an aircraft is climbing at 30° angle to the horizontal how fast is the aircraft gaining alitude if it’s speed is 500 mph
The speed rate at which the aircraft is gaining altitude is;
dx/dt = 250 miles per hour
Since the aircraft is climbing at 30° to the horizontal. it means there will be a vertical component which will be the altitude and also a horizontal component which will be the horizontal distance covered. while the hypotenuse will be how far it has climbed.
Let us call the vertical component x and the hypotenuse component z.
Thus, from trigonometric ratios, we can say that;
sin 30 = x/z
We are looking for how fast the aircraft is gaining altitude. Thus, using Liebniz notation, we can say this rate is; dx/dt. Thus;
sin 30 = (dx/dt)/(dz/dt)
0.5 = (dx/dt)/(dz/dt)
0.5 × (dz/dt) = dx/dt
Its' speed is 500 mph. This means dz/dt = 500
Thus;
dx/dt = 0.5 × 500
dx/dt = 250 mph
Hence, the speed rate at which the aircraft is gaining altitude is;
dx/dt = 250 miles per hour
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The sum of three numbers is 68. The first number is 8 more than the second. The third number is 2 times the second. What are the numbers?
The numbers are 23,15,30 if the sum of three numbers is 68.
What is an equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an equation is defined as having one or more variables in French.
Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.
Let the first number be x
The second number is 8 Less than the x is x-8
The third number is 2 times the second is 2(x-8)
Sum of the three numbers is 68
x+x-8+2(x-8)=68
4x-24=68
4x=92
X=23
Therefore, the numbers are 23,15,30
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What is the equation of the circle with center (-4, -1) and radius 3?
The equation of the circle for all the given values is obtained as x² + y² + 8x + 2y + 8 = 0.
How to write an equation for a circle?The equation for a circle can be written by knowing the coordinates of its centre and the length of its radius.
Since the radius is the distance from the centre to a point on the circle, the equation can be written by distance formula as s (x - h)² + (y - k)² = r² where (h, k) is the coordinate of the centre.
The coordinates of the centre of the circle is given as (-4, -1).
And, the radius is 3.
The general equation of the circle for centre at (h, k) and radius r is given as (x - h)² + (y - k)² = r².
Substitute the corresponding values to obtain,
(x - h)² + (y - k)² = r²
=> (x - (-4))² + (y - (-1))² = 3²
=> (x + 4)² + (y + 1)² = 9
=> x² + 8x + 16 + y² + 2y + 1 = 9
=> x² + y² + 8x + 2y + 8 = 0
Hence, the required equation for the circle is given as x² + y² + 8x + 2y + 8 = 0.
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How many terms are in this expression?
2 + 8u + 7v
Answer:
There are three terms in this expression: 2, 8u, and 7v. A term is a value or variable (or a combination of values and variables) that is separated from other terms by a plus or minus sign. In this expression, 2 and 8u are constants, while 7v is a variable.
How to Graph y-2=2/3(x+4)
Answer:
Step-by-step explanation:
To graph the equation y-2=2/3(x+4), you can follow these steps:
Begin by isolating the y term on one side of the equation. To do this, you can add 2 to both sides of the equation:
y-2+2=2/3(x+4)+2
y=2/3(x+4)+2
Next, you can simplify the right side of the equation by multiplying 2/3 by (x+4):
y=2/3(x+4)+2
y=(2/3)x+(2/3)4+2
y=(2/3)x+8/3+2
y=(2/3)x+14/3
This is the standard form of the equation y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=2/3 and the y-intercept is b=14/3.
To graph the equation, you can use the slope and y-intercept to plot the first point on the graph. The y-intercept is the point where the graph crosses the y-axis, so you can plot the point (0,14/3) on the graph.
From this point, you can use the slope to find the next point on the graph. The slope is the change in y over the change in x, so you can use the slope to find the change in y and the change in x between two points on the graph. For example, you could choose a point that is 1 unit to the right of the y-intercept, or (1,0). The change in y between these two points is (14/3)-0=14/3 and the change in x is 1-0=1. Using the slope, you can find the y-coordinate of the next point on the graph:
y2=y1+m(x2-x1)
y2=14/3+2/3(1-0)
y2=14/3+2/3
y2=20/3
You can repeat this process to plot additional points on the graph. For example, you could choose a point that is 2 units to the right of the y-intercept
Kylie reads about two popular cell phone apps one app uses 1/2 of a phones storage space the other app uses 5/12 of a phone storage space Explain how Kylie can find the difference in the two storage space of the two apps without drawing a visual model
Answer:
5/12 phone uses less storage space
Step-by-step explanation:
Find a common denominator so you can compare the fractions easily. Use 12.
1/2 = 6/12
5/12 < 6/12, so now you can see that the phone that uses 5/12 of storage space uses less than the one that uses 1/2
You have averaged a score of 150 in the previous 12 bowling games and just bowled a 156. What score do you have to bowl in the next game to have an average of 152?
Group of answer choices
152
172
Below 150
Higher than 172
150
I need to score 172 in the 14th game to have an average of 152 in 14 games.
What is the weighted average?When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.
To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.
The total score of 12 games is (12×150) = 1800.
Again I scored 156 is the 13th game.
Let I score 'x' in the 14th game.
∴ (1800 + 156 + x)/12 + 1 + 1 = 152.
(1800 + 156 + x)/14 = 152.
(1956 + x)/14 = 152.
1956 + x = 2128.
x = 2128 - 1956.
x = 172.
So, I need to score 172 in order to have an average of 152 for 14 games.
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PLEASE HELP FAST WILL GE T BRAINLIEST!!
Answer:
Step-by-step explanation:
bro get some lighting in ur room and set it on a table,i cant even see what im lookking at ._.
Joe wants to purchase a new 4-wheeler that costs $18,550. He decides to get it in installments plants but needs to leave an 15.25% down payment. How much will the finance charge be if he has a monthly payment of $250 for 10 years? ROUND TO THE NEAREST CENT!
Rates, however, differ for specific customers depending on their credit score, loan term, and other factors.
How much is a finance charge?In conclusion, the finance charge formula is as follows:
Finance fee = Balance that is owed. Annual Percentage Rate (APR) / 365 Days in Billing Cycle.
The average cost of an ATV is between $5,000 and $15,000, with a down payment that is often between 10% and 20%.The typical deposit for recreational vehicles is in the range of 10% to 20%. You might need between $500 and $5,000 for the down payment for a UTV that ranges in price from $5,000 to $25,000.
Conventional ATV loans are provided by banks and credit unions for set terms that are typically between three and six years long. The yearly percentage rates are also fixed. Your credit score, the loan period, the cost of the ATV, and the company funding the loan will all have an impact on the APR.
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I’ll give BRAINLIEST if correct I need asap question is in the photo attached
The domain and range of the function will be Real number and [0, ∞). The parent function f(x) is get shifted down by 2 units.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = |x - h| + k
The function is given below.
g(x) = |x + 3|
The graph of the function g(x) is given below. From the graph, the domain and range of the function will be Real number and [0, ∞).
The parent function and translated function are given below.
f(x) |x| and h(x) = |x| - 2
The parent function f(x) is get shifted down by 2 units.
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1/2 (2x + 5) = 3/4 (x + 1) + 5/2 show your work!!:)
Answer: 0
Step-by-step explanation:
1/2(2x+5)=3/4(x+1)+5/2
distribute 1/2 to 2x and 5
distribute 3/4 to x and 1
1/4x+5/2=5/2
subtract 5/2 to 5/2
1/4=0
multiply 1/4 by the reciprocal
4/1*1/4=0*4/1
Answer= 0
assume that there is a party consisting of people between the ages of 18 and 24 inclusive. how many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? note: assume the range of birth years include 2 leap years. (
The minimum number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year is Three (3).
To find the number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year, we need to consider the number of possible birthdays that exist within the given age range (18 to 24 inclusive).
There are 12 months in a year, and each month has between 28 and 31 days (depending on the month). Therefore, there are a total of 12 * 31 = 372 possible birthdays within a given year.
There are 7 possible birth years within the given age range (18 to 24 inclusive), which means there are a total of 7 * 372 = 2596 possible birthdays within the given age range.
Since we want to guarantee that at least three people share the same birthday, we need at least 3 people to be at the party.
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Complete Question:
Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years.
At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables show the distribution responses?
answer choices
Graph i
Graph ii
Graph iii
Graph iv
Graph v
Graph ii shows that 150 people preferred eating ice cream from a cone, while 60 people preferred eating ice cream from a cup. There was no association between age and preferred method of eating ice cream.
Graph ii is a table that shows the distribution of responses to the survey about preferred method of eating ice cream. The table shows that out of the 210 people surveyed, 70 were adults and 140 were children. Of the 210 people surveyed, 150 indicated the cone as the preferred method of eating ice cream, while 60 indicated the cup as the preferred method. This table indicates that there is no association between age and preferred method of eating ice cream, as the responses were evenly distributed between adults and children. This information can be used to determine the preferences of customers at the ice-cream store and can help inform decisions about how to serve the ice cream. For example, the store may choose to provide more cones than cups based on the survey results. Additionally, this table can be used to compare the preferences of different demographic groups, although in this case the survey showed that there was no association between age and preferred method of eating ice cream.
Adults: 70 people surveyed, 35 preferred cone, 35 preferred cup
Children: 140 people surveyed, 115 preferred cone, 25 preferred cup
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NO LINKS!!!
Write an expression for the apparent nth term a_n of the sequence. (Assume that n begins with 1.)
a. 1, -1, 1, -1, 1, . . .
a_n =
b. -1, 2, 5, 8, 11, . . .
a_n =
a_n=
Answer:
[tex]\textsf{a)} \quad a_n=(-1)^{n-1}[/tex]
[tex]\textsf{b)} \quad a_n=3n-4[/tex]
Step-by-step explanation:
Sequence aGiven sequence:
1, -1, 1, -1, 1, ...
The given sequence is geometric since there is a common ratio of -1 between consecutive terms.
To find the common ratio of a geometric sequence, divide a term by the previous term:
[tex]\dfrac{a_5}{a_4}=\dfrac{1}{-1}=-1[/tex]
[tex]\dfrac{a_4}{a_3}=\dfrac{-1}{1}=-1[/tex]
[tex]\dfrac{a_3}{a_2}=\dfrac{1}{-1}=-1[/tex]
[tex]\dfrac{a_2}{a_1}=\dfrac{-1}{1}=-1[/tex]
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
a = 1r = -1Substitute the values of a and r into the formula to create an equation for the nth term:
[tex]\implies a_n=1 \cdot (-1)^{n-1}[/tex]
[tex]\implies a_n=(-1)^{n-1}[/tex]
Sequence bGiven sequence:
-1, 2, 5, 8, 11, ...
The given sequence is arithmetic since there is a common difference of 3 between consecutive terms.
To find the common difference of an arithmetic sequence, subtract consecutive terms:
[tex]a_2-a_1=2-(-1)=3[/tex]
[tex]a_3-a_2=5-2=3[/tex]
[tex]a_4-a_3=8-5=3[/tex]
[tex]a_5-a_4=11-8=3[/tex]
[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
a = -1d = 3Substitute the values of a and d into the formula to create an equation for the nth term:
[tex]\implies a_n=-1+(n-1)3[/tex]
[tex]\implies a_n=-1+3n-3[/tex]
[tex]\implies a_n=3n-4[/tex]
what are the coordinates of the centroid of ABC with vertices A (-3, 1), B (-2, 4), and C (5, -2)
Answer:
(0, 1/3)
Step-by-step explanation:
To find the centroid of a triangle with vertices A, B, and C, we can use the following formula:
centroid = (x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3
where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices A, B, and C, respectively.
In this case, we have A = (-3, 1), B = (-2, 4), and C = (5, -2), so the centroid of the triangle is:
centroid = ((-3) + (-2) + 5) / 3, (1 + 4 + (-2)) / 3 = (0, 1/3)
Therefore, the coordinates of the centroid of ABC are (0, 1/3).
In a population where 25% of voters prefer Candidate A, an organization conducts a poll of 9 voters. Find the probability that 2 of the 9 voters will prefer Candidate A.
(Report answer accurate to 4 decimal places.That is, round to 4 decimal places.)
The probability that 2 of the 9 voters will prefer Candidate A is 0.30033
Given that 25 % of voters prefer candidate A
Total number of voters = 9
Do we have to calculate the probability that 2 of the 9 voters will prefer Candidate A =?
In this question, we used binomial distribution to find the probability that 2 of the 9 voters will prefer candidate A.
The binomial distribution follows the probability mass function of:
⁹C₂ * (0.25) ² * (0.75)⁷ =>
⁹C₂ = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/ (7 * 6 * 5 * 4 * 3 * 2 * 1) (2 * 1) =>
⁹C₂ = 9 * 8/2 = 36
Now, 36 * (1/4)² * (3/4)⁷ = 0.30033
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The scale of map is 4m = 18mi
map : 6.8m
actual : ____ mi
Answer:
30.6
Step-by-step explanation:
18/4 = 4.5
4.5 × 6.8 = 30.6
сделайте пожалуйста 5 заданий из этих
Answer:
Step-by-step explanation:
how do you graph 16x-4=2
Step-by-step explanation:
Manage into slope interrupt form
16x = 4y + 2
4y = 16x - 2
Separate by 4
Y = 4x -1/2
Because the equating is undeviating, find 3 points and plot ruling class
(0, -1/2), (1, 3.5), (-1, -4.5)
And last, set a limit through bureaucracy
Answer:
MC donalds is a scam
Step-by-step explanation: THEY KILL BABY CHICKENS THE ANSWER IS
Make it into slope intercept form
16x = 4y + 2
4y = 16x - 2
Divide by 4
Y = 4x -1/2
Since the equation is linear, find 3 points and plot them
(0, -1/2), (1, 3.5), (-1, -4.5)
And lastly, draw a line through them
Which BEST describes the decimal form of a rational number?
Responses
A either terminates in 0's or repeats. either terminates in 0's or repeats.
B eventually repeats a non-zero digit eventually repeats a non-zero digit
C neither terminates nor repeat sn either terminates or repeats
D always terminates in 0's
Answer:
Step-by-step explanation:
A.) either terminates in 0's or repeats.
Some decimals repeat and some decimals don't.
write the equation of the line that crosses the y-axis at "-2" and has a slope of 2/3
The slope intercept form of equation of required line is
[tex]y = \frac{2}{3}x - 2[/tex]
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Slope of the required line = [tex]\frac{2}{3}[/tex]
The line passes through (0, -2)
Equation of the required line =
[tex]y - (-2) = \frac{2}{3}(x - 0)\\y + 2 = \frac{2}{3}x\\y = \frac{2}{3}x-2[/tex]
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A tree casts a shadow 21 m long. The angle of elevation of the sun is 51. What is the height of the tree?
13.2m
25.9 m
17m
16.3m
The height of the tree would be 25.9 meters.
Option (B) is correct.
What is the tangent ratio in trigonometry?
The ratio of the opposite side of a right triangle to the adjacent is called the tangent and is given the symbol tan.
tan = Opposite side/Adjacent side
A tree casts a shadow 21 m long. The angle of elevation of the sun is 51.
In the given figure, Apply the tangent ratio
tan51° = AB/BC
1.23 = h/21
h = 1.23 * 21
h = 25.9 m.
Hence, the height of the tree would be 25.9 meters.
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Solve the system of equations graphed on
the coordinate axes below.
y=-3x - 5
y =4/3x-5
Placing a point at the graph's y-intercept offor the equation (0,-5).
How to solve the system of equations graphed?Placing a point at the graph's y-intercept of -4 for the equation y =3x - 5 (0,-5). From the point (0,-5) go one down, three to the right, and then add another point because the slope is -5The two points may be connected by drawing a line using a straightedge. Keep going after the two points. Past them, continue the line.same for y = 4/3x-5. Place a point at since the y-intercept is at 2, (0,-5). Since the slope is 4/3, go up 4and to the right 3 before drawing a second point from (0,-5). The two points may be connected by drawing a line using a straightedge. Don't, once more, end at the two points. Past them, continue the line.To learn more about graph's y-intercept refer to:
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HELP PLEASE
Look at the picture below
Answer:
a) TPR
b) NM
c) x=6
Step-by-step explanation:
a) since the angle K is the middle letter on in the first triangle, the second triangle's middle letter will be P since they correspond
b) TR is congruent to NM because if you flipped TR upside down, it would match directly with NM
c) 4x-3=21
4x=24
x=6
this is because TR and NM are congruent, so 4x-3 is equal to 21
What is 99 to the power of 74?
Answer:
4.75340042E147
Step-by-step explanation:
Paul pays the newspaper company 70% of what he collects how much would he keep for himself in a month when he collected 450.00
Answer:
135.00
Step-by-step explanation:
since,he pays 70% then he keeps 30%.
and 30% of 450.00 is 135.00
g which of the following is the most effective way to describe multivariate relationships? group of answer choices schedules graphs equations schedules and graphs
The most effective way to describe multivariate relationships is by means of graphs and multiple variables.
The term "multivariate analysis" refers to a broad variety of statistical methods, not simply one particular approach. These methods enable you to comprehend your data more thoroughly in light of particular commercial or real-world settings.
Multivariate analysis is therefore a key idea to understand if you're wanting to be a data analyst or data scientist.
The breadth of knowledge that multivariate analysis offers is its one key benefit. The insights you find are far more applicable to the actual world because you're drawing a lot more thorough picture of what's happening when you explore numerous factors.
There are two different kinds of multivariate analytic techniques: interdependence techniques, which examine the structure of a dataset, and dependency techniques, which examine the cause-and-effect interactions between variables.
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As a result, multivariate analysis is a crucial concept to comprehend if you wish to work as a data analyst or data scientist.
The main advantage of multivariate analysis is the breadth of knowledge it provides. Since you're looking at many different elements, you're getting a much more complete picture of what's going on, which makes the insights you discover much more applicable to the real world.
There are two major categories of multivariate analytic approaches: dependency techniques, which look at the cause-and-effect relationships between variables, and interdependence techniques, which look at the dataset's structure.
helpppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
d ≈ 11.4 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 5, 1 ) and (x₂, y₂ ) = (6, - 2 )
d = [tex]\sqrt{(6-(-5))^2+(-2-1)^2}[/tex]
= [tex]\sqrt{(6+5)^2+(-3)^2}[/tex]
= [tex]\sqrt{11^2+9}[/tex]
= [tex]\sqrt{121+9}[/tex]
= [tex]\sqrt{130}[/tex]
≈ 11.4 units ( to the nearest tenth )
Let f be a differentiable function, defined for all realnumbers x, with the following properties. Find f(x). Show yourwork.
i) f'(x)=ax2+bx
ii) f'(1)=6 and f"(1)=18
iii. =18
The differentiable function f with the given properties is [tex]f(x)=4x^3-3x^2+10[/tex].
What is a differentiable function:
A function with a differentiable value of one real variable is one whose domain contains a derivative. In other words, each interior point in the domain of a differentiable function's graph has a non-vertical tangent line.
The given properties for the differentiable function f are:
[tex](i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18[/tex]
From (i) we can get [tex]f''(x)=2ax+b[/tex]
By substituting (ii) in (i) we will get:
a+b=6 and 2a+b=18. By solving these two equations we will get the following:
a=12, b=-6.
We will integrate (i) on both sides, we will get:
[tex]f(x)=\frac{ax^3}{3} +\frac{bx^2}{2} +c[/tex] where c is the integration constant.
In this equation, we will substitute a,b.
[tex]f(x)=\frac{12x^3}{3} +\frac{-6x^2}{2} +c\\ \\ f(x)= 4x^3-3x^2+c[/tex]...................(iv)
Now we will substitute (iv) in (iii), and we will get:
[tex]\int\limits^2_1 {( 4x^3-3x^2+c)} \, dx =18\\ \\ (2^4-2^3+2c)-(1^4-1^3+c)=18\\ \\c=10[/tex]
Therefore [tex]f(x)=4x^3-3x^2+10[/tex].
Complete question:
Let f be a differentiable function, defined for all real numbers x, with the following properties. Find f(x). Show your work.
[tex](i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18[/tex]
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The charge-to tap time (m) for carbon steel in one type of open-hearth furnace is to be determined for each heat in a sample n. If the investigator believes that almost all times in the distribution are between 320 and 440, what sample size would be appropriate for estimating the true time to within 5 min confidence level of 95%
The sample size appropriate for estimating the true time to within 5 min confidence level of 95% is 139
How to solve for sample sizeWe have to get the range of the values in this distribution
The range is given as: 440 - 320
= 120
through the range rule, we would have to solve for the standard deviation
= 120 / 4
= 30
At the 95 percent level of confidence, the critical value of Z is solved as 1.96
To get the value of n which is the sample size, we would have to use the Margin of error formula
[tex]ME = z*\frac{sd}{\sqrt{n} }[/tex]
ME = 5
[tex]5 = 1.96 * \frac{30}{\sqrt{n} }[/tex]
n = 138.2976
n is approximately 139
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