Answer:
x=3
Step-by-step explanation:
2x+1=7
2x=7-1
2x=6
x=6/2
x=3
Answer:
Solution,
2x + 1=7
or 2x = 7 - 1
or, 2x= 6
or, x = 6
2
or, x = 3
.:. x = 3
A random variables X and Y are distributed according to the joint PDF. The value of constant a = _______.f(x,y)=ax if 1<=1x<=y<=2 and 0 otherwise
======================================================
Explanation:
PDF = probability density function
The given joint PDF is
[tex]f(x,y) = \begin{cases}ax \ \ \ \text{ if } 1 \le x \le y \le 2\\0 \ \ \ \ \ \text{ otherwise}\end{cases}[/tex]
Let's focus on the [tex]1 \le x \le y \le 2[/tex]. Specifically the x term for now. Erasing out the y term, we have the inequality [tex]1 \le x \le 2[/tex] which says x is between 1 and 2, inclusive. We have almost the same story for y, but there's another condition attached to it: y must also be equal to or larger than x.
So let's say x = 1.5. This would mean [tex]1.5 \le y \le 2[/tex]. As another example, x = 1.7 leads to [tex]1.7 \le y \le 2[/tex]. In general, we would say [tex]x \le y \le 2[/tex] where x is between 1 and 2.
As x gets bigger, the range of possible y values gets smaller. If x = 2, then y has no choice but to be 2 as well.
-----------------
Based on that, we'll have a double integral that looks like this:
[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\[/tex]
The outer integral handles the x terms that range from 1 to 2, describing [tex]1 \le x \le 2[/tex]. Note the dx on the outside. The order of the dy and dx matters.
On the inside, we have the integral for dy ranging from x to 2 to describe the interval [tex]x \le y \le 2[/tex]
To have f(x,y) be a PDF, the volume under the f(x,y) surface must be 1, where the volume is based on the bounds set up. So we must have V = 1. We'll use this later.
-----------------
Let's simplify the double integral.
We'll start by computing the inner integral with respect to y.
[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\\displaystyle V = \int_{1}^{2}\int_{x}^{2}\left(ax\right)dydx\\\\\displaystyle V = \int_{1}^{2}\left(axy\Bigg|_{x}^{2}\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(ax(2) - ax(x)\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\[/tex]
Then we'll finish it off by integrating with respect to x.
[tex]\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\\displaystyle V = \left(ax^2 - \frac{1}{3}ax^3\right)\Bigg|_{1}^{2}\\\\\displaystyle V = \left(a(2)^2 - \frac{1}{3}a(2)^3\right) - \left(a(1)^2 - \frac{1}{3}a(1)^3\right)\\\\\displaystyle V = \left(4a - \frac{8}{3}a\right)-\left(a - \frac{1}{3}a\right)\\\\[/tex]
[tex]\displaystyle V = 4a - \frac{8}{3}a-a + \frac{1}{3}a\\\\\displaystyle V = 3a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9}{3}a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9-8+1}{3}a\\\\\displaystyle V = \frac{2}{3}a\\\\[/tex]
Side note: We don't have to worry about the "plus C" integration constant when working with definite integrals.
Recall that V = 1. So,
[tex]\displaystyle V = \frac{2}{3}a\\\\\displaystyle \frac{2}{3}a = 1\\\\\displaystyle a = \frac{3}{2} = 1.5\\\\[/tex]
a = 3/2 is the final answer.
If a number has 8 as a factor, then both 2 and 4 are factors
Yes, that is correct because 2 and 4 can both go into 8 making it a factor of the number you are talking about. ANSWER: That is true
Which unit rate is equivalent to 12 miles per gallon? 24 miles 2 gallons 2 gallons 24 miles 36 miles 4 gallons 4 gallons 36 miles
Answer:
24/2
Step-by-step explanation:
If a rectangle has a base of 6' and a height of 4' its area would be what?
A= bxh
A= 6'x4'
A= 24 sq.ft.
Help on this algebra 2 question look at the pic. Is it’s A, B or C
Answer:
A is correct
Step-by-step explanation:
perimeter is twice the sum of the two adjacent sides
p = 2(x + (2x³ - 3x + 4))
p = 2(2x³ - 2x + 4)
p = 4x³ - 4x + 8
What is the area of a rectangle that has side lengths of 7 yard and yard?
10 square yard
18
20
square yard
15
24 square yard
8
square yard
My Progress
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is it like mutiplying and dividing
The area of the rectangle that has side lengths of 7 yards and 3 yards is 21 square yards.
What is the rectangular shape?Rectangles are quadrilaterals having four equal vertices and parallel sides that are equal to one another.
To find the area of the rectangle that has side lengths of 7 yards and 3 yards, use the formula as described below,
the area of the rectangle = length x width of the rectangle.
Substituting the value of the side lengths to the formula,
The area of the rectangle = 7 x 3
The area of the rectangle = 21 square yards.
Therefore, the area is 21 square yards.
To learn more about the rectangular;
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#SPJ7
What happens to the median of the data set
{10, 2, 8, 9, 5, 2, 6} if the number 12 is added to the data set?
A. The median increases by 2.
B. The median decreases by 1.
C. The median does not change.
D. The median increases by 1.
Answer:
D
Step-by-step explanation:
Median- The average
The average can be found by adding the numbers together and dividing by the amount of numbers, in this case that would be 7. 10+2+8+9+5+2+6=42. 42÷7= 6. So the average before 12 is 6. 42+12 is the total adding that 12 and would equal 54. 54÷8=6.75, averaging out to 7. The average increased by about 1. So, the answer is D.
Answer: D. The median increases by 1.
Step-by-step explanation: This is correct.
Simplify.
(2a2−3ab+5b2)−(a2−2ab+3b2)
A.a4−a2b2+2b4
B.3a2−5ab+8b2
C.a2−5ab+2b2
D.a2−ab+2b2
Simplify. (6x−3)−(2x−2)
A.4x2−1
B.4x−1
C.4x−5
D.4x2−5
Answer:
DBStep-by-step explanation:
You may find this easier if you distribute the minus sign first.
1)2a^2 -3ab +5b^2 -a^2 +2ab -3b^2
= (2 -1)a^2 +(-3+2)ab +(5 -3)b^2
= a^2 -ab +2b^2 . . . . . matches choice D
__
2)6x -3 -2x +2
= (6 -2)x +(-3 +2)
= 4x -1 . . . . . matches choice B
Last year, a gardening store ordered 8,910 potted plants. This year, they ordered 9,801 potted plants. What is the percent of increase in the number of potted plants ordered annually?
Answer:
Step-by-step explanation:
100(9801 - 8910)/8910 = 10%
Determine if the point (2,-1) is a solution of the system: 3x - y = 7 2x + 3y = 1
Answer: Yes (2,-1) is the solution for those systems.
becausee...
1. 3(2) - (-1) = 7
6 + 1 = 7
7 = 7
2. 2(2) + 3(-1) = 1
4 - 3 = 1
1 = 1
Hope this helps :)
Answer:
Yes the point (2,-1) is a solution of the system: 3x - y = 7 2x + 3y = 1
Step-by-step explanation:
(2,-1) = x = 2, y = -1
Now lets put these values in the given expressions
3x - y = 7
3 × 2 - (-1)
6 + 1
= 7 THIS EQUATION IS THE SOLUTION
2x + 3y = 1
2 × 2 + 3 × (-1)
4 - 3
= 1 THIS EQUATION IS THE SOLUTION
QD = 20000 -3P QS = 15000 +2P
The equilibrium price of the commodity at the given demand and supply is 1,000.
The given parameters:
Quantity demanded, QD = 20,000 - 3PQuantity supplied, QS = 15,000 + 2PThe equilibrium price of the commodity is calculated as follows;
At equilibrium price, the demand curve and supply curve cross each other.
[tex]QS= QD\\\\15,000 +2P = 20,000 - 3P\\\\2P+3P = 20,000 - 15,000\\\\5P = 5,000[/tex]
[tex]P = \frac{5,000}{5} \\\\P = 1,000[/tex]
Thus, the equilibrium price of the commodity is 1,000.
The complete question is below;
Determine the equilibrium price, if QD = 20000 -3P and QS = 15000 +2P.
Learn more about equilibrium price here: https://brainly.com/question/22569960
Tomika uses 6 1/9 inches of wire to make a necklace and 3 1/3 inches of wire to make a bracelet. How many necklace and bracelet sets can she make if she uses 28 1/3 inches of wire in all?
Answer:
3
Step-by-step explanation:
At a local college, 204 of the male students are smokers and 306 are non-smokers. Of the female students, 180 are smokers and 420 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers?
Step-by-step explanation:
Male ratio: 204:306 = 2:3 (66%)
Female ratio: 180:420 = 3:7 (42%)
Hope that helps
Answer:
both are non smokers is 0.48.
How do you solve multistep equations with variables on both sides
of the equals sign?
5x - 8 = 3x + 12
- 3x -3x
You have to subtract them both.
2x - 8 = 12
What is the vertical shift for the absolute value function below f(x) =9 |x+1|+2
Answer:
Slide UP 2
Step-by-step explanation:
In the equation,
f(x) = 9|x+1| + 2
There are three transformations of the parent function f(x)=|x| (this is the simplest form of this function, it's a v-shaped graph)
The 9 in front will vertically stretch the graph and make it look like a "skinny" v-shaped graph.
The +1 in close to the x inside the absolute value bars |x+1| will shift (slide) the graph to the left (it's the opposite of what you might think-- 'plus' shifts the graph left and 'minus' shifts the graph right)
The +2 at the end is the transformation you're looking for. It slides the graph as you would expect UP 2 units. If it was a minus it would shift the graph down instead.
Write and expression for the senqence of operations described below.
raise 6 to the 2nd power, then subtract r from the result
Do not simplify any part of the expression.
Raise [tex]6[/tex] to the second power, [tex]6^{2}[/tex], the subtract r from the result, that should be [tex]6^{2} - r[/tex], since we are not to simplify the expression, that's the answer.
HELP ME ASAP
Name the property below
9(x-5) = 9x -45
A. distributive
B. commutative
Answer:
A. distributive
Step-by-step explanation:
You would multiply the 9 with the x to get 9x, and then you would multiply the 9 with the negative -5 to get 9x-45.
Find the volume in cubic centimeters of a cube with a side length of 5 cm
Answer:
125 cm3
Step-by-step explanation:
V = l * w * h
V = 5 * 5 * 5
V = 125 cm3
Answer:
125 cm^3
Step-by-step explanation:
To calculate the area of a cube, just do the side length to the power of 3.
5^3=125
please help!! 100 points
[tex]\\ \tt\bull\rightarrowtail h(x)=1/5(x^2-6)-8[/tex]
[tex]\\ \tt\bull\rightarrowtail h(4)[/tex]
[tex]\\ \tt\bull\rightarrowtail 1/5(4^2-6)-8[/tex]
[tex]\\ \tt\bull\rightarrowtail 1/5(16-6)-8[/tex]
[tex]\\ \tt\bull\rightarrowtail 10/5-8[/tex]
[tex]\\ \tt\bull\rightarrowtail 2-8[/tex]
[tex]\\ \tt\bull\rightarrowtail -6[/tex]
he returns on share A follow the market model with coefficients αA = 0.01, βA =
1.25. If at time t, R~ MT = 0.02 and the actual return on share A is 0.025, calculate
∈�At (the error term)
Answer:
2 or more so it's be like 3 I guess he doesn't have the right for the tiger and in the heights block he it is a great game and to
A parallelogram is transformed according to the rule (x,y) - (x,y). Which is another way to state the transformation?
A. Ro.90
B. RO, 180
C. R0,270
D. RO,360°
112
121
124
137
147
156
173
189
Find the median revenue.
Answer:
142
Step-by-step explanation:
Median is the MID Number
Help me out Ik you love Algebra as much as I do
Answer:
pop
yes no total
country yes 11 38 49
no 43 8 51
total 54 46 100
Hope you understand this haha
The answer is in the file. Hope it helps.
What is an equation of the line that passes through the points (8,-4) and (6,-5)?
Answer:
y=1/2x-8
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-(-4))/(6-8)
m=(-5+4)/-2
m=-1/-2
m=1/2
y-y1=m(x-x1)
y-(-4)=1/2(x-8)
y+4=1/2(x-8)
y=1/2x-8/2-4
y=1/2x-4-4
y=1/2x-8
The ratio of the measures of the angles in a
triangle is 4:7:9. Find the measures of the
angles.
x=
The largest angle=
Explanation:-
We have given measure of angles of the triangle are in ratio 4 : 7 : 9 and here we need to find the measure of largest angle of a ∆.
Let, the three angles of a triangle be 4x, 7x, 9x.
We know that, Sum of all angles of a triangle is 180°.
4x + 7x + 9x = 180°
⇛20x = 180°
⇛x = 180°:20
⇛x = 9°
Now, finding largest angle by putting the value of “x”
4x = 4(9) = 36°7x = 7(9) = 63°9x = 9(9) = 81°Hence ,the measure of largest angle is 81°.
also read similar questions:The ratio of the measures of the three angles in a triangle is 2:9:4. Find the measures of the angels.....
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The ratio of the measures of the angles of a triangle is 4:6:8. Find the measure of the largest angle. Largest angle?....
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Pls help I’m failing I’ll brainlest and add extra points ASAP help with both
Answer:
The slope of the one of the top is -1/4
The slope of the one on the bottom is 1/6
Step-by-step explanation:
The one on the top goes down by 1 (negative) and goes 4 to the right (positive), which can be written as -1/4, which is the slope.
The one on the bottom goes up by 1 (positive) and goes to the right by 6 (positive), which can be written as 1/6, which is is the slope.
The length of a rectangle is times the width. If the perimeter is 32 inches, what is the width of the rectangle
Answer:
11
Step-by-step explanation:
Only 19 and 21!!!!!
Thank You!!!!
Step-by-step explanation:
19. 4x² - 13x + 3
4x² - 1x - 12x + 3
x(4x - 1) -3(4x - 1)
x-3 4x-1
pls can u help me with this question
Answer:
yes less than a min
Step-by-step explanation:
The penalty box on a soccer field extends
54 ft from the goal line. The line where a
player gets to take a penalty kick is 12 yards
from the goal line. What is the ratio of the
distance from the goal line and where a
player takes a penalty kick?
Answer:
I dont know sorry
next time
