Answer:
(a) The probability that the student made the Dean's list is 0.1655.
(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.
(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.
Step-by-step explanation:
The complete question is:
Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.
a) Find the probability that the student made the Dean's list.
b) Find the probability that the student came from a private high school, given that the student made the Dean's list.
c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.
Solution:
Denote the events as follows:
A = a student attended public high school
B = a student attended private high school
C = a student was home schooled
D = a student made the Dean's list
The provided information is as follows:
P (A) = 0.71
P (B) = 0.21
P (C) = 0.08
P (D|A) = 0.16
P (D|B) = 0.19
P (D|C) = 0.15
(a)
The law of total probability states that:
[tex]P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})[/tex]
Compute the probability that the student made the Dean's list as follows:
[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)[/tex]
[tex]=(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655[/tex]
Thus, the probability that the student made the Dean's list is 0.1655.
(b)
Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:
[tex]P(B|D)=\frac{P(D|B)P(B)}{P(D)}[/tex]
[tex]=\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411[/tex]
Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.
(c)
Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:
[tex]P(C^{c}|D^{c})=1-P(C|D^{c})[/tex]
[tex]=1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185[/tex]
Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.
A number cube is rolled 24 times and lands on the number 2 four times and on the number 6 three times what is the theoretical probability of landing on 6?
Answer:
A: 4 / 24 (or 1/6) B: (24 - 3) / 24 = 21/24 (or 7/8) C and D: Theoretical probability for each number is 1/6 on each roll, and we expect 4 occurrences of each number, on average. 2 came up as expected. 6 came up 3/4 as often as expected. Or "Not-6" came up 21 instead of 20 times, slightly more often than expected.
Step-by-step explanation:
Shiloh has to earn at least $200 to meet her fundraising goal. She has only 100 cakes that she plans to sell at $5 each. Which inequality shows the number of cakes, x, Shiloh can sell to meet her goal?
Answer:d
Step-by-step explanation:I took the test too
A phone company charges for service according to the formula C(n) = 23 + 0.2n, where n is the number of minutes
talked, and c(n) is the monthly charge, in dollars.
Find the rate of change.
Answer:
...........................
What is 24:30 as a decimal
Answer:
.800
Step-by-step explanation:
Answer:
0.8
Step-by-step explanation:
Let's see 24:30 as a fraction first...
24/30
Now let's simplify it,
(24 ÷ 3) / (30÷3)=
8/10
8/10= 0.8
Match each part of this algebraic expression with its appropriate description 12.1x - 4.7y + 6x + 1/6
Answer:Terms, like terms, constant(s),Variable (s),Coefficient(s)
Step-by-step explanation: 18.1x,4.7 and 1/6=Terms
The matched part with the respective appropriate description:
1) x and y → Variable(s)
2) 1/6 → Constant(s)
3) 12.1, 4.7, and 6 → Coefficient(s)
4) 12.1x and 6x → Like Terms
5) 12.1x, 4.7y, and 1/6 → Terms
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
We have the algebraic expression,
12.1x - 4.7y + 6x + 1/6.
From the definition,
x and y are the two variables.
And 12.1, 6 and -4.7 are the numbers in front of the variables.
So, 12.1, 6 and -4.7 are the coefficients.
And 1/6 is the constant.
So, 1) x and y → Variable(s)
2) 1/6 → Constant(s)
3) 12.1, 4.7, and 6 → Coefficient(s)
4) 12.1x and 6x → Like Terms
5) 12.1x, 4.7y, and 1/6 → Terms
Therefore, each part of the algebraic expression matched with its appropriate description.
To learn more about the expression;
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2 - 2x +5 -3x + 3x + 4
Answer:
-2x+11
Step-by-step explanation:
You need to combine like terms, so combine the x terms first.
You would have
-2x-3x+3x=-2x
Then combine the like terms of the normal numbers
2+5+4=11
Answer:
-2x+11
-hope this is what you were looking for:))
Step-by-step explanation:
what is the opposite of 1/2
Answer:
The opposite of 1/2 is -2/1, which can also be written as -2.
-2=k+7/3. solve for k
Answer:
K=-13
Step-by-step explanation:
-2=(k+7)/3
-6=k+7
-13=k
Please answer this correctly without making mistakes
Answer:
50%
Step-by-step explanation:
Answer:
50 present
Step-by-step explanation:
How do you determine what bn should be in a limit comparison test and a comparison test? When do you know that the series should use a limit comparison test or a comparison test to find if it is convergent/divergent? Examples would be greatly appreciated
Step-by-step explanation:
Pick a function that is the same "family". It needs to be a function that you know diverges or converges. So p-series and geometric series are common choices. Often we make the numerators the same so that it's easy to compare.
For example, if you have an = 1 / (n − 1), you would choose bn = 1 / n. Since n − 1 is less than n, we know an is greater than bn. And since we know bn diverges, that means the larger function an also diverges.
Or, if you have an = 1 / (n + 1), we again choose bn = 1 / n. However, comparison test is inconclusive here (an < bn, bn diverges), so we use limit comparison test instead.
lim(n→∞) an / bn
lim(n→∞) 1 / (n + 1) / (1 / n)
lim(n→∞) n / (n + 1)
1
The limit is greater than 0, and bn diverges, so an also diverges.
Let's try something more complicated. Let's say an = e⁻ⁿ / (n + cos²n). The numerator e⁻ⁿ is always less than 1, and the denominator is always greater than n.
If we again choose p-series bn = 1 / n, we know bn > an, and bn diverges, so comparison test is inconclusive. Limit comparison test is possible, but tricky.
But, if we choose geometric series bn = e⁻ⁿ / 1, we know bn > an, and bn converges, so by comparison test, an converges as well.
We can try one more: an = (n² + 2) / (n⁴ + 5). Let's choose bn = (n² + 2) / n⁴ = 1 / n² + 2 / n⁴.
The numerators are the same, but an has a larger denominator, so bn > an. bn is the sum of two p-series which converge, so bn converges. Therefore, an converges.
Write the equation of the line graphed below.
Answer:
In y intercept form, the equation would be: Y= -1/3x -6
Step-by-step explanation:
In order to find the equation, you can use any points given. In this case, I used (-6,-4) and (-3,-5).
With these points, you must find the slope. The change in our y values is -1 and the change in our x values is +3.
Now we have Y= -1/3x
To find the y intercept, you look on the graph for where there's a point that is lying on y line. In this case (0,-6) is lying on the y line. This means that the Y intercept for our equation is -6. Another example is (0,8), our y intercept would be 8 because the x value is 0!
In conclusion, our equation in y intercept form would be Y= -1/3x-6
Hope this helps!! :)
What is the scale factor from polygon ABCD to polygon PQRS??
Answer:
We need the grid to figure this out
50 apples cost $25.how much would 75 apples cost
Answer:
150
Step-by-step explanation: one apple cost $0.50, so 75/ $0.50= 150
Is the given function exponential function?
3x2 - 4x + 7 = 0 Yes or No? How do you know?
Answer: no
Step-by-step explanation:
because you can do what is known as the vertical line test to determine if it is a function you do that by plotting it and if it goes in a vertical line then it is a function
0.1 is 1/10 as much as
Answer:
10%
Step-by-step explanation:
Because 0.1 is equivalent to 1/10 and 10%
Please help
For the sequence 12,8,4...
write the explicit rule..
Find the 100th term...
Is this a function or relation? Why?
Answer: ion evn kno cuh
Step-by-step explanation:
Answer:
This is arithmetic sequence and the common difference is equal to -4.
Step-by-step explanation:
If yuh just want the answer here, not explained
Which equation has exactly one solution?
A. 4x – 4 + 2x = 6x - 4
B. 3x + 5 = 2x - 6
C. 2(4x + 5) = 8x + 10
D. 4x - 8 = 4(x - 4)
Answer:
its B
Step-by-step explanation:
I calaulated all the numbers
Mary Jo takes her son to get a haircut at the barbershop. The total cost of the haircut is $12.60, including a 20% tip. How much was the haircut before the tip?
Based on the total cost of the haircut with the tip included, the cost of the haircut before the tip was $10.50
How to find the cost of the haircut?The cost of the haircut give of $12.60 is merely the cost of the haircut including the 20% tip.
To find the cost of the haircut before the tip was included, assume that it is x. The relevant expression would then be:
Total cost including tip = x × (1 + tip percentage)
Solving for the haircut cost before the tip gives:
12.60 = x ( 1 + 20%)
12.60 = 1.20x
x = 12.60 / 1.20
x = $10.50
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which is the first step in simplifying the expresion 2(x+3)+5?
Answer:
[tex]2x + 11[/tex]
Step-by-step explanation:
1) Expand by distributing terms.
[tex]2x + 6 + 5[/tex]
2) Collect like terms.
[tex]2x + (6 + 5)[/tex]
3) Simplify.
[tex]2x + 11[/tex]
The first step to do this equation is to expand.which means to solve whats inside the parentheses first. If you expand you'll get a answer of 2x + 11.
Which model is 85% Shaded
Answer:
cant tell
Step-by-step explanation:
need more explanation
Solve.
(5a^2 + 3) (4a^2 + 3)
Answer:
I think its a... carrot
Answer:
204+272+9
Step-by-step explanation:
Sedato Company follows the practice of pricing its inventory at the lower-of-cost-or-market, on an individual-item basis.
Item No. Quantity Cost per Unit Cost to Replace Estimated Selling Price Cost of Completion and Disposal Normal Profit
1320 1,200 $3.20 $3.00 $4.50 $0.35 $1.25 1333 900 2.70 2.30 3.50 0.50 0.50
1426 800 4.50 3.70 5.00 0.40 1.00
1437 1,000 3.60 3.10 3.20 0.25 0.90
1510 700 2.25 2.00 3.25 0.80 0.60
1522 500 3.00 2.70 3.80 0.40 0.50
1573 3,000 1.80 1.60 2.50 0.75 0.50
1626 1,000 4.70 5.20 6.00 0.50 1.00
From the information above, determine the amount of Sedato Company inventory.
Answer:
$24,110
Step-by-step explanation:
From the given information, we have:
Item No. Quantity Cost per Unit Cost to Replace Estimated Selling Price
1320 1,200 $3.20 $3.00 $4.50
1333 900 2.70 2.30 3.50
1426 800 4.50 3.70 5.00
1437 1,000 3.60 3.10 3.20
1510 700 2.25 2.00 3.25
1522 500 3.00 2.70 3.80
1573 3,000 1.80 1.60 2.50
1626 1,000 4.70 5.20 6.00
Cost of Completion and Disposal Normal Profit Final Inventory
$0.35 $1.25 $3600
0.50 0.50 $2,250
0.40 1.00 $2960
0.25 0.90 $2950
0.80 0.60 $1400
0.40 0.50 $1450
0.75 0.50 $4800
0.50 1.00 $4700
$24,110
To determine the amount of Inventory, we multiply the designated market value with the quantity, then sum all the results up but in the last part,we use the cost per unit instead becuase it is lower than the designated market value.
Find the quotient in SIMPLEST form. 2/5 ÷ 5/8 =
A: 10/40
B: 1/4
C: 16/25
D: 4/5
Answer:
c. 16/25
Step-by-step explanation:
divide
Pls help
I have this question and I can’t figure it out
Start by crossing out absurd answers, it helps a lot. Then you're left with two and choose the correct answer by doing the math
Step-by-step explanation:
cross the ones that you think are not right
what is the model of 1/4 divided by 3
Answer:
bust a uhhh
Step-by-step explanation:
ya dig
A floor is made up of 20 triangular tiles, each with sides 40 cm, 24 cm and 32 cm. Find the cost of polishing the floor at the rate of 2 rupees per sq.cm.
Answer:
[tex]15360\,\,rupees[/tex]
Step-by-step explanation:
Let sides of the triangle be [tex]a,b,c[/tex]
[tex]a=40\,,\,b=24\,,\,c=32[/tex]
Semi-perimeter (s) = [tex]\frac{a+b+c}{2}[/tex]
[tex]=\frac{40+24+32}{2}\\ =\frac{96}{2}\\=48[/tex]
Area of one tile [tex]=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]=\sqrt{48(48-40)(48-24)(48-32)}\\ =\sqrt{48(8)(24)(16)}\\ =\sqrt{147456} \\=384\,\,cm^2[/tex]
So,
Area of 20 tiles [tex]=20(384)=7680\,\,cm^2[/tex]
Cost of polishing the floor at the rate of 2 rupees per sq.cm = [tex]7680(2)=15360\,\,rupees[/tex]
Kevin has 3 fewer leaves than sandy. Sandy has 3 leaves. How many leaves does Kevin have?
Answer:
0 leaves
Step-by-step explanation:
Answer:
tiene 0
Step-by-step explanation:
0 hojas
10. You just received your first job. Your starting salary is $750
weekly. Calculate your monthly and annual salary.
Answer:
3000 weekly
39000 annually
Step-by-step explanation:
Answer:
39,000 dollars
Multiply 5 1/2 x 1 2/5
Step-by-step explanation:
[tex]5 \frac{1}{2} \times 1 \frac{2}{5} \\ \\ \frac{11}{2} \times \frac{7}{5} \\ \\ \frac{77}{10 } = 7.7[/tex]
3x square - 6x + 3=0
Answer: 1
Step-by-step explanation:
First you need to multiply 3 x 3 (9), because that's all 3 squared means.
Now the equation should be 9x-6x+3=0
Next we need to combine like terms. Do 9x - 6x which should give you 3x
Now your equations should be 3x+3=0
Now for the somewhat harder part...
Under the three (the one without the x) write -3 and under the zero write the same thing. the +3-3 cancels out so just put a line or something across it.
0-3= -3
so now you should have...
3x=-3 ignore the 3x, at this point it's useless in getting the answer because it would cancel out.
-3 divided by -3 is 1 because a negative (-) divided by a negative (-) equals a positive (+).
The answer should be x = 1