Can someone help me write a proof for this

The IikeIihood that the hawk wiII first take a songbird and subsequentIy a rabbit is therefore (2/9) x (8/11) = 16/99, or roughIy 0.1616.

In mathematics, a percentage is a number or ratio that may be stated as a fraction of 100. Divide a number by the whole and multiply the result by 100 to calculate its percentage. As a result, the percentage represents a part per hundred. 100% is meant by the phrase %. The symbol "%" is used to indicate it.

The probability that a hawk will eat a songbird before a rabbit is calculated as the product of those probabilities.

Given that there are four songbirds with eight rabbits, the IikeIihood that a songbird wiII be consumed by a hawk is 4/(4+6+8) = 4/18 = 2/9.

Three songbirds & eight rabbits remain after the hawk consumes a songbird, hence the IikeIihood that the hawk wiII eat a rabbit next is 8/(3+8) = 8/11.

To know more about Percent visit:

https://brainly.com/question/28670903

#SPJ1

I - The collapse of the housing market due to low interest rates, easy credit, insufficient regulation, and toxic subprime mortgages: C. Problems in financial markets.

II - Consumers are very worried about the economy: B. Negative demand shift.

1 - The collapse of the housing market due to low interest rates, easy credit, insufficient regulation, and toxic subprime mortgages falls into the category of "Problems in financial markets" (C). This event can lead to a recession because it can cause a decrease in the wealth of households, leading to a decrease in consumer spending and a decrease in aggregate demand.

II - Consumers being very worried about the economy falls into the category of "Negative demand shift" (B). This event can lead to a recession because when consumers are worried about the economy, they tend to save more and spend less, leading to a decrease in aggregate demand. This decrease in demand can cause businesses to decrease production and lay off workers, leading to a decrease in income and further decrease in demand.

You can learn more about interest rates at

https://brainly.com/question/29415701

#SPJ11

There are 6 faces in a cube, the total surface area of the toy box is 6 x 4 = 24 square feet. So correct option is B.

In geometry, a cube is a three-dimensional shape that is bounded by six square faces, with each face meeting at right angles. A cube is a regular polyhedron, which means that all of its faces are congruent and all of its edges have the same length.

The cube has a total of eight vertices (corners) and twelve edges, with each vertex connecting three edges and each edge connecting two vertices. The volume of a cube can be calculated using the formula V = s^3, where s is the length of one edge.

Cubes are commonly used in mathematics, physics, and engineering to represent three-dimensional objects and to model various phenomena. For example, cubes can be used to represent the atoms in a crystal lattice, the cells in a grid, or the pixels in a digital image

The toy box is a cube, and each edge measures 2 feet. So, the surface area of one face of the cube is 2 x 2 = 4 square feet. Since there are 6 faces in a cube, the total surface area of the toy box is 6 x 4 = 24 square feet.

Therefore, the answer is (B) 24 feet squared.

To know more about area visit:

https://brainly.com/question/14994710

#SPJ1

The complete question is:

Difference in the medians as a multiple of the IQR = 5.

The Interquartile Range (IQR) formula computes the median of a set of data. One of the smallest statistical measurements of dispersion is the interquartile range. The interquartile range refers to the spread between the upper and lower quartiles.

The interquartile range is defined as Upper Quartile - Lower Quartile.

According to the question,

Data set of Mount Vernon= 55, 60, 65, 70, 75, 80, 85, 90

Data set of Lakewood= 65, 70, 75, 80, 85

Data sets are already in ascending order.

Median for Mount Vernon = 70+75/2 = 77.5

Median for lower half of set= 55+60+65+70/4 = 62.5

Median for upper half of set= 75+80+85+90/4 = 82.5

IRQ for Mount Vernon = 82.5-62.5 = 20

Now similarly in case of Lakewood,

Median= 75.

Median for lower half of set = 65+70/2 = 67.5

Median for upper half of set = 80+85/2 = 82.5

IRQ = 82.5 - 67.5 = 15.

Hence, difference in IRQ = 20-15 = 5.

To know more about IQR, visit:

https://brainly.com/question/29198800

#SPJ1

A basis for the subspace  of R4 defined by the equation−2x1​−7x2​+2x3​−4x4​=0 is the set of vectors {(-7/2, 1, 0, 0), (1, 0, 1, 0), (-2, 0, 0, 1)}.

A basis for the subspace of −2x1​−7x2​+2x3​−4x4​=0 can be found by solving for one of the variables in terms of the others and then finding the general solution.

First, solve for x1 in terms of the other variables:
-2x1 = 7x2 - 2x3 + 4x4
x1 = (-7/2)x2 + x3 - 2x4

Now, the general solution can be written as:
(x1, x2, x3, x4) = (-7/2)x2 + x3 - 2x4, x2, x3, x4

This can be rewritten in terms of the free variables x2, x3, and x4:
(x1, x2, x3, x4) = x2(-7/2, 1, 0, 0) + x3(1, 0, 1, 0) + x4(-2, 0, 0, 1)

Learn more about basis at https://brainly.com/question/30820548

#SPJ11

If three pens are randomly selected from the following basket of pens, without replacement,  the probability that all three pens are blue is 0.027, none of the pens are blue is 0.343, and  at least one of the pens is black is 0.657.

The probability of selecting three blue pens without replacement from the basket of pens is:  

P(all 3 blue) = (Number of blue pens / Total number of pens)³

= (3 / 10)³

= 0.027

The probability of selecting three pens that are not blue without replacement from the basket of pens is:  

P(none blue) = (Number of pens that are not blue / Total number of pens)3

= (7 / 10)³

= 0.343

The probability of selecting at least one black pen without replacement from the basket of pens is:

P(at least one black) = 1 - (Number of pens that are not black / Total number of pens)3

= 1 - (7 / 10)³

= 0.657

Learn more about probability at https://brainly.com/question/15584918

#SPJ11

Step-by-step explanation:

this represents a trigonometric triangle (right-angled) inside an imaginary circle.

imagine the triangle is turned 90° counterclockwise, so that A is the bottom left vertex, B is the bottom right vertex.

then x is the angle (40°) defining radius of the circumscribing circle.

remember, sine is the up/down leg, cosine is the left/right leg. and in a larger circle they are all multiplied by the radius.

so,

4 = cos(40) × x

x = 4 / cos(40) = 5.221629157... ≈ 5.22

(1) The polynomial x^2 − 2 can be factored into (x + 5)(x − 5) in Z7[x].
(2) The polynomials x^3 − k, where k = 0, 1, 2, 3, 4, 5, 6, are all irreducible in Z7[x].

(3) The polynomial x^4 − 1 can be factored into (x − 1)(x + 1)(x^2 + 1) in Z7[x].

This is because 5 and −5 are both roots of the polynomial, since 5^2 ≡ 2 (mod 7) and (−5)^2 ≡ 2 (mod 7).

This is because none of them have any roots in Z7, which means they cannot be factored into lower degree polynomials.

For example, x^3 − 0 has no roots in Z7, since there is no integer x such that x^3 ≡ 0 (mod 7). Similarly, x^3 − 1 has no roots in Z7, since there is no integer x such that x^3 ≡ 1 (mod 7), and so on for the other values of k.

This is because 1, −1, and ±i are all roots of the polynomial, since 1^4 ≡ 1 (mod 7), (−1)^4 ≡ 1 (mod 7), and (±i)^4 ≡ 1 (mod 7). Therefore, x^4 − 1 = (x − 1)(x + 1)(x^2 + 1) in Z7[x].

To know more about irreducible click on below link:

https://brainly.com/question/29502514#

#SPJ11

So the expression that shows how many glitter pens Lindsey puts in each goody bag is 24 divided by the number of goody bags, represented by "b".

How likely something is to happen can be determined using probability. For instance, while flipping a coin, there is a one in two chance of receiving heads because there is only one way to get a head and a total of two outcomes. the tail or the head. We set P(heads) = 12 in this case.

Let's represent the number of glitter pens Lindsey puts in each goody bag by the variable "p".

To find the value of "p", we can divide the total number of glitter pens by the number of goody bags:

p = 24 / b

So the expression that shows how many glitter pens Lindsey puts in each goody bag is 24 divided by the number of goody bags, represented by "b".

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

The mass of the sample decays by a factor of 3/5 every 4.27 months.

In science, decay refers to the natural process of deterioration or breakdown of a substance over time. Decay can occur in many different contexts, such as the decay of radioactive materials, the decay of organic matter, and the decay of physical structures.

In radioactive decay, unstable atoms release energy and subatomic particles as they decay into more stable forms. This process occurs at a predictable rate, which can be used to determine the age of rocks and other materials.

In organic decay, biological matter breaks down into simpler compounds through the action of bacteria and other decomposers. This process is an essential part of the natural cycle of life and death, and it helps to recycle nutrients and other vital substances in ecosystems.

To find the time it takes for the mass to decay by a factor of 3/5, we can set up the following equation:

M(t) = (3/5)M(0)

[tex]120(\frac{625}{81} )^{t} = \frac{3}{5} \\\frac{625}{81}= \frac{3}{5}^{\frac{1}{t} } \\ln(\frac{625}{81})=ln(\frac{3}{5}^{\frac{1}{t} })\\[/tex]

[tex]t=\frac{ln(\frac{625}{81})}{ln(\frac{3}{5})} = 4.27months[/tex]

To know more about mass visit:

https://brainly.com/question/14289726

#SPJ1

The solution of the heat equation subject to the boundary and the initial conditions is u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt).

The heat equation with the given boundary conditions is:

∂u/∂t = k ∂^2u/∂x^2

where k is a constant. We can use separation of variables to solve this equation. Let:

u(x, t) = X(x)T(t)

Substituting this into the heat equation, we get:

X(x)T'(t) = k X''(x)T(t) / X(x)T(t)

Dividing both sides by X(x)T(t) and rearranging, we get:

X''(x)/X(x) = T'(t)/(kT(t))

The left-hand side depends only on x, while the right-hand side depends only on t. Since they are equal, they must be equal to a constant:

X''(x)/X(x) = -λ

T'(t)/(kT(t)) = λ

where λ is a constant. The boundary conditions u(0,t) = u(1,t) = 0 imply that X(0) = X(1) = 0. The general solution for X(x) is then:

X(x) = A sin(nπx)

where A is a constant and n is a positive integer. The eigenvalues λ are:

λ = -(nπ)^2

The general solution for T(t) is:

T(t) = B exp(-kλt)

where B is a constant. The solution for u(x, t) is then:

u(x, t) = Σ[ A_n sin(nπx) exp(-(nπ)^2 kt) ]

where the sum is taken over all positive integers n.

We can now use the initial condition u(x,0) = 4sin3πx+8sin6πx to determine the constants A_n. Since the solution only contains sine terms, we can use the Fourier sine series to expand the initial condition:

4sin3πx+8sin6πx = Σ[ A_n sin(nπx) ]

where the sum is taken over all positive odd integers for n = 3 and all positive even integers for n = 6. The coefficients A_n are:

A_3 = 4π/3

A_6 = 16π/6

Substituting these values into the solution for u(x, t), we get:

u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt)

Learn more about Heat Equation at:

brainly.com/question/13415835

#SPJ4

The solution to the equation (2)/(3)m=(5)/(8) is m = (15)/(16)

To solve the equation (2)/(3)m=(5)/(8), we can use the Division Property of Equality and the Multiplication Property of Equality.

Here are the steps:

1. Start with the original equation: (2)/(3)m=(5)/(8)

2. Multiply both sides of the equation by the reciprocal of (2)/(3), which is (3)/(2): (2)/(3)m * (3)/(2) = (5)/(8) * (3)/(2)

3. Simplify the left side of the equation: m = (5)/(8) * (3)/(2)

4. Simplify the right side of the equation: m = (15)/(16)

5. Check your solution by plugging it back into the original equation: (2)/(3) * (15)/(16) = (5)/(8)

6. Simplify the left side of the equation: (30)/(48) = (5)/(8)

7. Simplify the right side of the equation: (5)/(8) = (5)/(8)

8. Since both sides of the equation are equal, the solution is correct.

So the solution to the equation (2)/(3)m=(5)/(8) is m = (15)/(16).

To know more about Division Property of Equality refer here:

https://brainly.com/question/13130806#

#SPJ11

Boulder takes 4.13 seconds to reach its maximum height.

The boulder's maximum height is 282.38 feet.

Velocity is a physical quantity that describes the rate of change of an object's position over time. Velocity has both magnitude as well as direction that's why it is a vector quantity.

Given that:

Upward velocity of the boulder = 132 ft/s

Function for the height of the boulder as a function of time, t:

h(t) = -16[tex]t^{2}[/tex] + 132t + 30

We can find the maximum height of the boulder and the time it takes to reach that height by finding the vertex of the parabolic function h(t) using the formula:

t = -b/2a

where a = -16 and b = 132.

First, we need to find the time it takes the boulder to reach its maximum height, t:

t = -b/2a = -132/(2*(-16)) = 4.125 seconds

So, it takes the boulder 4.125 seconds to reach its maximum height.

Next, we need to find the maximum height of the boulder, h:

h = h(t) = -16t^2 + 132t + 30 = -16(4.125)^2 + 132(4.125) + 30 = 282.375 feet

So, the boulder's maximum height is 282.375 feet.

Rounding to the nearest hundredth, the time it takes the boulder to reach its maximum height is 4.13 seconds and the boulder's maximum height is 282.38 feet.

To know more about speed, Visit:

https://brainly.com/question/13943409

#SPJ1

The baker will use 2.5 cups of flour.

Multiplication is a mathematical operation that involves combining two or more numbers to find their product or the total number of objects in equal groups. It is represented using the multiplication symbol (*) or a dot (·). For example, 2 * 3 = 6, which means that two groups of three objects will give you a total of six objects.

To solve this problem, we need to find the amount of flour required for each cupcake and cookie, and then multiply by the total number of cupcakes and cookies.

For the cupcakes:

1.5 cups of flour make 18 cupcakes

1 cup of flour will make 12 cupcakes (divide both sides by 1.5)

To make 30 cupcakes, we need 2.5 cups of flour (multiply both sides by 2.5)

For the cookies:

3 cups of flour make 36 cookies

1 cup of flour will make 12 cookies (divide both sides by 3)

To make 60 cookies, we need 5 cups of flour (multiply both sides by 5)

Therefore, to make 30 cupcakes and 60 cookies, the baker will need:

2.5 cups of flour for the cupcakes

5 cups of flour for the cookies

Total: 2.5 + 5 = 7 cups of flour

Therefore,  the baker will use 2.5 cups of flour.

To know more about multiplication visit:

https://brainly.com/question/1135170

#SPJ1

x = 1 is 68

The polynomial function that satisfies the given conditions is f(x) = (x-3)(x-3i)(x-4)(x-4i) = x4 - 11x3 + 34x2 + 104x - 324. Graphically, this function has 4 real zeros at x = 3, 3i, 4, and 4i, and the function value at x = 1 is 68.

Learn more about polynomial function

brainly.com/question/12976257

#SPJ11

The calculated probability that the selected member drinks champagne, given bridge is 82%

The statement derived from the question are stated as follows

The required conditional probability is calculated as

Probabiiity = Bridge and Drink/Bridge

So, we have the following equation

Probabiiity = 68%/83%

Evaluate

Probabiiity = 82%

Hence, the value of the probability is 82%

Read more about probability at

https://brainly.com/question/251701

#SPJ1

Answer:

To find 3.5% of 21, we can convert 3.5% to a decimal by dividing by 100:

3.5% = 3.5/100 = 0.035

Then, we can multiply 0.035 by 21 to find the answer:

0.035 * 21 = 0.735

Therefore, 3.5% of 21 is 0.735.

0.735

because o.31 percent of 21 is 0.735

The fund manager should invest $7.5 million in bonds and $27.5 million in mutual funds to maximize annual interest, and the maximum annual interest is given as  $2.595 million.

To solve this, we

Let x = amount invested in bonds and

y = amount invested in mutual funds.

We then can deduce the following constraints:

x + y ≤ 35 (total investment is at most $35 million)

x ≥ 5 (at least $5 million is invested in bonds)

y ≥ 20 (at least $20 million is invested in mutual funds)

100x + 200y ≤ 6000 (the total fees paid which cant exceed $6000)

Maximizing  the annual interest, which is given by:

0.06x + 0.09y

We will  use the method of Lagrange multipliers, to solve the optimization problems.

Let L(x, y, z) be the Lagrangian:

and we have that L(x, y, z) = 0.06x + 0.09y + z(x + y - 35) + μ(x - 5) + ν(y - 20) + ρ(100x + 200y - 6000)

We will have to take partial derivatives of L with respect to x, y, and z, and set them to be equals zero.

0.06 + z + μ + 100ρ = 0

0.09 + z + ν + 200ρ = 0

x + y - 35 = 0

Simplifying these equations, we have:

x = 7.5, y = 27.5, λ = -0.06, μ = 0, ν = 0, ρ = -0.02

0.06(7.5) + 0.09(27.5) = $2.595 million is the annual interest.

So then, It has been found that the fund manager should invest $7.5 million in bonds and $27.5 million in mutual funds to maximize annual interest, which is  $2.595 million.

Learn more about annual interest at: https://brainly.com/question/2699966

#SPJ1

What fraction of the trip has Andre completed.

A fraction is a way of representing a part of a whole or a quantity that is not a whole number. It is a mathematical expression that represents a ratio of two numbers, where the number above the line (numerator) represents the part being considered, and the number below the line (denominator) represents the whole or the total number of parts. Fractions are usually written in the form a/b, where a is the numerator and b is the denominator.

Given that the entire road to be covered is  1 5/8 kilometers and so far Andre has walked 1/3 kilometer, the expression represents the fraction that has been covered.

Learn more about fraction:https://brainly.com/question/10354322

#SPJ1

Missing parts;

Heathercain

01/24/2020

Mathematics

Middle School

answered • expert verified

3. Andre is walking from home to a festival that is 1 5\8 kilometers away. He takes a quick rest after walking 1\3 kilometers. In this situation, which question can be represented by the equation: ?× 1 5\8 = 1\3?

a. What fraction of the trip has Andre completed?

b. How many more kilometer does he have to walk to get to the festival?

c. What fraction of the trio is left.

d. How many kilometers is it from home to the festival and back home?

The mean is 389.875, the median is 333.5, and there is no mode for this set of numbers.

To find the mean, median, and mode for the set of numbers 244, 276, 114, 628, 572, 313, 354, 618, we will use the following steps:

1. Mean: The mean is the average of the numbers. To find the mean, we add up all the numbers and divide by the number of numbers in the set.

Mean = (244 + 276 + 114 + 628 + 572 + 313 + 354 + 618) / 8 = 3119 / 8 = 389.875

2. Median: The median is the middle number in the set when the numbers are arranged in ascending order. If there is an even number of numbers, the median is the average of the two middle numbers.

First, we arrange the numbers in ascending order: 114, 244, 276, 313, 354, 572, 618, 628
Since there are 8 numbers, the median is the average of the 4th and 5th numbers: (313 + 354) / 2 = 333.5

3. Mode: The mode is the number that appears most frequently in the set. If there are multiple numbers that appear the same number of times, they are all considered the mode.

In this set, there are no numbers that appear more than once, so there is no mode.

To know more about median click on below link:

https://brainly.com/question/28060453#

#SPJ11

The Noah’s mean is 87, median is 85.5, and mode is 85.

The Gabriel’s mean is 87.17, median is 86, and mode is 86.

The solution has been obtained by using measures of central tendency.

A central tendency measure seeks to define the core value of a data collection in order to characterise it. The metrics of central tendency are mean, median, and mode.

Noah’s scores: 84, 85, 85, 86, 90, 92

Mean = (84 + 85 + 85 + 86 + 90 + 92) / 6

Mean = 522 / 6

Mean = 87

Median = (85 + 86) / 2

Median = 85.5

Mode = 85

Gabriel’s scores: 82, 85, 86, 86, 90, 94

Mean = (82 + 85 + 86 + 86 + 90 + 94) / 6

Mean = 523 / 6

Mean = 87.17

Median = (86 + 86) / 2

Median = 86

Mode = 86

Hence, the mean, median and mode have been obtained.

Learn more about measures of central tendency from the given link

https://brainly.com/question/28180169

#SPJ1

Answer:

8 small and 14 large is the answer

Step-by-step explanation:

Answer:

2.4.1. To calculate how many litres of fuel are needed to travel 400km, we need to use the given fuel consumption rate of 8L/100km:

Fuel consumed for 400km = (8/100) x 400 = 32 litres

Therefore, 32 litres of fuel are needed to travel 400km.

2.4.2. To calculate how far you can travel with 50L of fuel, we can rearrange the formula from part 2.4.1 to solve for distance:

distance = (fuel consumed / fuel consumption rate) x 100

Plugging in the values we have:

distance = (50 / 8) x 100 = 625 km

Therefore, with 50 litres of fuel, you can travel 625 km.

Answer:

A - x= -13

Step-by-step explanation:

x + 3 = -10

Step 1) Subtract 3 on both sides

Step 2) x = -13

Answer:

False

Step-by-step explanation:

...............

Answer:

Sin A = [tex]\frac{12}{13}[/tex] ; Cos A = [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

The sine of a given angle is  [tex]\frac{opposite}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length opposite to angle A is 24, and the hypotenuse is 26. This gives  [tex]\frac{24}{26} = 12/13[/tex].

The cosine of a given angle is   [tex]\frac{adjacent}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length adjacent to angle A is 10, and the hypotenuse is 26. This gives  [tex]\frac{10}{26} = 5/13[/tex].

Answer:

8cfct on cypur574 6th 9

Step-by-step explanation:

f5g uh yo h tu g fn l dl uge ser k

The scale factor that Georgia used her scale drawing is 3/8.

A scale factor is simply a ratio between two corresponding lengths, areas, or volumes of two similar geometric figures.

Given that, Georgia made a scale drawing of her apartment. Her bathroom is 3 inches in the drawing and 8 feet in real life.

To find the scale factor, we need to determine how many inches in the drawing represent 1 foot in real life. We can set up a proportion:

3 inches : 8 feet = x inches : 1 foot

Cross-multiplying, we get:

3 inches × 1 foot = 8 feet × x inches

Simplifying, we get:

3 = 8x

Dividing both sides by 8, we get:

x = 3/8

Therefore, the scale factor is 3/8, which means that for every 3 inches in the drawing, there is 8 feet in real life.

Learn more about scale factors here: brainly.com/question/2826496

#SPJ1

Answer:

245

Step-by-step explanation:

The lateral and surface area of the given shape above in terms of π would be = 48π yd²:120π yd². That is option A.

To calculate the lateral surface area of the cylinder the formula below is used:

Lateral surface area = 2πrh

where;

r = diameter/2 = 12/2 = 6 yd

h = 4 yd

Lateral surface area = 2 ×π × 6×4 = 48π yd²

To calculate the surface area of the cylinder the following formula is used:

Surface area = 2πrh + 2πr²

r = diameter/2 = 12/2 = 6 yd

h = 4 yd

surface area = (2×π×6×4)+(2×π×36)

= 48π+72π

= 120π yd²

Learn more about area here:

https://brainly.com/question/25965491

#SPJ1