...
60° +2x +60° = 180°
2x = 60° . . . . . . . . . . . . subtract 120°
x = 30° . . . . . . . . . . divide by 2
Now, consider the left smaller triangle. The sum of its angles is ...
60° +x +y = 180°
60° +30° +y = 180° . . . . . . use the known value of x
y = 90° . . . . . . . . . . . . subtract 90°
__
Additional comment
The a.pex angle bisector of an isosceles triangle is always an altitude that meets the base at right angles. The meeting point is the midpoint of the base, so that segment is also a median.
The halves of the isosceles triangle are congruent right triangles, so the base angle is complementary to the angle marked x.
solve for z
[tex]\dfrac{z}{10} =5[/tex]
[tex]\dfrac{z}{10} =5[/tex]
Multiply both sides by 10:
[tex](\dfrac{z}{10} )\times10=(5)\times10[/tex]
[tex]\fbox{z = 50}[/tex]
z/10 = 5
Multiply both sides by 10:
z/10 * 10 = 5 * 10
z = 50
