The expected area of a circular sampling region is 531.56 m²
Given,
The radius of the circular sampling region = 13m
f(r) = [tex]\left \{ {\frac{3}{4} } \atop {0}} \right.[/tex] [1 - (13 - r)²] 12 ≤ r ≤ 14
We have to find the area of the circular sampling region = E (π r²)
E (π r²) = π E (r²)
Lets find E (r²)
E (r²) =₁₂ [tex]\int\limits^[/tex]¹⁴ r² f(r) dr
= ₁₂∫¹⁴ (3r²/4) (1 - (13 -r)²) dr
= 3/4 ₁₂∫¹⁴ r² (1 - 169 - r² + 26r) dr
= 3/4 ₁₂∫¹⁴ r² (26r³ - r⁴ - 168r²) dr
= 3/4 [ 26r⁴/4 - r⁵/5 - 168r³/3]₁₂¹⁴
= 3/4 [ (26 × 14⁴)/4 - 14⁵/5 - (168 × 14³)/3] - [ (26 × 12⁴)/4 - 12⁵/5 (168 × 12³)/3]
= 3/4 [ (26 × 38416)/4 - 537824/5 - (168 × 2744)/3] - [ (26 × 20736)/4 - 248832/5 - (168 × 1728)/3]
= 3/4 [ 249704 - 107564.8 - 153664] - [ 134784 - 49766.4 - 96768]
= 3/4 [-11524.8] - [-11750.4]
= 3/4 [225.6]
= 169.2
∴ E(r²) = 169.2
Now lets find the expected area of the circular sampling region:
Area = E(π r²) = π E (r²)
Here, E(r²) = 169.2
So, area = π × 169.2 = 531.56 m²
That is, the expected area of a circular sampling region is 531.56 m²
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400 g of
raspberries
500 g of strawberries cost £4.10
Work out the total cost of 200 g of raspberries and 200 g of strawberries.
and 300g of strawberries cost a total of £7.46
The most appropriate choice for unitary method will be given by
Total cost of 200g raspberries and 200 g strawberries is £4.14
What is unitary method?
It is the method by which we find the value of single unit form the value of multiple unit and value of multiple unit from the value of single unit.
Here,
500 g of strawberries cost £4.10
1 g of strawberries cost £[tex]\frac{4.10}{500}[/tex]
300 g of strawberries cost £[tex]\frac{4.10}{500} \times 300[/tex]
= £2.46
400 g of raspberries 300g of strawberries cost a total of £7.46
Let the cost of 400 g of raspberries be £x
so,
x + 2.46 = 7.46
x = 7.46 - 2.46
x = £5
cost of 400 g of raspberries = £5
cost of 1 g of raspberries = £[tex]\frac{5}{400}[/tex]
cost of 200 g of raspberries = £[tex]\frac{5}{400} \times 200[/tex]
= £2.5
cost of 300 g strawberries = £2.46
cost of 1 g strawberries = £[tex]\frac{2.46}{300}[/tex]
cost of 200 g of strawberries = £[tex]\frac{2.46}{300} \times 200[/tex]
= £1.64
Total cost of 200g raspberries and 200 g strawberries = £(2.5 + 1.64)
= £4.14
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Complete question
400 g of raspberries and 300 g of strawberries cost a total of £7.46.
500 g of strawberries cost £4.10.
Work out the total cost of 200 g of raspberries and 200 g of strawberries.
how do you solve x^2-11x+18=0
Answer: x = 9, 2
Step-by-step explanation:
I'm going to give you two main ways to solve this type of problem.
First is doing it mentally:
When we're given the setting of ax^2 + bx + c
We want to find two numbers that multiply to c and add to b. (If a isn't 1, then we need to add that into our calculation, but in this case a = 1)
So, what two numbers multiply to 18 and add to -11?
-9 and -2, so we rewrite the equation as (x-9)(x-2)
We then solve for x, x - 9 = 0, so x = 9 and x - 2 = 0, so x = 2
Second is we use the quadratic formula:
It would be [tex](-b+\sqrt{b^{2} -4ac})/2a\\(-b-\sqrt{b^{2} -4ac})/2a\\\\Plugging in your numbers: \\\\(11+\sqrt{11^{2} -72})/2\\(11-\sqrt{11^{2} -72})/2[/tex]
PLEASE HELP WITH THIS QUESTION!!!!!!!!!!
Answer:
Hope I helped you with this. Everything is explained in the photo
angle A and angle B are vertical angles. If mA = (2x +29)° and m
B = (3x - 17)°, then find the measure of angle B.
The angle B has a measure of 121 degrees
What are angles?Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the measure of the angle?The angles are given as
A = 2x + 29
B = 3x - 17
Also, we have:
The angles are vertical angles
Vertical angles are congruent angles
This means that
A = B
So, we have
2x + 29 = 3x - 17
Evaluate the like terms
x = 46
Substitute x = 46 in B = 3x - 17
B = 3 x 46 - 17
Evaluate
B = 121
Hence, the measure of the angle B is 121 degrees
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Answer:
Step-by-step explanation:
b=(3x-17) degrees.
Find the slope of the graph
Answer:
-1
Step-by-step explanation:
You just have to divide the change in the x axis by change in the y axis on any arbitrary interval.
Answer:
-1
Step-by-step explanation:
Do rise-over-run for linear equations. Its the vertical change over the horizontal change between two points. Ex. between (-2,0) and (-1,-1) the line drops 1 unit horizontally (-1) and moves to the right one unit (1) so the slope would be -1/1 = -1
What are the domain and range of this relation? pt3 last one
The Domain of this relation is {0,2,3,4} and the range of the relation is {-2,1,2,5}.
In the question
let us first write down the coordinates in the order from bottom to top .
The coordinates of the points are (4,-2) ,(2,1) ,(0,2) ,(0,5) ,(3,5) .
the x coordinates in the point (x,y) is called as Domain .
the y coordinates in the point (x,y) is called as Range .
Hence , the Domain of the given relation is {4,2,0,3}
writing in the order we get , Domain = {0,2,3,4}
and the range of the given relation is {-2,1,2,5}
writing in the order we get , Range = {-2,1,2,5}
Therefore , the Domain of this relation is {0,2,3,4} and the range of the relation is {-2,1,2,5} .
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Suppose that kellogg believes that the average weight for a box of frosted flakes is 18 ounces. As part of a quality control effort, they sample 30 boxes and find that the mean of those 30 boxes is 18. 2 ounces. Historical records show that the standard deviation of the filling process is 0. 32 ounces. How likely is it for the sample mean to have been 18. 2 ounces or larger if the actual mean is 18 ounces and the standard deviation of the filling process is 0. 32 ounces? round your answer to four decimal places.
Probability for the sample mean to have been 18.2 ounces or larger = 0.0003
Sample size, n = 30 boxes
Sample mean, [tex]\bar x[/tex] = 18.2 ounces
Population mean, μ = 18 ounces
Standard deviation of the population, σ = 0.32 ounces
We assume that this follows normal distribution.
Then the z-score, z = [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
= [tex]\frac{18.2-18}{\frac{0.32}{\sqrt{30}} }[/tex]
= 3.42
This z-score follows Standard Normal Distribution with mean = 0 and standard deviation = 1
Probability for the sample mean to have been 18.2 ounces or larger =
P(z ≥ 3.42) = 0.5 - P(0 < z < 3.423)
= 0.5 - 0.4997
= 0.0003
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MUEVE 1 CERILLA PARA ARREGLAR LA ECUACIÓN
what is 40% written as a fraction in its simplest form
Answer:
2/5
Step-by-step explanation:
40%= 40/100 = 4/10 = 2/5
Answer:
2/5
Step-by-step explanation:
Simplest form:
[tex]\sf 40 \%= \dfrac{40}{100}=\dfrac{4}{10}=\dfrac{2}{5}[/tex]
Select the correct answer. A soccer team wins 65% of its matches, and 15% of its matches end in a draw. If the team is scheduled to play 20 matches, about how many matches is it expected to lose? A. 13 B. 4 C. 8 D. 1 Reset
its B.4
Using percentage we can calculate that the team is expected to lose 4 matches.
A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. Although the abbreviations "pct," and occasionally "pc" is also used, the percent symbol "%" is most frequently used to denote it. A percentage is a number without any dimensions or established units of measurement.
By dividing the value by the entire value and multiplying the result by 100, the percentage may be computed. Calculating percentages using the formula (Value/Total Value)×100%.
Given in percentages the team will win 65% , team will draw =15%
Therefore in percentage the team will lose = 100 - ( 65 + 1 5 )% = 20 %
Now calculating the total number of matches the team will lose :
20% of 20 matches = 4 matches
Hence the team is expected to lose 4 matches out of 20.
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Help pls!! will award brainiest
a rectangle has an area of 35cm2
its width is 5cm
what is its length
Answer: L - 7 because 35/5
Answer:
The length is 7 cm
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
35 = l*5
Divide each side by 5
35/5 = l*5/5
7 = l
The length is 7 cm
I need help understanding this problem
The solution to the given inequalities is -7 < x ≤ 6. The graph of the inequality is shown below on a number line.
Solving Inequalities and Graphing Number lineFrom the question, we are to solve the given inequalities
The given inequalities are
-3x - 7 < 14 and -25 ≤ -3x - 7
Solving -3x - 7 < 14
-3x - 7 < 14
Add 3x to both sides of the inequality
-3x + 3x - 7 < 14 + 3x
-7 < 14 + 3x
Subtract 14 from both sides
-7 - 14 < 14 - 14 + 3x
-21 < 3x
Divide through by 3
-21/3 < 3x/3
-7 < x
Solving -25 ≤ -3x - 7
-25 ≤ -3x - 7
Add 3x to both sides
-25 + 3x ≤ -3x + 3x - 7
-25 + 3x ≤ - 7
Add 25 to both sides
-25 + 25 + 3x ≤ - 7 + 25
3x ≤ 18
Divide through by 3
3x/3 ≤ 18/3
x ≤ 6
Thus,
The solutions to the inequalities are
-7 < x and x ≤ 6
That is,
-7 < x ≤ 6
The number line is shown below
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The perimeter of a rectangle is 198 feet. Find the length and width if the length is an integer and the width is 3 times the next consecutive integer.
Answer:l=p/2-w=198/2-3=96
Step-by-step explanation:yes
the round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5 mm. round values to 4 decimal places when possible.
The following are the results for measuring the distance that a long jumper has jumped which is uniformly distributed between 0 and 5mm
a) Mean = 2.5
b) Standard deviation = 1.4434
c) P(X = 2.5) = 0
d) P(2 < X < 4) = (4 - 2)/(5 - 0) = 2/5 = 0.4
e) P(X > 1) =0.8
f) P(X > 4 | X > 2) = 0.33
g) 60th percentile = 3
h) Upper quartile = 3.75
Mean = (0 + 5)/2 = 2.5
Standard deviation =[tex]\sqrt{(5-0)^{2} }[/tex] / [tex]\sqrt{12}[/tex] = 1.4434
P(X = 2.5) = 0
P(2 < X < 4) = (4 - 2)/(5 - 0) = 2/5 = 0.4
P(X > 1) = (5 - 1)/(5 - 0) = 4/5 = 0.8
P(X > 4 | X > 2) = P(X > 4 and X > 2)/P(X > 2) = (5 - 4)/(5 - 2) = 1/3 = 0.33
60th percentile = 0.60*(5 - 0) = 3
Upper quartile = 75th percentile = 0.75*(5 - 0) = 3.75
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Can you please help? Thanks!
If a cylindrical barrel has a radius of 5.7 ft and a height of 8.4 ft, tripling the height of the concerned barrel will triple up its current volume.
As per the question statement, a cylindrical barrel has a radius of 5.7 ft and a height of 8.4 ft.
We are required to determine the dimension or dimensions which on tripling, will triple up the current volume of our question-mentioned barrel.
To solve this question, first we need to know the formula to calculate the volume of a cylinder, which goes as (π * r² * h)
Where [π = (22/7)], (r = radius of the cylinder)
And, (h = height of the cylinder).
Here, (r = 5.7 ft) and (h = 8.4 ft).
Now, considering [V = (π * r² * h)], where, ["V" is the volume]
if we triple our radius "r", our Volume "V₁" will become {π * (3r)² * h}
or, V₁ = 9πr²h
or, V₁ = 9(π * r² * h)
or, V₁ = 9V,
That is, 9 times the current volume. Hence, tripling the radius will not triple up the current volume of our concerned barrel.
Now, considering we triple our height "h", our Volume "V₂" will become {π * r² * 3h}
or, V₂ = 3πr²h
or, V₂ = 3(π * r² * h)
or, V₂ = 3V,
That is, 3 times the current volume. Hence, tripling the height will triple up the current volume of our concerned barrel.
As Proof,
Current Volume of our barrel = [(22/7) * (5.7)²* (8.4)]
= 857.74 ft²
And Volume of our barrel tripling the height = [(22/7) * (5.7)²* (3*8.4)]
= 2573.21 ft²
And, (2573.21/857.74) = 3.
Therefore, tripling the height of the concerned barrel will triple up its current volume, thus Proved.
Volume: In Mathematics and the whole of applied science, volume is defined as the space occupied within the boundaries of a three-dimensional object, or simply, the capacity of a three-dimensional object.To learn more about Volumes, click on the link below.
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make a table of values for the equation. Then graph the equation.
Check the picture below.
PLSSS HELP MEEE WILL GIVE 20 POINTS
Estimate the quotient of 42.4 ÷ 7.28.
9
8
7
6
Answer:
6
Step-by-step explanation:
Earning Money: Marcus works at an ice cream shop. He eamns $14.50 each
hour. Use Marcus's timesheet for the week to answer the questions
Date. Time in. Time out
April 11 8:45 am 12.00pm
April 12 9:00am 12.00pm
April 13 7:30am 12:00pm
April 14 8:00am 1:15pm
April 15 8:30am 11:15am
A. How many hours did Marcus work for the week?
B. How much money did Marucs earn for the week?
Answer:
A. Marcus worked 27 hours and 45 minutes in the week.
B. He earned $391.5 for the week.
Step-by-step explanation:
First you calculate the hours he worked daily and you add them together, when you have the weekly hours you multiply the hours times what he earns each hour.
It's 27 • 14.50= $391.5
Answer:
A 88hours and 5 minutesB $70.250Use the figure at the right . If JK=2x+6 and NO=11 what is the value of x
Answer: x=5/2
Step-by-step explanation:
JK=NO
2x+6=11
2x+6-6=11-6
2x=5
x=5/2
A student is running for president of student government. Her friend has designed a campaign poster that measures 27 feet by 14 feet. She duplicated the poster on a
rectangular button measuring 6 inches by 3 1/9 inches. What is the scale factor?
The scale factor that is used for student is running for president of student government is 1:54.
What is the scale factor?From the information, her friend has designed a campaign poster that measures 27 feet by 14 feet and she duplicated the poster on a
rectangular button measuring 6 inches by 3 1/9 inches.
1 feet = 12 inches
27 feet = 27 × 12 = 324 inches.
The scale factor will be the division of the values and this will be:
= 6/324
= 1/54
The scale factor is 1:54.
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What amount of pure acid must be added to 400 mL of a 30% acid solution to produce a 75% acid solution?
Step-by-step explanation:
pure acid is a 100% acid solution.
x = ml of 100% solution
1×x + 0.3×400 = 0.75×(400 + x)
x + 120 = 300 + 0.75x
0.25x = 180
x = 720 ml
we must add 720 ml of pure acid to the 400 ml of 30% solution to create a 75% solution (1,120 ml in total).
Question 9(Multiple Choice Worth 1 points) (04.05 MC) A company determines an employee's starting salary according to the number of years of experience, as detailed in the table. Years of experience Salary 0 $40,000 1 $42,150 $44,260 $46,785 $48,820 $51,126 2 3 4 5 Use the equation for the line of best fit to predict the salary for an employee with 7 years of experience? (Round your answer to the nearest dollar) O $52,900 O $53,340 O $53,914 O $55,573
By using the equation for the line of best fit, the salary for an employee who has seven (7) years of experience is: D. $55,573.
What is a line of best fit?A line of best fit is a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between a data.
In this scenario, the employee's salary would be plotted on the y-axis of the scatter plot while the years of experience would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the data in the given table, an equation for the line of best fit is given by:
y = 2233.3x + 39940
Next, we would use the above equation for the line of best fit to predict the salary for an employee with 7 years of experience:
y = 2233.3(7) + 39940
y = 15,633.1 + 39940
y = 55,573.1 ≈ $55,573.
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Lincoln high school have 75 less than four times as many students as washington high school right in expression to find the number of students at lincoln high school washington high school has w students
Main Answer:
Number of students in Lincoln high school is [tex]4w-75[/tex]
Explanation:
Number of students in Washington high school = w
Number of students in Lincoln high school = 75 less than four times number of students in Washington high school
Therefore, number of students in Lincoln high school = [tex]4w-75[/tex]
An entry level web developer's annual pay is $56,940 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its web developers. If the firm cuts the work year to 50 weeks but keeps the same rate of pay, how much should the web developer expect his annual pay to decrease? Round your answer to the nearest dollar.
Based on the first entry level web developer salary paid, and the new work year, the amount the web developer can expect his annual pay to decrease by is $2,190
How to find the decrease in pay?First, find the weekly pay of the web developer in the first salary:
= 56,940 / 52
= $1,095 per week
The new salary of the web developer as a result of the work week becoming 50 weeks is:
= 1,095 x 50
= $54,750
The decrease in this annual pay to the web developer is:
= 56,940 - 54,750
= $2,190
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Find the x-coordinates of the x-intercepts of the parabola
y = 2x^2 + 13x - 7. If you find more than one, then list the values separated by commas.
The x-coordinates of the x-intercepts of the parabola are 1/2 and -7
What are parabola equations?Parabola equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the x-coordinates of the x-intercepts?The parabola is given as
y = 2x^2 + 13x - 7
It should be noted that the x-intercept of the function is the point or points where the graph of the function crosses the x-axis
i.e. the point where the function equals 0
So, we have
y = 2x^2 + 13x - 7
Expand
y = 2x^2 + 14x - x - 7
Factorize the equation
So, we have
y = 2x(x + 7) - 1(x + 7)
Set the equation to 0
So, we have
2x(x + 7) - 1(x + 7) = 0
Factor out x + 7
So, we have
(2x - 1)(x + 7) = 0
Expand
2x - 1 and x + 7 = 0
Solve for x
x = 1/2 and x = -7
Hence, the x-coordinates of the x-intercepts are 1/2 and -7
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What is the slope of the line parallel to :y=-4/7x+2
Answer:Two lines are parallel if the have the same slope. To find the slope of the line parallel to the line y=4/7x-2 we need to get the line into slope-intercept form (y = mx + b), but the line is already in that form, so the slope is m = 4/7.
Step-by-step explanation:
Mahnoor owns and operates mahnoor's coffee shop. the city of laketown, australia, where mahnoor's coffee shop is located, recently enacted a ban on all foam cups to help protect the environment. instead of switching to paper cups, mahnoor has decided to risk being fined by the city and to continue to use foam cups. she estimates that this will save her 10{,}00010,00010, comma, 000 australian dollars. she also estimates that there is a 12\%12%12, percent chance that she will be fined. the fine would be for 100{,}000100,000100, comma, 000 australian dollars. find the expected value of mahnoor's decision to continue to use foam cups.
Answer: -2000
Step-by-step explanation:
8 squared plus x squared = 17 squared solve for x
Answer:
x ≈ 15
Step-by-step explanation:
using Pythagoras' identity in the right triangle
a² + b² = c²
with a = 8, b = x , c = 17
8² + x² = 17²
64 + x² = 289 ( subtract 64 from both sides )
x² = 225 ( take square root of both sides )
[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{225}[/tex]
x = 15
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form.
(−2,4) and (7,−8)
The distance between the sides of the right-angled triangle is given as follows:
Recall that a right-angled triangle is one that has at least one side equal to 90°
In the question, we know the endpoints and the line hypothenus. To find the length of the hypothenuse, we can state:
Distance = [tex]\sqrt{(x2 - x1)^{2} +(y2 - y1)^{2} }[/tex]
Recall that the distance between the two points is given as (−2,4) for first point and (7,−8) for the second point.; Hence:
Distance = √[(-2+7)²+ (4+-8)²]
Distance = √(5²) + (-4)²
Distance = √(25+16)
Distance = √41
Hence the third point is (-2-8).
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