what is scientific notation and how do you do it?​

Answer:

Answer: Given that a photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. Therefore, the actual length of the bacteria is = (5/50000) cm = 0.0001 cm.

Step-by-step explanation:

^^

a) X is an unbiased estimator of p. b) The Var(X) is p(1-p)/n. c) The E[X(1-X)] is (n-1)[p(1-p)/n]. d) The value of c is c = 1/(n-1).

(a) To show that X = Y/n is an unbiased estimator of p, we need to show that E[X] = p.

Since Y is a sum of n iid Bern(p) random variables, we have E[Y] = np.

Now, let's find the expected value of X:

E[X] = E[Y/n] = E[Y]/n = np/n = p.

Therefore, X is an unbiased estimator of p.

(b) To find the variance of X, we'll use the fact that Var(aX) = a^2 * Var(X) for any constant a.

Var(X) = Var(Y/n) = Var(Y)/n² = np(1-p)/n² = p(1-p)/n.

(c) To show that E[X(1-X)] = (n-1)[p(1-p)/n], we expand the expression:

E[X(1-X)] = E[X - X²] = E[X] - E[X²].

We already know that E[X] = p from part (a).

Now, let's find E[X²]:

E[X²] = E[(Y/n)²] = E[(Y²)/n²] = Var(Y)/n² + (E[Y]/n)².

Using the formula for the variance of a binomial distribution, Var(Y) = np(1-p), we have:

E[X²] = np(1-p)/n² + (np/n)² = p(1-p)/n + p² = p(1-p)/n + p(1-p) = (1-p)(p + p(1-p))/n = (1-p)(p + p - p²)/n = (1-p)(2p - p²)/n = 2p(1-p)/n - p²(1-p)/n = 2p(1-p)/n - p(1-p)²/n = [2p(1-p) - p(1-p)²]/n = [p(1-p)(2 - (1-p))]/n = [p(1-p)(1+p)]/n = p(1-p)(1+p)/n = p(1-p)/n.

Therefore, E[X(1-X)] = E[X] - E[X²] = p - p(1-p)/n = (n-1)p(1-p)/n = (n-1)[p(1-p)/n].

(d) To find the value of c such that cX(1-X) is an unbiased estimator of p(1-p)/n, we need to have E[cX(1-X)] = p(1-p)/n.

E[cX(1-X)] = cE[X(1-X)] = c[(n-1)[p(1-p)/n]].

For unbiasedness, we want this to be equal to p(1-p)/n:

c[(n-1)[p(1-p)/n]] = p(1-p)/n.

Simplifying, we have:

c(n-1)p(1-p) = p(1-p).

Since this should hold for all values of p, (n-1)c = 1.

Therefore, the value of c is c = 1/(n-1).

To know more about unbiased estimator:

https://brainly.com/question/32063886

#SPJ4

Answer:

The slope is 1/2

Step-by-step explanation:

y²-y¹/x²-x¹

=5-3/5-1

=2/4

=1/2

Step-by-step explanation:

The best way to solve these is by making them into a equation, rise over run, or y over x.

\( \frac{3}{1} - \frac{5}{5} \)

You will get the same answer nomatter which order these are values are in. Now, solve for this equation.

\( \frac{ - 2}{ - 4} \)

Now this is negative and kind of messy, although, we can turn both values into positive values without the answer changing, just be careful on other problems with this technique as it doesn't always work.

\( \frac{2}{4} \)

Now we can simplify again.

\(\frac{1}{2}\)

The slope is 1/2!

1.34

Step-by-step explanation:

1.34 1.34 1.34 1.34 1.34

According to  the solving the estimated sum of the numbers:

To estimate implies to come up with a solution that is close but not accurate. It's a reasonable solution to a problem. A sum is the solution to an addition issue. A difference is a solution to a subtraction issue.

To get the total, we round each number to the closest tenth and then add the rounded figures. Let us calculate 38 + 23. 38 is more like 40 than 30. As a result, 38 is rounded up to 40.

1 435 + 678 + 925 =  2,038

on round of  = 2040

2.359 + 814 + 207 = 1,380

on round of  = 1380

3. 6428 + 7154 + 9345 = 22,927

on round of  = 22930

4. 2987 + 6873 + 4555 = 14,415

on round of  = 14420

5. 6759 + 8210 + 7642 = 22,611

on round of  = 22610

2,040

1,380

22,930

14,420

22,610

To know more about estimated sum visit:

https://brainly.com/question/13106160

#SPJ9

I understand that the question you are looking for is:

Estimate the sum:

1 435 + 678 + 925 =

2.359 + 814 + 207 =

3. 6428 + 7154 + 9345 =

4. 2987 + 6873 + 4555 =

5. 6759 + 8210 + 7642 =

The equation of line is y+4 = 1/2*(x+4).

The point-slope form of a line with slope 'm' and passing through a point (a, b) is given by (y-b)= m(x-a)

Given:

As,  the points (4, 0) and (-4, -4) are two points on the straight line.

slope of line= -4-0/ -4-4

m= 1/2

Now,  line passes through the point (-4, -4), equation of the line is

y-(-4) = m(x-(-4))

y+4 = 1/2*(x+4)

Hence, required point-slope form of the graphed line is y+4 = 1/2*(x+4)

Learn more about this concept here:

https://brainly.com/question/2616640

#SPJ1

Answer:

-23\(x^{8}\)-2v

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

At point D rotate 90° counter-clockwise.  The translate 3 units left and 2 unit up.

Answer:

I need help on that too

Step-by-step explanation:

but i multiplied and got 1,050

Answer:

(x-1)^2

=x^2 - 2x + 1

Step-by-step explanation:

hope this helps

We would need to use 4 teaspoons of vanilla to make 72 muffins.

In order to find the constant of proportionality, we need to set up a proportion and solve for the constant of proportionality. In this case, we can set up the proportion:y/x = muffins/teaspoons of vanilla.

We know that the recipe makes 36 muffins and uses 2 teaspoons of vanilla, so we can substitute those values into the proportion:36/2 = y/x.

Simplifying this expression, we get:18 = y/x. Now, we can see that the constant of proportionality is 18. This means that for every 18 muffins made, 1 teaspoon of vanilla is used.

Alternatively, we could write the equation as:y = 18x. This equation shows the relationship between the number of muffins made, y, and the number of teaspoons of vanilla used, x.

For example, if we wanted to make 72 muffins, we could use the equation to find out how much vanilla we would need:y = 18x72 = 18x4 = x. So, we would need to use 4 teaspoons of vanilla to make 72 muffins.

For more such questions on muffins, click on:

https://brainly.com/question/28030858

#SPJ8

We can draw the conclusion that there is insufficient evidence to support the idea that the model explains the relationship between the independent  variable and dependent variables if the global test of statistical significance for a regression model does not reject the null hypothesis.

The global test of statistical significance for a regression model is used to assess the overall explanatory power of the model. If the global test of statistical significance does not reject the null hypothesis, this indicates that the model does not explain the relationship between the  independent variable and dependent variables as expected. This could be due to a lack of sufficient data, a poorly constructed model, or simply a lack of correlation between the variables. In any case, the results of the test should be interpreted with caution, and further investigation into the model and data may be necessary.

Learn more about independent variable here

https://brainly.com/question/29430246

#SPJ4

Given:

The two ways table.

To find:

The number of girls in year 9.

Solution:

Using the two ways table, we get

Boys in year 10 = Total student in year 10 - Girls in year 10

                        = 256 - 123

                        = 133

Boys in year 9 = Total boys - Boys in year 10 - Boys in year 11

                        = 407 - 133 - 125

                        = 149

Girls in year 9 = Total students in year 9 - Boys in year 9

                       = 303 - 149

                       = 154

Therefore, the number of girls in year 9 is 154 and the correct option is C.

Answer:

x = 1 and x = 3

Step-by-step explanation:

Compare the outputs of the functions for the same input. If they're the same, then f(x) = g(x).

To calculate the equity after 5, 10, and 20 years, disregarding appreciation, we need to consider the concept of equity and its relationship to loan repayment.

Equity represents the portion of an asset that the owner truly owns, and it increases as the loan is paid off. Assuming the equity is calculated based on the initial loan amount and regular payments, we can determine the equity at different time points using an amortization schedule.

An amortization schedule outlines the repayment of a loan over time, indicating the principal and interest portions of each payment. By analyzing the schedule, we can determine the equity at various points. Let's assume a loan with a 13-year term, quarterly payments, and a 9.6% interest rate. To calculate the equity after 5 years, we need to determine the number of payments made in that period.

Since there are four payments per year, after 5 years, there would be 5 * 4 = 20 payments made. Using an amortization schedule, we can find the principal portion of the 20th payment and subtract it from the initial loan amount to determine the equity. Similarly, to find the equity after 10 years, we calculate the number of payments made in that period (10 * 4 = 40 payments) and subtract the principal portion of the 40th payment from the initial loan amount.

For the equity after 20 years, we consider the total number of payments made (20 * 4 = 80 payments) and subtract the principal portion of the 80th payment from the initial loan amount. By following this approach, we can determine the equity at each time point. Remember to round the answers to the nearest cent as specified.

Learn more about payment here: brainly.com/question/32320091

#SPJ11

Answer:

See below for answer and explanations (as well as an attached graph)

Step-by-step explanation:

Pay attention to the behavior of the asymptotes. If the asymptotes are approaching a certain x-value or y-value, then that value is undefined for the function.

Take for example \(y=\frac{1}{x}\):

See the graph for a visual.

When two rays intersect an angle is created, As different classification of angles are there on the basis of measurement of angles and on the basis of properties of angles.

When two rays or straight lines intersect at one of their ends, an angle is created. Vertex of an angle refers to the point at which two points meet. The Latin word "angulus," which means "corner," is the origin of the English term "angle."

Symbol of Angle

The symbol ∠ represents an angle. Angles are measured in the form of degrees (°) using a protractor.

For example, 45 degrees is represented as 45°

Sections of Angles

Types of Angles

Based on their measurements, here are the many types of angles:

Interior and Exterior Angles:

Interior angles: Interior Angles are angle formed inside the shape.

Exterior angles: Exterior angles are to be angles that is formed outside a shape, between any side of  shape and to an extended adjacent side.

Complementary and Supplementary Angles:

Complementary angles: Angles that add up to 90° (a right angle) are called complementary angles.

Supplementary angles: Angles that add up to 180° (a straight angle) are called supplementary angles.

To learn more about angles, visit:

https://brainly.com/question/28451077

#SPJ4

Answer:

It would be -27

Step-by-step explanation:

Math

The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

For more questions on average score

https://brainly.com/question/13832161

#SPJ8

To calculate the probability that none of the tables have two of the same version of the quiz, we can use the permutation formula: 4*3*2=24 ways to distribute the quizzes to the students in the class randomly. We can start by calculating the number of ways to distribute the quizzes so that each table has different quizzes.

To do that, we'll use the following formula for permutations:

6! (4!2!2!)^6. For each table, there are 4! ways to distribute the quizzes among the two students and 2! ways to arrange the quizzes for each student.

There are six tables, so multiply this by (4!2!2!)^6. The denominator is the total number of possible permutations, which is 3^12. Therefore, the probability is:

6!(4!2!2!)^6/3^12

=0.01736

(b) Let's define the set of tables T = {T₁, T2, T3, T4, T5, T6} and the sample space S = {all ways to distribute two versions of the quiz to each table T, € T}. Then, we can define a Bernoulli random variable for each s € S as follows: X(s) = 0, if no tables in s have two of the same version X(s), if at least one table in s has two of the same version find the probability mass function (pmf) for X, we can count the number of ways to distribute the quizzes for each value of X(s, and divide by the total number of possible outcomes.

P(X=0) is the probability that none of the tables have two of the same version of the quiz, which we calculated in part (a) as 0.01736.

P(X=1) is the complement of P(X=0), which is

1 - P(X=0)

= 0.98264.

(c)To sketch a graph of the cumulative distribution function (cdf) for X, we need to calculate the cumulative probabilities for each value of X. The cdf for X is defined as:

F(x) = P(X ≤ x)

For X=0, the cumulative probability is simply

P(X=0) = 0.01736.

For X=1, the cumulative probability is

F(1) = P(X ≤ 1)

= P(X=0) + P(X=1)

= 0.01736 + 0.98264

= 1.0

Therefore, the graph of the cdf for X is shown below. The probability that none of the tables have two of the same version of the quiz is 0.01736. To find the probability mass function (pmf) for the Bernoulli random variable X, we counted the number of ways to distribute the quizzes for each value of X(s). We divided by the total number of possible outcomes.

We found that P(X=0) = 0.01736 and P(X=1) = 0.98264. Finally, we sketched the graph of the cumulative distribution function (cdf) for X, which shows that the probability of having at least one table with two of the same version of the quiz increases as the number of tables increases.

To know more about the permutation, visit:

brainly.com/question/1216161

#SPJ11

Answer:

The answer is 5.5

Step-by-step explanation:

6 x 6 = 36

2x2x2 = 8

36 + 8 =    44

2 + 6 = 8

44/8 = 5.5

Therefore, the answer to this problem is 5.5

I hope I helped! ^-^

Answer:

B. One whole number one over two. 1½

Answer:

- 116

Step-by-step explanation:

Given

28 - ( \(\sqrt{144}\) )²

= 28 - (12)²

= 28 - 144

= - 116

Answer:

X=1

Step-by-step explanation:

m<GCF=m<ACD because they are vertical

11x = 7x+4

subtract 7 from both sides to get 4x=4

divide both sides by four to get X=1

To find directional derivative of the function g(x, y, z), at point P(3, 9, 0) in the direction of the vector PO, where O is the origin (0, 0, 0), we haveto find derivative , The directional derivative of the function g(x, y, z) = \(xye^(3z)\) at point P(3, 9, 0) in the direction of the vector PO is 3√10.

To calculate the gradient of the function: \(∇g = (∂g/∂x, ∂g/∂y, ∂g/∂z) = (ye^(3z), xe^(3z), 3xze^(3z)\)) the gradient at point \(P:∇g(P) = (9e^(3*0), 3e^(3*0), 3*3*0e^(3*0)) = (9, 3, 0).\)

The unit vector in the direction of PO: OP = P - O = (3, 9, 0) Magnitude of OP = |OP| = \(√(3² + 9² + 0²) = √90\), Unit vector, \(u = OP / |OP| = (1/√90)(3, 9, 0) = (1/3√10, 3/√10, 0)\)

Compute the directional derivative of g at P in the direction of \(u: D_ug(P) = ∇g(P) · u = (9, 3, 0) · (1/3√10, 3/√10, 0) = (9(1/3√10)) + (3(3/√10)) + (0*0) = 3√10\)

The gradient of a function is a vector that points in the direction of the steepest increase in the function and its magnitude represents the rate of change of the function at that point.

The directional derivative of the function g(x, y, z) = \(xye^(3z)\) in the direction of the vector PO is 3√10.

Know more about function here:

https://brainly.com/question/12431044

#SPJ11

Answer:

p = -2

q = -3

Step-by-step explanation:

Let us get the equation of the two graphs

General equation form is;

y = mx + b

m is slope and b is the y-intercept

For the first one;

y intercept is 1

So the equation is;

y = mx + 1

The x-intercept is -2

the value of y at the x-intercept is 0

0 = -2m + 1

1 = 2m

m = 1/2

so;

1/2 * p

p/2

q added to y-intercept;

q + 1

Let us get the equation of the second plot

y-intercept is -2

Equation is;

y = mx - 2

We can get slope using x-intercept

x-intercept is -2

0 = -2m - 2

2m = -2

m = -1

So;

p/2 = -1

p = 2 * -1 = -2

For the value of q;

q + 1 = -2

q = -2-1 = -3

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

For similar question on amount.

https://brainly.com/question/25720319  

#SPJ8

Answer:

-7y+3=-25

Step-by-step explanation:

collect like terms together

-7y=-25-3

-7y=-28

cancel the negative

7y=28

simplify

y=4

A. The critical region value is tα = ± 1.753 for a two-tailed test with α = .05. Since 1.5 is less than 1.753, we fail to reject the null hypothesis and conclude that the treatment does not have a significant effect.

B. The value of degrees of freedom is df = 15.

The critical region value is tα = ± 1.753 for a two-tailed test with α = .05. Since 0.375 is less than 1.753, we fail to reject the null hypothesis and conclude that the treatment does not have a significant effect.

C.  the larger the variance, the less likely it is to reject the null hypothesis. This is because a larger variance indicates greater variability in the sample, making it harder to draw a conclusion about the treatment effect.

Sample variance is a measure of how far a sample of data is spread out from its mean. It is calculated by taking the sum of the squared differences between each data point in the sample and the sample mean, and then dividing by the number of data points minus one.

A. If the sample variance is s² = 16, then the estimated standard error is SE = s/√n

= 16/√16

= 4

The value of the test statistic is t = (M - µ)/SE

= (33 - 30)/2

= 1.5.

The value of degrees of freedom is

df = n - 1

= 15.

The critical region value is tα = ± 1.753 for a two-tailed test with α = .05. Since 1.5 is less than 1.753, we fail to reject the null hypothesis and conclude that the treatment does not have a significant effect.

B. If the sample variance is s² = 64, then the estimated standard error is SE = s/√n

= 64/√16

= 16.

The value of the test statistic is t = (M - µ)/SE

= (33 - 30)/8

= 0.375.

The value of degrees of freedom is df = n - 1

= 15.

The critical region value is tα = ± 1.753 for a two-tailed test with α = .05. Since 0.375 is less than 1.753, we fail to reject the null hypothesis and conclude that the treatment does not have a significant effect.

C. Increasing the variance of the sample affects both the standard error and the likelihood of rejecting the null hypothesis. As the variance increases, the standard error increases, meaning the test statistic value must be larger to reject the null hypothesis.

In other words, the larger the variance, the less likely it is to reject the null hypothesis. This is because a larger variance indicates greater variability in the sample, making it harder to draw a conclusion about the treatment effect.

For more questions related to standard error

https://brainly.com/question/14467769

#SPJ1