Answer:
(A) The correct option is (A).
(B) The correct option is (E).
Step-by-step explanation:
The events can be defined as follows:
X = students felt they learned better at home
Y = students plan on taking an online course in college
The information provided is:
P (X) = 0.24
P (Y|X) = 0.80
P (Y|X') = 0.40
[tex]P(Y'|X)=1-P(Y|X)\\=1-0.80\\=0.20[/tex]
[tex]P(Y'|X')=1-P(Y|X')\\=1-0.40\\=0.60[/tex]
The Bayes' theorem states that the conditional probability of an event E[tex]_{i}[/tex] given that another event A has already occurred is:
[tex]P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum {P(A|E_{i})P(E_{i})}}[/tex]
(A)
Compute the probability a person who does not plan on taking an online course felt they learned better at home as follows:
Use the Bayes' theorem.
[tex]P(X|Y')=\frac{P(Y'|X)P(X)}{P(Y'|X)P(X)+P(Y'|X')P(X')}[/tex]
[tex]=\frac{0.20\times 0.24}{(0.20\times 0.24)+(0.60\times 0.76)}\\\\=0.09524\\\\\approx 0.095[/tex]
Thus, the probability a person who does not plan on taking an online course felt they learned better at home is 0.095 or 2/21.
(B)
Compute the probability a person who does plan on taking an online course felt they did not learn better at home as follows:
[tex]P(X'|Y')=1-P(X|Y')\\=1-0.095\\=0.905[/tex]
Thus, the probability a person who does plan on taking an online course felt they did not learn better at home is 0.905.
You bought a magazine for $3 and two notepads. You spent a total of $13. How much did each notepad cost? *
Answer:
$5
Step-by-step explanation:
We want to find the cost of a notepad considering a magazine costs $3 and we buy 2 notepads and the total cost of the magazine and the 2 notepads is $13 so we can set up an equation to represent this situation. Let 'n' be notepads and that's the value we are solving for so,
⇒ Form the equation
→ 2n + 3 = 13
⇒ Minus 3 from both sides to isolate 2n
→ 2n = 10
⇒ Divide both sides by 2 to find the cost of one notepad
→ n = 5
The cost of one notepad is $5 considering that a magazine cost's $3 and two notepads and total is $13.
What is the value for f(x) = 32x+1 when x = 1/2
Answer:
9
Step-by-step explanation:
We can solve this by plugging x into the function:
3^(2(1/2) + 1)
=3^(1+1)
=3^2
= 9
Answer: The answer would be 9
Step-by-step explanation:
could i please get brainliest
Evaluate: 14/2 - 3 + 6/3
Answer:
Brainliest!!!
Step-by-step explanation:
see picture
Answer:
[tex]6[/tex]
[tex] \frac{14}{2?} - 3 + \frac{6}{3 ?} \\ 7 - 3 + \frac{6}{?3 } = 6 \\ 4 + \frac{6}{?3} = 6 \\ 4 + 2 = 6[/tex]
4.7 - 2.3 = 4.7 + (-2.3) =
Answer:
2.4
General Formulas and Concepts:
Math
Base 10 Decimal SystemPre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
4.7 - 2.3
Step 2: Evaluate
Subtract
2.4
Answer:
2.4
Step-by-step explanation:
The hypotenuse, c, of right triangle ABC is 5.0 cm long. Give the trigonometry ratio cosA=0.50 for angle A, what is the area of the triangle to the nearest tenth of a cm?
Answer:
[tex]\frac{25\sqrt{3} }{8}[/tex]
Step-by-step explanation:
CosA = [tex]\frac{1}{2}[/tex] , so <A is 60º
Hypotenuse (c) is 5
Opposite is (b)
Adjascent is (a)
cos A = [tex]\frac{adjascent}{hypotenuse}[/tex] -----> [tex]\frac{1}{2} = \frac{a}{5}[/tex] ---------> a = [tex]\frac{5}{2}[/tex]
Pytagoras
[tex]5^{2} = (\frac{5}{2}) ^{2} + b^{2}\\ b^{2} = 25 - \frac{25}{4} \\b^{2} = \frac{75}{4} \\\\b = \frac{5\sqrt{3} }{2}[/tex]
A = b . a . 1/2
A = [tex]\frac{25\sqrt{3} }{8}[/tex]
CosA = , so <A is 60º
Hypotenuse (c) is 5
Opposite is (b)
Adjascent is (a)
cos A = -----> ---------> a =
Pytagoras
A = b . a . 1/2
A =
Step-by-step explanation:
plz help me how would you solve 4x + 2y = 18, 3x - 5y =20 by elemination
Answer: x = 5, y = -1
Step-by-step explanation:
Equation 1: 4x + 2y = 18
Equation 2: 3x - 5y = 20
In order to eliminate one of the variables , find the LCM of either x or y.
I chose to eliminate y. The LCM of 2 & 5 is 10.
Multiply the entire equation so the coefficient of the variable equals the LCM.
Then add the equations and solve for the remaining variable.
5(4x + 2y = 18) --> 20x + 10y = 90
2(3x - 5y = 20) --> 6x - 10y = 40
26x = 130
÷26 ÷26
x = 5
Next, input x = 5 into either of the equations to solve for y.
Equation 1: 4x + 2y = 18
4(5) + 2y = 18
20 + 2y = 18
-20 -20
2y = -2
÷2 ÷2
y = -1
Help I don't understand it.
Answer:
6/15 * 2/14 = 12/210
Step-by-step explanation:
This is compound probability. To calculate compound probability, you need to multiply the probabilities of each event happening together.
In this example, the events are selecting a pineapple cake, then a strawberry cake.
Let's find the probabilities!
There are 2 strawberry cakes, 6 pineapple cakes, and 7 chocolate cakes. This means that he has 15 cakes in total.
Therefore, the probability of selecting a pineapple cake is 6/15.
Now, if we assume that he has selected a pineapple cake already, there are now 14 cakes.
Next, the probability of selecting a strawberry cake is now 2/14. This is because he already took a pineapple cake, and now he has to pick a strawberry cake out of the remaining 14 cakes.
Multiply these two probabilities to find the compound probability: 12/210 ( this could be further simplified, but that's how they give it to you! )
Hope this helps! Please feel free to contact me if you have any further questions :)
10x+9=4x -9 solve
please help
Answer:
x = -3
Step-by-step explanation:
To solve this, you need to isolate the variable x, this means only one side of the equation should have the variable x. To do this, you need to do the opposite operation from what's given (if it's addition, use subraction; if it's multiplication, use division; these work vise versa)
Subtract 9 from both sides of the equation. This gives you 10x = 4x - 18.Subtract 4x from both sides of the equation. This gives you 6x = -18.Divide both sides by 6. This gives you x = -3The final answer is x = -3
find the derivatives of the following implicit function
Answer:
[tex]\frac{d}{dx}\left(y\right)=\frac{2-6x+6y}{-6x+2y+1}[/tex]
Step-by-step explanation:
[tex]3x^2-6xy+y^2=2x-y\\\mathrm{Treat\:}y\mathrm{\:as\:}y\left(x\right)\\\mathrm{Differentiate\:both\:sides\:of\:the\:equation\:with\:respect\:to\:}x\\\frac{d}{dx}\left(3x^2-6xy+y^2\right)=\frac{d}{dx}\left(2x-y\right)\\\frac{d}{dx}\left(3x^2-6xy+y^2\right)=6x-6\left(y+x\frac{d}{dx}\left(y\right)\right)+2y\frac{d}{dx}\left(y\right)\\\frac{d}{dx}\left(2x-y\right)=2-\frac{d}{dx}\left(y\right)\\6x-6\left(y+x\frac{d}{dx}\left(y\right)\right)+2y\frac{d}{dx}\left(y\right)=2-\frac{d}{dx}\left(y\right)[/tex]
[tex]\mathrm{For\:convenience,\:write\:}\frac{d}{dx}\left(y\right)\mathrm{\:as\:}y^{'\:}\\6x-6\left(y+xy^{'\:}\right)+2yy^{'\:}=2-y^{'\:}\\\mathrm{Isolate}\:y^{'\:}:\quad y^{'\:}=\frac{2-6x+6y}{-6x+2y+1}\\y^{'\:}=\frac{2-6x+6y}{-6x+2y+1}\\\mathrm{Write}\:y^{'\:}\:\mathrm{as}\:\frac{d}{dx}\left(y\right)\\\frac{d}{dx}\left(y\right)=\frac{2-6x+6y}{-6x+2y+1}[/tex]
URGENT: At what annual rate of simple interest must $12,000 be invested to earn $135 in interest each quarter? (I will give brainliest)
Answer:
4.5%
Step-by-step explanation:
Firstly we should understand that a quarter is every three months.
So if $135 is earned each quarter, then 4 * 135 = $540 is earned per annnum
We use the simple interest formula to get the rate.
Mathematically;
I = PRT/100
where P is the amount deposited = 12,000
R is what we are looking for which is the rate
T is the time which is 1 year
I is the interest which is 540
We can rewrite the simple interest formula to be:
100I = PRT
R = 100I/PT
Thus substituting the values we have;
R = (100 * 540)/(12,000 * 1) = 4.5%
Answer:
4.5%Step-by-step explanation:
Using the simple interest formula to tackle this question.
[tex]SI = \frac{PRT}{100}[/tex]
P = principal = $12,000
R = rate (in %) = ?
T = Time(in years) = 1/4 years
135 = [tex]\frac{12000*R}{100*4}[/tex]
[tex]135 = \frac{12000R}{400}\\ 54000 = 12000R\\R = \frac{54000}{12000}\\ R = 4.5\ %[/tex]
The annual rate of simple interest is 4.5%
Determine the value of x in this polygon.
Answer:
X24
Step-by-step explanation:
Helpppppppp here plz
Answer:
x + x+12 + 3(x+12) = 123
x = 15
Step-by-step explanation:
Jamil : x
Kiera : x+12
Luther : 3 ( x+12)
x + x+12 + 3(x+12) = 123
Distribute
x + x+12 + 3x+36 = 123
Combine like terms
5x+ 48 = 123
Subtract 48 from each side
5x+48-48 = 123-48
5x =75
Divide by 5
5x/5 = 75/5
x = 15
Answer:
Equation:
123 = x + 12 + x + 3(12 + x)
Solution:
x = 15
Step-by-step explanation:
Jamil: x
Kiera: 12 + x
Luther: 3(12 + x)
Total: 123 badges
Equation:
123 = x + 12 + x + 3(12 + x)
Solve:
123 = x + 12 + x + 3(12 + x)
123 = x + 12 + x + 36 + 3x
123 = 5x + 48
-48 -48
75 = 5x
/5 /5
15 = x
Therefore, the value of x is 15.
The Arc de Triomphe measures 50 m in height. You are asked to make a replica model in art class using a scale of 1:275. What should the height of your model be in millimeters?
Answer:
180 millimeters.
Step-by-step explanation:
To find the height of the replica, a ratio can be set up:
[tex]\frac{x}{50}= \frac{1}{275}[/tex]
Cross multiply:
[tex]275x = 50[/tex]
Divide both sides by '275:
x≈0.18 meters
Convert 'meters' to 'millimeters' by multiplying by a thousand:
0.18 × 1000 = 180 millimeters.
Write an expression for the situation described. Each person's share if 'p' people share 8 slices of pizza equally.
Answer:
The expression that represent each person's share is: [tex]y(p) = \frac{8}{p}[/tex]
Step-by-step explanation:
To divide a pizza, or anything else, equally among a certain number of people, we need to divide the total of pizza available by the number of people who will eat the pizza. In this case there are 8 slices and 'p' people, therefore:
[tex]y(p) = \frac{8}{p}[/tex]
In order to validate the expression, we can see that if 8 people eat the pizza, each gets one slice, because 8 divided by 8 is 1, while if 4 people eat the pizza each get 2 and so on.
The expression that represent each person's share is: [tex]y(p) = \frac{8}{p}[/tex]
Which is true about the degree of the sum and difference of the polynomials
3x^5y - 2x^3y^4 - 7xy^3 and -8x^5y + 2x^3y^4 + xy^3 ?
Answers:
Both the sum and difference have a degree of 6
Both the sum and difference have a degree of 7
The sum has a degree of 6, but the difference has a degree of 7
The sum has a degree of 7, but the difference has a degree of 6
Answere is C
The sum has a degree of 6 but the difference haa a degree of 7
The true statement about the degree of the sum and difference of the polynomials 3x⁵y - 2x³y⁴-7xy³ and -8x⁵y +2x³y⁴ + xy³ is "the sum has a degree of 6, but the difference has a degree of 7."
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
There are two polynomials,
3x⁵y - 2x³y⁴-7xy³ and -8x⁵y +2x³y⁴ + xy³.
The sum of the polynomials,
= 3x⁵y - 2x³y⁴-7xy³ -8x⁵y +2x³y⁴ + xy³.
= 5x⁵y -6xy³.
And the degree is 6.
The difference of the polynomials,
= 3x⁵y - 2x³y⁴-7xy³ + 8x⁵y - 2x³y⁴ - xy³.
= 13x⁵y - 4x³y⁴-8xy³.
And the degree is 7.
Therefore, the sum has a degree of 6, but the difference has a degree of 7.
To learn more about the Polynomials;
brainly.com/question/11536910
#SPJ2
50 POINTS!
You have $10,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank's CDs have an 8% return, and the high‐risk account has an expected (hoped‐for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high‐risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year‐end yields are as expected, what are the optimal investment amounts?
Answer:
Optimal investment amount = $300
Step-by-step explanation:
discount = x
original price = 10,000
discount% = 7%
x/10,000 = 7/100
x · 100 = 7 · 10,000
100x = 70,000
100x/100 = 70,000/100
x = 700
discount = x
original price = 10,000
discount% = 8%
x/10,000 = 8/100
x · 100 = 8 · 10,000
100x = 80,000
100x/100 = 80,000/100
x = 800
discount = x
original price = 10,000
discount% = 12%
x/10,000 = 12/100
x · 100 = 12 · 10,000
100x = 120,000
100x/100 = 120,000/100
x = 1,200
So:
$1,200 - $800 - $700 = $300
We max out the high return investment, $2000 for 12%.
We have $8000 left to invest and we want to put as much in CDs at 8% as possible. Let's call b the bond investment and c the CD investment. We have
b ≥ 3c
Since munis have the lower return we want as many CDs as possible. So we choose:
b = 3c
b + c = 8000
3c + c = 8000
4c = 8000
c = 2000
That leaves b=3c=6000 for bonds.
Answer: $6000 in bonds, $2000 in CDs, $2000 in high-risk.
How is the graph of log (x – 2) + 1 translated from the graph of log x?
Answer:
See the two translations described below
Step-by-step explanation:
Start with the graph of y = log x. This graph passes through (1, 0) and exists only for x > 0. The line x = 0 is its vertical asymptote.
Translating this graph 2 units to the right results in h(x) = log (x - 2).
Translating the graph of h(x) = log (x - 2) upward by 1 unit results in the graph of log (x – 2) + 1.
What are the foci of the hyperbola represented by the equation (x^2)/64 - (y^2)/32 =1
Answer:
x = √2y^2 + 64 or x = √2y^2 + 64
Step-by-step explanation:
Solve for x.
x^2/64 - y^2/32 = 1
Step 1: Add 1/32 y^2 to both sides.
1/64 x^2 + -1/32 y^2 + 1/32 y^2 = 1 + 1/32 y^2
Step 2: Divide both sides by 1/64.
1/64 x^2/ 1/64 = 1/32 y^2 + 1/ 1/64
x^2 = 2y^2 + 64
Step 3:
x = √2y^2 + 64 or x = √2y^2 + 64
Answer:
x = √2y^2 + 64
Step-by-step explanation:
= 1/64 x^2 + -1/32 y^2 + 1/32 y^2 = 1 + 1/32 y^2
= 1/64 x^2/ 1/64 = 1/32 y^2 + 1/ 1/64
= x^2 = 2y^2 + 64
= x = √2y^2 + 64
Hope this helps!
Which expression is equivalent to (- 2c / d^2)^3
-8c^3/d^6 is equivalent to the expression
Answer:
-8c^3/d^6
You are correct!
What is the sum of the greatest and least numbers below: \[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\]
Answer:
[tex]\dfrac{47}{42} \ \ \ \ \ OR \ \ \ \ 1.1[/tex]
Step-by-step explanation:
The objective of this question is to find the sum of the greatest and least numbers below:
[tex]\[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\][/tex]
To do this ; we will need to find the decimal component of each of them and equate them on a number line before summing the greatest and least numbers.
[tex]8 \frac{1}{5} = \dfrac{8*5+1}{5} \\ \\ = \dfrac{41}{5} \\ \\ = 8.2[/tex]
[tex]-8 \frac{2}{5} =- \dfrac{8*5+2}{5} \\ \\ =- \dfrac{42}{5} \\ \\ = -8.4[/tex]
[tex]-\dfrac{26}{3}= - 8.7[/tex]
[tex]-\dfrac{54}{7} = - 7.7[/tex]
[tex]\dfrac{53}{6}= 8.8[/tex]
Thus; the above decimal component of the fractions given are :
8.2, -8.4, -8.7 , -7.7 and 8.8
We are to find the sum of the greatest and the smallest number ; on a number line; we will realize that the positive side is greater than the negative side , As such the greatest number from the positive side will be 8.8 and the smallest number will be -7.7
The sum of 8.8 + ( -7.7 ) = 8.8 - 7.7
= 1.1
i.e
[tex]\dfrac{53}{6} + (- \dfrac{54}{7} )[/tex]
[tex]\dfrac{53}{6} - \dfrac{54}{7}[/tex]
[tex]\dfrac{53}{6} - \dfrac{54}{7} = \dfrac{53*7 - 6*54}{42} \\ \\ = \dfrac{47}{42} \\ \\ = 1.1[/tex]
Answer:
47/42Step-by-step explanation:
slope (-5,12)(-17,4)
So the right answer is 4/11
please see attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex] = \frac{2}{3} [/tex]
Step-by-step explanation:
[tex]slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{12 - 4}{ - 5 - ( - 17)} \\ = \frac{8}{ - 5 + 17} \\ = \frac{8}{12} \\ = \frac{2}{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
evaluate -5+(-5r)+10
Solve and graph. Thank you so much.
Answer:
Step-by-step explanation:
-9 + b/4 >= -4
b/4 >= 5
b >= 20
the solution is d
PLEASE HELP!! if sec x=5/3 what is the value of b? NL=20 LM=3b angle of L is x degrees.
a. b=4
b. b=5
c. b=6
d. b=7
Answer:
a. b=4
Step-by-step explanation:
[tex]\sec \theta =\dfrac{1}{\cos \theta} = \dfrac{Hypotenuse}{Adjacent}[/tex]
From the attached triangle drawn below:
NL=20, LM=3b, [tex]\angle L=x^\circ[/tex]
[tex]\sec x =\dfrac{20}{3b}[/tex]
Since we are told that:
[tex]\sec x =\dfrac{5}{3}\\$Then:\\\dfrac{20}{3b} =\dfrac{5}{3}\\$Cross multiply\\5 \times 3b =20 \times 3\\15b=60\\$Divide both sides by 15\\15b \div 15 =60 \div 15\\b=4[/tex]
The correct option is A.
Answer:
B= 4
Step-by-step explanation:
I got it right on the test
HELP. ITS ABOUT FUNCTIONS! HELPPPPPPPPPPPPPP HELPPPPPPP
Answer:
B
Step-by-step explanation:
It cannot be C. The Y-intercept of Function W is 30, while the Y-intercept of Function Z is 15.8. Now, we are left with A, B, and D.
It cannot be D, because 30 is not less than 15.8. Now, we are left with options A and B.
Function Z as an equation is approximately y=-1/24x+15.8.
The slopes are NOT equal, so the answer cannot be A.
Explanation why it's B:
1/16 is bigger than 1/24, however, since the fractions are NEGATIVE, -1/16 is actually LESS THAN -1/24. The slopes of Function W is less than the slope of Function Z.
Answer:
B. the slope of function W is less than he slope of function Z
Step-by-step explanation:
Function W:
y= - 1/16x+30Function Z:
from the table we can see it is decreasing function with step change of -0.04
using the data from the table we can put the function in y= mx + b format:
x=0 ⇒ y= 15.8 ----- interceptx=1 ⇒ y= 15.7615.76- 15.8 = - 0.04= - 4/100 = -1/25 ----- slopeas per above, we get the the form of function Z
y= -1/25x+15.8we can now compare the slops and intercepts of functions W and Z
m - is the slope: -1/16 and - 1/25
-1/25>-1/16 ⇒ the slope of function W is less than Zb is the y-intercept: 30 and 15.8
30>15.8 ⇒ the y-intercept of function Z is lessAs per above the correct option is
B. the slope of function W is less than he slope of function ZRename 1 3/4 as an improper fraction.
Answer:
7/4
Step-by-step explanation:
1 3/4=1 x 4=4 + 3=7/4
Which function has a negative discriminant value?
Answer:
i believe that the answer is a but if its not that then it must be d
Step-by-step explanation:
sorry if i'm wrong
Answer:
The guy above me is wrong. The answer is B
Step-by-step explanation:
edge
Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
- 18y = 1
Step-by-step explanation:
Adding the 2 equations term by term on both sides gives
(- 5x + 5x) + (- 9y - 9y) = (3 - 2), that is
0 + (- 18y) = 1
- 18y = 1
Solve The System Of Equations
Answer:
x=4, y=-7
Step-by-step explanation:
A) -8x - 3y = -11 .(-5) -----> A) 40x + 15y = 55
B) -7x - 5y = 7 . (3) ------> B) -21x -15y = 21
A) + B) ----> 19x = 76 --------> x = 4
-8 . 4 - 3y = -11
-32 - 3y = -11
32 + 3y = 11
3y = 11 - 32
3y = -21
y = -7
150 miles converted to kilometres?
Answer:
erm
Step-by-step explanation:
241.402