Answer:
1) The probability that a person who tests positive actually has the disease is 0.1056 or 10.56%
2) 180 combinations
3) 5040 pin numbers can be chosen
4) 54439560 ways
5) 389283935040 ways
Step-by-step explanation:
1) From Bayes' theorem, we have;
[tex]P(A\mid B) = \dfrac{P(A)P(B\mid A)}{P(A)P(B\mid A)+P\left (\overline{A} \right )P\left (B\mid \overline{A} \right )}[/tex]
Where:
[tex]P(A\mid B)[/tex] = Percentage of the population that tests positive for the disease that actually have the disease
P(A) = Incidence rate = 0.5% = 0.005
[tex]P(B\mid A)[/tex] = Percentage of the population that have the disease and will tests positive = 1 - 0.06 = 0.94
[tex]P\left (\overline{A} \right )[/tex] = P(no disease) = 1 - 0.005 = 0.995
[tex]P\left (B\mid \overline{A} \right )}[/tex] = P(positive [tex]\mid[/tex] no disease) = False positive = 0.04
From which we have;
[tex]P(A\mid B) = \dfrac{0.005 \times 0.94}{0.005 \times 0.94 +0.995 \times0.04} = 0.1056[/tex]
Therefore, the probability that a person who tests positive actually has the disease = 0.1056 or 10.56%
2) The parameters given are;
The number of shirts that Karla has = 10 shirts
The number of shorts that Karla has = 6 shorts
The number of pairs of sandals that Karla has = 3 pairs
Therefore;
The number of ways Karla can choose her shirts = 10 ways
The number of ways Karla can choose her shorts = 6 ways
The number of ways Karla can choose her pair of sandals = 3 ways
The total combination of outfits Karla can make = 10 × 6 × 3 = 180 combinations
3) We have;
The number of permutations of 10 numbers taking 4 at a time is given as follows;
n!/(n-r)! = 10!/(10-4)! = 10!/6! = 5040 pin numbers can be chosen
4) The number of ways the first second and the third can be awarded is 380×379×378 = 54439560 ways
5) The number of ways is 210×209×208×207×206 = 389283935040 ways.
Which table represents a direct variation function?
A group of tourists can be sorted into tour boats in groups of 4 or in groups of 6. In either case, there are no empty seats. Find the number of tourists if there are more than 25 and fewer than 45.
Answer:
36
Step-by-step explanation:
First we need to write out some of the common multiples of 4 and 6.
12, 24, 36
The number 36 is between 25 and 45 so it is our answer
Assume that when adults with smartphones are randomly selected, 49% use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 23 of them use their smartphones
Answer: 0.0013684
Step-by-step explanation:
Given the following :
Probability (p) = 49% = 0.49
Number of selected adults (n) = 30
Find the probability that exactly 23 use their smartphone.
The problem is abive can be solved using the binomial probability function.
Binomial probability :
P(X = x) = [n! / x! (n-x)!] * P^x * (1 - P)^(n-x)
At x = 23
P(X = 23) = [30! / 23! (30-23)!] * P^23 * (1-0.49)^(30-23)
P(X = 23) = [30! / 23! (7)!] * 0.49^23 * (0.51)^7
P(X =23) = (2035800) × 6.72203E−10
= 0.0013684
Choose the correct simplification of the expression (5x^5)^2 5x^25 10x^10 25x^7 25x^10
Answer:
[tex]25x^{10}[/tex]
Step-by-step explanation:
[tex](5x^5)^2\\\\\text {Apply Rule: }(a*b)^n=a^n b^n\\\\(5x^5)^2=5^2(x^5)^2\\\\25(x^5)^2\\\\\text {Apply rule: } (a^b)^c=a^{bc}\\\\25(x^5)^2=\boxed{25x^{10}}[/tex]
Please help!! This is so confusing! 100 points!!
Answer:
The value of the expression given is:
4Step-by-step explanation:
First, you must divide the expression in three, and to the final, you can multiply it:
[(3^8)*(2^(-5))*(9^0)]^(-2) [(2^(-2))/(3^3)]^4 3^28Now, we can solve each part one by one:
First part.
3^8 = 6561 2^(-5) = 0.03125 9^0 = 1 (Whatever number elevated to 0, its value is 1) (6561 * 0,03125 * 1) = 205.03125And we elevate this to -2:
205.03125^-2 = 2.378810688*10^(-5) or 0.00002378810688Second part.
2^(-2) = 0.25 3^3 = 27 0.25 / 27 = 9.259259259 * 10^(-3) or 0.00925925925925And we elevate this to 4:
0.00925925925925^4 = 7.350298528 * 10^(-9) or 0.000000007350298528Third Part.
3^28 = 2.287679245 * 10^13 or 22876792450000At last, we multiply all the results obtained:
0.00002378810688 * 0.000000007350298528 * 22876792450000 = 3.999999999999999999 approximately 4We approximate the value because the difference to 4 is minimal, which could be obtained if we use all the decimals in each result.
Answer:
[tex]\Huge \boxed{\mathrm{4}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle \sf (3^8 * 2^{-5} * 9^0)^{-2} * (\frac{2^{-2}}{3^3 } )^4 *3^{38}[/tex]
Distributing the power of -2 to the parenthesis,
[tex]\displaystyle \sf (3^{-16} * 2^{10} * 9^0)* (\frac{2^{-2}}{3^3 } )^4 *3^{38}[/tex]
Distributing the power of 4 to the fraction,
[tex]\displaystyle \sf (3^{-16} * 2^{10} * 9^0)* (\frac{2^{-8}}{3^{12} } )*3^{38}[/tex]
Multiplying,
[tex]\displaystyle \sf \frac{3^{-16} * 2^{10} * 9^0* 2^{-8} *3^{38}}{3^{12} }[/tex]
Simplifying,
[tex]\displaystyle \sf \frac{2^2 *3^{22}}{3^{22} }[/tex]
[tex]\sf 2^2 =4[/tex]
[tex]\rule[225]{225}{2}[/tex]
I need helppppppppppppp
Answer:$140 for the train ride
$84 for the museum
Step-by-step explanation:
28×5
28×3
All the students + you = 28
If not, try 27×5 and 27×3
Answer:
$216 for the Train Ride and visit to the Museum.Step-by-step explanation:
There are two values to find and add together.
o The admission cost for the Museum
o The admission cost for the Train Ride
Let's make some equations.
x=number of people
Museum: 3x=total cost for Museum (m)
Train Ride: 5x=total cost for Train Ride (t)
m+t= total money spent
Now, let's replace the values.
Museum: 3(27)=$81
Train Ride: 5(27)=$135
$81+$135=$216 for the Train Ride and visit to the Museum.
Hope this helps!
-Emma
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
2x + 3y = 6
- 4x + 3y = 12
Answer:
D. [tex]x=-1, y=2\frac{2}{3}[/tex]
Step-by-step explanation:
Solving for x:
2x+3y=6
Subtract 3y from both sides
2x= -3y+6
Subtract 6 from both sides
2x-6= -3y
-4x+3y=12
Subtract 3y from both sides
-4x= -3y+12
Subtract 12 from both sides
-4x-12= -3y
Combine equations:
-4x-12=2x-6
Add 4x to both sides
-12=6x-6
Add 6 to both sides
-6=6x
6x= -6
Divide both sides by 6
x= -1
Solving for y:
2x+3y=6
Subtract 3y from both sides
2x= -3y+6
-3y+6=2x
Multiply both sides by -1
3y-6= -2x
Multiply both sides by 2
6y-12= -4x
-4x+3y=12
Subtract 3y from both sides
-4x= -3y+12
-3y+12= -4x
Combine equations:
6y-12= -3y+12
Add 3y to both sides
9y-12=12
Add 12 to both sides
9y=24
Divide both sides by 9
y= [tex]2\frac{2}{3}[/tex]
Answer:
x=−1,y=2
3
2
Step-by-step explanation:
x=-1,y=2 2/3
HELP ME PLEASE REALLY IMPORTANT OR ILL GET IN TROUBLE!! WILL MARK AS BRAINLEST IF YOU GET IT CORRECT!!
Answer: C, It stays the same.
Step-by-step explanation: If you simplify the ratio (the fraction) by canceling the t's, you get 2/1 or 2:1. This means that no matter the value of the variable t, the value of the expression will stay the same.
Tim and jane both work for a company that sells boxes of breakfast cereal the boxes of cereal cost 3 pounds and the amount of cereal in each box weighs 160g the company wants to have a special offer here is Tim's idea for the special offer: PUT 25% MORE CEREAL IN EACH BOX AND DO NOT LOWER THE PRICE here is Jane's idea: REDUCE THE PRICE AND DO NOT CHANGE THE AMOUNT OF CREAL IN EACH BOX Jane wants her idea to give the same value of money as Tim's idea by what percentage does she need to reduce the price?
Answer:
In order to give the same value for money as Tim's idea, Jane has to reduce the price by 25%
Step-by-step explanation:
The given parameters are;
Cost of each box of breakfast cereal = 3 pounds
Amount of cereal in each box of breakfast cereal = 160 g
160 g of cereal = 100%
25% of one box of cereal = 25% of 160 g = (25/100)×160 g= 40 g
Given that Jane wants her idea to give the same value of money as Tim's idea, we have;
160 g of cereal costs 3 pounds
1 g of cereal will cost 3/160 pounds
40 g of cereal will cost 40*3/160 = 3/4 pounds
Therefore, the percentage 3/4 pound is of 3 pounds = [tex]\dfrac{\frac{3}{4} }{3} \times 100 = 25 \%[/tex]
Which gives, Jane has to reduce the price by 25% to give the same value for money as Tim's idea.
To give the same value of money as Tim's idea, she need to reduce the price by 20%.
Given that:
Cost of one box of breakfast cereal is 3 pounds.
Weight of 1 box of cereal is 160g.
Tim's idea is to put 25% more cereal.
Let Jane's idea is to reduce price by x pounds such that the value of the item is same as that after applying Tim's idea.
Value in case of Tim's idea:
[tex]160g + \dfrac{160 \times 25}{100} \: \: in \: \: 3 \: pounds\\\\200g \: \: in \: \: 3 pounds\\1g \: \: in \: \: \dfrac{3}{200} \: pounds[/tex]
Value in case of Jane's idea:
[tex]160g \: \: in \: \: (3-x) \: pounds\\\\1g \: \: in \: \: \dfrac{(3-x)}{160} \: pounds\\[/tex]
Since values have to stay same, thus we have:
[tex]\dfrac{3}{200} = \dfrac{3-x}{160}\\\\\dfrac{12}{5} = 3-x\\\\5x = 3\\\\x = \dfrac{3}{5}\\\\x = 0.6 \:pounds[/tex]
To calculate percentage, we can do as follows:
[tex]\begin{aligned}percentage &= \dfrac{x \times 100}{3}\\&= \dfrac{60}{3}\\&= 20\end{aligned}[/tex]
Thus, to give the same value of money as Tim's idea, she need to reduce the price by 20%.
Learn more here:
https://brainly.com/question/8011401
Which of the ordered pairs below satisfy the following equation. Check all that apply!
Answer:
A, B, and C
Step-by-step explanation:
By substituting each of the ordered pairs into the equation you can determine that A, B and C all satisfy the equation.
What is a common reason for filing a 1040X?
A.
not using a tax preparer to file the initial return
B.
leaving off the cents of a dollar value
C.
forgetting to include miscellaneous income earned
D.
signing the form in blue ink
Answer:
c forgetting income
Step-by-step explanation:
qweddcs
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is
designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.
Assume that the groups consist of 16 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 16 births.
The value of the mean is u =
(Type an integer or a decimal. Do not round.)
Answer:
The found values are:
μ = 8
σ = 2
Step-by-step explanation:
Following data is given in the question:
p = 0.5
n = 16
Consider that it follows binomial distribution:
For binomial distribution, the mean is the product or probability 'p' and and the sample size 'n' :
μ = p · n
μ = 0.5 · 16
μ = 8
For binomial distribution, the standard deviation is the square root of product of sample size 'n' and the probabilities 'p' and 'q'.
σ = √(n·p·q)
where q = 1 - p = 1 - 0.5 = 0.5
σ = √(16 · 0.5 · 0.5)
σ = √4
σ = 2
salem had to withdraw 28.50 from his bank account every week for 5 weeks to pay a purchase. what number represents a change in his bank account
Answer:
Okay so he had to withdraw 28.50 from his bank account every week so that means he withdrew 142.5 that in 5 weeks
Step-by-step explanation:
What are the solution(s) to the quadratic equation 50 – x2 = 0?
A.x = +2V5
B.x = +63
C.x = +5V2
D.no real solution
Please help hurry :/
Answer:
±5 sqrt(2) =x
Step-by-step explanation:
50 – x^2 = 0
Add x^2 to each side
50 = x^2
Take the square root of each side
±sqrt(50) = sqrt(x^2)
±sqrt(25*2) = x
±sqrt(25)sqrt(2)=x
±5 sqrt(2) =x
Answer:
If you have to choose an alternative, it is C. [tex]x=5\sqrt{2}[/tex] is one of the solutions/roots of the quadratic equation, but the correct answer is actually [tex]x= \pm 5\sqrt{2}[/tex].
Step-by-step explanation:
[tex]50-x^2 = 0 \Rightarrow x^2=50[/tex]
[tex]x= \pm \sqrt{50}[/tex]
Once [tex]\sqrt{50} =\sqrt{2\cdot5\cdot 5}= 5\sqrt{2}[/tex]
[tex]x= \pm 5\sqrt{2}[/tex]
hi:) how to do question 5?
Answer:
a) Area of △ABC= 78.8cm² (3 s.f.)
b) AB= 17.3cm (3 s.f.)
c) h= 9.09cm (3 s.f.)
Step-by-step explanation:
Please see the attached picture for full solution.
Can you help me please.
Step-by-step explanation:
[tex]a) \\ (8 \times {10}^{ - 3} ) \times (2 \times {10}^{ - 4} ) \\ = 8 \times 2 \times {10}^{ - 3} \times {10}^{ - 4} \\ = 16 \times {10}^{ - 3 - 4} \\ = 16 \times {10}^{ - 7} \\ = 1.6 \times {10}^{ - 6} \\ \\ b) \\ (6 \times {10}^{ 2} ) \div (3\times {10}^{ - 5} ) \\ \\ = \frac{6 \times {10}^{ 2}}{3\times {10}^{ - 5}} \\ \\ = \frac{2\times {10}^{ 2}}{ {10}^{ - 5}} \\ \\ = 2 \times {10}^{ 2 + 5} \\ \\ = 2 \times {10}^{7} \\ [/tex]
Please answer these simultaneous equations ASAP. Thank you (lots of points only for full answers)
Step-by-step explanation:
for number 4:
2x + 5y = -10
2x - y = 8
subtract it
6y = -18
y = 6/-18
y = -0.3
now go back to the first equation
2x + 5 x -0.3 = -10
2x -1.5 = -10
2x = -8.5
-4.25
x = -4.25, y = -0.3
hope this help
Answer:try to answer the rest on your own and if it is not clear, let me know
Step-by-step explanation:
Which polynomial is prime?
THE CORRECT ANSWER IS OPTION ( B )
HOPE IT HELPS.PLEASE MARK AS BRAINLIEST AND FOLLOW ME .....Evaluate the expression for
x = 6, y = -10:
3x - 7y
Answer:
88
Step-by-step explanation:
hello,
we need to replace x by 6 and y by -10 so it comes
3*(6)-7*(-10)
= 18 + 70 = 88
hope this helps
Answer:
88Given,
X=6
y=-10
[tex]3x - 7y \\ = 3 \times x - 7 \times y \\ = 3 \times 6 - 7 \times ( - 10) \\ = 18 - ( - 70) \\ = 18 + 70 \\ = 88[/tex]
Hope this helps...
Good luck on your assignment..
Find the slope of the line that passes through (37, 57) and (38, -7).
Answer:
-64
Step-by-step explanation:
When given two points we can use the slope formula
m = (y2-y1)/(x2-x1)
= (-7 -57)/(38-37)
=-64/1
= -64
HURRY PLS!!!
which expression is equivalent to 3(b+ c) using only the distributive property?
3bc
3(c+b)
3b+3c
(b+c) • 3
Answer:
3b + 3c
Step-by-step explanation:
hope this helps you
Answer:
3(c+b)
Step-by-step explanation:
3(b+c) is essentially 3 times B+ 3 times c
and 3(c+b) is 3 times c + 3 times B
Explain how you can determine that the following system has one unique solution – without actually solving the system.
2x+y=4
2y=6-2x
Answer:
Step-by-step explanation:
Well, first you'd have to get the equations in slope-intercept form in order to make it easier for you to see it in the bigger picture. 2x+y=4 would be y= 2x-4, and the other equation would be y= x-3. If you were to solve it, there would be one solution since the y's cancel out. If you graphed it, there would be a point of intersection, unlike when the lines are parallel if there's 0 solutions or only one line's there if there's infinitely many solutions.
Can someone help me in this math problem plssssss
Answer:
D
Step-by-step explanation:
the x coordanate length is 9, because | -4-5 | = 9
and the y coordanate is 13 becasue | -7 - 6 | = 13
Then you do [tex]a^{2}+b^{2} = c^{2}[/tex] which equals 5√10 or approximately 15.81139 which rounds to 15.81
To find the distance an object has traveled, you use the formula D=RT; where D=distance, R=rate and T=time. What was the rate a person drove if they traveled 313.5 miles in 4 hours? A. 78.374 miles per hour B. 78.375 miles per hour C. 1,254 miles per hour D. 12,540 miles per hour
Answer:
78.375 miles per hour = R
Step-by-step explanation:
D= RT
The miles are 313.5 which is D and the time is 4 hours
313.5 = R * 4
Divide each side by 4
313.5/4 = R
78.375 miles per hour = R
Use the fundamental theorem of algebra to explain how many roots your expression can have. How many real roots and how many complex roots are possible?
(X+12)^9.
Answer:
hi
Step-by-step explanation:
In a football game, the home team scored 1 touchdown and one extra point during every quarter. How many points did the home team have at the end of the game?
Answer:
28 points
Step-by-step explanation:
A touch down is 6 points and an extra point is 1 point
There are 4 quarters
6+1 = 7
4 quarters
4*7 = 28
They scored 28 points
Who described gravity mathematically
Answer:
I believe Isaac Newton did with a formula.
gravity(F=Gm1m2/ r2)
Hope this helps
Step-by-step explanation:
Answer:
Isaac Newton was the first man to do so.
Step-by-step explanation:
gravity(f=gm=1m2/ r2)
Hope this helped and please mark me brainliest!If Shane weighs 120 pounds and Johnny weighs 150 pounds.If Shanie gains 60 pounds will Shanie and Johnny be the same weight.
Answer:
shane is 120 pounds and johnny is 150 pounds
Step-by-step explanation:
shane 120 and johnny gains weight 60 pounds so 120 plus 60 that is both of the together is 180 hope this helps you i think they maybe be the same weight because together they are more
Answer:
No, Shane will be heavier
Step-by-step explanation:
120 > 150
120 + 60= 180
180 > 150
Can anyone help me with this question?
Answer:
x² can be written as (3.8 * 10⁵)² = 3.8² * 10⁵ * ² = 14.44 * 10¹⁰.
x² / y = 14.44 * 10¹⁰ / 5.9 * 10⁴ ≈ 2.45 * 10⁶
help me with right answer plz
Answer:
13.5
Step-by-step explanation:
area: 1/2*[x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]