Answer:
[tex]P(50 < x < 150) =0.3834[/tex]
[tex]P(x = 100) =0.0074[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \left \{ {{\frac{1}{100}e^{-x/100}\ x\ge 0} \atop {0\ x<0}} \right.[/tex]
Solving (a): Probability that it will function between 50 and 150 hr before it breaks down
This is represented as:
[tex]P(50 < x < 150) = \int\limits^{150}_{50} {f(x)} \, dx[/tex]
So, we have:
[tex]P(50 < x < 150) = \int\limits^{150}_{50} {\frac{1}{100}e^{-x/100}} \, dx[/tex]
Integrate:
[tex]P(50 < x < 150) =- e^{-x/100}|\limits^{150}_{50}[/tex]
This gives:
[tex]P(50 < x < 150) =- e^{-150/100} - - e^{-50/100}[/tex]
[tex]P(50 < x < 150) =- e^{-150/100} + e^{-50/100}[/tex]
[tex]P(50 < x < 150) =- e^{-1.5} + e^{-0.5}[/tex]
[tex]P(50 < x < 150) =- 0.2231 + 0.6065[/tex]
[tex]P(50 < x < 150) =0.3834[/tex]
Solving (a): Probability that it will function exactly 100 hr before it breaks down
This is represented as:
[tex]P(x= 100)[/tex]
This can be rewritten as:
[tex]P(x= 100) = P(99<x<101)[/tex]
So, we have:
[tex]P(99 < x < 101) = \int\limits^{101}_{99} {f(x)} \, dx[/tex]
So, we have:
[tex]P(99 < x < 101) = \int\limits^{101}_{99} {\frac{1}{100}e^{-x/100}} \, dx[/tex]
Integrate:
[tex]P(99 < x < 101) =- e^{-x/100}|\limits^{101}_{99}[/tex]
This gives:
[tex]P(99 < x < 101) =- e^{-101/100} - - e^{-99/100}[/tex]
[tex]P(99 < x < 101) =- e^{-101/100} + e^{-99/100}[/tex]
[tex]P(99 < x < 101) =- e^{-1.01} + e^{-0.99}[/tex]
[tex]P(99 < x < 101) =- 0.3642 + 0.3716[/tex]
[tex]P(99 < x < 101) =0.0074[/tex]
Hence:
[tex]P(x = 100) =P(99 < x < 101) =0.0074[/tex]
Use the following information. (pls hurry)
SPORTS In a football game, each team earns 6 points for each touchdown it scores.
Write an equation to find y, the total number of points for scoring x touchdowns.
Pls help ASAP In the triangle below, what is the measure of AngleZ?
Answer:
50 degrees is the answer
What would be the final
price of a $59.99 video game
in a state that charges 6.5%
sales tax?
Answer:
$63.89
Step-by-step explanation:
just multiply 59.99 by 1.065
SOMEBODY PLEASE GIVE AND HELP ME IN THESE. I HAVE TO SUBMIT MY TEST IN 20 MINS.
Answer:
I only have this much
The rest you have to do on your own
Cora uses the following ingredients to make once more.
Answer:
10 if the other the numbers go up as well
Step-by-step explanation:
20/2= 10
Which would mean Kora could make 10 s'mores
Students in an environmental science class raised money to buy plants for a community garden. The students raised money by selling regular cupcakes for $2.00 each and gluten-free cupcakes for $3.00 each. The number of regular cupcakes sold was determined to be 2 times the number of gluten-free cupcakes sold. If a total $350 was raised through cupcake sales over a three-week period, how many cupcakes were sold altogether
Answer:
50 gluten-free cupcakes and 100 regular cupcakes.
Step-by-step explanation:
Let's define the variables:
R = number of regular cupcakes sold
G = number of gluten-free cupcakes sold
The total amount of money raised then is:
M = R*$2.00 + G*$3.00
We also know that:
The number of regular cupcakes sold was 2 times the number of gluten-free cupcakes sold.
then:
R = 2*G
And we also know that the amount of money raised is $350
Then we have the equations:
R = 2*G
R*$2.00 + G*$3.00 = $350
We can replace the first equation into the second one, so we have only one variable:
(2*G)*$2.00 + G*$3.00 = $350
Now we can solve this for G.
G*$4.00 + G*$3.00 = $350
G*$7.00 = $350
G = $350/$7.00 = 50
G = 50
50 gluten-free cupcakes where sold.
And using the equation:
R = 2*G = 2*50 = 100
We can conclude that 100 regular cupcakes were sold.
71 is 10% of what number?
52 is 97% of what Number?
Explain steps.
Answer:
71 is 10% of 710
52 is 97% of 5200/97
Step-by-step explanation:
Let’s start with 71 is 10% of what number.
basically, what this is saying, is that 71 = 10% times and unknown valu. We can set this as x.
so, 71=0.1x
divide on both sides,
710=x
now the second one.
repeat the same process.
52=0.97x
divide
5200/97 =x
Is 9a^2 +25 the difference of 2 squares?
Yes
No
[tex]\huge\text{Hey there!}[/tex]
“ [tex]\mathsf{Is\ 9a^2 +25\ the\ difference\ of\ 2\ squares?}[/tex]
[tex]\textsf{Well, when you see or hear the word difference it usually MEANS SUBTRACT}\\\textsf{or SUBTRACTION especially in MATHEMATICS!}[/tex]
[tex]\mathsf{\bold{+}\ usually\ means\ sum\ or\ more\ than}[/tex]
[tex]\textsf{So therefore to \boxed{\textsf{Answer}} to this giving question \boxed{\boxed{\huge \text{\bf No}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day}[/tex]!
~[tex]\frak{Amphitrite1040:)}[/tex]
5) If the property tax on a $100,000 home is $1500, what is the tax on a
$ 120,000 home?
Answer:
Calculate property taxes based on assessed value and a tax rate. California property tax calculations with annual assessment increases up to 2% ... Tax Rate: The annual tax rate used to compute your property taxes.
Out of 469 applicants for a job, 159 have over 10 years of experience and 116 have over 10 years of experience and have a graduate degree. Step 2 of 2 : Consider that 139 of the applicants have graduate degrees. What is the probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree? Enter a fraction or round your answer to 4 decimal places, if necessary. Answer
Answer:
[tex]\frac{116}{159} = 0.7296[/tex] probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Has a graduate degree.
Event B: Has over 10 years of experience.
Out of 469 applicants for a job, 159 have over 10 years of experience and 116 have over 10 years of experience and have a graduate degree.
This means that:
[tex]P(A) = \frac{159}{469}[/tex]
[tex]P(A \cap B) = \frac{116}{469}[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{116}{469}}{\frac{159}{469}} = \frac{116}{159} = 0.7296[/tex]
[tex]\frac{116}{159} = 0.7296[/tex] probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree.
please help me fast! thanks
Answer:
the answer is 15
Step-by-step explanation:
Just add
Answer:
15 grams
Step-by-step explanation:
In a survey of 292 students, about 9.9% have attended more than one play. Which
is closest to the number of students in the survey who have attended more than one
play?
3 students
10 students
20 students
30 students
Answer: it's 30 I rook the quiz and got 100
Step-by-step explanat
Five hundred students were asked whether they perfer apple juice or orange juice.
Answer:
Step-by-step explanation:
240 said apple juice and 340 said orange juice.
An airliner travels 95 miles in 12 minutes. What is its speed in miles per hour?
Answer:
475 miles per hour
Step-by-step explanation:
the plane traveled 95 miles in 12 minutes. the first thing we need to do is determine how many 12 minutes go into 1 hour. 12 minutes is repeated 5 times in order to get a total of 60 minutes and 60 minutes is 1 hour. the final thing we need to do is multiply 95 by 5 to get the total number of miles per hour traveled. the total of that is 475 miles per hour which is the answer
written math;
60/12=5
95*5=475
answer= 475 miles per hour
A. Scalene
B. Isosceles
C. Right
D. Obsute
Answer:
Isosceles
Step-by-step explanation:
Because an equilateral triangle is also isosceles, all triangles are either scalene or isosceles. But when people call a triangle isosceles, they're usually referring to a triangle with only two equal sides, because if the triangle had three equal sides, they'd call it equilateral.
The cost of 12 oranges and 7 apples is 5.36. Eight oranges and 5 apples cost 3.68. Find the cost of each
Answer:
Apple costs $0.26
and orange costs $0.32
sorry i don't have time to explain but if u have doubts don't hesitate to ask
1. A number cube is rolled 24 times and lands on 2 four times and on 6 three times.
a. Find the experimental probability of landing on a 2.
b. Find the experimental probability of not landing on a 6.
c. Compare the experimental probability you found in part a to its theoretical probability.
d. Compare the experimental probability you found in part b to its theoretical probability
Step-by-step explanation:
(A) you takeway 24 by 2 and add 6=28
pls help will give brainliest and only put 1 variable in it ty
Answer:
(2/3)r=30
r=45cm
Step-by-step explanation:
When trying to find a fraction of something, multiply to get your answer:
(2/3) of r = (2/3)r
The blue ribbon can be represented by both 30cm and (2/3)r cm:
(2/3)r=30
2r=90
r=45cm
PLS HELP THIS IS TRIGONOMETRY!!!! PLS SHOW STEPS
Answer:
third side =√{30²+16²)=34
sin theta/2=16/34
theta/2=sin-¹(16/34)
theta=28.07×2=56.14
Which expression is equivalent to ( + )?
Answer:
No entiendo que es lo que hay qué hacer
Carlos bikes 2 1/2 miles in 1/4 hours. At that rate, how many miles would he bike in 1 hour?
Answer:
10
Step-by-step explanation:
since it’s 1/4 1 out of the four is 2.5 so just multiply by four
The height of a ball dropped from a 160 foot building after 1 seconds is represented by h(t) = 160 - 1612
How high will the ball be after 3 seconds?
A. O feet
B. 9 feet
C. 16 feet
D. 112 feet
E. 151 feet
Answer:
C. 16 feet.
Step-by-step explanation:
How to find the maximum height of a projectile
if α = 90°, then the formula simplifies to: hmax = h + V₀² / (2 * g) and the time of flight is the longest.
if α = 45°, then the equation may be written as:
if α = 0°, then vertical velocity is equal to 0 (Vy = 0), and that's the case of horizontal projectile motion.
True/False?: A best-fit line is created to model data comparing the gasoline consumed by a car (x) and the distance traveled in the car (y). The equation is y=24x−1. One possible explanation for the y-intercept being −1 is that cars that idle (sit still) also use some gas. So, while the model predicts that cars get 24 miles of travel per gallon of gas consumed, some gas is consumed just by a car running (not traveling).
Answer:
TRUE
Step-by-step explanation:
Need some help a little bit stuck
Answer:
SA = 240
Step-by-step explanation:
SA = (10*10) + (8*10) + (6*10)
SA = 240
maths
[tex] \sqrt[3]{1 + x} + \sqrt[3]{1 - x} = \sqrt[3]{2} [/tex]
Answer:
X=0,1
Step-by-step explanation:
Remove the radical by raising each side to the index of the radical
Need help ASAP I will mark Brainlyist
58% of a $148 selling price goes toward paying expenses. How many dollars of the selling price is profit?
Answer:
62.16
Step-by-step explanation:
what is the place value of 5 in . number 4 256
Answer:
4 2 5 6
Ones : 6
Tens : 5
Hundreds : 2
Thousands : 4
Step-by-step explanation:
hope I'm right
Two fish tanks have measurements as shown. Which tank has a greater volume? How much greater is its volume? Use the drop-down menus to explain and show your answer. Fish Tank A shows an area of base that is 25 square feet and a height of 8 feet. Fish Tank B shows an area of base that is 40 square feet and a height of 4 feet. The volume of fish tank A is cubic feet, and the volume of fish tank B is cubic feet. So fish tank has a greater volume. Its volume is greater by cubic feet.
Answer:
The volume of fish tank A is 200 cubic feet, and the volume of fish tank B is 160 cubic feet. So fish tank A
has a greater volume. Its volume is greater by 40 cubic feet.
-
I just finished the Unit Test and got it right, so I hope this helps.
(Bold is the answer(s) for each slot)
How much money would you have to invest at 9% compounded semiannually so that the total investment has a value of $2,090 after one year?
Answer:
Im just doing this for points .,.
Step-by-step explanation: