Answer:
C
Step-by-step explanation:
C
The correct option is C. 4.75 for the side length, in inches, of one tile on the floor pattern.
What is termed as the dimensions of rectangle?Evey rectangular shape is distinguished by two dimensions: length and width.The dimensions are the longer side of a rectangle and the shorter side of the rectangle.For the given question.
Floor pattern is made up by 36 square tiles.
The long dimension is labeled 42.75 inches.
A 4 by 9 rectangle is shown containing 36 square tiles.
Thus, to obtain the side length, in inches, of one tile.
Divide long dimension 42.75/9 = 4.75.
Thus, the side length, in inches, of one tile on the floor pattern.
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Simplify the following expression (-8)-(-6)
Suppose that Y has density function
f(y) = ky(1 − y) if 0 ≤ y ≤ 1 0, elsewhere
A) Find the value of k that makes f (y) a probability density function.
B) Find P(Y ≤ .4|Y ≤ .8).
C) Find the .95-quantile, i.e., find a point φ.95 such that P(Y ≤ φ.95) = .95.
I'm assuming
[tex]f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}[/tex]
(a) f(x) is a valid probability density function if its integral over the support is 1:
[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1[/tex]
Compute the integral:
[tex]\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16[/tex]
So we have
k / 6 = 1 → k = 6
(b) By definition of conditional probability,
P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)
P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)
It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).
We have
[tex]\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y<0\\3y^2-2y^3&\text{for }0\le y<1\\1&\text{for }y\ge1\end{cases}[/tex]
Then
P(Y ≤ 0.4) = F (0.4) = 0.352
P(Y ≤ 0.8) = F (0.8) = 0.896
and so
P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393
(c) The 0.95 quantile is the value φ such that
P(Y ≤ φ) = 0.95
In terms of the integral definition of the CDF, we have solve for φ such that
[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95[/tex]
We have
[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95[/tex]
which reduces to the cubic
3φ² - 2φ³ = 0.95
Use a calculator to solve this and find that φ ≈ 0.865.
Using probability concepts, it is found that
a) The value is k = 6.
b) P(Y ≤ .4|Y ≤ .8) = 0.554.
c) The 95th percentile is x = 0.86465.
The density function is:
[tex]f(y) = ky(1 - y)[/tex]
Item a:
The condition that makes it a probability density function is:
[tex]\int_0^1 f(y) dy = 1[/tex]
Thus:
[tex]\int_0^1 f(y) dy = \int_0^1 ky - ky^2 dy[/tex]
[tex]\int_0^1 f(y) dy = k(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0}^{y = 1}[/tex]
[tex]\int_0^1 f(y) dy = k(\frac{1}{2} - \frac{1}{3})[/tex]
Then
[tex]k(\frac{1}{2} - \frac{1}{3}) = 1[/tex]
[tex]k(\frac{3-2}{6}) = 1[/tex]
[tex]k = 6[/tex]
The value is k = 6.
Item b:
This probability is:
[tex]\int_0.4^0.8 f(y) dy = 6(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0.4}^{y = 0.8}[/tex]
Then
[tex]p = 6\left(\frac{0.8^2}{2} - \frac{0.8^3}{3} - \frac{0.4^2}{2} + \frac{0.4^3}{3}\right)[/tex]
[tex]p = 0.554[/tex]
Thus, P(Y ≤ .4|Y ≤ .8) = 0.554.
Item c:
This is x for which:
[tex]\int_0^x f(y) dy = 0.95[/tex]
Thus:
[tex]6(\frac{x^2}{2} - \frac{x^3}{3}) = 0.95[/tex]
[tex]-2x^3 + 3x^2 - 0.95 = 0[/tex]
Solving a cubic equation with the help of a calculator, and considering [tex]0 \leq x \leq 1[/tex], this is x = 0.86465.
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Helppppp meeeee 3/5 Divided by 1/9
Answer: 5.4 or 5 2/5 Hope this helps have a GREAT night
Step-by-step explanation:
PLEASE HELP QUICKLY!!!!! PLZZZZZZ!!!!!!!
r−5r−6s+8s−15 what is the answer for this equation
Step-by-step explanation:
r-5r-6s+8s-15
-4r+2s-15
= 2s-4r-15
The simplified form of the given expression is -4r+2s-15.
The given expression is r-5r-6s+8s-15.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression can be solved as follows:
r-5r-6s+8s-15
= -4r+2s-15
Therefore, the simplified form of the given expression is -4r+2s-15.
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Factor the difference of cubes. Select prime if the polynomial cannot be factored
Answer:
(m-(1/3))(m^2+(1/3)m+(1/9)
Step-by-step explanation:
Just use the difference of cubes
a shirt was originally marked as $24.95 rings up at the register as 19.96 what is the percent discount on the shirt
Answer:
The discount is 20% off
hope this helps!
How do you simplify (1/2)^2 ● 1/2 ● (1/2)^3
Answer:
1 /64
Decimal Form:
0.015625
What is the value of Cosine (StartFraction x Over 2 EndFraction) if tangent x = one-half and x is in quadrant III?
[tex] - \sqrt{ \frac{5 - 2 \sqrt{5} }{10} } [/tex]
Answer:
a
Step-by-step explanation:
on edge
Today, 6 friends went out for lunch. Their total bill was $28.86, including tax and gratuity. They decided to split the bill equally and each paid with a $10 bill. How much money will each person get back?
Answer:
5.19
Step-by-step explanation:
first do 28.86 / 6 to find out how much each paid. then subtract that number (4.81) from 10
Answer - Every Person should get $5.19
Step-by-step explanation:
what i did is 6 x 10 = 60 then 60 - 28.86 = 31.14 / 6 = 5.19 Your welcome.
Peter collected 171 marbles but lost 3/4 of them on his way home through of hole in his bag when he arrived at home now many marbles did Peter have left?
The number of marbles Peter had when he arrived home was 43 marbles
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
The number of marbles Peter had on his way home = 171
The amount of marbles he lost on his way home = ( 3/4 ) th
Now , the amount of marbles Peter have left = 1 - amount of marbles he lost on his way home
The amount of marbles Peter have left = 1 - 3/4
= ( 1 / 4) th
So , The number of marbles Peter had left when he arrived home is =
Amount of marbles Peter have left x Number of marbles Peter had
The number of marbles Peter had left when he arrived home is = (1/4) x 171
= 171 / 4
= 42.75
≈ 43 marbles
Hence , the number of marbles Peter had left when he reached home is 43
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Can you help with these questions please i would appreciate it
Answer:
[tex]\boxed{k = \frac{log_{e}(\frac{L +A }{A} )}{t} }[/tex]
What is a secure line of credit?
a. A line of credit offered only to individuals with excellent credit ratings.
b. A line of credit offered to a business or corporation.
c. A line of credit backed by the government.
d. A line of credit backed by collateral.
Answer:
D. A line of credit backed by collateral.
Step-by-step explanation:
Answer:
D. A line of credit backed by collateral.
Step-by-step explanation:
did the quiz
The ratio of girls to boys in the coed soccer league is 3:7. Choose True or
False for each statement.
The ratio of girls to total students in the league is 3:10.
O Truc
False
Next >
Previous
Answer:
True
Step-by-step explanation:
3:7 is girls to boys, and to find the total, do 7+3. After that, you'd get 10, and the ratio would be 3:10, so TRUE
What is the surface area of this rectangular pyramid?
4 mm
5 mm
5 mm
square millimeters
Answer:
100 mm i think
Step-by-step explanation:
Frank ordered a set of beads. He received 70 beads in all. 21 of the beads were green. What percentage of the beads were green?
To compute a student's Grade Point Average (GPA) for a term, the student's grades for cach course are weighted by the number of credits for the course. Suppose a student had these grades: 3.6 in a 5 credit Math course 2.5 in a 2 credit Music course 3.0 in a 5 credit Chemistry course 3.4 in a 5 credit Journalism course What is the student's GPA for that term? Round to two decimal places. Student's GPA=_________
Answer:
The student's GPA = 3.24
Step-by-step explanation:
To determine the student's GPA for the term,
First, we will determine the weighted grade points and then divide the result by the total credit.
The weighted grade point is the sum of the grade points in the courses.
Grade point for a course is calculated by multiplying the grade by the course credit.
For the Math course,
Grade point = 3.6 × 5 = 18.0
For the Music course,
Grade point = 2.5 × 2 = 5.0
For the Chemistry course,
Grade point = 3.0 × 5 = 15.0
For the Journalism course,
Grade point = 3.4 × 5 = 17.0
Hence,
The weighted grade point = 18.0 + 5.0 + 15.0 + 17.0
The weighted grade point = 55.0
Total credit = 5 + 2 + 5 + 5 = 17
∴ The student's GPA = 55.0 / 17 = 3.24
Hence, The student's GPA = 3.24
2. I earned $9. I bought 4 candy bars for $0.85 each. How much money do I
have left? *
A. $5.60
B. $8.15
C. $9.85
D. $12.40
Answer:
A
Step-by-step explanation:
4 x $0.85= $3.40
$9-$3.40= $5.60
Answer:
A. $5.60
Step-by-step explanation:
4x0.85 =3.4 and 9 -3.4 = 5.6
There are 3.9 milligrams of calcium in a ½ ounce of cooked chicken. How many milligrams are in 6 ounces?
Answer:
there are 46.80 milligrams in 6 ounces.
Step-by-step explanation:
Select all intervals in which the function P(t) is decreasing
Answer:
we conclude that the intervals in which the function P(t) is decreasing are:
x < 13 < x < 4Step-by-step explanation:
At x< 1, the function P(t) is decreasing
A function p is an increasing function on an open interval if f(y) > f(x) for any two input values x and y in the given interval where y>xA function p is a decreasing function on an open interval if f(y) > f(x) for any two input values x and y in the given interval where y>xFrom the figure, it is clear that the function seems to be increasing
from (1, 3) and then 4 to onwards.
But it is clear that the function seems to be decreasing from the x < 1 and from the interval (3, 4).
Therefore, we conclude that the intervals in which the function P(t) is decreasing are:
x < 13 < x < 4If the simple interest on $3000 for 3 years is $720 , then what is the interest rate?
Answer:
8%
Step-by-step explanation:
Starting Principal: $
3,000.00
Years:
3
Annual Interest Rate:
8
%
Results
Future Value, using...
Simple Interest: $
3,720.00
Annually Compounded Interest: $
3,779.14
Please help me it’s very important please answer it correctly
Thank you
Answer:
a. m<CBA = m<DBA because of the definition of an angle bisector (angle bisector cuts the angle in half) We are also told that segment BD and Segment BC are congruent.
We don't know if segment AC and AD are congruent so we can't say those angles (the other two) are congruent.
b. point A and B will stay fixed because they are colinear to segment AB (on the same line)
c. Those two are needed because If those are true we can prove that they are congruent by SAS (Side Angle Side)
d. the reflection an prove that the lines and angles are congruent.
identify a pair of factors of -35 that has a sum of -2
Answer:
5, -7
Step-by-step explanation:
Answer:
5 and -7
Step-by-step explanation:
Which expression can be used to solve the problem below? On a recent math test,
Jill scored 3 points for each of the 18 multiple choice questions she answered
correctly and 5 points for each of the 6 short response questions she answered
correctly. What was her total score on the test?
1 : 3+16 • 18+6
2 : 3+18 • 5+6
3 : 3 • 5 + 18 • 6
4 : 3 • 18 + 5 • 6
Answer:
4
Step-by-step explanation:
Because she gets 3 per multiple choice question, so 3 times 18
she gets 5 per response question, so 5 times 6
Jill total score on the test is 3 • 18 + 5 • 6. The correct option is 4.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given;
Jill scored 3 points for each of the 18 multiple choice questions she answered correctly.
That means,
use the multiplication operation,
3 x 18
And 5 points for each of the 6 short response questions she answered correctly.
That means,
5 x 6
To find the total score:
Add the scores,
3 x 18 + 5 x 6
or, 3 • 18 + 5 • 6
Therefore, 3 • 18 + 5 • 6 is the required expression.
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120 passengers in 4 buses = passengers per bus
Answer:
30
Step-by-step explanation:
120/4
Answer:
30
Step-by-step explanation:
Just divide 120 with 4
Hope this helps!!!!!!
9. Solve the equation.
4(6 – x) + 4 = 2 (3x + 1) – 6
Answer:
x=3.2
Step-by-step explanation:
4(6 – x) + 4 = 2 (3x + 1) – 6
24 - 4x + 4 = 6x + 2 - 6
28 - 4x = 6x -4
-4x - 6x = - 4 - 28
-10x = - 32
divide both sides
x = 16/5 or x = 3.2
hope this helps :)
What is the best estimate of 157 divided by 2=
What is the best estimate of 108 divided by 5=
Answer:
157 divided by 2 is 78.5 round that to get 70
108 divided by 5 is 21.6 round that to get 22
The cost of an item is $0.30 per ounce. If total cost of the item is $3.60, how many ounces are in the item?
Answer:
Example 1: - If the item's label displays the weight as 3 lb 2 oz, type the shop name and item's brand, enter 3 in the pounds field, leave the 00 (decimal) value unchanged, enter 2 in the ounces field, leave the 00 (decimal) value unchanged, fill out the Price field and Calculate to get the price per ounce
Answer:
12 ounces
Step-by-step explanation:
3.60 = .3x
divide by .3 on both sides
12 = x
Give answer please
Water bottles are sold in cases of 24. Select the TWO expressions that can represent the total number of water bottles in c cases
Options:
24 X c,
24 ÷ c,
24 + c,
24 - c,
24c
Answer:
24c
Step-by-step explanation:
First off, we know what in each case there are 24 bottles. So if we have c crates and want to know the water bottles inside them, we need to multiply 24 by c resulting in 24c or 24 x c.
FOR 20 POINTS! GIVE REAL ANSWERS PLEASE. THANKS!
Davon's solution to the equation -2(x - 5) + 3 = -4 is shown below.
-2(x - 5) + 3 = -4
Step 1 -2x - 5 + 3= -4
Step 2 -2x - 2 = -4
Step 3 -2x = -2
Step 4 x = -1
In which step did the first mistake occur?
Step 1
Step 4
Step 2
Step 3
Answer:
8.5
Step-by-step explanation:
-2(x-5)+3=-4
Step 1 distribute
−2+10+3=−4
Step 2 add the numbers
-2x+13=-4
Step 3 subtract 13 from both sides of the equation
−2-13+13=-4-13
Step 4 get ride of the two 13
-2x=-4-13
Step 5 subtract -4 subtract 13
-2x=-17
Step 6 divide -17 by -2
-2x/-17
Step 6 answer
8.5