i need help with binomial expansion pls, the question is attached

(a) To guarantee that at least 2 people have a birthday on the same day of the week, at least 8 people must be selected.

(b) To guarantee that at least 6 people have a birthday on the same day of the week, at least 43 people must be selected.

(a) To find the minimum number of people needed to guarantee that at least 2 of them have a birthday on the same day of the week, we can apply the Pigeonhole Principle.

There are 7 days of the week, so each person can have their birthday on one of these 7 days. If we select 8 people, then there are 8 pigeons (people) and 7 pigeonholes (days of the week). Since we have more pigeons than pigeonholes, by the Pigeonhole Principle, at least 2 people must have their birthday on the same day of the week.

(b) Similarly, to find the minimum number of people needed to guarantee that at least 6 of them have a birthday on the same day of the week, we apply the Pigeonhole Principle. Again, there are 7 days of the week, and each person can have their birthday on one of these 7 days.

If we select 43 people, then we have 43 pigeons (people) and 7 pigeonholes (days of the week). Since we have more pigeons than pigeonholes, by the Pigeonhole Principle, at least 6 people must have their birthday on the same day of the week.

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Answer:

6

Step-by-step explanation:

Let the number be " n ".

4 times a number,

= 4n

The difference between 4 times a number and 6

= 4n - 6

The difference between 4 times a number and 6 is 18,

4n - 6 = 18

4n = 18 + 6

4n = 24

n = 24 / 4

n = 6

The value of "n" that satisfies the equation is n = 6.

Option B is the correct answer.

We have,

To solve the equation "The difference between 4 times a number and 6 is 18," let's define the unknown number as "n."

The difference between 4 times the number and 6 can be expressed as "4n - 6."

According to the given equation, this expression equals 18:

4n - 6 = 18

To solve for "n," we will isolate the variable by performing the necessary algebraic steps:

Add 6 to both sides of the equation:

4n - 6 + 6 = 18 + 6

This simplifies to:

4n = 24

Next, divide both sides of the equation by 4 to isolate "n":

(4n) / 4 = 24 / 4

This simplifies to:

n = 6

Therefore,

The value of "n" that satisfies the equation is n = 6.

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In a vertical stretch the image will give the shape in option D

A "vertical stretch" is a transformation in mathematics that stretches or compresses a graph along the vertical axis. It is the opposite of a vertical compression, which squeezes a graph along the vertical axis.

In general, a vertical stretch of a function y = f(x) is given by y = kf(x), where k is a constant greater than 0.

If k > 1, then the function is stretched vertically, and if 0 < k < 1, then the function is compressed vertically.

In the problem the value of k is 2, the x values remain same ut the y values will stretch further

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Answer:

its c

Step-by-step explanation:

a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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If the value stated by a null hypothesis is within the confidence interval, then the decision would have likely been to retain the null hypothesis.

In hypothesis testing, the null hypothesis represents the default assumption or the claim that there is no significant difference or relationship between variables. The confidence interval, on the other hand, provides a range of plausible values for the population parameter based on sample data. If the value stated by the null hypothesis falls within the confidence interval, it means that the null hypothesis value is considered plausible or consistent with the observed data.

In this case, there is insufficient evidence to reject the null hypothesis, and the decision would be to retain it. On the other hand, if the null hypothesis value is outside the confidence interval, it suggests that the null hypothesis is unlikely, and the decision would be to reject it in favor of an alternative hypothesis.

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The value in the leftmost node in the right subtree of the root is 10.

To determine the value in the leftmost node in the right subtree of the root in the given binary search tree, we need to construct the tree using the given integers: 4, 10, 12, 54, 19, 27, 7, 2.

The binary search tree is constructed based on the property that all values in the left subtree of a node are less than the node's value, and all values in the right subtree are greater than the node's value.

Starting with the root node, which is 4, we construct the tree as follows:

     4

   /   \

  2    10

        \

         12

           \

           19

             \

             27

               \

               54

The right subtree of the root contains the values 10, 12, 19, 27, and 54. The leftmost node in this subtree is 10.

Therefore, the value in the leftmost node in the right subtree of the root is 10.

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Answer:

Situation 2 (B)

Step-by-step explanation:

I think it would be B since the power of the gear increases proportionally with the radius.

D.

Its the only one going down 3 and over 1.

The answer would be D because it says -3 and not just 3.

The total budget spent by the group of friends on the student film was $600

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let x represent the total budget for the student film.

They spent all their budget on props and equipment. Hence:

Total budget = Cost of props + cost of equipment

They spent $192 on props, and 68% of the total budget on equipment. Hence:

192 + 68% of x = x

192 + 0.68x = x

0.32x = 192

x = 600

The total budget was $600

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The total budget for their student film is $600

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

In this case, the group of friends were working on a student film, they spent all their budget on props and equipment and spent $192 on props, and 68% of the total budget on equipment

Let C represents the total budget for their student film. Thus, we can write:

C = 192 + 68%C

C = 192 + 0.68C

C - 0.68C = 192

0.32C = 192

C = 192/0.32

C = $600

Therefore, the total budget is $600

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Answer:

x=11

Step-by-step explanation:

Please see attached image.

Answer: x = 11

Step-by-step explanation:

a) bottom triangle, bottom right angle: Using Linear Pair Postulate, 180° - 114° = 66°

b) bottom triangle, top angle: Congruent sides implies congruent angles = 66°

c) bottom triangle, bottom left angle: Using the Triangle Sum Theorem, 66° + 66° + y = 180° --> y = 48°

d) top triangle, bottom angle: Using Complimentary Angles Theorem, 90° - 48° = 42°

Congruent sides implies congruent angles:

42° = ∠2

42 = 2x + 20

22 = 2x

11 = x

The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.

An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.

Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).

The given interval is [1, 2]

The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'

The given statement is 'false'.

This is beacuse, an interval consists set of all the real values in between the two values given.

So, according to the definition, there are not only the end values but also many real values in between them.

Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.

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The value of the t test is 13.36, we have to conclude that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

H0: u = 24000

H1: u > 24000

we have n = 84 homes

bar x = 27500

s = 2400

Next we have to find the test statistic

The formula for this is given as

\(t = \frac{x-u}{s/\sqrt{n} }\)

When we out in the values we would have

\(t = \frac{27500-24000}{2400/\sqrt{84} }\)

This would give us the answeer of the t test as

t test = 13. 3658

We have alpha = 0.02

the degree of freedom = 84 - 1 = 83

we have to find tα/2, df

=  ±2.0865

Given that the value of the test statistic is greater than critical value we would have to then reject the null hypothesis.

Hence the conclusion that we can make is that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

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Answer:

Step-by-step explanation:

Student's t test for correlated groups reduces to Student's t test for single samples using difference scores. Therefore, the correct answer is (b).

In a t test for correlated groups (also known as paired-samples or dependent-samples t test), the same group of participants is measured twice, under two different conditions or at two different times. The difference between the two measurements for each participant is calculated and used as the sample data. The t test for correlated groups compares the mean difference score to zero to determine if there is a significant difference between the two conditions or times.

This can be seen as equivalent to a t test for single samples using difference scores, where the mean difference score is compared to a known or hypothesized value of the population mean difference. In fact, the formula for calculating the t statistic is the same in both cases.

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Answer:

the answer is D

Step-by-step explanation:

edu 2021

Answer:

250+20 = 270 cents or $2.70

Step-by-step explanation:

Each quarter is 25 cents

Each dime is 10 cents

Answer : 1618

Step-by-step explanation: add 128 and 254 together and you get 382. subtract that from 2000.

Final answer : 1618

We will use the proportional method to solve the question

Since the distance on the map of actual distance 3038 miles is 10.125 inches

Since we need to find the distance on the map of the actual distance of 3445 miles

Then by using the proportional method

By using the cross-multiplication

Divide both sides by 3038

On the map, the distance between city C and city D is 11.481 inches

Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

a) The function F represents the difference between the demand and supply functions. The implicit function P = f(l) exists if the demand function is invertible with respect to price.  b) An exogenous increase in income will increase the price of the good (assuming it is normal).

a) The function F represents the market equilibrium condition, where F(P,I) = D(P,I) - S(P) = 0. It shows the difference between the demand function D(P,I) and the supply function S(P). The equilibrium occurs when the quantity demanded equals the quantity supplied.

The implicit function P = f(l) exists when the demand function is invertible with respect to price. This means that for each level of income, there is a unique price that equates demand and supply. The necessary and sufficient condition for the existence of the implicit function is that the partial derivative ∂D/∂P is non-zero and continuous.

b) An exogenous increase in income will affect the price of the good. Assuming the good is normal, meaning that as income increases, the demand for the good also increases, the price will rise. This can be illustrated on a graph by plotting the demand and supply curves. When income increases, the demand curve shifts outward, causing an increase in price.

To determine the effect quantitatively, we can use the implicit function theorem to calculate the comparative-static derivative dP/dl. This derivative represents the change in price with respect to a change in income. By evaluating this derivative at the given point, we can determine the direction and magnitude of the price change in response to the increase in income.

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The marginal profit if you sell 150 pieces of pie is $1.20 per piece.E. The marginal profit if you sell 150 pieces of pie is the additional profit made by selling one more unit of a good.

Given,The cost to make x servings of apple pie is C(x) = 300+ 0.1x +0.003x².

The price to sell one piece of pie is $4.00.So, the revenue function, R(x) can be written asR(x) = price per unit × number of units soldR(x) = 4x.

The profit function, P(x) is given by the difference between the revenue function and cost function i.e.,P(x) = R(x) - C(x)

Substituting R(x) = 4x and C(x) = 300 + 0.1x + 0.003x² in P(x), we haveP(x) = 4x - (300 + 0.1x + 0.003x²)

P(x) = 4x - 300 - 0.1x - 0.003x²

P(x) = - 0.003x² + 3.9x - 300.

The marginal profit function is given by P'(x) = R'(x) - C'(x).Let's find R'(x) and C'(x).Differentiating R(x) = 4x with respect to x, we getR'(x) = 4Differentiating C(x) = 300 + 0.1x + 0.003x² with respect to x, we getC'(x) = 0.1 + 0.006x.

Substituting R'(x) = 4 and C'(x) = 0.1 + 0.006x in P'(x), we getP'(x) = 4 - (0.1 + 0.006x)P'(x) = 3.9 - 0.006x.

Now, let's find the marginal profit if we sell 150 pieces of pie.

Substituting x = 150 in P'(x), we getP'(150) = 3.9 - 0.006 × 150P'(150) = $1.20 per piece.

The marginal profit if we sell 150 pieces of pie is $1.20 per piece.

The marginal profit is the additional profit made by selling one more unit of a good.So, if we sell one more piece of pie, the profit will increase by $1.20.

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Answer:

25%

Step-by-step explanation:

25%

0, 25, 50, 100

That is 1/4 on the number line.

Q1: The regression intercept for stock A can be determined by considering the given regression results and assuming a constant risk-free rate (rf) of 8% with total returns instead of excess returns. The intercept represents the expected return of stock A when the market return (RM) is zero. To calculate the intercept, we need to subtract the product of the market return coefficient and the constant risk-free rate from the intercept of the excess return regression. In this case, the intercept for stock A would be -1.1% - (0.95 * 8%) = -1.87%.

Q2: To calculate the standard deviation of the portfolio, we use the given investment proportions and the standard deviations of stocks A and B. The standard deviation of a portfolio can be calculated by considering the investment proportions and the individual stock standard deviations. Using the given information, we can calculate the standard deviation of the portfolio to be 33.82 (rounded to two decimal places). The beta of the portfolio can be calculated by weighting the betas of stocks A and B according to their investment proportions. Based on the given information, the beta of the portfolio is calculated to be 1.09 (rounded to two decimal places).

Q3: The firm-specific variance of the portfolio represents the part of the portfolio's total variance that is not explained by the market index. To calculate the firm-specific variance, we need the portfolio's total variance and the square of the portfolio beta multiplied by the market variance. However, the necessary values are not provided in the given information, so the firm-specific variance cannot be determined without additional information.

Q4: The covariance between the portfolio and the market index represents the measure of their co-movement. It can be calculated by multiplying the portfolio beta, the standard deviation of the portfolio, and the standard deviation of the market index. However, the necessary values for the calculation are not provided in the given information, so the covariance between the portfolio and the market index cannot be determined without additional information.

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The equation of the parabola graphed is given as follows:

y = a(x + 1)² - 4.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

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Answer:

Step-by-step explanation:

the answer is

z=0.625

Answer:

Essentially, slope is rise/run. Rise is how many units up the graph, and run is how far to the left or right it goes. Rise will be negative if it's going down, and run will be negative if it's going left. There's two ways to find the slope in this case.

1. Stick to the more visual aspect of it, and count how many units up from one point to the next point. Point (1,2) is 2 units up from point (0,0). Then you count how many units right or left it goes. In this case, it's 1 towards the right. This means the rise/run comes out to be 2/1, which means the slope=2.

2. Look at the equations. y=mx+b is the linear format for these lines. y is the y coordinate, m is the slope, x is the x coordinate, and b is the y intercept (the point where x=0). These two lines have shared slope values, which means the slope for both of them is 2.

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Therefore, the measure of ∠D is approximately 60.96 degrees.

A measure is a function that assigns a number to each set in a given space, typically with the goal of describing the size or extent of the set. For example, the Lebesgue measure is a way of assigning a "volume" to sets in n-dimensional Euclidean space.

by the question.

To find the measure of ∠D in a right triangle with sides of 25 feet and 45 feet, we can use the inverse tangent function:

\(tan(∠D) = opposite/adjacent = CD/BC = 45/25\)

Taking the inverse tangent of both sides, we get:

\(∠D = tan⁻¹(45/25) = 60.95 degrees\)

Rounding this to the nearest hundredth, we get:

\(angleD = 60.95 degrees =60.96 degree.\)

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