Answer:
Recognize objects
Consider the following function. x6 1 + x2 dx (a) Determine an appropriate trigonometric substitution. Use x = sin(θ), where − π 2 ≤ θ ≤ π 2 , since the integrand contains the expression 1 + x2 . Use x = tan(θ), where − π 2 < θ < π 2 , since the integrand contains the expression 1 + x2 . Use x = sec(θ), where 0 ≤ θ < π 2 or π ≤ θ < 3π 2 , since the integrand contains the expression 1 + x2 . (b) Apply the substitution to transform the integral into a trigonometric integral. Do not evaluate the integral. x6 1 + x2 dx = dθ
Answer:
Step-by-step explanation:
In the first part, we are given the function:
[tex]\int \dfrac{x^6}{\sqrt{1+x}^2} \ dx[/tex]
Suppose we make x = tan θ
Then dx = sec² θ.dθ
[tex]= \int \dfrac{tan^6 (\theta)}{\sqrt{1+ tan ^2 \theta }}* dx[/tex]
[tex]= \int \dfrac{tan^6 (\theta)}{\sqrt{1+ tan ^2 \theta }}* sec ^2 (\theta) * d\theta[/tex]
Since; sec² θ - tan² θ = 1
sec² θ = 1+ tan² θ
[tex]sec \ \theta = \sqrt{1 + tan^2 \ \theta}[/tex]
∴
[tex]= \int \dfrac{tan^6 (\theta)}{sec \ \theta}* sec ^2 (\theta) * d\theta[/tex]
[tex]= \int tan^6 (\theta)* sec (\theta) * d\theta[/tex]
Thus; In the first part, Use x = tan θ, where [tex]- \dfrac{\pi}{2} < \theta <\dfrac{\pi}{2}[/tex], since the integrand comprise the expression [tex]\sqrt{1+x^2}[/tex]
From the second part by using substitution method;
[tex]\int \dfrac{x^6}{\sqrt{1+x^2}} \ dx = \int \mathbf{tan^6(\theta) * sec ( \theta) } \ d \theta[/tex]
HELPPP
Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be 17.
Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine.
15, 18, 30, 30, 30, 30, 34, n, 150
What is the value of n that will make the IQR of the data set equal to 172
Answer:
n = 78
Step-by-step explanation:
hope that helped!
How long will it take $3000 to earn $900 interest at 6% simple interest?
Answer:
5 years.
Step-by-step explanation:
3000x.06=180 interest per year.
900/180 =5 years.
What is the difference? complete the equation.
Answer:
-3/5
Step-by-step explanation:
Not sure.....................
PLEASE HELP ITS OVER DUE AND I NEED HELP PLEASE ILL GIVE BRAINLIEST TO CORRECT ANSWER. PLSSS ILL GIVE ALL MY POINTS IM DESPERATE
Answer:
i need to see all the answers but yeahStep-by-step explanation:
tan C-
I need help with this pleases help
Answer:
is 40/41 because is de answerv
HELPPP
Suppose that you head an insurance company. Your most popular insurance policy has a premium of $600 and a deductible of $1,000. This insurance policy provides your state’s minimum coverage of $30,000 for injury or death to one person, $50,000 for injury or death to two or more people, and $10,000 for damage to property, which is called 30/50/10 coverage.
Assume that, on average, 2 of your 100 customers have an accident every year. One of the accidents causes damage to property and the other causes injury or death to one person. Both drivers file for the maximum claims. After paying the claims, will your company still profit from the premiums collected in a year? Explain your answer
Answer:
Yes they will profit $22,000
Step-by-step explanation:
First find total money:
100 customers * $600 premium
= $60,000
add deductibles ($1000) because they are paying for the accident:
=$62,000
Then find the subtractions:
"One of the accidents causes damage to property and the other causes injury or death to one person."
based on the 30/40/10 coverage:
-$30,000 for injury or death to One person
-$10,000 for property damage
62,000 - 40,000 = 22,000
Overall profit : $22,000
I think I did that right...
The company will earn the profit of $22,000.
Profit= $22,000.
What is insurance deductible ?The amount you pay for covered health care services before your insurance plan starts to pay.
It is given that:
Most popular premium= $600
According to question there is estimation of 100 person
Total money = 100 customers * $600 premium
= $60,000
The deductible amount is $1000 because they are paying for the accident.
So, the deductible amount is= $2000
Total deductible amount =$62,000
As one of the accidents causes damage to property and the other causes injury or death to one person.
So, based on 30/40/10 coverage there will be:
-$30,000 for injury or death to One person-$10,000 for property damageSo, the profit will be: 62,000 - 40,000
= $22,000
Overall profit : $22,000
Learn more about insurance deductible here:
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For which equation is a = 4 not the solution?
9 a = 36
5 a = 54
8 a = 32
Answer:
nAnI
Step-by-step explanation:
The graph of f(x) = 3x2 – 5x – 22 passes through the point (0, –22) and one of its zeros is (–2, 0). What is the other zero of the function?
Step-by-step explanation:
this is your answer....
The other zero of the given function is [tex](\frac{11}{3}, 0)[/tex] .
How to find the x-intercept of a quadratic function ?Let us assume f(x) [tex]=ax^{2} +bx+c[/tex], then to find the x-intercepts of this quadratic equation, let y = 0, i.e. [tex]ax^{2} +bx+c=0[/tex]
How to find zeros of the given function ?Given, f(x)= [tex]3x^{2} -5x-22[/tex], whose one zero is (-2,0)
Now, to find the x-intercepts of the given quadratic equation, we have to take y = 0.
∴ [tex]3x^{2} -5x-22=0[/tex]
Now we have to solve this equation to find it's another zero.
[tex]3x^{2} -5x-22=0[/tex]
⇒ [tex]3x^{2} -(11-6)x-22=0[/tex]
⇒ [tex]3x^{2} -11x+6x-22=0[/tex]
⇒ [tex]x(3x-11)+2(3x-11)=0[/tex]
⇒ [tex](3x-11)(x+2)=0[/tex]
We know that, if multiplication of two terms is zero, then each of this term is seperately zero.
∴ [tex]3x-11=0[/tex] or [tex]x+2=0[/tex]
⇒ [tex]3x=11[/tex] or [tex]x=-2[/tex]
⇒ [tex]x=\frac{11}{3}[/tex] or [tex]x=-2[/tex]
So, another zero of the function is [tex](\frac{11}{3}, 0)[/tex].
Learn more about zeros of a quadratic equation here :
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Find the solution to the system of equations:
y - 4x = 8
y = 2 (2x +2)
Show work for brainliest
please solve for x and show work
Answer:
[tex]18 \times 14 = {(6x)}^{2} \\ {x}^{2} = \frac{18 \times 14}{36} = 7 \\ x = \sqrt{7} [/tex]
The sum of the digits of 1 874 (1 + 8 + 7 + 4) is equal to 20. How many natural numbers smaller than 10 000 have a sum of their digits equal to 34?
A. 8
B. 9
C. 12
D. 10
E. 11
ANSWER FAST AND NO FILES
The total of numbers smaller than 10,000 that have a sum of their digits equal to 34 is 8.
What numbers have a total sum of their digits equal to 34?Firstly, it is important to understand a number of at least 4 digits is required to have 34 by adding its digits. Now, from this principle find the possible numbers:
9997 = 349979= 349799 = 347999= 349988= 349898 = 348899 = 348989 = 34What is the total of numbers to get this result?The total numbers is 8.
Learn more about numbers in: https://brainly.com/question/17429689
Mr. Gill is draining his pool. The pump he is using changes the water level by −2 1/4 inches per hour. A stronger pump would drain the pool 2 1/2 times as fast. What would the change in water level be per hour if Mr. Gill used the stronger pump?
Answer:
-5.625 in/hour
Step-by-step explanation:
−2 1/4 * 2 1/2 = -5.625 in/hour
How many gallons of water does the shower
stream in 6 minuets (need lots of help lol) thanks ❤️❤️
Answer: The answer is 15 gallons. Hope this helped!
Step-by-step explanation:
Please need help will give brainliest
H(6) =.
The number in parentheses is the x value it will be equal to the y value.
When x = 6 the blue line is at y = 8
H(6) = 8
Which postulate describes that AABC – ADEF?
A)
AA
B)
ASA
C)
SAS
D)
SSS
describe a set of Transformations that will move triangle A on the graph below to match up with triangle B
9514 1404 393
Answer:
reflection over y = 2.5translation left 1Step-by-step explanation:
The orientation of the triangle is reversed, so a reflection is required. Horizontal lines remain horizontal, but up/down are reversed, so the reflection is across a horizontal line. The horizontal line that is halfway between each point and its image is the line y = 2.5.
The x-coordinates of the image points are 1 less than the x-coordinates of the original, so a left shift of 1 unit is involved.
The two transformations to get from A to B could be (in any order) ...
reflection over the line y = 2.5translation left 1 unit__
The transformation can be summarized by ...
(x, y) ⇒ (x -1, 5 -y)
True or false : 5/6 and 35/36 are equivalent fractions
Answer:
False
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
Test the hypothesis that the average content of containers of a particular lubricant is 15 liters if the contents of a random sample of 15 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, 10.5,11.2,11.3 and 9.8 liters. Use a 0.01 level of significance and assume that the distribution of contents is normal.
Also find 95% confidence interval for the population mean. Interpret your results
Answer:
Kindly check explanation
Step-by-step explanation:
Given The samples:
X = 10.2, 9.7, 10.1, 10.3, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, 10.5,11.2,11.3, 9.8
Using a calculator ;
Sample mean, xbar = 10.27
Sample standard deviation, s = 0.462
H0 : μ = 15
H1 : μ < 15
The test statistic :
(xbar - μ) ÷ (s/sqrt(n))
(10.27 - 15) / (0.462/sqrt(15))
-4.73 / 0.1192878
= - 39.65
Using the Pvalue form Tscore, calculator, df = 14
Pvalue = 0.000001,
Since, Pvalue < α ; then we reject the Null
Confidence interval :
Xbar ± Margin of error
Margin of Error = Tcritical * s/√n
TCritical at 95%, df = 14
Margin of Error = 2.145 * 0.462/sqrt(15) = 0.2559
Lower boundary :
10.27 - 0.2559 = 10.0141
Upper boundary :
10.27 + 0.2559 = 10.5259
(10.0141 ; 10.5259)
The true population means should reside within the interval
the answer with an explanation please
Answer:
5C
6C
7D
8B
Step-by-step explanation:
5) C because median is the middle of the set of numbers source A median is 4 source B median is 6 and 4 is 2 less than 6.
6) C because there are 6 numbers altogether and 1 6s on a dice so 6+6 because we have two dice and 2 6s on both so 2/12 or simplified 1/6
7) D because mean is all the numbers add up divided by the amount of numbers so 20+25+30+20+30 = 125 and 125 ÷ 5 = 25
8 B because mean is all the numbers add up divided by the amount of numbers so
5+6+7+8+8+8+8+8+8+9+9 = 76 ÷ by 10 is 7.6
7+7+7+7+8+8+8+8+10+10 = 80 ÷ by 10 = 8
8 + 7.6 = 15.6 ÷ 2 = 7.8 and B is closest to 7.8
Helllllllllppppppppppppppppppppppppp
would the graph of the following function be discrete or continuous?
y = 15 + 3x
You flip a fair coin 32 times. About how many times would you expect heads to appear?
Answer:15 heads out of 30 is the most likely outcome when flipping 30 coins, if you run the same calculation with 14 or 16 heads you will get two equal, but smaller probabilities, same with 13 and 17 heads, and so on.
Step-by-step explanation:
Write and solve the equation that represents the sentence below. The product of 18 and a number is 109.8. Which statements are correct? Check all that apply. It can be solved by using the division property of equality. It can be solved by using the multiplication property of equality. The equation should be StartFraction x Over 18 EndFraction = 109.8. The equation should be 18 x = 109.8. The answer is 6.1. The answer is 1,976.4.
Answer:
the answer is a, d, e
Step-by-step explanation:
the product of 18 and a number is 109.8=
18n=109.8
to find n, you need to divided by 109.8 by 18. You will get 6.1
To check, replace c with 6.1.
18x6.1=109.8
Answer:
ade
Step-by-step explanation:
100 points please OMG HELP ME PLEASE I WILL DO ANYTHING I AM TIMED HELP MEEEEEEEEEEEEEEEE 5. Find the distance between the
points (3,9) and (8,-5)
Answer:
The answer is 14.86. I hope that this helps
Solve the following system of equations x-2y=14
X+3y=9
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Answer:
(x, y) = (12, -1)
Step-by-step explanation:
I find the simplest solution is often found using a graphing calculator.
(x, y) = (12, -1)
__
We notice that the coefficients of x are identical, so we can eliminate x by subtracting the first equation from the second.
(x +3y) -(x -2y) = (9) -(14)
5y = -5 . . . . simplify
y = -1 . . . . . divide by 5
x = 14 +2y = 14 +2(-1) . . . . using the first equation to find x
x = 12
The manager of a grocery store wants to determine the average amount of money spent at his store as it compares to the average dollar amount spent at his competitor's store. At the end of the day, he reviews the amounts of the last 15 grocery orders. The amounts rounded to the nearest dollar are: 41, 38, 19, 30, 21, 53, 34, 34, 37, 29, 50, 43, 57, 28, 50 He then visits the store of his competitor and surveys the first 15 people leaving the store with groceries. The amounts he records, also rounded to the nearest dollar, are: 86, 15, 75, 40, 51, 60, 27, 45, 112, 7, 65, 31, 18, 27, 69 What is the average amount of money spent at each store to the nearest cent
Answer:
The average spent at his store is of $37.60.
The average spent at his competitor's store is of $48.53.
Step-by-step explanation:
Average of a data set:
The mean of a data set is the sum of all values divided by the number of values.
His store:
15 orders.
Prices of: 41, 38, 19, 30, 21, 53, 34, 34, 37, 29, 50, 43, 57, 28, 50
The average is:
[tex]M = \frac{41 + 38 + 19 + 30 + 21 + 53 + 34 + 34 + 37 + 29 + 50 + 43 + 57 + 28 + 50}{15} = 37.6[/tex]
The average spent at his store is of $37.60.
Store of the competitor:
15 orders
Prices of: 86, 15, 75, 40, 51, 60, 27, 45, 112, 7, 65, 31, 18, 27, 69
The average is:
[tex]M = \frac{86 + 15 + 75 + 40 + 51 + 60 + 27 + 45 + 112 + 7 + 65 + 31 + 18 + 27 + 69}{15} = 48.53[/tex]
The average spent at his competitor's store is of $48.53.
Answer:
a) Manager's store: mean = $37.60
Competitor's store: mean = $48.53
b) Manager's store has a mean that is a better representation of the data because the competitor's data has an outlier of $112.
Step-by-step explanation:
used this for my test and it was correct.
(u + 4.5)(1.2) please help
What are the dimensions of this matrix?
2 x 1
2 x 2
1 x 1
1 x 2
Answer:
el primero es 2
el segundo es 4
el trersero es 1
y la última es 2
si multiplicas 2 x 1 y los otros el resultado sería
9
2 5/8 - 6 1/4 + 8 1/2
Answer:
2 5/8 - 6 1/4 + 8 1/2\
= 227 /8
Step-by-step explanation:
hope this helps :)