If K = {(x, y )|x - y = 5}, find the corresponding range of y for the domain {0, 2, 4}.
Let f(x) = k(9x − x2) if 0 ≤ x ≤ 9 and f(x) = 0 if x < 0 or x > 9. (a) for what value of k is f a probability density function?
To find the value of k that makes f(x) a probability density function, we need to satisfy two conditions: f(x) must be non-negative for all x and the total area under the curve of f(x) must equal 1. Solving the integral of the function f(x) = k(9x - x^2) from x = 0 to x = 9, we find that the value of k that satisfies these conditions is approximately 0.0696.
Explanation:In order for the function f(x) to be a probability density function, it must satisfy two conditions:
The function must be non-negative for all values of x.
The total area under the curve of the function must be equal to 1.
Let's analyze the function f(x) = k(9x - x^2) for 0 ≤ x ≤ 9 and f(x) = 0 for x < 0 or x > 9:
If 0 ≤ x ≤ 9, the function f(x) is given by f(x) = k(9x - x^2).The function f(x) is non-negative in the interval [0, 9] if k(9x - x^2) ≥ 0. This is true when k > 0.To find the value of k that makes the total area under the curve equal to 1, we need to integrate the function f(x) = k(9x - x^2) from x = 0 to x = 9 and set it equal to 1:∫09 k(9x - x^2) dx = 1Simplifying the integral gives us k(405 - 364.5) = 1Solving for k, we get k ≈ 0.0696 (rounded to four decimal places).Therefore, the value of k that makes f(x) a probability density function is approximately 0.0696.
Learn more about Probability Density Functions here:https://brainly.com/question/35625239
#SPJ2
What is the value of the expression? 56−(18÷34) as a fraction in simplest form
The value of the expression [tex]\( 56 - \left( \frac{18}{34} \right) \)[/tex] as a fraction in simplest form is [tex]\( \frac{943}{17} \)[/tex].
To solve the expression, we first perform the division within the parentheses:
[tex]\[ \frac{18}{34} \][/tex]
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[ \frac{18 \div 2}{34 \div 2} = \frac{9}{17} \][/tex]
Now we have:
[tex]\[ 56 - \frac{9}{17} \][/tex]
We need to express the whole number as a fraction with the same denominator as the fraction we are subtracting.
[tex]\[ \frac{56 \times 17}{17} - \frac{9}{17} \][/tex]
[tex]\[ \frac{952}{17} - \frac{9}{17} \][/tex]
[tex]\[ \frac{952 - 9}{17} \][/tex]
[tex]\[ \frac{943}{17} \][/tex]
What’s the answer to simply
1
-
2
-
4 it’s a fraction.
Your mid-morning break begins at 10:30 A.M. and lasts for 15 minutes. You work 2 hours and 50 minutes until your lunch break. What time does your lunch break begin?
Final answer:
The lunch break begins at 1:20 P.M. after working for 2 hours and 50 minutes from the mid-morning break at 10:30 A.M.
Explanation:
The mid-morning break begins at 10:30 A.M. and lasts for 15 minutes.
You work 2 hours and 50 minutes from 10:30 A.M.
To find the start time of your lunch break, add 2 hours and 50 minutes to 10:30 A.M.
Lunch break begins at 1:20 P.M.
A student pays for 8.9 pounds of apples with a $10 bill. How much change does the student receive?
Find the sale price of the item. Round to two decimal places if necessary.
Original price: $217.90
Markdown: 79%
The sale price is $___
Find the slope of the line that passes through (90, 93) and (-4, 49).
pls help with fractions. (Operations with Rational Numbers) thx, xoxo
ps. This is 7th grade math
12.917 rounded to the nearest ones
can someone double check my answers on this integers sheet? (53 points)
Find the area bounded by the curve y = x 1/2 + 2, the x-axis, and the lines x = 1 and x = 4 A. 16 B. 10 2/3 C. 7 1/2 D. 28 1/2
in the greenhouse holds 467 plants how many plants can 6 shelves hold
Twenty-five bakery customers were surveyed to determine if they like cake or pie. The results are shown in the Venn diagram.
Given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie
A. 2/7
B. 2/5
C. 4/7
D.4/5
From the given Venn diagram. The probability that the customer also likes pie is 2/7.
Given that a randomly chosen customer likes cake
The results are shown in the Venn diagram.
To determine the probability that the customer also likes pie
In total, 14 people liked the cake (10+4).
4 of those 14 also like pie.
What is the formula for probability?The probability of event A is given by the ratio of the no of a favorable outcome in event A divided by the total outcome in a sample space A.
4/14= 2/7
Option A is correct.
To learn more about the probability visit:
https://brainly.com/question/24756209#SPJ3
What is the slope of the line passing through the points (−1, 7) and (4, −1)?
2nd picture is the choices I have.
Rohan is checking in poodles for a dog show. A miniature poodle must be between 10 in. and 15 in. at the shoulder. The body length must be no more than 16 in. In addition, the poodle’s shoulder height must be no more than 1 in. longer than its body length.
The graph shows the feasible region, where x represents the poodle’s body length and y represents the shoulder height.
Which ordered pairs meet all the constraints for a successful poodle measurement and make sense in context of the situation?
Select each correct answer.
(11, 14)
(10, 12)
(12, 10.5)
(15, 11)
(11, 9)
Let
x-------> represents the poodle’s body length
y-------> represents the shoulder height
Constraints
[tex]10\ in \leq y \leq 15\ in[/tex] --------> constraint A
[tex]x \leq 16\ in[/tex] --------> constraint B
[tex]y \leq x+1[/tex] --------> constraint C
Using a graphing tool
see the attached figure
The solution is the shaded area
we know that
If a pair ordered is a solution for a successful poodle measurement
then
the pair ordered meet all the constraints
Let's check each case to determine the solution to the problem
Replace the values of x and y of the point in the different constraints. If all constraints are met, then the point is a system solution
Case A) [tex](11,14)[/tex]
constraint A
[tex]10\ in \leq 14 \leq 15\ in[/tex] ------> is true
constraint B
[tex]11 \leq 16\ in[/tex] --------> is true
constraint C
[tex]14 \leq 11+1[/tex]
[tex]14 \leq 12[/tex] -------> is not true
therefore
the pair [tex](11,14)[/tex] does not meet all constraints
Case B) [tex](10,12)[/tex]
constraint A
[tex]10\ in \leq 12 \leq 15\ in[/tex] ------> is true
constraint B
[tex]10 \leq 16\ in[/tex] --------> is true
constraint C
[tex]12 \leq 10+1[/tex]
[tex]12 \leq 11[/tex] -------> is not true
therefore
the pair [tex](10,12)[/tex] does not meet all constraints
Case C) [tex](12,10.5)[/tex]
constraint A
[tex]10\ in \leq 10.5 \leq 15\ in[/tex] ------> is true
constraint B
[tex]12 \leq 16\ in[/tex] --------> is true
constraint C
[tex]10.5 \leq 12+1[/tex]
[tex]10.5 \leq 13[/tex] -------> is true
therefore
the pair [tex](12,10.5)[/tex] meets all constraints
Case D) [tex](15,11)[/tex]
constraint A
[tex]10\ in \leq 11 \leq 15\ in[/tex] ------> is true
constraint B
[tex]15 \leq 16\ in[/tex] --------> is true
constraint C
[tex]11 \leq 15+1[/tex]
[tex]11 \leq 16[/tex] -------> is true
therefore
the pair [tex](15,11)[/tex] meets all constraints
Case E) [tex](11,9)[/tex]
constraint A
[tex]10\ in \leq 9 \leq 15\ in[/tex] ------> is not true
constraint B
[tex]11 \leq 16\ in[/tex] --------> is true
constraint C
[tex]11 \leq 15+1[/tex]
[tex]11 \leq 16[/tex] -------> is true
therefore
the pair [tex](11,9)[/tex] does not meet all constraints
therefore
the answer is
[tex](12,10.5)[/tex]
[tex](15,11)[/tex]
20 children plays a game there are 5 children on each team how many teams play the game write a division sentence to represent the problem
Final answer:
To find the number of teams playing the game, divide the total number of children by the number of children on each team. In this case, there are 20 children and 5 children on each team, so there are 4 teams playing the game.
Explanation:
To find the number of teams playing the game, you can divide the total number of children by the number of children on each team. In this case, there are 20 children and 5 children on each team. So, the division sentence to represent the problem is:
20 ÷ 5 = 4
Therefore, there are 4 teams playing the game.
The data from 200 endothermic reactions involving sodium bicarbonate are summarized as follows: calculate the probability mass function of final temperature
write the following comparison as a ratio reduced to lowest terms.
114 hours to 13 days
To write the comparison as a ratio reduced to lowest terms, we need to convert both the hours and the days to a common unit of time. There are 24 hours in a day, so we can convert 13 days to hours by multiplying 13 by 24: 13 days x 24 hours/day = 312 hours. Now, the comparison is 114 hours to 312 hours. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. 114 ÷ 6 = 19, and 312 ÷ 6 = 52. Therefore, the simplified ratio is 19:52.
Explanation:To write the comparison as a ratio reduced to lowest terms, we need to convert both the hours and the days to a common unit of time. There are 24 hours in a day, so we can convert 13 days to hours by multiplying 13 by 24: 13 days x 24 hours/day = 312 hours. Now, the comparison is 114 hours to 312 hours. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. 114 ÷ 6 = 19, and 312 ÷ 6 = 52. Therefore, the simplified ratio is 19:52.
People drive, on average, 11,900 miles per year. About how many miles each week is that
To calculate the average weekly driving mileage based on an annual average of 11,900 miles, divide the total miles by 52 weeks, resulting in approximately 228.85 miles driven per week.
Explanation:The question asks us to calculate how many miles are driven each week if an average person drives 11,900 miles per year. To find the weekly mileage, we can divide the total annual miles by the number of weeks in a year. Since there are 52 weeks in a year, we would perform the following calculation:
Divide 11,900 by 52.11,900 miles \/ 52 weeks = 228.85 miles per week.Therefore, on average, a person drives approximately 228.85 miles each week.
the sum of partial products is equal to the final product?
multiply 4xy^3(3×^2y)^2
One root of is x = 6. What are all the factors of the function? Use the Remainder Theorem.
Answer:
C. (x - 6)(x + 4)(x - 2)
Step-by-step explanation:
i just took the test goodluck
Help please :) ! The dashed triangle is the image of the pre-image solid triangle. What is the scale factor used to create the dilation? Enter your answer in the box.
Let
x---------> measure of the base of the triangle of the image
y---------> measure of the base of the triangle of the pre-image
sf-------> the scale factor
we know that
the scale factor is equal to
[tex]sf=\frac{x}{y}[/tex]
in this problem we have
[tex]x=6\ units\\y=3\ units[/tex]
Find the scale factor
substitute the values of x and y in the formula above
[tex]sf=\frac{6}{3}=2[/tex]
therefore
the answer is
the scale factor is equal to [tex]2[/tex]
How do I multiply 8.354 by 11.81?
981,657 rounded to nearest ten thousand
The sum of a 1 digit number and a 3 digit number is 217. The product is 642. One number is between 200 and 225. What are the numbers?
WILL GIVE A BRAINLEST AND 20PTS
Which figures can be precisely defined by using only undefined terms? Check all that apply.
angle
arc
circle
line segment
parallel lines
Answer:
We can define circle, line segment and parallel lines with the help of undefined terms.
Step-by-step explanation:
The undefined terms in geometry are line, plane and points.
So, we can define line segment, circles and parallel lines with the help of undefined terms.
A line segment is a part of a line that contains two distinct end points.
A circle is defined as a figure with a set of points that are all equidistant from a fixed point called the center.
Parallel lines are lines in a plane that never meet or intersect at any point.
You drove at 55mph for 4.5 hours. Which of the following equations will tell you how far you drove? A: d=(55)(4.5) B: 55=r(4.5) C: 4.5=55t D: 4.5=r(55)
Answer : The correct equation will be, (A) [tex]d=(55)\times (4.5)[/tex]
Step-by-step explanation :
As we are given that:
Speed = 55 mph
Time = 4.5 hr
As we know that:
[tex]Distance=Speed\times Time[/tex]
So,
[tex]Distance=55mph\times 4.5hr[/tex]
[tex]Distance=55\times 4.5[/tex]
or,
[tex]d=(55)\times (4.5)[/tex]
Thus, the correct equation will be, (A) [tex]d=(55)\times (4.5)[/tex]
There are 56 trees in an apple orchard. They are arranged in equal rows. There are 8 trees in each row. How many rows of apple trees are there? Which equation can be used to solve this problem?
Final answer:
In this case, there are 56 trees in the orchard and 8 trees in each row, so there are 7 rows of apple trees in the orchard.
Explanation:
To find the number of rows of apple trees in the orchard, we need to divide the total number of trees by the number of trees in each row.
In this case, there are 56 trees in the orchard and 8 trees in each row.
We can use the equation:
Number of rows = Total number of trees / Number of trees in each row
Plugging in the values:
Number of rows = 56 trees / 8 trees = 7 rows
Therefore, there are 7 rows of apple trees in the orchard.