What is the formula to find P(A) for a series of simple events (ex: tossing a coin and selecting a number at the same time)

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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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

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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Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

Non-parametric methods assume the sample used is the population and do not make assumptions about the underlying distribution of the population. Results obtained from non-parametric methods are specific to the sample used and cannot be generalized to the larger population.

The methods that assume the sample used is the population, and so results cannot be extrapolated beyond that particular sample, are known as non-parametric methods. Non-parametric methods do not make any assumptions about the underlying distribution of the population, and instead rely solely on the observed data. As a result, the results obtained from non-parametric methods are specific to the sample used and cannot be generalized to the larger population.

Examples  of non-parametric methods include the Wilcoxon rank-sum test, the Kruskal-Wallis test, and the Spearman's rank correlation coefficient test.

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An interval that is likely to contain the exact percent of all U.S adults who would support this policy if the margin of error is 2.2% is 67.8% and 72.2%.

Given that,

In a survey of 2000 U.S. adults, 70% said that they would support a national policy requiring rooftop solar panels to be installed on all new homes.

Margin of error = ±2.2%

Using this,

Interval of the exact percent = (70 - 2.2, 70 + 2.2)

                                               = 67.8% and 72.2%

Hence the interval is 67.8% and 72.2%.

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The complete question is given below.

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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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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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 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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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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Theorem 4.4.2 states that the only divisors of the integer 1 are 1 and -1. In other words, no other integer except 1 and -1 can divide 1.

To prove this theorem, we can use the definition of divisibility, which states that if a and b are integers, then a divides b if and only if there exists an integer k such that b = ak. Since 1 is the smallest positive integer, it has only two divisors, namely 1 and -1.

If a is a positive integer that divides 1, then a must be equal to 1, since it is the only positive integer that is smaller than or equal to 1. If a is a negative integer that divides 1, then a must be equal to -1, since it is the only negative integer that is greater than or equal to -1.

Thus, we have shown that the only divisors of 1 are 1 and -1, which proves Theorem 4.4.2. This theorem is a simple but important result in number theory, as it establishes a fundamental property of the number 1 and its divisors.

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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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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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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 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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[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]

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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Group A shows greater variability in mass than Group B.

Group A:

Masses: 4, 6, 8, 12, 14

Minimum: 4

Q1: (4+6)/2 = 5

Median (Q2): 8

Q3: (12+14)/2 = 13

Maximum: 14

Group B:

Masses: 6, 8, 10, 12, 14

Minimum: 6

Q1: (6+8)/2 = 7

Median (Q2): 10

Q3: (12+14)/2 = 13

Maximum: 14

Now let's construct the box plots for each group:

Group A encompasses the numeric figures 4, 5, 8, 13, and 14.

Group B encompasses the digits 6, 7, 10, 13, and 14.

We compare the groups:

Range (Group A): 14 - 4 = 10

Range (Group B): 14 - 6 = 8

IQR (Group A): Q3 - Q1 = 13 - 5 = 8

IQR (Group B): Q3 - Q1 = 13 - 7 = 6

With its range of 10 and IQR of 8, Group A exhibits a greater degree of variance in weight compared to Group B, which has a range of 8 and IQR of 6.

Thus, the variability in mass is higher for Group A.

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A scientist reports the information shown about the masses (in grams) of two groups of salamanders. Group A consists of salamanders with masses 4, 6, 8, 12, and 14 grams, and Group B consists of salamanders with masses 6, 8, 10, 12, and 14 grams. Construct a box plot for each data set. Which group of salamanders shows greater variability in mass, and explain how you know.

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 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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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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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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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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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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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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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].

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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