Answer: Option 'B' is correct.
Step-by-step explanation:
since we have given that
Group radii of fertilized tomatoes is given by
[tex]0.8, 1.1, 0.9, 0.8, 1.0, 1.2, 0.9, 1.1, 1.0, 1.2[/tex]
Group radii of unfertilized tomatoes is given by
[tex]1.4, 1.6, 1.3, 1.5, 1.1, 1.5, 1.6, 1.2[/tex]
So, we will first find the mean of both the group i.e.
Mean radii of fertilized tomatoes is given by
[tex]=\frac{0.8+1.1+0.9+0.8+1.0+1.2+0.9+1.1+1.0+1.2}{10}\\\\=1[/tex]
Similarly,
Mean radii of unfertilized tomatoes is given by
[tex]\frac{1.4+1.6+1.3+1.5+1.1+1.5+1.6+1.2}{8}\\\\=\frac{11.2}{8}\\\\=1.4[/tex]
So, the difference between the mean radii of fertilized and unfertilized tomatoes will be
[tex]1.4-1=0.4\ cm[/tex]
Hence, Option 'B' is correct.
check my answer?
what are the real and imaginary parts of the complex number?
-7+8i
the real part :: -7 ( my answer )
the imaginary part :: 8i ( my answer )
Answer:
The real part is -7
The imaginary part 8i
Step-by-step explanation:
A complex number is in the from a +bi
The real part is a and the imaginary part is bi
-7+8i
The real part is -7
The imaginary part 8i
What is the value of x?
5
6
2
-2
Answer:
x= -2
Step-by-step explanation:
The distance from one end of the line to the other is -3x-1.
Counting on the number line we count 6 units. Setting them equal we get
-3x-1 = 5
Add 1 to each side
-3x-1+1 = 5+1
-3x = 6
Divide each side by -3
-3x/-3 = 6/-3
x = -2
What is the value of A in the matrix equation below?
Answer:
Option (b) is correct.
The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]
Step-by-step explanation:
Given : A matrix form,
[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]
we have to find the value of matrix A
Consider the given matrix form,
[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]
when A + B = C
Then A = C - B
That is
[tex]A=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}-\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}[/tex]
Subtract the elements in the matching position, we get,
[tex]A=\begin{pmatrix}0-3&\left(-5\right)-9&6-\left(-1\right)&10-\left(-8\right)\\ 3-16&0-\left(-2\right)&\left(-2\right)-3&7-13\end{pmatrix}[/tex]
Simplify, we get,
[tex]A=\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]
Thus, The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]
Complex Roots #4 Problem
1. What is the value of x? Show your work to justify your answer.
2. What is the value of the exterior angle? Show your work to justify your answer.
Answer:
see explanation
Step-by-step explanation:
the exterior angle of a triangle equals the sum of the 2 opposite interior angles, that is
2x + 4 = x + 60 ( subtract x from both sides )
x + 4 = 60 ( subtract 4 from both sides )
x = 56
exterior angle = 2x + 4 = (2 × 56) + 4 = 112 + 4 = 116°
Write the equation of a line that is perpendicular to the given line and that passes through the given point. y-3=-1/5(x+2); (-2, 7)
A. y=5x+7
B. y=5x+17
C. y=(1/5)x-2
D. y=-2x+3
Plz answer quickly!! Thank you :) <3
To find the equation of a line perpendicular to a given line, find the negative reciprocal of the slope and use the point-slope form of a line.
Explanation:To find the equation of a line that is perpendicular to the given line and passes through the given point, we first need to determine the slope of the given line. The given line has a slope of -1/5, which is the negative reciprocal of the slope we want for the perpendicular line. The negative reciprocal of -1/5 is 5/1 or 5. Now we have the slope of the perpendicular line and a point it passes through (-2, 7), we can use the point-slope form of a line to find the equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the values, we get: y - 7 = 5(x - (-2))
y - 7 = 5(x + 2)
y - 7 = 5x + 10
y = 5x + 10 + 7
y = 5x + 17
Therefore, the equation of the line that is perpendicular to the given line and passes through the given point (-2, 7) is y = 5x + 17. Option B is the correct answer.
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The correct answer is B. y=5x+17.
To write the equation of a line that is perpendicular to the given line y-3=-1/5(x+2) and that passes through the point (-2, 7), first, we need to find the slope of the given line and then determine the slope of the perpendicular line, which will be the negative reciprocal of the given line's slope. The slope of the given line is -1/5, so the slope of the line perpendicular to it will be 5 (since the negative reciprocal of -1/5 is 5).
Next, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Plugging in our slope of 5 and the point (-2, 7), the equation becomes:
y - 7 = 5(x - (-2))
Expand and simplify to solve for y:
y - 7 = 5x + 10
y = 5x + 17
The correct answer is B. y=5x+17.
Based on the polynomial remainder theorem, what is the value of the function when x=-5
f(x)=x^4+9x^3+17x^2-8x+50
Answer: 15
Step-by-step explanation:
Using synthetic division:
-5 | 1 9 17 -8 50
| ↓ -5 -20 15 -35
1 4 -3 7 15 ← this is the remainder
Check:
f(x) = x⁴ + 9x³ + 17x² - 8x + 50
f(-5) = (-5)⁴ + 9(-5)³ + 17(-5)² - 8(-5) + 50
= 625 - 1125 + 425 + 40 + 50
= 15
Points A and B on the coordinate grid below show the positions of two midfield players of a soccer team: Coordinate grid shown from negative 4 to positive 4 on x-axis and negative 4 to positive 4 on y-axis. From the origin, point A is located 1 unit to the left and 3.5 units down. From the origin, point B is located 1 unit to the right and 3.5 units down. Which statement best describes the relationship between the positions of the two midfield players? B is A reflected across the y-axis; only the signs of the x-coordinates of A and B are different. B is A reflected across the y-axis; only the signs of the y-coordinates of A and B are different. B is A reflected across the x-axis; only the signs of the x-coordinates of A and B are different. B is A reflected across the x-axis; only the signs of the y-coordinates of A and B are different.
Answer:
Point B is Point A reflected across the y-axis.
Step-by-step explanation:
Answer:
B is A reflected across the y-axis; only the signs of the x-coordinates of A and B are different.
Step-by-step explanation:
When a point is reflected across the y-axis, the x-coordinate of the point is negated. Algebraically,
(x, y)→(-x, y)
Point A is located at (-1, -3.5) and point B is located at (1, -3.5). The only difference between the two points is that the x-coordinate is negated; this means it is a reflection through the y-axis.
Write an explicit formula for the sequence 2,-3,-8,-13,-18 then fin the 13th term
The given sequence is an arithmetic sequence with a common difference of -5. The explicit formula for the sequence is A_n = 2 + (n-1)*-5. Using this formula, the 13th term of the sequence is -58.
Explanation:The given sequence is 2, -3, -8, -13, -18. We find that the common difference of the sequence is -5 because each term subtracts 5 from the previous term. This is an arithmetic sequence. The explicit formula for an arithmetic sequence is given by A_n = A_1 + (n-1)*d where A_n is the nth term, A_1 is the first term, d is the common difference and n is the position in the sequence. So in this case, our formula becomes A_n = 2 + (n-1)*-5.
Now let's find the 13th term in the sequence. Substituting n=13 into the formula we get: A_13 = 2 + (13-1)*-5 = 2 - 60 = -58. Therefore, the 13th term of the sequence is -58.
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Math help!
What is the value of a?
Answer:
a = 8
Step-by-step explanation:
Put the given information into the function equation and solve for a.
f(x) = a/(x-h) +k . . . . for (h, k) = (4, 2) and (x, y) = (12, 3)
3 = a/(12 -4) +2 . . . . . . . givens substituted in
1 = a/8 . . . . . . subtract 2
8 = a . . . . . . . multiply by 8
The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00 , how much will a 19 foot length with 3 inches diameter cost?
Answer:
$273.60
Step-by-step explanation:
The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing.
i.e [tex]C\propto L\cdot D[/tex]
i.e [tex]C=k\cdot L\cdot D[/tex]
A 5 foot or 60 inches length with diameter 2 inches costs $48.00, so
[tex]\Rightarrow 48=k\times 60\times 2[/tex]
[tex]\Rightarrow k=\dfrac{48}{60\times 2}=0.4[/tex]
Now the equation becomes,
[tex]C=0.4\cdot L\cdot D[/tex]
So the cost of a 19 foot or 228 inches length with 3 inches diameter is,
[tex]C=0.4\times 228\times 3=\$273.60[/tex]
A scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours. How many hours will it take for the bacteria colony to decrease to 1000? Round your answer to the nearest tenth of an hour.
Answer:
3.3 hours.
Step-by-step explanation:
We have been given that a scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours.
Since number of bacteria is decreasing exponentially, so we will use exponential decay function.
[tex]y=a*b^x[/tex], where,
a= Initial value,
b = For decay b is in form (1-r), where r is rate in decimal form.
Let us convert our given rate in decimal form.
[tex]75\%=\frac{75}{100}=0.75[/tex]
As number of bacteria is decreasing every 2 hours, so number of bacteria decreased in 1 hour will be x/2.
Upon substituting our given values in above formula we will get,
[tex]y=10,000(1-0.75)^{\frac{x}{2}}[/tex]
To find the number of hours it will take to for the bacteria colony to decrease to 1000, we will substitute y = 1,000 in our equation.
[tex]1,000=10,000(0.25)^{\frac{x}{2}}[/tex]
Let us divide both sides of our equation by 10,000.
[tex]\frac{1,000}{10,000}=\frac{10,000(0.25)^{\frac{x}{2}}}{10,000}[/tex]
[tex]0.1=(0.25)^{\frac{x}{2}}[/tex]
Let us take natural log of both sides of our equation.
[tex]ln(0.1)=ln((0.25)^{\frac{x}{2}})[/tex]
[tex]ln(0.1)=\frac{x}{2}*ln(0.25)[/tex]
[tex]-2.302585=\frac{x}{2}*-1.386294[/tex]
[tex]x=\frac{-2.302585}{-1.386294}*2[/tex]
[tex]x=1.660964*2[/tex]
[tex]x=3.3219\approx 3.3[/tex]
Therefore, it will take 3.3 hours for the bacteria colony to decrease to 1000.
Final answer:
It will take 4 hours for the bacteria colony to decrease from 10,000 to 1,000, considering a 75% decrease every two hours.
Explanation:
To find out how many hours it will take for the bacteria colony to decrease from 10,000 to 1,000 with a 75% decrease every two hours, we can use the formula for exponential decay: [tex]N = N0(1 - r)^t[/tex], where N is the final amount, N0 is the initial amount, r is the rate of decrease (expressed as a decimal), and t is the time in units of the rate's period (in this case, every two hours).
Here, N0 = 10,000, N = 1,000, and r = 0.75. Plugging the values into the formula gives [tex]1,000 = 10,000(1 - 0.75)^t.[/tex]Simplifying, we find [tex](1 - 0.75)^t = 0.1.[/tex]
Solving for t, we find that t equals 2 cycles or 4 hours, because the bacteria population decreases by 75% every 2 hours, and it takes 2 cycles for the population to reach 1,000 from 10,000.
Peter has two coupons from Gussini's Department Store, one for $10 off and another for 10% off. Peter wants to purchase a shirt for $64. His friend Casey told him to use the 10% of coupon because it is the best deal and his friend Josue told him to use the $10 off coupon because it is the best deal. Which friend is correct?
Answer:
Josue is Write
Step-by-step explanation:
64 x .10 = 6.4 in savings while $10 off is better
2+2^2=???????????????????????????
Answer:
6
Step-by-step explanation:
First, you multiply 2 to the 2nd power, then add 2
Question
2+2^2
Answer:
6Step-by-step explanation:
2² = 2*2
----------------------
power first then sum
2 + 2² =
2 + 4 =
6
A fruit punch recipe calls for 3/4 cup of pineapple juice and 1 1/2 cups of orange juice. I have 4 1/2 cups of pineapple juice and want to use all of it. How many cups of orange juice will I need?
Answer: If the recipe wants 3/4 cup of pineapple juice for every 6/4 cups of orange juice, 18/4 is 6x more than the recipe so 6/4 must be 6x larger too.
6 x 3/2 = 18/2 or 9 cups of orange juice. Hope this helps :) Please mark brainliest if you can ;)
Quentin has 6 5/8 feet of lumber but needs another 2 3/4feet to complete the project he's working on. How much total wood will the project have used when finished?
Answer:
Total wood required for the project will be 9 3/8 feet.
Step-by-step explanation:
As given in the question Quentin has lumber of length = 6 5/8
feet =53/8 feet.
Now Quentin needs more lumber = 2 3/4 feet =11/4 feet or 22/8 feet.
So we can get total wood required by adding these two figures
That is = 53/8 + 22/8
= (53 +22)/8
= 75/8
= 9 3/8 feet
Answer:
[tex]The\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]
Step-by-step explanation:
As given
[tex]Quentin\ has\ 6 \frac{5}{8}\ feet\ of\ lumber\ but\ needs\ another\ 2 \frac{3}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]
i.e
[tex]Quentin\ has\ \frac{53}{8}\ feet\ of\ lumber\ but\ needs\ another\ \frac{11}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]
[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53}{8} + \frac{11}{4}[/tex]
L.C.M of (8,4) = 8
Than
[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 11\times 2}{8}[/tex]
[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 22}{8}[/tex] [tex]Total\ wood\ will\ the\ project\ have\ used =\frac{75}{8}[/tex]
[tex]Total\ wood\ will\ the\ project\ have\ used = 9 \frac{3}{8}[/tex]
[tex]Therefore\ the\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]
What is the first step in simplifying the following expression: 2 + 3(4 + 5×2) − 8 + 3^2
Question options:
2 + 3
5 x 2
3^2
4 + 5
Answer:
5 x 2 inside the parenthesis
Step-by-step explanation:
We need an order of operations to ensure we always arrive at the correct answer. It gives us a consistent way to work with numbers. We use the mnemonic device like PEMDAS to remember the correct order.
P-parenthesis
E-exponents
M-multiplication
D-division
A-add
S-subtract.
We apply them left to right doing inner operations before outer operations.
There fore our first step is in the parenthesis and multiplication because it is the inner most operations. 5 x 2 inside the parenthesis.
Monday Janel and $16 for two hours of babysitting getting paid the same rate she earns $40 for babysitting on Saturday how many hours did you know babysit on Saturday
Please help on this one ?
1 ║ 1 2 -3 2
1 3 0
--------------------------------------------------------------------
1 3 0 [tex]\boxed{2}[/tex]
⇒ The Remainder is 2
Please help me with these problems
Answer:
1.a=2
2. C x=2 and x=-3
Step-by-step explanation:
The standard form for the quadratic function is
ax^2 +bx+c
so we need to rewrite the function to be in this form
2x^2 -10 = 7x
Subtract 7x from each side
2x^2 -7x-10 = 7x-7x
2x^2 -7x-10 = 0
a =2, b= -7 c=-10
2. The quadratic formula is
-b ± sqrt(b^2 -4ac)
----------------------------
2a
2x^2 + 2x=12
Lest get the equation in proper form
2x^2 + 2x-12 = 12-12
2x^2 +2x-12 =0
a=2 b=2 c=-12
Lets substitute what we know
-2 ± sqrt(2^2 -4(2)(-12))
----------------------------
2(2)
-2 ± sqrt(4+96)
----------------------------
2(2)
-2 ± sqrt(100)
----------------------------
4
-2 ± 10
----------------------------
4
-2 + 10 -2-10
----------- and --------------
4 4
8/4 and -12/4
2 and -3
Write an addition equation that will have a new thousand, a new hundred, and a new ten. Then solve. Explain how you chose your numbers.
Answer:
1987 + 1257 = 3247
Step-by-step explanation:
We are going to use a base number to start from. That number is 1,987 where the thousand is 1, the hundred is 9 and the ten is 8.
Then we are going to add 1,257 which will be 3,247. Thus we will have a new thousand which is 3 (formerly 1), a new hundred which is 2 (formerly 9), and finally, a new ten which is 5 (formerly 7).
1987 + 1257 = 3247 gives you a new thousand, a new hundred and a new ten.
Answer:
Step-by-step explanatcagion:
use the given information to prove that FG=HF
1. EG = HJ (Given)
2. EG = EF + FG, HJ = HF + FJ (Seg. Add. Prop.)
3. EF + FG = HF + FJ (Subst. Prop.)
4. EF = FJ (Given)
5. FG = HF (Subtraction Prop.)
It's challenging to demonstrate that FG equals HF as these may represent different elements or variables in different mathematics or physics contexts. At its simplest, FG seems to represent the gravitational force between two masses, and HF would need to represent the same force to hold true.
The equation given seems to pertain to gravitational forces where FG represents the gravitational force between two masses, electron and proton.
Given that FG = GMM where G is the gravitational constant (6.67×10-¹1 N·m²/kg²), m and M represent the masses of the electron and proton, to prove that FG=HF, it implies that HF represents the same gravitational pull.
However, without more detailed context or information, I can't further demonstrate or prove that FG does equal HF as these terms may refer to different elements or variables in different contexts of mathematics or physics problems.
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If William has 5 different shirts and 7 different pairs of pants, how many different combinations could he wear?
The question is asking how many different outfit combinations William can form if he has 5 shirts and 7 pants. It's a simple multiplication of the two numbers (5*7) resulting in 35 different combinations. Therefore, William could wear a different outfit for 35 days without repeating.
Explanation:The subject of this question is combinatorics, a branch of mathematics concerned with counting, both as a means and an end. In this specific context, we are looking at the number of different combinations that William can wear with the clothes he has. Since each shirt can be worn with any pair of pants, this translates into a simple product calculation.
William has 5 different shirts and 7 different pairs of pants. So, the total number of combinations of outfits he can put together is calculated by multiplying these numbers together. Hence, 5 shirts * 7 pants = 35 combinations.
This means that if William chooses a different combination each day, he could go for 35 days without wearing the same outfit twice.
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13. Find a cubic function with the given zeros. 7, -3, 2
[tex]\bf \begin{cases} x=7\implies &x-7=0\\ x=-3\implies &x+3=0\\ x=2\implies &x-2=0 \end{cases}~\hspace{7em}(x-7)(x+3)(x-2)=\stackrel{y}{0} \\\\\\ (x^2-4x-21)(x-2)=y \\\\\\ x^3-4x^2-21x-2x^2+8x+42=y\implies x^3-6x^2-13x+42=y[/tex]
Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does a cinnamon cost per pound?
Divide the cost for 3 ounces by 3, to find the cost per ounce:
2.40 / 3 = 0.80
It cost 80 cents per ounce.
Now multiply the cost per ounce by 16 ounces:
16 x 0.80 = 12.80
It will cost $12.80 for one pound.
How much money should be deposited today in an account that earns 3 % compounded semiannually so that it will accumulate to $8000 in three? years
To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the compound interest formula.
Explanation:To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, the future value (A) is $8000, the interest rate (r) is 3% or 0.03, the number of compounding periods per year (n) is 2 (semiannual compounding), and the number of years (t) is 3. Plugging these values into the formula, we get:
A = P(1 + r/n)^(nt)
$8000 = P(1 + 0.03/2)^(2*3)
$8000 = P(1 + 0.015)^(6)
$8000 = P(1.015)^(6)
To find the value of P, we divide both sides of the equation by (1.015)^6: P = $8000 / (1.015)^6. Using a calculator, we find that P ≈ $7383.42. Therefore, approximately $7383.42 should be deposited today in the account.
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Find the equation of a line parallel to y = 3x - 6, passing through the point (-6, -7). options:
y = 3x + 11
y = 3x - 11
y = 3x - 7
y = -1/3x - 9
Parallel lines have the same a slope. Therefore if
k: y = 3x - 6 → slope = 3
and l: y = mx + b
l || k ⇔ m = 3
l: y = 3x + b
We have the point (-6, -7). Put the coordinates to the equation:
-7 = 3(-6) + b
-7 = -18 + b add 18 to both sides
11 = b → b = 11
Answer: y = 3x + 11A public pool opened for summer. A total of 246 people came swimming over the first 3 days it was open on the first day79came to swim on the second day 104 people swam how many people swam on the third day
63 People came on the third day
Hi there!
So there was a public pool opened for summer and a total of 246 people came swimming over the first 3 days. On the first day 79 came to swim and on the second day 104 came to swim. To find how much people swam on the third day, we need to add 104 + 79 and subtract the answer with 246.
104 + 79 = 183
246 - 183 = 63
63 people came to swim on the third day.
Hope this helped!~
Find the missing value
8
14
45
15
Answer:
The correct option is B.
Step-by-step explanation:
From the given figure it is nices that the length of sides AB, BC and AC are 20, 22 and 35. The line AD is angle bisector.
Let the missing value be x.
The Triangle Angle Bisector Theorem states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
Since AD is angle bisector, therefore
[tex]\frac{AB}{AC}=\frac{BD}{CD}[/tex]
[tex]\frac{20}{35}=\frac{22-x}{x}[/tex]
[tex]20x=35(22-x)[/tex]
[tex]20x=770-35x[/tex]
Add 35x both sides.
[tex]55x=770[/tex]
Divide both sides by 55.
[tex]x=\frac{770}{55}[/tex]
[tex]x=14[/tex]
Therefore, second option is correct.
HELP PLEASE!!!
1. There are two bags of marbles. Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one Green marble from Bag A and one black marble from Bag B. These events are:
a. independent
b. dependent
c. neither
d. can not be determined
2. You are asked to find the probability of selecting two cards from a standard deck of cards. What is the probability that you select an Ace then a King? These events are:
a. can not be determined
b. independent
c. dependent
d. neither
Problem 1
Answer: Independent
The reason why is because each bag is separate from one another, so one event doesn't affect the other. If we know the result of what we pulled out of one bag, it doesn't change the probability of the other event.
======================================
Problem 2
Answer: Dependent
Assuming you do not put the first card back, then the probability of picking a King on the second draw will be different than if you picked a King on the first draw. With all 52 cards in the deck, the probability of getting a king is 4/52 = 1/13. It changes to 4/51 after we picked out an ace for the first card (and didn't put that first card back).