An examination consists of multiple-choice questions, each having five possible answers. Linda estimates that she has probability 0.4 of knowing the answer to any question that may be asked. If she does not know the answer, she will guess, with conditional probability 1/5 of being correct.A. What is the probability that Linda gives the correct answer to a question? B. What is the conditional probability that Linda knows the answer, given that she supplies the correct answer?
Answer:
a. 0.52 = 52% probability that Linda gives the correct answer to a question.
b. 0.7692 = 76.92% probability that Linda knows the answer
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: Supplies the correct answer:
Event B: Knows the answer
A. What is the probability that Linda gives the correct answer to a question?
0.4(knows the answer)
1/5 = 0.2 of 1 - 0.4 = 0.6(guesses the answer). So
[tex]P(A) = 0.4 + 0.2*0.6 = 0.52[/tex]
0.52 = 52% probability that Linda gives the correct answer to a question.
B. What is the conditional probability that Linda knows the answer, given that she supplies the correct answer?
Intersection of events A and B is knowing the answer and giving the correct answer, which means that [tex]P(A \cap B) = 0.4[/tex]
The desired probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.52} = 0.7692[/tex]
0.7692 = 76.92% probability that Linda knows the answer
what is the solution to the system of equations?
3x - 6y = -12
2x - 4y = -16
please help!!
Solve the system using elimination. 4y+x= -17 -2y+2x =16
Answer:
(3, -5)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
4y + x = -17
-2y + 2x = 16
Step 2: Rewrite Systems
-2y + 2x = 16
[Multiplication Property of Equality] Multiply 2 to both sides: 2(-2y + 2x) = 32[Distributive Property] Distribute 2: -4y + 4x = 32Step 3: Redefine Systems
4y + x = -17
-4y + 4x = 32
Step 4: Solve for x
Elimination
Combine equations: 5x = 15[Division Property of Equality] Divide 5 on both sides: x = 3Step 5: Solve for y
Substitute in x [Original Equation]: 4y + 3 = -17[Subtraction Property of Equality] Subtract 3 on both sides: 4y = -20[Division Property of Equality] Divide 4 on both sides: y = -5Answer:
Step-by-step explanation:
Let's solve your system by elimination.
4y+x=−17;−2y+2x=16
Multiply the first equation by -2,and multiply the second equation by 1.
−2(4y+x=−17)
1(−2y+2x=16)
Becomes:
−2x−8y=34
2x−2y=16
Add these equations to eliminate x:
−10y=50
Then solve −10y= 50 for y:
−10y=50
−10y /−10 = 50/ −10 (Divide both sides by -10)
y = −5
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
4y + x = −17
Substitute −5 for y in 4y+x=−17:
(4)(−5)+x=−17
x−20=−17(Simplify both sides of the equation)
x−20+20=−17+20(Add 20 to both sides)
x=3
Answer:
x=3 and y=−5
HOPE IT WILL HELP :)
What the solution for CED
Answer:
Step-by-step explanation:
The two adjacent angles must have a sum of 180
CED=180-122
CED=58 degrees
If x = 0, what is f(x)?
Explain why 3/4 is graphed to the right of 1/4 but -3/4 is graphed to the left of -1/4
Mathilde has 20 pints of green paint. She uses 2/5 of it to paint a landscape and 3/10 of it while painting a clover. She decides that, for her next painting, she will need 14 pints of green paint. How much more paint will she need to buy?
Answer:
She would need one more pint.
Step-by-step explanation:
Estimate 98.7 / 10.1 = ? (Show work)
Answer:
10
Step-by-step explanation:
Round both numbers to the nearest tens place.
98.7 rounds up to 100
10.1 rounds down to 10
100/10=10
Can someone help me I’m really bad in geometry
He travelled 52.6 feet which is the hypotenuse. Then use sin ratio to solve for h.
whats the answer a b or c
Answer:
∠C & ∠P
Step-by-step explanation:
PLEASE HELP ONLY GENIUSES! THANK YOU IN ADVANCE!
Answer:
By trigonometric properties that is NOT an identity By trigonometric properties this is an identifyA random sample of 300 parts was taken from a particular grinding machine. Of those parts, 12 were defective. (a) Construct a 99% upper bound for the proportion of all parts produced by this machine that will be defective. 0.0109 (b) Construct a 99% confidence interval for the proportion of all parts produced by this machine that will be defective. [ Select ] (c) It is decided that the interval produced in part (b) is too wide, and thus a new sample must be taken and a new confidence interval calculated. What sample size would be necessary to ensure that the width of the 99% confidence interval will be 0.02 or less
Answer:
a) Ub = 0,069
b) CI 99 % = ( 0,0287 ; 0,069 )
c) n = 2536
Step-by-step explanation:
Confidence Interval (CI) for proportion is
p₀ ± z(c) * √ ( p₀*q₀ ) /n
Where p₀ is the sample proportion
n = size of the sample
and z(c) is z score for the significance level α
As CI = 99 % α = 1% α = 0,01 α/2 = 0,005
from z-table we find z(c) = 2,57
p₀ = 12/300 p₀ = 0,04 ;
n*p₀ = 12 > 10 and n*q₀ = 300*0,96 n*q₀ = 288 > 10
We can use normal distribution as a valid aproximation of binomial distibution
Then z(c) = 2,57
a) upper bound for CI Ub
Ub = p₀ + z(c) * √ p₀q₀/300
Ub = 0,04 + 2,57 * √ (0,04*0,96)/300
Ub = 0,04 + 0,0113
Ub = 0,069
b) CI at 99% is
CI = p₀ ± z(c) * √ ( p₀*q₀ ) /n
we have already calculated the Ub = 0,069
the Lower bound would be Lb = 0,04 - 0,0113
Lb = 0,0287
Then CI 99 % = ( 0,0287 ; 0,069 )
c) If CI ≤ 0,02 we can find the minimun n value with the equation:
p₀ ± z(c) * √ ( p₀*q₀ ) /n = CI or p₀ - z(c) * √ ( p₀*q₀ ) /n = 0,01
For symmetry respect to p₀
z(c) *√ (p₀*q₀) / n = 0,01
Solving for n
z(c) * √ ( p₀*q₀ ) /n = 0,01
2,57 * √ (0,04*0,96)/n = 0,01
2,57 * √ 0,0384/n = 0,01
2,57 = 0,01/√ 0,0384/n
Squaring both sides of the equation
6,6049 = (0,01)² *n / 0,0384
0,0384*6,6049 / 0,0001 = n
n = 2536
2.6 - c/0.2 = -15.9 find what c is
Answer:
3.7
Step-by-step explanation:
c/0.2=2.6+15.9
c=(2.6+15.9)0.2
A large restaurant chain is curious what proportion of their customers in a given day are new customers. They are thinking of taking a sample of either n=50 or n=100 customers and building a one-sample z interval for a proportion using the data from the sample. Assuming the sample proportion is the same in each sample, what is true about the margins of error from these two samples?
Answer:
none of the above
Select the statement that describes this expression: (3,647 + 123) + 72. (2 points)
Group of answer choices
72 more than the sum of 3,647 and 123
72 times the sum of 3,647 and 123
72 more than the difference between 3,647 and 123
72 more than the product of 3,647 and 123
Answer:
A
Step-by-step explanation:
someone help me with math :):
Which of the following is not an integer?
1. 0
2. 1\2
3. 9
4. -13
what number? 1,2,3, or 4?
please help!! 14 points!!!
Find the area of of a regular octagon with side length 20 cm.
A=2(1+[tex]\sqrt{2}[/tex])a^2=2·(1+[tex]\sqrt{2}[/tex])·20^2≈1931.37085cm²
PLEASE HELP!!!!!! I WILL GIVE Brainliest!
Answer:
just sub
Step-by-step explanss
What is the area of the part that is not shaded.
Answer: 48
Step-by-step explanation:
big square is 64, shaded square is 16
64-16= the unshaded region
GIVING BRAINIEST TO WHOEVER ANSWERS THIS!!!!
Answer:
Step-by-step explanation:
2x + a = bx - 5
3). a ≠ - 5 and b ≠ 2
4). a ≠ - 5 and b = 2
(5) a = - 5 and b = 2
Select the statement that describes this expression: fraction 1 over 2 x (734 − 246).
A) Half the sum of 734 and 246
B) fraction 1 over 2 the difference between 734 and 246
C) fraction 1 over 2 the quotient of 734 and 246
D) 2 times the difference between 734 and 246
The statement to represent the expression is fraction 1 over 2 the difference between 734 and 246. Therefore, option B is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 1/2 ×(734-246)
= 1/2 ×488
= 244
Therefore, option B is the correct answer.
To learn more about an expression visit;
https://brainly.com/question/28170201.
#SPJ3
a survey was taken of twenty dentists about Sparkly toothpaste. sixteen of the dentists recommended sparkly toothpaste to their patients. the same survey was given to dentists in a different state. the time they ask thirty dentists. twenty-four of those dentists recommended sparkly toothpaste to their patients continue, how many dentists out of fifty would recommend sparkly toothpaste?
Answer:
40
Step-by-step explanation:
So they asked 50 people total but they want to know how many agreed they should use it so 16 said yes and 24 said yes add those two numbers and get your answer
Answer:
40
Step-by-step explanation:
Just add 24 and 16 together.
PLEASE HELP ME OVER HERE
Answer:
Ummm what am i helping you with? You did not say anything, so i can't help you
Step-by-step explanation:
8m > 67
Which value of m satisfies the inequality?
A.5
B.6
C.8
D.9
Answer:
D
Step-by-step explanation:
A is wrong because 8 x 5 = 40
40 < 67
B is wrong because 8 x 6 = 30
48 < 67
C is wrong because 8 x 8 = 64
64 < 67
D is correct because 72 > 67
Hope this helps!! ♥︎
Find the area of this trapezoid
Answer:
a= 1024
Step-by-step explanation:
Jenny is 9 years younger than Sammie. Five years ago, Sammie was four times older than Jenny. How old is each now?
Answer:
Jenny's is 8 now and Sammie is 17.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
Jenny's age is x.
Sammie's age is y.
Jenny is 9 years younger than Sammie.
This means that:
[tex]x = y - 9[/tex]
Five years ago, Sammie was four times older than Jenny.
This means that:
[tex]y - 5 = 4(x - 5)[/tex]
Since [tex]x = y - 9[/tex]
[tex]y - 5 = 4(y - 9 - 5)[/tex]
[tex]y - 5 = 4(y - 14)[/tex]
[tex]y - 5 = 4y - 56[/tex]
[tex]3y = 51[/tex]
[tex]y = \frac{51}{3}[/tex]
[tex]y = 17[/tex]
[tex]x = y - 9 = 17 - 9 = 8[/tex]
Jenny's is 8 now and Sammie is 17.
plz help me
which number describes the center of the data set below?
The net for a rectangular prism is shown below. Which is total surface area of the figure?
Sally is making 15 individual blueberry cheesecakes. How many pounds of blueberries will be in each cheesecake if 5 1/4 pounds of blueberries are divided equally among them?
Answer:
0.35 pounds in each cheesecake
Step-by-step explanation:
Number of individual blueberry cheesecakes = 15
Pounds of blueberries = 5 1/4 pounds
How many pounds of blueberries will be in each cheesecake if 5 1/4 pounds of blueberries are divided equally among them?
= 5 1/4 ÷ 15
= 21/4 ÷ 15
= 21/4 × 1/15
= (21*1)/(4*15)
= 21/60 pounds
Equivalent to 0.35 pounds in each cheesecake