According to Chebyshev's theorem, at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.
Chebyshev's theorem states that for any set of data, regardless of its distribution, a certain percentage of the data lies within a certain number of standard deviations from the mean. Specifically, Chebyshev's theorem states that for any data set, at least 1 – 1/k² of the data values will lie within k standard deviations of the mean, where k is any number greater than 1. If k=2, at least 75% of the data values lie within 2 standard deviations of the mean. If k=3, at least 89% of the data values lie within 3 standard deviations of the mean.
Therefore, for a data set with a mean of 63.6 minutes and a standard deviation of 2.5 minutes, we can use Chebyshev's theorem to determine that at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.
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There is a bag filled with 5 blue, 2 red and 3 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 the same colour?
Answer:
2/9 + 5/36 = 17/36
So the probability of getting 2 marbles of the same color is 17/36 or 0.472.
Answer:
17/36
Step-by-step explanation:
please help quickly, this needs to be finished soon
Accοrding tο the fοrmula fοr the quadratic equatiοn, the maximum height is 98 ft.
What is a quadratic equatiοn?A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn οf the fοrm:
[tex]ax^2 + bx + c = 0[/tex]
where a, b, and c are cοnstants, and x is the variable. The term "quadratic" cοmes frοm the Latin wοrd "quadratus," meaning square, because the variable is squared in this type οf equatiοn.
Quadratic equatiοns can have οne, twο, οr zerο real sοlutiοns, depending οn the values οf the cοnstants a, b, and c. The sοlutiοns can be fοund using the quadratic fοrmula:
[tex]x = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex] οr by factοring the quadratic expressiοn intο twο linear factοrs.
The quadratic functiοn tο mοdel the vertical mοtiοn is:
[tex]h(t) = -16t^2 + v0t + h0[/tex]
where:
h(t) is the height at time t
t is the time in secοnds
v0 is the initial vertical velοcity in ft/s
h0 is the initial height in ft
Given v0 = 32 ft/s and h0 = 82 ft, the functiοn becοmes:
[tex]h(t) = -16t^2 + 32t + 82[/tex]
Tο find the maximum height, we can use the vertex fοrm οf a quadratic equatiοn:
[tex]h(t) = a(t - t0)^2 + h0[/tex]
where:
a is the cοefficient οf the quadratic term
t0 is the time at which the maximum height is achieved
h0 is the initial height
Cοmparing the twο fοrms, we see that a = -16 and t0 = -b/2a, where b is the cοefficient οf the linear term. In this case, b = 32, sο:
t0 = -32 / (2(-16)) = 1
Therefοre, the maximum height is achieved at t = 1 secοnd. Substituting intο the οriginal equatiοn, we get:
[tex]h(1) = -16(1)^2 + 32(1) + 82 = 98 ft[/tex]
Sο the maximum height is 98 ft.
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plese help with the following questions PLESE
Assignment:
Sebastian Salazar opened a Sporting Goods Store. He has some new inventory that needs to be priced. He also has some seasonal inventory that hasn’t sold and he needs to put them on sale.
Help Sebastian with his pricing questions:
1. The retail prices are: $44.36, $34.10 and $67.57
2. The sales prices are: $263.20 and $65.59
Define the term retail price?Retail price refers to the price at which a product or service is sold to the final consumer by a retailer. This price includes the cost of production, transportation, marketing, and other related expenses, as well as a markup to generate profit for the retailer.
1. New Items - Calculate Retail Prices
Item Wholesale Mark Up Calculation Retail
Cost ($) Percent% Price ($)
a. Louisville $22.75 95% 22.75+(95%×22.75) =$44.36
Slugger bat and
batting glove set
b. Wilson $11.00 210% 11+(210%×11) =$34.10
Basketball
c. Element $26.50 155% 26.50+(155%×26.50) =$67.57
Skateboard
2. Items on sale - Calculate Sale Prices
Item Retail Discount Calculation Sales
price ($) Percent % Price ($)
a. Head $329.00 20% 329-(20%×329) $263.20
Snowboard
b. Kelly $79.99 18% 79.99-(18%×79.99) $65.59
Ski poles
All data is filled in below table.
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Which expression represents the perimeter of a triangle in simplest form that has side lengths: 2x, 3x + 5, x + 2
Answer:
6x + 7
Step-by-step explanation:
triangle has 3 sides right, which is 2x, 3x+5 and x+2
so basically you just have to add everything up since perimeter is just the total number of each sides combined
2x + (3x+5) + (x+2)
expand from the brackets
2x + 3x + 5 + x + 2
rearrange the numbers to avoid confusion
2x + 3x + x + 5 + 2
add everything up
6x + 7
Which of the following equations is equivalent to 2 x + 6 = 30 - x - 3 2 x + 6 = 10 - x - 3 2 x + 6 = 30 - x + 3
The equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.
What is equation?
In mathematics, an equation is a statement that two expressions are equal, usually written with an equal sign (=) between them. Equations can contain variables, which are symbols that represent unknown or unspecified values.
We can simplify and solve the equation 2x + 6 = 30 - x - 3 as follows:
2x + 6 = 30 - x - 3
Adding x and adding 3 to both sides, we get:
3x + 9 = 30
Subtracting 9 from both sides, we get:
3x = 21
Dividing both sides by 3, we get:
x = 7
So the given equation simplifies to x = 7.
We can now substitute this value of x into each of the answer choices to see which one is equivalent to the given equation:
a) 2x + 6 = 30 - x - 3
Substituting x = 7, we get:
2(7) + 6 = 30 - 7 - 3
14 + 6 = 20
20 = 20
b) 2x + 6 = 10 - x - 3
Substituting x = 7, we get:
2(7) + 6 = 10 - 7 - 3
14 + 6 = 0
20 ≠ 0
Therefore, this equation is not equivalent to the given equation.
c) 2x + 6 = 30 - x + 3
Substituting x = 7, we get:
2(7) + 6 = 30 - 7 + 3
14 + 6 = 26
20 ≠ 26
Therefore, this equation is not equivalent to the given equation.
Therefore, the equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.
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7. Complete a dilation with scale factor of ½ around the origin and then
reflect over the y-axis. What are the new ordered pair of A'?
The new ordered pairs of points A', B', and C' after the reflection over the y-axis are (1,-2.5), (0,1.5), and (-3,-1.5), respectively.
WHAT IS AXIS ?
An axis is a straight line around which an object rotates or is symmetrical. In geometry, it is a reference line that is used to measure distances, angles, and other geometric properties of objects. In a two-dimensional plane, there are two axes: the x-axis and the y-axis. The x-axis is the horizontal line that runs from left to right, while the y-axis is the vertical line that runs from bottom to top. Together, the x-axis and y-axis form a coordinate system that is used to plot points and graph functions. In three-dimensional space, there is also a z-axis that runs perpendicular to the x-axis and y-axis
To perform a dilation with a scale factor of 1/2 around the origin, we need to multiply the coordinates of each point by 1/2. This gives us:
A' = (1/2)A = (1/2)(-2,-5) = (-1,-2.5)
B' = (1/2)B = (1/2)(0,3) = (0,1.5)
C' = (1/2)C = (1/2)(6,-3) = (3,-1.5)
The new coordinates of points A, B, and C after the dilation are (-1,-2.5), (0,1.5), and (3,-1.5), respectively.
To reflect each point over the y-axis, we need to change the sign of its x-coordinate, while leaving the y-coordinate unchanged. This gives us:
A" = (-x,y) = (-(-1),-2.5) = (1,-2.5)
B" = (-x,y) = (-0,1.5) = (0,1.5)
C" = (-x,y) = (-3,-1.5) = (-3,-1.5)
The new ordered pairs of points A', B', and C' after the reflection over the y-axis are (1,-2.5), (0,1.5), and (-3,-1.5), respectively.
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the ratio of students who ade the honor roll to the total number of stoudents is 1:50. if there are 500 students in total how many made the honor roll?
If there are 500 students in total, the number of students who made the honor roll is 10 students, given that the ratio of students who made the honor roll to the total number of students is 1:50.
The number of students who made the honor roll can be found using proportions. Here's how to do it:
Let X be the number of students who made the honor roll.
The proportion can be set up using the given ratio as follows:
1:50 = X:500
Cross-multiplying this equation and solving for X gives:
50X = 500
X = 10
Therefore, 10 students made the honor roll.
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Austin has a dimes and y nickels, having at most 28 coins worth a minimum of $2
combined. At least 18 of the coins are dimes and no more than 6 of the coins are
nickels. Solve this system of inequalities graphically and determine one possible
solution.
The solution of system of inequalities solved graphically is (18,6).
What is system of linear inequalities?A group of two or more linear inequalities are graphed together on a coordinate plane to discover the solution that concurrently satisfies all the inequalities. This is known as a system of linear inequalities. The location where all the half-planes overlap is where the system is solved. Each inequality defines a half-plane on the coordinate plane. Every point in this area, which is referred to as the feasible region, fulfils all of the system's inequalities. To identify the optimum solution for an optimization problem given a set of constraints, systems of linear inequalities are frequently utilised.
Let us suppose the number of dimes = a.
Let us suppose the number of nickels = y.
According to the problem we have the following conditions:
a + y ≤ 28 (at most 28 coins)
0.10a + 0.05y ≥ 2 (worth at least $2)
a ≥ 18 (at least 18 dimes)
y ≤ 6 (no more than 6 nickels)
Using different values of a and y plot the points.
The solution of this system of inequality is any point that lies in the feasible region.
One such point is (18, 6).
Hence, the solution of system of inequalities solved graphically is (18,6).
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HELP ASAP!!
A kite is flying 10 feet off the ground. It’s line is pulled out in casts a 9 foot shadow, find the length of the line if necessary round to the nearest 10th.
Answer:
We can use similar triangles to solve this problem. Let's call the length of the kite's line "x". Then, we can set up a proportion:
(length of kite) / (length of shadow) = (height of kite) / (length of shadow)
x / 9 = 10 / 9
To solve for x, we can cross-multiply and simplify:
x = 90 / 9
x = 10
Therefore, the length of the kite's line is 10 feet.
Step-by-step explanation:
It takes 56 minutes for 7 printing machines to
produce a batch of newspapers.
a) How many minutes would it take just 1 machine?
b) How many minutes would it take 8 machines?
Answer:392
Step-by-step explanation:
a) It would take one machine 392 minutes.
b) It would take one machine 49 minutes.
Define the term proportion?Two ratios are said to be equal when a proportion is stated. When comparing two quantities, ratios are used to divide one quantity by the other.
a) Here given that, to produce a batch of newspaper 7 printing machines needed 56 minutes.
Using this relationship, we can set up a proportion:
as given, 7 printing machine needed = 56 minutes
So, 1 printing machine needed = 7 × 56 minutes = 392 minutes
Therefore, it would take one machine 392 minutes to produce the same batch of newspapers.
b) Similarly, to find out for 8 machines to produce the same batch of newspapers, we can use the same relationship:
1 printing machine needed = 392 minutes
So, 8 printing machine needed = (392 / 8) minutes = 49 minutes
Therefore, it would take one machine 49 minutes to produce the same batch of newspapers.
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The supervisor at vector control wants your report of how the mosquito population is growing. Do you think your report is better supported by the table above or by a graph of the growth function as show below? WHY? Explain the reasoning behind your conclusion.
As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .
what is vector ?A vector is a mathematical concept that possesses both magnitude (or length) and direction. In physics, engineering, and other sciences, physical quantities with both a size and a direction, such as velocity, force, and acceleration, are frequently represented by vectors. In geometry, vectors can be represented as arrows, with the direction of the arrow indicating the vector's magnitude and the length of the arrow indicating its magnitude. In addition to being able to represent points in space and describe curves and surfaces, vectors may also be added, subtracted, and multiplied by scalars to create new vectors.
given
Based on the provided table and the growth function graph, I would argue that the report on the growth of the mosquito population is better supported by the graph.
On the other hand, there is no visual representation of the growth of the mosquito population in the table; it merely displays the data in a tabular format.
Although the table contains the same data as the graph, it is more difficult to understand and evaluate.
As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .
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AOC is a right-angle AOB: BOC - 2:3 what is the size of angle BOC
Angles AOB and BOC are complimentary angles if AOC is a right angle. Let's use x to represent the angle BOC's size. Next, we have: Angle AOB plus Angle BOC equals 90° (definition of complementary angles).
BOC/AOB angle equals 2/3 (given) Angle AOB may be expressed in terms of angle BOC using the second equation: (3/2) × angle BOC, where angle AOB (multiplying both sides by angle AOB) Angle BOC plus angle (3/2) equals 90 degrees. When we simplify this equation, we obtain: BOC angle (5/2) times equals 90 degrees. By multiplying both sides by 5, we obtain: BOC angle = (2/5) x 90 degrees BOC angle is 36 degrees. Hence, the angle's size Substituting this expression into the first equation, we get: (3/2) x angle BOC + angle BOC = 90 degrees Simplifying this equation, we get: (5/2) x angle BOC = 90 degrees.
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three traffic lights on a street span 120 yards. if the second traffic light is 85 yards away from the first, how far in yards is the third traffic light from the seccond
The distance between the third traffic light from the second traffic light is 35 yards.
What is the distance?Three traffic lights on a street span 120 yards.
If the second traffic light is 85 yards away from the first.
Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.
This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.
Thus, the distance between the third traffic light from the second traffic light is 35 yards.
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The tape diagram represents an equation.
Write an equation to represent the image.
Answer: y+y=7
Step-by-step explanation:
7 is as big as 2 y's therefore y+y would be equal to 7
determine the smallest integer value of x in -2x+1< -9
Answer: The smallest integer value of x that satisfies the inequality -2x+1<-9 is x=5.
Step-by-step explanation:
Answer: The smallest integer value of x that satisfies the inequality -2x+1<-9 is x=5.
Explanation:
To solve the inequality, we need to isolate the variable x on one side of the inequality symbol. Here are the steps:
Subtract 1 from both sides of the inequality:
-2x < -10
Divide both sides of the inequality by -2, remembering to reverse the direction of the inequality symbol:
x > 5
Therefore, the smallest integer value of x that satisfies the inequality is x = 5, since any value less than 5 would make the inequality false.
Answer:
x = 6
Step-by-step explanation:
- 2x + 1 < - 9 ( subtract 1 from both sides )
- 2x < - 10
divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
x > 5
since x must be greater than 5, it cannot equal 5
then the smallest integer value of x is x = 6
how long will a car take to travel 140km averaging a speed of 35km/h
Answer:
Step-by-step explanation:
To calculate the time it will take a car to travel 140km at an average speed of 35km/h, we can use the formula:
time = distance ÷ speed
Plugging in the given values, we get:
time = 140km ÷ 35km/h
time = 4 hours
Therefore, it will take a car 4 hours to travel 140km at an average speed of 35km/h.
Answer:
ㅤ
Car will take 4 hours
ㅤ
Step-by-step explanation:
ㅤ
[tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{Time = \dfrac{Distance}{Speed}}}}}}}[/tex]
ㅤ
[tex]\large{\leadsto{\sf{Given_{(Distance)} = 140 \: km}}}[/tex]
ㅤ
[tex]\large{\leadsto{\sf{Given_{(Speed)} = 35 \: km/hr}}}[/tex]
ㅤ
[tex]\large{\underline{\underline{\sf{Applying \: Formula:-}}}}[/tex]
ㅤ
[tex]\large{\leadsto{\sf{Required_{(Time)} = \bigg(\dfrac{\cancel{140}}{\cancel{35}}\bigg)} \: hr}}[/tex]
ㅤ
[tex]\large{\purple{\boxed{\leadsto{\sf{Required_{(Time)} = 4 \: hr}}}}}[/tex]
ㅤ
━━━━━━━━━━━━━━━━━━━━━━
[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]
ㅤ
[tex]\large{\dashrightarrow{\sf{Time = \dfrac{Distance}{Speed}}}}[/tex]
ㅤ
[tex]\large{\dashrightarrow{\sf{Speed = \dfrac{Distance}{Time}}}}[/tex]
ㅤ
[tex]\large{\dashrightarrow{\sf{Distance = Speed \times Time}}}[/tex]
Question 8
Which division expression is the given figure modeling?
A
B
C
D
1
4÷3
3÷/1/1
1
12 ÷ 4
3 ÷ 1/1/
1
1
The division problem provided by the model shown here is [tex]3[/tex] ÷ [tex]\frac{1}{4}[/tex].
How are fractions divided?The first step of dividing fractions is to get the reciprocal of a second fraction, which involves flipping its numerator and denominator. Multiply all two numerators after that. Multiply the 2 denominators after that. Then finish, if required, simplify the fractions.
Simple division: What is it?Simple Division: Little numbers can be divided into groups and pieces using the simple division method in mathematics. Divide easy and basic division problems into terms that can be divided using simple division sums. Arithmetic, subtraction, multiplying, & division are the four fundamental mathematical operations.
Given:
We have three section [tex]1+ 1 + 1= 3[/tex]
[tex]= \frac{4}{12}[/tex]
[tex]= \frac{1}{3}[/tex]
In this case, the model yields the division issue.
[tex]3[/tex] ÷ [tex]\frac{1}{4}[/tex]
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Fractions of money question
1/6 + 1/4= 10/24 (5/12 simplified)
2.50× 12= 30
This is the total sum of money shared.
7/12 is given to Farooq
7/12 of 30 is 17.5
answer= £17.5
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
X
The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.
What is surface area ?
Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.
To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.
First, let's find the area of the triangular base.
Area of triangle = (1/2) x base x height
Area of triangle = (1/2) x 18 x 24
Area of triangle = 216 [tex]feet ^2[/tex]
Next, let's find the area of each rectangular face.
Area of rectangle = length x width
Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]
Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]
Area of rectangle 3 = 22 x 30 = 660 [tex]feet ^2[/tex]
Now, we can add up the areas of all three faces to get the total surface area of the prism:
Surface area = area of rectangle (1+2+3) + 2 x area of triangle
Surface area = 528 + 396 + 660 + 2(216)
Surface area = 2016 [tex]feet ^2[/tex]
Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].
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The numbers of trading cards owned by 7 middle-school students are given below.
(Note that these are already ordered from least to greatest.)
360, 373, 402, 499, 548, 644, 646
Suppose that the number 646 from this list changes to 639. Answer the following.
a) If the number 646 from the ordered list changes to 639, c) the median stays the same.
b) a) If the number 646 from the ordered list changes to 639, a) the mean decreases by 1.
What are the median and the mean?The median is the middle value in an ordered list (descending or ascending).
The mean refers to the average value.
The mean or average is computed as the quotient of the division of the total data value by the total number of items in the data set.
The ordered numbers of trading cards owned by 7 middle-school students = 360, 373, 402, 499, 548, 644, 646
The total value (sum) = 3,472
The number of cards = 7
The median = 499
The mean = 496 (3,472/7)
If the number 646 changes too 639:
The total value (sum) = 3,465
The median = 499
The mean = 495 (3,465/7)
Difference in mean = 1 (496 - 495)
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Function P represents the perimeter, in inches, of a square with the side length x inches.P = x + x + x + x ... but it would be more efficient to write it this way: P =4xComplete the table.x 0 1 2 3 4 5 6P(x) 0
Function P represents the perimeter, in inches, of a square with the side length x inches. So, the perimeter of a square can be represented as P = x + x + x + x, which simplifies to P = 4x. This way is more efficient to write than the former.
Complete the table provided: x 0 1 2 3 4 5 6 P(x) 0 4 8 12 16 20 24. When x = 0, the perimeter of the square is 0.When x = 1, the perimeter of the square is P = 4(1) = 4. When x = 2, the perimeter of the square is P = 4(2) = 8. When x = 3, the perimeter of the square is P = 4(3) = 12. When x = 4, the perimeter of the square is P = 4(4) = 16. When x = 5, the perimeter of the square is P = 4(5) = 20. When x = 6, the perimeter of the square is P = 4(6) = 24.
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can someone please explain?
It would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.
What is cost?Cost is the amount of money or resources required to purchase or produce something. It can be the total expenditure on a product, service, or activity. It can also refer to the amount of money or resources consumed in order to maintain or achieve something. Cost can also be the value of a resource lost or sacrificed in order to obtain something.
To make the price of smoothies a function of the size, the sign should be modified to include the following additional information:
8 ounce $2.29/ounce
12 ounce $2.79/ounce
12 ounce. $3.09/ounce
16 ounce $3.69/ounce
20 ounce $4.09/ounce
22 ounce
( Bonus size). $4.09/ounce
This change would make the price of smoothies a function of the size, as each smoothie size would then have its own associated cost per ounce. This would make it easier for customers to compare the cost of different sizes and make an informed decision. Furthermore, it would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.
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Find the slope-intercept form of the line with the slope m= 1/7 which passes through the point (-1, 4).
Answer:
y = 1/7x + 29/7
Step-by-step explanation:
Slope intercept form is y = mx + b
m = the slope
b = y-intercept
m = 1/7
Y-intercept is located at (0, 29/7)
So, the equation is y = 1/7x + 29/7
2. Oil is leaking from an uncapped well and polluting a lake. Ten days after the leak is discovered, environmental engineers measure the amount of oil in the water to be 200 gallons with a current inflow rate of 30 gallons per day. The leak is slowing so that on the tenth day, the inflow rate is decreasing by 5 gallons/day each day. Suppose Q(t) is the amount of oil (in gallons) t days after the leak is discovered. (a) Find the second degree Taylor polynomial for Q(t) centered at t=10. (b) Use your answer in the previous part to estimate the amount of oil in the lake at t=12
As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).
what is polynomial ?A polynomial is a mathematical equation that only uses addition, subtraction, multiplication, and non-negative integer exponents and is made up of variables and coefficients. To put it another way, a polynomial is an algebraic expression made up of terms that are sums, products, and/or products of variables and coefficients. The leading coefficient is the coefficient of the term with the highest degree, while the degree of a polynomial is the maximum power of the variable in the expression.
given
(a) We need to determine Q(10), Q'(10), and Q" in order to determine the second degree Taylor polynomial for Q(t) with a center at t=10 (10).
As we are aware, Q(10) = 200. (given in the problem statement).
We must take the derivative of Q(t) with respect to t in order to determine Q'(10):
Q'(t) = -5t + 250
Q'(10) = -5(10) + 250 = 200
We must take the derivative of Q'(t) with respect to t in order to determine Q"(10):
Q''(t) = -5
Q''(10) = -5
The second degree Taylor polynomial can now be calculated using the following formula: P2(t) = Q(10) + Q'(10)(t-10) + (1/2)Q"(10)(t-10)2.
With the numbers we discovered, we can calculate P2(t) as 200 + 200(t-10) + (1/2)(-5)(t-10)2.
[tex]P2(t) = 200 + 200(t-10) - (5/2)(t-10)^2[/tex]
(b) We must assess the second degree Taylor polynomial at t=12 in order to determine how much oil is in the lake at that time.
P2(12) = 210 gallons because P2(12) = 200 + 200(12-10) - (5/2)(12-10)2. (rounded to the nearest gallon)
As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).
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How does the standard deviation of the sampling distribution of all possible sample means (for a fixed sample size n) from a population compare numerically to the standard deviation of the population?
The standard error of the mean is defined as the standard deviation of the sampling distribution of all potential sample means drawn from a population.
The standard error is also known as the standard deviation of the sampling distribution.
The standard deviation of the population is known as the population standard deviation.
The population standard deviation is an estimate of the amount of variation or dispersion of the values in the population.
It represents the average distance of the values from the mean of the population.
The standard deviation of the sampling distribution of all possible sample means (for a fixed sample size n) from a population is lower than the standard deviation of the population.
The standard deviation of the sampling distribution of all possible sample means is a measure of the variation of the sample means around the population mean.
The sample means are less variable than the individual observations in the population; therefore, the standard deviation of the sample means is lower than the standard deviation of the population.
In general, the standard error is given by:
$$SE = \frac{{{\sigma _p}}}{{\sqrt n }}$$
where, σp represents the population standard deviation and n represents the sample size.
The standard deviation of the sampling distribution is lower than the population standard deviation.
The standard deviation of the sampling distribution is dependent on the sample size n.
As the sample size increases, the standard deviation of the sampling distribution decreases.
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Solve the following proportion for y. 13 11 8 y Round your answer to the nearest tenth. 1 X Ú
Answer:
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Step-by-step explanation:
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The equation to show the relationship between x and y is y = 0.08x, where y is the amount of sales tax in dollars for the item and x is the cost of the item in dollars before tax.
What is tax?Tax is a compulsory financial charge or some other type of levy imposed upon a taxpayer by a governmental organization in order to fund various public expenditures. A failure to pay, along with evasion of or resistance to taxation, is punishable by law. Taxes consist of direct or indirect taxes and may be paid in money or as its labour equivalent. Most countries have a tax system in place to pay for public, common or agreed national needs and government functions. Some levy a flat percentage rate of taxation on personal annual income, but most scale taxes based on annual income amounts.
This equation reflects the fact that the amount of sales tax for an item is 8% of its cost before tax.
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Sales tax: The equation to show the relationship between x and y is x + y = C,
What is equation?An equation is a mathematical statement that expresses two mathematical expressions to be equal. It usually consists of two numbers, variables, or a combination of the two. An equation may be used to calculate a desired result, or to determine the relationship between two variables. Equations can also be used to test whether a statement is true or false. Most equations are written in the form of "a = b," where a and b are two numbers or variables.
where C is the cost of the item plus the sales tax. This equation can be explained mathematically as follows: the cost of the item (x) is added to the amount of sales tax (y) to give the total cost of the item with tax (C).
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12x²+11x-56 box method
The product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.
WHAT IS BOX METHOD ?
The box method, also known as the grid method, is a visual method used to multiply two numbers or two binomials. It involves creating a grid or box and filling it in with the products of the digits in each row and column. The method works for both single-digit and multi-digit numbers.
To use the box method for multiplying two numbers, we draw a box with two rows and two columns. We write one number along the top row and the other number along the left column. Then, we multiply the digits in each row and column and write the products in the corresponding cell of the box. Finally, we add the numbers in each cell of the box to get the product of the two numbers.
The box method can be used to multiply two binomials, such as (4x + 7) and (3x - 8). To use the box method, we draw a box with four cells, and we write the two binomials along the top and left sides of the box, like this:
| 4x | 7
-------------------
3x | |
-------------------
| |
Then, we fill in the four cells of the box by multiplying the corresponding terms. For example, the top-left cell is filled by multiplying 4x and 3x, which gives 12x². The other cells are filled in a similar way:
| 4x | 7
-------------------
3x | 12x² | 28x
-------------------
| -21x | -56
Next, we combine the terms in each row and column of the box, and write the final answer as the sum of these terms:
12x² + 28x - 21x - 56
Simplifying this expression gives:
12x² + 7x - 56
Therefore, the product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.
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A cylindrical tank is one-fifth full of oil. The cylinder has a base radius of 80 cm. The height of the cylinder is 200 cm. 1 litre 1000 cm3 How many litres of oil are in the tank? Round your answer to the nearest litre
The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).
The volume of any cylinder can be calculated using the formula,
V = πr²h
(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)
As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:
Volume of oil = (1/5) x Total Volume
Substituting the given values, we have:
Total Volume = π(80cm)²(200cm) = 4,031,240 cm³
Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³
Converting cm³ to litres, we have:
1 litre = 1000 cm³
Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres
Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.
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The distance from school to Regina's house is 4. 2 kilometers. After school, Regina stops at a grocery store on her way home. If the distance from the school to the grocery store is 1. 4 kilometers, how much farther in meters does Regina need to get home?
meters
Regina needs to travel an additional 5,600 meters to get home.
The total distance Regina travels from school to the grocery store and then to her house is
4.2 km + 1.4 km = 5.6 km
To find out how much farther Regina needs to get home, we need to subtract the distance from the grocery store to her house (which we don't know yet) from the total distance she travels.
Let's say the distance from the grocery store to Regina's house is x kilometers. Then we can set up an equation
5.6 km - x km = the distance Regina needs to get home
To solve for x, we can isolate it on one side of the equation by subtracting the distance Regina needs to get home from both sides
5.6 km - (the distance Regina needs to get home) = x km
We know that Regina needs to get home, so we can substitute that into the equation
5.6 km - 0 km = x km
Simplifying, we get
x = 5.6 km
Now we know that the distance from the grocery store to Regina's house is 5.6 km. We need to convert this to meters to find out how much farther Regina needs to get home
5.6 km = 5,600 meters
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