What conditions must be satisfied to make the probabilities from a binomial probability distribution approximated well by using a normal distribution with a mean μ = np, and a standard deviation σ = √(npq)?

T-tests are used to test for differences between group means.

So, the correct answer is A.

T-tests can be used to compare two groups, or multiple groups, and can be either independent or dependent samples.

T-tests are often used in research studies to analyze data and draw conclusions about the differences between groups.

It is important to note that T-tests assume normal distribution of data and homogeneity of variance between the groups being compared.

In other words, the variances of the groups should be similar enough to accurately compare their means. If the variances are not equal, then other statistical tests such as Welch's T-test should be used instead

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The maximum range is 20.

As, per the data the number of observations of each interval is:

1 to 5: 2 observations.

6 to 10: 5 observations.

11 to 15: 2 observations.

16 to 20: 6 observations.

21 to 25: 1 observations.

Here are two similarly high bins, hence the distribution can be said to be bimodal.

The maximum range is

= 25 - 5

= 21 - 1

= 20.

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The correct answer is d. num1 = 4, num2 = 4.

After executing the method with arguments num1 and num2, the value of num2 is set to the value of num1 (which is 4) and num1 is set to 0 within the method. However, these changes are local to the method and do not affect the values of num1 and num2 in the client code. Therefore, num1 remains 4 and num2 becomes the returned value from the method, which is 4.

Here's the step-by-step explanation:

1. The method m() takes two parameters, x and y, and sets y equal to x and x equal to 0.
2. The method then returns the value of y.
3. In the client code, num1 is set to 4 and num2 is set to 9.
4. When calling m(num1, num2), x becomes 4 (value of num1) and y becomes 9 (value of num2).
5. Inside the method, y is set to the value of x, which is 4. Then x is set to 0.
6. The method returns the value of y, which is 4.
7. The returned value (4) is assigned to num2 in the client code.
8. The final values are num1 = 4 (unchanged) and num2 = 4 (updated).

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[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=33\\ \theta =1.5 \end{cases}\implies s=(33)(1.5)\implies s=49.5[/tex]

Brenda should poll at least 847 students to create a 98% confidence interval with a margin of error of at most 4%.

To calculate the sample size needed for a 98% confidence interval with a margin of error of at most 4%, we'll need to use the following formula:
[tex]n = (Z^2 * p * (1-p)) / E^2[/tex]
where:
- n is the sample size
- Z is the Z-score corresponding to the desired confidence level (98% in this case)
- p is the estimated proportion of students with job offers before graduation (we'll use 0.5 for a conservative estimate)
- E is the margin of error (4% or 0.04)
Here's a step-by-step process to calculate the sample size using Excel:
Find the Z-score for a 98% confidence interval:

Using the NORM.S.INV function in Excel, enter "=NORM.S.INV(0.99)" to get the Z-score for a 98% confidence interval. The result is approximately 2.33.

Use the formula with the given values:

In a new cell, enter the formula with the calculated Z-score,

p=0.5,

and E=0.04:
 [tex]=(2.33^2 * 0.5 * (1-0.5)) / 0.04^2[/tex]

Press Enter to calculate the sample size:

After entering the formula, press Enter to get the sample size.

The result is approximately 846.25.
Round up the sample size:

Since you cannot poll a fraction of a student, round up the sample size to the nearest whole number. In this case, round up 846.25 to 847.

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Answer:

Step-by-step explanation:

im in 7th so i can help.

Any ways heres an example 2( 5 + 7)

what your going to do is take the number outside the bracket which is 2

and multipy it with 5 AND 7

2x5 and 2x7 so thats 10 and 14 THEN you add them together 10 +14 = 24

make sure you multiply whatever number outside the bracket with EACH of the numbers inside the bracket MULTIPLY FIRST

The surface area of the rectangular prism is 166 in².

To arrive at the surface area, we will use the following formula which gets the area for the right, left, and bottom parts.

Surface Area = 2(wl+hl+hw)

Surface Area = 2 (6*2 + 9*2 + 9*6)

SA = 2(12 + 18 + 54)

SA =2(84)

SA = 166 in²

So, the surface area is 166 in².

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The points that form a linear function must be collinear with respect to each other.

The set of points are not given. A linear function is of the form -

y = mx + c

In this equation, we can write -

{m} : slope of the line

{c} : the y - intercept

Now, the points that form a linear function must be collinear with respect to each other. This means that the slope of the line joining the two consecutive points should be equal.

Therefore, the points that form a linear function must be collinear with respect to each other.

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The length of the major axis of the ellipse x² + 16y² - 96y + 128 = 0 will be 8 units.

Given that:

Equation, x² + 16y² - 96y + 128 = 0

It is taken from the cone by cutting it at an angle.

Convert the equation into standard form, then we have

x² + 16y² - 96y + 128 + 16 = 16

x² + 16(y² - 6y + 9) = 16

x²/16 + (y - 3)²/1 = 1

The length of the major axis of the ellipse x² + 16y² - 96y + 128 = 0 will be given as,

⇒ 16 / 2

⇒ 8

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The given terms represent various logical statements and operations. ¬A ∧ B → C implies that if "not A" and "B" are both true, then "C" is true. C ∨ B means either "C" or "B" or both must be true.

1. ¬A ∧ B → C: This term represents a logical statement where if "not A" (¬A) and "B" are both true, then it implies (→) that "C" is also true.
2. C ∨ B: This term represents a logical disjunction, meaning that either "C" or "B" or both must be true.
3. ¬(C ∧ D): This term represents the negation (¬) of the conjunction of "C" and "D". In other words, it is not true that both "C" and "D" are true.
4. D: This term simply represents a logical variable, which can be either true or false.
The given terms represent various logical statements and operations. ¬A ∧ B → C implies that if "not A" and "B" are both true, then "C" is true. C ∨ B means either "C" or "B" or both must be true. ¬(C ∧ D) denotes that it's not true that both "C" and "D" are true, and "D" is a logical variable that can be either true or false.

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Tiffany should have expected the spinner to land in the orange section 10 more times.

To find out how many more times Tiffany should have expected the spinner to land in the orange section, we need to determine the expected number of times the spinner would land in the orange section based on the given information.

Tiffany spun the spinner 96 times, and it landed in the orange section 10 times. To find the expected number of times the spinner would land in the orange section, we can calculate the proportion of spins that landed in the orange section.

Proportion of spins in the orange section = (Number of orange spins) / (Total number of spins)

Proportion of spins in the orange section = 10 / 96

Now, to find the expected number of orange spins, we multiply the proportion by the total number of spins:

Expected number of orange spins = Proportion of spins in the orange section * Total number of spins

Expected number of orange spins = (10 / 96) * 96

Expected number of orange spins = 10

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1. The norm of E is the greatest absolute row sum because E is the identity matrix. The single non-zero element in each row of E is 1, so the absolute maximum row sum of E is 1. Consequently, ||E|| 1.

2. (2) By applying the operator standard definition, we get ||A-1|| = max||A-1x||/||x||, where max is computed for all vectors with x-values ​​that are non-zero. As a result of A being invertible, there is A-1, and we can multiply both sides of A-1A = I by A to get A-1. The inequality is then ||A-1x|| = ||A-1Ix|| = ||a-1(ax)|| ||A-1|| ||axe|| For any non-zero x, where the operator norm is defined. to both sides ||x|| dividing by, we get

||A-1|| ≤ ||A-1|| ||A||.

We get both sides ||A|| can be divided by ||A-1||/||A|| 1/||A|| Since A is invertible and its value is non-zero. We divide both sides by ||A||-1: ||A-1|| We get the desired result by multiplying by ||A||-1.

(3) Because E is the identity matrix, its norm is set up to be the largest possible complete row sum of E. The single non-zero element in each row of E is 1, so the absolute maximum row sum of E is 1. As a result, ||E|| = 1.

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The set of all possible outcomes of a random experiment is called the sample space associated with the experiment. Option A.

The sample space encompasses all the potential outcomes that could occur when conducting the experiment. It represents a complete and exhaustive collection of all the possible results or states that the experiment can produce.

Each outcome within the sample space is a distinct element or member of the set, allowing for the analysis and calculation of probabilities for various events and combinations of outcomes. The sample space provides a foundational framework for understanding and quantifying the probabilities associated with the random experiment.

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We can calculate the probabilities of getting a specific number of science majors in the class, as well as the expected number of science majors.

The number of students that are science majors can be thought of as a binomial random variable if the following conditions are met:

Under these conditions, we can model the number of science majors as a binomial random variable, which is the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, each student is a trial, and the probability of success is the probability of being a science major. The binomial distribution describes the probability of getting a specific number of successes in a fixed number of trials, given a specific probability of success.

This makes the binomial distribution a useful tool for modeling situations where we are interested in the number of successes in a fixed number of independent trials, such as the number of students who are science majors in a class.

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The probability that the sample mean will be larger than 49 can be calculated using the standard normal distribution.



Since we know the population mean and standard deviation, we can use the central limit theorem to assume that the distribution of sample means is normal with a mean of 52 and a standard deviation of 20/√50) = 2.83.

To find the probability that the sample mean will be larger than 49, we can standardize the distribution using the z-score formula:

z = (sample mean - population mean) / (standard deviation / √(sample size))

z = (49 - 52) / (20/√(50)) = -1.77

Using a standard normal distribution table or calculator, we can find that the probability of z being less than -1.77 is approximately 0.0384.

Therefore, the probability that the sample mean will be larger than 49 is:

1 - 0.0384 = 0.9616

or 96.16%.

Calculation:

z = (49 - 52) / (20/√50)) = -1.77

Probability of z being less than -1.77 = 0.0384

Probability of sample mean being larger than 49 = 1 - 0.0384 = 0.9616 or 96.16%.

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The problem is to determine if a singly linked list is a palindrome. This can be achieved by using a two-pointer approach to find the middle of the linked list, reversing the second half, and then comparing the first half with the reversed second half.

To determine if a singly linked list is a palindrome, we can use a two-pointer approach.

First, we need to find the middle of the linked list. We can do this by using two pointers, one moving one step at a time (slow pointer) and another moving two steps at a time (fast pointer). When the fast pointer reaches the end of the linked list, the slow pointer will be pointing to the middle of the linked list.

Next, we need to reverse the second half of the linked list. We can do this by using another pointer to traverse the second half of the linked list and reversing the links between the nodes.

Finally, we can compare the first half of the linked list with the reversed second half of the linked list. If they are the same, then the linked list is a palindrome.

Here's the Python code to implement this approach:

```
class ListNode:
   def __init__(self, val=0, next=None):
       self.val = val
       self.next = next

def isPalindrome(head: ListNode) -> bool:
   # Find the middle of the linked list
   slow = fast = head
   while fast and fast.next:
       slow = slow.next
       fast = fast.next.next
   
   # Reverse the second half of the linked list
   prev, curr = None, slow
   while curr:
       curr.next, prev, curr = prev, curr, curr.next
   
   # Compare the first half with the reversed second half
   p1, p2 = head, prev
   while p2:
       if p1.val != p2.val:
           return False
       p1, p2 = p1.next, p2.next
   
   return True
```

In this code, we define a `ListNode` class to represent a node in the linked list. The `isPalindrome` function takes the head of the linked list as input and returns a boolean indicating whether or not the linked list is a palindrome.

We first find the middle of the linked list using the two-pointer approach. We then reverse the second half of the linked list using a `prev`, `curr` pointer approach. Finally, we compare the first half of the linked list with the reversed second half of the linked list using two pointers `p1`, `p2`. If the values of the nodes at `p1` and `p2` differ at any point, we return `False`. If we reach the end of the linked list without finding a mismatch, we return `True`.

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The equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM

We know, In order to find the measure of LM, we will take the ratio of the sides of the similar triangles.

Using the equation as

DF/EF = LK/LM

DF/LK = EF/LM

So, 9/13.5 = 14/LM

Thus, the equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM

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Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

The imperial unit of length are inches, feet, miles etc, the imperial units of mass are pounds, ounces and the imperial units of capacity are pints, quarts, gallons etc

The imperial system of measurement is defined as a system of measuring quantities such as length, mass, volume, area, etc in the units that are commonly used in the UK, and other commonwealth countries. The units used in this system include inches, feet, pounds, gallons, tons, fluid ounces,

The imperial unit of length could be inches, feet, miles etc.

The imperial unit of mass is pounds, ounces

The imperial unit of capacity is pints, quarts, fluid ounces etc.

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7 masons and 3 helpers working together will earn in 4 days = 4*5600 = Rs. 22400.

7 masons and 3 helpers working together will earn in 4 days = 4*(7*(1-day earning of a mason) + 3*(1-day earning of a helper))

Let the daily earning of a mason be M.

Therefore, the daily earning of a helper will be M-150.

From the first statement, we know that:

3M + 2(M-150) = 2950

5M = 3200

M = 640

So the daily earning of a mason is Rs. 640 and the daily earning of a helper is Rs. 490.

Therefore, 7 masons and 3 helpers working together will earn in 1 day = 7640 + 3490 = Rs. 5600.

So, 7 masons and 3 helpers working together will earn in 4 days = 4*5600 = Rs. 22400.

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We would expect the size of the population to increase by 12 individuals.

Here are the terms we'll be using:
- Initial population size: 100 individuals
- Per capita birth rate: 0.25
- Per capita death rate: 0.13
To find the expected increase in population size, follow these steps:
Calculate the net per capita growth rate by subtracting the per capita death rate from the per capita birth rate:
Net per capita growth rate = Per capita birth rate - Per capita death rate
Net per capita growth rate = 0.25 - 0.13
Net per capita growth rate = 0.12.

Multiply the net per capita growth rate by the initial population size to find the expected increase in the number of individuals:
Expected increase = Net per capita growth rate × Initial population size
Expected increase = 0.12 × 100
Expected increase = 12 individuals.

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The volume of the rectangular prism is 882 cubic units.

To find the volume of the rectangular prism, we need to first determine its dimensions. Since there are 42 slices, and each slice is made up of 21 unit cubes, we can divide 42 by 21 to get the number of cubes along one dimension.

This gives us 2, which means that the rectangular prism is 2 units wide.
To find the other two dimensions, we need to know how many slices there are along each of these dimensions. Since there are 42 slices in total, and we know that each slice is made up of 21 unit cubes, we can divide 42 by 21 to get the number of slices along one of the other dimensions.

This gives us 2, which means that the rectangular prism is 2 units high.
Finally,

We need to determine the length of the rectangular prism.

To do this, we can divide the total number of unit cubes by the product of the width and height.

This gives us 42 x 21 = 882, and dividing this by 4 (since the width and height are each 2) gives us 220.

Therefore, the rectangular prism is 220 units long.
To calculate the volume of the rectangular prism, we simply multiply the width, height, and length together.

This gives us:
2 x 2 x 220 = 880

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The statements that complete the proof of similar triangles are (1) AA criterion for similarity and (1) segment addition

From the question, we have the following parameters that can be used in our computation:

The incomplete proof

In proof (2), we have

Corresponding angles are congruent

This represents the AA similarity

So, the first blank can be completed with (1) AA criterion for similarity

In proof (5), we have

AB = AD + DB and CB = CE + EB

This represents addition of segments

So, the second blank can be completed with (1) segment addition

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Answer: h = 14

Step-by-step explanation:

   To solve, we will isolate the variable h.

   Given:

7h - 5(3h - 8) = -72

   Distribute the -5:

7h - 15h + 40 = -72

   Combine like terms:

-8h + 40 = -72

   Subtract 40 from both sides of the equation:

-8h = -112

   Divide both sides of the equation by -8:

h = 14

A variable declared as `final` in Java cannot be changed after it is initialized and acts as a constant. Static variables are used to share a common value across all instances of a class.

In Java, the `final` keyword is used to declare a variable that cannot be changed after it is initialized. Such a variable is often referred to as a constant. If a variable is declared as `final`, it must be initialized at the time of declaration, and once initialized, its value cannot be changed. Therefore, if a `final` variable is declared and initialised , but never changed, it will effectively act as a constant throughout the program.

Static variables are used to share a common value across all instances of a class, and can be changed during the program's execution. Literals are used to represent fixed values in code, such as string or numeric literals. Formal parameters are variables used to pass values into a method, and their values can be changed by the method code.

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Answer: 15 m²

Step-by-step explanation:

Area of a parallogram is:

A=bh       here b=5 and h=3    b, base is the bottom line

                                                 h, is the straight line going up and dow

A=(5)(3)

=15 m²

At the end of the second year, Alfonso has saved $4,512.92 in his college savings account.

To complete the table, we can use the formula for compound interest:

A = [tex]P(1+r/n)^{nt}[/tex]

where:

A is the amount after t years

P is the principal amount (initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

We are given that the principal amount is $4,300, the annual interest rate is 2.3%, and the interest is compounded annually. We need to find the amount after 1 year and 2 years.

Year Amount

0 $4,300

1 $4,404.90

2 $4,512.92

To find the amount after 1 year, we can substitute the values into the formula:

A = [tex]P(1+r/n)^{nt}[/tex]

A = $4,300(1 + 0.023/1[tex])^{1*1}[/tex]

A = $4,404.90

Therefore, the amount after 1 year is $4,404.90.

To find the amount after 2 years, we can substitute the values into the formula:

A = [tex]P(1+r/n)^{nt}[/tex]

A = $4,300(1 + 0.023/1[tex])^{1*2}[/tex]

A = $4,512.92

Therefore, the amount after 2 years is $4,512.92.

Thus, at the end of the second year, Alfonso has saved $4,512.92 in his college savings account.

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Answer:

[tex]C = 43.96 \text{ miles}[/tex]

Step-by-step explanation:

The circumference (perimeter) of a circle is defined as:

[tex]C = \pi \cdot d[/tex],

where [tex]d[/tex] is the circle's diameter.

We can plug in 14 for the diameter and 3.14 for π, then solve for C.

[tex]C = 3.14 \cdot 14[/tex]

[tex]C = 43.96 \text{ miles}[/tex]

Note that we can also write the circumference formula as:

[tex]C = 2\pi r[/tex]

because [tex]d = 2\cdot r[/tex].