2. Create a portfolio composed of two independent bets of $5 each, both on 3 numbers. (a) Construct the probability distribution of the portfolio, beginning with the sample points. (b) Find the expected value, the variance, and the standard deviation of the portfolio bet, on 3 numbers. (c) By what multipliers do the results change when switching from a single $10 bet to the portfolio bet, again on 3 numbers

Answer:

the answer is 5

Step-by-step explanation:

a right angle has a total of 90 degrees

so you subtract 65 from 90 and get 25

that is the total degrees in the rest of the angle

then you would have to divide 25 by 5

leaving you with 5

Since p(1) is true, by induction we conclude that p(n) is true for all positive integers n.

To prove the predicate p(n) by induction, we need to show that it is true for the base case n = 1, and that if it is true for some positive integer k, then it is also true for k+1.

Base case:

When n = 1, we have 2n - 1 = 1 player. In this case, there is no pairwise-distance, so the predicate p(1) is vacuously true.

Inductive step:

Assume that p(k) is true for some positive integer k. That is, whenever 2k - 1 players stand at distinct pairwise-distances and play arena dodgeball, there is always at least one survivor.

We will show that p(k+1) is also true, that is, whenever 2(k+1) - 1 = 2k + 1 players stand at distinct pairwise-distances and play arena dodgeball, there is always at least one survivor.

Consider the 2k+1 players. We can group them into two sets: the first set contains k players, and the second set contains the remaining player. By the pigeonhole principle, at least one player in the first set is at a distance of d or greater from the player in the second set, where d is the smallest pairwise-distance among the k players.

Now, remove the player in the second set, and consider the remaining 2k - 1 players in the first set. Since p(k) is true, there is always at least one survivor among these players. This survivor is also a survivor among the original 2k+1 players, since the removed player is farther away from all of them than the surviving player.

Therefore, we have shown that if p(k) is true, then p(k+1) is also true. Since p(1) is true, by induction we conclude that p(n) is true for all positive integers n.

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Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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Answer:

Explanation:

180 = 6x + 2x + 2x

180 = 10x

x = 180/10

x = 18

C = 2x

C = 18×2

C = 36°

The area of any prism is base*height.

The main trick in this problem is determining which face is the base, since this is a triangular prism. We need to calculate the area of the triangle base.

11*8/2=44

Now we just need to multiply by the height.(note height is b this case because the prism is actually printed with the base facing towards you.

44*5=220

Done!

So answer choice B 220.

Answer:

220 is the right answer

Given the n™ term of a number sequence, the first three terms of the sequence are 0, 2 and 6

The sequence is given as:

n^2 - n​

To write down the first three terms of the sequence, we set n =1, 2 and 3

So, we have:

When n = 1

n^2 - n​ = 1^2 - 1

Evaluate

n^2 - n​ = 0

When n = 2

n^2 - n​ = 2^2 - 2

Evaluate

n^2 - n​ = 2

When n = 3

n^2 - n​ = 3^2 - 3

Evaluate

n^2 - n​ = 6

Hence, the first three terms of the sequence are 0, 2 and 6

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Answer: The answer would be 9.125.

Step-by-step explanation:

I can't really find an explanation for it.  Sorry.

The remaining angles are 80 and 30

The sum of angles of a triangle = 180

One angle is given as                 = 70

The sum of the remaining angles= 110

Now we apply the theory of ratios

The ratio between the angles are given as 3:8

So one angle will be 3 parts of 110 and other eight parts of 110

Total number of parts = 3+8 = 11

Angle 1                         = (3*110)/11

                                     =  30

Angle 2                        = (8*110)/11

                                     = 80

So the other two angles are 30 and 70.

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We have a problem of a sysmtem of equation

x is the number tickets sold of general admission

y is the number o tickets sold for seniors

The first equation is about the number of ticktes sold

x+y=155

the second equation is about the amount of money

12x+9y=1680

we isolate x of the first equation

x=155-y

we substitute the equatio above in the second equation

12(155-y)+9y=1680

1860-12y+9y=1680

we isolate the y

-3y=1680-1860

-3y=-180

y=-180/-3

y=60

then we substitute the value of y in order to find x

x=155-y

x=155-60

x=95

They sold 95 tickets of general admission

Answer: $33.48

Step-by-step explanation:

Given that:

Capacity of car tank =. 16 gallons

Gallons of already filled = 6.6 gallons

Amount left of tank capacity = 16 - 6.7

Amount left of tank capacity = 9.3 gallons

Cost of gas per gallon = $3.60

Hence, amount spent in gas will be

Amount left of tank capacity * cost per gallon of gas

= 9.3 gallons * $3.60

= $33.48

Total amount spent on gas = $33.48

any more help just ask :)

The number of dimes in the box is 23 and the number of nickels in the box is 63.

The sum of two consecutive terms in the arithmetic sequence 1​, 4​, 7​, 10​, ... is 299.

The first consecutive term of the arithmetic sequence is 148 and the second consecutive term of the arithmetic sequence is 151.

Let the number of dimes in the box be "d" and the number of nickels be "n".

Total number of coins = d + n

Given that the box contains 86 coins

d + n = 86

The amount of money in the box is $5.45.

Number of dimes = "d"

Value of each dime = 10 cents

Value of "d" dimes = 10d cents

Number of nickels = "n"

Value of each nickel = 5 cents

Value of "n" nickels = 5n cents

Total value of the coins in cents = Value of dimes + Value of nickels

= 10d + 5n cents

Also, given that the amount of money in the box is $5.45, i.e., 545 cents.

10d + 5n = 545

Multiplying the first equation by 5, we get:

5d + 5n = 430

10d + 5n = 545

Subtracting the above two equations, we get:

5d = 115d = 23

So, number of dimes in the box = d

= 23

Putting the value of "d" in the equation d + n = 86

n = 86 - d

= 86 - 23

= 63

So, the number of nickels in the box =

n = 63

Therefore, there are 23 dimes and 63 nickels in the box. We have found the answer to the first two questions.

Let the first term of the arithmetic sequence be "a".

As the common difference between two consecutive terms is 3.

So, the second term of the arithmetic sequence will be "a+3".

Given that the sum of two consecutive terms in the arithmetic sequence 1​, 4​, 7​, 10​, ... is,

299.a + (a + 3) = 2992a + 3

= 2992

a = 296

a = 148

So, the first consecutive term of the arithmetic sequence is "a" = 148.

The second consecutive term of the arithmetic sequence is "a + 3" = 148 + 3

= 151

Conclusion: The number of dimes in the box is 23 and the number of nickels in the box is 63.

The sum of two consecutive terms in the arithmetic sequence 1​, 4​, 7​, 10​, ... is 299.

The first consecutive term of the arithmetic sequence is 148 and the second consecutive term of the arithmetic sequence is 151.

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Answer:            23,187 x 2/3 < 23187     is the answer

Step-by-step explanation:  

The student's error is adding two non-adjacent angles and then solving for x.

What are the opposite angles?

Opposite angles are the angles directly opposite each other where two lines cross. The intersection point is called the vertex, which is where the lines connect to form the angle. Opposite angles are also called vertical angles.

The student's error is that they incorrectly added the two given angles together.

The angles 2x+6 and 60 are not adjacent angles and therefore cannot be added together to find the sum of the two angles.

In the figure, if the angle formed by the intersection of the lines is labeled as angle A, then we know that angle A is equal to 2x+6 and angle B is equal to 60.

These two angles are opposite angles and not adjacent angles, so they do not add up to 180 degrees.

Therefore, the student's error is adding two non-adjacent angles and then solving for x.

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Answer:

0

Step-by-step explanation:

−2−(−4)−2

=2−2

=0

Answer:

Step-by-step explanation:

-2 - (-4) - 2   = -2 + 4 - 2

                    = -4 + 4

                   = 0

Hint : -(-4) = 4

The height of the cube brick is 7 units and the volume is equal to 343 unit³

The volume of a cube is defined as the total number of cubic units occupied by the cube. The formula is given as V = a³ where "a" is the length of edge or sides.

The length of an edge for the cube brick is 7 units which implies the height represented by h is also 7 units and the volume is calculated as follows:

volume of cube brick = 7 units × 7 units × 7 units

volume of cube brick = 343 units ³

Therefore, the height of the cube brick is 7 units and the volume is equal to 343 unit³

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Complete question is;

A researcher wants to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual containers are randomly assigned to two different groups. Plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with a kelp extract, while the plants in group 2 are not. After the first frost, 12 of the 50 plants in group 1 exhibited damage and 18 of the 50 plants in group 2 showed damage. Let p1 be the actual proportion of all tomato plants of this variety that would experience damage under the kelp treatment, and let p2 be the actual proportion of all tomato plants of this variety that would experience damage under the no-kelp treatment. Is there evidence of a decrease in the proportion of

tomatoes suffering frost damage for tomatoes sprayed with kelp extract? To determine

this, yo u test the hypotheses H0: p1 = p2, Ha: p1 < p2. The p - value of your test is

A) greater than 0.10.

B) between 0.05 and 0.10.

C) between 0.01 and 0.05.

D)between 0.001 and 0.01.

E) below 0.001.

Answer:

B) between 0.05 and 0.10.

Step-by-step explanation:

We are given;

Number of plants in group that exhibited damage = 12

Number of group 1 plants; n₁ = 50

Number of plants in group 2 that exhibited damage = 18

Number of group 2 plants; n₂ = 50

Proportion of plants in group 1 that exhibited damage; p₁^ = 12/50 = 0.24

Proportion of plants in group 2 that exhibited damage; p₂^ = 18/50 = 0.36

Pooled proportion; p¯ = (12 + 18)/(50 + 50) = 0.3

q¯ = 1 - p¯

q¯ = 1 - 0.3 = 0.7

Z-score will be;

z = ((p₁^ - p₂^) - 0)/√((p¯•q¯)×((1/n₁) + (1/n₂))

Plugging in the relevant values;

z = (0.24 - 0.36)/√((0.3 × 0.7) × ((1/50) + (1/50))

z = -0.12/0.092

z = -1.3

From z-distribution table attached, we have;

p-value = 0.0968

Correct answer is option B.

The values for x, y, and z are 95, -9, and -21, respectively, resulting in a three-digit number: 95-9-21 = 95921.

To solve the system of equations:

x + 3y - 2z = 1

2x + y + 3z = 20

2x - 2y + z = 6

By the use of the method of Gaussian elimination or matrix algebra. Here, the Gaussian elimination:

1. Multiply equation 1 by 2 and subtract equation 3:

2(x + 3y - 2z) - (2x - 2y + z) = 2 - 6

2x + 6y - 4z - 2x + 2y - z = -4

8y - 5z = -4

2. Multiply equation 1 by 2 and subtract equation 2:

2(x + 3y - 2z) - (2x + y + 3z) = 2 - 20

2x + 6y - 4z - 2x - y - 3z = -18

5y + z = -18

3. Rearrange equation 2:

2x + y + 3z = 20

2x + 2y + 6z = 40

4. Subtract equation 3 from equation 2:

(2x + 2y + 6z) - (5y + z) = 40 - (-18)

2x + y + 5y + 6z - z = 58

2x + 6y + 5z = 58

Now we have a new system of equations:

8y - 5z = -4

5y + z = -18

2x + 6y + 5z = 58

We can solve this system using any method of our choice. In this case, solving the system yields:

x = 95

y = -9

z = -21

Therefore, the values for x, y, and z are 95, -9, and -21, respectively, resulting in a three-digit number: 95-9-21 = 95921.

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Step-by-step explanation:

since it's an Equilateral triangle

180/3=60°

6x=60

x=10°

Note that the triangle is attached accordingly. The ordered pair used are :

(1,5)

(1,1)

(4,1)

Ordered pairs are numbers that indicate a point's position in a two-dimensional space, usually represented as (x, y). They are important for graphing and representing mathematical relationships visually.

Ordered pairs provide a way to identify the location of points on a coordinate plane, where the x-value represents the horizontal position and the y-value represents the vertical position. They are essential for understanding and analyzing mathematical relationships, such as functions and equations.

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Answer:

712÷6=118 remainder 4

No it is not evenly divisible by 6

Answer:

£21

Step-by-step explanation:

Sarah : Gavyn = 5:3

Sarah's share = 5x

Gavyn's share = 3x

5x - 3x = 14

2x = 14

x = 14/2

x = £ 7

Gavyn's share = 3x = 3 * 7 = £21

The intervals corresponding to the given expressions are (-6, -3) for the first expression and (-7, -3) for the second expression.

For the first expression, "+24 AND x + 5 < 2x, in the interval (-6, -3)", we need to find the values of x that satisfy the inequality. We start by subtracting x from both sides of the inequality, giving us 5 < x. However, since we also have the condition that x is in the interval (-6, -3), we need to consider the intersection of these two conditions.

In the given interval, (-6, -3), the values of x range from -6 to -3, excluding the endpoints. Therefore, the intersection of 5 < x and (-6, -3) is the interval (-6, -3).

For the second expression, "+24 OR | x + 5 < 2x, in the interval (-6, 2) U (-7, -3)", we need to find the values of x that satisfy either of the conditions.

The condition |x + 5 < 2x| means that either x + 5 < 2x or -(x + 5) < 2x, which simplifies to -5 < x or x < -7.

In the given intervals, (-6, 2) and (-7, -3), the values of x range from -6 to 2 and from -7 to -3, excluding the endpoints. Therefore, the union of -5 < x and (-6, 2) U (-7, -3) is the interval (-7, -3).

In summary, the intervals corresponding to the given expressions are (-6, -3) for the first expression and (-7, -3) for the second expression.

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We can categorize the statements as true and false as -

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed

Given is a scatter plot as shown in the image attached.

The  given graph is a scatter plot that uses the points to display the relationship between the number of customers and the temperature. We can categorize the statements as true and false as -

Therefore, we can categorize the statements as true and false as -

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Answer:

288 cm³

Step-by-step explanation:

cuboid formular: lengtg×width×height

Answer:

V = 288 cm³

Step-by-step explanation:

the volume (V) of a cuboid is calculated as

V = length × width × height

  = 8 × 9 × 4

  = 72 × 4

  = 288 cm³

Answer: \(\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}\)

Step-by-step explanation:

A or B = A+B

Given: In a fish tank, \(\dfrac15\) of the fish are guppies and \(\dfrac{1}{12}\) of the fish are goldfish.

Then,  the fraction of the fish that are guppies or goldfish in the tank=\(\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{2+5}{5\times2}\)

\(\dfrac{7}{10}\)

Hence, the equation most closely estimates the fraction of the fish that are guppies or goldfish in the tank:

\(\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}\)

Answer:

the triangles are congruent

Step-by-step explanation:

method 1: Angle-Angle-Angle congruency test

angle BAC = angle DEC(given)

angle ABC = angle EDC

angle BCA = angle DCE

method 2: Side Angle Side Congruency test

BC = DC (both are 4 cm)

angle BCA = angle DCE (vertically opp. angles, straight lines intersect)

AC = EC (both are 6 cm)

side note:

1. when testing for congruency and giving the different congruency test, always ensure that the sides or angles mentioned are in corresponding order of the congruent triangles.

2. see that from the explanation given i do not anyhow mix up the sides with any sides or mess up points with any points(will show drawing of an example of what i mean)

pls dont mind the ugly handwriting as well since i dont have a stylus

Answer:

$25.44

Step-by-step explanation:

35% of $39 is $13.65

$39-$13.65=$25.44

Therefore, The pair (2/5, 1/5) minimizes the sum of squares x^2 + y^2 for 2x + y = 9.

To find the pair of (x, y) that minimizes the sum of squares x^2 + y^2, we can use the method of Lagrange multipliers. Let f(x, y) = x^2 + y^2 be the function to minimize subject to the constraint g(x, y) = 2x + y - 9 = 0. The Lagrange multiplier method states that the minimum occurs when the gradient of f and a multiple of the gradient of g are parallel. Solving these equations gives x = 2/5 and y = 1/5 as the pair of fractions that minimize x^2 + y^2.
To find the pair (x, y) that minimizes the sum of squares x^2 + y^2, follow these steps
1. From the given equation 2x + y = 9, isolate y: y = 9 - 2x
2. Substitute this expression for y in the sum of squares: x^2 + (9 - 2x)^2
3. Expand the equation: x^2 + 4x^2 - 36x + 81
4. Combine like terms: 5x^2 - 36x + 81
5. To minimize the sum of squares, differentiate the equation with respect to x and set it equal to zero: 10x - 36 = 0
6. Solve for x: x = 18/5
7. Substitute x back into y = 9 - 2x to find y: y = 9 - 2(18/5) = 27/5
The pair (x, y) that minimizes the sum of squares is (18/5, 27/5).

Therefore, The pair (2/5, 1/5) minimizes the sum of squares x^2 + y^2 for 2x + y = 9.

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Answer:

Solving \(v = \frac{4}{3}\pi r^3\) for r gives us: \(r=\sqrt[3]{\frac{3v}{4\pi}}\)

Solving \(a_{ave} = \frac{v_2-v_1}{t_2-t_1}\) for v2 gives us: \(v_2 = (t_2-t_1)a_{ave}+v_1\)

Step-by-step explanation:

Solving an equation for a variable or constant means that we have to isolate the value on one side of the equation or write the whole equation in terms of that variable or constant.

Now,

Solving \(v = \frac{4}{3}\pi r^3\) for r

\(v = \frac{4}{3}\pi r^3\)

Multiplying whole equation by 3/4

\(\frac{3}{4}.v = \frac{3}{4}.\frac{4}{3} \pi r^3\)

\(\frac{3}{4}v = \pi r^3\)

Dividing by Pi on both sides

\(\frac{3v}{4\pi} = \frac{\pi r^3}{\pi}\\\frac{3v}{4\pi} = r^3\)

Taking cube root on both sides

\(\sqrt[3]{r^3} = \sqrt[3]{\frac{3v}{4\pi}} \\r = \sqrt[3]{\frac{3v}{4\pi}}\)

Now

Solving \(a_{ave} = \frac{v_2-v_1}{t_2-t_1}\) for v2

Multiplying both sides by (t2-t1)

\((t_2-t_1)a_{ave} = \frac{v_2-v_1}{t_2-t_1}(t_2-t_1)\\(t_2-t_1)a_{ave} = v_2-v_1\)

Adding v1 on both sides

\((t_2-t_1)a_{ave}+v_1 = v_2-v_1+v_1\\(t_2-t_1)a_{ave}+v_1 = v_2\)

Hence,

Solving \(v = \frac{4}{3}\pi r^3\) for r gives us: \(r=\sqrt[3]{\frac{3v}{4\pi}}\)

Solving \(a_{ave} = \frac{v_2-v_1}{t_2-t_1}\) for v2 gives us: \(v_2 = (t_2-t_1)a_{ave}+v_1\)

The first statement says that if we multiply two positive real numbers and get a result larger than 400, then at least one of the two numbers must be greater than 20 Second statement talks about the sum of two positive real numbers being greater than 400

Similarly, the second statement talks about the sum of two positive real numbers being greater than 400. In this case, if both numbers were less than or equal to 200, their sum would be less than or equal to 400. Thus, for the sum to be greater than 400, at least one of the two numbers must be greater than 200.

These statements are important in solving problems related to real-life scenarios, such as finding the dimensions of a room or the possible values of a variable in an equation. They help us identify the minimum value of a variable or the minimum condition that must be met to achieve a certain result.

In conclusion, the two statements show us that the multiplication and addition of real numbers have certain conditions that must be met to obtain a specific result. They are useful in problem-solving and understanding mathematical concepts.

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Complete question is

"a. If the product of two positive real numbers is larger than 400, then at least one of the two numbers is larger than 20.

b. If the sum of two positive real numbers is larger than 400, then at least one of the two numbers is larger than 200."