Split up the integral:
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]
For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get
[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]
and
[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]
Then
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
A. Combination.
B. 17020
Step-by-step explanation:
A. Determination whether it is permutation or combination.
From the question given above, we were told that the student body of 185 students wants to elect two (2) representatives.
This is clearly combination because it involves a selecting process (i.e selecting 2 out of 185).
NOTE: Combination involves selecting while permutation involves arranging.
B. Determination of the combination.
Total number of people (n) = 185
Number of chosen people (r) = 2
Number of combination (ₙCᵣ) =?
ₙCᵣ = n! / (n – r)! r !
₁₈₅C₂ = 185! / (185 – 2)! 2!
₁₈₅C₂ = 185! / 183! 2!
₁₈₅C₂ = 185 × 184 × 183! / 183! 2!
₁₈₅C₂ = 185 × 184 / 2!
₁₈₅C₂ = 185 × 184 / 2 × 1
₁₈₅C₂ = 34040 / 2
₁₈₅C₂ = 17020
The The Laplace Transform of a function , which is defined for all , is denoted by and is defined by the improper integral , as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of as a fixed constant) 1. Find (hint: remember integration by parts)
Answer:
a. L{t} = 1/s² b. L{1} = 1/s
Step-by-step explanation:
Here is the complete question
The The Laplace Transform of a function ft), which is defined for all t2 0, is denoted by Lf(t)) and is defined by the improper integral Lf))s)J" e-st . f(C)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of s as a fixed constant) 1. Find Lft) (hint: remember integration by parts) A. None of these. B. O C. D. 1 E. F. -s2 2. Find L(1) A. 1 B. None of these. C. 1 D.-s E. 0
Solution
a. L{t}
L{t} = ∫₀⁰⁰[tex]e^{-st}t[/tex]
Integrating by parts ∫udv/dt = uv - ∫vdu/dt where u = t and dv/dt = [tex]e^{-st}[/tex] and v = [tex]\frac{e^{-st}}{-s}[/tex] and du/dt = dt/dt = 1
So, ∫₀⁰⁰udv/dt = uv - ∫₀⁰⁰vdu/dt w
So, ∫₀⁰⁰[tex]e^{-st}t[/tex] = [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ - ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]
∫₀⁰⁰[tex]e^{-st}t[/tex] = [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ - ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]
= -1/s(∞exp(-∞s) - 0 × exp(-0s)) + [tex]\frac{1}{s}[/tex] [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰
= -1/s[(∞exp(-∞) - 0 × exp(0)] - 1/s²[exp(-∞s) - exp(-0s)]
= -1/s[(∞ × 0 - 0 × 1] - 1/s²[exp(-∞) - exp(-0)]
= -1/s[(0 - 0] - 1/s²[0 - 1]
= -1/s[(0] - 1/s²[- 1]
= 0 + 1/s²
= 1/s²
L{t} = 1/s²
b. L{1}
L{1} = ∫₀⁰⁰[tex]e^{-st}1[/tex]
= [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰
= -1/s[exp(-∞s) - exp(-0s)]
= -1/s[exp(-∞) - exp(-0)]
= -1/s[0 - 1]
= -1/s(-1)
= 1/s
L{1} = 1/s
Solve for a.
5a + 2 - 7-8 = 0
What is the root? If there is no root, choose none.
Answer:5
Step-by-step explanation: root5a+2 +7a-8 = 0
squaring both side
5a+2=7a-8
8+2=7a-5a
10=2a
a=5
Answer:
[tex]\sqrt{5a+2}-\sqrt{7a-8}=0[/tex]
Isolate a square root on the left-hand side
[tex]\sqrt{5a+2} =\sqrt{7a-}8+0[/tex]
Eliminate the radical :-
[tex]5a+2 = 7a-8[/tex]
Solve:-
[tex]2a -10 = 0[/tex]
Add 10 to both sides, then Divide both sides by 2:-
[tex]a = 5[/tex]
OAmalOHopeO
what is 5 2/3 - 11 1/6
Answer:
Check the photo for the answer
Find the length of BC again
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.
tan(61) = 47 / BC
BC = 47 / tan(61)
BC = 26.05 units
Hope this helps!
Answer:
BC = 26.05
Step-by-step explanation:
SOH CAH TOA
tan 61 = 47/BC
BC = 47/tan 61
A survey showed that, in one city, 20.7% of the population used
product X, 50% use product Y and among users Y, 36.5% use X. Randomized interview
However, a resident in that city, calculate the probability that that person
a) Use both X and Y;
b) Neither X nor Y
Answer:
Step-by-step explanation:
a) 0.5*0.365=18.25%
b) (100%-20,7%-50%)=29.3
The acceleration of car that comes from a velocity of 10m/s in distance of 25m is
Answer:
what is the time given ???
Step-by-step explanation:
either initial velocity is 0 or final velocity is zero
V=U+AT
converting it we get
V/T = u+a
V/T - U= a
where
v= final velocity
u= initial velocity
a= acceleration
t= time
plz write the full question
SOMEONE PLS HELP ME!!!
Answer:
No
Step-by-step explanation: Bye
An article describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from soil. Out of 155 seeds planted in soil containing 3% mushroom compost by weight, 74 germinated. Out of 155 seeds planted in soil containing 5% mushroom compost by weight, 86 germinated. Can you conclude that the proportion of seeds that germinate differs with the percent of mushroom compost in the soil
Solution :
Let [tex]p_1[/tex] and [tex]p_2[/tex] represents the proportions of the seeds which germinate among the seeds planted in the soil containing [tex]3\%[/tex] and [tex]5\%[/tex] mushroom compost by weight respectively.
To test the null hypothesis [tex]H_0: p_1=p_2[/tex] against the alternate hypothesis [tex]H_1:p_1 \neq p_2[/tex] .
Let [tex]\hat p_1, \hat p_2[/tex] denotes the respective sample proportions and the [tex]n_1, n_2[/tex] represents the sample size respectively.
[tex]$\hat p_1 = \frac{74}{155} = 0.477419[/tex]
[tex]n_1=155[/tex]
[tex]$p_2=\frac{86}{155}=0.554839[/tex]
[tex]n_2=155[/tex]
The test statistic can be written as :
[tex]$z=\frac{(\hat p_1 - \hat p_2)}{\sqrt{\frac{\hat p_1 \times (1-\hat p_1)}{n_1}} + \frac{\hat p_2 \times (1-\hat p_2)}{n_2}}}[/tex]
which under [tex]H_0[/tex] follows the standard normal distribution.
We reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance, if the P-value [tex]<0.05[/tex] or if [tex]|z_{obs}|>Z_{0.025}[/tex]
Now, the value of the test statistics = -1.368928
The critical value = [tex]\pm 1.959964[/tex]
P-value = [tex]$P(|z|> z_{obs})= 2 \times P(z< -1.367928)$[/tex]
[tex]$=2 \times 0.085667$[/tex]
= 0.171335
Since the p-value > 0.05 and [tex]$|z_{obs}| \ngtr z_{critical} = 1.959964$[/tex], so we fail to reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance.
Hence we conclude that the two population proportion are not significantly different.
Conclusion :
There is not sufficient evidence to conclude that the [tex]\text{proportion}[/tex] of the seeds that [tex]\text{germinate differs}[/tex] with the percent of the [tex]\text{mushroom compost}[/tex] in the soil.
5 oranges weigh 1.5 kg, 8 apples weigh 2 kg. What would be the total weight of 3 apples and 4 oranges?
Answer: oranges 1.2 Kg and apples 0.75 Kg.
Step-by-step explanation:
Oranges (4)(1.5)/5
Apples (3)(2)/8
A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 85% of the time if the person has the virus and 5% of the time if the person does not have the virus, (This 5% result is called a false positive.) Let A be the event "the person is Infected" and B be the event "the person tests positive", a) Find the probability that a person has the virus given that they have tested positive, l.e. find P(AB). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(AIB)= % b) Find the probability that a person does not have the virus given that they test negative, I.e. find P(A'B'). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A'B') =
This question is solved using the conditional probability concept.
Using this concept, we find that:
a) P(AIB)= 5.3%b) P(A'|B') = 99.9%First, the concept is presented.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]
In which
P(A|B) is the probability of event A happening, given that B happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(B) is the probability of B happening.
----------------------------------------------------
Question a:
For relation with the formula presented above, I will change events A and B.
Event A: Person is infected.
Event B: Positive test.
Probability of a positive test:
85% = 0.85 out of 1/300 (person has the virus).5% = 0.05 out of 299/300(person does not have the virus)Thus:
[tex]P(B) = 0.85\frac{1}{300} + 0.05\frac{299}{300} = \frac{0.85\times1 + 0.05\times299}{300} = 0.0527[/tex]
Probability of a positive test and the person is infected.
85% = 0.85 out of 1/300. Thus:
[tex]P(A \cap B) = \frac{0.85}{300} = 0.0028[/tex]
Desired probability:
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.0028}{0.0527} = 0.053[/tex]
0.053*100% = 5.3%, thus:
P(AIB)= 5.3%
---------------------
Question b:
Event A: Does not have the virus
Event B: Test negative.
Probability of a negative test:
100% - 85% = 15% = 0.15 out of 1/300 (person has the virus).100% - 5% = 95% = 0.95 out of 299/300(person does not have the virus)Thus:
[tex]P(B) = 0.15\frac{1}{300} + 0.95\frac{299}{300} = \frac{0.15\times1 + 0.95\times299}{300} = 0.9473[/tex]
Probability of a negative test and the person is not infected.
0.95 out of 299/300
Thus:
[tex]P(A \cap B) = \frac{0.95\times299}{300} = 0.9468[/tex]
Desired probability:
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.9468}{0.9473} = 0.999[/tex]
0.999*100% = 99.9%, so:
P(A'|B') = 99.9%
A similar question can be found at https://brainly.com/question/24275491
PLEASE HELP, IGNORE ALL ANWSERS FILLED IN CURRENTLY I WILL GOVE BRAINLIST
Answer:
32.64°
Step-by-step explanation:
From triangle Given :
The sides of the missing angle given are the Adjacent and hypotenus.
Since the triangle is right angled, we can apply trigonometry :
cosθ = adjacent / hypotenus
Cosθ = 16 / 19
θ = Cos^-1(16/19)
θ = 32.6368
θ = 32.64°
A car is traveling at a constant speed of 60 miles per hour. How many feet does it travel in 10 seconds?
Answer:
880 ft.
Step-by-step explanation:
First! We have to establish how many feet the car travels per hour.
60 (number of miles per hour) x 5280 (number of feet in a mile) = 316,800 (number of feet in an hour)
Next, since we know that there are 60 minutes in an hour we are going to divide our "number of feet in an hour" by 60 to get the "number of feet in a minute"
316,800 ÷ 60 = 5280
Once again, we are going to divide our "number of feet in a minute" by 60 to get the "number of feet per second".
5280 ÷ 60 = 88
Finally! We will multiple our "number of feet per second" by 10 to get how many feet the car can travel in 10 seconds.
88 × 10 = 880
So! Our car can travel 880 feet in 10 seconds.
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Find the unit price of each of the following items Round your answer to the nearest tenth
frozen orange juice
16.0% at $2.01
12 oz at $1.69
Answer:
12.56 cents
14.08 cent
Step-by-step explanation:
The unit price for each of the following items could be obtained thus :
The unit price = price of one item
Therefore, given that x numbers of a certain item cost y ;
The unit price will be : y / x
frozen orange juice
16.0 oz at $2.01
12 oz at $1.69
If 16 oz cost $2.01
1 oz = $2.01 / 16 = $0.125625 * 100 = 12.56 cents
If 12 oz = $1.69
1 oz = $1.69 / 12 = $0.1408333 * 100 = 14.08 cent
What is the slope line that passes through the points (10, 8) and (-15, 18)? Write your answer in simplest form
Answer: [tex]y=-\frac{2}{5}x+12[/tex]
y = mx + b
m = slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{18-8}{-15-10}=\frac{10}{-25}=\frac{2(5)}{-5(5)}=-\frac{2}{5}[/tex]
The y-intercept(b) can be found by substituting a point into the function.
[tex]y = -\frac{2}{5}x + b \\\\8=-\frac{2}{5}(10) + b\\\\8=-4+b\\\\b=8+4=12[/tex]
Therefore, the function is:
[tex]y=-\frac{2}{5}x+12[/tex]
(1,-19),(-2,-7) finding slope
Answer:
The slope is -4.
Step-by-step explanation:
Slope(m)=(y2-y1)/(x2-x1)
y2=-7, y1=-19, x2=-2, x1=1
(-7+19)/(-2-1)
=12/-3
=-4
Answer: -4
Step-by-step explanation:
The slope formula is: [tex]y_{2} -y_{1}/x_{2}-x_{1} \\[/tex]
So it is: (-7+19)/(-2-1) = 12/-3 = -4
I hope this helped!
When multiplying by 10 how many spaces do you move the decimal point
Answer:
If you multiply a decimal by 10, the decimal point will move one place to the right. If you divide a decimal by 10, the decimal point will move one place to the left.
Step-by-step explanation:
Multiplying a decimal by 10 increases the value of each digit by 10. Multiplying a decimal by a power of 10 increases the value of each digit by a number of times that is equivalent to that power of 10. When a digit's value is changed, that digit is moved to the appropriate place.
A drinks factory packed their drinks into red and yellow boxes. There were 24 more red boxes than yellow boxes. Each red box contained 60 packets of milk and each yellow box contained 75 packets of fruit juice. There were 120 fewer of milk than packets of fruit juice in all
boxes.
(a) How many yellow boxes were used ?
(b) How many packets of milk were packed into the the red boxes?
Answer:
A) 128
B) 7800
Step-by-step explanation:
Trial and error until I got to 75 x 104 and 60 x 128 (which abides by the fact that there has to be 24 more red boxes) which equals 7800 and 7680 and if you take them away from each other you get 120
Answer pleaseeeeeeee
Answer:
17x^2-9x-9 -->B
Step-by-step explanation:
7x^2 -12x +3 +10x^2+3x-12
The degree of the polynomial function f(x) is 4. The roots of the equation f(x) =0 are -2,-1,1 and 3. Which graph could be the graph of f(x)?
Answer:
top right
Step-by-step explanation:
roots of an equation = x-intercepts
Answer:
top right is the answer from my calculatins
The perimeter of a rectangle is 202 the length is 26 more than 4 times the width find the dimensions
Answer:
Width = xLength = 26 + 4xPerimeter
[tex]202 = x + x + 26 + 4x + 26 + 4x\\202-26-26=10x\\150=10x\\x=15[/tex]
Therefore, the dimensions are
Width = x = 15Length = 26 + 4x = 26 + 4(15) = 86Select the correct answer.
What is the value of this expression when x = -6 and ?
4(x2 + 3) − 2y
Answer:
D. 157
Step-by-step explanation:
4(x^2+3)-2y
4(6^2+3)-2(-1/2) add in given values
4(39)+1. start with parentheses
156+1. combine like terms
157. answer
Answer:
D. 157
Step-by-step explanation:
Hi there!
We want to find the value of the expression 4(x²+3)-2y is when x=-6 and y=-1/2
Let's first simplify the expression, as that will likely make it easier
Distribute 4 to both x² and 3
4x²+12-2y
That's the expression
Substitute -6 as x into the expression
4(-6)²+12-2y
Raise (-6) to the second power
4*36+12-2y
Multiply 36 by 4
144+12-2y
Add 12 and 144 together
156-2y
Now the expression is 156-2y
But remember that we know that y=-1/2, and we haven't substituted it into the expression yet
Substitute -1/2 as y into the expression
156-2(-1/2)
Multiply
156+2/2
Simplify
156+1
Add
157
Hope this helps!
I need help for this math question!
Answer:
D
Step-by-step explanation:
Assuming that the expression is referring to sin²(2πft) and not sin²(2)πft, we can solve as follows:
One trigonometric identity states that sin²x+cos²x = 1. We want to express this in terms of cos²x, so we need to solve for sin²x. Subtracting cos²x from both sides, we get 1-cos²x = sin²x. Plugging (2πft) for x, we get
1-cos²(2πft) = sin²(2πft)
We can plug that into our equation to get
P = I₀²R(1-cos²(2πft)), or D
A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students were recorded and analyzed. The results are shown in the computer output.
Which of the following represents the standard deviation of the residuals?
1.223
34.55
78.712
124.13
I think it's (B), 34.55
Answer:
34.55
Step-by-step explanation:
S = 34.55 represents the standard deviation of the residuals which is the correct answer that would be option (B).
What is the standard deviation?A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.
Students' proficiency in math and English is assessed by a particular standardized test. Ten students were chosen at random, and their math and English test results were recorded and examined.
The computer output displays the outcomes.
Predictor Coef SE Coef t-ratio p
Constant -124.13 78.712 0.046
Math 1.223 0.1966 6.220 0.000
S = 34.55 R-Sq = 82.8% R-Sq (Adj) = 83.5%
In the above ANOVA table, S = 34.55 represents the residual standard deviation.
Therefore, the correct answer is Option B = 34.55.
Option A = 1.223 represents the coefficient of the math score.
Option C = 78.712 represents the Standard Error (S.E).
Option D = 124.13 is the coefficient value.
Hence, the correct answer would be an option (B).
Learn more about the standard deviation here:
https://brainly.com/question/16555520
#SPJ2
Hhhhhhhhhhhhhhhhuuiuu
Answer:
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
;)
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is 10 .
Answer:
The probability of getting two numbers whose sum is 10 is 25%.
Step-by-step explanation:
Given that a single die is rolled twice, and there are 36 equally-likely outcomes, to find the probability of getting two numbers whose sum is 10 the following calculation must be performed:
1 = +9
2 = +8
3 = +7
4 = +6
5 = +5
6 = +4
7 = +3
8 = +2
9 = +1
9/36 = 0.25
Therefore, the probability of getting two numbers whose sum is 10 is 25%.
(x - 7)2 = x2 - 49
O True
O False
Answer:
False
Step-by-step explanation:
Find the Antilog of 547.840
Answer:
It's impossible because the figure is greater than 10
Step-by-step explanation:
[tex]{ \boxed{ \bf{antilog \: of \: x = \frac{x}{ log} = {10}^{x} }}}[/tex]
Therefore:
[tex]{ \sf{anti(547.840) = {10}^{547.840} }} \\ { \tt{ \red{math \: error \: !}}}[/tex]
Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $21.51 and a 95% confidence interval of [$20.52, $22.48]. Which of the following statements is a valid interpretation of the confidence interval?
a. we are 95% confident that a randomly selected taxi fare will be between $2051 and $2421.
b. 95% of all taxi fares are between $2051 and $2421.
c. We are 95% confident that the average tau fare between Logan Airport and downtown Boston will fall between $2051 and $2421.
d. The mean amount of a taxi fare is $22.31, 95% of the time.
Answer:
c. We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
95% confidence interval of [$20.52, $22.48].
We can be 95% sure that the true mean amount of taxis fares in downtown Boston is in this interval, and thus, the correct answer is given by option C.
Does anyone know the answer??
Answer:
I think the answer is 39x, 13y
Step-by-step explanation:
point : extra points
1 : 3
y : 39
y= 39÷3
y= 13
