let X1 and X2 have the joint pdf, f(x1, x2) 0
Answers
Answer:
Please find the complete question in the attached file.
Step-by-step explanation:
For point a:
\(\to fx_1(x_1)=\int^{x_{1}}_{0} f(x_1,x_2)\ dx\\\\\)
\(=\int^{x_{1}}_{0} e^{-x_1}\ dx_2\\\\= e^{-x_1} \ [x_2]^{x_1}_0 \\\\\therefore f x_1(x_1)=x_1e^{-x_1}; \ \ x_1>0\\\\\)
For point b:
\(\to f(x_2|x_1)=\frac{f(x_1,x_2)}{f(x_1)}\ =\frac{e^{-x_1}}{x_1\ e^{-x_1}}=\frac{1}{x_1} ; \\\\ \ \ 0\leq x_2 \leq x_1 \\\\\)
For point c:
\(P(x_1>2|x_2=7)= 1.00 \\\\\because x_2=7\to x_1>7\to x_1>2\\\\\)
Related Questions
expand and simplify (6x-2)^2
Answers
Answer:
\(\sf 36x^2 -24x +4\)
solving step wise:
\(\sf (6x-2)^2\)
\(\sf (6x-2)(6x-2)\)
\(\sf 36x^2 -12x -12x +4\)
\(\sf 36x^2 -24x +4\)
or
\(\sf (6x-2)^2\)
\(\sf (6x)^2 +2*6x*-2+(-2)^2\)
\(36x^2 -24x +4\)
Answer:
36x²-24x+4
Step-by-step explanation:
6x-2² 6x-2 6x-2
From the chart, estimate (roughly) the number of transistors per IC in 2016. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040?
Please explain
Answers
The estimates for the number of transistors per IC, using an exponential function, are given as follows:
2016: 16,777,216,000.2040: 6.87 x 10¹³.What is the format of an exponential function?An exponential function has the general format presented as follows:
\(y = ab^\frac{x}{n}\)
In which the parameters of the function are listed as follows:
a is the initial value of the function.b is the rate of change of the function.n is the period relative to the rate of change.By Moore's Law, the number of transistors per IC doubles every two years, hence the values of parameters b and n are both two, that is:
b = 2, n = 2.
We take 1972 as the reference year, when the amount was of 4000 transistors per IC, hence the value of parameter a is given as follows:
a = 4000.
Thus the equation is:
\(A(t) = 4000(2)^{\frac{t}{2}}\)
Giving the number of transistors per IC in t years after the reference year of 1972.
2016 was 44 years after 1972, hence the estimate for the amount of transistors by IC was of:
\(A(44) = 4000(2)^{\frac{44}{2}} = 16,777,216,000\)
2040 will be 68 years after 1972, hence the estimate for the amount of transistors by IC is of:
\(A(68) = 4000(2)^{\frac{68}{2}} = 6.87 \times 10^{13}\)
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what is the maximum number of students among whom 100 orange ,150 cirtrus, and 250 guavas can be equally distirbuted ? what is the share of each fruits for a student?
Answers
Answer:
Hello,
Step-by-step explanation:
HCF(100,150,250)=50*HCF(2,3,5)=50*1=50
Part of each fruits for a student:
2 oranges, 3 cirtrus and 5 guavas.
what are the steps to solve this
Answers
Answer:
The equation of this line is y = -4.
Answer:
y=-4
Step-by-step explanation:
zero slope m=0
y-y1=m(x-x1)
y-(-4)=0(x-(-9))
y+4=0
y=-4
Graph the equation by the translating y=|x|Y=|x+2|A. Graph a B. Graph c C. Graph d D. Graph b
Answers
What is the sample space for each one of the following statements? (7.5 points each)
a) We have a bag containing white and black balls( number of balls are infinite). we keep drawing the balls until we see two white balls (or black balls) in consecutive draw.
b) We have a bag containing 10 balls (numbered from 1 to 10) we choose 4 balls and save the order(of the numbers).
Answers
We can define the sample space for a given experiment as the set of all the possible outcomes for the experiment.
For example, tossing a coin has a space sample of 2 elements, tails and heads.
The spaces are:
a) {WW, BB, WBB, BWW, WBWW, BWBB,... }
b) { 1-2-3-4, 1-2-3-5,..., 7-6-5-4,...}
a) We can write one element in this sample space as:
WBB
This would mean that first we draw a white ball, then a black ball, and then the second black ball, thus we stop drawing.
So all the elements in this set will have the form
{WW, BB, WBB, BWW, WBWW, BWBB,... }
As we have infinite balls in the bag, we have infinite elements in this set.
b) Now we have only 10 balls numbered from 1 to 10, and we draw 4.
So each element in the sample space can be written as:
1-2-3-4
This element means:
"first we draw ball number 1, then ball number 2, then ball number 3, then ball number 4"
Then the sample space will have the form:
{ 1-2-3-4, 1-2-3-5,..., 7-6-5-4,...}
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PLS ANSWER ASAP!!!!!!!!! I WILL GIVE EXTRA POINTS AND BRAINLIEST FOR THE CORRECT ANSWER!!!
You need to find a Number with 10 digits.
The first digit is divisible by 1
The second digit is divisible by 2
The third digit is divisible by 3
The fourth digit is divisible by 4
The fifth digit is divisible by 5
The sixth digit is divisible by 6
The seventh digit is divisible by 7
The eigth digit is divisible by 8
The ninth digit is divisible by 9
The full number is divisible by 10
Answers
Answer:
3816547290
Step-by-step explanation:
this is from a puzzle called notable numbers
MATH QUESTION SCREEN SHOT DOWN BELOW
Answers
f(x)=(x-1)²-2
min point is (1,-2)
the answer is first picture
A division of a company produces income tax apps for smartphones. Each income tax app sells for $8. The monthly fixed costs incurred by the division are $20,000, and the variable cost of producing each income tax app is $3.
Answers
The break-even point for the division is as follows:
Break-even point in units = 4,000 unitsBreak-even point in dollars = $32,000.What is the break-even point?The break-even point is the unit or dollar value where the total revenue equals the total costs.
The total costs consist of the fixed and variable costs.
Selling price per unit of the income tax app = $8
The variable cost per unit = $3
Contribution margin per unit = $5 ($8 - $3)
Contribution margin ratio = 62.5% ($5 ÷ $8 x 100)
Fixed cost per month = $20,000
Break-even point in units = Fixed Costs/Contribution margin per unit
= 4,000 units ($20,000 ÷ $5)
Break-even point in dollars = Fixed Costs/Contribution margin ratio
= $32,000 ($20,000 ÷ 62.5%)
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Question Completion:Find the break-even point for the division.
Find the interest.
. 750$, 6.5%, 2years
Answers
Answer:
simple interest=$97.50.
compound interest= $100.668
Step-by-step explanation:
Given:
Principal (P) = $750
Rate (R) = 6.5% (in decimal form, 0.065)
Time (T) = 2 years
Simple Interest = Principal*Rate*Time
Using the formula, the simple interest is calculated as follows:
Simple Interest = $750*0.065*2 = $97.50
Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.
Again:
Compound Interest = Principal*(1 + Rate)^(Time)-Principal
Using the same values as above, the compound interest can be calculated as follows:
Compound Interest = $750*(1+0.065)^(2)-$750
= $750*1.065^2 -$750
= $750 × 1.134225 - $750
= $850.66875-$750
= $100.668
Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668
Graph the line with slope 6 and y-intercept -6
Answers
The graph of the line with slope 6 and y-intercept -6 is given below.
What is slope intercept form?
One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfils.
y = mx + c
where m is the slope
c is the y-intercept
Given, slope (m) = 6
y-intercept = -6
So, the equation of line become
y = 6x - 6
And, the graph of the given equation is given below.
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What does 4/5 minus 1/5 equal
Answers
Answer:
3/5
Step-by-step explanation:
Answer:
3/5
Step-by-step explanation:
This one is easier than others because it has the same denominator (bottom number).
All you have to do is subtract the numerators (top numbers) and keep the denominators the same!
4/5 - 1/5 = 3/5
I hope this helps, and have a great day!
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Robin, Steven, and John are comparing tree diagrams for rolling double sixes on two six-sided number cubes (6, 6). Robin thinks the probability is 136 based on the tree diagram they created. Steven disagrees and argues that the probability of rolling double sixes is 16. John counts twelve outcomes and claims the probability is 112.
Who correctly found the probability of rolling double sixes using the tree diagram?
A
Robin because there are 36 outcomes and only one is (6, 6).
B
Steven because there are 6 outcomes and only one is (6, 6).
C
Steven because there are 36 outcomes and six of them are (6, 6).
D
John because there are 6 outcomes for each and only one is (6, 6).
Answers
Answer:
A. Robin because there are 36 outcomes and only one is (6, 6).Step-by-step explanation:
You would get the probability of double sixes as:
P(6, 6) = 1/6*1/6 = 1/36Correct choice is A
The Robin because there are 36 outcomes and only one is (6, 6) is the correct option.
We have given that,
Robin, Steven, and John are comparing tree diagrams for rolling double sixes on two six-sided number cubes (6, 6).
Robin thinks the probability is 136 based on the tree diagram they created.
Steven disagrees and argues that the probability of rolling double sixes is 16.
John counts twelve outcomes and claims the probability is 112.
What is the probability?The formula to calculate the probability of an event is as follows. Probability(Event) = Favorable Outcomes/Total Outcomes
You would get the probability of double sixes as:
P(6, 6) = 1/6*1/6 = 1/36
Correct choice is A.
Therefore the Robin, because there are 36 outcomes and only one is (6, 6).
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Based on the function F(x) = 2x° +2x² - 4 and the graph of G(x) below, which of the following statements is true? TH O A. F(x) has 3 real roots x 70 G() O B. as x → = G(x) > 0 x → F(x) → O c. as x →-, F(x) — - O D. G(X) has 3 real roots
Answers
We could graph the function F:
\(F(x)=2x^3+2x^2-4\)As follows:
As you can see,
\(\begin{gathered} as\text{ x}\to\infty,\text{ f(x)}\to\infty \\ as\text{ x}\to-\infty,\text{ f(x)}\to-\infty \end{gathered}\)Therefore, the correct answer is C.
Information from a sample of 157 restaurant bills collected at the First Crush bistro is available in RestaurantTips. Two intervals are given below for the average tip left at a restaurant; one is a 90% confidence interval and one is a 99% confidence interval Interval A: 3.55 to 4.15 Interval B: 3.35 to 4.35
(a) which one is the 90% confidence interval? | Interv.. which one is the 99% confidence interval?
(b) One waitress generally waits on 20 tables in an average shift. Give a range for her expected daily tip revenue, using both 90% and 99% confidence intervals. Round your answers to the nearest integer.
Confidence level Confidence interval
90% 0.6 to 7.7
99% -1 to 7.7
Answers
Answer:
a) The 99% confidence interval is interval B: 3.35 to 4.35
The 90% confidence interval is interval A: 3.55 to 4.15.
b) Check Explanation.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value is obtained from either the t-distribution or the z-distribution tables. It depends on sample size and for smaller sample sizes, whether there is information provided for the population mean and standard deviation.
But whether z-distribution or t-distribution, the critical value increases as the confidence level increases.
Hence, the critical value for the 99% confidence level will be higher than the critical value for the 90% confidence level.
And since all the other parameters that determine the confidence interval and it's width (sample mean and the standard error of the mean) are the same for the 90% and the 99% confidence interval, the larger critical value for the 99% confidence interval means that it has the bigger width.
Hence, of the two intervals given,
Interval A: 3.55 to 4.15
Interval B: 3.35 to 4.35
The larger interval, (3.35, 4.35) is the 99% confidence interval and the smaller interval, (3.55, 4.15) is the 90% confidence interval.
b) The data required for this second part isn't available, but the answer for the confidence interval can be obtained using the steps I have given above and below.
Like I have given above,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error = (Critical value) × (standard Error of the mean)
The sample mean and the standard error of the mean are obtained from the sample data (which is missing).
Sample mean = (Σx)/N
x = each variable
N = number of variables = 20
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation (obtained from the sample data)
90% critical value for sample size of 20 = 1.73
99% critical value for sample size of 20 = 2.86
Hope this Helps!!!
Calculate the volume of this cylinder in terms of Pi and to the nearest hundredth
Answers
The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.
What is the volume of the given cylinder?It follows from the task content that the volume of the cylinder which is as represented is to be determined.
Since the volume of a cylinder is;
V = 2πr²h
where r = 10 and h = 25.
V = 2π × 10² × 25.
V = 5000π.
Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.
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What is this product
____ = 5x9
Answers
Answer:
45
Step-by-step explanation:
9x1=9
9x2=18
9x3=27
9x4=36
9x5=45
HELP PLZ!
Is this graph of a function?
Yes or no
Answers
If you get it right I will give brainiest.
Answers
9. Solve the equation.
x + 4 = 3(3x - 4)
A 9
4
B 1
C 2
Lounge
D 7
4
Answers
Answer:
x=2
Step-by-step explanation:
x + 4 = 3(3x - 4)
Distribute
x+4 = 9x -12
Subtract x from each side
x+4 -x = 9x-x-12
4 = 8x-12
Add 12 to each side
4+12 = 8x-12+12
16 = 8x
Divide by 8
16/8 = 8x/8
2 =x
Answer:
x = 2
Step-by-step explanation:
x + 4 = 3(3x - 4)
Expand the brackets.
x + 4 = 9x - 12
Add -x and 12 on both sides.
4 + 12 = 9x - x
16 = 8x
Divide 8 into both sides.
16/8 = x
2 = x
Switch sides.
x = 2
Which point could represent 5/3 ?
Answers
Answer:D
Step-by-step explanation:
5/3 is 2/3 and its also between 0 and 1
Answer:
the answer is C
Step-by-step explanation:
i got it right
A. y = -1
B. X = -1
C. y = 1
D. X = 1
Answers
The highest point in the number is X=1
A common aspect ratio for computer screens today is width : height = 16 : 9. The advertised size of a screen is given by the measure of its diagonal. Measure the width, height, and diagonal of at least three screens (computers, tablets, phones) in your home. Are they similar? How do you know? Are any of your screens congruent? If so, what postulates prove it? List your measurements and describe your findings carefully.
Please follow these guidelines for your discussion posts:
Write at least 150–300 words.
Answers
A common aspect ratio for computer screens is 16:9, which means that for every 16 units of width, there are 9 units of height. This aspect ratio is also used on many televisions and mobile devices.
How to explain the ratio?If a screen has an aspect ratio of 16:9, the width and height will be similar on all screens with this aspect ratio. However, the diagonal measurement will vary depending on the size of the screen.
Congruent screens are two or more screens that have the same dimensions. Two screens are congruent if and only if corresponding sides are equal and corresponding angles are equal. This can be proven using the postulates of congruence, such as the SSS (Side-Side-Side) postulate or the SAS (Side-Angle-Side) postulate.
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Given the right angle triangle shown here, calculate:
1. a) sin(a)
17
2. a) sin(b)
8
b) cos(a)
b
b) cos(b)
15
c) tan(a)
c) tan(b)
Write trig. ratios for each.
Answers
Answer:
see explanation
Step-by-step explanation:
(1)
(a)
sin(a) = \(\frac{opposite}{hypotenuse}\) = \(\frac{15}{17}\)
(b)
cos(a) = \(\frac{adjacent}{hypotenuse}\) = \(\frac{8}{17}\)
(c)
tan(a) = \(\frac{opposite}{adjacent}\) = \(\frac{15}{8}\)
----------------------------------------------------
(2)
(a)
sin(b) = \(\frac{opposite}{hypotenuse}\) = \(\frac{8}{17}\)
(b)
cos(b) = \(\frac{adjacent}{hypotenuse}\) = \(\frac{15}{17}\)
(c)
tan(b) = \(\frac{opposite}{adjacent}\) = \(\frac{8}{15}\)
Write the set using interval notation. How to simplify if you need to and what if your answer involves a union with a singleton set.
Answers
For the set notation { x | x ≤ -9 or x ≥ 9}, we get the interval notation as ( - ∞ , -9 ] U [ 9, ∞ )
We are given a set that:
{ x | x ≤ -9 or x ≥ 9}
We need to write it an interval notation.
For x ≤ -9:
Since x is smaller than or equal to -9, we will get the interval as:
( - ∞ , -9 ]
For x ≥ 9:
Since x is greater than or equal to 9, we will get the interval as:
[ 9, ∞ )
or means union.
So, the final interval becomes:
( - ∞ , -9 ] U [ 9, ∞ )
Therefore, for the set notation { x | x ≤ -9 or x ≥ 9}, we get the interval notation as ( - ∞ , -9 ] U [ 9, ∞ )
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find the ordered pair
Answers
The ordered pair that is a solution of the system is (-3, -3), the second option.
Which ordered pair is a solution of the system of inequalities?There are two ways of finding this.
You can use your graph and identify which of the given pointes lies in the region where the two shaded areas intersect.
Another way, is replacing the values of the coordinate points in both inequalities and checking that both are true when evaluated in the point.
Here we will use the graph, because you already had it (and you can see a more precise graph in the image at the end).
We can see that the region os solutions is on the left side of the graph, and the only point that lies on there is (-3, -3)
So that point is the solution.
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pls HELP ASAP PLS HELP
Answers
commutative property, the one top
combining like terms, the 1st one on the bottom
(Irrational Numbers MC)
Approximate -10 + √30 to the nearest tenth. HELP PLS
Answers
-10 + 5.47722~
=4.523~
round to nearest tenth = 4.5
Answer:
-4.5
Step-by-step explanation:
\(\sqrt{30}\) is approximately 5.47722557505. You can find this number with a calculator.
-10 + 5.47722557505 = -4.52277442495
To add a negative and a positive number, you subtract the absolute values and take the sign of the number that has the larger absolute value. Absolute value just means thinking of both numbers as positive numbers.
Helping in the name of Jesus.
Which word describes the slope of the line?
O positive
O negative
zero
O undefined
Answers
The slope of a horizontal line is always zero.
What is slope?
The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are any two points on the line.
The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.
By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:
slope = change in y / change in x = 0 / (any non-zero value of x) = 0
So, the slope of a horizontal line is always zero.
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Jermaine kicked a soccer ball at a speed of 24 feet per second. If the ball never leaves the ground, then it can be represented by the function H(t) = −16t2 + 24t. Determine the time the ball traveled. (1 point) t = 24 seconds t = 8 seconds t = 1.5 seconds t = 0.67 seconds
Answers
The time that the ball traveled is given as follows:
1.5 seconds.
How to obtain the time traveled by the ball?The quadratic function determining the ball's height after t seconds is given as follows:
H(t) = -16t² + 24t.
The roots of the quadratic function in this problem are given as follows:
-16t² + 24t = 0.
16t² - 24t = 0
8t(2t - 3) = 0.
Hence we apply the factor theorem as follows:
8t = 0 -> t = 0.2t - 3 = 0 -> 2t = 3 -> t = 1.5.Hence the time is given as follows:
1.5 - 0 = 1.5 seconds.
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