A fair sortition trial is carried out, and one of the candidates is assigned the number 32,041. If each digit can be chosen from 0-4, and if each of the possible sequences is assigned to a candidate, how many candidates are there?

Answer:

The answer is C

[tex]3x-y=14\\-9x+3y=-42[/tex]

Step-by-step explanation:

In order to determine the system, we have to know the condition to produce infinitely solutions. A solution of a system is the coordinate (x,y) which is common between two lines ( in a 2D plane). A system does not have solution when the lines do not intercept each other, that it means, they are parallele. When two lines are coincident in all points, there are infinitely solutions.

I have attached an image that shows different systems of two lines.

So, to find the system, we have to find two equal equation. If we multiply by 3 the third system:

[tex]3x-y=14\\-9x+3y=-42\\\\(-3)*(3x-y)=(-3)*14\\(1)*(-9x+3y)=(1)*-42\\\\-9x+3y=-42\\-9x+3y=-42[/tex]

This system has infinitely solutions.

Probability is the likelihood or chance that an event will occur. If the probability of the spinner showing an even number if the odds against a spinner showing an even number are 3:8 is 8/11

Probability is the likelihood or chance that an event will occur. The formula for calculating probability is expressed as:

Probability = expected/total outcome

If the odds against a spinner showing an even number are 3:8, the  total number of spins is 11 spins

From the ratio

Number of odd spin = 3

Number of even spin = 8

Find the probability of spinning even

pr(even spin) = 8/11

Hence the probability of the spinner showing an even number if the odds against a spinner showing an even number are 3:8 is 8/11

Learn more on probability here:  https://brainly.com/question/24756209

Solution:

The given inequality is :

3 x - 2 y ≤ 6

To draw the graph we will first draw the graph of line : 3 x - 2 y = 6

The graph of this function i.e 3 x - 2 y = 6 will be a straight line.

Then we will check whether origin lies on which side of line .

Put x=0, and y = 0 in the inequality 3 x - 2 y ≤ 6, we obtain

LHS = 0 ≤ 6

It means the line will contain the Origin.

Equation of line in Intercept form is : [tex]\frac{x}{2} -\frac{y}{3}\leq 1[/tex]

Answer: The height of the stacked boxes is 31 meters.

Step-by-step explanation:

Since, the Volume of a cube = (side)³

The volume of first box = 1331 cubic meters,

⇒ (side)³ = 1331

⇒

Similarly, the side of second box = 11 meters ( Because, both boxes have the same volume )

Now, the volume of third box = 729 cubic meters

⇒ ⇒ (side)³ = 729

⇒

Thus, the height of the stacked boxes = Side of first box + side of second box + side of third box

= 11 + 11 + 9

= 31 meters.

Answer:

2 times

Step-by-step explanation:

Note that since we can only use positive integers for , the minimum will be x = 1. Testing x = 2, we get . Since , we know that only  will work, thus, there are  positive integer values of  such that this function is less than 20.

In mathematics especially in verifying certain statements regarding geometry, two column proofs are used. A two-column proof contains a table with a logical series of statements and reasons that reach a conclusion. It is commonly present in geometry. Two column proofs always have two columns: statements and reasons. The other choices don’t fit in the definition of two column proof.

In science, the four ways to incorporate proof into the research paper are:

1.    If the research you are investigating has been with other research paper before.

2.    There is an experimental proof that the evidence is true.

3.    The research published belongs to a reliable source.

4.    There are citations of the evidence that you are investigating

Answer:

50.24 square units

Step-by-step explanation:

Hope this helps.

Final answer:

Working backwards from the $10 Julia has left after spending and losing money, we calculate that she initially had $30 for her birthday.

Explanation:

To find out how much birthday money Julia initially had, we can work backwards from the $10 she has left. Julia lost half of her money after spending 1/3 of it, which means that the $10 is half of what remained after spending 1/3. Therefore, before she lost half, she must have had $20 (since $10 is half of $20). We can then calculate the original amount by understanding that $20 is 2/3 (the remaining amount after spending 1/3) of the original amount. To find the full amount, we divide $20 by 2/3.

Here's the calculation step-by-step:

Let the original amount of birthday money be X.

Julia spent 1/3 of X, leaving her with 2/3 of X.

She then lost half of the remaining money, leaving her with (1/2)(2/3)X, which equals $10.

Solving for X: (1/2)(2/3)X = $10 -> (1/3)X = $10 -> X = $10 / (1/3) -> X = $10 × 3 -> X = $30.

Julia originally had $30 for her birthday.

Answer:

3/4z-1/4z+1=2/4z+1

Combine like terms to get

1/2z+1=1/2z+1

Subtract one from both sides to get

1/2z=1/2z

Multiply both sides by 2 to get

z=z.

This is D, has infinitely many solutions because any number you enter as z will equal itself.

Ex. 5 as z would be 5=5 which is true with any number.

C(n,r)=C(7,6) 

Final answer:

There are 7 different ways to select a committee of 6 people from a group of 7 candidates, calculated using the combinations formula C(7, 6) = 7! / (6! * (7 - 6)!) = 7.

Explanation:

The question is asking to determine the number of different ways a committee can be selected from a group of candidates, which is a common problem in combinatorics, a branch of mathematics. To find the number of different ways a committee of 6 people can be selected from a group of 7 candidates, you can use combinations. Since the order in which the committee is chosen does not matter, you calculate combinations and not permutations. The formula for combinations is:

C(n, k) = n! / (k! * (n - k)!)

Applying the formula:

C(7, 6) = 7! / (6! * (7 - 6)!) = 7 / 1 = 7

Therefore, there are 7 different ways to select a committee of 6 people from a group of 7 candidates.

Chang needs to bike 65 miles on the last day to have an average of 65 miles per day.

To find how many miles Chang needs to bike on the last day, we need to find the total miles he has biked so far. So, we add up the miles he has biked on the first three days: 70 + 63 + 66 = 199 miles.

To find the average of 65 miles per day, we need to divide the total miles by the number of days: 199 / 4 = 49.75 miles per day.

Since Chang wants to have an average of exactly 65 miles per day, he needs to bike 65 miles on the last day. Therefore, he needs to bike 65 miles on the last day.

Final answer:

The velocity of the ball at t = 1 second is found by taking the derivative of the position function s(t) and evaluating it at t = 1. The derived velocity function is v(t) = -32t + 20, and the velocity at t = 1 second is 8 ft/sec.

Explanation:

The student wants to find the velocity of a ball at t = 1 second when thrown vertically upward from the top of a 100-foot tower with an initial velocity of 20 ft/sec. The position function given is [tex]s(t) = -16t^2 + 20t + 100[/tex]. To find velocity, we need to take the derivative of the position function with respect to time, which represents the velocity function v(t).

The derivative of the position function is:
v(t) = −32t + 20.

To find the velocity at t = 1 second, substitute 1 for t:
v(1) = −32×1 + 20 = −12 + 20 = 8 ft/sec.

Therefore, the velocity of the ball at t = 1 second is 8 ft/sec.

It's geometric sequence:

[tex]a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....[/tex]

Calculate the common ratio:

[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5[/tex]

The explicit formula of geometric sequence:

[tex]a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}[/tex]

Substitute:

[tex]a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}[/tex]

Answer: "f(x) = 1.2(2.5)x-1"

Answer:

Step-by-step explanation:

100% righttt