Answers
Answer:
0.23.
Step-by-step explanation:
We can use the formula L(x) = f(a) + f'(a)(x-a)
Our f(x) is clearly ln(x), while a = 1. At a=1, ln(1) = 0, therefore f(a) = 0.
We then need to find the derivative of ln(x), which is 1/x. Therefore f'(a) = 1/a, and with a = 1, f'(a) is therefore 1.
Finally, x is equal to 1.23. Substituting this value in for x in the formula results in:
L(x) = 0 + 1 ( 1.23 - 1)
Giving us a final answer of 0.23.
Related Questions
The sum of two integers is -186. The larger integer is 14 less than
three times the smaller number. Find the two integers.
Answers
The values of the two integers are -43 and -143.
What are the values of the two integers?Let the value of the smaller integer be "x".
Smaller integer = xLarger integer = 3x - 14Sum of the integers = -186Since, the sum of two integers is -186.
Smaller integer + Larger integer = -186
x + ( 3x - 14 ) = -186
Solve for x
x + 3x - 14 = -186
4x - 14 = -186
4x = -186 + 14
4x = -172
x = -172/4
x = -43
Hence;
The smaller integer = x = -43
The largere integer = 3x - 14 = 3(-43) - 14 = -143.
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The sum of two consecutive integers is 201 find the integers
Answers
100 and 101
the two integers are n and n+1. this means that 2n+1=201. n=100 and n+1=101
You buy a collectible for $200. For the first six years, the collectible loses 6% of its value each year. After that, the collectible increases in value by 8% each year. Determine how long it takes for the collectible to be worth more than $200. Round your answer to the nearest year.
Answers
It takes abοut 14.25 years fοr the cοllectible tο be wοrth mοre than $200.
What are Percentage?Percentage is a way οf expressing a prοpοrtiοn οr ratiο as a fractiοn οf 100. It is οften used tο indicate a part οf a whοle οr tο cοmpare twο quantities.
Let V(t) be the value οf the cοllectible after t years. We knοw that V(0) = 200 (the initial value οf the cοllectible).
Fοr the first six years, the value οf the cοllectible decreases by 6% each year, sο we have:
\(V(6) = 200*(1-0.06)^6\)
After six years, the value of the collectible starts to increase by 8% each year, sο we have:
\(V(t) = V(6)*(1+0.08)^(t-6)\)
We want tο find οut when V(t) > 200, so we set up the inequality:
V(t) > 200
\(V(6)*(1+0.08)^(t-6) > 200\)
Substituting in the value οf V(6) from above, we get:
\(200*(0.94)^6*(1+0.08)^(t-6) > 200\)
Simplifying, we get:
\((1.08)^(t-6) > (0.94)^6\)
Taking the natural lοgarithm of bοοth sides, we get:
\((t-6)ln(1.08) > 6ln(0.94)\)
Dividing bοth sides by ln(1.08), we get:
\(t > 6 + 6*ln(0.94)/ln(1.08)\)
Using a calculatοr, we get:
t > 14.25
Therefοre, it takes about 14.25 years for the cοllectible to be worth more than $200. Rounded tο the nearest year, the answer is 14 years.
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The points A, B, C and D lie in order on a straight line
such that
AB:BD = 1:2
AC:CD= 7:2
Find AB:BC:CD
Answers
Answer:
7 + 2 = 9, so AC = 7/9 and CD = 2/9
1 + 2 = 3, so AB = 1/3 = 3/9 and
BD = 2/3 = 6/9
AB + BC = AC
3/9 + BC = 7/9, so BC = 4/9
AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2
The volume of a cuboid is 540cm³. The length is 6cm and the width is 150mm. Work out the height of the cuboid in cm.
Answers
Step-by-step explanation:
To work out the height of the cuboid, we need to use the formula:
Volume = Length x Width x Height
We have been given the volume and the length, so we can substitute those values into the formula:
540 = 6 x Width x Height
Now we need to convert the width from millimeters to centimeters, so we divide it by 10:
150mm ÷ 10 = 15cm
Substituting this value into the formula:
540 = 6 x 15 x Height
Simplifying:
540 = 90 x Height
Dividing both sides by 90:
6 = Height
Therefore, the height of the cuboid is 6cm.
Which graph represents x > 23
A. 23 To the right
B. 23 to the left
In a number line?
Answers
Answer:
eStep-by-step explanation:
O
Lola used 2 1/2 ink cartridges while her friends used 1 3/4 ink cartridges. How many more ink cartridges did Lola use than her friends
Answers
Answer:
Lola used 3/4 more ink cartridges than her friends
Step-by-step explanation:
Evaluate the expression when x=-4.
x2 +7x-6
Answers
• -18
-8+ -34
-42
I think this is right lol
Is
A person's batting average is determined by dividing the number of hits by the
number of at bats. William has 11 hits in 53 at bats and has a batting average of
0.208. He wants to have a batting average of at least 0.300.
Which equation could be used to determine x, the number of hits in a row William
needs to get in order to have a batting average of at least 0.300?
11x
A. 0.300 s
53x
11
B. 0.300x s
53
11 + x
C. 0.300 s.
53
11 + x
D. 0.300 s
53 + x
Answers
Hope this helps!!
The equation that could be used to determine x is \(\frac{11+x}{53+x} \leq 0.300\).
What is inequality?Inequality is a relation that makes a non-equal comparison between two expressions.
Batting average of William = 11/53
Desired batting average = 0.300
Suppose the number of more hits in a row to have desired batting average =x
Number of hits now =11+x
Number of bats now =53+x
It is given that the batting average should be a minimum of 0.300.
This means \(\frac{11+x}{53+x} \leq 0.300\)
Therefore, the equation that could be used to determine x is \(\frac{11+x}{53+x} \leq 0.300\).
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The combined city/highway fuel economy of a 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range of 21mpg to 26mpg answer A and B URGENT
Answers
a)The range of 95% of the data is from 21 mpg to 26 mpg, which is a range of 5 mpg.
b)We need a sample size of 543 to estimate the mean with 98% confidence and an error of 0.25 mpg
What is Empirical Rule for a normal distribution?
If a dataset is normally distributed, we can expect that about 68% of the data points will fall within one standard deviation of the mean, about 95% of the data points will fall within two standard deviations of the mean, and about 99.7% of the data points will fall within three standard deviations of the mean. This rule is a useful guideline for understanding the spread of data in a normal distribution.
(a) Using Method 3 (the Empirical Rule for a normal distribution), we know that for a normally distributed random variable, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.
Since the range of the combined city/highway fuel economy of a 2016 Toyota 4Runner 2WD 6-cylinder 4-L automatic 5-speed using regular gas is from 21 mpg to 26 mpg, the midpoint of the range is (21 + 26) / 2 = 23.5 mpg.
Using the Empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Therefore, the range of 95% of the data is from 21 mpg to 26 mpg, which is a range of 5 mpg.
We can set up the following equation to solve for the standard deviation, σ:
2σ = 5
σ = 5 / 2
σ = 2.5
Therefore, the estimated standard deviation is 2.5 mpg. Rounded to 4 decimal places, the estimated standard deviation is 2.5000 mpg.
(b) The formula for the margin of error is:
Margin of error = z-value×(standard deviation / √(sample size))
We want the margin of error to be 0.25 mpg and the confidence level to be 98%. Since we are using a z-value, we can look up the z-value for a 98% confidence level in a standard normal distribution table.
The z-value for a 98% confidence level is approximately 2.33 when rounded to 3 decimal places.
Plugging in the given values, we have:
0.25 = 2.33×(2.5 / √(sample size))
Solving for the sample size, we get:
√(sample size) = 2.33 × (2.5 / 0.25)
√(sample size) = 23.3
sample size = (23.3)²
sample size = 542.89
Rounded to the nearest whole number, we need a sample size of 543 to estimate the mean with 98% confidence and an error of 0.25 mpg.
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i will give 25 points for these 4 answers
Answers
Answer:
oh really
Step-by-step explanation:
but from what am seeing here I'm able to get 5 pts
so how do you wannna do it
Classify the triangle by side length and angle measurement.
A: Scalene, acute
B: Isosceles, acute
C:Scalene, right
D: equilateral, obtuse
Answers
Answer:
C
Step-by-step explanation:
The sides are different lengths when you look at them and then the 90° angle is already given
Answer:
The triangle is classified as a "right angle" because the little box at the bottom left mean it's exactly 90 degrees.
Step-by-step explanation:
Evaluate the integral. (Use C for the constant of integration.)
2x^2+ 5x + 2/(x² + 1)2 dx
Answers
Answer:
\(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x - \frac{5}{2(x^2 + 1)} + C\)
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)
Derivative Property [Addition/Subtraction]: \(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Rule [Reverse Power Rule]: \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Property [Multiplied Constant]: \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
Integration Property [Addition/Subtraction]: \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)
Integration Method: U-Substitution
Step-by-step explanation:
Step 1: Define
Identify.
\(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx\)
Step 2: Integrate Pt. 1
[Integrand] Rewrite [Factor]: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2(x^2 + 1) + 5x}{(x^2 + 1)^2}} \, dx\)Rewrite [Integration Property - Addition/Subtraction]: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2(x^2 + 1)}{(x^2 + 1)^2}} \, dx + \int {\frac{5x}{(x^2 + 1)^2}} \, dx\)[Left Integral] Simplify: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2}{x^2 + 1}} \, dx + \int {\frac{5x}{(x^2 + 1)^2}} \, dx\)[Integrals] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \int {\frac{1}{x^2 + 1}} \, dx + 5 \int {\frac{x}{(x^2 + 1)^2}} \, dx\)[Left Integral] Trigonometric Integration: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + 5 \int {\frac{x}{(x^2 + 1)^2}} \, dx\)Step 3: Integrate Pt. 2
Identify variables for u-substitution for the remaining integral.
Set u: \(\displaystyle u = x^2 + 1\)[u] Differentiate [Derivative Properties and Rules]: \(\displaystyle du = 2x \ dx\)Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \int {\frac{2x}{(x^2 + 1)^2}} \, dx\)[Integral] U-Substitution: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \int {\frac{1}{u^2}} \, du\)Apply Integration Rule [Reverse Power Rule]: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \bigg( \frac{-1}{u} \bigg) + C\)[u] Back-substitute: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \bigg( \frac{-1}{x^2 + 1} \bigg) + C\)Simplify: \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x - \frac{5}{2(x^2 + 1)} + C\)∴ the integration of the given integral \(\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx\) is equal to \(\displaystyle \bold{2 \arctan x - \frac{5}{2(x^2 + 1)} + C}\).
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---
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Please help me with the answer to this question
Answers
The answer as a result of the numerical expression above is B) 1/36
How to solve rank equationThis expression is rank number:
\(( {6}^{ - 4} ) {}^{ \frac{1}{2} } = 6 {}^{ - 2} = \frac{1}{ {6}^{2} } = \frac{1}{36}.
So the answer as a result of the numerical expression above is 1/36.
From these calculations it can be seen that the rank between what is inside the brackets and what is outside it can be multiplied.
In the question above the power of -4 multiplied by the power of ½ ( (-4×½) the result is -2.
So all that's left is 6⁻². Another form of 6⁻² is 1/6² or 1/36.
This refers to the exponential rule in mathematics, namely a⁻ⁿ can be written as 1/aⁿ.
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4)
At a concert, Sam pays $10 for a bucket of popcorn. Each refill costs $2. Write an expression using x for
the amount of refills that will show the total cost he will pay.
stean
Answers
That is saying he only refilled once
If the sinø=7/12, what is cosø?
Answers
Sine and cosine
The sine and cosine are the basic trigonometric functions.
The sine is positive in the first and second quadrant
The cosine is positive in the first and fourth quadrant
We'll assume the angle is in the first quadrant, so the cosine and the sine are positive
The basic identity that relates the sine and the cosine of a given angle is:
\(\sin ^2\varnothing+\cos ^2\varnothing=1\)If we are given the sine of the angle:
\(\sin \varnothing=\frac{7}{12}\)The cosine can be calculated by solving the above identity for the cosine:
\(undefined\)find the mean 12,13,9,5,11,10
Answers
Answer:
10
Step-by-step explanation:
5+9+10+11+12+13=60 divided by 6 = 10
Mean = Sum of all observations/Number of observations
Mean = 12 + 13 + 9 + 5 + 11 + 10/6
=60/6
= 10
dont forget to like and mark me
translate into an algebraic expression: 120 is increased by d % and increased by 25% . What is the result ?
Answers
Answer:
1.5d+150
Step-by-step explanation:
125 since it increased by 25%. look at the problem below:
125( 1 + 0.01d) then you plug those numbers in and theres your answer :00!!
sammy-6th grade-
The algebraic expression is 1.5d+150.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that 120 is increased by d % and increased by 25% then the expression will be written as below.
E = 1.5d+150.
Hence the algebraic expression is 1.5d+150.
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Albertson's grocery planned a big sale on apples and received 840 crates from the wholesale market. Albertsons will bag these apples in plastic. Each plastic bag holds 19 a crate. If Albertsons has no loss to perishables, how many bags of apples can be prepared?
Answers
Answer:
45 bags
Step-by-step explanation:
Answer:
the answer is 45 bags
Step-by-step explanation:
840 divided by 19 is 44 r 4
Which graph shows the solution to the inequality lx+3l≥2 ?
Answers
When solving absolute value equations, we solve for two conditions, positive and negative.
calculate the VAT charged on this amount R1599.00(VAT included)
Answers
Answer:
VAT = R239.85
Step-by-step explanation:
VAT = 15%
15/100 = 0.15
R1599 × 0.15 = 239.85
VAT = R239.85
geometric series $b 1 b 2 b 3 \cdots b {10}$ has a sum of $180$. assuming that the common ratio of that series is $\dfrac{7}{4}$, find the sum of the series $b 2 b 4 b 6 b 8 b {10}.$
Answers
The sum of the series b 2 b 4 b 6 b 8 b {10} is \($\dfrac{180}{3}$\) since it is a geometric series with a common ratio of \($\dfrac{7}{4}$\).
Since the given series \($b 1 b 2 b 3 \cdots b {10}$\) has a sum of 180, it can be deduced that the series is a geometric series with a common ratio of\($\dfrac{7}{4}$\). This means that the ratio of any two consecutive terms in the series is a constant, \($\dfrac{7}{4}$\). Therefore, the sum of the series b 2 b 4 b 6 b 8 b {10} can be calculated as follows:
\($S = b2 + b4 + b6 + b8 + b_{10}$\)
\($= b2\left(\dfrac{7}{4}\right)^0 + b2\left(\dfrac{7}{4}\right)^2 + b2\left(\dfrac{7}{4}\right)^4 + b2\left(\dfrac{7}{4}\right)^6 + b2\left(\dfrac{7}{4}\right)^8$\)
\($= b2 \left[1 + \left(\dfrac{7}{4}\right)^2 + \left(\dfrac{7}{4}\right)^4 + \left(\dfrac{7}{4}\right)^6 + \left(\dfrac{7}{4}\right)^8\right]$\)
\($= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{1-\left(\dfrac{7}{4}\right)^2}\right]$\)
\($= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{\dfrac{3}{4}}\right]$\)
\($= \dfrac{4b2}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)
Since the sum of the series\($b 1 b 2 b 3 \cdots b {10}$\) is 180, we can substitute $b2$ with \($\dfrac{180}{3}$\)nd calculate the sum of the series $b 2 b 4 b 6 b 8 b {10}$:
\($S = \dfrac{4\left(\dfrac{180}{3}\right)}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)
\($= \dfrac{180}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)
Therefore, the sum of the series \($b 2 b 4 b 6 b 8 b {10}$ is $\dfrac{180}{3}$\).
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Which value of a makes the equation true?
Answers
Answer:
a = -2
Step-by-step explanation:
3(a + 1.5) = -1.5
3a + 4.5 (-4.5) = -1.5 (-4.5)
3a = -6
a = -2
Clarence walks 3.1 miles around Lake Johnson every day for five days.
If it takes him a total of 6 hours to walk the 15.5 miles, what is his
average time per day?
minutes per day.
Answers
Answer:
Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day
Step-by-step explanation:
To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.
Let's calculate his average time per day:
Average time per day = Total time / Number of days
Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:
Average time per day = 6 hours / 5
Average time per day = 1.2 hours per day
To convert hours to minutes, we'll multiply the average time per day by 60:
Average time per day = 1.2 hours * 60 minutes
Average time per day = 72 minutes per day
Therefore, Clarence's average time per day is 72 minutes.
Anna sold 1 tie for every 4 shirts. Which proportion would determine how many shirts she would need to sell along with 16 ties?
Answers
Answer:
64 shirts
Step-by-step explanation:
The ratio of ties to shirts is 1:4, so if the number of ties was 16, then you would have to multiply 16(number of ties) by 4(number of shirts), 16 x 4=64. therefore the awnser will be 64 shirts. Your welcome
Solve the equation: x²-2x=8
Show all the Steps with explanation.
Answers
Answer:
x = 4, -2
Step-by-step explanation:
x^2-2x=8
Move the constant term to the right side of the equation.
x^2 - 2x = 8
Take half of the coefficient of x and square it.
(-2/2)^2 = 1
Add the square to both sides of the equation.
x^2 - 2x + 1 = 8 + 1
Factor the perfect square trinomial.
(x - 1)^2 = 9
Take the square root of both sides of the equation.
x-1=\(\sqrt{9}\)
x-1=±3
Isolate x to find the solutions.
Taking positive
x=3+1=4
x=4
Taking negative
x=-3+1
x=-2
The solutions are:
x = 4, -2
Answer:
\(x = -2,\;\;x=4\)
Step-by-step explanation:
To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:
\(x^2-2x-8=8-8\)
\(x^2-2x-8=0\)
Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.
The two numbers whose product is -8 and sum is -2 are -4 and 2.
Rewrite the coefficient of the middle term as the sum of these two numbers:
\(x^2-4x+2x-8=0\)
Factor the first two terms and the last two terms separately:
\(x(x-4)+2(x-4)=0\)
Factor out the common term (x - 4):
\((x+2)(x-4)=0\)
Apply the zero-product property:
\(x+2=0 \implies x=-2\)
\(x-4=0 \implies x=4\)
Therefore, the solutions to the given quadratic equation are:
\(\boxed{x = -2,\;\;x=4}\)
Tina wants to save money for school. Tina invests $700 in an account that pays an interest rate of 4%.
How many years will it take for the account to reach $1,800? Round your answer to the nearest hundredth.
Answers
It will take approximately 10.21 years for the account to reach $1,800.
To find out how many years it will take for Tina's account to reach $1,800 with an interest rate of 4%, we can use the formula for compound interest:
\(A = P(1 + r/n)^{(nt)\)
Where:
A is the future value of the investment ($1,800 in this case)
P is the principal amount ($700)
r is the interest rate (4% or 0.04 as a decimal)
n is the number of times interest is compounded per year (we'll assume it's compounded annually)
t is the number of years we want to find.
Plugging in the values, we have:
\(1,800 = 700(1 + 0.04/1)^{(1\times t)\)
Simplifying the equation further:
\(1,800/700 = (1.04)^t\)
\(2.5714 = (1.04)^t\)
To solve for t, we take the logarithm of both sides:
\(log(2.5714) = log((1.04)^t)\)
Using logarithm properties, we can bring down the exponent:
\(log(2.5714) = t \times log(1.04)\)
Now we can solve for t by dividing both sides by log(1.04):
t = log(2.5714) / log(1.04)
Using a calculator, we find:
t ≈ 10.21
Rounding to the nearest hundredth, it will take approximately 10.21 years for the account to reach $1,800.
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let's see who can solve this. pleseeee
Answers
The correlation coefficient between X and Y is Corr(X, Y) = 0.
To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.
a. Marginal distribution of X:
To find the marginal distribution of X, we integrate the joint PDF over the range of Y:
∫[0, 1] J(x, y) dy
Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:
∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1
So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.
b. Expectation of X:
The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:
\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)
Therefore, the expectation of X is E(X) = 1/3.
c. Variance of X:
The variance of X can be calculated using the formula:
\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)
Therefore, the variance of X is Var(X) = 5/36.
d. Covariance of X and Y:
The covariance of X and Y can be calculated as:
Cov(X, Y) = E(XY) - E(X)E(Y)
Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:
\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)
\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)
Cov(X, Y) = 1/6 - (1/3)(1/6) = 0
Therefore, the covariance of X and Y is Cov(X, Y) = 0.
e. Correlation coefficient between X and Y:
The correlation coefficient can be calculated using the formula:
Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))
Since the covariance of X and Y is 0, the correlation coefficient will also be 0.
Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.
f. Conclusion based on the correlation coefficient:
The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the
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transversal t cuts parallel lines r and s which angles must be congruent to 2?
Answers
r and s are parallel lines so the angle 2 and 6 are called, corresponding angles 2 and 3 are opposite angle but 3 and 7 are also interior corresponding angles so 7 and 3 are congruent, and so are 7 and 2 .
the angles must be congruent to 2 are 3, 6 , 7
Answer:
r and s are parallel lines so the angle 2 and 6 are called, corresponding angles 2 and 3 are opposite angle but 3 and 7 are also interior corresponding angles so 7 and 3 are congruent, and so are 7 and 2 .
the angles must be congruent to 2 are 3, 6 , 7
Step-by-step explanation:
A couple plans to purchase a house. The bank requires a 20% down payment on the $240,000 house. The couple will finance the rest of the cost with a fixed- rate mortgage at 8.5% annual interest with monthly payments over 30 years.
Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent if necessary. If necessary, refer to the list of financial formulas.
(a) Find the required down payment.
(b) Find the amount of the mortgage.
(c) Find the monthly payment.
Answers
(A) The required down payment is $48,000.
(B) The amount of the mortgage is $192,000.
(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)
(a) To find the required down payment, we need to calculate 20% of the house price.
Down payment = 20% of $240,000
Down payment = 0.2 * $240,000
Down payment = $48,000
The required down payment is $48,000.
(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.
Mortgage amount = Total cost of the house - Down payment
Mortgage amount = $240,000 - $48,000
Mortgage amount = $192,000
The amount of the mortgage is $192,000.
(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:
Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal amount (mortgage amount)
r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)
n = Total number of monthly payments (30 years multiplied by 12 months)
Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)
Using this formula and performing the calculation will give you the monthly payment amount.
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