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
Find the area of the parallelogram. Round to the nearest hundredth if necessary.
6 m
8 m
cm2
Area =
The area of the parallelogram willl be equal to 48 square meters.
What is an area?
The space occupied by any two-dimensional figure in a plane is called the area. The parallelogram occupied by the parallelogram in a two-dimensional plane is called as the area of the parallelogram .
Given that:-
Height = 6 mBase = 8 mThe area will be calculated as:-
Area = Height x Base
Area = 6 x 8
Area = 48 square meters.
Therefore the area of the parallelogram willl be equal to 48 square meters.
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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
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.
An _____ is a single outcome or group of outcomes.
a.) event
b.) probability
c.) sample
d.) None of these
Answer:
D
Step-by-step explanation:
The article "an" can only be used with the word "event" so that automatically takes the choices b and c out of the way. An event is something that happens and causes the outcome, it is not the outcome, so it is not A. Thus, the answer is D
5) What does QRST → Q'R'S'T' mean?
Answer:
QRST becomes Q prime, R prime, S prime, T prime.
Step-by-step explanation:
Any figure that is rotated, translated or reflected on the corrdinate plane is considered a prime (as long as it is congruent (the same as, or equal to) with the original). The apostrophe stands for prime.
Ex. If you reflect triangle ABC across one of the axes, the original triangle will continue being ABC, while the reflection would be A' B' C' (or A prime, B prime, C prime). I hope this helps :)
A rectangle with length n and height m. A right triangle with hypotenuse n + 1, length n, and height m.
The perimeter of the rectangle is 34 cm. The perimeter of the triangle is 30 cm. Find the value of n.
Please select the best answer from the choices provided
A. 10cm
B. 14cm
C. 12cm
D. 16cm
9514 1404 393
Answer:
C. 12cm
Step-by-step explanation:
The equation for the perimeter of the rectangle is ...
P = 2(L+W)
34 = 2(n +m)
Solving for m, we get
m = 17 -n . . . . . . . divide by 2, subtract n
__
The Pythagorean theorem gives the relationship between the sides and the hypotenuse
m^2 +n^2 = (n+1)^2
(17 -n)^2 +n^2 = (n +1)^2 . . . . . . substitute for m
289 -34n +n^2 +n^2 = n^2 +2n +1 . . . . eliminate parentheses
n^2 -36n +288 = 0 . . . . . . . put in standard form
(n -12)(n -24) = 0 . . . . . . . . . factor
n = 12 . . . . . . . . . . n=24 is an extraneous solution here
The value of n is 12 cm.
Answer:
12 cm. Just took the quiz! 12 is the right answer not 14 cm.
Step-by-step explanation:
Amy mows 7 lawns in 4 hours. How long does it take
her to mow one lawn? Round your answer to the
hundredths place.
Answer:
0.57 hours
Explanation:
4 ÷ 7 = 0.5714285714285714
Rounded to the nearest 100th is :
0.57
Answer:
1 hour and 45 minutes
Step-by-step explanation:
I got this answer by dividing, so it takes her 1 3/4 hours which is converted to 1 hour and 45 minutes
Can you conclude that the
parallelogram below is a
rectangle?
Yes
No
Answer:
yes
Step-by-step explanation:
Answer:
Yes. If no right angle exists, then it's not a rectangle.
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!! ♥︎
A cell phone plan charges $19.90 a month, plus $0.05 per text message
Create & solve an inequality that represents the number of texts, t, that can be
sent while still keeping the monthly bill under $25?
Answer:
[tex]19.9+0.05t<25[/tex]
Less than 102 text messages.
Step-by-step explanation:
Monthly charge of cell phone = $19.90
Cost of one text message = $0.05
Let number of text messages be [tex]t[/tex]
The monthly bill should be less than $25. So,
[tex]19.9+0.05t<25[/tex]
The required inequality is [tex]19.9+0.05t<25[/tex]
[tex]19.9+0.05t<25\\\Rightarrow 0.05t<25-19.9\\\Rightarrow t<\dfrac{5.1}{0.05}\\\Rightarrow t<102[/tex]
So, the number of text messages that can be sent while keeping the bill under $25 is less than 102.
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
Solve for x.
Your answer must be simplified.
17x>−17
Answer:
x>-1
Step-by-step explanation:
[tex] \frac{17}{17}x > - \frac{17}{17} \\x > - 1 [/tex]
PLEASE HELP!!!!!! I WILL GIVE Brainliest!
Answer:
just sub
Step-by-step explanss
What is the answer to -20=p/15
Answer:
Solve for p by simplifying both sides of the equation, then isolating the variable.
p = − 300
Step-by-step explanation:
have a nice day
I think p=300???
Sorry if thiz is wrong. i dont really know that much
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.
A 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
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:
plz help me
which number describes the center of the data set below?
Brett finds 70c while doing laundry which set of coins could be the coins that Brett found
Answer:
A is the correct set of coins
Explain why 3/4 is graphed to the right of 1/4 but -3/4 is graphed to the left of -1/4
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
what is the solution to the system of equations?
3x - 6y = -12
2x - 4y = -16
please help!!
whats the answer a b or c
Answer:
∠C & ∠P
Step-by-step explanation:
Find two numbers such that their sum, their difference, and their product have the ratio 3:2:5.
Answer:
2 and 10
Step-by-step explanation:
We will assume to numbers represented by x and y.
From the question, we can write the following :
sum = x + y
difference = x - y
product = xy or x*y
Since we have two unknowns, general rule of thumb is that we require
2 equations to solve for them.
Using the ratio, of sum: difference and sum : product,
I can form these 2 equations:
(x + y) / (x -y) = 3/2 (1)
(x + y) / (x*y) = 3/5 (2)
In (1),
we cross multiply and do some tidying we will get
x = 5y
In (2),
we have 5x + 5y = 3x*y
We can then substitute x = 5y into (2) and get the following
5*5y + 5y = 3*5y*y
30y = 15y^2
2y = y^2
y^2 - 2y = 0
After factorization,
y(y - 2) = 0
you will have to options either use y = 0 or y = 2
If we use 2, then using equation (1),
we can solve for x which is 10.
Answer:
2 , 10
Step-by-step explanation:
(x+y) / (x-y) = 3/2 ..(1)
3x-3y = 2x+2y
x = 5y
(x+y) / xy = 3/5
(5y+y) / (5y*y) = 3/5
6y/5y² = 3/5
15y² = 30y
y = 2
x = 10
check: (2+10) : (10-2) : (10*2) = 12 : 8 : 20 = 3 : 2 : 5
The net for a rectangular prism is shown below. Which is total surface area of the figure?
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 ONLY GENIUSES! THANK YOU IN ADVANCE!
Answer:
By trigonometric properties that is NOT an identity By trigonometric properties this is an identifyFor the function f(x) = 3x
Find f(4)
Answer:
F(4) = 3*4 = 12
Step-by-step explanation:
ТDaP is a booster shot that prevents Diphtheria, Tetanus, and Pertussis in adults and adolescents. It should be administered every 8 years in order for it to remain effective. A random sample of 500 people living in a town that experienced a pertussis outbreak this year were divided into two groups. Group 1 was made up of 132 individuals who had not had the TDaP booster in the past 8 years, and Group 2 consisted of 368 individuals who had. In Group 1, 15 individuals caught pertussis during the outbreak, and in Group 2, 11 individuals caught pertussis. Is there evidence to suggest that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were? Test at the 0.05 level of significance.
Enter the test statistic - round to 4 decimal places.
Enter the P-Value - round to 4 decimal places.
Is there evidence to suggest the proportion of those who caught pertussis is higher for those who were not up to date on their booster?
Answer: 76.8356 and 12.5372
Step-by-step explanation: