(q11) Find the center of mass of the system of objects that have masses 2 , 3 and 5 at the point (-1,2),(1,1) and (3,3) respectively.

The number of zeros of the function f(x) = 24 − 223 + 922 + 2 − 1 in the disk D[0, 2] is two.Answer: Two.

The given function is f(x) = 24 − 223 + 922 + 2 − 1.The number of zeros of the function in the disk D[0, 2] is to be determined.Solution:We need to use Rouche's theorem to find the number of roots of the given function f(x) = 24 − 223 + 922 + 2 − 1 in the disk D[0, 2].

Rouche's theorem: Suppose f and g are holomorphic in the domain D and on the boundary ∂D, |f(z)| > |g(z)| for all z on ∂D, then f(z) and f(z) + g(z) have the same number of zeros in the domain D.

Now, let's consider two functions. Let f(x) = 922 + 2 and g(x) = 24 − 223 − 1.Let z be any complex number such that |z| = 2.

Then we have|f(z)| = |9(2^2) + 2| = 38|g(z)| = |24 − 223 − 1| = 197. By Rouche's theorem,

we have f(z) and f(z) + g(z) have the same number of zeros in the disk D[0, 2].

The function f(z) + g(z) = 922 + 2 + 24 − 223 − 1 = 10 – 223 has two roots in the disk |z| < 2. Hence, the function f(z) = 922 + 2 has two roots in the disk D[0, 2].

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The goal of hypothesis testing is to gather sample data and evaluate whether it provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

a. Expressing the original claim in symbolic form: Let μ be the population mean pulse rate of adult males.

b. Identifying the null and alternative hypotheses:

Null hypothesis (H₀): The population mean pulse rate of adult males is equal to 69 bpm. (μ = 69)

Alternative hypothesis (H₁): The population mean pulse rate of adult males is not equal to 69 bpm. (μ ≠ 69)

In this case, the original claim is that the mean pulse rate of adult males is equal to 69 bpm. To express this claim symbolically, we use the population mean μ. Therefore, the claim can be expressed as μ = 69.

For hypothesis testing, we have the null hypothesis (H₀) stating that the population mean pulse rate is equal to 69 bpm, and the alternative hypothesis (H₁) stating that it is not equal to 69 bpm. The null hypothesis is typically the assumption we want to test and challenge with evidence. In this case, the null hypothesis is μ = 69, while the alternative hypothesis is μ ≠ 69.

The goal of hypothesis testing is to gather sample data and evaluate whether it provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

i am unsure

Step-by-step explanation:

I HEART POINTS

Answer:

20 rides

Step-by-step explanation:

35-4.5=30.5

20*1.5=30 and 30 plus 4.5 equals 34.5

The probability that exactly 10 patients are referred to an oncologist in a month is 0.036

The probability that between five and 15 inclusive are referred to an oncologist in a month is 0.98.

The probability that more than 10 patients are referred to an oncologist in a month is 0.873

Given:

A researcher used Poisson distribution to model the number of patients per month referred to an oncologist. The researcher uses a rate of 16 patients per month. We have to find the probabilities for different conditions:

a) The probability of exactly 10 patients are referred to an oncologist.  

b) The probability that between five and 15 inclusive are referred to an oncologist.

c) The probability that more than 10 are referred to an oncologist.

Solution:

a) The number of patients referred to an oncologist per month follows Poisson distribution with parameter λ = 16.

The probability of exactly 10 patients are referred to an oncologist is:

`P(X = 10) = e^(-λ) * (λ^x) / x!` = `e^(-16) * (16^10) / 10! = 0.036`

Therefore, the probability that exactly 10 patients are referred to an oncologist in a month is 0.036.

b) The probability that between five and 15 inclusive are referred to an oncologist is:

`P(5 ≤ X ≤ 15) = P(X ≤ 15) - P(X ≤ 4)``= ∑_(x=0)^4 (e^(-16) * (16^x) / x!) + ∑_(x=5)^15 (e^(-16) * (16^x) / x!)`≈ 0.98

Therefore, the probability that between five and 15 inclusive are referred to an oncologist in a month is 0.98.

c) The probability that more than 10 are referred to an oncologist is:

`P(X > 10) = 1 - P(X ≤ 10)` `= 1 - ∑_(x=0)^10 (e^(-16) * (16^x) / x!)` ≈ 0.873

Therefore, the probability that more than 10 patients are referred to an oncologist in a month is 0.873.

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Answer:

90

Step-by-step explanation:

Answer:

8.5 inches

Step-by-step explanation:

Let the center of the circle = C

Now CK = CL = 6

Using Pythagoras theorem  

LK^2 = CL^2 + CK^2

        = 6^2 +6^2

          = 36 + 36

          = 72

LK = 72 ^1/2

     = ( 36*2)^1/2

       = 6(2)^1/2

      = 8.5 inches

Answer:

1000

Step-by-step explanation:

From the above question

We have the following parameters

30 were intially Marked

600 were caught and out of it 18 was marked

The formula for the best estimate of the population is calculated as:

Total population = Initial marked kangaroo × Number of caught kangaroo/Number of kangaroo marked after they were caught

= 30 × 600/18

= 1000

Answer:

kangaroos are found in austraillia i don't kno where in austrailla u can find one but they are cute as a pumpkin

Step-by-step explanation:

Answer:

the answer is a/ 21 kilometers

Answer: red 36 m

Step-by-step explanation: base plus base = 18 / 2 = 9 * 4 = 36 m

Answer:

36 m²

Step-by-step explanation:

To answer this question you will need the equation to find the area of a trapezium:

[tex]\frac{(a + b)}{c}[/tex] × height

Substitute the figures into the equation:

[tex]\frac{(6+12)}{2}[/tex] × 4

6+12= 18

After substituting use BIDMAS/ PETMAS to solve

18÷2= 9

9×4= 36 m²

Answer:

X = 60 degrees

Answer

80°

Step by Explanation:

the angle right to 60°= 180-60 (linear pair)

= 120°

total angle of 5 sided polygon= 540°

540° = x + 110° + 130° + 100° + 120°

540° = x + 460°

x= 540° - 460°

x = 80°

Answer:

yy

Step-by-step explanation:

bi

Answer:

the rate of change is 3

Step-by-step explanation:

if im wrong im sorry but if im right give me brainliest

Answer:

B. A(n) = P + (n-1)i*P

Step-by-step explanation:

The formula to determine the simple interest formula is given below:

Simple interest = P×r × t

where

P denotes the principal

r denotes the rate of interest

And, t denotes the number of years

Now we replace i with the t

So,

SI = Pni

Now for n-1 years, the simple interest is

SI = P(n - 1)×i

So, the total amount would be

A(n) = P + (n - 1)i × P

Answer:

im pretty sure youre right :/ dont know why it marked you as wrong

Answer:

I think its F im not sure but i did 12x12 witch is 144 the rest is self explanory

Step-by-step explanation:

Answer:

32+48

Step-by-step explanation:

80- 32= 48

80-48= 32

Answer:  32; 48

Step-by-step explanation:

Let x be the smaller number, and y be the larger number, then we get

x + y = 80

x - y = 16

x - y = 16

x = 16 + y

x + y = 80

16 + y + y = 80

16 + 2y = 80

2y = 64

y = 32

x - y = 16

x - 32 = 16

x = 48

Option B is correct, x ≤ 2  is the domain of the function shown on the graph.

A relation is a function if it has only One y-value for each x-value.

We have to find the domain of the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis.

The graph has x values less than or equal to two.

x ≤ 2 is the domain of the given function.

Hence, option B is correct, x ≤ 2  is the domain of the function shown on the graph.

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1.23 is a decimaland 123/100 OR 123% is the percentage for 123/100.

HOW TO WRITE 123/100 AS A DECMAL?

Step-by-step explanation:

Fraction=123/101

Decmial=1.21782

percentage=121.782%

Step-by-step explanation:

The given equation `mx cx kx=f(t)` is a second-order linear differential equation with constant coefficients. The general solution to this type of equation is given by the sum of the complementary solution `x_c(t)` and the particular solution `x_p(t)`.

The complementary solution x_c(t) is the solution to the associated homogeneous equation mx cx kx=0. The characteristic equation for this homogeneous equation is mr^2 + cr + k = 0. Solving this quadratic equation gives two roots r_1 and r_2. The complementary solution can then be written as x_c(t) = C_1e^(r_1t) + C_2e^(r_2t).

The particular solution x_p(t) depends on the form of the function f(t). There are several methods for finding the particular solution, such as undetermined coefficients or variation of parameters.

Once the complementary and particular solutions are found, the general solution to the given differential equation is given by x(t) = x_c(t) + x_p(t). The constants C_1 and C_2 can then be determined using the initial conditions x(0)=0 and x'(0)=0.

Without more information about the function f(t), it is not possible to find a more specific solution to the given differential equation.

Answer:

x intercept = -3.15

y intercept = 6.3

Step-by-step explanation:

Given the expression

-6x+3y=18.9

x intercept occurs at y = 0

-6x+3(0)=18.9

-6x = 18.9

x = -18.9/6

x = -3.15

Hence the x intercept is -3.15

y intercept occurs at x= 0

-6(0)+3y=18.9

3y = 18.9

y = 18.9/3

y = 6.3

Hence the y intercept is 6.3

Answer:

46.56 pounds

Step-by-step explanation:

Given data

4.3 pounds

2 pounds

3.8 pounds, and

5.9 pounds

Let us find the total weight of all the items

=4.3+2+3.8+5.9

=16 pounds

We are told that he is charged $2.91 per pound for shipping

Hence the cost of shipping 16 pounds is

=2.91*16

=46.56 pounds

Answer:

22, 30

Step-by-step explanation:

52/2=26

26-4=22

26+4=30

30+22=52

Answer:

30 and 22

Step-by-step explanation:

This can be solved using system of equations

Let x = the bigger number

Let y = the smaller number

The sum of two numbers is 52

x + y = 52

The difference is 8

x - y = 8

x + y = 52

x - y = 8

I will solve using elimination

 (x + y = 52)

+ (x - y = 8)

-----------------------

2x = 60

/2     /2

x = 30

x + y = 52

30 + y = 52

-30         -30

y = 22

Answer: D

Step-by-step explanation: On Edge2021

Answer:

The 99% confidence interval for the mean length of the songs on Marcelina's phone is approximately (3.08 minutes, 3.78 minutes).

Step-by-step explanation:

To calculate the 99% confidence interval for the mean length of the songs on Marcelina's phone, we can use the formula:

Confidence Interval = Sample Mean ± (Z * Standard Error)

Where:

Sample Mean is the mean length of the sample songs (3.43 minutes).

Z is the critical value associated with the desired confidence level (99% confidence level corresponds to a Z-value of approximately 2.576).

Standard Error is the standard deviation of the sample divided by the square root of the sample size.

Given that the sample size is 28 songs and the standard deviation is 0.72 minutes, we can calculate the standard error as:

Standard Error = Standard Deviation / √(Sample Size)

Standard Error = 0.72 / √28 ≈ 0.136

Now we can substitute the values into the formula:

Confidence Interval = 3.43 ± (2.576 * 0.136)

Calculating the confidence interval:

Confidence Interval = 3.43 ± 0.350

Confidence Interval = (3.08, 3.78)

Therefore, based on this sample, the 99% confidence interval for the mean length of the songs on Marcelina's phone is approximately (3.08 minutes, 3.78 minutes).

Hope this helps!

Answer:

same here hyarhaha what to do

The equation of the least-squares line that best fits the given data points is y = -0.25x + 0.25.

To find the equation of the least-squares line that best fits the data points, we need to apply the method of least squares, which is a statistical technique used to minimize the sum of the squared differences between the observed data points and the values predicted by the line. In this case, we are dealing with a linear relationship between the variables x and y.

The equation y = Bo + B12 represents a linear regression model, where Bo is the y-intercept (the value of y when x is 0) and B12 is the slope of the line (the change in y corresponding to a unit change in x). By using the method of least squares, we can determine the values of Bo and B12 that minimize the sum of the squared differences between the observed y-values and the predicted y-values based on the equation.

By applying the method of least squares to the given data points (1, 0), (2, 1), (4, 2), and (5, 3), we can calculate the values of Bo and B12. After performing the necessary calculations, we find that Bo is 0.25 and B12 is -0.25. Therefore, the equation y = -0.25x + 0.25 represents the least-squares line that best fits the given data points.

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There are 25,200 different ways in which 6 adults and 3 children can stand together in a line such that no two children are next to each other.

To determine the number of ways in which 6 adults and 3 children can stand together in a line such that no two children are next to each other, we can use the concept of permutations.

Let's consider the adults and children as distinct entities. First, we will calculate the number of ways to arrange the adults in a line, and then we will insert the children into the gaps between the adults.

Step 1: Arrange the adults

Since there are 6 adults, there are 6! (6 factorial) ways to arrange them in a line.

Step 2: Insert the children

Now, we have 7 possible positions between the adults where the children can be inserted. These positions include the spaces before the first adult, between each pair of adjacent adults, and after the last adult.

To ensure that no two children are next to each other, we need to choose 3 distinct positions out of the 7 available positions. This can be done in 7C3 ways, which represents the combination of 7 positions taken 3 at a time.

Using the formula for combinations, 7C3 can be calculated as follows:

7C3 = 7! / (3! * (7-3)!)

= 7! / (3! * 4!)

= (7 * 6 * 5) / (3 * 2 * 1)

= 35

Step 3: Multiply the results

Finally, we multiply the number of ways to arrange the adults (6!) by the number of ways to insert the children (35) to obtain the total number of arrangements:

Total number of arrangements = 6! * 35

= 720 * 35

= 25,200

Therefore, there are 25,200 different ways in which 6 adults and 3 children can stand together in a line such that no two children are next to each other.

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