In a box of 7 different banknotes 1, 2, 5, 10, 20, 50, 100 dollars. You pick at random 2 notes from this box. Let X is the larger number in these two notes, and Y be the smaller one.
(a) Find the distributions of X, Y and their joint distribution.
(b) Find the distribution of Z=X-Y.
(c) Compute E(X), Var(X), E(Z) and Var(Z).

Glenn has 1/20 of the granola bar left.

How to find?

If Glenn has 2/5 of a granola bar and eats 7/8 of it, we need to find out how much is left.

First, we need to find out how much Glenn ate. To do this, we can multiply the fraction of the granola bar that Glenn had (2/5) by the fraction that he ate (7/8):

2/5 × 7/8 = (27)/(58) = 14/40

Simplifying this fraction, we get:

14/40 = 7/20

So, Glenn ate 7/20 of the granola bar.

To find out how much is left, we can subtract the fraction that he ate from the fraction that he had:

2/5 - 7/20

To subtract these fractions, we need to find a common denominator. The least common multiple of 5 and 20 is 20, so we can convert both fractions to have a denominator of 20:

2/5 = 8/20

7/20 = 7/20

Now we can subtract the fractions:

8/20 - 7/20 = 1/20

So, Glenn has 1/20 of the granola bar left.

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The game is fair in the sense that the expected value is not negative.

The expected value serves as a gauge for a random variable's typical value. It is determined by multiplying each of the variables' potential outcomes by its corresponding probability, then adding the resulting products. In order to comprehend the typical outcome of a random process and determine if a given course of action is likely to be lucrative or not, the expected value is a valuable tool in decision-making.

The probability of getting a spade is 13/52 or 1/4.

The probability of getting anything else is 3/4.

he expected value of playing the game can be calculated as:

Expected value = (probability of winning x amount won) - (probability of losing x amount lost)

Expected value = (1/4 x $10) - (3/4 x $3)

Expected value = $2.50 - $2.25

Expected value = $0.25

Since the expected value is positive, this means that on average, you can expect to win $0.25 for every time you play the game.

Hence, game is fair in the sense that the expected value is not negative.

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A serving of skinny popcorn has 4 grams of fiber, which is about 16% of the recommended daily amount of fiber. The recommended daily amount of fiber is 25 grams.

If a serving of skinny popcorn has 4 grams of fibre and provides 16% of the necessary daily fibre intake, we can apply a proportion to calculate the entire recommended daily fibre intake:

If x is the required daily fibre intake in grams, we may calculate the following proportion:

4 / x = 16 / 100

We may cross-multiply and simplify to find x:

4 × 100 = 16 × x

400 = 16x

x = 25

As a result, the daily fibre recommendation is 25 grams.

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Answer:

The median of the data set is 18.5

Step-by-step explanation:

To find the median of this set of data values, we need to first arrange them in numerical order:

10, 14, 15, 17, 20, 21, 22, 25

The middle value is the median. If there is an odd number of values, there will be exactly one middle value, and if there is an even number of values, the median will be the average of the two middle values.

In this case, there are 8 values, which is an even number. So, we take the average of the sum of the 2 middle numbers:

Median of Data Set = (17 + 20)/2 = 18.5

Therefore, the median of the data set is 18.5.

Answer:

because 7*3*4 is 88 ft^3

5. Vertex: (2, 2)

Dοmain: All real numbers

Axis οf symmetry: x = 2

Increasing οn: (-∞, 2)

Decreasing οn: (2, ∞)

A quadratic functiοn is a pοlynοmial functiοn οf degree 2, where the highest pοwer οf the variable is 2. It has a parabοlic graph and is cοmmοnly used tο mοdel real-wοrld phenοmena.

5. Vertex: (2, 2)

Dοmain: All real numbers

Axis οf symmetry: x = 2

Increasing οn: (-∞, 2)

Decreasing οn: (2, ∞)

7. Vertex: (2, 3)

Dοmain: All real numbers

Axis οf symmetry: x = 2

Increasing οn: (-∞, 2)

Decreasing οn: (2, ∞)

Range: y ≥ 3

6.Vertex: (-2, -4)

Vertical shift: -4 units

Hοrizοntal shift: -2 units

Width: Cοmpressed hοrizοntally by a factοr οf 1/3

Reflected: Nο

8. Vertex: (-2, -2)

Vertical shift: -2 units

Hοrizοntal shift: -2 units

Width: Stretched by a factοr οf 3 in the vertical

Reflected: Nο

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Answer:

A answer that is not yet known.

Step-by-step  

For example x is to sub in 21 but you do not know that yet

until you solve the question.

To find the product of the face values (the values of the digits as they appear in the number) of all digits in 91250, we can simply multiply the face values of each digit together.

The face value of a digit is simply the value of the digit itself, regardless of its position in the number.

So, we have:

9 * 1 * 2 * 5 * 0 = 0

Note that the face value of the digit 0 is 0, so any product that includes a 0 will also be 0.

Therefore, the product of the face values of all digits in 91250 is 0.

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The only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]

The term "common" means "same for both." The two numbers' common factor is one that applies to both numbers.

The common factor between [tex]6[/tex] and [tex]10[/tex] is [tex]2[/tex], for instance. Although it is not the sole quality shared by each number, it is a trait that they both have in common.

To find the GCF of [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] we need to find the largest factor for both

[tex]14b^{3}[/tex] = 2*7*[tex]b^{2}[/tex]*[tex]b[/tex]

[tex]5b^{2}[/tex] = [tex]5*b^{2}[/tex]

Therefore the only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]

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Answer:

600ft²

Step-by-step explanation:

Volume of a cube V = a³

a³ = 1000

Cube root of both sides

a = 10ft

Surface area A =6a²

A = 6 x 10 x10 ft²

Answer:

600 feet²

Step-by-step explanation:

1) Break down the info

To answer this question we have to figure out the values of the sides. As it is a cube all sides should have the same area and length!

We know that the equation for volume is...

This means that to simply find the sides, we can cube root 1000

Let's check...

2) Find the surface area

We now know that the sides are 10 feet each so to find the surface area is [tex]6a^2[/tex] where a is the length of one side!

We can solve the question by plugging our numbers into the equation...

Our surface area is 600 feet!

Hope this helps, have a lovely day! :)

Mike cannot attain a mean grade of 85% for every one of his studies since a grade higher than 100% is not feasible.

The sum of all numbers divided by the entire number of values determines the mean (also known as the arithmetic mean, which differs from of the median) of a dataset. This central tendency is usually referred to as the "average".

Just dividing the total amount of information in a data collection even by sum of all of the values yields it. Both raw data and data that have been compiled into a frequency distribution table can be used for the computation.

mean = (sum of all numbers) / (number of numbers)

80% = (82% + 75% + 78% + 80% + m) / 5

85% = m

The another equation is,

85% = (82% + 75% + 78% + 80% + m) / 5

425% = 315% + m

110% = m

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Addressing issue hand, we state that Therefore, the linear equation solution to the system of equations is: x = 0.5, y = 0.1667, z = -0.5 and x = 0.500, y = 0.167, z = -0.500

In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.

values of x, y, and z, we can use the system of equations

3x - 2y + z = 1

2x + y - z = 0

x + 2y + 3z = -1

We can use Gaussian elimination or any other suitable method to solve the system. Here's one way to do it:

3x - 2y + z = 1          (eq. 1)

2x + y - z = 0           (eq. 2)

x + 2y + 3z = -1         (eq. 3)

       3x - 2y + z = 1          (eq. 1)

       0.6667x + 1.3333y - 1.3333z = -0.6667    (eq. 2')

       -0.3333y + 2.3333z = -1.3333    (eq. 3')

       3.3333x - 0.3333z = 0.1667    (eq. 1')

       0.6667x + 1.3333y - 1.3333z = -0.6667    (eq. 2')

       2.1667z = -1.0833    (eq. 3')

       z = -0.5

       y = 0.1667

       x = 0.5

Therefore, the solution to the system of equations is:

x = 0.5, y = 0.1667, z = -0.5

x = 0.500, y = 0.167, z = -0.500

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Answer:

The volume of one cone-shaped cup can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the cone and h is the height. Substituting the given values, we get:

V = (1/3)π(5 cm)^2(10 cm)

V ≈ 261.8 cm^3

Therefore, one cup can hold approximately 261.8 cubic centimeters of flower petals.

To find the total volume of petals that all 150 cups will hold, we can multiply the volume of one cup by the total number of cups:

Total volume = 150 cups × 261.8 cm^3/cup

Total volume ≈ 39,270 cm^3

Rounding to the nearest whole number, we get that the total volume of petals that all the cones will hold is approximately 39,270 cubic centimeters.

Answer:

I forgot how to do this sorry

Answer: 64 Rs

Step-by-step explanation:

Let x be the number of tables

4 x 48 = 3x

192 = 3x

x = 64

Answer:

No , they are not

Step-by-step explanation:

Checking the ratios:

32/48 = 0.67

48/80 = 0.6

80/150 = 0.53

Since the values are not equal, they are not in proportion.

Answer:

32, 48, 80, and 150 are not in proportion.

Step-by-step explanation:

To determine if 32, 48, 80, and 150 are in proportion, we need to check if the ratio of any two numbers is equal to the ratio of any other two numbers in the set.

Let's check:

Ratio of 32 to 48: 32/48 = 2/3

Ratio of 48 to 80: 48/80 = 3/5

Ratio of 80 to 150: 80/150 = 8/15

Since the ratios are not equal, 32, 48, 80, and 150 are not in proportion.

The retail price of each art supply bundle, including the markup, would be $127.50.

The gross or whole profit on a certain item or service is what is meant by markup. Moreover, it can be shown as a % of the cost price. For instance, if a product costs Rs. 100 and is sold for Rs. 150, the markup in this case will be 50%.

In studying the fundamentals of business, students come across the words selling price and cost price. A commodity's cost price is the amount paid when buying it from a retailer. The selling price, however, is the cost at which it is offered for sale.

Given that, the products were marked them up by 70%, then the selling price would be:

Selling price = $75 + 70% of $75

Selling price = $75 + $52.50

Selling price = $127.50

Therefore, the retail price of each art supply bundle, including the markup, would be $127.50.

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Answer:

-10

Step-by-step explanation:

BODMAS

Brackets

Of

Division

Multiplication

Addition

Subtraction

●When simplifying an equation follow the above order.

•Since division comes before subtraction, first divide -24 by -8 to get 3

•Then subtract 13 from 3 to give you -10.

The sum of the first 31 terms in the new sequence is 5.

Let S = {-4, 0, 2, 3}

New Sequence = {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............}

The four terms are repeatedly separated, as we can see above. Below are some of the first four terms = -4 + 0 + 2 + 3 = 1

Now, first four terms sum = 1

Next four terms sum = 1.

So sum of first 28 terms is given as

1 + 1 + 1 + 1 + 1 + 1 + 1 = 7

Now we find sum of first 31 terms = 7 - 4 + 0 + 2 = 5

So, sum of first 31 terms of new sequence {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............} is 5.

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To the nearest degree, the angle of the incline was approximately 39°.

What is an angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

We can use the inverse tangent function to calculate the angle of the incline. The angle θ is given by:

θ = tan⁻¹(opposite/adjacent)

where opposite is the vertical distance (the height Nick hiked) and adjacent is the horizontal distance (the distance he traveled eastward).

Using the Pythagorean theorem, we can find the height Nick hiked:

height = [tex]\sqrt{(10)^{2} - (8)^2}[/tex]≈ 6

So, the opposite is approximately 6 miles.

Now we can plug in the values to find the angle:

θ = tan⁻¹(6/8)

θ ≈ 38.66°

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Answer:

its a negative slope because the battery is going down, not staying the same, or going up

Step-by-step explanation:

The statement: If ∠F is a 60° angle, then cos (F) = sin (F), is never true.

Two of the six trigonometric functions used to connect angles to the sides of a right triangle are sine and cosine. The length of the opposite side of an angle divided by the length of the hypotenuse of a right triangle is known as the sine function. The length of the adjacent side of an angle divided by the length of the hypotenuse of a right triangle is known as the cosine function.

We know that,

If angle F is 60 degrees, then the value of cos F = 1/2 and sin F = sqrt(3)/2.

Therefore, cos F is not equal to sin F and the statement is never true.

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The point [-8,-6] would be graphed 8 units left and 6 units down from the origin (0,0) on a coordinate grid.

A coordinate grid, also called a Cartesian plane, is a two-dimensional plane formed by a horizontal x-axis and a vertical y-axis that intersect at the origin (0,0). It is used to graph and locate points in a two-dimensional space by their x- and y-coordinates.

The coordinate grid is formed by two perpendicular lines, the horizontal x-axis and the vertical y-axis.

The point [-8,-6] represents an ordered pair where -8 is the x-coordinate and -6 is the y-coordinate.

To graph this point on a coordinate grid, start at the origin (0,0), which is where the x-axis and y-axis intersect. Then, move 8 units to the left along the x-axis since the x-coordinate is negative.

After that, move 6 units down along the y-axis since the y-coordinate is negative. The point where you end up after moving left 8 units and down 6 units is the point (-8,-6).

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After answering the provided question, we can conclude that As a result, expression the answer is D. 144n.

In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators.  Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

According to the scale, 1 inch on the drawing equals 3 feet in real life. As a result, the pool's length is 4 inches x 3 feet/inch = 12 feet. Similarly, the pool's width is 4 inches x 3 feet/inch = 12 feet.

As a result, the pool's area equals the length multiplied by the width, which is:

144 square feet = 12 feet x 12 feet.

As a result, the answer is D. 144n.

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Answer:

L = 20 , B = 10

Step-by-step explanation:

L = 2B

we know perimeter of rectangle = 2( L + B )

By substitution , 2( 2B+ B) =60

4B + 2B = 60

6B = 60

B= 10

L = 2 * B = 2 * 10 = 20

Yeah, it seems fine so you're doing great so far! ^^

Answer:

[tex]y=(x+4)^2-8[/tex]

Step-by-step explanation:

[tex]y=x^2-8x-8[/tex]

complete the square.

[tex](x+4)^2-8[/tex]

set y equal to the new right side.

[tex]y=(x+4)^2-8[/tex]

Hope this helps!

Brainliest is much appreciated!

Answer:

Step-by-step explanation:

a = 1

c = -8

b= -8

the formula of vertex form is a(x-h)^2 +k = y

First find H and k using the formula -b/2a = h

h = 4

so, k = -24

y =1(x-4)^2 -24

Assuming the family size selected is 6 persons,

Assuming the family size selected is 6 persons, the minimum diameter of a circular table to seat all members would be:

Minimum diameter = (Number of persons x Minimum distance between two persons) / π

= (6 x 24) / 3.14

= 45.86 inches (rounded up to 46 inches)

The minimum length of the side of a square table to seat all members would be:

Minimum length of side = (Number of persons x Minimum distance between two persons) / √2

= (6 x 24) / 1.41

= 101.41 inches

The area of the top of the circular table would be:

Area = π x (Diameter / 2)²

= π x (46 / 2)²

= 1,660.51 In²

The area of the top of the square table would be:

Area = (Length of side)²

= 102²

= 10,404 In²

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The airplane is approximately 1.7 miles from the runway at the start of the approach.

What is trigonometry?

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry

To solve this problem, we need to use trigonometry. The angle of descent is 7 degrees, which means that the angle between the horizontal ground and the plane's flight path is 7 degrees. We can use the tangent function to find the distance from the runway:

tangent (7 degrees) = opposite / adjacent

The opposite side is the height of the plane above the ground, which is 1069 feet. The adjacent side is the distance from the plane to the runway, which we need to find.

tangent (7 degrees) = 1069 / adjacent

We can solve for the adjacent side by multiplying both sides by the denominator:

adjacent = 1069 / tangent(7 degrees)

Using a calculator, we get:

adjacent = 1069 / 0.122173048

adjacent = 8743.3 feet

To convert this to miles, we divide by the number of feet in a mile:

adjacent = 8743.3 / 5280

adjacent = 1.655 miles

Rounding to the nearest tenth of a mile, we get:

The airplane is approximately 1.7 miles from the runway at the start of the approach.

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In a case whereby concrete sidewalk is being put around a square park. If the diagonal line across the center of a square park is 24 feet, the exact length of each side is 12 feet.

Based on the given condition from the question, We know that A diagonal is a line segment that joins two opposing polygonal vertices (or corners). In other terms, a diagonal is a line segment that joins two polygonal vertices that are not next to one another. One type of straight line is the diagonal. There is no straight up, down, or across in a diagonal line. It is a line that joins two shape's corners.

Then we can formulate as 24/2

= 12 feet.

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Answer:

1st=3/50

2nd=2/50

3rd=1/50

thats is if the only possible number you can roll are only from 2,6 not 1,6