A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d, e- and only one correct answer. What is the probability that she answered neither of the problems correctly? Do not round your answer. (If necessary, consult a list of formulas.)
Answer:
there is a 64% chance that the student got both problems wrong
a 32% chance that they got only 1 correct
and a 4% chance that they got both correct
Step-by-step explanation:
There are 25 total possible combinations of answers, with 8 possible combinations where the student would get 1 answer right, and 1 combination where the student would get both answers correct.
[tex]25-9=16[/tex]
[tex]\frac{16}{25} =\frac{x}{100}[/tex]
[tex]\frac{64}{100}[/tex]
[tex]64[/tex]%
[tex]\frac{8}{25} =\frac{y}{100}[/tex]
[tex]\frac{32}{100}[/tex]
[tex]32[/tex]%
[tex]\frac{1}{25} =\frac{z}{100}[/tex]
[tex]\frac{4}{100}[/tex]
[tex]4[/tex]%
Assume that there is a 8% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
Answer:
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
Step-by-step explanation:
For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used to solve this question.
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.
Assume that there is a 8% rate of disk drive failure in a year.
So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]
Two disks are used:
This means that [tex]n = 2[/tex]
What is the probability that during a year, you can avoid catastrophe with at least one working drive?
This 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_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
Identify an equation in point-slope from for the line perpendicular to y=-4x-1 that passes through (-2, 4)
Answer:
y - 4 = ¼(x + 2)
Step-by-step explanation:
Point-slope form equation is given as y - b = m(x - a). Where,
(a, b) = a point on the line = (-2, 4)
m = slope = ¼ (sleep of the line perpendicular to y = -4x - 1 is the negative reciprocal of its slope value, -4 which is ¼)
✔️To write the equation, substitute (a, b) = (-2, 4), and m = ¼ into the point-slope equation, y - b = m(x - a).
y - 4 = ¼(x - (-2))
y - 4 = ¼(x + 2)
None of the options are correct
Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency, duration, and type of use. One study involving heavy use of the phones showed the mean of the battery life to be 15.25 hours with a standard deviation of 2.2 hours. Then the battery needs to be recharged. Assume the battery life between charges is normally distributed.
Required:
a. Find the probability that with heavy use, the battery life exceeds 11 hours.
b. You are planning your recharging schedule so that the probability your phone will die is no more than 5%. After how many hours should you plan to recharge your phone?
Answer:
a) The probability that with heavy use, the battery life exceeds 11 hours is 0.4602.
b) Using the standard normal table, After 6.8 hours should you plan to recharge your phone.
Step-by-step explanation:
a) The probability that with heavy use, the battery life exceeds 11 hours:-
P(x > 11) = 1 - p( x< 11)
[tex]=1- p P[(x - \mu) / \sigma < (11 - 10.75) / 2.4]\\\\=1- P(z < 0.10)[/tex]
Using z table distribution,
= 1 - 0.5398
= 0.4602
b) Using the standard normal table,
[tex]P(Z < z) = 5%\\\\\\\\= P(Z < -1.645 ) = 0.05 \\z = -1.645[/tex]
Using the z-score formula,
[tex]x = z \times \sigma + \mu\\x = -1.645 * 2.4 + 10.75\\x = 6.8 hours.[/tex]
What is the average rate of change for this quadratic function for the interval from x = 0 to x = 3 ?
Answer:
-1/2
Step-by-step explanation:
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
Which sentence correctly compares the two numbers 5.395 and 5.385?
05.395 < 5.385
05.385 > 5.395
o 5.395 = 5.385
5.385 < 5.395
h
Submit
Pass
Don't know answer
Answer:
5.385 < 5.395
Step-by-step explanation:
Compare digits one by one starting form the left.
5.395 and 5.385
The 5s in the ones place are equal.
5.395 and 5.385
The 3s in the tenths place are equal.
5.395 and 5.385
The 9 in the hundredths place is greater than the 8 in the hundredths place, so the number with the 9 is grater than the number with the 8.
That makes the number with the 8 less than the number with the 9.
Answer: 5.385 < 5.395
A card is drawn from a well shuffled pack of 52 cards . find the probability of '2' of spades
Answer:
[tex] \frac{1}{52} [/tex]Step-by-step explanation:
Given,
Total no. of cards = 52
No. of 2 of spades cards = 1
Therefore,
Probability of getting 2 of spades
[tex] = \frac{no. \: of \: required \: outcomes}{total \: outcomes} [/tex]
[tex] = \frac{1}{52} (ans)[/tex]
Cuanto es 91972×898972819
Answer:
82,680,328,109,068
Step-by-step explanation:
Use the on-line Big Number calculator
i gave someone a Brainliest pls
Answer:
i think the mistake was in step 1
Step-by-step explanation:
Laura lives 15 miles east of Kevin’s place. Kevin lives 8 miles south of Michelle’s place. How far does Michelle live from Laura’s place?
17 miles
24 miles
32 miles
36 miles
Answer:
17 miles.
Step-by-step explanation:
Let's define:
North as the positive y-axis
East as the positive x-axis.
We know that Laura lives 15 miles east of Kevin's place.
Kevin lives 8 miles south of Michelle's place.
So, if we define the origin, (0, 0) as Laura's place.
From:
"that Laura lives 15 miles east of Kevin's place."
We have that the location of Kevin's house is 15 miles west from Laura's place, then Kevin's house is at:
(0, 0) + (-15mi, 0) = (-15mi, 0)
From Kevin lives 8 miles south of Michelle's place, we know that Michelle's live 8 miles north of Kevin's place.
Then the location of Michele's house is the location of Kevin's plus (0, 8mi).
Michelle's house is located at:
(-15mi, 0) + (0, 8mi) =(-15mi, 8mi)
Now we want to find the distance between Michelle's house and Laura's house.
Michelle's house is at (-15mi, 8mi)
Laura's house is at (0mi, 0mi)
Remember that the distance between two points (a, b) and (c, d) is given by:
[tex]D = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
Then the distance between (-15mi, 8mi) and (0mi, 0mi) is:
[tex]D = \sqrt{(-15mi - 0mi)^2 + (8mi - 0mi)^2} = 17mi[/tex]
The correct option is the first one, 17 miles.
Heeeelp me pleaseeee
Answer:
sorry but the pic is too blurr
Step-by-step explanation:
if u could fix the blurr so I can answer properly
2 - (-8) + (-3) =
O A) 12
OB) 7
O C
C) 14
OD 1
Answer:
B)7
Step-by-step explanation:
2-(-8)=10
10+(-3)=7
Whole numbers are closed under addition because the sum of two whole numbers is always a whole number. Explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.
Answer:
Sample Answer: If there is no remainder, then the dividend is equal to the quotient times the divisor.
The quotient and divisor are both polynomials, and their product, the dividend, is a polynomial.
If there is a remainder, then it gets added on to the product of the quotient and the divisor.
The sum of the remainder and the product of the quotient and divisor is the dividend, which is a polynomial.
Step-by-step explanation:
for sure enjoy!
Answer:
If there is no remainder, then the dividend is equal to the quotient times the divisor.
The quotient and divisor are both polynomials, and their product, the dividend, is a polynomial.
If there is a remainder, then it gets added on to the product of the quotient and the divisor.
The sum of the remainder and the product of the quotient and divisor is the dividend, which is a polynomial.
HELPPPP ME ASAP
If f(x) = x2, g(x) = 5x, and h(x) = x +4, find each value.
Find g[h(-2)]
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Answer:
10
Step-by-step explanation:
Put the values where the arguments are and do the arithmetic.
g(h(-2)) = g(-2+4) = g(2) = 5(2)
g(h(-2)) = 10
which exponential equation is equivalent to this logarithmic equation log x5 + log x12 =7
Answer:
x⁷ = 60
Step-by-step explanation:
Given :-
log x⁵ + log x ¹² = 7 .To Find :-
The expotential equation .Solution :-
Given logarithmic equation is ,
⇒ log x⁵ + log x ¹² = 7
⇒ log x ⁵ * ¹² = 7 [ log aⁿ + log aⁿ' = log aⁿ * ⁿ' ]
⇒log x ⁶⁰ = 7
In expotential form we can write it as ,
⇒ x⁷ = 60
What is the product?
(ay3)2 + 3y - 5)
What is the product of x(x + 1)?
1. 2x + x
2. x2+ 2x
3. 212 + x
4. x2 + x
Answer:
4. x²+x
Step-by-step explanation:
the product of x(x + 1) = (x)(x) + (x)(1)
= x²+x
It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before. Suppose you want to test the hypothesis that students who study one week before score less than students who study the night before. A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789. What is the appropriate conclusion
Answer:
The p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.
Step-by-step explanation:
It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before.
At the null hypothesis, we test if the two means are equal, that is, the subtraction of them is 0.
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, we test if the two means are different, that is, the subtraction of them is different of 0. So
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789.
Considering a standard significance level of 0.02789, the p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.
Based on a sample survey, a company claims that 86% of their customers are satisfied with their products. Out of 1,100 customers, how many would you predict to be satisfied?
Answer:
946 people
Step-by-step explanation:
Find how many you would predict to be satisfied by multiplying 1,100 by 0.86:
1,100(0.86)
= 946
So, you could expect 946 people to be satisfied
Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.
Answer:
[tex]x^2 + 4x + y^2 +8y = 0[/tex]
Step-by-step explanation:
Given
[tex]A = (-1,-2)[/tex]
[tex]B = (2,4)[/tex]
[tex]AP:BP = 1 : 2[/tex]
Required
The locus of P
[tex]AP:BP = 1 : 2[/tex]
Express as fraction
[tex]\frac{AP}{BP} = \frac{1}{2}[/tex]
Cross multiply
[tex]2AP = BP[/tex]
Calculate AP and BP using the following distance formula:
[tex]d = \sqrt{(x - x_1)^2 + (y - y_1)^2}[/tex]
So, we have:
[tex]2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}[/tex]
[tex]2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}[/tex]
Take square of both sides
[tex]4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2[/tex]
Evaluate all squares
[tex]4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16[/tex]
Collect and evaluate like terms
[tex]4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20[/tex]
Open brackets
[tex]4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20[/tex]
Collect like terms
[tex]4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y + 20 - 20 = 0[/tex]
[tex]3x^2 + 12x + 3y^2 +24y = 0[/tex]
Divide through by 3
[tex]x^2 + 4x + y^2 +8y = 0[/tex]
the average of two number is xy.if one number is x the other i
Answer:
z = (2xy-x)
Step-by-step explanation:
Let the first number be x and the other number is z.
According to question,
The average of two number is xy i.e.
[tex]\dfrac{x+z}{2}=xy\\\\x+z=2xy\\\\z=2xy-x[/tex]
So, the value of z is (2xy-x) i.e. the other number is (2xy-x).
Determine how much simple interest you would earn on the following investment:
$13,400 invested at a 6 1/2% interest rate for 4 years.
Answer: $3,484 (I hope this is the correct way to do it)
Step-by-step explanation:
The formula is: [tex]SI=\frac{PRT}{100}[/tex]
SI = simple interest P = principal amount = $13,400 R = interest rate (in percentage) = [tex]6\frac{1}{2}[/tex]% = 6.5% T = time duration (in years) = 4 years[tex]SI=\frac{13400*6.5*4}{100} =\frac{13400*26}{100} =\frac{348400}{100} =3484[/tex]
If you want to find the total amount, add the principle amount and the interest.
How would I draw the reflection over the line y=2x+5?
Answer:
Step-by-step explanation:
sets A and B have 3 and 6 elements respectively. what can be the minimum number of elements in AUB
Answer:
6
Step-by-step explanation:
n(AUB) = n(A) + n(B) - n(AnB)
n(AUB) can have the minimum number of elements if n(AnB) has the maximum number of elements.
n(AnB) maximum = 3
so n(AUB) = 3+6-3 = 6
PLZ PLZ HELP
Mark is investing $47,000 in an account paying 5.26% interest compounded continuously.
What will Mark's account balance be in 17 years?
O $114,932.80
$114,925.39
$114,921.47
$114.925.46
===============================================
Work Shown:
A = P*e^(r*t)
A = 47000*e^(0.0526*17)
A = 114,932.799077198
A = 114,932.80
Notes:
P = 47,000 is the principal or amount depositedr = 0.0526 is the decimal form of 5.26%The "e" refers to the special constant e = 2.718... which is similar to pi = 3.14... I would let your calculator handle this constant. There should be a button labeled "e".Mark's account balance after 17 years would be $114,932.8
What is the formula for the continuous compounding?[tex]A=Pe^{rt}[/tex]
where,
A = Accrued amount
P = Principal amount
r = interest rate as a decimal
R = interest rate as a percent
r = R/100
t = time in years
For given question,
P = $47000, t = 17 years
R = 5.26%
[tex]\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526[/tex]
Using the Continuous Compounding Formula,
[tex]\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8[/tex]
Therefore, Mark's account balance after 17 years would be $114,932.8
Learn more about the Continuous Compounding here:
https://brainly.com/question/24246899
#SPJ2
In 1980, the median age of the U.S. population was 30.0; in 2000, the median age was 35.3. Consider 1980 as the starting point (time zero) for this problem. Create an explicit exponential formula for the median age of the U.S. population t years after 1980, assuming the median age has exponential growth.
Answer: [tex]30e^{0.00813x}[/tex]
Step-by-step explanation:
Given
Median age in 1980 is [tex]30[/tex]
It is [tex]35.3[/tex] in year 2000
Suppose the median age follows the function [tex]ae^{bx}[/tex]. Consider 1980 as starting year. Write the equation for year 1980
[tex]\Rightarrow 30=ae^{b(0)}\\\Rightarrow 30=a[/tex]
For year 2000
[tex]\Rightarrow 35.3=30e^{20b}\\\\\Rightarrow \dfrac{30e^{20b}}{30}=\dfrac{35.3}{30}\\\\\Rightarrow e^{20b}=1.17666\\\\\Rightarrow b=0.00813[/tex]
After t years of 1980
[tex]\Rightarrow 30e^{0.00813x}[/tex]
Can someone give me the letter to all answers 1-4 or at least one 3
Answer:
hello there here are your answers:
1) a- 12, 18, 24, 30, 36
2) b- 31
3) a-communitive property of addition
4) a- 6a
Step-by-step explanation:
1: go through all the numbers and add 6 like 12+6=16 etc.
2: the common difference is 4 so 27+4 =31
3: communitive property because you can change the number in any order and still get the same sum
4: 6a because only 24ab has a b in it
Can someone help me solve this? Thanks!
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Answer:
p(x) = x³ -3x²+4x -2
Step-by-step explanation:
When the polynomial has real coefficients, the complex roots come in conjugate pairs. You are given one root as 1+i, so there is another that is 1-i.
Each root r gives rise to a factor (x -r). Then the three roots tell you the factorization is ...
p(x) = (x -1)(x -(1+i))(x -(1-i))
The last two factors can be recognized as the factors of the difference of squares:
((x -1) +i)((x -1) -i) = (x -1)² -i²
= (x² -2x +1) -(-1) = x² -2x +2
Now the whole polynomial can be seen to be ...
p(x) = (x -1)(x² -2x +2) = x(x² -2x +2) -1(x² -2x +2)
p(x) = x³ -2x² +2x -x² +2x -2 . . . . eliminate parentheses
p(x) = x³ -3x²+4x -2
(2cosA+1) (2cosA-1)=2cos2A+1 prove that
To prove that: (2cosA+1) (2cosA-1) = 2cos2A+1
We try to solve one side of the equation to get the other side of the equation.
In this case, we'll solve the right hand side (2cos2A + 1) of the equation with the aim of getting the left hand side of the equation (2cosA + 1)(2cosA - 1)
Solving the right hand side: 2cos2A + 1
i. We know that cos2A = cos(A+A) = cosAcosA - sinAsinA
Therefore;
cos2A = cos²A - sin²A
ii. We also know that: cos²A + sin²A = 1
Therefore;
sin²A = 1 - cos²A
iii. Now re-write the right hand side by substituting the value of cos2A as follows;
2cos2A + 1 = 2(cos²A - sin²A) + 1
iv. Expand the result in (iii)
2cos2A + 1 = 2cos²A - 2sin²A + 1
v. Now substitute the value of sin²A in (ii) into the result in (iv)
2cos2A + 1 = 2cos²A - 2(1 - cos²A) + 1
vi. Solve the result in (v)
2cos2A + 1 = 2cos²A - 2 + 2cos²A + 1
2cos2A + 1 = 4cos²A - 2 + 1
2cos2A + 1 = 4cos²A - 1
2cos2A + 1 = (2cosA)² - 1²
vii. Remember that the difference of the square of two numbers is the product of the sum and difference of the two numbers. i.e
a² - b² = (a+b)(a-b)
This means that if we put a = 2cosA and b = 1, the result from (vi) can be re-written as;
2cos2A + 1 = (2cosA)² - 1²
2cos2A + 1 = (2cosA + 1)(2cosA - 1)
Since, we have been able to arrive at the left hand side of the given equation, then we can conclude that;
(2cosA + 1)(2cosA - 1) = 2cos2A + 1
Answer:
[tex]\boxed{\sf LHS = RHS }[/tex]
Step-by-step explanation:
We need to prove that ,
[tex]\sf\implies (2 cosA +1)(2cosA-1) = 2cos2A+1[/tex]
We can start by taking RHS and will try to obtain the LHS . The RHS is ,
[tex]\sf\implies RHS= 2cos2A + 1 [/tex]
We know that , cos2A = 2cos²A - 1 ,
[tex]\sf\implies RHS= 2(2cos^2-1)-1 [/tex]
Simplify the bracket ,
[tex]\sf\implies RHS= 4cos^2A - 2 +1 [/tex]
Add the constants ,
[tex]\sf\implies RHS= 4cos^2-1 [/tex]
Write each term in form of square of a number ,
[tex]\sf\implies RHS= (2cos^2A)^2-1^2 [/tex]
Using (a+b)(a-b) = a² - b² , we have ,
[tex]\sf\implies RHS= (2cosA+1)(2cosA-1) [/tex]
This equals to LHS , therefore ,
[tex]\sf\implies \boxed{\pink{\textsf{\textbf{ RHS= LHS }}}} [/tex]
Hence Proved !
Question 4
Which term in the sequence given by n th term formula 7n - 50 has a value of 41?
th term
Answer:
13th term
Step-by-step explanation:
41 = 7n - 50
41 + 50 = 7n
91 = 7n
7n = 91
n = 91/7
n = 13
13th term has value 41
Answer:
n = 13
Step-by-step explanation:
7n - 50 = 41
Add 50 to both sides
7n = 41 + 50
7n = 91
Divide both sides by 7
n = 91/7
n = 13
