You expect him to flip tails and roll an even number 10 times
How many times would you expect him to flip tails and roll an even number?From the question, we have the following parameters that can be used in our computation:
Sample space 1 = 1, 2, 3, 4, 5, 6
Sample space 2 = H, T
Using the above as a guide, we have the following:
P(Even) = 3/6
P(Tail) = 1/2
So, we have
P(Even and Tail) = 3/6 * 1/2
P(Even and Tail) = 1/4
In 40 times, we have
Expected = 1/4 * 40
Expected = 10
Hence, the number of times is 10
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Batteries are sold in packs
and boxes.
There are 8 batteries in each
pack.
There are 30 batteries in
each box.
Emily buys p packs of
batteries and b boxes of
batteries.
Write down an expression,
in terms of pand b, for the
total amount of batteries
that Emily buys.
Answer:
The total number of batteries that Emily buys can be expressed as:
8p + 30b
Here, 8p represents the total number of batteries in the packs that Emily buys, and 30b represents the total number of batteries in the boxes that Emily buys. By adding these two terms together, we can find the total number of batteries that Emily buys.
Find the volume of the right circular cone with r=22.1 mm and h=5.91 mm.
Answer:
radius r = 22.1 m
height h = 5.91 m
slant height s = 22.8765841 m
volume V = 3022.73898 m^3
lateral surface area L = 1588.30288 m^2
base surface area B = 1534.38527 m^2
total surface area A = 3122.68815 m^2
Step-by-step explanation:
Help please !!
The volume of a fixed amount of a gas varies directly as the temperature 7 and inversely as the pressure P. Suppose that I'-70 cm³ when 7-420 kelvin
kg
kg
and P-18-
Find the temperature when
is 60 cm and P-7
X
Answer:
420 K x (60 cm³ / 70 cm³) x (7 / 18) = 294.29 K
Step-by-step explanation:
can someone help me with this
please show work
Answer:
1) S=31.68 yd A=174.23 [tex]yd^{2}[/tex]
2) S=36.65 in A=256.56 [tex]in^{2}[/tex]
3) S=8.9 ft A=13.35 [tex]ft^{2}[/tex]
4)S=17.28 in. A=51.84 [tex]in^{2}[/tex]
5)S=25.31 yd. A=126.54 [tex]yd^{2}[/tex]
6)S=3.4ft A=5.11 [tex]ft^{2}[/tex]
Step-by-step explanation:
Notes:
360 was divided by 1/2, making the denominator 180. This is why there is a 1/2 at the front.
You also do not need to simplify if you're using a calculator.
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
- r is the radius
- θ is [tex]\frac{angle\pi }{180}[/tex]
S= r θ
-r is the radius
- θ is [tex]\frac{angle\pi }{180}[/tex]
1)
S=r θ
S=11([tex]\frac{165\pi }{180}[/tex])........................................plug in values
S=11( [tex]\frac{11\pi }{12}[/tex]).........................................simplify
S=31.68 yd....................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]11^{2}[/tex]) [tex]\frac{165\pi }{180}[/tex]....................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]121[/tex]) [tex]\frac{11\pi }{12}[/tex]....................................simplify
A=174.23 [tex]yd^{2}[/tex].....................................solve and round.
2)
S=r θ
S=14([tex]\frac{150\pi }{180}[/tex])...........................................plug in values
S= =14( [tex]\frac{5\pi }{6}[/tex]).........................................simplify
S=36.65 in........................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]14^{2}[/tex]) [tex]\frac{150\pi }{180}[/tex]......................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]196[/tex]) [tex]\frac{5\pi }{6}[/tex]......................................simplify
A=256.56 [tex]in^{2}[/tex]....................................solve and round.
3)
S=r θ
S=3([tex]\frac{170\pi }{180}[/tex]).........................................plug in values
S= 3( [tex]\frac{17\pi }{18}[/tex]).......................................simplify
S=8.9 ft..........................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]3^{2}[/tex]) [tex]\frac{170\pi }{180}[/tex]........................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]9[/tex]) [tex]\frac{17\pi }{18}[/tex].......................................simplify
A=13.35 [tex]ft^{2}[/tex]........................................solve and round.
4)
S=r θ
S=6([tex]\frac{165\pi }{180}[/tex]).......................................plug in values
S=6( [tex]\frac{11\pi }{12}[/tex]).......................................simplify
S=17.28 in....................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]6^{2}[/tex]) [tex]\frac{165\pi }{180}[/tex].....................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]36[/tex]) [tex]\frac{11\pi }{12}[/tex]..................................simplify
A=51.84 [tex]in^{2}[/tex].....................................solve and round.
5)
S=r θ
S=10([tex]\frac{145\pi }{180}[/tex]).........................................plug in values
S=10( [tex]\frac{29\pi }{36}[/tex]).........................................simplify
S=25.31 yd.......................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]10^{2}[/tex]) [tex]\frac{145\pi }{180}[/tex].......................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]100[/tex]) [tex]\frac{29\pi }{36}[/tex]....................................simplify
A=126.54 [tex]yd^{2}[/tex].....................................solve and round.
6)
S=r θ
S=3([tex]\frac{65\pi }{180}[/tex])..........................................plug in values
S= 3( [tex]\frac{13\pi }{36}[/tex]).......................................simplify
S=3.4ft............................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]3^{2}[/tex]) [tex]\frac{65\pi }{180}[/tex].......................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]9[/tex])[tex]\frac{13\pi }{36}[/tex]......................................simplify
A=5.11 [tex]ft^{2}[/tex].........................................solve and round.
As economy of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.02 worth of coal, $0.30 worth of electricity, and 0.30 worth of steel, the electric industry needs $0.04 worth of coal, $0.04 worth of electricity, and 0.02 worth worth of steel, and the steel industry needs $0.10 worth of coal and $0.04 worth of steel. The sales demand is estimated to be $1 billion for coal, $1 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and demand for coal doubles, whereas the demand for for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand.
Answer:
Step-by-step explanation:
Let’s denote the production levels of coal, electricity and steel as x, y and z respectively. We can set up a system of equations to represent the inter-industry demand for each industry’s output.
For coal: 0.02x + 0.04y + 0.10z = x For electricity: 0.30x + 0.04y = y For steel: 0.30x + 0.02y + 0.04z = z
Solving this system of equations gives us x = (50/3)y and z = (25/2)y.
The new sales demand for coal is $2 billion (double the original), for electricity is $3 billion (triple the original) and for steel is $6 billion (an increase of 50%). Substituting these values into our equations gives us:
(50/3)y = $2 billion y = $3 billion (25/2)y = $6 billion
Solving these equations gives us y = $3 billion, x = $5 billion and z = $18.75 billion.
So to satisfy the new demand, the coal industry should produce at a level of $5 billion, the electric industry should produce at a level of $3 billion and the steel industry should produce at a level of $18.75 billion.
Standard Scores
Use both the Student ID and Distance to Work variables.
List the Student ID at TESU in ascending order of Distance to Work.
Calculate the z-scores associated with each student (use the sample standard deviation for this calculation).
Identify potential outliers and explain your reasoning.
Confidence Intervals/Samples
Take a sample of the first four data points for the variable Distance to Work (unsorted - use the original order in the dataset).
Determine the 95% and 99% confidence intervals using the same size of 4.
Describe and compare the two intervals.
Take a sample of the first seven data points for the variable Distance to Work (unsorted - use the original order in the dataset).
Determine the 95% confidence interval. Use the same mean and SD, but change the sample size to 20 and determine the 95% confidence interval.
Describe and compare the two intervals.
STUDENT DATA TABLE
ID School Enrolled Months enrolled Birthday month Distance to Work Height Foot Size Hand Size Sleep Homework
1 Arts and Sciences 12 January 0 60 8 5 360 30
2 Applied Science and Technology 6 February 0 62 7 6 400 45
3 Business and Management 8 April 5 66 10 7 420 60
4 Nursing 10 June 10 68 12 8 440 15
5 Public Service 48 July 15 68 14 8 540 75
6 Arts and Sciences 48 June 30 70 12 9 480 120
7 Applied Science and Technology 36 October 32 72 12 8 320 80
8 Applied Science and Technology 32 November 36 75 14 7 440 60
9 Nursing 6 July 8 63 9 7 300 90
10 Arts and Sciences 22 May 22 80 14 9 420 30
11 Business and Management 15 February 10 65 8 6 500 60
12 Public Service 20 April 4 71 10 8 400 20
13 Applied Science and Technology 11 March 15 66 9 7 440 60
14 Arts and Sciences 18 November 28 64 9 7 300 30
15 Arts and Sciences 29 January 12 72 10 8 360 80
16 Nursing 13 December 6 63 8 6 480 100
17 Business and Management 49 August 0 79 13 9 410 25
18 Applied Science and Technology 16 April 10 74 12 8 430 15
19 Business and Management 24 September 30 66 10 6 330 60
20 Arts and Sciences 8 May 0 65 9 7 480 30
For the sample size of 20, the 95% confidence interval is (-4.87, 27.16), which is narrower than the previous interval due to the larger sample size.
What is mean?In statistics, mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total number of values in the set. Mean is also commonly referred to as the arithmetic mean. It is a commonly used statistical measure in many fields including finance, economics, social sciences, and more.
Here,
To calculate the z-scores associated with each student, we first need to calculate the sample mean and standard deviation for the Distance to Work variable:
Sample mean: (0+0+5+10+15+30+32)/7 = 10.71
Sample standard deviation: √(((0-10.71)² + (0-10.71)² + (5-10.71)² + (10-10.71)² + (15-10.71)² + (30-10.71)² + (32-10.71)²)/6) = 10.72
Now we can calculate the z-scores for each student:
Student 1: (0 - 10.71) / 10.72 = -0.94
Student 2: (0 - 10.71) / 10.72 = -0.94
Student 3: (5 - 10.71) / 10.72 = -0.53
Student 4: (10 - 10.71) / 10.72 = -0.07
Student 5: (15 - 10.71) / 10.72 = 0.40
Student 6: (30 - 10.71) / 10.72 = 1.80
Student 7: (32 - 10.71) / 10.72 = 1.98
Student 8: (8 - 10.71) / 10.72 = -0.25
Student 9: (36 - 10.71) / 10.72 = 2.37
Student 10: (9 - 10.71) / 10.72 = -0.16
Student 11: (22 - 10.71) / 10.72 = 1.05
Student 12: (10 - 10.71) / 10.72 = -0.07
Student 13: (15 - 10.71) / 10.72 = 0.40
Student 14: (28 - 10.71) / 10.72 = 1.54
Student 15: (12 - 10.71) / 10.72 = 0.12
Student 16: (6 - 10.71) / 10.72 = -0.44
Student 17: (0 - 10.71) / 10.72 = -0.94
Student 18: (10 - 10.71) / 10.72 = -0.07
Student 19: (30 - 10.71) / 10.72 = 1.80
Student 20: (0 - 10.71) / 10.72 = -0.94
To identify potential outliers, we can look for z-scores that are more than 2 standard deviations away from the mean (i.e., greater than 2 or less than -2). From the list above, we can see that Students 6, 7, 9, and 19 have z-scores greater than 2, indicating that they may be potential outliers.
For the second sample of seven data points (0, 0, 5, 10, 15, 30, 32), the mean is 11.14 and the standard deviation is 12.05. Using a t-distribution with 6 degrees of freedom (n-1), the 95% confidence interval is (-7.54, 29.82).
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What is the approximate value of this logarithmic expression?
The approximate value of the given logarithmic expression as required to be determined in the task content is; 1.528.
What is the value of the logarithmic expression as required?It follows from the task content; it is required that the value of the logarithmic expression is to be determined.
Therefore, we have;
let the result of the expression be x; so that we have;
log₈ (24) = x
x log (8) = log (24)
x = log (24) - log (8)
x = 1.528
Ultimately, the approximate value of the logarithmic expression in discuss is; 1.528.
Complete question: The correct expression is; log₈ (24) .
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Use the drawing tools to form the correct answer on the provided graph.
Given the equation of the parabola x = -1/8(y - 3)^2 + 1, graph its focus and directrix.
Using drawing tools parabola graph has been made and uploaded in answer for the given equation.
Standard form of parabola having vertical axis of symmetry given by:
[tex](y - k)^2 = 4p(x - h)[/tex]
where (h, k): vertex and p: distance between the vertex and the focus or directrix.
Comparing the given equation[tex]x = -1/8(y - 3)^2 + 1[/tex] with the standard form, we can see that the vertex is at (1, 3) and p = -1/32.
Since the parabola opens to the left, the focus is to the left of the vertex at a distance of p = -1/32 units. Thus, the focus is located at (-1/32, 3).
The directrix is a vertical line to the right of the vertex and is located at a distance of p = -1/32 units. Thus, the directrix is the vertical line x = 33/32.
To graph the focus and directrix, we can plot the vertex (1, 3) on the coordinate plane, draw a horizontal line through the vertex, and then plot the focus (-1/32, 3) to the left of the vertex and the directrix x = 33/32 to the right of the vertex.
Note that the parabola [tex]x = -1/8(y - 3)^2 + 1[/tex] is symmetric with respect to the vertical line passing through the vertex.
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Write a polynomial function of the least degree with integral coefficients that have the given zeros.1+3i,-2i
The polynomial function of the least degree with integral coefficients that has the zeros [tex]1 + 3i[/tex], [tex]-2i[/tex] is f(x) = x⁴ - 2x³ + 14x² - 8x + 40.
Writing a polynomial function of the least degreeFrom the question, we are to write a polynomial function of the least degree with integral coefficients that have the given zeros.
The given zeros are [tex]1+3i[/tex],[tex]-2i[/tex].
If [tex]1 + 3i[/tex] and [tex]-2i[/tex]are zeros of a polynomial function with integral coefficients, then their conjugates [tex]1 - 3i[/tex] and [tex]2i[/tex] are also zeros of the function.
To find the polynomial function, we can use the fact that if r is a zero of a polynomial function, then (x - r) is a factor of the function. Thus, we can start by writing out the factors corresponding to each of the zeros:
[tex](x - (1 + 3i))(x - (1 - 3i))(x - (-2i))(x - 2i)[/tex]
Next, we can simplify these factors by multiplying them out:
[tex][(x - 1) - 3i][(x - 1) + 3i](x + 2i)(x - 2i)\\= [(x - 1)^2 - (3i)^2](x^2 - (2i)^2)[/tex]
= [(x - 1)² + 9](x² + 4)
Expanding the terms, we get:
(x² - 2x + 10)(x² + 4)
Multiplying out the factors, we obtain:
x⁴ - 2x³ + 10x² + 4x² - 8x + 40
Simplifying this expression, we get:
x⁴ - 2x³ + 14x² - 8x + 40
Hence, the polynomial function is f(x) = x⁴ - 2x³ + 14x² - 8x + 40
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Combine like terms: -4x+3-7x-8
A. -7x-5
B. -11x-5
C. -3x -11
D. none of the above
Answer:
answer is B
Step-by-step explanation:
-4x-7x=-11x
+3-8=-5
=-11x-5
answer: B -11x-5
[tex] \sf \implies \: - 4x +3 - 7x - 8[/tex]
[tex] \sf \implies \: - 11x +3 - 8[/tex]
[tex] \sf \implies \: - 11x - 5[/tex]
Hence, Option B is correct!!
x 2 −51=14xx, squared, minus, 51, equals, 14, x 1) Rewrite the equation by completing the square.
Answer:
(x -7)² = 100
Step-by-step explanation:
You want to rewrite the equation x² -51 = 14x by completing the square.
Complete squareWhen we're finished, the equation will be of the form ...
(x +a)² = b
Expanding this, we have ...
x² +2ax +a² = b
That is, the value of 'a' is half the coefficient of x when the equation is written with the x-terms together.
RearrangementAdding 51 -14x to both sides of the given equation, we get ...
x² -51 = 14x
x² -14x = 51
Now, we can see that a=-14/2 = -7. We can add a² = (-7)² = 49 to both sides to complete the square:
x² -14x +49 = 51 +49
(x -7)² = 100 . . . . . . . rewritten equation
Need Help (25 Points)
Answer:
Opposite (or a any synonyms)
Addition (Or sum)
division
inverse
Step-by-step explanation:
The first one is the most complicated, theres so many words can fit. Probably try with an synonyms of reverse like "Opposite"
For the 2nd,3rd and 4th options:
Addition (Or sum) since is the reverse of subtraction
division since is the reverse of multiplication
inverse since those functions (Exponent and radicals) are also inverse of each other
Write an inequality to describe each situation. a. The minimum age for voting in the United States is 18 years old. Let a represent a voter's age. b. A theater seats up to 275 people. Let p represent the number of people attending a performance in the theater.
According to this inequality, the number of persons attending a theatrical inequality play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.
What is inequality?In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. We resuming our current status quo. Yet a variety of things lead to inequality: Negative values on both sides are split or added.
a. The disparity in representing the voting age in the United States is as follows:
a ≥ 18
In order to be eligible to vote, a voter's age, denoted by a, must be more than or equal to 18 years old.
b. The inequality used to depict a theater's seating capacity is:
p ≤ 275
According to this inequality, the number of persons attending a theatrical play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.
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P12 000 is deposited in an account earning 4% interest per year. What is the amount
after 15 years
Answer:
After 15 years, the amount in the account will be $21.611.32, assuming the interest is compounded annually.
Step-by-step explanation:
To calculate the amount after 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
In this case, P = $12,000, r = 0.04 (4% expressed as a decimal), n = 1 (compounded annually), and t = 15 years.
Plugging in the values, we get:
A = $12,000(1 + 0.04/1)^(1*15)
A = $12,000(1.04)^15
A = $12,000(1.801)
A = $21,611.32
Therefore, after 15 years, the amount in the account will be $21.611.32, assuming the interest is compounded annually.
Please help me find the answer
The name of this circle is Circle R.
The name of the radius is RB.
The name of the diameter is RI or RD.
What is a circle?In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
What is a line segment?In Mathematics, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.
In this context, we have the following names;
Circle R.
Radius = RB.
Diameter = RD or RI.
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What are some mistakes when solving a 2 step equation with a single variable
Answer:Not dividing the entire side of the equation.
Not distributing properly using F.O.I.L.
Confusing the rules for adding and subtracting negative numbers with the rules for multiplying and dividing negative numbers.
Multiplying exponents with the base.
Step-by-step explanation:
Write in Slope-Intercept form:
Slope = -2
Y-Intercept = ( -5 , -4 )
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Given the slope m = -2 and the y-intercept (a, b) = (-5, -4), we can substitute these values into the equation to get:
y = mx + b
y = -2x + (-4)
y = -2x - 4
Therefore, the equation in slope-intercept form is y = -2x - 4.
Someone help I’ll mark BRAINLIEST
Answer:
1. c
2. b
3. B
Step-by-step explanation:
1. the hypotenuse is the longest side of the triangle.
2. think of it as the leg that helps form angle A (or forms right angle) that is NOT the hypotenuse
3. if "c" is the hypotenuse,, & b is the adjacent leg,, the opposite angle is across from the given angle which in this case is A
Solve for x.
0≤3x-6≤18
A 0≤x≤8
B 2≤x≤8
C x≤0 orx≥8
D x≤2 or x ≥8
Answer:
B) 2≤x≤8.
Step-by-step explanation:
Add 6 to all sides of the inequality.
0+6≤3x-6+6≤18+6
6≤3x≤24
Divide all sides by 3.
2≤x≤8
The correct answer is B) 2≤x≤8.
Please help i’m struggling
The vertices will be D = (-3,2) E=(1,2) F=(-2,0).
What is dilatiοn?resizing an οbject is accοmplished thrοugh a change called dilatiοn. The οbjects can be enlarged οr shrunk via dilatiοn. A shape identical tο the sοurce image is created by this transfοrmatiοn. The size οf the fοrm dοes, hοwever, differ. A dilatatiοn οught tο either extend οr cοntract the οriginal fοrm. The scale factοr is a phrase used tο describe this transitiοn.
The scale factοr is defined as the difference in size between the new and οld images. An established lοcatiοn in the plane is the center οf dilatatiοn. The dilatiοn transfοrmatiοn is determined by the scale factοr and the centre οf dilatiοn.
Here the scale factοr is 1/2
Sο the vertices will be D = (-3,2)
E=(1,2)
F=(-2,0)
Hence the vertices will be D = (-3,2) E=(1,2) F=(-2,0).
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I will mark you brainiest!
Pat needs to paint an 8 ft × 36 ft rectangular wall. What is the area that needs to be painted?
A) 300 ft2
B) 288 ft2
C) 282 ft2
D) 276 ft2
The demand equation for a certain commodity is given by the
following equation.
p= =1/2+². - 20x + 1200, 0≤x≤ 120
Find x and the corresponding price p that maximize revenue.
The maximum value of R(x) occurs at x =0.
In the given demand equation, the value of x and corresponding price p that maximize revenue are x = 31.8 and p = $514.60.
How to Solve the Equation?To find the value of x and corresponding price p that maximize revenue, we first need to determine the revenue function. Revenue (R) is given by the product of price (p) and quantity demanded (x), so:
R(x) = xp
Substituting the given demand equation for p, we get:
R(x) = x(1/2 + ² - 20x + 1200)
Simplifying and rearranging:
R(x) = 1/2x + ²x - 20x² + 1200x
R(x) = -20x² + (1200 + ²)x + 1/2x
To find the value of x that maximizes revenue, we take the derivative of R(x) with respect to x, set it equal to zero, and solve for x:
dR/dx = -40x + (1200 + ²) + 1/2 = 0
Solving for x:
x = (1200 + ² + 1/2) / 40
x = 31.8
To find the corresponding price, we substitute this value of x back into the demand equation for p:
p = 1/2 + ² - 20(31.8) + 1200
p = $514.60
Therefore, the value of x and corresponding price p that maximize revenue are x = 31.8 and p = $514.60.
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Find the general solution to the differential eauation y 0 cos x = y sinx+sin 175x Assume x ∈ (−π/2,π/2), and use C (capital C) for your arbitrary constant.
The general sοlutiοn tο the differential equatiοn is [tex]\mathrm{y = Ce^{(sin(x))}}[/tex].
Describe Differentiatiοn?The derivative οf a functiοn represents the instantaneοus rate οf change οf the functiοn at a specific pοint. It is calculated by finding the limit οf the difference quοtient as the interval between twο pοints οn the functiοn apprοaches zerο. The derivative can be expressed as a functiοn οf the independent variable, and it prοvides valuable infοrmatiοn abοut the behaviοr οf the οriginal functiοn.
The prοcess οf differentiatiοn invοlves applying a set οf rules tο functiοns tο οbtain their derivatives. These rules include the pοwer rule, prοduct rule, quοtient rule, chain rule, and οther mοre advanced rules that are used tο differentiate mοre cοmplex functiοns.
Tο sοlve the given differential equatiοn, we can use the methοd οf integrating factοrs.
First, we can rewrite the equatiοn as:
y'cοsx = ysinx + sin(175x)
Next, we can multiply bοth sides by the integrating factοr, which is [tex]e^{(\int(cos(x) dx))} = e^{(\sin(x) + C)}[/tex], where C is a cοnstant οf integratiοn:
[tex]\mathrm {e^{(sin(x)) }y'cosx = e^{(sin(x))} ysinx + e^{(sin(x))}sin(175x) + Ce^{(sin(x))}}[/tex]
Nοw, we can recοgnize the left-hand side as the derivative οf [tex]e^{(sin(x))}y[/tex]:
[tex](e^{(sin(x))y)}' = e^{(sin(x))} y' + cos(x) e^{(sin(x))}y[/tex]
Substituting this intο the abοve equatiοn, we get:
[tex]\mathrm{(e^{(sin(x))y)}' = e^{(sin(x)) }ysinx + e^{(sin(x))}sin(175x) + Ce^{(sin(x))}}[/tex]
[tex]cos(x) e^{(sin(x))}y = e^{(sin(x))y)}'[/tex]
Separating variables and integrating bοth sides, we get:
[tex]\int e^{sin(x) }dy/y = \int cos(x) dx[/tex]
ln|y| + C = sin(x) + C'
where C' is anοther cοnstant οf integratiοn.
Therefοre, the general sοlutiοn tο the differential equatiοn is:
[tex]\mathrm{|y| = e^{(sin(x)) }e^{(C' - sin(x))}}[/tex]
[tex]\mathrm{y = \± e^{(C' - sin(x) + sin(x))}}[/tex]
[tex]\mathrm{y = Ce^{(sin(x))}}[/tex]
where C is an arbitrary cοnstant.
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5. A rock is thrown directly upward with an initial velocity of 79 feet per second from a cliff 50 feet above a beach. The height of the rock above the beach (h) after t seconds is given by the equation h = -16t² + 79t + 50. The graph below shows the rock's height as a function of time.
The rock will be 125 feet above the beach at: The values of t are 3.911 or 1.28 and (b) The minimum height is h= 346 feet
How to find velocity?Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time
The given parameters are
h = -16t² + 79t + 50
In the equation put h = 125 to find t
125 = -16t² +79t+50
Rearrange the equation to have
16t²-79t -50 +125 = 0
this is also written as 16t² -79t + 75 =0
Solving for t we have
[-b±√b²-4ac]/2z
[79 ±√79²-4*16*75]/2*16
[(79 ±√6241-4800)] / 32
Simplify further to get
[79 ±√1441] / 32
(79 ±38) / 32
117/32 or 41/32
The values of t are 3.911 or 1.28
The minimum height of the rock at t = 1.28 is
h = -16(3.28)² + 79( 3.28)+ 50
h = -16(10.7584) + 79(3.28) +50
h = - 172.1344 +259.12 + 50
h= 346 feet
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for the following right triangle. find the side length x. round your answer to the nearest hundreth.
Answer:
answer is 11.60
Step-by-step explanation:
formula is C^2 = a^2 + b^2
c = 13
a = 8
b = ?
169 = 64 + x^2
135 = x^2
I hope this helps!
Is -x=y proportional
Answer:
no
Step-by-step explanation:
I forgot where to start in solving this equation
Someone help me with this question please. I attached the screenshot. Thanks.
prove or disprove the quadrilateral be low is a rectangle by using the concepts of slope and congruence
(100 points)
The proof that the quadrilateral is a rectangle is shown below
Proving or disproving that the quadrilateral is a rectangleFrom the question, we have the following parameters that can be used in our computation:
A = (-2, 3)
B = (-4, 1)
C = (2, -1)
D = (0, -3)
From the graph, we have the following lengths
AB = √8
CD = √8
BD = √32
AC = √32
The above shows that opposite sides are equal
From the graph, we have the following slopes
AB = 1
CD = 1
BD = -1
AC = -1
The above shows that opposite sides are have equal slopes and adjacent sides are their slopes to be opposite reciprocals
Hence, the quadrilateral is a rectangle
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Find the linear function with the following properties.
f(0)=8
Slope of f=−6
The linear function with the given properties is: f(x) = 8 - 6x.
What is linear function?A linear function is a mathematical equation that describes a straight line when graphed. It is the most basic type of function, where the output is equal to the input multiplied by a constant, known as the slope, and a constant added, known as the y-intercept. Linear functions are used to model relationships between two quantities and can be used to describe a wide range of phenomena, from physical properties to economic trends.
This linear function is used to calculate the value of a variable (x) when given the starting value of the function (f(0)) and the slope of the line (the rate at which the value of the function changes for each unit increase in x). In this case, the starting value of the function (f(0)) is 8, and the slope of the line is -6, meaning that the value of the function decreases by 6 for each unit increase in x. Therefore, the linear function that satisfies these properties is f(x) = 8 - 6x.
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