Answers
Answer:
1) 8/15
Step-by-step explanation:
When dividing by a number, multiply by its reciprocal.
2/5 ÷ 3/4
2/5 × 4/3
8/15
Related Questions
[tex] \rm\frac{d}{dx} \left ( \bigg( \int_{1}^{ {x}^{2} {}{} } \frac{2t}{1 + { t}^{2} } dt\bigg) \bigg( \int_{ 1 }^{ lnx} \frac{1}{(1 + {t)}^{2} }dt \bigg)\right) \\ [/tex]
Answers
Applying the product rule gives
[tex]\displaystyle \frac{d}{dx}\int_1^{x^2}\frac{2t}{1+t^2}\,dt \times \int_1^{\ln(x)}\frac{dt}{(1+t)^2} + \int_1^{x^2}\frac{2t}{1+t^2}\,dt \times \frac{d}{dx}\int_1^{\ln(x)}\frac{dt}{(1+t)^2}[/tex]
Use the fundamental theorem of calculus to compute the remaining derivatives.
[tex]\displaystyle \frac{4x^3}{1+x^4} \int_1^{\ln(x)}\frac{dt}{(1+t)^2} + \frac{1}{x(1+\ln(x))^2}\int_1^{x^2}\frac{2t}{1+t^2}\,dt[/tex]
The remaining integrals are
[tex]\displaystyle \int_1^{\ln(x)}\frac{dt}{(1+t)^2} = -\frac1{1+t}\bigg|_1^{\ln(x)} = \frac12-\frac1{1+\ln(x)}[/tex]
[tex]\displaystyle \int_1^{x^2}\frac{2t}{1+t^2}\,dt=\int_1^{x^2}\frac{d(1+t^2)}{1+t^2}=\ln|1+t^2|\bigg|_1^{x^2}=\ln(1+x^4)-\ln(2) = \ln\left(\frac{1+x^4}2\right)[/tex]
and so the overall derivative is
[tex]\displaystyle \frac{4x^3}{1+x^4} \left(\frac12-\frac1{1+\ln(x)}\right) + \frac{1}{x(1+\ln(x))^2} \ln\left(\frac{1+x^4}2\right)[/tex]
which could be simplified further.
A study was conducted investigating the long-term prognosis of children who have suffered an acute episode of bacterial meningitis, an inflammation of the membranes enclosing the brain and spinal cord. Listed below are the times to the onset of seizure for 13 children who took part in the study [10]. In months, the measurements are: 0.10 0.25 0.50 4 12 12 24 24 31 36 42 55 96 60 Chapter 3 Numerical Summary Measures
(a) Find the following numerical summary measures of the data.
i. mean
ii. range
iii. median
iv. interquartile range
v. mode
vi. standard deviation
(b) Show that L.~,: 1 (x;- X) is equal to 0.
Answers
Answer:
I'll help you
Step-by-step explanation:
In the given set of data, mean is 0.352, range is 0.86, median is 0.31, interquartile range is 0.28, mode is 0.12 and 0.24, and standard deviation is 0.81.
What is a data set?A data set is a certain number of data given in any order.
Given, the measurements for 13 children are: 0.10, 0.25, 0.50, 0.4, 0.12, 0.12, 0.24, 0.24, 0.31, 0.36, 0.42, 0.55, 0.96.
By rearranging the data set in ascending order we get:
(0.10, 0.12, 0.12, 0.24, 0.24, 0.25, 0.31, 0.36, 0.4, 0.42, 0.50, 0.55, 0.96.)
1. Therefore, mean
= (0.10 + 0.25 + 0.50 + 0.4 + 0.12 + 0.12 + 0.24 + 0.24 + 0.31 + 0.36 + 0.42 + 0.55 + 0.96)/13
= 4.57/13
= 0.352
2. Therefore, range
= (0.96 - 0.10)
= 0.86
3. Therefore, median = 0.31
4. Here, median of the first half of the data set is
= Q₁
= (0.12 + 0.24)/2
= 0.18
Again, median of the second half of the data set is
= Q₃
= (0.42 + 0.50)/2
= 0.46
Therefore, the interquartile range
= (Q₃ - Q₁)
= (0.46 - 0.18)
= 0.28
5. Therefore, mode = 0.12, 0.24
6. Therefore, standard deviation is
= √[(x₁ - X)² + (x₂ - X)² + (x₃ - X)² + (x₄ - X)² + (x₅ - X)² + (x₆ - X)² + (x₇ - X)² + (x₈ - X)² + (x₉ - X)² + (x₁₀ - X)² + (x₁₁ - X)² + (x₁₂ - X)² + (x₁₃ - X)²]
Here, x₁, x₂,......, x₁₃ are given data set in ascending order.
X = mean of the given data set.
Therefore, standard deviation is
= √[(0.10 - 0.352)² + (0.12 - 0.352)² + (0.12 - 0.352)² + (0.24 - 0.352)² + (0.24 - 0.352)² + (0.25 - 0.352)² + (0.31 - 0.352)² + (0.36 - 0.352)² + (0.40 - 0.352)² + (0.42 - 0.352)² + (0.50 - 0.352)² + (0.55 - 0.352)² + (0.96 - 0.352)²]
= √[.064 + 0.054 + 0.054 + 0.013 + 0.013 + 0.01 + 0.0018 + 0.00006 + 0.0023 + 0.0046 + 0.023 + 0.039 + 0.37]
= √(.6488)
= 0.81
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what is the magnitude of an account of -218 Dollars
Answers
Hey there!
The magnitude of 218 will always be 218 because the absolute value of a positive number is always itself. The magnitude of -218 will be 218 as well because the absolute value of a negative number is the positive version of the number without the negative sign. You are essentially dropping or ignoring the negative sign.
Therefore, the magnitude of an account of -218 Dollars is 218 dollars
What is the measure of DE ? Would the correct answer be 5in
Answers
Answer:
I think it would be 5 I'm honestly not 100% sure though!
three notebooks and 4 binders are $9.00. two notebooks and 4 binders cost $8.00. how much does a binder cost?
Answers
Jackson weighed all of his pet guinea pigs and found the average weight to be 2.4 pounds. If the standard error of the sample mean was 0.2227 and the sample standard deviation was 0.63 pounds, how many guinea pigs does Jackson have
Answers
Using the Central Limit Theorem, it is found that Jackson has 8 guinea pigs.
What does the Central Limit Theorem state?It states that the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], in which [tex]\sigma[/tex] is the standard deviation of the population.
In this problem, we have that [tex]s = 0.2227, \sigma = 0.63[/tex], hence we solve for n to find the number of guinea pigs that he has.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.2227 = \frac{0.63}{\sqrt{n}}[/tex]
[tex]0.2227\sqrt{n} = 0.63[/tex]
[tex]\sqrt{n} = \frac{0.63}{0.2227}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{0.63}{0.2227}\right)^2[/tex]
[tex]n = 8[/tex]
Jackson has 8 guinea pigs.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
A news organization interested in chronicling winter holiday travel trends conducted a survey. Of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays. Of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays. Construct a 99% confidence interval for the difference in population proportions of people in the eastern half of a country who fly to visit family members for the winter holidays and people in the western half of a country who fly to visit family members for the winter holidays. Assume that random samples are obtained and the samples are independent. (Round your answers to three decimal places.) z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576
Answers
Answer:
(-0.481 , -0.144)
Step-by-step explanation:
Confidence Interval for difference is proportion formula is given as:
p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]
For p1
Of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays.
n1 = 96 people
p1 = x/n
x = 42 people
p1 = 42/96
= 0.4375
1 - p1 = 0.5625
For p2
Of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays.
n2 = 108 people
p2 = x/n
x = 81 people
p2 = 81/108
= 0.75
1 - p2 = 0.25
99% confidence interval = 2.576
p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]
= 0.4375 - 0.75 ± 2.576 ×√[0.4375(1 -0.4375)/96 +0.75 (1 - 0.75)/108]
= -0.3125 ± 2.576 × √0.4375× 0.5625/96 + 0.75 × 0.25 /108
= -0.3125 ± 2.576 × √0.0025634766 + 0.0017361111
= -0.3125 ± 2.576 × √0.0042995877
= -0.3125 ±2.576 × 0.0655712414
= -0.3125 ± 0.1689115178464
Confidence Interval
-0.3125 - 0.1689115178464
= -0.4814115178
Approximately to 3 decimal places = -0.481
= -0.3125 + 0.1689115178464
= -0.1435884822
Approximately to 3 decimal places = -0.144
Therefore, the 99% confidence interval for difference in proportion = (-0.481 , -0.144)
A 50 foot rope weighing a total of 32 lbs extended over a cliff that is 35 feet to the ground. A large 8 pound bucket with 19 gallons of water was tied to the end of the rope at the ground. A group of hikers at the top of the cliff lifted the bucket by pulling up the rope, but when the bucket reached the top, only 12 gallons of water remained (the water spilled out steadily on the way up). If water weighs 8.3 lbs. / gallon. write a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground, and use it to find the work to get the bucket to the top of the cliff.
Answers
Answer:
A function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is [tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex] and the work to get the bucket to the top of the cliff is 3726 foot-lbs
Step-by-step explanation:
Work done to lift the rope by distance x feet:
[tex]W_1=32(\frac{50-x}{2})[/tex]
Work done to lift the bucket by distance x feet:
[tex]W_2=(19-\frac{x}{5})(8.3)x[/tex]
On reaching top 7 gallons of water spilled out so , on going up by x feet [tex]\frac{7x}{35}=\frac{x}{5}[/tex] gallons of water spilled out.
a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground:
[tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex]
Now the work to get the bucket to the top of the cliff i.e. x =35
[tex]W=16(50-35)+(19-\frac{35}{5})(8.3)(35)[/tex]
W=3726
Hence, a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is [tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex] and the work to get the bucket to the top of the cliff is 3726 foot-lbs
Triangle EFG has vertices E(–3, 4), F(–5, –1), and G(1, 1). The triangle is translated so that the coordinates of the image are E’(–1, 0), F’(–3, –5), and G’(3, –3).
Which rule was used to translate the image?
T4, –4(x, y)
T–4, –4(x, y)
T2, –4(x, y)
T–2, –4(x, y)
Answers
Answer:
T2, –4(x, y)
Step-by-step explanation:
Pre image has taken place ⇒ 2 units Horizontally right and 4 unit vertically down to obtain vertices of Image.
Hence, Answer = T2, –4(x, y)
~Lenvy~
Answer: T2, –4(x, y)
Step-by-step explanation:
right on edge 2023
Ok what is the time and how do I actually get this free trial lol
Answers
the time is only 9:30 and fine in it lol
what is -5½×2¾ ????
Answers
Answer:
Mixed fraction: -15 1/8
Improper fraction: 121/8
A rectangular table top has length 1.8 m and width 1.2 m.
A force of 600 N is applied to the whole table top.
Calculate the pressure in N/m2 to the nearest integer.
Answers
The equation of pressure is given by:
[tex]p = \frac{f}{s} [/tex]
where p is the pressure.
f is the applied force.
s is the surface area to which the force is applied.
I will start off by calculating the surface area of the table top given by:
[tex]s = l \times w = 1.8 \times 1.2 = 2.16[/tex]
s=2.16 m²
We know that f=400 N, that is given.
[tex]p = \frac{400 \: n}{2.16 \: m {}^{2} } [/tex]
Plug this on your calculator (excluding the units lol)
[tex]p = 185.185 \frac{n}{m {}^{2} } [/tex]
[tex]p = 185 \frac{n}{m {}^{2} } [/tex]
Question 44 of 44
Which of these is an optional deduction for money to be taken out of an
employee's paycheck?
A. Federal income tax
B. Medicare
C. Life insurance
D. Social Security
Answers
Answer : Life Insurance
Explanation : Have A Good Day
◊ YusuCr ◊
The optional deduction for money to be taken out of an employee's paycheck is life insurance.
Option C is the correct answer.
What is an employee's paycheck?An employee's paycheck is a document issued by an employer that lists the amount of money an employee has earned during a certain pay period and the amount of money that has been withheld for taxes, insurance, and other deductions.
It also includes the net amount of money that the employee is entitled to receive after all deductions have been made.
We have,
Life insurance is an optional deduction for money to be taken out of an employee's paycheck.
The other options listed (Federal income tax, Medicare, and Social Security) are typically mandatory deductions required by law.
Thus,
The optional deduction for money to be taken out of an employee's paycheck is life insurance.
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What is the slope of the line that passes through the points (9, 5)(9,5) and (21, 1) ?(21,1)? Write your answer in simplest form.
Answers
Answer:
i know this but do not lol
Step-by-step explanation:
Answer:
did u mean to put (9,5) and (21,1) in there twice? but if so ur answer is m= -1/3
TRY USING SYMBOLAB I USE ALL THE TIME
Parallel Lines and Transversals Find the measure of each angle indicated. Pls help me on these at least a couple of them I really need help I'll give brainliest if it is correct
Answers
Answer:
75°, 112°, 125°, 113°, 89°, 98°, 90°, 130°
Step-by-step explanation:
The marked angle pairs are one of ...
vertical angles -- congruentlinear pair -- supplementaryconsecutive interior -- supplementaryalternate interior -- congruentcorresponding -- congruentalternate exterior -- congruent1) vertical angles (congruent): ? = 75°
2) linear pair (supplementary): ? = 180° -68° = 112°
3) consecutive interior (supplementary): ? = 180° -55° = 125°
4) alternate interior (congruent): ? = 113°
5) corresponding (congruent): ? = 89°
6) alternate exterior (congruent): ? = 98°
7) alternate interior (congruent): ? = 90°
8) alternate interior (congruent): ? = 130°
_____
Additional comment
For parallel lines in general, all of the obtuse angles are congruent, and all of the acute angles are congruent. All of the obtuse angles are supplementary to the acute angles. (In (7), all angles are right angles, so all are congruent.) These facts can help you with problems like this one.
Learning the language (names/relationships) of these angles will be helpful to you in the future.
find three consecutive integers whose sum is 1266
Answers
Answer:
(x)t(xt1)t(xt2)=1266
Step-by-step explanation:
here here we will use the algebra to find three consecutive integers whose sum is 1266 we start by assigning x to the first integer since there are consecutive it means that the second number will be x plus 1 and the third will be x plus 2 they shall all add up to 1 2 6 6 therefore you can write the equation as a following
help is needed here please and thank you!
Answers
PLEASE HELP IM BEGGING YOU!!!
Find the value of x. Round angle measures to the nearest degree.
Answers
Answer:
61°Step-by-step explanation:
sin x = 29/33sin x =0.8787x = arcsin(0.8787)arcsin (0.8787) = 61.5°Correct choice is 61°
1. The full Renegade dance Jalaiah created is 56 seconds long. For a 15-second-long TikTok, what percent of Renegade is used?
Answers
Answer:
3.7
Step-by-step explanation:
You have to divide
Answer:
i do not know tbh .
Step-by-step explanation:
Question 2
A classroom has 15 girls and 11 boys.
(a) Find the ratio of boys to girls.
Answers
Answer:
11:15
Step-by-step explanation:
Please click on this picture and explain why I got this answer wrong
Answers
Answer: $79.12
Step-by-step explanation:
We have to find total amount that was paid for dinner
5 people each order was worth $12.80
Therefore, total bill = 12.80*5
= $64
Tax: 7.5%
Therefore, the bill after tax was:
[tex]=64(\frac{100+7.5}{100})\\= 64(1.075)\\[/tex]
Bill with tax = $68.8
Gratuity = 15.0% of bill with tax
Therefore, gratuity = 0.15 * 68.8
= $10.32
Ended up paying in total = Gratuity + Bill with tax
= $68.8 + $10.32
= $79.12
Find the LCD for the following pair of fractions 1/10 and 17/45
Answers
Answer:
Step-by-step explanation:
LCD: 90
10: 10, 20, 30, 40, 50, 60, 70, 80, 90
45: 45, 90
9/90 and 34/90
how many more grains of rice are in a fifty-pound bag of valencia rice than in a fifty pound bag of basmati rice
Answers
Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A fifty pound bag of basmati rice has 1.1 * 10³ grains in each ounce of 8 * 10² ounce and fifty pound bag of valencia rice has 1.2 * 10⁶ grains
Difference in number of grains = 1.2 * 10⁶ grains - (1.1 * 10³ grains * 8 * 10² ounce) = 3.2 * 10⁵ grains
Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice
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Help ! What do we know about the slopes of two lines if we are told that the lines are parallel?
Answers
Answer:
they have the same slope
Step-by-step explanation:
because if they are parallel they have the same slope
Please help with the attached file! Thank you
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
There is no 'y'. Your problem statement has a typo.
Pick any values of x you like. I find small integers are usually convenient. I also find a spreadsheet does repetitive evaluation very nicely. See the attached for an appropriate table.
y – 3(2y – 7) = 76
solve for Y!!
Answers
Answer:
y=-11
Step-by-step explanation:
Answer:
y = -11
Step-by-step explanation:
y – 3(2y – 7) = 76
y - 6y + 21 = 76
-5y + 21 = 76
-5y = 55
y = -11
Select the correct answer from the drop-down menu.
The design of a building that has a square pyramid roof as a roof is shown. The cost of material for the outside of the building and for the roof
ranges from $25 per square foot to $50 per square foot. The budget for this material is $500,000. The rectangular front of the building has a
length twice as long as its height. The slant height of the roof is the same as the height of the rectangular front of the building.
What is the maximum possible length of the rectangular front of the building to the nearest foot?
feet
The maximum possible length of the rectangular front of the building is
Answers
The maximum length of the rectangular front is the highest length of the rectangular front, and the value is 128.1 feet
How to determine the maximum possible length?Let the dimension of the rectangular front be x and y.
Such that:
y = 2x
So, the area of the rectangular front is:
A = xy
[tex]A = 2x^2[/tex]
The surface area of the pyramid roof is:
A = 4bh
Where:
b = base =25
h = height =18
So, we have:
[tex]A = 4* 25 * 18[/tex]
[tex]A = 1800[/tex]
The total surface area of the figure is:
[tex]T = 1800 +2x^2[/tex]
The range of the cost of material is: $25 per square foot to $50 per square foot.
So, the maximum cost is:
[tex]50 * (1800 +2x^2) = 500000[/tex]
Divide both sides by 50
[tex]1800 +2x^2 = 10000[/tex]
Subtract 1800 from both sides
[tex]2x^2 = 8200[/tex]
Divide both sides by 2
[tex]x^2 = 4100[/tex]
Take the square root of both sides
x = 64.03
Recall that:
y = 2x
So, we have:
y = 2 * 64.03
y = 128.06
Approximate
y = 128.1
Hence, the maximum possible length of the rectangular front of the building is 128.1 feet
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Answer: 82
Step-by-step explanation:
Let f be the continuous function defined on [-6,6]. Let g be the function given by g(x) = [tex]\int\limits^x_{-1} {f(t)} \, dt[/tex] . Write an equation for the tangent to the graph of g at x=4
Answers
Answer:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle g(x) = \int_{-1}^x f(t)\, dt[/tex]
And we want to write the equation for the tangent to the graph of g at x = 4.
First, determine g(4):
[tex]\displaystyle \begin{aligned} g(4) & = \int_{-1}^{(4)} f(t)\, dt \end{aligned}[/tex]
This is equivalent to the area of f from -1 to 4:
[tex]\displaystyle \begin{aligned} g(4) & = \frac{1}{2}(2)(3) + \frac{1}{2}(2)(-3)+\frac{1}{2}(-3+(-2))(1) \\ \\ & = \frac{1}{2}(6-6-5) \\ \\ & = -\frac{5}{2}\end{aligned}[/tex]
Note that areas under the x-axis are negative.
Find g'(4):
[tex]\displaystyle \begin{aligned} g'(x) = \frac{d}{dx}\left[ \int_{-1}^x f(t)\, dt\right]\end{aligned}[/tex]
By the Fundamental Theorem of Calculus:
[tex]\displaystyle \begin{aligned} g'(x) & = f'(x) \\ \\ g'(4) & = f'(4) \\ \\ & =1 \end{aligned}[/tex]
Note f is a line for 3 < x < 6 with a slope of 1.
Therefore:
[tex]\displaystyle \begin{aligned} h(x) -g(x_1) & = g'(x_1)(x-x_1) \\ \\ h(x) - \left(-\frac{5}{2}\right) & = (1)(x-(4)) \\ \\ h(x)& = (x-4) - \frac{5}{2} \\ \\ & = x - \frac{13}{2}\end{aligned}[/tex]
In conclusion, the equation of the tangent line is:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
Find a third degree polynomial with the given zeros and a leading coefficient of 4. 1/2, 3/2, 2
Answers
Answer:
[tex]4x^3-16x^2+19x-6[/tex]
Step-by-step explanation:
P(x)=a(x-r1)(x-r2)(x-r3)
This is a third degree polynomial of leading coefficient a, where r1, r2 and r3 are the roots.
So just replace it with the values you are asked for :
[tex]4\left(x-\frac{3}{2}\right)\left(x-\frac{1}{2}\right)\left(x-2\right)\\[/tex]
Then expand and you will find the answer : [tex]4x^3-16x^2+19x-6\\[/tex]
A hypothesis test in which rejection of the null hypothesis occurs for values of the
point estimator in either tail of the sampling distribution is called
a. The null hypothesis
b. The alternative hypothesis
c. A one-tailed test
d. A two-tailed test