If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:

Answers

Answer 1

If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually. This can be obtained by using formulas for simple interest and compound interest.

What is the formulas of simple interest and compound interest?Simple interest

A = P(1 +Rt/100) , P = principle amount ,R = rate of interest, t = time(in years)

Compound interest (annually)

A = P(1 + R/100)^t , P = principal amount, R = rate of interest,                                t = time(in years)

   

What is the value of investment?

Given that,  

P = $11,000 , R = 8%,  t = 25 years

8% simple interest

A = P(1 +Rt/100) = [tex]11000(1+\frac{(8)(25)}{100} )[/tex] = $33,000

8% compounded annually

A = P(1 + R/100)^t = [tex]11000(1+\frac{8}{100} )^{25}[/tex] = [tex]11000(1.08 )^{25}[/tex] = $75,333.23

Hence If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually.

         

     

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:

(a) 8% simple interest

(b) 8% compounded annually


Related Questions

(06.03 HC)
Solve the following system of equations. Show all work and solutions.
y = 3x2 + 6x + 4
y = -3x2 + 4

Answers

Answer: [tex](x,y)=\{(-1,1), (0,4) \}[/tex]

Step-by-step explanation:

[tex]3x^2 +6x+4=-3x^2 +4\\\\6x^2 +6x=0\\\\x^2 +x=0\\\\x(x+1)=0\\\\x=-1, 0\\\\x=-1 \longrightarrow y=1\\\\x=0 \longrightarrow y=4\\\\\therefore (x,y)=\{(-1,1), (0,4) \}[/tex]

The solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).

What is a quadratic equation?

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given quadratic equations are given as below:-

y = 3x² + 6x + 4

y = -3x² + 4

Equate the equations and solve for the value of x.

3x² + 6x + 4 = -3x² + 4

6x² + 6x = 0

x² + x = 0

x ( x + 1 ) = 0

x = 0 and x = -1

At x=0 and x=-1 the values of y are calculated as below:-

y = -3x² + 4

y = 0+ 4 = 4

y = -3 + 4 = 1

Therefore, the solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).

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Find the equation for a parabola with its focus at (0, 3) and a directrix of y = -3.

x = 1/12y^2
y = 1/9x^2
y = 1/12x^2
y = -1/12x^22

Answers

The equation of the parabola is [tex]y=\frac{1}{24} x^2+3[/tex]

None of the given options is correct

Given:

Focus: (0, 3)

Directrix: y = -3

Note that:

f - k = k - (-3)

f - 3 = 3 + 3

f = 6 + 3

f = 9

The equation of the parabola is of the form:

[tex]y=\frac{1}{4(f-k)} (x-h)^2+k[/tex]

Substitute f = 9, k = 3, h = 0 into the equation

[tex]y=\frac{1}{24} (x-0)^2+3\\\\y=\frac{1}{24}x^2+3[/tex]

The equation of the parabola is [tex]y=\frac{1}{24} x^2+3[/tex]

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If x=y= 2z and x*y*z = 500, then x equals?​

Answers

Answer:

x is equal to 5

Step-by-step explanation:

When y=x and z=1/2x

xyz= 500
x(x)(1/2x)= 500
1/2x^3=500
x^3= 1000
x= 10

How to check your answer?

xyz= 500
(10)(10)(10/2)= 500
500= 500

Both LHS and RHS is equal therefore this answer is correct. x=10.

Hope it helps : )

prove that: 1-sin^2x cos*2x/cos^2x = tan^2x + cos^2x

Answers

LHS = (1-sin² cos²)/(cos²)

= (sin² + cos² - sin² cos²)/(cos²)

= (sin/cos)² + 1 - sin²

= tan² + cos²

= RHS

Accounts Receivable has a balance of $645,000; Allowance for Doubtful Accounts has a credit balance of $6,000; and sales for the year total $2,900,000. Bad debt expense is estimated at 1/4 of 1% of sales.

Answers

1. The amount of the adjusting entry for Uncollectible Accounts is $1,250.

2. The adjusted balances of Accounts Receivable Allowance for Doubtful Accounts Bad Debt Expense are:

Accounts Receivable = $3,545,000

Allowance for Doubtful = $7,250

Accounts Bad Debt Expense = $1,250

3. The net realizable value of the accounts receivable is $3,537.750 ($3,545,000 - $7,250).

Data and Calculations:

                               Accounts Receivable    Allowance for Doubtful Accounts

Beginning balance     $645,000 DR               $6,000 CR

Sales                          2,900,000

Bad Debt Estimate = $7,250 ($2,900,000 x 0.0025)

Ending balance      $3,545,000                     $7,250 CR

Bad Debts Expense = $1,250 ($7,250 - $6,000)

Thus, the net realizable value of the accounts receivable shows the amount that the company expects to recover from customers after allowing for doubtful accounts.

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Question Completion:

1. Determine the amount of the adjusting entry for uncollectible accounts.

2. Determine the adjusted balances of Accounts Receivable, Allowance for Doubtful Accounts, and Bad Debt Expenses.

3. Determine the net realizable value of accounts receivable

What do l do??? Need help

Answers

Answer:

you have to put the formula of perimeter

Answer:

12a. L+8m + 14m

12b. 10m+8m +14m

12c. 66

12d.420m

12e.252m

quick questions

volume= 288cm cubed

In a class there are 15 boys and 15 girls 5/6 of the children have brown hair if someone is chosen at random what is the probability that they will not have brown hair

Answers

Probability someone chosen at random will not have brown hair = 1/6

Probability of two variables

The number of girls = 15

The number of boys = 15

The total number of children = 15 + 15 = 30

Probability that someone chosen at random will have a brown hair, P(Brown hair) = 5/6

P(Brown hair) + P(Not Brown hair) = 1

5/6  +  P(Not brown hair) = 1

P(not brown hair) = 1 - 5/6

P(not brown hair) = 1/6

Therefore, if someone is chosen at random, probability that they will not have brown hair = 1/6

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PLEASE HELP 80 POINTS!!!!!!

Answers

The sequence pattern for 3¹/₃, 3¹/₄, 3¹/₅, ...... is; f(n) = 3 + 1/(2 + n)

How to find the sequence pattern?

We are given the sequence;

3¹/₃, 3¹/₄, 3¹/₅, ......

Now, we can see that;

First term is 3¹/₃.

However, for the second term, 1 has been added to the denominator.

Thus, we can suggest that the sequence pattern here is;

f(n) = 3 + 1/(2 + n)

where n is the nth term.

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the volume formula for a cylinder is v=nr^h. isolate for the variable r in this formula .

Answers

Answer:

[tex]r=\sqrt{\frac{V}{\pi h}}[/tex]

Step-by-step explanation:

[tex]V = \pi r^{2} h \\ \\ r^{2} =\frac{V}{\pi h} \\ \\ r=\sqrt{\frac{V}{\pi h}}[/tex]

The medical assistant weighs patients each month. Mrs. Smith weighed 120 pounds last month.
Over the last 2 months she gained 1½ and - pounds. What is Mrs. Smith's current weight?

Answers

13) 120 + 1.5 + 0.25 = 121.75 pounds

14) 4 - 1.5 = 2.5 pints

15) (2.25)(32)= $72

13. Mrs. Smith's current weight is 121.75 pounds.

14. The students should consume an additional 2.5 pints of water.

15. The nurse's overtime earnings amount to $72.00.

Given are words problems based on mixed numbers:

13. To find Mrs. Smith's current weight, we need to add the weight gained over the last two months to her weight last month.

Weight gained in the first month: 1 1/2 pounds

Weight gained in the second month: 1/4 pounds

Total weight gained over the last two months: 1 1/2 + 1/4 = 1 3/4 pounds

Now, to find Mrs. Smith's current weight, we add the total weight gained to her weight last month:

Current weight = Weight last month + Total weight gained

Current weight = 120 pounds + 1 3/4 pounds

Hence, Mrs. Smith's current weight is 121.75 pounds.

14. To calculate the additional water the students should consume to meet the school nurse's recommendation of at least 4 pints daily, we need to find the difference between the recommended amount and the average amount the students currently drink.

The recommended amount is 4 pints, and the average amount the students currently drink is 1 1/2 pints, which can be written as 1.5 pints.

Additional water needed = Recommended amount - Current average amount

Additional water needed = 4 pints - 1.5 pints

Additional water needed = 2.5 pints

Therefore, the students should consume an additional 2.5 pints of water daily to meet the school nurse's recommendation.

15. To calculate the nurse's overtime earnings, you can use the formula:

Overtime Earnings = Overtime Hours × Overtime Pay Rate

First, let's convert the mixed number of overtime hours into an improper fraction:

2 1/4 hours = 2 + 1/4 = 9/4 hours

Now, we can calculate her overtime earnings:

Overtime Hours = 9/4 hours

Overtime Pay Rate = $32.00/hour

Overtime Earnings = (9/4) hours × $32.00/hour

To simplify the calculation, you can convert the fraction to a decimal:

Overtime Earnings = (9/4) hours × $32.00/hour

Overtime Earnings = 2.25 hours × $32.00/hour

Overtime Earnings = $72.00

So, the nurse's overtime earnings amount to $72.00.

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A restaurant hands out a scratch-off game ticket with prizes being worth
purchases at the restaurant. The back of the ticket lists the odds of winning
each dollar value: 0.4 for $5, 0.3 for $25, 0.2 for $50, and 0.004 for $75. What
are the odds that the ticket is worth at least $25?

Answers

Answer:

0.7

Step-by-step explanation:

Because 0.4 is $5 and 0.3 is $25. So 0.3+0.4=0.7

Si: x;y∈ℜ y f={(2;8),(x;x+1),(2;x2−2x),(−2;9),(3;9),(y;y−1),(3;y+4)} es una función, calcúlese x y y, dando como respuesta la representación de la función.

Answers

La relación dada es una función si x = 4 y y = - 1. La representación de la función es f= {(2, 8), (4, 5), (- 2, 9), (3, 9), (5, 4)}.

¿Que valores tienen dos variables reales tal que una relación dada es una función?

Las relaciones están formadas por dos conjuntos relacionados entre sí, un conjunto de entrada denominado dominio y uno de salida denominado rango. Una función es una relación cuyos elementos del dominio solo están asociados a un solo valor del rango.

Bajo estas consideraciones, tenemos que (2, 8) = (2, x² - 2 · x) y (3, 9) = (3, y + 4), cuyas ecuaciones algebraicas se resuelven a continuación:

x² - 2 · x = 8     (1)

y + 4 = 9     (2)

By (1):

x² - 2 · x - 8 = 0

(x - 4) · (x + 2) = 0

x = 4 ∨ x = - 2

By (2):

y = 5

Si sabemos que x = 4 y y = - 1, entonces la representación de la función es:

f= {(2, 8), (4, 5), (- 2, 9), (3, 9), (5, 4)}

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) Consider the following probability density function of the random variable X. f(x) = k(2x + 3x2 ), 0 ≤ x ≤ 2. (i) Determine the value of the constant k.

Answers

I assume [tex]f(x)=0[/tex] otherwise. If [tex]f(x)[/tex] is indeed a proper PDF, then its integral over the support of [tex]X[/tex] is 1.

[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = k \int_0^2 (2x + 3x^2) \, dx = 1[/tex]

Compute the integral.

[tex]\displaystyle \int_0^2 (2x + 3x^2) \, dx = (x^2 + x^3)\bigg|_{x=0}^{x=2} = (2^2 + 2^3) - (0^2 + 0^3) = 12[/tex]

Then

[tex]12k = 1 \implies \boxed{k=\dfrac1{12}}[/tex]

The city has an average of 13 days of rainfall for April.

What is the probability of having exactly 10 days of precipitation in the month of April?
What is the probability of having less than three days of precipitation in the month of April?
What is the probability of having more than 15 days of precipitation in the month of April?

Answers

Using the Poisson distribution, we have that:

There is a 0.0859 = 8.59% probability of having exactly 10 days of precipitation in the month of April.There is a 0.00022 = 0.022% probability of having less than three days of precipitation in the month of April.There is a 0.2364 = 23.64% probability of having more than 15 days of precipitation in the month of April.

What is the Poisson distribution?

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.

For this problem, the mean is given as follows:

[tex]\mu = 13[/tex]

The probability of having exactly 10 days of precipitation in the month of April is P(X = 10), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 10) = \frac{e^{-13}13^{10}}{(10)!} = 0.0859[/tex]

There is a 0.0859 = 8.59% probability of having exactly 10 days of precipitation in the month of April.

The probability of having less than three days of precipitation in the month of April is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-13}13^{0}}{(0)!} \ approx 0[/tex]

[tex]P(X = 1) = \frac{e^{-13}13^{1}}{(1)!} = 0.00003[/tex]

[tex]P(X = 2) = \frac{e^{-13}13^{2}}{(2)!} = 0.00019[/tex]

Then:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0.00003 + 0.00019 = 0.00022

There is a 0.00022 = 0.022% probability of having less than three days of precipitation in the month of April.

For more than 15 days, the probability is:

P(X > 15) = P(X = 16) + P(X = 17) + ... + P(X = 20)

Applying the formula for each of these values and adding them, we have that P(X > 15) = 0.2364, hence:

There is a 0.2364 = 23.64% probability of having more than 15 days of precipitation in the month of April.

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In the trapezoid below, AP = 6, PB = x + 3, CD = 2x + 6, AC = 10 and the area is 174. Find the value of x to the nearest tenth.​

Answers

The value of x in the trapezoid given, to the nearest tenth, is: 10.5.

What is a Trapezoid?

A trapezoid is a quadrilateral that has two sides only that are parallel to each other.

What is the Area of a Trapezoid?

To find the area of a trapezoid, the formula used is expressed as: 1/2(a + b) × h, where:

a and b are length of the two base sides that are parallel.h is the height of altitude of the trapezoid.

Given the following:

Area of trapezoid = 174 units²

AP = 6

PB = x + 3

CD = 2x + 6

AC = 10

Using the formula, we variables in the formula are:

a = AP + PB = 6 + x + 3 = x + 9

b = CD = 2x + 3

h = PC = √(AC² - AP²)

h = √(10² - 6²) = 8

Plug in the values into 1/2(a + b) × h:

174 = 1/2(x + 9 + 2x + 3) × 8

174 = 1/2(3x + 12) × 8

174 = (3x + 12) × 4

174 = 12x + 48

174 - 48 = 12x

126 = 12x

126/12 = x

10.5 = x

x = 10.5

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To support the tree a guy wire 8.1 m long is attached to the trunk and then secured in the ground find the height of the leafty part of the tree to the nearest tenth

Answers

The height of the leafy part will be 6m.

How to calculate the height?

Other part of the question:

At the same time, a vertical pole 3m high vast s shadow 4m long.

Based on the information given, the height will be:

h/8 = 3/4

h = (3 × 8)/4

h = 6

Therefore, the height is 6m.

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Suppose f(x)=2^x. What is of g(x)=f(3x)?

Answers

Answer:

All you need to do is suppose x = 3x :

[tex] \tt \: g(x) = \boxed{ \tt{2^{3x} }} [/tex]

------ Happy LearninG <3 ----

Write in standard form: x² - 10x + y² - 4y = -28

Answers

Answer:

(x - 5) ^2 + (y -2)^2 = 1

Step-by-step explanation:

This is for a circle.

We need to complete the square

(x^2 -10x      ) + ( y^2 -4y       )  = -28

(x^2 - 10x +25) + (y^2 - 4y 2y) = -28 + 25 + 4

(x-5)^2 + (y-2)^2 = 1

The center of this circle would be (5,2)  with a radius of 1.

pls helpppp a gurllll outtttt : )))))))))

Answers

Answer:

2

Step-by-step explanation:

[tex]\frac{3[2(-2)-6] + (-2)^{2} +4[2(-2)+1]}{3[(-2)-5]+2}[/tex]

[tex]\frac{3(-10) - 4 + 4(-3)}{-16}[/tex]

[tex]\frac{-30-4-12}{-16}[/tex]

[tex]\frac{-46}{-16}[/tex]

okay you know what i dont know what im doing but i know the answer is for sure 2..

i dont know answer please im in summer school

Answers

The centre and the radius of the circle is (-7, -1) and 6 units

Equation of a circle

The equation of the circle in standard from is expressed as:

x^2+y^2+2gx+2fy+C = 0

where;

(-g, -f) is the centre

r= √g²+f²-C

Given the equation below

x^2+y^2+14x+2y+14 = 0

2g = 14

g = 7

2f = 2

f =1

Hence the centre of the circle is (-7, -1)

Radius = √49+1-14

Radius = √36 = 6 units

Hence the centre and the radius of the circle is (-7, -1) and 6 units

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A two-digit locker combination is made up of non-zero digits and no digit is repeated in any combination. Event A = the first digit is 4 Event B = the second digit is odd If a combination is chosen at random with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?
A.5/8
B.4/81
C.1/18
D.5/72

Answers

Answer:

D. 5/72

Step-by-step explanation:

The non-zero digits are 1 through 9.

There are 9 different non-zero digits.

p(A) = 1/9

There are 5 odd digits.

p(B) = 5/8

p(A and B) = p(A) × p(B) = 1/9 × 5/8 = 5/72

I think the answer is

A: 1/18

Use two formulas for volume to find the volume of the figure. Express the volume in terms of 3.14 and than round to the nearest whole number. Note that the figure may not be drawn to scale

Answers

The volume of the figure to the nearest whole number = 756π m³.

How to estimate the volume of the given figure?

The figure shown exists composed of a cone and a cylinder.

The volume of the figure = volume of cone + volume of the cylinder

Height of cone = 12 - 8 = 4

Radius (r) of cone = 18/2 = 9 m

The volume of the cone V = 1/3hπr²

= 1/3 [tex]*[/tex] 4π [tex]*[/tex] 9² = 108π

The volume of the Cylinder = πr²h

radius (r) = 18/2 = 9 m

height (h) = 8 m

Volume of cylinder = π [tex]*[/tex] 9² [tex]*[/tex] 8 = 648π m³

Volume of the figure = 108π + 648π = 756π

The volume of the figure to the nearest whole number = 756π m³.

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find x and y

pls help

Answers

Answer:

Step-by-step explanation:

no idea tbh

x is 40 degrees

y is 40 degrees

Hope this helps!

A restaurant hands out a scratch-off game ticket with prizes being worth
purchases at the restaurant. The back of the ticket lists the odds of winning
each dollar value: 0.4 for $10, 0.2 for $25, 0.01 for $30, and 0.004 for $75.
What are the odds that the ticket is worth at least $25?

Answers

Using the probability concept, the odds that the ticket is worth at least $25 are of 1:3.67.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering the probability, the odd is given by:

o = probability:(1 - probability)

From the given table, the probability that the ticket is worth at least $25 is:

p = 0.2 + 0.01 + 0.004 = 0.214.

Hence the odd is:

o = 0.214/(1 - 0.214) = 0.214/0.786 = 1:3.67.

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Find possible zeroes
f(x)=3x^6+4x^3-2x^2+4

Answers

The possible zeros of f(x) = 3x^6 + 4x^3 -2x^2 + 4 are [tex]\mathbf{\pm\{1,2,4,\frac 13, \frac 23,\frac{4}{3}}\}[/tex]

How to determine the possible zeros?

The function is given as:

f(x) = 3x^6 + 4x^3 -2x^2 + 4

The leading coefficient of the function is:

p = 3

The constant term is

q = 4

Take the factors of the above terms

p = 1 and 3

q = 1, 2 and 4

The possible zeros are then calculated as:

[tex]\mathbf{Zeros = \pm\frac{Factors\ of\ q}{Factors\ of\ p}}[/tex]

So, we have:

[tex]\mathbf{Zeros = \pm\frac{1,2,4}{1,3}}[/tex]

Expand

[tex]\mathbf{Zeros = \pm\frac{1,2,4}{1},\pm\frac{1,2,4}{3}}[/tex]

Solve

[tex]\mathbf{Zeros = \pm\{1,2,4,\frac 13, \frac 23,\frac{4}{3}}\}[/tex]

Hence, the possible zeros of f(x) = 3x^6 + 4x^3 -2x^2 + 4 are [tex]\mathbf{\pm\{1,2,4,\frac 13, \frac 23,\frac{4}{3}}\}[/tex]

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10-A biased die is thrown thirty times and the number of sixes seen is eight. ( The probability of face six is 8 = 4 ) If the die is thrown a further twelve times find:
30 15
(a) the probability that a six will occur exactly twice; (b) the expected number of sixes: () = ;
(c) the variance of the number of sixes.

Answers

Using the binomial distribution, we have that:

a) There is a 0.2111 = 21.11% probability that a six will occur exactly twice.

b) The expected number of sixes is of 3.2.

c) The variance of the number of sixes is of 2.35.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

For this problem, the parameters are given by:

p = 8/30 = 0.2667, n = 12.

Item a:

The probability is P(X = 2), hence;

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{12,2}.(0.2667)^{2}.(1-0.2667)^{10} = 0.2111[/tex]

Item b:

The expected number of the binomial distribution is:

E(X) = np.

Hence:

E(X) = 12 x 8/30 = 3.2.

Item c:

The variance of the binomial distribution is:

V(X) = np(1-p).

Hence:

E(X) = 12 x 8/30 x 22/30 = 2.35.

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Part A Your presentation should make a convincing argument that human activity is the major cause of climate change. Your presentation should answer some of these questions: What is climate? How is Earth’s climate changing? What are the natural and human factors that affect climate? How do scientists know that human activity is the major force behind climate change? What evidence do scientists have that climate is changing? Write down two additional questions you have about climate change that will help you make this argument in your presentation. 12pt

Answers

Climate is the long-term weather pattern that can be seen in an area over a period of years.

How to explain the climate?

Earth’s climate changing as the Earth's atmosphere heats up, it collects, retains, and drops more water, thereby changing weather patterns and making wet areas wetter and dry areas drier.

The factors that affect climate includ deforestation, desertification, urbanization, etc.

Scientists know that recent climate change is largely caused by human activities from an understanding of basic physics by comparing observations with models, and then fingerprinting the detailed patterns of climate change caused by different human and natural influences

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Trail A is 6 3/4 miles long. Trail B is 8 1/2 miles long. How many miles longer is Trail B than Trail A

Answers

Given the length of both trail, Trail B is 7/4 miles longer than Trail B.

How many miles longer is Trail B than Trail A?

Given that;

Length of Trail A = 6 3/4 = [ (6×4 + 3 )/4 = 27/4 miles Length of Trail B = 8 1/2 =  [ (8×2 + 1 )/4 = 17/2 miles

To determine how many miles longer is Trail B more than Trail A, we subtract the length of tail A from Tail B.

Trail B - Trail A

17/2 - 27/4

17/2 is the same as; 34/4

34/4 - 27/4

We combine the numerators over common denominator

(34 - 27 )/4

7/4 miles

Given the length of both trail, Trail B is 7/4 miles longer than Trail B.

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Suppose that X is a random variable that has a binomial uncertainty distribution with parameters n = 10 and π = 0.4. Calculate the numerical value of the probability that X = 6. What are the numerical values of the mean and standard deviation of the uncertainty distribution?

Answers

The numerical values of the mean and standard deviation are 4 and 1.55, respectively

The numerical value of the probability that x = 6.

The given parameters are:

n = 10

π = 0.4

The probability is then calculated as:

[tex]P(x) = ^nC_x * \pi^x *(1-\pi)^{n-x}[/tex]

So, we have:

[tex]P(6) = ^{10}C_6 * 0.4^6 *(1-0.4)^4[/tex]

Apply the combination formula

[tex]P(6) = \frac{10!}{6!4!} * 0.4^6 *0.6^4[/tex]

So, we have:

[tex]P(6) = 210 * 0.4^6 *0.6^4[/tex]

Evaluate

P(6) = 0.1115

Hence, the numerical value of the probability that x = 6 is 0.1115

The numerical values of the mean and standard deviation

The mean value is:

[tex]\bar x = n\pi[/tex]

This gives

[tex]\bar x = 10 * 0.4[/tex]

[tex]\bar x = 4[/tex]

The standard deviation value is:

[tex]\sigma = \sqrt{\bar x(1-\pi)[/tex]

This gives

[tex]\sigma = \sqrt{4(1-0.4)[/tex]

[tex]\sigma = 1.55[/tex]

Hence, the numerical values of the mean and standard deviation are 4 and 1.55, respectively

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Emma has money in two savings accounts. One rate is 6% and the other is 14%. If she has $950 more in the 14% account and the total interest is $342, how much is invested in each savings account?

Answers

$1045 was invested at the interest rate 6% whereas $1,995 was invested at 14%

How is interest computed?

Interest is determined as the amount invested multiplied by the interest rate.

Let Y be the amount invested at 6%

Interest=Y*6%

Interest=0.06Y

The amount invested at 14%, which is $950 more , is Y+950

Interest=(Y+950)*14%

Interest=0.14Y+133

Total interest =0.06Y+0.14Y+133

Note that total interest is 342

342=0.06Y+0.14Y+133

342=0.20Y+133

342-133=0.20Y

209=0.20Y

Y=209/0.20

Y=$1,045(amount invested at 6%)

Amount invested at 14%=$1,045+$950

Amount invested at 14%=$1,995

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