The PDF for the wait time (denoted by the random variable X) is
[tex]f_X(x) = \begin{cases}\lambda e^{-\lambda x} & \text{if }x \ge 0 \\ 0 &\text{otherwise}\end{cases}[/tex]
where λ = 1/75. We want to find Pr[X > 70 | X ≥ 40]. Pierre has already been waiting for 40 min, so if he waits another 30 min he will have waited for a total of 70 min.
By definition of conditional probability,
Pr[X > 70 | X ≥ 40] = Pr[X > 70 and X ≥ 40] / Pr[X ≥ 40]
If X > 70, then automatically X ≥ 40 is satisified, so the right side reduces to
Pr[X > 70 | X ≥ 40] = Pr[X > 70] / Pr[X ≥ 40]
Use the PDF or CDF to find the remaining probabilities. For instance, using the PDF,
[tex]\mathrm{Pr}[X > 70] = \displaystyle \int_{-\infty}^{70} f_X(x) \, dx = \int_0^{70} f_X(x) \, dx \approx 0.3932[/tex]
Or, using the CDF,
[tex]F_X(x) = \displaystyle \int_{-\infty}^x f_X(t) \, dt = \begin{cases}0&\text{if }x<0 \\ 1-e^{-\lambda x} & \text{if }x \ge 0\end{cases}[/tex]
[tex]\implies \mathrm{Pr}[X > 70] = 1 - \mathrm{Pr}[X \le 70] = 1 - F_X(70) \approx 0.3932[/tex]
Similarly, you'll find that Pr[X ≥ 40] ≈ 0.5866.
It follows that
Pr[X > 70 | X ≥ 40] ≈ 0.3932 / 0.5866 ≈ 0.6703
Question 1 (Fill-In-The-Blank Worth 3 points)
(6.03)
How many variable terms are in the expression 3x?y + 5x2 + y + 9? (Input a numeric value only.)
Numerical Answers Expected!
Answer for Blank 1:
helpp plsss right now
Answer:
<DEF = 107
Step-by-step explanation:
The way to best solve this problem is by starting with angle F. Remember that all angles in a straight line must add up to 180. So by subtracting 135 from 180 we get 45 for angle F.
180 - 135 = 45
After that, we can figure out the measure of <DEF. All the angles of a triangle must add up to 180. So:
180 - 28 - 45 = 107
Making the answer 107 for the measure of <DEF
When a number is multiplied by itself and 2 is added to it, the result is 227. What is the number?
Let number be x
[tex] \leadsto \sf {x}^{2} + 2 = 227[/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \sf {x}^{2} = 227 - 2[/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \sf {x}^{2} = 225[/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \sf {x} = \sqrt{225} [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \sf {x} = \sqrt{15 \times 15} [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \sf {x} = 15[/tex]
Number = 15
Sasha runs at a constant speed of 3.5 meters per second for hour. Then, she walks at a rate o 2 1 1.6 meters per second for hour. How far did Sasha run and walk in 60 minutes? 2 Sasha ran and walked meters. (Type an integer or a decimal.)
Answer:
22
Step-by-step explanation:
Julian owns a small business selling bagels. He knows that in the last week 57 customers paid cash, 12 customers used a debit card, and 70 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a debit card as a fraction in simplest form.
Considering the definition of probability, the probability that the next customer will pay with a debit card is [tex]\frac{12}{139}[/tex].
Definition of probabilityProbability is the greater or lesser chance that a given event will occur.
In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.
Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases.
[tex]P(A)=\frac{number of favorable events}{ total number of possible events}[/tex]
The probability of event A can only be a number between 0 and 1; although it can also be written as a percentage.
Probability that the next customer pay with a debit cardIn this case, you know:
Total number of customers = 57 +12 +70= 139 (total number of possible cases)The number of customers that used a debit card = 12 (number of favorable cases)Replacing in the definition of probability:
[tex]P(A)=\frac{12}{ 139}[/tex]
Finally, the probability that the next customer will pay with a debit card is [tex]\frac{12}{139}[/tex].
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An angle measures 84° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
3 degrees and 87 degrees
Step-by-step explanation:
If the angle is x, its complement is (90-x).
This means that x+84=90-x.
2x=6
x=3.
So the measures are 3 degrees and 90-3=87 degrees
0.02852(3 significant figures)
Hi!
I can help you with joy!
Remember that
* Zeros in the beginning of decimals are not significant figures.
For example, 0.021 has only 2 significant figures: 2 and 1.
* Zeros in the end of decimals are significant.
For example, 2.100 has 4 significant digits.
Now, let's round 0.02852 to 3 significant digits.
Right now it has 4.
Recall the Rounding Rules:
If the number you are rounding is followed by a number less than 5, you round down.If the number you are rounding is followed by a number greater than or equal to 5, you round up.[tex]\text{5 is followed by a number less than 5, so we round down.}[/tex]
[tex]\text{0.02852 Round down: 0.0285 (Answer)}[/tex]
Hope it helps!
Enjoy your day!
Answered by
~Silent~
does it look correct?
Answer:
on the third column it should be tens and not ones.good job so far tho!
help help help help help
Answer:
8 science fiction movies
Step-by-step explanation:
2+s=10
-2 -2
s=8
Travis streamed 8 science fiction movies
Use a ratio identity to find tan given the following values.
Answer:
5
Step-by-step explanation:
tan(0) = sin(0)/cos(0) = 5sqrt(26)/(26)/sqrt(26)/26
Cancel the common factor which is sqrt(26)
tan(0) = sin(0)/cos(0) = 5/26 * 26
Cancel common factor again which is 26 here
tan(0) = sin(0)/cos(0) = 5
Solve - 3/5t = 15
t = -25
t = 15
t = -15
t = 25
Answer: -25
Step-by-step explanation:
-3/5t=15 mulitply both sides of the equation by -5/3.
-5/3x3/5t= -5/3x15 multiplying an even number makes it positive.
t= -5x5 multiply remaining numbers.
Answer: t = -25
Brainliest pls :)
The volume of this prism Is ___
cubic inches
Answer:
The answer is 140 cubic in
Step-by-step explanation:
The formula for the volume of a prism is V=Bh, where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw. Hope this helped! :) (ps. I am sorry if it does not help.)
Answer:
140 cubic inches
Step-by-step explanation:
8x5x3.5
8x5 = 40
40x 3.5= 140
Which of the following are solutions to the quadratic equation below?
Check all that apply.
x2 + 8x - 9 = 0
A. 1
B. 3
C. -3
D. -9
E. -1
Answer:
[tex]\huge\boxed{\sd -9, \ 1}[/tex]
Step-by-step explanation:
Given quadratic equation is:
x² + 8x - 9 = 0
Using mid-term break formula
x² + 9x - x - 9 = 0 (When we multiply middle terms, we get side terms as answer which is mid term break formula.)
Taking common
x(x + 9) - 1(x + 9) = 0
Take (x + 9) common
(x + 9)(x - 1) = 0
According to zero's method:
Either:
x + 9 = 0 OR x - 1 = 0
x = -9 OR x = 1
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807How do I solve this equation?
through: (-2, 4), slope = -7/-2
the formula is: y=mx+b
Answer:
[tex]y=\frac{7}{2}x+11[/tex]
Step-by-step explanation:
To solve, we need to find the y-intercept (b). In order to find the y-intercept, we can plug in the slope and the (x,y) coordinate pair given to us into the equation to solve for the y-intercept:
y=mx+b
4=(-7/-2)*-2+b
4=14/-2+b
4=-7+b
Add 7 to both sides
b=11
Therefore the equation is:
[tex]y=\frac{7}{2}x+11[/tex] (note that the fraction is positive since the two negatives cancel out)
A parallelogram has adjacent sides 25 cm and 6 cm . if one diagonal is 29 cm then find area , height corresponding to the sides 25 cm and perimeter.
very important question.....
plz do fast.
Answer:
height = 4.8 cm
area = 120 cm²
perimeter = 62 cm
Step-by-step explanation:
**Please refer to the attached diagram when following the step-by-step**
First, find m∠C (green angle on diagram) by using the cosine rule:
[tex]c^2=a^2+b^2-2abcos(C)[/tex]
[tex]\implies 29^2=6^2+25^2-2(6)(25)cos(C)[/tex]
[tex]\implies cos(C)= \frac{29^2-6^2-25^2}{-2(6)(25)}[/tex]
[tex]\implies cos(C)= \frac{180}{-300}=-\frac{3}{5}[/tex]
[tex]\implies cos(C)=126.8698976... \textdegree[/tex]
Therefore, the interior angle of the right triangle at point C (blue angle on diagram) is:
[tex]180-cos^{-1}(-\frac{3}{5})=53.13010235... \textdegree[/tex]
Now use the Sine Rule (for finding sides) to determine height (h):
[tex]\frac{6}{sin(90)}=\frac{h}{sin(53.13..)}[/tex]
[tex]\implies \frac{6}{1}=\frac{h}{\frac{4}{5}}[/tex]
[tex]\implies 6 \times \frac{4}{5}=h[/tex]
[tex]\implies h=\frac{24}{5}=4.8[/tex]
So the height = 4.8 cm
Now we have determined the height, we can calculate the area by using the area of a parallelogram formula:
Area of a parallelogram = base x perpendicular height
⇒ area = 25 x 4.8 = 120 cm²
Parallelogram is a four-sided shape made up of two pairs of straight parallel lines that are equal in length.
Perimeter = sum of the sides
⇒ perimeter = 6 + 6 + 25 + 25 = 62 cm
Find the slope for this question please
to get the slope of any straight line we only need two points off of it, hmmm let's use the points in the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{4}{2}\implies 2[/tex]
How can you determine the number of solutions of a system by looking at the equationz
Answer:
Look at the variables and numbers in the equation, and what it equals
Step-by-step explanation:
Expressions that are the exact same have infinite solutions
[tex]5x+3=5x+3[/tex]
Expressions that are different have 1 solution
[tex]6x+7=5x-2[/tex]
Expressions that are the same with different operands have no solution
[tex]5x-3=5x+3[/tex]
Explanation:
The short of it is that when the equations are in the same form, if one equation is the same as or a multiple of the other, there are infinite solutions. If one equation is the same as or a multiple of the other, except for the constant terms, there are no solutions. Otherwise, there is one solution.
Example:
If one equation is x +2y = 3, then you can consider the other equation:
3x +6y = 9 . . . . 3 times the first equation: infinite solutions
3x +6y = 6 . . . . 3 times the first equation; constants differ: no solutions
3x -6y = 9 . . . . not a multiple of the first equation: one solution
_____
Here's a more formal method.
Put both equations of the linear system of two equations into general form:
ax +by +c = 0
dx +ey +g = 0
Perform the following arithmetic:
p = ae -db . . . . . this is called the system "determinant"
q = bg -ec
r = cd -ga
If p = q = r = 0, the equations describe the same line, so there are infinite solutions.
If p = 0 and either of q ≠ 0 or r ≠ 0, the equations describe parallel lines, so there are no solutions.
If p ≠ 0, there is one solution: (x, y) = (q/p, r/p).
_____
Additional comment
This method can always be used to find the solution to a system that is known to have one solution. It often requires fewer arithmetic operations than other solution methods. It is a variation of what is sometimes called the "cross multiplication method."
A biology class has 29 students. Find the probability that at least two students in the class have the same birthday. For simplicity, assume that there are always 365 days in a year and that birth rates are constant throughout the year. (Hint: First, determine the probability that no 2 students have the same birthday and then apply the complementation rule.)
I WILL GIVE BRAINLY TO WHOEVER GETS THIS RIGHT PLAESE HELPPP. LOOK AT THE PICTURE.
Answer:
10.99
Step-by-step explanation:
I JUST HAD THAT AND GOT IT RIGHT TRUST ME NOW GIVE ME BRAINLY I SWEARRR
For each pair of numbers, determine by what percent the second number is greater than the first. Also determine by what percent the first number is less than the second.
100 and 110
The percentage by which it is less than the other is 10%
How do we find the percentage?From the question we are asked to find the percentage of which the difference of the two numbers are. To do this, we take the subtraction of both
110 - 100 = 10
Then we find the percentage of this number.
10/100 * 100 = 10%
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this is confusing hard
Answer:
My best recommendation is to find the median.
Step-by-step explanation:
To find a median, find the averaging number and divide by 2. Round them up for odd numbers. For even numbers, leave them and if it's a decimal, find a remainder. If the median method does not work, put the numbers on a ratio comparison and see if that gives you the next patterns.
I tried my best so I really do hope this helps you.
What is the length and area of a rectangle whose perimeter is 24 cm and the breadth is 4 cm?
[tex] \\ [/tex]
What is the length and area of a rectangle whose perimeter is 24 cm and the breadth is 4 cm?
[tex] \\ [/tex]
Given:-[tex] \\ [/tex]
Breadth of the rectangle = 4 cm[tex] \\ [/tex]
Perimeter of the rectangle = 24 cm[tex] \\ [/tex]
To find:-[tex] \\ [/tex]
Length of the rectangle[tex] \\ [/tex]
Area of the Rectangle[tex] \\ [/tex]
Solution:[tex] \\ [/tex]
❁We know:-
Perimeter of rectangle =2 ( Length + Breadth )
[tex] \\ [/tex]
By using this formula we can find length of rectangle
[tex] \\ [/tex]
So:-
↣ Perimeter of rectangle =2 ( Length + Breadth )
[tex] \\ [/tex]
↣ 24 =2 ( Length + 4 )
[tex] \\ [/tex]
↣24 = 2(Length) + 2(4)
[tex] \\ [/tex]
↣24 = 2(Length) + 2 × 4
[tex] \\ [/tex]
↣24 = 2(Length) + 8
[tex] \\ [/tex]
↣24 - 8 = 2(Length)
[tex] \\ [/tex]
↣ 16 = 2(Length)
[tex] \\ [/tex]
↣2(Length) = 16
[tex] \\ [/tex]
↣ Length = 16/2
[tex] \\ [/tex]
↣ Length = 8 cm
[tex] \\ [/tex]
Now Finally Let's find area :-
[tex] \\ [/tex]
❁We know:-
Area of rectangle = Length × Breadth
[tex] \\ [/tex]
So:-
⇢Area of rectangle = Length × Breadth
[tex] \\ [/tex]
⇢Area of rectangle = 4 × 8
[tex] \\ [/tex]
⇢Area of rectangle = 32 cm²
find the volume of a sphere with a circumference of 28.7 yd
Answer:
399.77 yd³
Step-by-step explanation:
Circumference: 2πr
Solve for r:
28.7 = 2πr9.14 = 2r4.57 = rSolve for volume: 4/3(πr³)
4/3(πr³)4/3(π(4.57)³)4/3(π(95.44))4/3(95.44)π127.25(π)399.767 ≈ 399.77-Chetan K
what is the equation to the graph
Answer: y=2/(x-1)
Step-by-step explanation:
We can tell this is a rational function that looks somewhat like y=1/x, execpt that the asymptote is at x=1, not x=0. This means we have y=k/(x-1), where k is a constant.
Substituting in the coordinates of a point on the graph, say (0, -2), we get that -2=k/-1, meaning k=2.
So y=2/(x-1).
Problem Solving
If the integer m is a multiple of both 10 and 12, then all of the following must be
factors of m EXCEPT
O 15
O 12
O 10
O 8
O 6
Answer: 12 and 8
Step-by-step explanation:
there not
The integer m whose factors are 15,12,10 and 6 is 60 and 8 is not, therefore, for integer 60, 8 will be not the factor so option (D) is correct.
What is an integer?An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.
Integer ; ....-2 , -1 , 0 , 1 , 2 , .....
Integers are non-decimal numbers and all integers are rational numbers.
The factors of 10 ⇒ 2 × 5
The factors of 12 ⇒ 2 × 2 × 3
The factors of 10 × 12 ⇒ 2 × 5 × 2 × 2 × 3
We can make all factors by 2 × 5 × 2 × 2 × 3 like 5 × 3 = 15 , 2 × 2 × 2 = 8.
So find a number whose all will be a factor except one.
The factor of 60 ⇒ 2 × 2 × 3 × 5
We cannot make 8 by this factor but can make 15,12,10,6.
Example 15 = 3 × 5 , 12 = 2 × 2 × 3
Hence "The integer m whose factors are 15,12,10 and 6 is 60 and 8 is not, therefore, for integer 60, 8 will be not the factor".
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The tail of a Boeing 747 is 63 2/3 feet.
How many inches tall is the tail?
Answer:
1 foot is 12 inch so the tail of boeing will be 63 2/3 x 12
Step-by-step explanation:
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Hoped this helped and have a nice day
Each 1/2 centimeter on a map represents an actual length of 1/8 of a meter.
What length on the map represents 1 meter?
1/16 centimeter
5/8 centimeters
2 centimeters
4 centimeters
Answer:
4 cm
Step-by-step explanation:
1/8·n = 1/2
multiply each side by 8/1
n = 8/2 or 4
The length on the map that represents 1 meter in real is 4 centimeters.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that Each 1/2 centimeter on a map represents an actual length of 1/8 of a meter. Therefore, the ratio can be written as,
Length on Map / Actual Length = (1/2) centimeters / (1/8) meters
Length on Map / Actual Length = 4 centimeters per meters
Now, the length on the map that represents 1 meter in real is,
Length on Map / Actual Length = 4 centimeters per meters
Length on Map / 1 meter = 4 centimeters / 1 meters
Length on Map = 4 centimeters
Hence, the length on the map that represents 1 meter in real is 4 centimeters.
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13ab+15ab I’m in 6th grade and I need big help
Find the average yearly salary of an architect and a lawyer. The average yearly salary of an architect is $____ thousand
Answer:
Let x = salary of the architect, in thousands
Let 2x - 25 = salary of a lawyer, in thousands
2x + 2x - 25 = 206 (combined salaries, in thousands)
4x - 24 = 206
4x = 206 - 25 = 181
x = 45.25, in thousands.
The architect earns $45,250 yearly
The lawyer earns $65,500 yearly
If you want to set up a system of equations with 2 variables.
Let x = the salary of the architect, in thousands.
Let y = the salary of the lawyer, in thousands.
x + y = 206
y = 2x - 25
Solving by substitution will yield the same equation as above: x = 45.25 or $45,250
Then y = 2(45,250) - 25,000 = $66,500
Why is the domain of the square root parent function x ≥ 0 and the domain of the cube root parent function all real numbers?
Answer:
here may be more than one correct answer.
Cubic, f(x)=x^3
Quadratic, f(x)=x^2
Square root, f(x)=√x
Constant, f(x)=c
Linear, f(x)=x
Step-by-step explanation:
The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.
What is a function?A function is a relation between a dependent variable f(x) and an independent variable x, where for every value of x in its domain, there is one and only one value of f(x).
What is the domain of a function?The domain of a function is the set of values of x, for which f(x) exists.
What is the range of a function?The range of a function is the set of values of f(x), in a given domain of x.
How do we solve the given question?We are asked why is the domain of the square root parent function x ≥ 0 and the domain of the cube root parent function all real numbers.
We know that the domain of a function is the set of values of x, for which f(x) exists.
Let the square root parent function be f(x) = √x.
The domain of this function is x ≥ 0, as the square root of negative values does not exist in the real number system.
Let the cube root parent function be g(x) = ∛x.
The domain of this function is all real numbers, as the cube root of all values does exist in the real number system.
∴ The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.
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