Find the mean of the following probability distribution? Round your answer to one decimal.
x 0,1,2,3,4
P(x) 0.0017, 0.3421, 0.065, 0.4106, 0.1806
mean = ___

You have been investing money in this account for approximately 15 years.

To determine the number of years you have been investing money in the account, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)ⁿ- 1] / r

Where:

FV = Future value (final balance in the account) = $461,103.46

P = Annual deposit amount = $8,500

r = Annual interest rate = 3.8% or 0.038 (expressed as a decimal)

n = Number of years

By substituting the given values into the formula and solving for n, we can determine the number of years you have been investing:

$461,103.46 = $8,500 * [(1 + 0.038) ⁿ- 1] / 0.038

54.24 = (1.038 ⁿ - 1) / 0.038

To solve for n, we can rearrange the equation:

1.038  ⁿ- 1 = 54.24 * 0.038

1.038  ⁿ= 2.0632

n = log base 1.038 of 2.0632

Using a logarithmic calculator, we find that n ≈ 14.96. Rounding up, we conclude that you have been investing money in this account for approximately 15 years.

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To minimize the annual holding and setup costs of purchasing bathroom tissue, you should buy single rolls of bathroom tissue. Purchasing the bathroom tissue in 12-packs is not more economical in this scenario.

To determine the optimal choice between buying single rolls and 12-packs of bathroom tissue, we need to consider the annual holding and setup costs.

a. To minimize the annual holding and setup costs, we need to compare the costs of buying single rolls versus 12-packs.

For single rolls:

Cost per roll = $0.45

Holding cost per roll per year = opportunity cost of money * cost per roll = 0.25 * $0.45 = $0.1125

Setup cost per purchase = $1

Consumption rate = 1 roll every 3 months = 4 rolls per year

For 12-packs:

Cost per pack = $5

Number of rolls in a 12-pack = 12

Holding cost per roll per year = 0.25 * ($5 / 12) = $0.1042

Setup cost per purchase = $1

To minimize the annual holding and setup costs, we need to compare the costs of purchasing the required number of single rolls and the cost of purchasing 12-packs.

b. Comparing the costs, it is more economical to purchase single rolls because the holding cost per roll per year is lower for single rolls ($0.1125) compared to 12-packs ($0.1042). Additionally, the setup cost is the same for both options ($1).

Therefore, to minimize the annual holding and setup costs, you should buy single rolls of bathroom tissue rather than 12-packs.

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The rancher can run approximately 19,425 mature 200 lb. ewes. To calculate the number of mature 200 lb. ewes the rancher can run on the remaining forage, we need to find the available forage after accounting for the 30 head of elk.

A rancher in Central California has a 5,000-acre BLM grazing allotment in the Oak Woodlands. Seventy percent of the allotment has loam soils producing 900 lbs. (DM) of forage per year, while the remaining 30% with sandy loam soil produces 500 lbs. of forage (DM) per year. The rancher must also account for 30 head of elk (500 lbs.). We need to determine how many mature 200 lb. ewes can be run on the remaining forage.

The total forage available from the loam soil is 70% of 5,000 acres, which is 3,500 acres. This amounts to 3,500 acres * 900 lbs./acre = 3,150,000 lbs. of forage (DM) per year.

Similarly, the total forage available from the sandy loam soil is 30% of 5,000 acres, which is 1,500 acres. This amounts to 1,500 acres * 500 lbs./acre = 750,000 lbs. of forage (DM) per year.

With the elk accounting for 30 * 500 lbs. = 15,000 lbs. of forage, the remaining available forage is 3,150,000 lbs. + 750,000 lbs. - 15,000 lbs. = 3,885,000 lbs.

Dividing the remaining forage by the weight of a mature ewe (200 lbs.), we get 3,885,000 lbs. / 200 lbs. = 19,425 ewes. Therefore, the rancher can run approximately 19,425 mature 200 lb. ewes on this allotment, considering the given forage production and the presence of elk.

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Answer:

if you round of. 20 the answer is 10

Answer:

B

Step-by-step explanation:

I did it on khan academy

Answer:

Step-by-step explanation:

The square root of 16 and the square root of 17

Answer:

29 and 34

Step-by-step explanation:

cause

Answer:

20 inches

Step-by-step explanation:

Since the cape is trapezoid shaped and has an area of 600 in², the area of a trapezoid is given by

A =1/2(a + b)h where a = length along the top of the cape = 24 in, b =  length along the bottom of the cape = 36 in and h = height of the cape

So, h = 2A/(a + b)

= 2 × 600 in²/(24 in + 36 in)

= 1200 in²/60 in

= 20 in

So, the height of the cape is 20 inches

Answer:

Perimeter of pizza slice = 27.85 inches (Approx.)

Step-by-step explanation:

Given:

Diameter of pizza = 20 inches

So,

Radius of pizza slice = Diameter of pizza / 2

Radius of pizza slice = 20 / 2 = 10 inches

∠IPZ = 45°

Find:

Perimeter of pizza slice

Computation:

Perimeter of pizza slice = 2[Radius of pizza slice] + [θ/360][2πr]

Perimeter of pizza slice = 2[10] + [45/360][(2)(22/7)(10)]

Perimeter of pizza slice = 20 + [0.125][(2)(3.14)(10)]

Perimeter of pizza slice = 20 + [0.125][62.8]

Perimeter of pizza slice = 20 + 7.85

Perimeter of pizza slice = 27.85 inches (Approx.)

The perimeter of the slice of the pizza that is eaten, measured in inches, for the considered case, is 31.9635 inches.

[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]

The superscript 'c' shows angle measured is in radians.

If radius of the circle is of r units, then:

[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]

For this case, we're given that:

Not using the above formula, but the concept, we know that:

Since diameter of pizza = 20 inches, its radius r = 10 inches.

Thus, the length of the arc IZ = [tex]\dfrac{2 \times \pi \times 10}{8} \approx 1.9635 \: \rm inches.[/tex]

Perimeter of the slice of the pizza eaten = sum of the length of its boundaries = Length of arc IZ + length of line IP + length of line ZP

Since line IP and ZP are radius, thus:

Perimeter of the slice of the pizza eaten ≈ 1.9635 + 10 + 10 = 31.9635 inches.

Thus, the perimeter of the slice of the pizza that is eaten, measured in inches, for the considered case, is 31.9635 inches.

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Answer:

∠ H = 59°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

121° is an exterior angle of the triangle, then

6x - 1 + 5x + 12 = 121 , that is

11x + 11 = 121 ( subtract 11 from both sides )

11x = 110 ( divide both sides by 11 )

x = 10

Then

∠ H = 6x - 1 = 6(10) - 1 = 60 - 1 = 59°

Answer:

SECTION C (i think)

Please mark as brainliest

Have a great day, be safe and healthy  

Thank u  

XD

Answer:

section c

it's square root is 4.123......

Answer:

D

Step-by-step explanation:

lol this is a weird math question

jk

Hydrogen bonds occur only when hydrogen is covalently bonded to one of three elements: fluorine, oxygen, or nitrogen. Anything else isn't considered a hydrogen bond.

Answer:

zero point zero zero one two five

Step-by-step explanation:

Answer: Question 1, debit card because debit cards are used for atms which requires a pin. A positive is that you’re using your own money for a debit card and not from another source, so you don’t have to pay extra frees

Step-by-step explanation:

Answer:

OE=53 and UH = 53

Step-by-step explanation:

Pythagoras theorem

Answer:

The age of the boy is 15 years

Step-by-step explanation:

Let us assume a be the age of the boy

So, two-third of his age is 2 ÷ 3 × a

As the boy said that two-third minus 1 so it would be equivalent to

  2 ÷ 3 × to - 1

ANd, his current age is a and now if we deduct 6 so

a - 6

AFter this, two-third minus 1 is equivalent to a minus 6

So,  

 2 ÷ 3 × a - 1 = a - 6

- 1 + 6 = a -  2 ÷ 3 × a  

5 =  1 ÷ 3 × a  

a = 3 × 5

 = 15

Hence, The age of the boy is 15 years

Answer:

Z=[tex]7\sqrt{2}[/tex] m

Step-by-step explanation:

This is a 45º-45º-90º triangle. That means the side lengths are x, x, and [tex]x\sqrt{2}[/tex].

In this case 14 m is equal to [tex]x\sqrt{2}[/tex]. Now solve for X, which is equal to Z.

The rest of the work is written down in the file attached

Don't forget the units though!

hope I could help

Answer:

4mph

Step-by-step explanation:

Answer:

5! HOPE I HELPED

Step-by-step explanation:

Answer: 19 mins

Step-by-step explanation:

hope this helps

Answer:

(x+2)^2 + (y+2)^2 = 0.75^2

Step-by-step explanation:

equation of a circle in standard form: (x-h)^2 + (y-k)^2 = r^2

center: (-2, -2)

radius: 0.75

equation of the circle in provided graph: (x+2)^2 + (y+2)^2 = 0.75^2

Answer:

x=6

Step-by-step explanation:

3x- 4=14

   +4 +4

    3x=18

      x=6

Answer & explanation:

The student made an error by adding an r after removing the parentheses instead of subtracting an r.

Correct Steps:

(6b + 4r) – (2b + r)

6b + 4r - 2b - r

4b + 3r

Answer:

yo

Step-by-step explanation:

this was the sample response on edge

The student did not distribute the negative when subtracting. Distributing the negative, the expression is equal to 6b + 4r – 2b – r. Then use the commutative property to rewrite it as 6b – 2b + 4r – r. Then you can use the distributive property to write as (6 – 2)b + (4 – 1)r, which simplifies to 4b + 3r.

The linear transformation T: R^2 → R^2, defined by T(v) = Av, where A = [[-2, -2], [1, 2]], maps a two-dimensional vector space onto itself. The dimension of R^2 is 2.

In the given linear transformation T: R^2 → R^2, the transformation is defined as T(v) = Av, where A is the transformation matrix. The given matrix A = [[-2, -2], [1, 2]] represents the coefficients of the linear transformation. This means that the transformation T takes a two-dimensional vector v in R^2 and applies the matrix A to it.

The dimension of R^2 is 2, indicating that the vector space R^2 consists of all ordered pairs (x, y) where x and y are real numbers. In this case, the linear transformation T maps a vector in R^2 to another vector in R^2, so both the input and output dimensions are 2.

The dimension of R^n refers to the number of components or variables in a vector in R^n. For example, R^2 consists of vectors with two components, while R^3 consists of vectors with three components. In this case, the dimension of R^2 is 2 because each vector in R^2 has two components.

To summarize, the given linear transformation T: R^2 → R^2, with the matrix A = [[-2, -2], [1, 2]], maps a two-dimensional vector space onto itself. The dimensions of both R^2 and R^2 are 2, representing the number of components in the vectors of each space.

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Answer:

Is this high school math or middle school?.

Step-by-step explanation:

a²+b² = c²

8²+2²

↓    ↓

64+4

   ↓

square root 68 and it should give you 8.24 and then you round.

Given:

The vertices of a triangle are A(-1,-1), B(-1,-5), C(0.5,-5).

The figure is translated 2 units left.

To find:

The vertices and the diagram of the triangle after the given translation.

Solution:

if a figure is translated 2 units left, then

[tex](x,y)\to (x-2,y)[/tex]

Using the above rule, we get

[tex]A(-1,-1)\to A'(-1-2,-1)[/tex]

[tex]A(-1,-1)\to A'(-3,-1)[/tex]

Similarly,

[tex]B(-1,-5)\to B'(-1-2,-5)[/tex]

[tex]B(-1,-5)\to B'(-3,-5)[/tex]

And,

[tex]C(0.5, -5)\to C'(0.5-2,-5)[/tex]

[tex]C(0.5, -5)\to C'(-1.5,-5)[/tex]

So, the vertices of the triangle after the translation are A'(-3,-1), B'(-3,-5), C'(-1.5,-5).

Therefore, the correct option is B.

Answer:

B

Step-by-step explanation:

The system of linear differential equations is given as y₁' = 3y₁ + 3y₂² and y₂' = 2y₁ + t*y₂ - 4. By comparing it with the general form y' = P(t)y + g(t), we determine that P(t) = [[3, 3y₂²], [2, t]] and g(t) = [0, -4].

To determine the coefficient matrix P(t) and the forcing term g(t), we can compare the given system of linear differential equations with the general form y' = P(t)y + g(t).

The given system is:

y₁' = 3y₁ + 3y₂²

y₂' = 2y₁ + t*y₂ - 4

Comparing the first equation with the general form, we have:

P₁₁ = 3

P₁₂ = 3y₂²

g₁(t) = 0

Comparing the second equation with the general form, we have:

P₂₁ = 2

P₂₂ = t

g₂(t) = -4

Therefore, the coefficient matrix P(t) and the forcing term g(t) for the given system are:

P(t) = [[3, 3y₂²], [2, t]]

g(t) = [0, -4]

Note that the value of y₂ is not provided in the equation for g₂(t), so it remains as y₂ in the expression.

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Answer:

C?

Step-by-step explanation:

Answer:

I think the answer is 1/2 but dont take my word

Answer:

They will each get 9 pieces of candy.

Step-by-step explanation:

if she has 4 friends and she shares with them, she would be sharing  with 4 people plus herself, so you would do the problem 45 ÷ 5 = 9.