Answer:
Using Newton's Method, the points of intersection between f(x) = x^6 and g(x) = cos(x) are approximately (0.8241, f(0.8241)) and (2.3111, f(2.3111)), where f(x) = x^6.
To find the points of intersection of the graphs of f(x) = x^6 and g(x) = cos(x), we can solve the equation h(x) = f(x) - g(x) = x^6 - cos(x) = 0.
Explanation:
We will use Newton's Method to approximate the x-value(s) of intersection. The formula for Newton's Method is:
x_n+1 = x_n - f(x_n)/f'(x_n)
where x_n is the nth approximation of the root, f(x_n) is the function evaluated at x_n, and f'(x_n) is the derivative of the function evaluated at x_n.
Let h(x) = x^6 - cos(x), then
h'(x) = 6x^5 + sin(x)
Now we need to choose a starting value for x. By graphing the two functions, we can see that there are two points of intersection in the interval [0,1]. Let's choose x = 0.5 as our starting value.
x_0 = 0.5
x_1 = x_0 - h(x_0)/h'(x_0) = 0.5352
x_2 = x_1 - h(x_1)/h'(x_1) = 0.8656
x_3 = x_2 - h(x_2)/h'(x_2) = 0.8249
x_4 = x_3 - h(x_3)/h'(x_3) = 0.8241
Thus, the approximate value of the first intersection point is x = 0.8241.
Now we need to find the second intersection point. By graphing the two functions, we can see that there is another intersection point in the interval [2,3]. Let's choose x = 2.5 as our starting value.
x_0 = 2.5
x_1 = x_0 - h(x_0)/h'(x_0) = 2.3214
x_2 = x_1 - h(x_1)/h'(x_1) = 2.3111
x_3 = x_2 - h(x_2)/h'(x_2) = 2.3111
Thus, the approximate value of the second intersection point is x = 2.3111.
Therefore, the points of intersection of the two graphs are approximately (0.8241, f(0.8241)) and (2.3111, f(2.3111)), where f(x) = x^6.
Hope this helps you in some way! I'm sorry if it doesn't. If you need more help, ask me! :]
The following system of equations are given:
3x+z+y=8
5y-x=-7
3z+2x-2y=15
4x+5y-2z=-3
a. Is it possible to solve for any of the variables using only Equation #1 and Equation #2? Explain your answer. If possible, solve for the variables using only equations #1 and #2.
b. Is it possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3? Explain your answer. If possible, solve for the variables using only equations #1, #2, and #3.
c. If you found solutions in part b, do these solutions also hold for Equation #4?
The solution for the system of equations using Equations #1, #2, and #3 is x=-55, y=-9.6, z=39.2.
What is Linear Equation ?
Linear equation can be defined as equation in which highest degree is one.
We can solve for one variable using Equations #1 and #2, but not for all three variables. From Equation #2, we can solve for x in terms of y as x=5y+7. Substituting this expression for x into Equation #1 gives:
3(5y+7)+z+y=8
Simplifying this equation, we get:
16y+z=-13
We still have two unknowns, y and z, so we cannot solve for any variable using only Equations #1 and #2.
b. It is possible to solve for all three variables using Equations #1, #2, and #3. We can use the following steps to solve for the variables:
Use Equation #2 to solve for x in terms of y as x=5y-7.
Substitute this expression for x into Equation #3 to get:
3z+2(5y-7)-2y=15
Simplifying this equation, we get:
13y+3z=29
Substitute the expression for x from Step 1 into Equation #1 to get:
3(5y-7)+z+y=8
Simplifying this equation, we get:
16y+z=29
Solve for z in terms of y by subtracting the equation from Step 3 from the equation from Step 2:
(13y+3z)-(16y+z)=29-(-13)
Simplifying this equation, we get:
-3y+2z=42
Solve for z in terms of y by adding twice the equation from Step 1 to the equation from Step 4:
2(5y-7)+(-3y+2z)=42
Simplifying this equation, we get:
7y+2z=56
Solve for y by adding the equation from Step 4 to twice the equation from Step 5:
(7y+2z)+2(-3y+2z)=56+84
Simplifying this equation, we get:
5z=196
So, z=39.2. Substituting this value for z into the equation from Step 4 gives:
-3y+2(39.2)=42
Solving for y, we get y=-9.6. Finally, substituting the values for y and z into the equation from Step 1 gives:
x=5(-9.6)-7=-55.
Therefore, the solution for the system of equations using Equations #1, #2, and #3 is x=-55, y=-9.6, z=39.2.
c. To check if the solution found in part b holds for Equation #4, we substitute the values of x, y, and z into Equation #4 and see if the equation is satisfied:
4(-55)+5(-9.6)-2(39.2)=-3
Simplifying this equation, we get:
-220-48-78.4=-3
This equation is not satisfied, so the solution found in part b does not hold for Equation #4. Therefore, the system of equations does not have a unique solution.
Therefore, the solution for the system of equations using Equations #1, #2, and #3 is x=-55, y=-9.6, z=39.2.
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find the lateral surface area of a square 14 mm 13mm 6 mm
The lateral surface area of the square is 784mm².
What is square?Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
If the square has a side length of 14 mm, then all sides are equal in length.
The lateral surface area of a square is simply the perimeter multiplied by the height of the shape. Since a square has equal length and width, the perimeter of the square is simply 4 times its side length. Therefore, we have:
Perimeter = 4 × 14 mm = 56 mm
The height of the shape is the same as the length of any of its sides, which is also 14 mm. Therefore, we have:
Lateral Surface Area = Perimeter × Height = 56 mm × 14 mm = 784 mm^2
Therefore, the lateral surface area of the square is 784mm².
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find the lateral surface area of a square box with dimensions 14 mm, 13mm and 6 mm.
Please help superrr confused :(
Step-by-step explanation:
Week 1, you eat 10 out of 95
Week 1 r ( 1) = 95 - 10(1) =85
Week 5 r(5) = 95 - 10r
=95 - 10(5)
=95 - 50
=45lbs
Week 8 r(8) = 95 - 10.r
=95 - 10(8)
=95 - 80
= 15 lbs
Week w r(w) = 95 - 10.w
= 95 - 10W (lbs)
f(r) = 95 - 10r
Where r is the number of weeks.
r(w) =35 means that at the end of w weeks, there were 35 candies left.
If the original candy was 95 and 35 was left after w weeks
r(w) = 95 - 10w
35 = 95 - 10w
Subract 95 from both sides
-60 = - 10w
Divide both sides by - 10
6= w
The solution means that 35 candies were left after w weeks and w represents 6weeks.
(you can c compare my answer with a second response)
3/10 Students go for the music class and 2/3 students go for the dance class. which class has more students?
Answer: The dance class has more students
Step-by-step explanation:
3 divided by 10 = 0.3
2 divided by 3 = 0.66
Since 0.66 is more than 0.3, we can say that more students entered the dance class than the music class.
Write a decimal and a fraction for the shaded part of the diagram.
A decimal and fraction and shaded part of the first diagram second diagram is 100/100 or 1 and 0.63 or 63/100 respectively.
What is fraction?
A fraction is a way of expressing a part of a whole, or a part of a group, by using two numbers separated by a line. The number above the line is called the numerator, and the number below the line is called the denominator.
The first 10 by 10 matrix is fully colored, which means all 100 cells are colored. Therefore, the fraction of colored cells is:
100/100 = 1
The decimal representation of this fraction is simply 1.
For the second 10 by 10 matrix, the first 6 columns are fully colored, which means there are 6 x 10 = 60 colored cells. The 7th column has only the first 3 rows colored, which means there are 3 colored cells in this column. Therefore, the total number of colored cells is:
60 + 3 = 63
The fraction of colored cells is:
63/100
To convert this fraction to a decimal, we can divide the numerator by the denominator:
63 ÷ 100 = 0.63
Therefore, the shaded part of the second matrix is 0.63 or 63/100.
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Question 7 What equation is parallel to y=-(1)/(4)x+5 and passes through (2,-3)?
The equation of the line that is parallel to y = -(1/4)x + 5 and passes through (2, -3) is y = -(1/4)x - 5/2.
To find the equation of the line that is parallel to the line y = −(1/4)x + 5 and passes through the point (2, −3), follow these steps:Step 1: Determine the slope of the given line.The slope-intercept form of the equation of the line is y = mx + b where m is the slope of the line. y = −(1/4)x + 5 is already in slope-intercept form, so its slope is −1/4. Step 2: Determine the slope of the line that is parallel to the given line. The slope of a line parallel to another line is the same as the slope of the given line. Therefore, the slope of the line we need to find is also −1/4. Step 3: Determine the y-intercept of the line we need to find. We already know that the line passes through the point (2, −3). To determine the y-intercept of the line, substitute x = 2 and y = −3 into the slope-intercept form of the equation of the line. −3 = −(1/4)(2) + b b = −3 + 1/2 = −5/2 Therefore, the y-intercept of the line we need to find is −5/2. Step 4: Write the equation of the line in slope-intercept form. The equation of the line we need to find is y = mx + b where m = −1/4 and b = −5/2. y = −(1/4)x − 5/2 is the equation of the line that is parallel to y = −(1/4)x + 5 and passes through (2, −3).Answer: The equation of the line that is parallel to y = -(1/4)x + 5 and passes through (2, -3) is y = -(1/4)x - 5/2.
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Question 7 (3 points)
solve for c: -2=c/16
Question 7 options:
c = - 1/8
c = -32
c = 32
c = 8
The solution of the equation -2 = c/16 by making c the subject of equation is c = -32
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
Given the equation:
-2 = c/16
We are to solve for c by making c the subject of equation. To solve for c, we multiply both sides of the equation by 16 and simplify. Therefore:
-2 * 16 = c/16 * 16
Simplifying:
c = -32
The solution of the equation -2 = c/16 is c = -32
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Claudia organizes a team carpool with 5 vans. Each van carries 2 adults and an equal number
of children. There are 30 people in the carpool
altogether. Determine how many children are
in each van
Number of children in the each van is 4.
Let's start by using algebra to solve the problem. Let's call the number of children in each van "x".
Since each van carries 2 adults and "x" children, the total number of people in each van is:
2 + x
And since there are 5 vans in total, the total number of people in the carpool is:
5(2 + x) = 10 + 5x
We know from the problem that there are 30 people in the carpool altogether, so we can set up the equation
10 + 5x = 30
Solving for "x", we get:
5x = 20
x = 4
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5, 6, 8, ___ , 15, ___
18, 20, 24, ___ , 38, ___
25, 28, 34, ___ , ___ , 70
55, 54, 51, 46, ___ , ___ , 19
82, 81, 78, ___ , 66
0 + 6 = ___+ 0
___ + 9 = 9 + 14
20 x ( 4 + ___) = ( 20 x 4 ) + (20 x 3)
9 + ( 6 + 5 ) = (9 + 6) + ___
10 x (___ + 6) = (10 x 8) + (10 x ___)
Answer:
5, 6, 8, 11, 15, 20
5+1=6+2=8+3=11+4=15+5=20
18, 20, 24, 30, 38, 48
18+2=20+4=24+6=30+8=38+10=48
55, 54, 51, 46, 39, 30, 19
55-1=54-3=51-5=46-7=39-9=30-11=19
82, 81, 78, 73, 66
82-1=81-3=78-5=73-7=66
0+6=6+0
6=6
14+9=9+14
23=23
20x(4+3)=(20x4)+(20x3)
20x7=80+60
140=140
9+(6+5)=(9+6)+5
9+11=15+5
20=20
10x(4+6)=(10x8)+(10x2)
100=100
Step-by-step explanation:
Jane has a pre-paid cell phone with Splint. She can't remember the exact costs, but her plan has a
monthly fee and a charge for each minute of calling time. In June she used 350 minutes and the cost
was $177.00. In July she used 900 minutes and the cost was $397.00.
A) Express the monthly cost C as a function of x, the number of minutes of calling time she used.
Answer: c(x) = 4x +
syntax error.
B) If Jane used 622 minutes of calling time in August, how much was her bill?
Answer: $
Please help super confused
The value of the function notations are;
a) d(20) = 10
b) d(0) = 0
c) d(20) < d(30)
d) d(0) = 0
e) d(30) = d(40)
f) d(t) = 5, when t = 5
How to Interpret Function Notation?
The notation f(x) defines a function named f. This is read as “y is a function of x.” The letter x represents the input value, or independent variable. The letter y is replaced by f(x) and represents the output value, or dependent variable.
a) d(20)
The value of distance (d) when the time is 20 is; 10
b) d(0)
The value of distance (d) when the time is 0 is; 0
c) d(20) = 10
d(30) = 20
Thus;
d(20) < d(30)
d) The value of the time at d = 0 is 0. Thus;
d(0) = 0
e) d(30) = 20
d(40) = 20
Thus; d(30) = d(40)
f) d(t) = 5
The value of t at d = 5 is;
t = 5
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Which algebraic expression is equivalent to -2(4x - 5y - 5x)?
Answer: -2x-10y
Step-by-step explanation:i'm in the 8th grade so i know im right
the domain for the first input variable to predicate t is a set of students at a university. the domain for the second input variable to predicate t is the set of math classes offered at that university. the predicate t(x, y) indicates that student x has taken class y. sam is a student at the university and math 101 is one of the courses offered at the university. give a logical expression for each sentence. (a) sam has taken math 101. (b) every student has taken at least one math class. (c) every student has taken at least one class other than math 101. (d) there is a student who has taken every math class other than math 101. (e) everyone other than sam has taken at least two different math classes. (f) sam has taken exactly two math classes.
The logical expressions for each sentence can be written as follows:
(a) t(Sam, Math 101)
This expression states that Sam has taken Math 101.
(b) ∀x∃y t(x, y)
This expression states that for every student x, there exists a math class y such that the student x has taken the math class y.
(c) ∀x∃y (t(x, y) ∧ y ≠ Math 101)
This expression states that for every student x, there exists a class y such that the student x has taken the class y and the class y is not Math 101.
(d) ∃x∀y (t(x, y) ∧ y ≠ Math 101)
This expression states that there exists a student x such that for every math class y, the student x has taken the math class y and the math class y is not Math 101.
(e) ∀x∃y∃z (t(x, y) ∧ t(x, z) ∧ x ≠ Sam ∧ y ≠ z)
This expression states that for every student x, there exists two different math classes y and z such that the student x has taken the math classes y and z and the student x is not Sam.
(f) ∃y∃z (t(Sam, y) ∧ t(Sam, z) ∧ y ≠ z ∧ ∀w (t(Sam, w) → (w = y ∨ w = z)))
This expression states that there exists two different math classes y and z such that Sam has taken the math classes y and z and for every math class w, if Sam has taken the math class w, then the math class w is either y or z.
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 10. There are two dots above 6, 7, and 9. There are three dots above 8.
Which of the following is the best measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 8.
The median is the best measure of center, and it equals 7.3.
The mean is the best measure of center, and it equals 7.3.
The median is the best measure of center, and it equals 8.
Suppose given a representation of the symmetric group S3 on a vector space V. Let x and y denote the usual generators for S3. (a) Let u be a nonzero vector in V. Let v = u + xu + xều and w = u + yu. By analyzing the G-orbits of v, w, show that V contains a nonzero invariant subspace of dimension at most 2. (b) Prove that all irreducible two-dimensional representations of G are isomorphic, and determine all irreducible representations of G
The orbits of v and w imply a nonzero invariant subspace of dimension at most 2. All 2-dimensional irreducible representations of S3 are isomorphic and can be determined by the character table.
To show that V contains a nonzero invariant subspace of dimension at most 2, we analyze the G-orbits of v and w. Since x and y are the generators for S3, we can see that xv = x(u + xu + xều) = x²u + xều = u and yw = y(u + yu) = u + y²u = u. This implies that the G-orbits of v and w are the same, so V contains a nonzero invariant subspace of dimension at most 2. To prove that all irreducible two-dimensional representations of G are isomorphic, we must show that they all have the same character table. To do this, we can use the fact that the character table is an invariant of a representation, meaning that it is the same for all isomorphic representations. Therefore, all irreducible two-dimensional representations of G have the same character table, which can be determined by examining the character table for S3.
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Given the equation 6x + 18 = 72:
Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points)
Part B: Solve the equation showing all work. (4 points)
Part C: Explain what the value of the variable represents. (2 points)
simplify 4divide root 5 plus 5 minus 3 divide root 5 minus root 2
Answer:[tex]\frac{25+\sqrt{5} -5\sqrt{2} }{5}[/tex]
Step-by-step explanation:
The solid shown here is a cube. Count the number of faces, edges, and vertices. Remember, you can use the formula V – E + F = 2 to make sure that you counted correctly.
Vertices
Edges
Faces
In the given cube, the required data is as follows:
Faces = 6
Edges = 12
Vertices = 8
What is a cube?A cube is a solid three-dimensional form with six square faces that all have the same length sides. It is one of the five platonic solids and is also referred to as a regular hexahedron.
Six square faces, eight vertices, and twelve edges make up the form.
Here in the question as asked,
Faces = 6
Edges = 12
Vertices = 8
Now to prove that we are correct,
V -E + F =2
= 8 - 12 + 6
=2
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the shape is formed from two straight lines and two arcs. work out the total shaded area correct to the nearest 0.1cm^2.
Check the picture below.
so we're really looking for the area of a sector of a circle with 63° and a radius of 3, twice.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =63\\ r=3 \end{cases}\implies A=\cfrac{(63)\pi (3)^2}{360} \\\\\\ A=\cfrac{63\pi }{40}\implies \stackrel{\textit{now let's double that}}{2\cdot \cfrac{63\pi }{40}}\implies \cfrac{63\pi }{20}\implies 9.9~cm^2[/tex]
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
1) The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill.
2) The solution x=60 represents the total food bill.
These both answers are correct.
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Since there are 8 group of friends, and the total amount spent by them is $76 including the tip i.e $16.
If x is the food bill our equation can be:
(x+16)/8 = 76/8
Solving the equation
(x+16)/8 = 9.5
x+16= 9.5*8
x= 76 -16
x= 60
The food bill is x=60.
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Find each quotient using synthetic division. (m^(4)-7m^(3)-39m^(2)-28m-3)-:(m+3)
The quotient using a synthetic method of division is m³ - 10m² - 9m - 1
How to evaluate the quotient using a synthetic methodThe quotient expression is given as
(m⁴ -7m³ -39m² - 28m - 3) divided by m + 3
Using a synthetic method of quotient, we have the following set up
-3 | 1 -7 -39 -28 -3
|__________
Bring down the first coefficient, which is 1:
-3 | 1 -7 -39 -28 -3
|__________
1
Multiply -3 by 1 to get -3, and write it below the next coefficient and repeat the process
-3 | 1 -7 -39 -28 -3
|____-3__ 30__27__3____
1 -10 -9 -1 0
So, the quotient is m³ - 10m² - 9m - 1
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Given that the measurement is in centimeters, find the area of the circle to the nearest tenth. (use 3.14 for π) circle with a radius of 3 cm
The area of the circle to the nearest tenth is 28.3 square centimeters.
To find the area of a circle with a given radius, we use the formula
A = π[tex]r^2,[/tex]
where A is the area and r is the radius.
In this case, the radius is 3 cm, so we can substitute it into the formula to get:
A = 3.14 x [tex]3^2[/tex]
Simplifying this equation, we get the following:
A = 3.14 x 9
A = 28.26
To round this to the nearest tenth, we look at the digit in the hundredth place, 6. Since 6 is greater than or equal to 5, we round up the number in the tenth place, which is 2. Therefore, the final answer is:
A ≈ 28.3 [tex]cm^2[/tex]
So, the area of the circle to the nearest tenth is 28.3 square centimeters.
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QX←→ is a tangent to circle R at point Q. Circle R with a chord and tangent. Point Q at 4 o clock on the circle. Point X at 2 o clock is outside the circle. Secant Line R Q and tangent line Q X. Angle XRQ is labeled 56 degrees. What is m∠RXQ ?
If Secant Line RQ and tangent line QX, angle XRQ is labeled 56 degrees, then the measure of angle RXQ is 34 degrees.
Since the line QX is tangent to the circle R, we know that angle QXR is a right angle. We also know that angle XRQ is labeled as 56 degrees. Therefore, we can find angle RXQ using the fact that the sum of the angles in a triangle is 180 degrees.
We have:
m∠RXQ + m∠QXR + m∠XRQ = 180 degrees
Since m∠QXR is a right angle (90 degrees), we can substitute:
m∠RXQ + 90 degrees + 56 degrees = 180 degrees
Simplifying:
m∠RXQ = 34 degrees
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4. The fabrication team will be starting with 20-ft lengths of the
tubing. How many 20-ft lengths are needed for each workbench?
(Hint: To convert inches to feet, divide by 12.)
The number of lengths required by the fabrication team for each workbench is 2.5 units.
What is length of an object?The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric form or object. For instance, the length and width of a rectangle define its dimensions. In the International System of Quantities, length is also a quantity having the dimension distance.
The total length of the workbench is given as 589.95.
Given that, 20 ft lengths are used for fabrication.
Thus, the number of lengths required are:
N = 589.95/ 20 (12) = 2.457 = 2.5
Hence, the number of lengths required by the fabrication team for each workbench is 2.5 units.
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The complete question is:
On Sunday, the owners of the Middletown Café are giving away muffins. The owners budgeted $75 to spend on muffins for the event, and each muffin costs $0.82. The inequality 75≥0.82m 75 ≥ 0 . 82 , where m is the number of muffins, represents the situation. How many customers could possibly get a muffin? Select all that apply.
Answer:
We can solve the inequality for m to find the maximum number of muffins that can be purchased within the budget of $75:
75 ≥ 0.82m
Divide both sides by 0.82:
m ≤ 91.46
Since m must be a whole number, the maximum number of muffins that can be purchased is 91. Therefore, 91 customers could possibly get a muffin.
Step-by-step explanation:
PLEASE SHOW WORK!!!!!!!!!
please help if you can I will give brainliest- Black tape is used to create the lines and circles for a basketball court. How much tape is used in all? Use π=3.14.
Answer:
see below.
Step-by-step explanation:
So first, find the perimeter.
94*2= 188
50*2=100
100+188=288ft <----This is our perimeter
Next, find the length of the center line.
It is 50 feet.
Next, we are going to figure out the circumference of the big half circle.
C=[tex]\pi[/tex]d
C=(3.14)(44)=138.16 <------circumference of a WHOLE circle.
Divide 138.16 by 2 to get the half circle
138.16/2=69.08
There are 2 half circles, so multiply 69.08 by 2 to get 138.16
Next, we need to find the circumference of the center circle.
C=(3.14)(12)=37.68
Finally, add all the totals together
288+50+138.16+37.68=513.84 FEET <---dont forget units.
What is the value of sinD?
The value of sin(D) is 7/25 after the application of the Pythagoras theorem.
What is a Pythagoras theorem?The Pythagorean theorem is a fundamental theorem in geometry that describes the relationship between the sides of a right triangle. It claims that the hypotenuse's square length, which is the side that faces the right angle, is equivalent to the total of the squares of the lengths of the other two sides in a right triangle. The theorem can be formulated mathematically as:
c² = a² + b²
where, even the lengths for the remaining two sides (the legs) of the right triangle are a and b, and c is the length of the hypotenuse.
The Pythagorean theorem may be employed to determine the triangle's third side's length:
DE²= FD² + EF²
25² = 24² + EF²
625 = 576 + EF²
EF² = 49
EF = 7
Now, we can use the definition of sine to find sin(D):
sin(D) = opposite/hypotenuse = EF/DE = 7/25
Therefore, the value of sin(D) is 7/25.
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I need help this question is so confusing!
The bearing of B from C is calculated to be 115 degrees
The bearing of D from B is calculated to be 213.65 degrees
How to find the bearingsThe bearing from B to C is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The direction of movements describes a right triangle of
opposite = 30 km
adjacent = 30 km
The bearing is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
tan x = 30 / 30
tan x = 1
x = arc tan 1
x = 45 degrees
The bearing is 90 + 45 = 115 degrees
The bearing of D from B
x = arc tan (45/30)
x = 56.31
90 - 56.31 = 33.65
180 + 33.65 = 213.65 degrees
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In a box of 7 different banknotes 1, 2, 5, 10, 20, 50, 100 dollars. You pick at random 2 notes from this box. Let X is the larger number in these two notes, and Y be the smaller one.
(a) Find the distributions of X, Y and their joint distribution.
(b) Find the distribution of Z=X-Y.
(c) Compute E(X), Var(X), E(Z) and Var(Z).
The distribution of X is P(X = x) = 1/7 for x = 1, 2, 5, 10, 20, 50, 100 and Distribution of Y is P(Y = y) = 1/6 for y = 1, 2, 5, 10, 20, 50, 100, y ≠ X and their joint distribution is P(X = x, Y = x) = 0.
Find the joint distribution?(a) The possible values of X and Y are as follows:
(i) X can be any of the 7 banknotes.
(ii) Y can also be any of the 7 banknotes, except the one that was already picked for X.
Since each of the 7 banknotes is equally likely to be picked, the probability distributions of X and Y are both uniform distributions over the set {1, 2, 5, 10, 20, 50, 100}:
P(X = x) = 1/7 for x = 1, 2, 5, 10, 20, 50, 100
P(Y = y) = 1/6 for y = 1, 2, 5, 10, 20, 50, 100, y ≠ X
The joint distribution of X and Y can be computed as follows:
P(X = x, Y = y) = P(X = x) × P(Y = y|X = x)
Since the second banknote must be smaller than the first, we have:
P(Y = y|X = x) = 1/(6 - 1) = 1/5, for y ≠ x
And for y = x:
P(Y = x|X = x) = 0
Therefore:
P(X = x, Y = y) = 1/7 × 1/5 = 1/35, for x ≠ y
P(X = x, Y = x) = 1/7 × 0 = 0
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