Use the midpoint rule with the given value of n to approximate the integral. (Round your answer to four decimal places.)
16
0
sin
x
dx, n = 4
Answers
Split up [0, 16] into 4 equally-spaced subintervals of length [tex]\frac{16-0}4=4[/tex],
[0, 16] = [0, 4] U [4, 8] U [8, 12] U [12, 16]
with midpoints 2, 6, 10, and 14, respectively.
Then with the midpoint rule, we approximate the integral to be about
[tex]\displaystyle \int_0^{16} \sin(\sqrt x) \, dx \approx 4 \left(\sin(\sqrt2) + \sin(\sqrt6) + \sin(\sqrt{10}) + \sin(\sqrt{14})\right) \approx \boxed{4.1622}[/tex]
Related Questions
Geometry and Modeling:
Mike completely filled the container shown below with 616 small cubes that were each [tex]\frac{1}{2}[/tex] inch long.
Part A: Calculate the volume of the prism.
Part B: Crate a graphical model of a prism with base 5.5 by 3.5 that has the same volume as Part A.
Show how Mike can calculate the volume of the prism, in cubic inches, by using a volume formula instead of filling the container with small cubes.
Answers
What are the first five terms in the recursive sequence defined by the following? (only one is correct)
a1= 1
a2=1
an= an-2+an-1
a) {1,1,2,3,5}
b) {1,1,0,-1,-1}
c) {2,3,5,8,13}
d) {1,-1,2,-3,5}
Answers
Answer:
d 1-12-3-5 is the answer
Captain's Autos sells 22 used cars on
Monday, and 18 cars on Tuesday. This was
25% of the number of sales for the week.
How many cars did they sell altogether that
week
Answers
Answer:
160
Step-by-step explanation:
22 + 18 = 25 percent
40 = 25 percent
100 / 25 = 4
40 x 4 = 160.
Marin corporation had a projected benefit obligation of $3235000 and plan assets of $3474000 at January 1, 2020 . Marin also had a net acturial loss of $505740 in accumulated OCI at January 1, 2020.The average remaining service period of Marin's employees is 7.80 years . Compute Marin's minimum amortization of the actuarial loss. Minimum amortization of the actuarial loss
Answers
the minimum amortization is given as 20300 dollars
How to solve for the amortizationWe have the value of A to be $3235000
while we have the value of B to be $3474000
Of these two values the greatest or the highest is that of the option B.
Next we have to find the corridor value using 10 percent
0.10 * 3474000
= 347400
$505740 - 347400
= 158340
The number of years = 7.8
minimum amortization = 158340/7.8
= 20300 dollars
Hence the minimum amortization is given as 20300 dollars
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Find the volume of the figure
h=9.5', r=1.8'
Answers
Answer:
Volume=96.7
Step-by-step explanation:
V=πr^2h=
V=π·1.8^2·9.5=
96.69822
In pentagon ABCDE shown above, each side is 1 cm. If a particle starts at point A and travels clockwise 723 cm along ABCDE, at which point will the particle stop?
Answers
The particle will stop at D.
What is the fundamental principle of multiplication?If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
In pentagon ABCDE shown above, each side is 1 cm. If a particle starts at point A and travels clockwise 723 cm along ABCDE, then
Number of sides = 5
Let x be the one complete revolution.
5 x = 725
x = 145
Now, 145 - 2 = 143
Hence, it will stop at D which is 2 less than A.
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what is 4,928 will rounded to the nearest hundred
Answers
Answer:
4900
Step-by-step explanation:
When rounding a number such as 4928 to the nearest hundred, we use the following rules:
A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
In this case, Rule B applies and 4928 rounded to the nearest hundred is:
4900
Answer:
Step-by-step explanation:
4,928, look at the last two numbers 28 if they are above 50 you round up, if below 50 round down,
The answer is 4,900
ASAP HELP ME WITH THIS QUESTION
Answers
11 units * scale factor of 6 = 66 units
need heeeelp please
Answers
Answer:
x = 1.086
Step-by-step explanation:
Formula
6^x = 7 Take the log of both sides.
Solution
log 6^x = log 7 Bring the power down You are now dealing with log 6
x * log 6 = log 7 Divide by log 6
x = log 7/log 6
x = .8451 / .7782 Divide
Answer
x = 1.086
50 POINTS! Plot function h on the graph.
NO LINKS
Answers
See attachment for the graph of the piecewise function h(x)
How to plot the function?The function is given as:
h(x) = | -4, x < 3
| x + 5, x >= 3
The above function is a piecewise function.
It has 2 separate functions at two domains
This means that we plot the sub-functions in the piecewise function at their respective domain
See attachment for the graph of the piecewise function h(x)
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PLSSSSSSSS HELPPPPPP AYUDAAAAAAS
Answers
Answer:
(3+3) x (3+1)
Step-by-step explanation:
» (1 + 3) × (3 + 3)
» (4) × (6)
» 24
Here's our answer..!!
01
5. Solve the polynomial by typing it into a graphing calculator and identifying the zeros. Round to the nearest tenth.
5x^4-7x^3-5x^2+5x+1=0
Answers
Answer:
-0.8, -0.2, 0.8, 1.6
Step-by-step explanation:
pLEASE answer as fast as possible REALLY URGENT
Answers
Using proportions, it is found that you would expected the white counter to be chosen 128 times.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
From the table, the proportion of the white counter is given as follows:
p = 32/(32 + 18) = 32/50 = 0.64.
Hence, out of 200 trials, the number of trials in which the white counter is expected to be chosen is given by:
0.64 x 200 = 128 times.
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Carey's annual salary is $67 600 before tax.
How much is his weekly salary before tax?
[Assume 52 weeks in a year.]
Answers
Carey's weekly salary before tax is $1300.
What is the weekly salary before tax?The mathematical operation that would be used to determine the required value is division. Division is a mathematical operation that entails grouping a number into equal parts using another number.
In order to determine Carey's weekly salary before tax, divide the yearly salary by the number of weeks in a year.
Carey's weekly salary before tax = yearly salary / number of weeks in a year
$67,600 / 52 = $1300
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7
O x-3
O x-1
O x + 1
O x + 3
3
2-
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
3
N
3
I NEED HELP !!!!!
Answers
Answer:
x-1 gave ggs is it correct
Factors of the polynomial can be solved to get the zeros of the function (where the graph crosses the x-intercept). If we examine this graph we see that it crosses the x-int at 3, so 3 is a zero of the function. This would be (x-3) as a factor because when solved you get x = 3 (see below).
0 = x - 3
+3 +3
3 = x
Questions are in the pictures
Answers
The values of h and r to maximize the volume are r = 4 and h = 2
The formula for h in terms of rFrom the question, we have the following equation
2r + 2h = 12
Divide through by 2
r + h = 6
Subtract r from both sides of the equation
h = 6 - r
Hence, the formula for h in terms of r is h = 6 - r
Formulate a function V(r)The volume of a cylinder is
V = πr²h
Substitute h = 6 - r in the above equation
V = πr²(6 - r)
Hence, the function V(r) is V = πr²(6 - r)
The single critical pointV = πr²(6 - r)
Expand
V = 6πr² - πr³
Integrate
V' = 12πr - 3πr²
Set to 0
12πr - 3πr² = 0
Divide through by 3π
4r - r² = 0
Factor out r
r(4 - r) = 0
Divide through by 4
4 - r = 0
Solve for r
r = 4
Hence, the single critical point on the interval [0. 6] is r = 4
Prove that the critical point is a global maximumWe have:
V = πr²(6 - r)
and
V' = 12πr - 3πr²
Determine the second derivative
V'' = 12π - 6πr
Set r = 4
V'' = 12π - 6π* 4
Evaluate the product
V'' = 12π - 24π
Evaluate the difference
V'' = -12π
Because V'' is negative, then the single critical point is a global maximum
The values of h and r to maximize the volumeWe have
r = 4 and h = 6 - r
Substitute r = 4 in h = 6 - r
h = 6 - 4
Evaluate
h = 2
Hence, the values of h and r to maximize the volume are r = 4 and h = 2
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The average THC content of marijuana sold on the street is 10.5%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,
a. What is the distribution of X? X ~ N(
,
)
b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 8.9.
c. Find the 76th percentile for this distribution.
%
Answers
a. This information is given to you.
b. We want to find
[tex]\mathrm{Pr}\{X > 8.9\}[/tex]
so we first transform [tex]X[/tex] to the standard normal random variable [tex]Z[/tex] with mean 0 and s.d. 1 using
[tex]X = \mu + \sigma Z[/tex]
where [tex]\mu,\sigma[/tex] are the mean/s.d. of [tex]X[/tex]. Now,
[tex]\mathrm{Pr}\left\{\dfrac{X - 10.5}2 > \dfrac{8.9 - 10.5}2\right\} = \mathrm{Pr}\{Z > -0.8\} \\\\~~~~~~~~= 1 - \mathrm{Pr}\{Z\le-0.8\} \\\\ ~~~~~~~~ = 1 - \Phi(-0.8) \approx \boxed{0.7881}[/tex]
where [tex]\Phi(z)[/tex] is the CDF for [tex]Z[/tex].
c. The 76th percentile is the value of [tex]X=x_{76}[/tex] such that
[tex]\mathrm{Pr}\{X \le x_{76}\} = 0.76[/tex]
Transform [tex]X[/tex] to [tex]Z[/tex] and apply the inverse CDF of [tex]Z[/tex].
[tex]\mathrm{Pr}\left\{Z \le \dfrac{x_{76} - 10.5}2\right\} = 0.76[/tex]
[tex]\dfrac{x_{76} - 10.5}2 = \Phi^{-1}(0.76)[/tex]
[tex]\dfrac{x_{76} - 10.5}2 \approx 0.7063[/tex]
[tex]x_{76} - 10.5 \approx 1.4126[/tex]
[tex]x_{76} \approx \boxed{11.9126}[/tex]
If 5 bags weigh the same as 3 blocks, how many blocks will 9 bags weigh?
OA) 3 blocks
OB) 4.4 blocks
OC) 5.4 blocks
OD) 15 blocks
Answers
Answer: C. 5.4 Blocks
Step-by-step explanation:
Given information
5 bags = 3 blocks
Set variable
Let x be the number of blocks
Constructure proportional equation
[tex]\frac{3}{5} } ~=~\frac{x}{9}[/tex]
Cross multiply the fraction
[tex](3)~*~(9)~=~(5)~*~(x)[/tex]
[tex]27~=~5x[/tex]
Divide 5 on both sides
[tex]27~/~5~=~5x~/~5[/tex]
[tex]\Large\boxed{x=5.4~blocks}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
oc
Step-by-step explanation:
5 times .6 equals 3
9 times .6 equals 5.4
after henry gave away 2/3 of his stamps and ken gave away 3/4 of his the two boys had an equal number of the stamps left. they had 1156 stamps at first how many stamps did they have left altogather
Answers
Answer:
See below.
If the correct sum is 1155, then Ken had 495 stamps, and Henry had 660 stamps.
Step-by-step explanation:
Henry had h stamps.
Ken had k stamps.
After giving away 2/3 of his stamps, Henry ended up with 1/3 of his stamps, or h/3.
After giving away 3/4 of his stamps, ken ended up with 1/4 of his stamps, or k/4.
h/3 = k/4
h + k = 1156
4h = 3k
h = 1156 - k
4(1156 - k) = 3k
4624 - 4k = 3k
4624 = 7k
k = 4624/7
Stamps left: 0.25 × 4624/7 = 1156/7
h = 1156 - k
h = 1156 - 4624/7
h = 8092/7 - 4624/7
h = 3468/7 =495.43
Stamps left: 1/3 × 3468/7 = 1156/7
Total number of stamps left: 1156/7 + 1156/7 = 2312/7 = 330.29
The problem is solved correctly, but the numbers given must be incorrect since you cannot have a fraction of a stamp.
In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1360 U.S. adults (selected randomly) during 2020 revealed that 626 had never smoked cigarettes. Using α = 0.05, test whether there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes. State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.
Answers
Using the z-distribution, it is found that since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is still of 44%, that is:
[tex]H_0: p = 0.44[/tex]
At the alternative hypothesis, it is tested if the proportion is now different of 44%, that is:
[tex]H_1: p \neq 0.44[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.44, n = 1360, \overline{p} = \frac{626}{1360} = 0.4603[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.4603 - 0.44}{\sqrt{\frac{0.44(0.56)}{1360}}}[/tex]
z = 1.51
What is the p-value and the conclusion?Using a z-distribution calculator, for a two-tailed test, as we are testing if the proportion is different of a value, with z = 1.51, the p-value is of 0.1310.
Since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.
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A machine is programmed to run an algorithm for 972 hours starting at 9 A.M. on Monday. When will the machine stop running the algorithm.
A) 9 A.M. on Saturday
B) 9 P.M. on Saturday
C) 9 A.M. on Sunday
D) 9 P.M. on Sunday
Answers
Using proportions, it is found that the correct option for when the machine will stop running the algorithm is:
B) 9 P.M. on Saturday.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The algorithm runs for 972 hours. Each day has 24 hours, hence we apply the proportion to find the number of days as follows:
972/24 = 40.5 days.
The remainder of the division of 40.5 by 7, as a week has 7 days, is of 5.5, which means that the code will finish running 5.5 days after the 9 A. M. Monday, that is at 9 P. M. on a Saturday, which means that option B is correct.
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hey can you help me answer this question by giving me the answer?
Answers
The value of f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].
Given a function f(x)=4-2x+6[tex]x^{2}[/tex].
We are told to find out the value of f(a), f(a+h) and [f(a+h)-f(a)]/hwhere h≠0.
Function is like a relationship between two or more variables expressed in equal to form.The value which we entered in the function is known as domain and the value which we get after entering the values is known as codomain or range.
f(a)=4-2a+6[tex]a^{2}[/tex] (By just putting x=a).
f(a+h)==[tex]4-2(a+h)+6(a+h)^{2}[/tex]
=4-2a-2h+6([tex]a^{2} +h^{2} +2ah[/tex])
=4-2a-2h+6[tex]a^{2} +6h^{2} +12ah[/tex]
=[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]
[f(a+h)-f(a)]/h=[[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]-(4-2a+6[tex]a^{2}[/tex] )]/h
=[tex](6a^{2} +6h^{2} -2a-2h+12ah)/h[/tex]
=[tex](6h^{2} -2h+12ah)/h[/tex]
=6h+12a-2.
Hence the value of function f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].
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Question 8
Ben decides to build a rabbit run to keep his children's rabbits in. The run will be
rectangular with a width of 4 m. He has a maximum of 34 m of fencing to use, but
wants the area to be greater than 50 m². Find the range of values for the length of
the run, using inequalities.
Answers
2(4) + 2x <= 34
AreA
4x > 50
—-> x > 12.5
From perimeter inequality:
2x <= 34-8
—> 2x <= 26
—> x <= 13
So the range for the length
Is
12.5 < x <= 13
Consider the given statement.
If it is not Monday, then there are students in the gym.
For each statement below, determine whether it is equivalent to the given statement, the negation of the given statement, or neither of these.
Statement Equivalent Negation Neither
It is not Monday and there are not students in the gym.
It is Monday or there are students in the gym.
If there are not students in the gym, then it is Monday.
There are not students in the gym or it is not Monday.
Answers
Answer:
NegationStatementEquivalentNeitherStep-by-step explanation:
If it is not Monday, then there are students in the gym.
Negation: It is not Monday and there are not students in the gym.
Statement: It is Monday or there are students in the gym.
Equivalent: If there are not students in the gym, then it is Monday.
Neither: There are not students in the gym or it is not Monday.
The data to the right represent the cost of living for 20 states. The cost of living is a measure of the average price paid for housing, utilities, groceries, healthcare, transportation, and miscellaneous expenses. The national average cost of living is 100. The data can be used to compare a state to the national average and to other states.
Answers
The frequency distribution based on the information given is illustrated below.
What is the frequency distribution of table?A frequency distribution table is the
chart that summarizes all the data under two columns - variables/categories, and their frequency.
It should be noted that the distribution table has two or three columns and the first column lists all the outcomes as individual values or in the form of class intervals, depending upon the size of the data set.
Given the above information the frequency distribution table is:
Cost of living Number of states
85.0 - 94.9 9
95.0 - 104.9 5
105.0 - 114.9 0
115.0 - 124.9 2
125.0 - 134.9 2
135.0 - 144.9 1
145.0 - 154.9 1
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Find the value of x.
Answers
Answer:
x = 106 degrees
Step-by-step explanation:
x + 104 + 40 + 110 = 360
x + 254 (No more 254)
- 254 (Again no more 254)
x = 106
Step by step.
Using supplementary angle theory I was able to find three of the interior angles. The 4th interior angle was found by subtracting the three known angles from 360, finding the 4th angle is 74.
So again we use supplementary angle to find the value of x.
180 - 74 = 106
change the following fraction to a percent 4/50
Answers
Answer:
For finding Percentage u have to multiply the number with 100
e.g.,
[tex] \frac{4}{50} \times 100[/tex]
[tex]4 \times 2 = 8\%[/tex]
Hopefully this helps u...
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Riverbed company purchased a delivery truck for $33,000 on January 1, 2022 the truck has an expected salvage value of 2760 and he suspected to be driven 108,000 miles over estimated useful life of 10 years actual miles driven was 16,000 802,022 and 12,000 602,023 how much is the depreciation expense per mile
Answers
Answer:
0.28
Step-by-step explanation:
Depreciation Expense per mile:
= (Cost of delivery truck - Salvage value) ÷ Expected miles driver
=(33000-2760)÷108000=0.28 per mile
A radar unit is used to measure speeds of cars on a miter way the speed are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr what is the probability that’s a car picked at random is traveling at more than 100 km/hr
Answers
Using the normal distribution, there is a 0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 90, \sigma = 10[/tex]
The probability that’s a car picked at random is traveling at more than 100 km/hr is one subtracted by the p-value of Z when X = 100, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 90}{10}[/tex]
Z = 1
Z = 1 has a p-value of 0.8413.
1 - 0.8413 = 0.1587.
0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.
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Two cyclists start at the same point and travel in opposite directions. One cyclist travels 5 faster than the other. If the two cyclists are 74 miles apart after 2 hours, what is the rate of each cyclist?
Answers
The rate of the slower cyclist is 16 mph while the rate of the faster cyclist is 21 mph.
How to calculate the rate of speed?let us assume the following;
x = rate of slower cyclist
x + 5 = rate of faster cyclist
We know that formula for distance is;
distance = travel time*rate
Thus;
2x + 2(x + 5) = 74
Since the two cyclists are a distance of 74 miles apart after a time 2 hours. Thus;
2x + 2x + 10 = 74
4x + 10 = 74
4x = 74 - 10
4x = 64
x = 64/4
x = 16
Rate of faster cyclist = 16 + 5 = 21 mph
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