Answer:
[tex]Probability = \frac{18}{1860480}[/tex]
Step-by-step explanation:
Given
Soda = 10
Sprite = 4
Dr. Pepper = 3
Cherry Coke = 3
Required
Determine the probability of picking Dr. pepper the fourth and fifth
First, we need to sum up the number of drinks
[tex]Total = 10 + 4 + 3 + 3[/tex]
[tex]Total = 20[/tex]
First Selection: Dr. Pepper
[tex]P_1= \frac{3}{20}[/tex]
Since its probability without replacement;
At this stage: Dr. Pepper = 2 and Total = 19
Second Selection: Cherry Coke
[tex]P_2= \frac{3}{19}[/tex]
At this stage: Dr. Pepper = 2; Cherry Coke = 2 and Total = 18
Third Selection: Cherry Coke
[tex]P_3= \frac{2}{18}[/tex]
[tex]P_3= \frac{1}{9}[/tex]
At this stage: Dr. Pepper = 2; Cherry Coke = 1 and Total = 17
Fourth Selection: Dr. Pepper
[tex]P_4= \frac{2}{17}[/tex]
At this stage: Dr. Pepper = 1; Cherry Coke = 1 and Total = 16
Fifth Selection: Dr. Pepper
[tex]P_5= \frac{1}{16}[/tex]
Multiply the calculated probabilities, to give the required probability
[tex]Probability = P_1 * P_2 * P_3 * P_4 * P_5[/tex]
[tex]Probability = \frac{3}{20} * \frac{3}{19} * \frac{1}{9} * \frac{2}{17} * \frac{1}{16}[/tex]
[tex]Probability = \frac{3 * 3 * 1 * 2 * 1}{20 * 19 * 18 * 17 * 16}[/tex]
[tex]Probability = \frac{18}{1860480}[/tex]
Simplify the equation 5(3m-2)+4m
Answer:
19m - 10
Step-by-step explanation:
Order of Operation: BPEMDAS
Step 1: Write out equation
5(3m - 2) + 4m
Step 2: Distribute parenthesis
15m - 10 + 4m
Step 3: Combine like terms
19m - 10
A complicated mechanical system contains 8 components. If there is a 18% chance that each component will fail during processing, and components fail independently of each other, then
(a) What is the probability that fewer than 3 components will fail?
(b) What is the meet likely number of failures?
Answer:
(a) The probability that fewer than 3 components will fail is 0.8392.
(b) The mean likely number of failures is 1.44.
Step-by-step explanation:
We are given that a complicated mechanical system contains 8 components. If there is an 18% chance that each component will fail during processing, and components fail independently of each other.
Let X = Number of components fail during processing
The above situation can be represented through the binomial distribution;
[tex]P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=0,1,2,.....[/tex]
where, n = number of samples (trials) taken = 8 components
r = number of success = fewer than 3 components will fail
p = probability of success which in our question is the probability
that each component will fail during processing, i.e. p = 18%
SO, X ~ Binom(n = 8, p = 0.18)
(a) The probability that fewer than 3 components will fail is given by = P(X < 3)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{8}{0}\times 0.18^{0} \times (1-0.18)^{8-0}+ \binom{8}{1}\times 0.18^{1} \times (1-0.18)^{8-1}+ \binom{8}{2}\times 0.18^{2} \times (1-0.18)^{8-2}[/tex]
= [tex]1 \times 1 \times 0.82^{8}+ 8 \times 0.18^{1} \times 0.82^{7}+28 \times 0.18^{2} \times 0.82^{6}[/tex]
= 0.8392
(b) The mean likely number of failures is given by the following formula;
Mean of X, E(X) = n [tex]\times[/tex] p
= [tex]8 \times 0.18[/tex] = 1.44
Hence, the mean likely number of failures is 1.44.
A seagull is gliding 53 feet above the surfaces of the water. It then dives 70 feet to catch a fish. How many feet below the surface of the water does the seagull dive?
Answer:
17 feet
Step-by-step explanation:
the seagull is originally 53 feet above water and dives 70 feet down. so 53-70=-17. 17 feet below water.
15.2, 3,6,11,18, ...
Describe the pattern. Then write the next three numbers
Answer:
27, 38, and 51
Step-by-step explanation:
3, 6, 11, 18, ...
We increase the first number by 3. Then 5. Then 7.
The pattern is that the difference increases by 2.
That means this is a quadratic sequence.
y = x² + 2, where x = 1, 2, 3, etc.
The next three numbers are 27, 38, and 51.
A rectangle is 6 ft long and 11 ft wide. What is the length of the diagonal of the
rectangle?
Answer:
sqrt(157) ft is the length of the diagonal
Step-by-step explanation:
We can use the Pythagorean theorem to find the length of the diagonal
a^2 + b^2 = c^2
6^2 + 11 ^2 = c^2
36+ 121 = c^2
157 = c^2
Take the square root of each side
sqrt(157) = sqrt(c^2)
sqrt(157) = c
Answer:
sqrt(157) ft is the length of the diagonal
Step-by-step explanation:
We can use the Pythagorean theorem to find the length of the diagonal
a^2 + b^2 = c^2
6^2 + 11 ^2 = c^2
36+ 121 = c^2
157 = c^2
Take the square root of each side
sqrt(157) = sqrt(c^2)
sqrt(157) = c
-2 1/3 - (-5) A: -7 1/3 B: 3 1/3 C: 3 3/2 D: 2 2/3
Answer:
2 2/3 (D)
Step-by-step explanation:
The position of an object in circular motion is modeled by the given parametric equations. Describe the path of the object by stating the radius of the circle, the position at time t = 0, the orientation of the motion (clockwise or counterclockwise), and the time t that it takes to complete one revolution around the circle.
x = 4 cos 3t, y = 4 sin 3t
How do you get to that solution?
Answer:
4 units ; counter clockwise ; 2.09 units
Step-by-step explanation:
Given the following :
x = 4 cos 3t
y = 4 sin 3t
The Radius (r) could be obtained using Pythagoras:
R = √(x^2 + y^2)
R = √[(4cos3t)^2 + (4sin3t)^2]
R = √[16cos^(2)3t + 16sin^(2)3t]
Recall : cos^2θ + sin^2θ = 1
Therefore, cos^(2)3t + sin^(2)3t= 1
Where, 3t stands for θ
R = √[16cos^(2)3t + 16sin^(2)3t]
Factorizing:
R = √16[cos^(2)3t + sin^(2)3t)]
R = √16[1]
R = √16
R = 4 units
Position at time t = 0
x = 4 cos 3(0)
x = 4 cos 0
x = 4 * 1 = 4 units
y = 4 sin 3t
y = 4 sin 3(0)
y = 4 * sin 0
y = 0
Position at t = 0;
(x, y) = (4, 0) = counterclockwise
Time taken to complete 1 complete revolution:
2π/3 = 6.2831853 /3 = 2.0943951
= 2.09
Caleb has worked hard and is offered a salaried position with the same company. He is offered $28,000, but will be expected to work 44 hours per week with no overtime pay. How much would he be paid per year if he remained in his present job and worked 44 hours per week, and was paid for the overtime? (Caleb makes $11.15 an hour and gets time and a half for overtime.)
Answer:
$7.50 (paid per hour) times 70 hours (times 2 of 35 hours) = $525 gross pay
Step-by-step explanation:
525 is the gross pay.
Hello there! :D
We know that Caleb has two options:
Let's say that Option A is taking the new job, and Option B is solving for the new one. We know that Option A will leave him with $28,000. Let's do some math to see how much he would make with Option B.
We can do this by calculating how many ours he would work in one year and multiplying that by $11.15.
So, we have 44 hours a week. There are 52 weeks in a year.
52*44= 2288
Now, we can mutltiply that by his hourly wage.
2288*11.15=$25,511.2
Let's see how much time it would take to make the same amount of money since he is allowed to work overtime at half price:
Subtract the amount he makes in Option A by Option B:
28,000-25,511.2= 2488.8
Now we need to divide his hourly wage in half, because he gets paid half as much for overtime (I am assuming the wording is weird here).
11.15/2= 5.575
Now we can find out how many hours he needs to do per year to make the same amount.
2488.8/5.575=432.834 hours
Per week that is 8.3 extra hours! (Sounds like a lot of work)
If I was Caleb, I would take the new job offer, because it is unlikely that he will make much more in his current job.
I hope this helped you and that you have a wonderful day,
Kai xx
Combine the like terms to create an equivalent expression: \large{-4p+(-2)+2p+3}−4p+(−2)+2p+3
Answer:
-2p+1
Step-by-step explanation:
-4p+2p+(-2)+3
-2p+1
The equivalent expression of the expression {-4p+(-2)+2p+3}−4p+(−2)+2p+3 is -4p+2.
What is expression?An expression is a combination of numbers, variables, function, indeterminants, symbols like addition, multiplication, subtraction and division. It is not usually present in equal to form.
How to create equivalent expression?We have been given one expression {-4p+(-2)+2p+3}−4p+(−2)+2p+3 and we have to find the equivalent expression by solving the expression.
First we need to put appropriate signs by solving brackets and the expression will look like after opening brackets and after opening of brackets the signs may change:
=-4p-2+2p+3-4p-2+2p+3
=-4p+2p-4p+2p-2+3-2+3
=-4p+2
Hence the equivalent expression of {-4p+(-2)+2p+3}−4p+(−2)+2p+3 is -4p+2.
Learn more about expressions at https://brainly.com/question/723406
#SPJ2
During each summer, many families spend part of their vacation time at a beach along the East or West Coast. Due to the popularity of movies like Jaws and The Shallows, and publicity about recent shark attacks on surfers, swimmers, snorkelers, and spearfishermen, Americans have become increasingly concerned about water activities. Research suggests that 58% of all shark attacks involve surfers. One thousand records of shark attacks are selected, and each is categorized by the victim group. Identify the population, sample, and variable for the study.
Answer:
a
POPULATION : The population is the surfers , swimmers, snorkelers and spear-fishermen in America
SAMPLE : The 1000 records of shark attacks selected
VARIABLE FOR STUDY: 580 surfers
Step-by-step explanation:
Generally the population is the surfers , swimmers, snorkelers and spear-fishermen in America
This is because it is the entire pool from which a statistical sample is drawn
Generally the sample is the 1000 records of shark attacks selected
This is because this the number drawn from the population for statistical testing also this contain the characteristics of the population
Generally the variable for study is 58% of 1000 = 580 surfers
This is because the this 580 surfer is the major focus of the Researchers study
What equals 4 tens and 6 ones
Answer:46
Step-by-step explanation:
Answer:
46
Step-by-step explanation:
4 times 10 = 40
6 times 1 = 6
40 plus 6 = 46
Which numbers are factors of 42? Check all that apply.
1
2
3
6
8
Answer:
1, 2, 3, 6
Step-by-step explanation:
Miguel runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
Answer:
We use the rule of three
7 miles ---------------> 60 minutes
So x ------------------> 24 minutes
So x= (24 minutes × 7 miles )/60 minutes .
We simplify by 《minutes》 because it's in the numerator and the denominator .
So x= (24×7 miles )/60
x = 168 miles /60
x=2,8 miles
So Miguel runs 2,8 miles in 24 minutes.
Perform the operation. (Write fractional answers in simplest form.) 4x/5 + x/7
Answer:
simplest form:
[tex]\frac{33 x}{35}[/tex]
what is 4 3/7 as a decimal.
According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this increased by approximately 0.6% per year. If this trend continues, in which year will 49% of babies be born out of wedlock
Answer:
2029
Step-by-step explanation:
We can write an equation:
0.28+0.006x=0.51
A few things explained:
The constant 0.28 comes from the fact in 1990, 28% of babies were born to parents who were not married. 28%=0.28
0.006 represents 0.6% and x represents the number of years will pass until 49% of babies will be born out of wedlock
0.51 represents 51%. 51% represents the percentage of babies who will be born to parents not married (100% - 49%=51%). You want to use 51% instead of 49% because the right side represents the babies born to parents not married.
We can solve the equation:
0.28+0.006x=0.51
0.006x=0.23
x=38.33
Since you can't have 38.3333 years, we'll say that 39 will pass until 49% of babies are born out of wedlock.
So, we add 39 years to 1990.
1990+39=2029
Hope this helps!
$325.50 of 30% what is the price
What is the reciprocal of 3?
Answer:
reciprocal of 3 is 1/3..
Answer:
0.33333333333
Step-by-step explanation:
A. 3^2+2x8
—————
16-11
B. (32x1/2+6)-(4-1)
C. ((8-10.3)+2^3-5)
Answer:
=3²+2×8
=9+2×8
=9+16
=25
PROVED!!
20 points, I HAVE SCHOOL IN 1 HOUR PLEASE HELP, ONLY 2 QUESTIONS,
1. use distributive property to simplify the expression 7(6x + 1)
2. Simplify the expression 4 + ( 14 + x )
Answer:
[tex]\Huge \boxed{42x+7} \\ \\ \\ \Huge \boxed{x+18}[/tex]
Step-by-step explanation:
Part 1:
[tex]7(6x + 1)[/tex]
Distribute 7 to the terms in the brackets.
[tex]7(6x)+7(1)[/tex]
[tex]42x+7[/tex]
Part 2:
[tex]4+(14+x)[/tex]
Removing brackets.
[tex]4+14+x[/tex]
Combining like terms.
[tex]18+x[/tex]
19
Write
as a mixed number.
7
Answer:
2 5/7
Step-by-step explanation:
Set up the division problem in long division format. Divide 19 by 7. Place this digit in the quotient on top of the division symbol. Multiply the newest quotient digit (2) by the divisor 7. Subtract 14 from 19. Then you have your answer of 2 5/7.
hope this helps :3
36 1 3 2. 13 = 20
Order of operations
Answer: (36 - 1) ÷ (3 + 2) + 13 = 20
Step-by-step explanation:
PEMDAS rule calls for parenthesis to be solved first, then exponents, then multiplication or division then addition or subtraction depending on which comes first in the equation.
Using the PEMDAS rule the 20 can be gotten to if the equation is expressed as follows;
(36 - 1) ÷ (3 + 2) + 13 = 20
The parenthesis will be solved first;
35 ÷ 5 + 13 = 20
The division will be done first;
7 + 13 = 20
Then the addition;
7 + 13 = 20
Steve rides his bike at a rate of 1760 feet per minute. What is his rate in miles per hour?
Answer:
The answer is 19.36 miles per hoursStep-by-step explanation:
this problem is a unit conversion problem
In this problem, we are expected to convert from feet/min to miles per hour
given that the rate is 1760 feet per minute
from tables, we are given that
1 foot per minute is 0.011 miles per hour hence
1760 feet per minutes will give x miles per hour
cross multiplying we have
x= 1760*0.011
x= 19.36 miles per hours
Express 4/5 in
a) percentage
b) decimal
c)decimal
Answer:
4/5 = 80/100 = 80%
4/5 = 0.8
Solve equation
56=-8d+8
Answer:
d = - 6
Step-by-step explanation:
56 = -8d +8
-8 . -8
48 = -8d
__ . __
-8 -8
-6 = d
-12divided by 3 help me plz
Answer:
-4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
Write it out: -12 ÷ 3-12 ÷ 3 = -47/9 x 1/2 =
what’s the answer guys
Answer:
0.388
Step-by-step explanation:
7/9 x 1/2 = 0.388
A model plane has a scale of 1 in: 6 yd. If
the model plane is 3 in tall then how tall is
the real plane?
Answer:
18 yards
Step-by-step explanation:
Let's set up a proportion using the following setup.
inches / yards = inches / yards
We know the scale is 1 inch to 6 yards.
1 inch / 6 yards = inches / yards
We know the model plane is 3 inches tall, but we don't know how tall the real plane is. Therefore, we can it is 3 inches to x yards.
1 inch / 6 yards= 3 inches / x yards
1 /6= 3/x
Cross multiply. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the denominator of the first by the numerator of the second.
1*x= 6*3
1x= 6*3
x= 6*3
x=18
x= 18 yards
The real plane is 18 yards.
The sum of two numbers is 15, and their product is 16. What is the sum of the reciprocals of the two numbers? Express your answer as a common fraction.
Answer:
The sum of the reciprocal of two numbers are
[tex]\frac{1}{x} + \frac{1}{y}= \frac{15}{16}[/tex]
Step-by-step explanation:
Step(i):-
Let x , y are two numbers
Given data the sum of two numbers = 15
x + y = 15 ...(i)
The product of two numbers = 16
x y = 16 ...(ii)
we know that
(x-y)² = (x + y)² - 4 x y
= (15)²- 4(16)
= 225 - 64
= 161
x-y = 12.68 ≅13 ...(iii)
Step(ii):-
We have
x + y = 15 ...(a)
x -y = 13 ...(b)
Solving (a) and (b)
2x = 27.68
x = 13.84
Substitute x = 13.84 in equation (i)
x + y = 15
13.84 + y = 15
y = 15 - 13.84
y = 1.16
Step(iii):-
The positive numbers are x = 13.84 and y = 1.16
The sum of the reciprocal of two numbers are
[tex]\frac{1}{x} + \frac{1}{y} = \frac{1}{13.84} + \frac{1}{1.16}[/tex]
= [tex]\frac{15}{16}[/tex]
Conclusion:-
The sum of the reciprocal of two numbers are
[tex]\frac{1}{x} + \frac{1}{y}= \frac{15}{16}[/tex]
Does anyone know this? Need it ASAP
Answer:
D) P = 80 feet, A = 360 square feet
Step-by-step explanation:
Perimeter=15+20+17+8+20=80 feet
Area=(15*20)+(1/2*8*15)=300+60=360 square feet