The probability that the train arrives on time, given that it leaves on time is 0.7
Explanation:The question asks for the probability that the train arrives on time, given that it leaves on time. This is a conditional probability problem, and we can use the formula for conditional probability, which is P(A|B) = P(A and B)/P(B).
In this case, event A is the train arrives on time, event B is the train leaves on time. We know that P(A and B) = 0.28 (the probability that the train arrives on time and leaves on time) and P(B) = 0.4 (the probability that the train leaves on time).
By substituting these values into the formula, we get P(A|B) = 0.28/0.4 = 0.7. So, the probability that the train arrives on time, given that it leaves on time is 0.7.
Learn more about Conditional Probability here:https://brainly.com/question/32171649
#SPJ11
Evaluate P(6,2).
A.) 12
B.) 30
C.) 360
The value of the [tex]\rm ^6p_2[/tex] is 30.
We have to determineThe value of P(6,2).
According to the question
The value of the [tex]\rm ^6p_2[/tex] is determined by using permutation.
The probability of selecting an ordered set of 'r' objects from a group of 'n' number of objects.
The order of objects matters in the case of permutation.
The formula to find [tex]\rm ^np_r[/tex] is given by:
[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}[/tex]
Substitute n = 6 and r = 2 in the formula;
[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}\\ \\ \rm ^6p_2 = \dfrac{6!}{(6-2)!}\\ \\ \rm ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4!}\\ \\ ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4\times 3 \times2 \times 1}\\ \\ ^6p_2= 6 \times 5}\\ \\ ^6p_2= 30[/tex]
Hence, The value of the [tex]\rm ^6p_2[/tex] is 30.
To know more about Permutation click the link given below.
https://brainly.com/question/10148445
Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth
The sum of the first and third of three consecutive even integers is 136. find the three even integers.
The sum of the first and third even integers is 136. By setting up an equation and solving for x, where x is the first integer, we determine that the consecutive even integers are 66, 68, and 70.
The problem asks us to find three consecutive even integers where the sum of the first and third integer is 136. Let's denote the first integer as x, the second integer as x + 2, and the third integer as x + 4 (since consecutive even numbers have a difference of 2). To solve for the values, we set up the equation x + (x + 4) = 136. Simplifying, we get 2x + 4 = 136. Subtracting 4 from both sides gives us 2x = 132. Dividing both sides by 2, we find out that x = 66. So, the first integer is 66, the second integer is 66 + 2 = 68, and the third integer is 66 + 4 = 70.
Therefore, the three consecutive even integers are 66, 68, and 70.
Angles θ and Φ are supplementary, and theta equals 3pi/7 find the measure of theta
From Plato: Φ =7π/7 or π.
You have a cone with a radius of 4 ft and a height of 12 ft. What is the height of the triangle formed by a perpendicular cross-section through the cone’s center?
if 6a-8b=0 and c=12b, the ratio of a to c is equivalent to the ratio of one to what number?
2x+3y=-2 4x+7y=-6 solve for the system of equations
The function h(x) = x2 + 14x + 41 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)
Part C: Determine the axis of symmetry for h(x). (2 points)
to anyone who may be a lil' sus, the previous answer is correct.
SOMEONE PLEASE HELP ME WITH MATH! WILL GIVE BRAINLIEST TO FIRST PERSON WHO ANSWERS!!
Solve each system by substitution.
1. -5x-8y=9
y= -3.
2. y= -3x
-6x-2y=3
3. 6x+5y=10
y=-8x+2
4.6x+2y= -6
y= -3x -3
Thank you!
The coordinates of the midpoint of GH¯¯¯¯¯¯¯¯are M(−2, 5) and the coordinates of one endpoint are H(−3, 7) .
The coordinates of the other endpoint are ( __ , __ )
The coordinate point of the other endpoint, G is (-1, 3)
The given parameters;
the midpoint = M(-2, 5)
one end point = H(-3,7)
To find:
the coordinate point of the other endpoint, GLet the coordinate point of the other endpoint = G(x, y)
The coordinate point of the other endpoint, G will be calculated using midpoint formula.
[tex]M(-2, 5) =( \frac{x + (-3)}{2} , \frac{y + 7}{2} )\\\\-2 = \frac{x - 3}{2} \ \ \ and \ \ 5 = \frac{y+ 7}{2} \\\\x-3 = 2(-2)\\\\x - 3 = -4\\\\x = -4 + 3\\\\x = -1\\\\y+ 7 = 2(5)\\\\y + 7 = 10\\\\y = 10 -7\\\\y = 3\\\\G= (-1, 3)[/tex]
Thus, the coordinate point of the other endpoint, G is (-1, 3)
Learn more here: https://brainly.com/question/10812174
Let $f$ be a function such that $f(x+y) = x + f(y)$ for any two real numbers $x$ and $y$. if $f(0) = 2$, then what is $f(2012)?$
Given:
f(0) = 2
So first of all, we let x = 2012, y = 0:
Then, F(2012) = 2012 + f(0)
Since f(0) = 2, then f(2012) = 2012 + 2 = 2014.
To add, the process that relates an input to an output is called a
function.
There are always three main parts of a
function, namely:
Input
The Relationship
The Output
The classic way of writing a function is "f(x) = ... ".
What goes into the function is put inside parentheses () after the name of the function: So, f(x) shows us the function is called "f", and "x" goes in.
What a function does with the input can be usually seen as:
f(x) = x2 reveals to us that function "f" takes "x" and squares it.
Wich of the operations ,+,-,x➗are inverse o each other
I want to make sure of my answer is right?
20 2/7 = 142/7 -20/35
find common denominator ( in this case it is 35)
35/7 =5 , multiply 142*5=710, 7*5 =35
142/7 = 710/35
710/35 - 20/35 = 710-20 = 690
690/35 now simplify that fraction
690/35 = 19.714
19*35 = 665
690-665=25
19 25/35
25/35 can reduce to 5/7
answer = 19 5/7
Use the arc length formula to find the length of the curve y = 5x − 4, −1 ≤ x ≤ 3. check your answer by noting that the curve is a line segment and calculating its length by the distance formula
The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.
To find the length of the curve y = 5x − 4 over the interval −1 ≤ x ≤ 3, we can use the arc length formula for a function y = f(x). The formula for the arc length L is given as:
L = ∫ab√(1 + (dy/dx)2) dx, where dy/dx is the derivative of y with respect to x.
1. Calculate the derivative dy/dx:
y = 5x − 4, so dy/dx = 5.
2. Substitute the derivative into the arc length formula:
L = ∫-13√(1 + 5²) dx = ∫-13√26 dx.
3. Integrate the function:
L = √26 ∫-13 dx = √26 [x]-13 = √26 (3 − (-1)) = 4√26 ≈ 20.396.
To verify this using the distance formula (since the curve is a straight line), we take the points (−1,−9) and (3,11) from the given curve:
4. Apply the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) = (-1, -9) and (x2, y2) = (3, 11).
Therefore,
Distance = √((3 - (-1))² + (11 - (-9))²) = √((4)² + (20)²) = √(16 + 400) = √416 = 4√26 ≈ 20.396.
Thus, the arc length calculated using the formula and the distance formula are consistent.
The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.
Can someone solve #4 and explain it? I really appreciate it on this problem! Thank you :)
WILL MARK BRAINIEST!!
e) Isabel’s competition,who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. (5 points)
f) Graph the function in part e. (10 points)
g) Is your graph discrete or continuous? Explain. (5 points)
Answer:
Isabel’s competition,who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. (5 points)
The price of the shipping ( f(x)) is equal to the cost of the fixed fee per order (3) plus the product of the number of books ordered (x) and the cost of the fee per book (1.99).
f(x)= 1.99x +3
for f(0) = 1.99(0)+3
f(0) =3
For F(0) there is a order of 0 books. The price is only for the shippping.
Step-by-step explanation:thats it buddy
A function that expresses f(x) is f(x) = 1.99x + 3. Graph is continuous.
What is continuous function?A continuous function is a function that does not have discontinuities that means any unexpected changes in value. A function is continuous if we can ensure arbitrarily small changes by restricting enough minor changes in its input.
For this case we have the following data:
A shipping fee of $ 1.99 is charged for each book sold.
There is a fixed fee of 3 dollars per order.
We must express the total cost by a function of the form .
If x represents the number of books sold, we have an expression of the form:
f(x) = 1.99x + 3
That is, according to the number of books sold, represented by x, a different value will be obtained for the total cost given by function f (x). For example:
If 3 books are sold, we have:
f(x) = 1.99x + 3
f(0) = 1.99(0) + 3
f(0) = 3
Thus, the value of f(x) for x = 0 is f(0) = 3.
The graph is continuous. Continuous is something that can and must be able to be broken down into fractions and decimals. Discrete means something that cannot be broken down into fractions or decimals.
Find out more information about continuous function here:
https://brainly.com/question/21447009
#SPJ2
Use the functions h(x) = 2x + 5 and t(x) = 7x − 6 to complete the function operations listed below.
Part A: Find (h + t)(x). Show your work. (3 points)
Part B: Find (h ⋅ t)(x). Show your work. (3 points)
Part C: Find h[t(x)]. Show your work. (4 points)
(48.9, -53.3) (84.6, -19.9) (-62.6, 81.7) (-14.4 ,-42.6) (71.2, -84.1) (71.2, 76.8 ) state the domain
Oh Plz help - I can't handle this one :)
What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 2?
an = 5 − 2(n − 1); all integers where n ≥ 1
an = 5 − 2(n − 1); all integers where n ≥ 0
an = 5 − 3(n − 1); all integers where n ≥ 1
an = 5 − 3(n − 1); all integers where n ≥ 0
The easiest way to answer this is to try all choices, plug in values for the 1st term and 2nd term then check if the answer matches with 5 and 2. (n = 1 and n = 2)
We know that n starts with 1 because that is our 1st term, we do not have 0th term, therefore that leaves us with 2 choices.
Choice 1: an = 5 − 2(n − 1); all integers where n ≥ 1
n = 1
a1 = 5 – 2 (1 – 1) = 5 – 2 (0)
a1 = 5
n = 2
a2 = 5 – 2 (2 – 1) = 5 – 2 (1)
a2 = 3 (FALSE!)
Choice 2: an = 5 − 3(n − 1); all integers where n ≥ 1
n = 1
a1 = 5 – 3 (1 – 1) = 5 – 3 (0)
a1 = 5
n = 2
a2 = 5 – 3 (2 – 1) = 5 – 3 (1)
a2 = 2 (TRUE)
Therefore the correct answer is:
an = 5 − 3(n − 1); all integers where n ≥ 1
Answer:
A is INCORRECT
Step-by-step explanation:
Just finished the FLVS test
How can you eliminate the fraction from each side of the equation to make finding the
solution easier?
The equation is 1/2(x - 4) = 1/3x + 2
Walter bought a square plot of land. the perimeter is 544 feet. how wide is the property?
perimeter of a square = is side times 4
so divide 544 by 4
544/4 = 136
the property is 136 feet wide
One number is 2 more than 3 times another. their sum is 22. find the numbers. 8, 14
An amusement park is installing a new roller coaster. The park intends to charge $5 per adult and $4 per child for each ride. It hopes to earn back more than the $650,000 cost of construction in four years. With the best of weather, the park can provide 125,000 adult rides and 50,000 child rides in one season
Answer:
Step-by-step explanation:
5x+ 4y greater than or equal to 650,000
500,000
y greater than or equal to 200,00
Answer is : 5x+4y greater than or equal to 650,000
X less than or equal to 500,000
Y is less than or equal to 200,000
how would you solve it. I know the answer already. my problem working it out.
4b/2 + 3 = 11 + b.
The graph shows the number of paintballs a machine launches, y, in x seconds::
A graph titled Rate of Launch is shown. The x axis label is Time in seconds, and the x axis values are from 0 to 20 in increments of 4 for each grid line. The y axis label is Number of Balls, and the y axis values from 0 to 80 in increments of 16 for each grid line. A line is shown connecting points on ordered pair 4, 16 and 8, 32 and 12, 48 and 16, 64.
Which expression can be used to calculate the rate per second at which the machine launches the balls?
fraction 64 over 4
fraction 4 over 64
fraction 16 over 4
fraction 4 over 16
a fraction should be number of balls over time per second
so it should be 16/4 which is 4 balls per second
Answer: fraction 16 over 4
Step-by-step explanation:
The given graph shows the number of paintballs a machine launches, y, in x seconds.
We know that the rate of change of a line is given by :-
[tex]k=\frac{y_2-y_1}{x_2-x_1}[/tex]
The ordered pairs on the line in graph are (4, 16) and (8, 32) and (12, 48) and (16, 64).
Thus, the rate per second at which the machine launches the balls is given by :-
[tex]k=\frac{32-16}{8-4}=\frac{16}{4}
A quadratic equation is shown below: 3x2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 3x2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answer:
[tex]\text{The roots of }3x^2+5x-8=0\text{ are }x=1,\frac{-8}{3}[/tex]
Step-by-step explanation:
[tex]\text{Part A: Given a quadratic equation }3x^2-15x+20=0[/tex]
[tex]\text{Comparing above equation with }ax^2+bx+c=0[/tex]
a=3, b=-15, c=20
Discriminant can be calculated as
[tex]D=b^2-4ac[/tex]
[tex]D=(-15)^2-4(3)(20)=225-240=-15<[/tex]
The roots are imaginary
The solution is
[tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
[tex]x=\frac{-(-15)\pm \sqrt{-15}}{2(3)}=\frac{15\pm\sqrt{15}i}{6}[/tex]
The roots are not real i.e these are imaginary
[tex]\text{Part B: Given a quadratic equation }3x^2+5x-8=0[/tex]
[tex]\text{Comparing above equation with }ax^2+bx+c=0[/tex]
a=3, b=5, c=-8
Discriminant can be calculated as
[tex]D=b^2-4ac[/tex]
[tex]D=(5)^2-4(3)(-8)=25+96=121>0[/tex]
The roots are real
By quadratic formula method
The solution is
[tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
[tex]x=\frac{-5)\pm \sqrt{121}}{2(3)}=\frac{-5\pm 11}{6}[/tex]
[tex]x=1,\frac{-8}{3}[/tex]
which are required roots.
I choose this method because I can get the solutions directly by substituting the values in formula, and I don't have to guess the possible solutions.
In a store 60 cans of soup are arranged to be this play into equal rows why does the fraction 10 over 60 not represent the situation explain
A textile corporation buys equivalent with an initial purchase price of $750000. It is estimated its useful life will be 3 years and at that time it's value will be$75000. The total depreciation is depreciation is divided equally among the three years. What is the total amount of depreciation declared each year?
33.
In quadrilateral PQRS, the coordinates are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). How can you use coordinate geometry to show that the diagonals are perpendicular?
Apply the Distance Formula to show that opposite sides to show they are congruent.
Find the slopes of their product is 1.
Apply the Distance Formula to show that opposite sides to show sides are congruent.
Find the slopes and show that their product is -1.
Answer: The answer is (d) Find the slopes and show that their product is -1.
Step-by-step explanation: Given in the question and shown in the attached figure that the vertices of the quadrilateral PQRS are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). We are asked to use geometry to show that the diagonals PR and QS are perpendicular to each other.
We know that the two lines are perpendicular if the product of their slopes is --1.
So, first we will find the slopes of PR and QS, multiply them, and check the value.If the value is -1, then the diagonals are perpendicular to each other.
That is, if 'm' and 'p' are the slopes of the diagonals PR and QS, and if m × p = -1, then the two diagonals are perpendicular.
Thus, the correct answer is (d).