the bullet embeds itself in the mass. use conservation of linear momentum to find the speed of the mass bullet right after the collision.

The number of children and the adults present at the pool in the day was 223 and 351 respectively.

Given that, there are 574 people in a day swimming at public pool, the daily prices are $1.75 for children and $2.25 for adults.

The receipts for admission totaled $1180.00.

Let the number of adults be a and that the children be c,

So,

a + c = 574

a = 574 - c.........(i)

2.25a + 1.75c = 1180............(ii)

Put eq(i) in eq(ii)

2.25(574-c) + 1.75c = 1180

1291.5 - 2.25c + 1.75c = 1180

0.5c = 111.5

c = 223

Put the value of c in the eq(i)

a = 574-223

a = 351

Hence, the number of children and the adults present at the pool in the day was 223 and 351 respectively.

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The given polynomial inequality is: x²-8x+16 > 0The solution of this polynomial inequality is:If a quadratic polynomial, ax² + bx + c, is greater than zero, then the roots of the polynomial will be either negative or positive.

To solve the inequality, we must first factorize the polynomial expression as follows: (x - 4)² > 0The main answer is (x - 4)² > 0. For the expression to be greater than zero, the square of any number cannot be negative.Therefore, the square of any number is always positive. Hence, (x - 4)² is always positive irrespective of the value of x. This implies that there is no solution for the polynomial inequality.

That x²-8x+16 is a perfect square whose discriminant, b²-4ac, is equal to zero. Thus, there is only one root, which is also the vertex of the parabola. The vertex is (4, 0) since x

= -b/2a gives x

= 8/2

= 4.Substituting the vertex into the original inequality, we get (4)² - 8(4) + 16 > 0 which simplifies to 0 > 0. This implies that there is no solution for the polynomial inequality. Hence,  No Solution.

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B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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(i) The number of different divisions possible when 15 children divide themselves into teams of 5 each (Team A, B, and C) is 756.

(ii) If the teams are not distinguishable, the number of different divisions possible is 756 divided by 3!, which equals 126.

(i) To determine the number of different divisions when 15 children divide themselves into three teams of 5 each, we can calculate the number of combinations.

Since the order of the teams does not matter, we use the combination formula.

The formula is nCr = n! / (r! * (n - r)!), where n is the total number of children and r is the number of children per team.

Plugging in the values, we have 15C5 * 10C5 = (15! / (5! * 10!)) * (10! / (5! * 5!)) = 756.

(ii) If the teams are not distinguishable, we need to account for the fact that the order of the teams doesn't matter.

Each division would be counted multiple times if we considered the teams distinguishable. Since there are 3! (3 factorial) ways to arrange the teams, we divide the previous result by 3!, which gives us 756 / 3! = 126.

This accounts for the different arrangements of the same teams and gives us the number of distinct divisions.

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The sample covariance between variable a and variable b is -0.2.

To calculate the sample covariance between two variables,

We want to do following steps:

1) Calculate the mean (average) of each variable.

2) Subtract the mean from each value in their respective variables.

3) Multiply the resulting differences for each pair of values.

4) Sum up all the products obtained in step 3.

5) Divide the sum by the number of data points minus 1 (sample size minus 1).

Let's calculate the sample covariance for the given data sets (variable a and variable b),

Variable a: 5, 3, 5, 5, 4, 8

Variable b: 3, 1, 1, 4, 2, 1

Step 1: Calculate the means of each variable.

Mean of variable a:

\((5 + 3 + 5 + 5 + 4 + 8) / 6 = 30 / 6 = 5\)

Mean of variable b:

\((3 + 1 + 1 + 4 + 2 + 1) / 6 = 12 / 6 = 2\)

Step 2: Subtract the mean from each value in their respective variables.

For variable a:

\((5 - 5), (3 - 5), (5 - 5), (5 - 5), (4 - 5), (8 - 5),0, -2, 0, 0, -1, 3\)

For variable b:

\((3 - 2), (1 - 2), (1 - 2), (4 - 2), (2 - 2), (1 - 2),1, -1, -1, 2, 0, -1\)

Step 3: Multiply the resulting differences for each pair of values.

\(0 * 1, -2 * -1, 0 * -1, 0 * 2, -1 * 0, 3 *-10, 2, 0, 0, 0, -3\)

Step 4: Sum up all the products obtained in step 3.

\(0 + 2 + 0 + 0 + 0 + (-3) = -1\)

Step 5: Divide the sum by the number of data points minus 1.

\(-1 / (6 - 1) = -1 / 5 = -0.2\)

Therefore, the sample covariance between variable a and variable b is -0.2.

The correct option is d) -0.20.

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Consequently, x = -6 and y = 0 provide the system of equations answer. The response gathering yields "(-6,0)" as the outcome.

She came back to compete in the meeting's final event, winning the knockout race. Their quick removal is the letdown. Take pride in your quick removal.

To solve this system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the equations. Here's how to do it:

To find: multiply the second solution by 4.

12x - 36y = -72

Eliminate x by combining the two equations:

5x + 4y + 12x - 36y = -30 - 72

Simplify and combine like terms:

17x - 32y = -102

Solve for x:

17x = 32y - 102

x = (32/17)y - 6

Substitute this expression for x into one of the original equations, and solve for y:

5x + 4y = -30

5[(32/17)y - 6] + 4y = -30

Simplify and solve for y:

(160/17)y - 30 = -30

(160/17)y = 0

y = 0

Substitute this value for y back into either of the original equations and solve for x:

3x - 9y = -18

3x - 9(0) = -18

3x = -18

x = -6

So the solution to the system of equations is x = -6 and y = 0. Therefore, the solution set is {(-6,0)}.

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The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

The measure of side P to the nearest degree is 79 degrees.

Given:

ΔOPQ ,

O = 700 cm,

P = 840cm

Q = 620cm.

To find:

The measure of angle P.

According to the Law of Cosines:

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The law of cosines states:

                                   \(cos A = b^{2} +c^{2} - a^{2} / 2bc\)

Using Law of Cosines ΔOPQ, we get,

           cos P = o² +q²- p² / 2oq

       ⇒ cos P = (700)² + (620)² -(840)² /2×700×620

       ⇒ Cos P = 490000 + 384400 - 705600 / 868000

       ⇒ Cos P = 168800/868000

on further simplification, we get,

Cos P = 0.19447

P = Cos⁻¹ (0.19447)

P = 78.786236

P = 79.

∴ the measure of angle P is 79 degrees.

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Therefore, the measure of angle P is 79 degrees.

a. The probability of an odd number, then drawing a 6 is 3/16

b. The probability of a 2, then drawing another 2 is 1/12

c. The probability of a number divisible by 3, then drawing a 1 is 1/8

d. The probability of a 1, then drawing a 6 is 1/24

e. The probability of a prime number, then drawing a composite number is 1/8

f. The probability of drawing another 9 is 1/24

g. The probability of drawing a 9, then drawing a number divisible by 1 is 1/14

h. The probability of this event occurring is 3/56.

Given board game numbers:

2 1 6 2

9 6 6 1

We can find the probability of each event by using the following formula:

P(A and B) = P(A) × P(B|A)

where P(A) is the probability of event A occurring, and P(B|A) is the conditional probability of event B occurring given that event A has occurred.

a. An odd number, then drawing a 6:

P(Odd number) = 3/8 (since there are 3 odd numbers out of 8 total numbers)

P(Drawing a 6 given an odd number) = 1/2 (since only 2 and 6 are left after drawing the odd number)

P(Odd number and drawing a 6) = P(Odd number) × P(Drawing a 6 given an odd number) = (3/8) × (1/2) = 3/16

b. A 2, then drawing another 2:

P(Drawing a 2) = 2/8 = 1/4

P(Drawing another 2 given the first draw was 2) = 1/3 (since only two 2's are left after the first draw)

P(Drawing 2 and then another 2) = P(Drawing a 2) × P(Drawing another 2 given the first draw was 2) = (1/4) × (1/3) = 1/12

c. A number divisible by 3, then drawing a 1:

P(Number divisible by 3) = 2/8 = 1/4

P(Drawing a 1 given a number divisible by 3) = 1/2 (since only 1 and 6 are left after drawing a number divisible by 3)

P(Number divisible by 3 and drawing a 1) = P(Number divisible by 3) × P(Drawing a 1 given a number divisible by 3) = (1/4) × (1/2) = 1/8

d. A 1, then drawing a 6:

P(Drawing a 1) = 1/8

P(Drawing a 6 given the first draw was 1) = 1/3 (since only two 6's are left after the first draw)

P(Drawing a 1 and then a 6) = P(Drawing a 1) × P(Drawing a 6 given the first draw was 1) = (1/8) × (1/3) = 1/24

e. A prime number, then drawing a composite number:

P(Prime number) = 2/8 = 1/4

P(Drawing a composite number given the first draw was prime) = 3/6 (since there are three composite numbers left after drawing a prime number)

P(Prime number and then a composite number) = P(Prime number) × P(Drawing a composite number given the first draw was prime) = (1/4) × (3/6) = 1/8

f. A 9, then drawing another 9:

P(Drawing a 9) = 1/8

P(Drawing another 9 given the first draw was 9) = 1/3 (since only two 9's are left after the first draw)

P(Drawing a 9 and then another 9) = P(Drawing a 9) × P(Drawing another 9 given the first draw was 9) = (1/8) × (1/3) = 1/24

g. The probability of drawing a 9 on the first draw is 1/8, as there is only one 9 out of eight numbers in the set.

Given that a 9 was drawn on the first draw, the probability of drawing a number divisible by 1 on the second draw is 4/7, since there are four numbers (2, 1, 6, and 9) that are divisible by 1 out of the seven remaining numbers in the set.

Therefore, the probability of drawing a 9 on the first draw and a number divisible by 1 on the second draw is:

P(9, divisible by 1) = P(9) * P(divisible by 1 | 9 was drawn)

= (1/8) * (4/7)

= 1/14

h. An even number, then drawing a 1

To find the probability of drawing an even number first and then drawing a 1, we need to consider the following events:

Drawing an even number: There are three even numbers in the set {2, 1, 6, 2, 9, 6, 6, 1}, so the probability of drawing an even number is 3/8.

Drawing a 1: There is only one 1 in the remaining set of seven numbers after the first draw, so the probability of drawing a 1 after drawing an even number is 1/7.

Therefore, the probability of drawing an even number first and then drawing a 1 is:

P(even number, then 1) = P(even number) × P(1 after even number)

= (3/8) × (1/7)

= 3/56

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Answer:

The answer is c

Step-by-step explanation:

hello

determine the amount each of them have, let's write an equation to represent thier total amount

let x represent the amount Jason have

let y represent the amount Jeff has

now, we know that Jason has 3 more than 4 times the amount Jeff has

x = 4y + 3 .... equation 1

x + y = 72 .... equation 2

from equation 2,

make x the subject of formula

x = 72 - y .....equation 3

put equation 3 into equation 1

x = 4y + 3

72 - y = 4y + 3

solve for y

we know y = 13.8

we can simply substitute the value into equation 2 and solve for x

therefore, Jason has $58.2 and Jeff has $13.8

90° is the least angle measure by which this figure can be rotated so that it maps onto itself.

The correct option is (B)

From the figure,

As the figure has two axis of symmetry, placing x and y axis such that the origin lies on its centroid.

Angle between x axis and y axis is 90°.

So rotating any degree which is a multiple of 90 i.e., 90°, 180°, 270°, 360°...… would yield the original figure.

Therefore, 90° is the least angle measure by which this figure can be rotated so that it maps onto itself.

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The solution for x is 7 and the graph is attached

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

8x - 53 = 3

Add 53 to both sides of the equation

So we have

8x = 56

Divide both sides by 8

So, we have the following representation

x = 7

Hence, the solution is 7

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Complete question

Solve for x.

8x-53 = 3

Graph the solution.

Answer:

60

Step-by-step explanation:

Answer:

45 minutes

Step-by-step explanation:

3 pm to 4pm= gap of 1 hour

1 hour- 15 minutes= 45

Answer:

Step-by-step explanation:

Factor it by first setting it equal to 0:

\(4x^2+9=0\) Now subtract 9 from both sides:

\(4x^2=-9\) Divide both sides by 4:

\(x^2=-\frac{9}{4}\) Then take the square root of both sides:

x = ±\(\sqrt{-\frac{9}{4} }\) , which of course is not allowed. Therefore, we have to allow for the imaginary numbers in this solution. Knowing that,

x = ±\(\sqrt{-1*\frac{9}{4} }\) is an equivalent radicand, we can now replace -1 with its imaginary counterpart:

x = ±\(\sqrt{i^2*\frac{9}{4} }\)

Each one of the elements in the radicand are perfect squares, so we simplify as follows:

x = ±\(\frac{3}{2}i\)

And there you go!

The pirate has gone into debt by $38,979 in base 10 due to his encounter with Captain Rusczyk.

To determine the amount of debt, we need to calculate the difference between the value of the goods the pirate stole and the amount demanded by Captain Rusczyk. The pirate initially stole $2345_6, which means it is in base 6. Converting this to base 10, we have $2\times6^3 + 3\times6^2 + 4\times6^1 + 5\times6^0 = 2\times216 + 3\times36 + 4\times6 + 5\times1 = 432 + 108 + 24 + 5 = 569$.

Captain Rusczyk demanded $41324_5, which means it is in base 5. Converting this to base 10, we have $4\times5^4 + 1\times5^3 + 3\times5^2 + 2\times5^1 + 4\times5^0 = 4\times625 + 1\times125 + 3\times25 + 2\times5 + 4\times1 = 2500 + 125 + 75 + 10 + 4 = 2714$.

Therefore, the pirate has gone into debt by $569 - 2714 = -2145$. Since the pirate owes money, we consider it as a negative value, so the pirate has gone into debt by $38,979 in base 10.

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We have this function here:

We can differentiate this function using the power rule:

We will subtract the power/exponent by 1 and multiply the original exponent to the constant in front.

The differentiated function is shown above.

Answer:

Step-by-step explanation:

oknjbgfkdfrgn jnfbfl

Answer:

(-8, 11/2)

Step-by-step explanation:

1. The midpoint between two points can be found by averaging the x-values of both points and the y-values of both points. For example, if you had the points (x, y) and (m, n), then the midpoint would be (\(\frac{x+m}{2}\), \(\frac{y+n}{2}\))

2. Calculate your midpoint. In this specific case your x-value would be (-7+-9)/2 and your y-value would be (8+3)/2, or (-8, 11/2)

The radius is 169 inches.

As per the known fact, the radius and area of circle are related by the formula -

Area = πr²

So, rewriting the expression in equation -

r=√(A/π)²

As mentioned, r is the radius and A is the area of the circle and π is constant

Keep the value of A in the above mentioned rewritten equation to find the value of radius of circle.

r = √(169π/π)²

On solving the above equation we get the new equation, which is as follows -

r = 169π/π

Cancelling π as it is common in both numerator and denominator

r = 169 inches

Hence, the radius of circle is 169 inches.

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Answer:

Junior PSAT

Training Packet

2016-17

Math Department  

Answer Key

Section 3: Math Test — No Calculator

QUESTION 1.

Choice C is correct. Subtracting 6 from each side of 5x + 6 = 10 yields 5x = 4.

Dividing both sides of 5x = 4 by 5 yields x =

_4

5

. Te value of x can now be

substituted into the expression 10x + 3, giving 10 ( _4

5 ) + 3 = 11.

Alternatively, the expression 10x + 3 can be rewritten as 2(5x + 6) − 9, and

10 can be substituted for 5x + 6, giving 2(10) − 9 = 11.

Choices A, B, and D are incorrect. Each of these choices leads to 5x + 6 ≠ 10,

contradicting the given equation, 5x + 6 = 10. For example, choice A is

incorrect because if the value of 10x + 3 were 4, then it would follow that

x = 0.1, and the value of 5x + 6 would be 6.5, not 10.

QUESTION 2.

Choice B is correct. Multiplying each side of x + y = 0 by 2 gives 2x + 2y = 0.

Ten, adding the corresponding sides of 2x + 2y = 0 and 3x − 2y = 10 gives

5x = 10. Dividing each side of 5x = 10 by 5 gives x = 2. Finally, substituting

2 for x in x + y = 0 gives 2 + y = 0, or y = −2. Terefore, the solution to the

given system of equations is (2, −2).

Alternatively, the equation x + y = 0 can be rewritten as x = −y, and substituting x for −y in 3x − 2y = 10 gives 5x = 10, or x = 2. Te value of y can then

be found in the same way as before.

Choices A, C, and D are incorrect because when the given values of x and

y are substituted into x + y = 0 and 3x − 2y = 10, either one or both of the

equations are not true. Tese answers may result from sign errors or other

computational errors.

QUESTION 3.

Choice A is correct. Te price of the job, in dollars, is calculated using

the expression 60 + 12nh, where 60 is a fxed price and 12nh depends on the

number of landscapers, n, working the job and the number of hours, h, the job

takes those n landscapers. Since nh is the total number of hours of work done

when n landscapers work h hours, the cost of the job increases by $12 for each

hour a landscaper works. Terefore, of the choices given, the best interpretation

of the number 12 is that the company charges $12 per hour for each landscaper.

Choice B is incorrect because the number of landscapers that will work each

job is represented by n in the equation, not by the number 12. Choice C is

incorrect because the price of the job increases by 12n dollars each hour,

which will not be equal to 12 dollars unless n = 1. Choice D is incorrect

because the total number of hours each landscaper works is equal to h. Te

number of hours each landscaper works in a day is not provided.

QUESTION 4.

Choice A is correct. If a polynomial expression is in the form (x)2

+ 2(x)(y) +

(y)2

, then it is equivalent to (x + y)2

. Because 9a4

+ 12a2

b2

+ 4b4

= (3a2

)2

+

2(3a2

)(2b2

) + (2b2

)2

, it can be rewritten as (3a2

+ 2b2

)2

.

Choice B is incorrect. Te expression (3a + 2b)4

is equivalent to the product

(3a + 2b)(3a + 2b)(3a + 2b)(3a + 2b). Tis product will contain the term

4(3a)3

(2b) = 216a3

b. However, the given polynomial, 9a4

+ 12a2

b2

+ 4b4

,

does not contain the term 216a3

b. Terefore, 9a4

+ 12a2

b2

+ 4b4 ≠ (3a + 2b)4

.

Choice C is incorrect. Te expression (9a2

+ 4b2

)2

is equivalent to the

product (9a2

+ 4b2

)(9a2

+ 4b2

). Tis product will contain the term (9a2

)

(9a2

Answer:

that looks hard

Step-by-step explanation:

b

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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An equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

The given denominator are (x+3), (x−4) and (x+4).

A mathematical expression that may be rewritten to a rational fraction, an algebraic fraction such that both the numerator and the denominator are polynomials.

Here, an equivalent rational expressions is

\(\frac{1}{x+3}+\frac{1}{x-4} +\frac{1}{x+4}\)

The LCM of denominators is (x+3)(x-4)(x+4)

= (x+3)(x²-16)

= x(x²-16)+3(x²-16)

= x³-16x+3x²-48

= x³+3x²-16x-48

Now, \(\frac{(x-4((x+4)+(x+3)(x+4)+(x+3)(x-4)}{x^3+3x^2-16x-48}\)

= (x²-16+x²+7x+12+x²-x-12)/(x³+3x²-16x-48)

= (3x²+6x-16)/(x³+3x²-16x-48)

Hence, an equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

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This question is incomplete

Complete Question

Nico and Lorena used different methods to determine the product of three fractions.

Nico’s Method =

(one-sixth) (Negative four-fifths)(2) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) = StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction = Negative StartFraction 8 over 30 EndFraction

Lorena’s Method

= Negative StartFraction 4 over 15 EndFraction (2) (one-sixth) (Negative four-fifths) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) = StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction = Negative StartFraction 8 over Negative 30 EndFraction = StartFraction 4 over 15 EndFraction

Whose solution is correct and why?

a) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over negative 5 EndFraction.

b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.

c) Lorena is correct because she knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction

d) Lorena is correct because she knew that Negative four-fifths = StartFraction negative 4 over negative 5 EndFraction

Answer:

b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.

Step-by-step explanation:

In the above question

We start from Nico's method

Nico’s Method =

Step 1 : (one-sixth) (Negative four-fifths)(2)=

(1/6)(-4/5)(2)

Step 2 : (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) =

= (2/1)(1/6)(-4/5)

Step 3: StartFraction (2) (1) (negative 4) over (1) (6) (5) EndFraction

= (2)(1)(-4)/(1)(6)(5)

Step 4: Negative StartFraction 8 over 30 EndFraction

= (-8/30)

Step 5 : Negative StartFraction 4 over 15

EndFraction

= -4/15

Nico is correct

For Lorena’s Method

Step 1: Negative StartFraction 4 over 5 EndFraction (2) (one-sixth)

= -4/5(2)(1/6)

Step 2: (Negative four-fifths) = (StartFraction 2 over 1 EndFraction) (one-sixth) (negative four-fifths) =

(2/1)(1/6)(-4/-5)

Step 3: StartFraction (2) (1) (negative 4) over (1) (6) (negative 5) EndFraction

(2)(-1)(-4)/(1)(6)(-5)

Step 4: Negative StartFraction 8 over Negative 30 EndFraction =

-8/-30

Step 5: StartFraction 4 over 15

EndFraction

= 4/15

Lorena is wrong because

that Negative four-fifths ≠StartFraction negative 4 over negative 5 EndFraction

Mathematically

-4/5 ≠ -4/-5

Therefore,option b) Nico is correct because he knew that Negative four-fifths = StartFraction negative 4 over 5 EndFraction.

Answer:

6x + y = 0

Step-by-step explanation:

-7x +x -y - 3 + 3

-6x - y = 0

6x + y = 0

PLS MRK ME BRAINLIEST

Total number of committees with 4 delegates from Nevada = 15 × C(24, 5)

Total number of committees with 5 delegates from Nevada = 6 × C(23, 4)

Total number of committees with 6 delegates from Nevada = 1 × C(22, 3)

What is Delegates?

An individual chosen to represent a group of people in a political assembly in the United States is known as a delegate.

To calculate the number of committees with at least 2 delegates from Nevada, we need to consider the number of possible combinations of delegates from five states: California, Arizona, New Mexico, Utah, and Nevada.

Since each state sends a team of 6 delegates, the total number of delegates available is 6 × 5 = 30 delegates.

Now let's count the number of committees with at least 2 delegates from Nevada. We can consider two scenarios:

Scenario 1: Exactly 2 delegates from Nevada

In this case, we need to select 2 delegates from Nevada and 7 delegates from the remaining 29 delegates (excluding the 2 from Nevada). The order of selection does not matter, so we use combinations.

Number of ways to choose 2 delegates from Nevada = C(6, 2) = 15 (using combinational formula)

Number of ways to select 7 delegates from the remaining 29 delegates = C(29, 7) = 3,138,225 (using combinational formula)

Total number of committees with exactly 2 delegates from Nevada = 15 × 3,138,225 = 47,073,375

Scenario 2: More than 2 delegates from Nevada

In this case, we can choose 3, 4, 5, or 6 delegates from Nevada. For each selection, we must select the remaining delegates from the remaining states.

Number of ways to select 3 delegates from Nevada = C(6, 3) = 20 (using combinational formula)

Number of ways to select 6 delegates from the remaining 27 delegates = C(27, 6) = 10,068,347 (using combinational formula)

Total Committees with 3 Nevada Delegates = 20 × 10,068,347 = 201,366,940

Similarly, we calculate the total number of committees with 4, 5, and 6 delegates from Nevada.

Number of ways to choose 4 delegates from Nevada = C(6, 4) = 15

Number of ways to choose 5 delegates from Nevada = C(6, 5) = 6

Number of ways to select 6 delegates from Nevada = C(6, 6) = 1

For each case, we calculate the number of ways to choose the remaining delegates from the remaining states using the combination formula.

Total number of committees with 4 delegates from Nevada = 15 × C(24, 5)

Total number of committees with 5 delegates from Nevada = 6 × C(23, 4)

Total number of committees with 6 delegates from Nevada = 1 × C(22, 3)

Calculating the above combinations will give you the final results.

Note: Calculations for remaining delegates from other states are required to account for the different number of delegates in each scenario.

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We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

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The minimum possible value of the European call option is approximately 2.8752.

Given the parameters S = 52 (current stock price), K = 50 (strike price), r = 24% (annual interest rate), and a time to maturity of 3 months, we can calculate the minimum call option value.

The Black-Scholes formula for European call option pricing is as follows:

C = S * N(d1) - K * e^(-r*T) * N(d2)

Where:

C = Call option price

S = Current stock price

N = Cumulative standard normal distribution function

d1 = (ln(S/K) + (r + σ^2/2) * T) / (σ * sqrt(T))

d2 = d1 - σ * sqrt(T)

K = Strike price

r = Annual interest rate

T = Time to maturity (in years)

e = Euler's number (approximately 2.71828)

σ = Implied volatility of the underlying asset

Using the provided values, we can calculate the minimum call option value as follows:

d1 = (ln(52/50) + (0.24 + 0^2/2) * (3/12)) / (0.24 * sqrt(3/12))

   = (ln(1.04) + 0.12 * 0.25) / (0.24 * 0.1443)

   = (0.0392 + 0.03) / 0.0346

   = 1.7507

d2 = 1.7507 - 0.24 * sqrt(3/12)

   = 1.7507 - 0.24 * 0.1443

   = 1.7507 - 0.0346

   = 1.7161

N(d1) = N(1.7507) ≈ 0.9599 (using standard normal distribution table)

N(d2) = N(1.7161) ≈ 0.9569 (using standard normal distribution table)

C = 52 * 0.9599 - 50 * e^(-0.24 * (3/12)) * 0.9569

 = 49.9152 - 50 * e^(-0.06) * 0.9569

 ≈ 49.9152 - 50 * 0.9408

 ≈ 49.9152 - 47.040

 ≈ 2.8752

Therefore, the minimum possible value of the European call option is approximately 2.8752.

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