(a) X has a probabiliity density of
[tex]f_X(x) = \begin{cases}\dfrac1{b-a}&\text{if }a<x<b\\0&\text{otherwise}\end{cases}[/tex]
If the lower quartile is 5 and the upper quartile is 9, then
[tex]\displaystyle \int_a^5 f_X(x)\,\mathrm dx = 0.25 \text{ and } \int_9^b f_X(x)\,\mathrm dx = 0.25[/tex]
Computing the integrals gives the following system of equations:
[tex]\displaystyle \int_a^5\frac{\mathrm dx}{b-a} = \frac{5-a}{b-a} = 0.25 \\\\ \int_9^b \frac{\mathrm dx}{b-a} = \frac{b-9}{b-a} = 0.25[/tex]
5 - a = 0.25 (b - a) ==> 0.75a + 0.25b = 5 ==> 3a + b = 20
b - 9 = 0.25 (b - a) ==> 0.25a + 0.75b = 9 ==> a + 3b = 36
Eliminate a :
(3a + b) - 3 (a + 3b) = 20 - 3×36
-8b = -88
==> b = 11 ==> a = 3
and so P(X = x) = 1/(11 - 3) = 1/8 for all 3 < x < 11.
(b)
[tex]\displaystyle P(6<X<7) = \int_6^7f_X(x)\,\mathrm dx = \int_6^7\frac{\mathrm dx}8 = \boxed{\frac18}[/tex]
(c) The distribution function is then
[tex]\displaystyle F_X(x) = \int_{-\infty}^x f_X(t)\,\mathrm dt = \begin{cases}0&\text{if }x\le3 \\ \dfrac x8 &\text{if }3<x<11 \\ 1&\text{if }x\ge11\end{cases}[/tex]
Fourteen percent of the towns population are above the age of 65. If there are about 320 residents over the age of 65 then what is the towns population.
Answer:
Step-by-step explanation:
Answer:
About 2286
Step-by-step explanation:
Let x be the number of the towns population.
14% x = 320
[tex]\frac{0.14x}{0.14} =\frac{320}{0.14}[/tex]
x = [tex]2285\frac{5}{7}[/tex]
x is about 2286.
You roll a six sided die 2 times what is the probability of rolling a 5 then a 2 pls help
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Yeah, don't know how to explain :/
Find the coordinates of the point 7/10 of the way from A to B A -3,-7 B 11,4
9514 1404 393
Answer:
(6.8, 0.7)
Step-by-step explanation:
That point is ...
A + (7/10)(B -A)
= (-3, -7) +(7/10)(11 -(-3), 4 -(-7)) = (-3, -7) +7/10(14, 11)
= (-3, -7) +(9.8, 7.7) = (6.8, 0.7)
The point 7/10 from A to B is (6.8, 0.7).
Identify the equation of the circle that has its center at (9, 12) and passes through the origin.
Answer: [tex](x-9)^2 + (y-12)^2 = 225\\\\[/tex]
This is the same as writing (x-9)^2 + (x-12)^2 = 225
========================================================
Explanation:
Any circle equation fits the template of [tex](x-h)^2 + (y-k)^2 = r^2\\\\[/tex]
The center is (9,12) which tells us the values of h and k in that exact order.
h = 9
k = 12
To find the radius r, we need to find the distance from the center (9,12) to a point on the circle. The only point we know on the circle is the origin (0,0).
Apply the distance formula to find the distance from (9,12) to (0,0)
[tex]d = \sqrt{ (x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{ (9-0)^2+(12-0)^2}\\\\d = \sqrt{ (9)^2+(12)^2}\\\\d = \sqrt{ 81+144}\\\\d = \sqrt{ 225}\\\\d = 15\\\\[/tex]
The distance from (9,12) to (0,0) is 15 units. Therefore, r = 15
An alternative to finding this r value is to apply the pythagorean theorem. The distance formula is effectively a modified version of the pythagorean theorem.
---------------------
Since h = 9, k = 12 and r = 15, we can then say:
[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-9)^2 + (y-12)^2 = 15^2\\\\(x-9)^2 + (y-12)^2 = 225\\\\[/tex]
which is the equation of this circle.
Change the denominators into powers of 10 and write the decimal form.
a)
.
[tex] \frac{4}{5} [/tex]
b)
.
[tex] \frac{1}{20} [/tex]
c)
.
[tex] \frac{3}{160} [/tex]
9514 1404 393
Answer:
a) 0.8
b) 0.05
c) 0.01875
Step-by-step explanation:
The denominator will need to have equal powers of 2 and 5 to be a power of 10.
a) 4/5 = (4/5)(2/2) = 8/10 = 0.8
__
b) 1/20 = 1/(2²·5) = (1/20)(5/5) = 5/100 = 0.05
__
c) 3/160 = 3/(2⁵·5) = (3/160)(625/625) = 1875/10000 = 0.01875
Which statement best defines a circle?
ОА.
the set of all points in a plane that are the same distance from a given point called the center
OB.
the set of all points that are the same distance from a given point called the center
OC. points in a plane that surround a given point called the center
OD the set of all points in a plane that are the same distance from each other surrounding a given point called the center
9514 1404 393
Answer:
А. the set of all points in a plane that are the same distance from a given point called the centerStep-by-step explanation:
A circle is a plane figure, so the descriptor "in a plane" is part of the definition. The notion of "surrounding" is not defined, so does not specify any particular relationship.
The appropriate definition is ..
the set of all points in a plane that are the same distance from a given point called the center
Every morning before going to class, Knut takes a shower, checks his email, does 100 pushups, and makes a milk, egg, and tuna smoothie.
Knut always takes his shower last. How many different ways are there for him to order the different steps of his morning routine?
Answer:
Step-by-step explanation:
The number of different ways there for him to order the different steps of his morning routine will be 5040.
What is a combination?The arrangement of the different things or numbers in a number of ways is called the combination.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
It is given that every morning before going to class, Knut takes a shower, checks his email, does 100 pushups, and makes a milk, egg, and tuna smoothie. Knut always takes his shower last.
The arrangement will be calculated as below:-
The number of the activities is 7.
The number of ways = 7!
The number of ways = ( 7x 6 x 5 x 4 x 3 x 2 )
The number of ways = ( 5040 ).
Therefore, the number of different ways there for him to order the different steps of his morning routine will be 5040.
To know more about combinations follow
https://brainly.com/question/11732255
#SPJ2
Chase thought that only 23 people would come to the banquet, but 48 people ended up coming. What was his percent error?
Answer:
The answer is 52%
ssmoga membantu
Im so bad at math but i swear im trying my best :( i really tried learning and understanding this but i just can’t , pls pls help me , thank you
Answer:
angle j=104 degrees
angle m= 127 degrees
Step-by-step explanation:
angle n=53 degrees
angle h=104 degrees
angle m=180-53(angles on a staright line)
angle m= 127 degrees
angle j=104 degrees (vertically opposite angles)
Can anyone help me out? (120)(-0.5) =
Answer:
-60
Step-by-step explanation:
Calculator.
find x if 8.4% of x is 420. explain with steps
Step-by-step explanation:
Pls mark brainliest
Plssssssssssssssss
A percentage is a way to describe a part of a whole. The value of x is 5,000.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that 8.4% of x is 420. Therefore, we can write the given statement in the form of an equation as,
8.4% of x = 420
8.4% × x = 420
(8.4/100) × x = 420
x = (420 × 100)/8.4
x = 5,000
Hence, the value of x is 5,000.
Learn more about Percentages here:
https://brainly.com/question/6972121
#SPJ2
I badly need help with this!!! Pls pls help, thank you
Answer:
DAC=18(corresponding angles)
EAD= 162 degrees
Step-by-step explanation:
DAC=18(corresponding angles)
EAD=180-18(angles on a straight line)
EAD= 162 degrees
Answer:
Here, we have,
<HBA=18°
<DAC=?
<EAD=?
Now,
i)<DAC=<HBA=18°[being corresponding angle]
ii)<EAD+<DAC=180°[being straight angle]
or, <EAD+18°=180°
or, <EAD=180°-18°
or, <EAD=162°
Thus, <DAC=18° and<EAD=162°.
Jessica Rabbit is the manager of shipping and receiving and has been working at the Leanup Company for thirty years. She rarely calls in sick and gets good performance reviews every year. In the past year, her wife’s company has been in serious financial trouble; they likely will not be able to make the payroll for next month and may have to close down. Which leg of the Fraud Triangle best applies to Jessica's situation?
Question 2 options:
Motive
Opportunity
Rationalization
Financial pressure
The fraud triangle is used to model the causes of frauds in an organization or company.
The scenario in her wife's company shows that the fraud leg that applies to Jessica is pressure.
From the question, we understand that:
They may not be able to make payroll for next monthThey may likely close downFinancial trouble as used in the question implies that her wife's company are in debts or mismanagement.
This means that Jessica is under pressure to commit fraud in her own company in other to assist her wife's company.
Hence, the leg of the Fraud Triangle best applies to Jessica's situation is pressure
Read more about fraud triangle at:
https://brainly.com/question/15108051
Mary takes 8 days to do a full check of the
library's online catalog. Her assistant takes
12 days. If they work together, determine the
fraction of the catalog that is checked after
4 days.
Answer:
Step-by-step explanation:
[tex]\begin{array}{|c|c|c|c|c}day&1&2&3&4\\----&-----&-----&-----&-----\\Mary&\frac{1}{8} &\frac{2}{8} &\frac{3}{8} &\frac{4}{8} \\Assis&\frac{1}{12} &\frac{2}{12} &\frac{3}{12} &\frac{4}{12} \\Sum&\frac{1}{8}+\frac{1}{12}&\frac{2}{8}+\frac{2}{12}&\frac{3}{8}+\frac{3}{12}&\frac{4}{8}+\frac{4}{12}\\part&\frac{5}{24}&\frac{10}{24}&\frac{15}{24}&\frac{20}{24}=\boxed{\frac{5}{6}}\\----&-----&-----&-----&-----\\\end{array}[/tex]
The fraction of the catalog that is checked after 4 days is 5/6
If Mary takes 8 days to do a full check and her assistant takes 12 days then if they work together then the fraction of the catalog that is checked after 4 days is 1000/12.
What is fraction?Fraction is a combination of numerator and denominator. The number above division sign is known as numerator and the number below the division sign is known as denominator. It is in p/q form in which q cannot be equal to 0.
How to find fraction?let the catalog contains 100 things.So in this way ,
In 1 day Mary does 100/8 things completed and her assistant does 100/12 things completed in 1 day.
So in four days they will complete =100*4/8+100*4/12
=400/8+400/12
=(4800+3200)/96
=8000/96
=1000/12
Hence if Mary takes 8 days to do a full check and her assistant takes 12 days then if they work together then the fraction of the catalog that is checked after 4 days is 1000/12.
Learn more about fraction at https://brainly.com/question/78672
#SPJ2
What is the relationship between the 6s in 675,002 and 385,621?
Answer:
6647 is a whole. For you to know the relationship between the 6s in this number write their values. The value of the first 6 is 6000. The value of the second 6 is 600.
Sorry for my small handwriting..
Answer:
9.067cm
Step-by-step explanation:
x--- amount by which the length is reduced
area=(18-x)(15)=134
(18-x)=134/15
x=18-(134/15)
x= 9.067cm
Please help I’ll give brainly !! FAST THANK YOUUUU
[tex]\\ \rm\longmapsto \sqrt[3]{8}=2[/tex]
[tex]\\ \rm\longmapsto \sqrt[3]{-8}=-2[/tex]
Answer:
All integers have only one cube root.
Because it is an inverse of an odd degree (3) exponent.
x³ = 8∛x³ = ∛8x = 2And
x³ = -8∛x³ = ∛-8x = -2Enter the correct answer in the box.
Linear function is shown in the graph. Write the slope-intercept form of the equation representing this function.
Y
10
8
6-
4
2
-75
-8
-6
X
- 5
-4
O
4
6
8
10
-2-
-4
-6-
N
-84
Answer:
Slope = 3
y-intercept: - 7
y = 3x -7
Step-by-step explanation:
Alyssa is buying a new tv that is priced at $570. The sales tax is 8%. How much will she pay total, including the original price and the sales tax
Answer:
In total she will pay $615.60
Step-by-step explanation: Because 8% of 570 is 45.60 and if you add 45.60 to 570 you get 615.60.
Factors and rewrite the expression 99x+9
Answer:
9(11x+1)
Step-by-step explanation:
99x + 9
The greatest common factor is 9 so put 9 outside of parenthesis
9(11x+9)
Answer:
9(11x+1)
Step-by-step explanation:
We can see that these two values in the equation can be factored by 9 so divide both by 9
99/9= 11
9/9= 1
Rewrite expression by inputting the numbers in parenthesis while keeping the 9 "outside"
9(11x+1)
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! NOT A MULTIPLE CHOICE!!!
In a hotel building, the lobby is located at sea-level. The first floor is located 18 feet above the lobby, and the basement is located 22 feet below the lobby.
a. Write an inequality to compare the elevations of the first floor and the basement.
b. What is the distance from the lobby to the basement? Write your answer as an absolute value statement.
c. Which is a greater distance from the lobby: the first or basement? Justify your response.
9514 1404 393
Answer:
-22 < 0|-22-0| = 22distance to basement is greaterStep-by-step explanation:
a) If we let B, L, F represent the elevations of the basement, lobby, and first floor, respectively, then we have ...
B = -22
L = 0
F = 18
Your inequality could be either of ...
B < L
-22 < 0
__
b. We're not sure exactly the form you're looking for. Use whichever absolute value statement is appropriate to your needs.
distance = |B -L| = |-22 -0| = |-22| = 22
__
c. The distance from the lobby to the first floor is |18 -0| = 18.
The distance from the lobby to the basement is |-22-0| = 22.
The distance 22 is greater than the distance 18, so the distance to the basement is greater.
_____
Additional comment
The difficulty with this question is not figuring out whether -22 is farther from 0 than is +18. The difficulty is in figuring out the form of the answer that is expected. Without looking at your curriculum materials, we cannot even make an appropriate guess.
Can someone help me solving this differential equation?
Find the general solution of [tex]x^4y''+x^3y'-4x^2y=1 given tha [tex]t y_1=x^2 is a solution of the associated homogeneous equation.
Use reduction of order. Given a solution [tex]y_1(x) = x^2[/tex], look for a second solution of the form [tex]y_2(x) = y_1(x)v(x)[/tex].
Compute the first two derivatives of [tex]y_2(x)[/tex]:
[tex]y_2 = x^2v \\\\ {y_2}' = x^2v' + 2xv \\\\ {y_2}'' = x^2v''+4xv' + 2v[/tex]
Substitute them into the ODE:
[tex]x^4 (x^2v'' + 4xv' + 2v) + x^3 (x^2v' + 2xv) - 4x^2 (x^2v) = 1 \\\\ x^6v'' + 5x^5v' = 1[/tex]
Now substitute [tex]w(x) = v'(x)[/tex] and you end up with a linear ODE:
[tex]x^6w'+5x^5w=1[/tex]
Multiply through both sides by [tex]\frac1x[/tex] (if you're familiar with the integrating factor method, this is it):
[tex]x^5w'+5x^4w = \dfrac1x[/tex]
Bear in mind that in order to do this, we require [tex]x\neq0[/tex]. Just to avoid having to deal with absolute values later, let's further assume [tex]x>0[/tex].
Notice that the left side is the derivative of a product,
[tex]\left(x^5w\right)' = \dfrac1x[/tex]
Integrate both sides with respect to [tex]x[/tex] :
[tex]x^5w = \displaystyle \int\frac{\mathrm dx}x \\\\ x^5w = \ln(x) + C_1[/tex]
Solve for [tex]w(x)[/tex] :
[tex]w = \dfrac{\ln(x)+C_1}{x^5}[/tex]
Solve for [tex]v(x)[/tex] by integrating both sides:
[tex]v = \displaystyle \int \frac{\ln(x)+C_1}{x^5} \,\mathrm dx[/tex]
Integrate by parts:
[tex]\displaystyle f = \ln(x) + C_1 \implies \mathrm df = \frac{\mathrm dx}x \\\\ \mathrm dg = \frac{\mathrm dx}{x^5} \implies g = -\frac1{4x^4} \\\\ \implies v = -\frac{\ln(x)+C_1}{4x^4} + \frac14 \int \frac{\mathrm dx}{x^5} \\\\ v = -\frac{\ln(x)+C_1}{4x^4} - \frac1{16x^4} + C_2 \\\\ v = -\frac{4\ln(x)+C_1}{16x^4}+C_2[/tex]
Solve for [tex]y_2(x)[/tex] :
[tex]\displaystyle \frac{y_2}{x^2} = -\frac{4\ln(x)+C_1}{16x^4}+C_2 \\\\ y_2 = -\frac{4\ln(x)+C_1}{16x^2} + C_2x^2[/tex]
But since [tex]y_1(x)=x^2[/tex] is already accounted for, the second solution is just
[tex]\displaystyle y_2 = -\frac{4\ln(x)+C_1}{16x^2}[/tex]
Still, the general solution would be
[tex]\displaystyle \boxed{y(x) = -\frac{4\ln(x)+C_1}{16x^2} + C_2x^2}[/tex]
Find the area of the triangle with the vertices A (3, -5), B (-2, -7) and C (18, 1) such that A, B and C are collinear.
9514 1404 393
Answer:
0
Step-by-step explanation:
Many authors do not recognize three points on a line as forming a triangle. This is because its area is zero. (The "base" is the length of the line segment; the "height" is the width of the line (zero).)
Which of the following is a qualitative observation?
Question 7 options:
This leaf has grown 3 cm this week.
This leaf is 30 cm long.
This leaf has 8 curved edges.
This leaf is light green in color.
Answer:
so i think answer of this quiestion is option D
to divide fractions invert the second fraction and multiply
True
Flase
Answer:
TrueStep-by-step explanation:
Example of dividing fraction:Givens: 1/2 and 3/61/2 ÷ 3/6= 1/2 × 6/3= 6/6= 1[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
What is the factored form of 250x^3 − 16? A. 2(5x − 2)(25x2 + 10x + 4) B. 2(5x + 2)(25x2 − 10x + 4) C. (5x − 2)(25x2 + 10x + 4) D. (5x + 2)(25x2 − 10x + 4)
Answer:
The choose A.
[tex]250 {x}^{3} - 16 \\ 2(5x - 2)(25 {x}^{2} + 10x + 4)[/tex]
I hope I helped you^_^
Find the slope of the line through each pair of points. (Will give brainliest!)
Answer:
17 Ans is -3/7
Step-by-step explanation:
Let ( x1,y1)=(-3,8)
(X2,y2)=(-17,14)
By the formula,
slope (m)=y2-y1/x2-x1
=14-8/-17+3
=6/-14
=-3/7
Do others with same steps and process
What does this mean ?
Step-by-step explanation:
Area= 13.86 cm²
πr²= 13.86 cm²
r= √13.81 ×7/22
r= 2.1 cm
Circumference= 2πr
= 2 × 22 × 2.1 / 7
=13.2 cm
Answer:
circumference is the outside area of a circle
area of the circle is the inside area
What is the area (in square feet) of a rectangle that measures 12'-7" by 9'-9"?
Answer:
122.6875 (122 ft 8.25 in)
Step-by-step explanation:
12 ft 7in = 151 in
9 ft 9 in = 117 in
151 x 117 = 17667
17667in = 122 ft and 8.25 in = 122.6875 ft
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Help please due tomorrow
Answer:
Can you put a fraction. It is 1/3