A straw is placed inside a rectangular box that is
6 inches by 6 inches by 10 inches, as shown. If
the straw fits exactly into the box diagonally
from the bottom left corner to the top right back
corner, how long is the straw? Leave your answer
in simplest radical form.
10 in.
I
6 in.
6 in.

Using the binomial theorem, we can find the coefficient of the term containing 2 in the expansion of (3 - 4)^23 without actually expanding the entire expression.

The binomial theorem states that for any two numbers a and b, and a positive integer n, the expansion of (a + b)^n can be written as the sum of the terms of the form C(n, r) * a^(n-r) * b^r, where C(n, r) represents the binomial coefficient.

In this case, we want to find the coefficient of the term containing 2 in the expansion of (3 - 4)^23. Let's denote this coefficient as C.

The formula for the binomial coefficient C(n, r) is given by:

C(n, r) = n! / (r! * (n - r)!)

Given that C = -27, we can set up the equation:

C = C(23, r) * 3^(23-r) * (-4)^r

Since we are interested in the term containing 2, we set r = 2:

-27 = C(23, 2) * 3^(23-2) * (-4)^2

Simplifying this equation will give us the value of C, which represents the coefficient of 2 in the expansion.

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The correct option is (b) sample size.

In the formula for calculating the standard deviation, the letter n represent  sample size.

What is standard deviation?

Standard deviation is a statistical standard measure in finance that, when applied to an investment's annual rate of return, sheds light on its historical volatility.

Some key features regarding the standard deviation are-

A square root of a value deduced from correlating data points to a population's collective mean is used to calculate standard deviation. The formula is:

Standard Deviation = \(\sqrt{\frac{summation n to i=1 (x_{i}-bar x )}{n-1} }\)

Where,

\(x_{i}\)= value of the i th point the the given data set.

\(barx\)= mean value

n = total number of data points.

Thus, the standard deviation, on the other hand, determines all ambiguity as risk, even when it is in the investor's favor, like above-average returns.

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Answer:B

Step-by-step explanation:

The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

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The residual for this day is -6, indicating that there are six packages missing beyond what the fraternities had. This means that not only were the 11 packages stolen, but there were also six additional missing packages.

1. We start with the total number of packages, which is 5 (as given in the question).

2. Then, we subtract the number of stolen packages, which is 11 (as given in the question).

3. Residual = 5 (total number of packages) - 11 (number of stolen packages).

4. Performing the subtraction, we get a result of -6.

5. A negative residual value indicates that there are missing packages beyond the ones that were stolen.

6. Therefore, on this day, besides the 11 stolen packages, there are an additional six missing packages.

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Answer:

The first one is B

Step-by-step explanation:

if you count how many faces or sides it has its 5

Answer:

1. B

2. D

3. D

4. A

5. C

REMEMBER TO DOUBLE-CHECK JUST IN CASE.

Answer:

I only / 1 only

Step-by-step explanation:

Function rules: no same x-values and must pass vertical line test

1: all different x-values

2: has two of the same x-values

3: doesn't pass vertical line test

Hopefully this helps!

Brainliest please?

Answer:

1 only (I hope im right)

Step-by-step explanation:

Hope this helps:)

Answer:

C = 9.5 + 1.25t

Step-by-step explanation:

C = 9.5 + 1.25t

16 = 9.5 + 1.25t

6.5 = 1.25t

6.5/1.25 = t

5.2 = t

you cant have 0.2 toppings so 5 is the max number of toppings Jonas can have

Answer:

Step-by-step explanation:

2 cus why not

Answer:

D. -2x+12

Step-by-step explanation:

you combine all values with x because they are like terms.

:) hope this helps

Answer:

-2x+12

D is the best answer.

The rectangle with dimensions 21 m by 21 m has the largest area among rectangles with a perimeter of 84 m.

To find the dimensions of a rectangle with a perimeter of 84 m that maximizes the area, we need to use the properties of rectangles.

Let's assume the length of the rectangle is l and the width is w.

The perimeter of a rectangle is given by the formula: 2l + 2w = P, where P is the perimeter.

In this case, the perimeter is given as 84 m, so we can write the equation as: 2l + 2w = 84.

To maximize the area, we need to find the dimensions that satisfy this equation and give the largest possible value for the area. The area of a rectangle is given by the formula: A = lw.

Now we can solve the perimeter equation for l: 2l = 84 - 2w, which simplifies to l = 42 - w.

Substituting this expression for l into the area equation, we get: A = (42 - w)w.

To maximize the area, we can find the critical points by taking the derivative of the area equation with respect to w and setting it equal to zero:

dA/dw = 42 - 2w = 0.

Solving this equation, we find w = 21.

Substituting this value of w back into the equation l = 42 - w, we get l = 42 - 21 = 21.

Therefore, the dimensions of the rectangle that maximize the area are l = 21 m and w = 21 m.

In summary, the dimensions of the rectangle are 21 m by 21 m, so the answer is A. 21, 21.

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Answer: 4.5

Step-by-step explanation:

Answer: x = -3, x=+/2=1.4142

Answer:

-5,3

Step-by-step explanation:

The net payoff obtained during the game is $40. Option D is the correct answer.

The term "net payoff" describes the profit or loss realised from a transaction or operation after deducting all costs, charges, and taxes. It is determined by deducting the total cost of the activity or investment from the total income received. A gain is shown by a positive net reward, whereas a loss is indicated by a negative net payoff.

Given that, each round cost $20, and each win gives $50.

Now, for 3 rounds the total cost is:

$20 x 3 = $60

After winning the two round the win amount is:

$50 x 2 = $100

Now, the net payoff is:

$100 - $60 = $40.

Hence, the net payoff obtained during the game is $40. Option D is the correct answer.

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a) If any values in the data set are greater than the upper boundary, then those values are the upper outliers.

b) If any values in the data set are less than the lower boundary, then those values are lower outliers.

The complete question is attached with an answer.

If a number in distribution is more than 1.5 times the length of the box away from either of the upper and lower quartile of the distribution, then that number is said to be an outlier.  

The lower quartile is  and the upper quartile of distribution is

Then lower boundary is given by \(=Q_1-1.5\times IQR\)

The Upper boundary is given by  \(=Q_3+1.5\times IQR\)

If any number or value of the distribution is greater than  \(=Q_3+1.5\times IQR\)  then that is called Upper Outlier.

Similarly, if any value or number of the distribution is less than \(=Q_1-1.5\times IQR\) then that is called Lower Outlier.

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Answer:

D. 105

Step-by-step explanation:

D

Answer:

y = 0

Step-by-step explanation:

can you post the graph picture so this question can be answered better?

The change in the elevation is 0.275 miles.

An elevation simply means the her that above the sea level. It's used to describe a geographical location.

Thethe change in elevation from the top of the grade to the bottom of the grade in feet will be:

= Percentage of change × Length given

= 5% × 5.5 miles

= 0.05 × 5.5 miles

= 0.275 miles.

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Answer:

$6.96

Step-by-step explanation:

5.25% of 5.79

5.79 × 5.25/100 = $0.303975 or $0.30

15% of 5.79

5.79 × 15/100 = $0.8685 or $0.87

total

$5.79 + $0.30 + $0.87 = $6.96

we can calculate the test statistic as follows:

t = (mean A - mean B) / √((sA² / nA) + (sB² / nB))

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

To determine if the data suggests that the two methods provide the same mean value for natural vibration frequency, we can perform a hypothesis test.

Let's define the hypotheses:

H0: The mean value for natural vibration frequency using Method A is equal to the mean value using Method B.

H1: The mean value for natural vibration frequency using Method A is not equal to the mean value using Method B.

We can use a two-sample t-test to compare the means. We calculate the test statistic and the p-value to make our decision.

If we have the sample means, standard deviations, and sample sizes for both methods, we can calculate the test statistic as follows:

t = (mean A - mean B) / √((sA² / nA) + (sB² / nB))

Here, mean A and mean B are the sample means, sA and sB are the sample standard deviations, and nA and nB are the sample sizes for Methods A and B, respectively.

The p-value corresponds to the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

To find the interval for the p-value, we need more information such as the sample means, standard deviations, and sample sizes for both methods. With that information, we can perform the calculations and determine the p-value interval.

Hence, we can calculate the test statistic as follows:

t = (mean A - mean B) / √((sA² / nA) + (sB² / nB))

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Complete question:

do the data suggest that the two methods provide the same mean value for natural vibration frequency? find interval for p-value: enter your answer; p-value, lower bound

The expected value of buying one ticket in this charity raffle is $0.42. This means that, on average, a person can expect to win approximately $0.42 if they purchase a single ticket.

To calculate the expected value, we need to consider the probability of winning each prize multiplied by the value of the prize. Let's break it down:

- There is a 1/5000 chance of winning the $600 prize, so the expected value contribution from this prize is (1/5000) * $600 = $0.12.

- There are 3/5000 chances of winning the $300 prize, so the expected value contribution from these prizes is (3/5000) * $300 = $0.18.

- There are 5/5000 chances of winning the $40 prize, so the expected value contribution from these prizes is (5/5000) * $40 = $0.04.

- Finally, there are 20/5000 chances of winning the $5 prize, so the expected value contribution from these prizes is (20/5000) * $5 = $0.08.

Summing up all the expected value contributions, we get $0.12 + $0.18 + $0.04 + $0.08 = $0.42.

Therefore, if you buy one ticket in this raffle, the expected value of your winnings is $0.42.

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Answer:

A) 2 units

Step-by-step explanation:

Given;

x² + y² - 4x - 4y + 4 = 0

Consider general circle equation;

(x - h)² + (y - k)² = r²

where;

(h , k ) is the center of the circle

r is the radius of the circle

x² + y² - 4x - 4y + 4 = 0

subtract 4 from both sides of the equation

x² + y² - 4x - 4y  =  - 4

square half of coefficient of x and y, and add them to both sides of the equation

x² +  - 4x + (-2)² +  y² - 4y + (-2)² = - 4 +  (-2)² +  (-2)²

factorize x and y

(x - 2)² + (y - 2)² = - 4 + 4 + 4

(x - 2)² + (y - 2)² = 4

(x - 2)² + (y - 2)² = 2²

Compare this final equation to general equation of a circle

(x - 2)² + (y - 2)² = 2²  

(x - h)² + (y - k)² = r²

r = 2

Thus, the length of a radius of the circle is 2 units

Answer:

67.5

Step-by-step explanation:

Take the amount that you deposited and multiply it by the interest rate. Then would multiply it by 3 cause its 3 years that you would be getting that interest.

900 * 0.025 = 22.5

22.5 * 3 = 67.5

Answer:

6b

Step-by-step explanation:

6 + b = 6b

The statement which is true about the end behaviour of the graphed function is; As the x-values go to positive infinity, the function’s values go to positive infinity.

The graph given according to the task content is described to have its first minimum at (-2,0), and then a maximum at; (-0.5, 5) and finally a minimum at; (1.05, -41).

Additionally, since the graph has 3 zeroes as given, it follows that the graph is that of a cubic function which takes the w-form.

Consequently, it can be inferred from the statements above that; As the x-values go to positive infinity, the function’s values go to positive infinity.

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Answer:

A

Step-by-step explanation:

edge 23

Two values have frequency 2, so both are modes. They are 5 and 6. Therefore, the mode is 5 and 6.

Given measure: 3, 5, 4, 6, 10, 5, 6, 9, 2, 13.(D) To calculate \(x_2\), first we need to sort the data in ascending order: 2, 3, 4, 5, 5, 6, 6, 9, 10, 13

Now, we need to find the median, which is the middle value of the data. Since the data has even number of values, we will calculate the mean of middle two values, that is:(5+6)/2 = 5.5 Therefore, \(x_2 = 5.5\).\( \frac{2}{x}= \) To find the value of x, we will first cross-multiply and then take the reciprocal of both sides:\[\frac{2}{x} = y \Rightarrow 2 = xy \Rightarrow x = \frac{2}{y}\] Therefore, \( \frac{2}{x}= \frac{2}{y}\).

(b) To calculate Fried m, we will use the formula: \[f_m = L + \frac{(n/2 - F)}{f} \times c\]where L is the lower limit of the modal class, F is the cumulative frequency of the class preceding the modal class, f is the frequency of the modal class, c is the class interval, and n is the total number of values.

First, we will calculate the class interval:c = (upper limit of class - lower limit of class) = (7-6) = 1 Next, we will construct a frequency table to find the modal class:| Class Interval | Frequency ||-------------------|------------|| 2-3 | 1 || 3-4 | 1 || 4-5 | 1 || 5-6 | 2 || 6-7 | 2 || 7-8 | 1 || 9-10 | 1 || 10-11 | 1 || 13-14 | 1 |The modal class is the class with highest frequency.

Here, two classes have frequency 2, so both are modes. They are 5-6 and 6-7.

Therefore, L = 5, F = 2, f = 2, n = 10, and c = 1. Substituting the values, we get:\[f_m = L + \frac{(n/2 - F)}{f} \times c = 5 + \frac{(10/2 - 2)}{2} \times 1 = 7\] Therefore, Fried m = 7.

(c) To find the mode, we look for the value(s) with highest frequency. Here, two values have frequency 2, so both are modes. They are 5 and 6. Therefore, the mode is 5 and 6.

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Answer:

a percent is a variable of proportionality describing the part of the whole.

The percentage of any quantity can be defined as the product of that quantity with the percent value divided by 100. The complete phrase of the given question is " a percent is a  constant of proportionality describing the part of the whole."

The percentage can be defined as the proportion of any quantity as a part of the whole. To change the percentage into a fraction it is divided by 100.

The proportionality constant is a quantity that is used to change the proportionality relation into an equation.

And, the part of any quantity is always less than the whole.

Thus, the given question can be rephrased as,

A percent is a  constant of proportionality describing the part of the whole.

Hence, for the given statement the correct choice of words in sequence is  constant, part and whole.

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Answer:

4 snacks

Step-by-step explanation:

44 from the overall date - 25 from the movie = 19 dollars. 19 divided by four is 4.75. I'm not sure if this is a real question and you can have a decimal of a snack but you can just write approximately four snacks.

The solution is: given below.

Given data :

AB = 15

BC = 8

AC = 6

1) sinA = perpendicular / hypotenues

In the given triangle , perpendicular is BC which is always opposite to the angle .

sinA = BC / AB

= 8 / 15

2) cosA = Base / Hypotenues

= AC / AB

= 6 / 15

= 2 / 5

3) tanA = perpendicular / base

= BC / AC

= 8 / 6

= 4 / 3

4) sinB = perpendicular / hypotenues

In given triangle , perpendicular is AC which is according to the angle which we have to find.

sinB = AC / AB

= 6 / 15

= 3 / 5

5) cosB = base / hypotenues

= BC / AB

= 8 / 15

6) tanB = perpendicular / base

= AC / BC

= 6 / 8

= 3 / 4

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complete question:

I. Find the following ratio: B 1. Sin A 4. Sin B 2. Cos A 5. Cos B 3. Tan A 6.Tan B 8 15 С 6 A