There are 130 people in a sport centre.
65 people use the gym.
51 people use the swimming pool.
44 people use the track.
15 people use the gym and the pool.
14 people use the pool and the track.
10 people use the gym and the track.
1 person uses all three facilities.
Given that a randomly selected person uses the gym and the track, what is the probability they
do not use the swimming pool?
Answer:
1/13
Step-by-step explanation:
there are 10 people that use the gym and track and 10 is 1/13 of 130
If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm.
Answer:
The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.
Step-by-step explanation:
Surface area of a snowball:
A snowball has a spheric format, which means that it's surface area is given by:
[tex]A = 4\pi r^2[/tex]
In which r is the radius, which is half the diameter. In function of the diameter, the area is given by:
[tex]A = 4\pi(\frac{d}{2})^2 = \pi d^2[/tex]
Solving the question:
To solve this question, we have to implicitly derivate the area in function of t. So
[tex]\frac{dA}{dt} = 2d\pi\frac{dd}{dt}[/tex]
Snowball melts so that its surface area decreases at a rate of 3 cm2/min
This means that [tex]\frac{dA}{dt} = -3[/tex]
Find the rate at which the diameter decreases when the diameter is 10 cm.
This is [tex]\frac{dd}{dt}[/tex] when [tex]d = 10[/tex]. So
[tex]\frac{dA}{dt} = 2d\pi\frac{dd}{dt}[/tex]
[tex]-3 = 20\pi\frac{dd}{dt}[/tex]
[tex]\frac{dd}{dt} = -\frac{3}{20\pi}[/tex]
[tex]\frac{dd}{dt} = -0.0477[/tex]
The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.
The number of bacterial colonies of a certain type in samples of polluted water has a Poisson distribution with a mean of 3 per cubic centimeter (cm3). (a) If eight 1 cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacterial colonies. (Round your answer to four decimal places.) 1 Correct: Your answer is correct. seenKey 1.000 (b) How many 1 cm3 samples should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony
Answer:
a) 1 = 100% probability that at least one sample will contain one or more bacterial colonies.
b) 1 sample should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony
Step-by-step explanation:
To solve this question, we need to understand the poisson and the binomial distributions.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Probability of a single sample having at least one bacterial colonies.
Poisson distribution with a mean of 3 per cubic centimeter (cm3), which means that [tex]\mu = 3[/tex]
This is:
[tex]P(X \geq 3) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0495[/tex]
[tex]P(X \geq 3) = 1 - P(X = 0) = 1 - 0.0495 = 0.9505[/tex]
(a) If eight 1 cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacterial colonies.
Multiples samples means that the binomial distribution is used.
0.9505 probability of a sample having at least one colony, which means that [tex]p = 0.9505[/tex]
8 samples means that [tex]n = 8[/tex]
The desired probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.9505)^{0}.(0.0495)^{8} \approx 0[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0 = 1[/tex]
1 = 100% probability that at least one sample will contain one or more bacterial colonies.
(b) How many 1 cm3 samples should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony
We have to find [tex]P(X \geq 1)[/tex] for samples of 1,2,3,..., until this probability is 0.95. So
n = 1
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{1,0}.(0.9505)^{0}.(0.0495)^{1} = 0.0495[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0495 = 0.9505[/tex]
0.9505 > 0.95
1 sample should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony
I need help with solving this
Answer:
x=12
.......................
what is the slope of the line for 3x+ 4y = 20?
Answer:
[tex]-\frac{3}{4}[/tex]
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, subtract 3x from both sides of the equation:
3x (-3x) + 4y = (-3x) + 20
4y = -3x + 20
Next, divide 4 from both sides of the equation:
(4y)/4 = (-3x + 20)/4
y = (-3/4)x + 5
[tex]y = -\frac{3}{4}x + 5[/tex]
~
Note the equation.
y = mx + b
y = y
m = slope = [tex]-\frac{3}{4}[/tex]
x = x
b = y-intercept = 5
six people wen put to dinner, split the check, and paid $18. How much was the check
Answer:
$180
Step-by-step explanation:
$18 × 6
=$180
That's your answer
Solve this inequality for x.
A.
B.
C.
D.
Answer:
D
Step-by-step explanation:
dd
Graph the compound inequality on the number line. x> -7 and x<-3
Answer:
Step-by-step explanation:
suppose 11 out of 22 students said they were attending the football game. how many students out of 580 would you expect to attend the football game.
Answer: 290
Step-by-step explanation:
11/22 is half so the percentage would be 50%.
As we know it's a half you would just have to half or divide 580 by 2.
580÷2=290
Hope this helps :)
Find the volume of the rectangular prism. 1 ft 2 6 ft 1 3 2 ft The volume is 1
Answer:
31.5 or 31 1/2
Step-by-step explanation:
The formula for volume of a rectangular prism is lwh or length times width times height.
Multiply the numbers and you get 31.5 or 31 1/2
Hint: It is easier to multiply mixed numbers when converting them to decimals. When you are done just convert it back to a fraction if needed. :)
What is the probability of flipping a coin 85 times and getting tails 30 times or
fewer?
A. 99.8%
B. 33.2%
C. 95.9%
D. 0.4%
Answer:
C
Step-by-step explanation:
Answer:
0.4
Step-by-step explanation:
WHat is the sum of the rational expressions below 3x+1/2x+7x/x+5
A restaurant chef has designed a new set of dishes for his menu. His set of dishes contains 10 10 main courses, and he will select a subset of them to place on the menu each night. To ensure variety of main courses for his patrons, he wants to guarantee that a night's menu is neither completely contained in nor completely contains another night's menu. What is the largest number of menus he can plan using his 10 10 main courses subject to this requirement
Answer:
252 menu
Step-by-step explanation:
Total number courses, n = 10
The largest number of menu the chef can plan using his 10 main courses.
There are various combinations of menu obtainable from the available courses :
Ranging from :
nC0 to nCn
The largest number of menu he can plan is the highest output obtainable between :
10C0 to 10C10
10C0 = 1
10C1 = 10
10C2 = 45
10C3 = 120
10C4 = 210
10C5 = 252
10C6 = 210
10C7 = 120
10C8 = 45
10C9 = 10
10C10 = 1
Hence, the largest number of menu he can plan using his 10 main courses is 252
Of the 220 tickets available for a school play,45% have been sold. What is the number of tickets that have sold?(pls help due very soon!)
i will give a crown if you are the first one to answer and if you get it right and if you just get it right then i will i give you a full star rating and a thanks
Answer:
30x+15
Step-by-step explanation:
The sum of two consecutive integers is - 163. Find the two integers.
Answer: -100 and -63
Step-by-step explanation: Don't overthink it by trying to divide it.
Answer:
-81, - 82
Step-by-step explanation:
Let the two consecutive integers be x and (x + 1)
According to the given information:
x + (x + 1) = - 163
2x + 1 = - 163
2x =-163 - 1
2x = - 164
x = - 164/2
x = - 82
x + 1 = - 82 + 1 = - 81
Thus, the two consecutive integers are - 81, - 82
Can someone help me ?
Answer:
The second one doesn't match.
What are the two solutions to 2x2−x−4=0 ? Use the quadratic equation
Help me solve this, it’s trig
Answer:
The answer is 6.451 or 6.5 rounded
Step-by-step explanation:
The way to solve this is to find all the degrees inside the triangle first
you have two given degrees which are 21 and 90 degrees
add those numbers up and subtract it from 180. That is the last corner degree
you then use that information to find all the side lengths using the given hypotenuse length.
Btw its geometry not really trig.
Answer: 6.45 units
Step-by-step explanation:
To solve for x, we will set up an equation using the trigonometric functions. We are given an angle (21 degrees), the opposite side of that angle (x), and the hypotenuse (18). For this, we will use the sine function.
sin(21) = [tex]\frac{opposite}{hypotenuse }[/tex]
sin(21) = [tex]\frac{x}{18}[/tex]
18sin(21) = x
x = 18sin(21)
x = 6.4506230 ≈ 6.45 units
Find ONLY the measure of angle A (just the number): *
20 points
Answer:
360 - 169 equals 191
Step-by-step explanation:
191
Urgent 35 points !!! What should the radius of
your container be?
Answer:
2.88 inStep-by-step explanation:
Volume formula:
V = 4/3πr³Find r if V = 100 in³:
4/3πr³ = 100πr³ = 100*3/4πr³ =75r³ = 75/3.14r³ = 23.88r = ∛23.88r = 2.88 in (rounded)???????????????????????
Answer:
try
Step-by-step explanation:
try solving it on ur own or take a educated guess
all muntiple of 5 is an odd number true proposition?
The correct answer is false.
Multiples 5 include: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, etc.
Bold numbers: even
Normal numbers: odd
Can someone please help with this one I will report false/fake answers please someone.
I will also give brainiest.
Answer:
I belive it is 2.9716
Step-by-step explanation:
Happy Tuesday! Looking for some help with my geometry.
Please only answer if you know the answer, the comment section is right below. Please don't waste my points!
Also, please show all of your work, you are trying to help me better understand the concept, not just give me the answer.
The image is down below. This is a multi step question and please answer all five. Show work! Thanks!
Answer:
Q1
cos 59° = x/16x = 16 cos 59°x = 8.24Q2
BC is given 23 mi
Maybe AB is needed
AB = √34² + 23² = 41 (rounded)Q3
BC² = AB² - AC²BC = √(37² - 12²) = 35Q4
Let the angle is x
cos x = 19/20x = arccos (19/20)x = 18.2° (rounded)Q5
See attached
Added point D and segments AD and DC to help with calculation
BC² = BD² + DC² = (AB + AD)² + DC²Find the length of added red segments
AD = AC cos 65° = 14 cos 65° = 5.9DC = AC sin 65° = 14 sin 65° = 12.7Now we can find the value of BC
BC² = (19 + 5.9)² + 12.7²BC = √781.3BC = 28.0 ydAll calculations are rounded
Rex has a collection of 160 toy dinosaurs to put into 4 boxes. He puts 5 handfuls of toy dinosaurs in each box. There are no toy dinosaurs left. Four friends estimate how many toy dinosaurs Rex has in each handful. Which estimation is the best?
Answer: 8 dinos
Step-by-step explanation:
there are 4 boxes and 5 handfuls in each. divide 160 by 4 and divide that, 40, by 5 to get 8
Pls helppppppp!!!!!!!!!!!
Answer:
part of it is cutted out show a better picture please ill answer it
Step-by-step explanation:
Solve three fourths times two thirds. Leave answer as improper fraction
a. 5/12
b.6/12
c.5/7
d. 6/7
Answer:
B) [tex]\frac{6}{12}[/tex]
Step-by-step explanation:
Note that you do not need to simplify. Simply multiply straight across:
[tex]\frac{3}{4} * \frac{2}{3} = \frac{3 * 2}{4 * 3} = \frac{6}{12}[/tex]
B) [tex]\frac{6}{12}[/tex] is your answer.
`
v=Xf; speed = wavelength x frequency
f= 1/T; frequency = 1/Period
Problems: 1. The frequency of a wave is 4.0 x 10 Hz. What is its wavelength?
2. A wave with a frequency of 31,200 Hz and travels at 790m/s? What is the wavelength in centimeters?
3. A wave has a wavelength of 25cm and a velocity of 630 m/s, what is the frequency?
Mark works as a librarian and makes $16.75 per hour. He gets paid time-and-a-half for overtime. How much will he make if he works 52 hours this week?
Play media comment.
Group of answer choices
$670.00
$971.50
$1,005.00
$871.00
PLZZZ HURRY
Answer:
$871.00
Step-by-step explanation: