yk = m + n
Solve the following equation for k:

(a) It is a listing of values and their frequencies. It is useful because it shows the values of observations and how many times they occur.

A frequency distribution of qualitative data is a graph that shows the individual values ​​of qualitative data on the horizontal axis and the frequency of those values ​​on the vertical axis. This is useful because it provides a graphical representation of observations and their frequency of occurrence.

A frequency distribution is a representation that shows the number of observations in a given time interval in graphical or tabular form. Frequency is how often a value occurs in an interval while distribution is the frequency pattern of a variable.

The size of the range depends on the data analyzed and the objectives of the analyst. Ranges must be mutually exclusive and complete. Frequency distributions are often used in statistical contexts. In general, a frequency distribution can be associated with a map of a normal distribution.

Qualitative data is defined as proxy and characterization data. This can observe and record qualitative data. This type of data is non-numeric in nature. These data are collected through observation, individual interviews, focus groups and similar methods. Qualitative data in statistics is also called categorical data, that is, data that can be classified and organized according to the characteristics and attributes of things or phenomena.

The correct answer here is:- (A)This is a graph that shows the different values ​​of qualitative data on the horizontal axis and the frequency of these values ​​on the vertical axis. This is useful because it graphically shows sightings and how often they occur.

This makes it easy to compare two sets of data and identify patterns or trends in the data. For example, if the data is about the types of cars owned in a certain city, a frequency distribution might show how many people own each type of car. This information may be used to make decisions regarding marketing, production and other business activities.

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In a set S whic is said to be infinite if there is a one-to-one correspondence between S and a proper subset of S, then
the set of integers is infinite, the set of real numbers is infinite and if a set S has a subset A which is infinite, then S must be infinite.

Given that a set S is said to be infinite if there is a one-to-one correspondence between S and a proper subset of S, we want to prove the following statements:

(a) The set of integers is infinite.

(b) The set of real numbers is infinite.

(c) If a set S has a subset A which is infinite, then S must be infinite.

(a) Let A be the set of positive integers, i.e., A = {1, 2, 3, 4, 5, ...}. We define a function f: A → Z (the set of integers) by f(n) = n - 1. It can be shown that f is both one-to-one and onto. This means that there is a one-to-one correspondence between A and Z. By repeating the same argument, we can also prove that there is a one-to-one correspondence between the negative integers and A. Hence, Z is infinite.

(b) Suppose, for contradiction, that the set of real numbers, R, is finite. Then there would be a one-to-one correspondence between R and some finite set F. Without loss of generality, let F = {a_1, a_2, ..., a_n} where a_1 < a_2 < ... < a_n. Let ε > 0 be such that ε < min{|a_1|, |a_2| - |a_1|, ..., |a_n| - |a_(n-1)|, |a_n|}. For any x ∈ R, we consider different cases:

- If x < 0, then x < -ε < a_1.

- If 0 ≤ x < a_1, then 0 ≤ x + ε < a_1.

- If a_i < x < a_(i+1) where 1 ≤ i ≤ n - 1, then a_i + ε < x + ε < a_(i+1) - ε < a_(i+1).

- If x > a_n, then x - ε > a_n.

We define a function g: R → F by:

- g(x) = a_1 + ε if x < 0,

- g(x) = x + ε if 0 ≤ x < a_n,

- g(x) = a_(i+1) - ε if a_i < x < a_(i+1) where 1 ≤ i ≤ n - 1,

- g(x) = a_n - ε if x > a_n.

It can be shown that g is both one-to-one and onto. This contradicts the assumption that R is finite. Therefore, R must be infinite.

(c) Let S be a set such that A is a subset of S, and A is infinite. Suppose, for contradiction, that S is finite. Then, there would be a one-to-one correspondence between S and some finite set F. Let F = {a_1, a_2, ..., a_n}. There are finitely many elements in S that are not in A, denoted as {b_1, b_2, ..., b_m}. We choose ε > 0 such that ε < min{|a_1 - b_1|, |a_2 - b_2|, ..., |a_m - b_m|}. We define a function f: A → S as follows: f(a_i) = a_i for 1 ≤ i ≤ n, and f(a_i) = b_i + ε for 1 ≤ i ≤ m. It can be shown that f is both one-to-one and onto. This contradicts the assumption that S is finite. Therefore, S must be infinite.

Hence, we have proved the statements:(a) The set of integers is infinite, (b) The set of real numbers is infinite and (c) If a set S has a subset A which is infinite, then S must be infinite.

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Answer:311111892109

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

that's just the correct answer, I know.

Tn = a + ( n- 1 ) d

T 26 = -33 + ( 26 - 1 ) 4

T 26 = -33 + ( 25 x 4 )

= -33 + 100

= 67.............. Option D

Answer:

I get the equation

y = \(\frac{1}{2}\) x + 1

Step-by-step explanation:

The x intercept would be (-2,0)

The y intercept would be (0,1)

The slope is the change in y over the change in x.

The y's are 1 and 0

The x's are 0 -2

\(\frac{1-0}{0- -2}\) = \(\frac{1}{2}\)  Now that we have the slope, we need the y intercept and we have been given that as 1.

y = mx +b  We substitute in the slope of 1/2 and the y intercept of 1

y = 1/2x + 1

Answer:

E-It is a well-designed experiment because there is random assignment, replication, and comparison of at least two treatment groups.

Random assignment, replication, and the ability to compare at least two treatment groups are all criteria for a well-designed experiment.

Answer:

333 coins

Step-by-step explanation:

Simply multiply 37% by the total number of coins, 900:

37%(900)

= (37/100)(900)

= (900 / 100) * 37

= 9 * 37

= 333 coins

Also, optionally check this by dividing 333 by 900 to get 0.37:

333 ÷ 900 = 0.37 = 37%

Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

Answer:

The answer I got was 2. hope that helps.

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

68% falls between the first standard deviation from the mean.

plus minus two would fall under 95%

The equation of the line of fit, obtained from the points on the line and the point-slope form of the equation of a line is; y = -50·x/3 + 3950/3

The equation of the line of fit is the equation that best fits the data points on the graph.

The points on the graph are; (28, 850), (16, 1,050)

The above points indicates that the slope of the graph is; (1050 - 850)/(16 - 28) = -50/3

The equation of the graph in point-slope form using the point (28, 850), therefore is; (y - 850) = (-50/3)·(x - 28)

Therefore; y = -50·x/3 + 28 × 50/3 + 850

The equation of the line of fit is; y = -50·x/3 + 3950/3

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If A and B are disjoint events, then the probability of A or B is the sum of their individual probabilities. However, this does not necessarily mean that A and B are independent events.

If A and B are independent events, then the probability of both A and B occurring is the product of their individual probabilities. However, if A and B are disjoint, then the probability of both A and B occurring is zero. Therefore, A and B cannot be independent if they are disjoint events.Hence, the correct answer is (ii) No. A and B are disjoint events, which means that they do not have any outcomes in common. If A and B are independent events, then the occurrence of one event will not affect the occurrence of the other event. If A and B are not independent events, then the occurrence of one event will affect the occurrence of the other event.

Since A and B are disjoint events, they cannot be independent events. If A and B are independent events, then they cannot be disjoint events. Hence, the correct answer is (ii) No

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The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.

The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:

F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx

a. Write the formula for P(x < x_0):

Using integration, we can solve this formula as follows:

F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]

= [-4e^(-x_0/3) + 4]/3

b. Find P(x < 2):

To find P(x < 2), we simply substitute x_0 = 2 in the above formula:

F(2) = [-4e^(-2/3) + 4]/3

≈ 0.4866

Therefore, the probability that x is less than 2 is approximately 0.4866.

c. Find P(x > 3):

To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:

P(x > 3) = 1 - P(x < 3) = 1 - F(3)

= 1 - [-4e^(-1) + 4]/3

≈ 0.3528

Therefore, the probability that x is greater than 3 is approximately 0.3528.

d. Find P(x < 5):

To find P(x < 5), we simply substitute x_0 = 5 in the above formula:

F(5) = [-4e^(-5/3) + 4]/3

≈ 0.6321

Therefore, the probability that x is less than 5 is approximately 0.6321.

e. Find P(2 < x < 5):

To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:

P(2 < x < 5) = P(x < 5) - P(x < 2)

= F(5) - F(2)

= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3

≈ 0.1455

Therefore, the probability that x is between 2 and 5 is approximately 0.1455.

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Answer:

Hello,

Step-by-step explanation:

Do you remember the formula

\(\boxed{a^3-b^3=(a-b)(a^2+ab+b^2)}\\\\\\27x^6y^9-64=(3x^2y^3)^3-4^3\\\\=(3x^2y^3-4)((3x^2y^3)^2+(3x^2y^3*4)+4^2)\\\\\\=(3x^2y^3-4)(9x^4y^6+12x^2y^3+16)\\\)

I believe your first answer would be 3, and your second would be 1/8, but I'm not sure. I hope this helps!

The weight is 140 kg, the diameter is 4 mm and the length is 54 m. We need to find diameter D in terms of the weight W and length.Diameter D in terms of weight W and length L is given by sqrt((W * (54 * 16)) / 140).

To solve this problem, we can use the joint variation equation:

W = k * L * D^2  where k is the constant of variation. We can plug in the given values to find the value of k:

140 = k * 54 * 4^2

Simplifying the equation, we have:

140 = k * 54 * 16

Dividing both sides by (54 * 16), we get:

k = 140 / (54 * 16)

Now we can substitute the value of k into the joint variation equation and solve for D:

W = (140 / (54 * 16)) * L * D^2

Rearranging the equation to solve for D, we have:

D^2 = (W * (54 * 16)) / 140

Taking the square root of both sides, we get:

D = sqrt((W * (54 * 16)) / 140)

Therefore, the diameter D in terms of the weight W and length L is given by sqrt((W * (54 * 16)) / 140).

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Answer:

5

Step-by-step explanation:

Using Pythagoras' identity

The horizontal distance between A and B is 3 units

The vertical distance between A and B is 4 units

Thus

AB = \(\sqrt{3^3+4^2}\)

      = \(\sqrt{9+16}\)

      = \(\sqrt{25}\)

      = 5

The store should have 445 picks remaining, not 450 as estimated by the manager. To determine if the store manager's estimate is reasonable, let's analyze the situation.

The store initially has 500 guitar picks. They order 15 boxes, and each box contains 9 picks. So the total number of picks they receive from the order is:

15 boxes * 9 picks/box = 135 picks

Next, the store sells 19 boxes, with each box containing 10 picks. Therefore, the total number of picks sold is:

19 boxes * 10 picks/box = 190 picks

To find the remaining number of picks, we can subtract the sold picks from the received picks:

Total remaining picks = Initial picks + Received picks - Sold picks

Total remaining picks = 500 + 135 - 190 = 445 picks

According to the calculations, the store should have 445 picks remaining, not 450 as estimated by the manager.

However, it's important to note that we are working with whole numbers, so there might be some rounding involved in the manager's estimate. It's possible that the manager rounded up to 450 for simplicity or other reasons.

Given the small discrepancy of 5 picks between the calculated value and the manager's estimate, it is reasonable to conclude that the manager's estimate is close enough to the actual number of picks. The discrepancy could be due to rounding or a small counting error. It's unlikely to have a significant impact on the store's operations or inventory management.

In summary, while the manager's estimate of 450 guitar picks may not be exactly accurate, it is reasonably close to the actual remaining number of picks based on the given information.

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Answer:

It will take Machine A 20 additional minutes.

Step-by-step explanation:

First we have get the rate of work per hour, Machine A builds 1/2 of a car per hour, while Machine B builds 1/3 of a car per hour.

Using this we can determine the amount of work that has been done so far in one hour before Machine B broke down:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

Now we can produce an equation accordingly to determine how much time it'll take machine a to finish the job:

5/6 + 1/2x = 1

1/2x = 1/6

x = 1/3 hours = 20 minutes

Note: In the question you typed "how much additional time will it take machine b to finish" but I think you meant machine a because machine b broke down. Please correct me if I'm wrong.

Hope this helps! And let me know if you have any questions!

Answer:

The actual ages of all runners are needed to decide.

The point (1, 60). on the graph how's the speed that the car travels.

It should be noted that car traveled at a constant speed. The distance traveled is 210 miles and the time to travel is 3.5 hours.

Therefore, it should be noted that the point (3.5, 120) shows the distance.

The slope of the like which is the speed will be:

= Distance / Time

= 210 / 3.5

= 60 mph

Therefore, it should be noted that the point B(1, 60) lies on the graph.

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0.6928 or 69.28% is the probability of at least one ace among five cards .

in order to get the probability that at least one of the five cards is an ace, then we implement the use of  complement rule.

as we know this rule states that the probability of an event happening  which is equal to 1 minus the probability of the event  which is not happening.

In this order of situation the event is drawing no aces from the five cards. hence the  probability of drawing no aces is (48/52)^5, as we are having   48 non-ace cards in the deck and the value of the  probability of drawing a non-ace is 48/52.

the calculation to get the probability of drawing at least one ace is:

1 - (48/52)^5 = 1 - (0.9231)^5 = 0.6928

hence  the probability value  of at least one ace among five cards is 0.6928 or 69.28%.  

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Using the conversion to find, the tank holds 379 liters.

In the given question,

There are about 3.79 liters in 1 gallon. Kendra’s fish tank contains 100 gallons of salt water.

We have to find how many liters the tank holds.

Firstly we learn about gallon

The gallon is a unit of volume.

We measure liquid things in gallon.

As given that

1 gallon = 3.79 liters

We have to find the 100 gallons in liters.

To find the 100 gallons in liters we multiply 100 by 3.79 because 1 gallons equal to 3.79 liters.

So 1 gallon = 3.79 liters

100 gallon = 100 × 3.79 liters

100 gallon = 379 liters

Hence, the tank holds 379 liters.

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Answer:

= -3

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

C the probability that a customer buys a hat given that the customer has bought a sweater.

There are 66 ways to choose two vehicles from the dealer's inventory.

A combination is a grouping of items from a larger set in which the order of the items is irrelevant. In other words, it is a method of selecting a subset of items from a larger set without regard for their order of selection.

The formula C(n, k) = n! / (k! (n - k)!) can be used to calculate the number of combinations.

where n represents the total number of items in the set and k represents the number of items in the combination.

The exclamation mark (!) represents the factorial function, which is the sum of all positive integers up to a certain number.

The number of ways to select two vehicles from 8 cars and 4 trucks is 8 + 4 = 12 vehicles.

To find the number of combinations, we use the formula for combinations, which is:

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

where n is the total number of vehicles and k is the number of vehicles we want to choose.

So, for n = 12 and k = 2,

we have:

So, putting the value in above formula:

We will get it as:

C(12, 2) = 12! / (2! (12 - 2)!) = (12 * 11) / (2 * 1) = 66

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Answer:The numbers are 162,164,166,168,

Step-by-step explanation:

The solution is in the attached

Answer: The numbers are 162,164,166,168,

Step-by-step explanation: