The limit as a definite integral on the interval [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π , 4π] is [tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex].
What is meant by definite integral?
A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.
Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.
If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.
Let the equation be
[tex]$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$[/tex]
substitute the values in the above equation, we get
= [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π, 4π],
simplifying the above equation
[tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex]
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What is the slope-intercept equation for the linear function represented by the
table?
Answer: y= 3/2x - 6
Step-by-step explanation:
The equation is y=mx + b
The y-intercept is when x = 0, so on the table y-intercept = -6
The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2
to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}[/tex]
now, the y-intercept occurs when x = 0, recheck the picture below.
Yuri and Trina sold boxes of cookies. Yuri sold 14 boxes, while Trina sold n boxes. Together, they sold a total of 37 boxes. Which equation represents the number of boxes Trina sold? How many boxes did she sell?(1 point)
n + 37 = 14; Trina sold 23 boxes.
n + 14 = 37; Trina sold 23 boxes.
.
n − 37 = 14; Trina sold 51 boxes.
n − 14 = 37; Trina sold 51 boxes.
Answer: n + 14 = 37; Trina sold 23 boxes
Step-by-step explanation:
Answer:
The equation that represents the number of boxes Trina sold is: n + 14 = 37.
To solve for n, we can subtract 14 from both sides of the equation:
n + 14 - 14 = 37 - 14
n = 23
Therefore, Trina sold 23 boxes.
Step-by-step explanation:
please help !
Find The Value Of X.
Answer:
x = 65 degrees
Step-by-step explanation:
Let's say z=the angle adjacent (next to) to the 145 degrees angle.
80 + x + z = 180 ==> 180 is the total number of degrees in a triangle
z + 145 = 180 ==> In addition, if you add up Angle z and 145
degrees, you get a straight line which totals to 180
degrees
z + 145 - 145 = 180 - 145 ==> solve for z
z = 35 degrees
80 + x + z = 180
80 + x + 35 = 180 ==> plug in 35 for z
80 + 35 + x = 180
115 + x = 180 ==> solve for x
115 - 115 + x = 180 - 115 ==> simplify
x = 65 degrees
he national flufferball association decides to implement a drug screening procedure to test its athletes for illegal performance enhancing drugs. 3% of the professional flufferball players actually use performance enhancing drugs. a test for the drugs has a false positive rate of 2% and a false negative rate of 4%. in other words, a person who does not take the drugs will test positive with probability 0.02. a person who does take the drugs will test negative with probability 0.04. a randomly selected player is tested and tests positive. what is the probability that she really does take performance enhancing drugs?
The probability is it that she actually uses performance-enhancing drugs is 0.5975.
Given that,
The national flufferball association makes the decision to put in place a drug testing programme to check its athletes for the use of illicit performance-enhancing substances. In reality, 3% of professional flufferball players abuse performance-enhancing substances. A drug test has a 2% false positive rate and a 4% false negative rate. Alternatively, a person who abstains from drug use has a 0.02 percent chance of testing positive. With a 0.04 probability, a person who uses the medications will test negative. A player is tested at random, and the results are positive.
We have to find how probable is it that she actually uses performance-enhancing drugs.
We know that,
The provided data is
P(D)=0.03
P(D')=1-0.03=0.97
P(T|D')= 0.02
P(T'|D)=0.04
P(T|D)=1-P(T'|D)=1-0.04=0.96
The probability that she really takes the drugs is,
P(D|T)=P(D)P(T|D)/P(D)P(T|D)+P(D')P(T|D')
P(D|T)=(0.03×0.96)/(0.03×0.96)+(0.02×0.97)
P(D|T)=0.5975
Therefore, The probability is it that she actually uses performance-enhancing drugs is 0.5975.
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This is a two part question. For the first blank, type the letter associated with with
the correct graph of this system. For the second blank, type the correct solution to
the system in point notation: (x,y).
Let
f(x) = (x + 2)² +3
g( )=2x+6
Answer: c
Step-by-step explanation:
Solve -12x-3x²=0 by factoring.
The solutions are x =
and x =
Answer:
Step-by-step explanation:
solve for x on a right triangle
A= 18x-2 B= 20 C= ?
The value of x will be;
⇒ x = 4
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
On a Right triangle,
⇒ A = 18x - 2 , B = 20 , C = ?
Now,
Since, On a Right triangle,
One angle is at 90 degree.
Hence, C = 90°
Since, A = 18x - 2 , B = 20 , C = 90°
Hence, We get;
⇒ 18x - 2 + 20 + 90 = 180
⇒ 18x - 2 + 110 = 180
⇒ 18x + 108 = 180
⇒ 18x = 180 - 108
⇒ 18x = 72
⇒ x = 4
Thus, The value of x will be;
⇒ x = 4
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How do you write 2 4/5 as a decimal?
Answer:
2.8
Step-by-step explanation:
Set aside the 2 for now.
Divide 4÷5=0.8 NOTE: Order Matters!!
Add: 2 + 0.8 = 2.8 (Just put the 2 to the Left of the decimal.)
eighty-four percent of non-teacher workers were employed in private schools. if a random sample of 200 non-teacher workers from private schools was selected, what is the probability that between 78% and 86% were non-teacher workers from private schools? eighty-four percent of non-teacher workers were employed in private schools. if a random sample of 200 non-teacher workers from private schools was selected, what is the probability that between 78% and 86% were non-teacher workers from private schools? 0.2798 0.7202 0.7695 0.2925 0.2305
The probability that between 78% and 86% were non-teacher workers from private schools is 0.7689
Eighty-four percent of non-teacher workers were employed in private schools.
p = 0.84
q = 1 - p = 1 - 0.84 = 0.16
if a random sample of 200 non-teacher workers from private schools was selected
We need to find the probability that between 78% and 86% were non-teacher workers from private schools.
n = 200
μρ = 0.84
αp = √(p(1 - p)/n) = √(0.84(0.16)/200) = 0.026
P(0.78 < P < 0.86) = P((0.78 - 0.84)/0.026 < (p - μp)/σp < (0.86 - 0.84)/0.026)
= P(-2.31 < z < 0.77)
= P(z < 0.77) - P(z < -2.31)
using z table
0.7794 - 0.0103
= 0.7689
Therefore, the probability that between 78% and 86% were non-teacher workers from private schools is 0.7689.
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Meena sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
53 visitors purchased no costume.
151 visitors purchased exactly one costume.
22 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase exactly one costume as a percent to the nearest whole number.
The probability that the next person will purchase exactly one costume is 67%.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
53 visitors purchased no costume.
151 visitors purchased exactly one costume.
22 visitors purchased more than one costume.
Total visitor = 53 + 151 + 22
= 226
Probability that the next person will purchase exactly one costume will be:
= Those with one custome / Total visitors × 100
= 151 / 226 × 100
= 67%
The probability is 67%.
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What is half of 1 1/3 cups?
Answer:
2/3
Step-by-step explanation:
4/3 or 1 1/2 divided by 2 is equal to 2/3
ompany x produces canned soup in batches of 100. they believe that the percent of defenctive cans of soup is 2%. if in 5 batches, the percent of defective cans were 3%, 8%, 1%, 2%, and 7%, how many of these fell outside of the upper or lower control limits for the proportion of defective cans of soup in the batch?
A process is said to be out of control if proportion of defective lies outside the control limits. Since 8% and 7% are outside our upper control limit (UCL) So, 2 batches are defective.
Given that,
100-piece batches of canned soup are produced by Company X. They estimate that there are 2% faulty soup cans in circulation.
We have to find how many of the 3%, 8%, 1%, 2%, and 7% defective can percentages in the five batches fell beyond the higher or lower control limits for the percentage of defective soup cans in the batch.
We know that,
LCL= p-3√(p(1-p)/n)
=0.02-3√(0.02(1-0.02)/100)
=-0.022
Since probability can not be negative.
LCL=0
UCL= p-3√(p(1-p)/n)
=0.02-3√(0.02(1-0.02)/100)
=0.062
Therefore. A process is said to be out of control if proportion of defective lies outside the control limits. Since 8% and 7% are outside our upper control limit (UCL) So, 2 batches are defective.
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what is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement? group of answer choices there is no distinction; both types of tests are used to analyze data on any scale of measurement. parametric tests are used for ordinal or interval data, whereas nonparametric tests are used for nominal data only. parametric tests are used for ordinal and nominal data, whereas nonparametric tests are used for interval and ratio data parametric tests are used for interval and ratio data, whereas nonparametric tests are used for nominal and ordinal data.
Key distinction between parametric tests and nonparametric tests in terms of scales of measurement is that parametric tests are used for interval and ratio data and non parametric tests are used for ordinal and nominal data.
i.e., the last given option.
For interval and ratio data, parametric tests are employed, while non-parametric tests are used for ordinal and nominal data
Data containing discrepancies or intervals are displayed in interval data.
The ratio data, which may be added to, subtracted from, multiplied by, or split, is the one in which statistical conclusions are used.
Ordinal data are measurements of quantitative data that are in order, such height and weight.
Nominal data are those that we measure quantitatively but do not require order or sequence, such as hair color or eye color.
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evaluate.(w2x 12)÷10⋅z when w=−4, x=2, and z=−5
The solution of the given equation (w² x 12) ÷ 10⋅z is obtained as (-0.64).
Explain the method of substitution?Three stages are involved in the substitution method: first, solve an equation for the one of the variables. Put this expression (or plug it in) into the other equation, then solve it. To identify the matching variable, rewrite the value's original equation.The stated equation is-
= (w² x 12) ÷ 10⋅z
The values are-
w = −4, x = 2, and z = −5, put in the equation-
= [(-4)² × 2)]/ [10 × -5 ]
= [16 x 2]/)-50)
= 32 / -50
= -0.64
Thus, the solution of the given equation (w² x 12) ÷ 10⋅z is obtained as (-0.64).
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If a shopkeeper made a profit of Rs100 by selling 10 pens, how much had the shopkeeper paid for buy one pen? ten pen =RS.1200
Answer:
Rs. 110Step-by-step explanation:
Details provided:Profit of Rs 100 by selling 10 pens.Selling price of 10 pens is Rs 1200.Solution:Given,
No. of pens the shopkeeper has = 10
Selling price of 10 pens = Rs. 1200
Profit made by selling them = Rs 100
So,
Actual price or Cost price of 10 pens
= Rs (1200 - 100)
= Rs 1100
Now,
Cost price for each pen
= [tex]\frac{Total cost of the pens}{No. of pens}[/tex]
= [tex]Rs \frac{1100}{10}[/tex]
= Rs 110
Hence,
The cost price for each pen the shopkeeper bought is Rs. 110 (Ans)
If the area of an equilateral triangle is
[tex]64 \sqrt{3} cm {}^{2} [/tex]
find its perimeter
The perimeter of the equilateral triangle is 48 cm
How to find the perimeter of an equilateral triangle?equilateral triangle
An equilateral triangle is a type of triangle in which all three sides are equal in length and all three angles are also equal, measuring 60 degrees each.
Given that: the area of an equilateral triangle is 64√3 cm²
The formula for the area of an equilateral triangle is given by:
A = (√3)/4 × a²
Where a is the length of the side
64√3 = (√3)/4 × a²
4 × 64√3 = (√3) × a²
4 × 64 = a²
a² = 4 × 64
a² = 256
a = √256
a = 16 cm
Perimeter of the equilateral triangle = a + a + a = 3a
Perimeter of the equilateral triangle = 3 × 16 = 48 cm
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Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?
Oy=x-2
Oy=x+2
Oy=x+3
Oy=x-5
Answer:
y = x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 1 , then
y = x + c ← is the partial equation
to find c substitute (5, 3 ), that is x = 5, y = 3 into the partial equation
3 = 5 + c ⇒ c = 3 - 5 = - 2
y = x - 2 ← equation of line
Solve pls brainliest
Answer:
A and C
Step-by-step explanation:
The angles and their images are congruent.
simplify value of 3a-2
Nothing further can be done with simplifying the given expression.
the nth term of this sequence: 1/2,4/3,9/4,16/5
URGENT
Answer: [tex]\frac{n^{2} }{n+1}[/tex]
Step-by-step explanation:
The numerator (top digit) are squares. For example,
1 is [tex]1^{2}[/tex]
4 is [tex]2^{2}[/tex]
9 is [tex]3^{2}[/tex]
and so on.
The bottom digit increases by one.
Therefore, the Nth term would be that number (N) squared on the numerator, and n+1 on the denominator.
fill in the numbers resulting from the indicated operation: 2 −1 −4 7 3 4 5 5 −1 2 1 −1 2 −1 −4 7
The numbers resulting from the indicated operation:
-1 2 1 -1
3 4 5 5
What is number?A number is a numerical value that is used to represent quantity. Hence, a number is a mathematical concept used to count, measure, and label. Thus, numbers form the basis of mathematics. A number is an arithmetic value used for representing the quantity and used in making calculations. Numericals are written symbols that represent numbers, such as "3." A number system is a writing system for representing numbers using digits or characters in a logical manner. Numbers are used to count, measure, and compare quantities. A number system is a set of symbols, or numerals, that are used to represent numbers.
Here,
The numbers resulting from the indicated operation:
-1 2 1 -1
3 4 5 5
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Answer:
-1 2 1 -1
3 4 5 5
identify the linear transformations from the list. group of answer choices is defined by . is defined by . is defined by . is defined by is defined by the derivative . is defined by
If f:RR, then Munkres' definition (f′(a) is a 11 matrix) is the definition of the derivative as it is presented in elementary calculus and real analysis. The linear map yf′(a)y must be defined as the derivative if the first definition from above must be used.
What is Derivative?The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value).
Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.
When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable.
The function closest to that input value is best approximated linearly by the tangent line. Because of this, the derivative is
According to our question-
The linear mapping Dfa:RmRn that obeys limh0f(a+h)f(a)Dfa(h)h2=0 is typically used to compute the derivative (or "total derivative") of a function f:RmRn at some point aRm.
both are true. If f:RR, then Munkres' formulation (f′(a) is an 11 matrix) is the definition of the derivative as taught in introductory calculus and real analysis. The linear map yf′(a)y must be defined as the derivative if the first definition from above must be used.
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simplify p=sqrt5.2^3
Answer:
11.857
Hope this helps!
Answer: p≈11.86
Step-by-step explanation:
[tex]p=\sqrt{5.2^3} \\\\p=\sqrt{5.2^2(5.2)} \\\\p=5.2\sqrt{5.2}\\\\p\approx5.2(2.28)\\\\p\approx11.86[/tex]
Which ratio is equivalent to 3/7
A) 6 to 10
B) 9:21
C) 12/35
D) 7 to 3
Answer: B 9:21
Step-by-step explanation:
9 reduces to three and 21 reduced to 7
approximate fx(3,5)fx(3,5) using the contour diagram of f(x,y)f(x,y) shown below.
The approximate of [tex]f_{x}(3,5)[/tex] ≈ 4
We have to find an approximate of [tex]f_{x}(3,5)[/tex] using the contour diagram, x and y, which was shown below. The slope of a second line is used to estimate the x and y direction. The curl f divides by the curl x is almost equal to the delta x. At the point of x, 13 is equal to 17 and 2 is equal to 18. The points are in a diagram. The curly f divides by curly x is equal to the delta f divided by delta x, which is 18 minus 17 divided by 2 minus 1. The value of a f is equal to 1. From here we can say that f of x 13 is equal to 1.
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How long will it take for $4600 to grow $29900 at an interest rate of 4.8% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
YALL PLS ANSWER ASAP, IM TAKING A TIMED ASSIGNMENT
It will take about 39 years for a principal of $4600 to grow to $29900 continuously compounded
Compound InterestCompound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
The formula to calculate compound interest is given as
A = P(1 + r/n)^nt
A = Pe^rt (Continuously compounded)
A = Final amountP = principalr = raten = number of times compounded t = timeLet's substitute the values into the formula and solve
29900 = 4600e^(0.048 * t)
t = 39 years
The time it takes to compound the principal to $29900 is approximately 39 years
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what performs all arithmetic operations (for example, addition and subtraction) and all logic operations?
An arithmetic logic unit (ALU) performs all arithmetic operations (for example, addition and subtraction) and all logic operations.
An arithmetic logic unit (ALU) is a digital circuit used to perform arithmetic and logic operations. It represents the fundamental building block of the central processing unit (CPU) of a computer. Modern CPUs contain very powerful and complex ALUs. In addition to ALUs, modern CPUs contain a control unit (CU).
Basic arithmetic and logical operations are carried out using an ALU. Addition, subtraction, multiplication, and division are a few examples of arithmetic operations.
Binary numbers, or 0 and 1, are used to store and modify every piece of data in computers. Since a switch has just two possible states—open or closed—transistor switches are used to alter binary numbers. An open transistor, through which no current flows, is equivalent to a 0. A closed transistor with a current flowing through it symbolizes a 1.
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Need a response bias question. So i have a Statistics project where I need to interview people at my school with a certain response bias question. Can anyone come up with any ideas?? also using random assignment or sample?
Answer:
Response bias would be something where answers would be skewed one way or another because of the way you asked. So maybe ask something embarrassing for someone to admit, like asking random students if they pick their nose. Some people will answer truthfully as no, and the people who do will likely also say no because they do not want to tell you that.
6. Leah is reading a book that is 646 pages long. She is currently on page
340. If she wishes to finish reading the book in the next 17 days and reads
the same number of pages each day, how many pages per day should she
read in order to meet her goal?
please helpits 7th grade math im just bad at math
Answer:
10
Step-by-step explanation:
the answer is 10 because of everything I did
