YOU PUT 1205 IN AN ACCOUNT THAT EARNS 2.5% SIMPLE INTEREST. FIND THE TOTAL AMOUNT IN THE ACCOUNT AFTER 4 YEARS

The width of the path is approximately 7.45 meters.

What is meant by width?

The width refers to the measurement of something from side to side, typically in a direction perpendicular to its length or height, such as the width of a door or the width of a piece of paper.

What is meant by meters?

Meters are a unit of measurement used to measure the length in the metric system. One meter is equal to 100 centimetres or approximately 3.28 feet. It is commonly used to measure distances, heights, and lengths.

According to the given information

The area of the pool is given by the product of its length and width:

18 × 30 = 540 square meters

The area of the entire region, including the pool and the path, is given by the product of the length and width of the outer rectangle:

(18 + 2x) × (30 + 2x)

Expanding this expression, we get:

540 + 36x + 60x + 4x²

Simplifying, we get:

4x² + 96x + 540

We are given that the area of the entire region is 1900 square meters:

4x² + 96x + 540 = 1900

Subtracting 1900 from both sides, we get:

4x² + 96x - 1360 = 0

Dividing both sides by 4, we get:

x² + 24x - 340 = 0

We can use the quadratic formula to solve for x:

x = (-24 ± √(24² - 4 × 1 × (-340))) / (2 × 1)

Simplifying, we get:

x = (-24 ± √(1216)) / 2

x ≈ -17.45 or x ≈ 7.45

Since the width of the path cannot be negative, we can ignore the negative solution.

Therefore, the width of the path is approximately 7.45 meters.

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Answer: 32.5

Step-by-step explanation:

13 is 40% of 32.5

Answer: The product of two consecutive even numbers is 12 more than the square of the smaller number. The product of the numbers is 6 and 8 is 48. Square of the smaller number (here 6) is 36. so, 12 + 36 = 48.

hope this helps:)

Step-by-step explanation:

The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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Given that: y = x + 7

y = 4

y = x + 7

y = 4

substitute the value of y into the above question

4 = x + 7

Isolate x

x = 4 - 7

x = - 3

For the second question

y = x + 5 ------ equation 1

y = 3x ----------equation 2

Substitute the value of y = 3x into the equation 1

3x = x + 5

Collect the like terms

3x - x = 5

2x = 5

Divide both sides by 2

2x/2 = 5/2

x = 5/2

substitute the value of x = 5/2 into the equation 2

y = 3x

y = 3 (5/2)

y = 3 x 5 / 2

y = 15/2

The longest distance between vertices on an 3- dimensional, 4-dimensional, 5-dimensional, and n-dimensional cube is the square root of 1.723, 2, square root 2.236, and square root of n respectively.

The ability to execute numerous tasks or calculations concurrently may greatly enhance a system's overall performance, which makes parallel processing important in computer science. A system can perform processes in parallel by employing many processors or cores, which cuts down on the time needed to do complicated calculations or activities.

The longest distance between vertices on an n-dimensional cube, is given by:

d = sqrt(n)

where d is the distance between vertices.

n is the number of dimensions.

For a 3-dimensional cube, we have:

d = sqrt(3) ≈ 1.732

For a 4-dimensional cube, we have:

d = sqrt(4) = 2

For a 5-dimensional cube, we have:

d = sqrt(5) ≈ 2.236

In general, for an n-dimensional cube, we have:

d = sqrt(n)

So the longest distance between vertices on an n-dimensional cube is the square root of n.

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Answer:

Idkkkkkkkkkkkkkkkkkkkkk

Step-by-step explanation:

Answer:

no of student take speech at college = 1/3*7533=2511

Step-by-step explanation:

Answer:

166 legos are required

Step-by-step explanation:

In this case, let's analyze the data. We need 3 trophies, using at most 324 legos in total. The big trophy requires 220 legos, the smallest requires 135, so we need to know how much will be used in the medium trophy. This number should be 135 < X < 220

Now, if we know that the total legos to be used are 324, then, we can make a difference and sum for all the legos, and then, calculate the number of legos used.

Total legos = A + B + C

324 = 220 + 135 + C

324 = 355 + C

C = -31

This means that there is difference of 31 legos between the smallest and biggest trophy, therefore, this difference should be used and added to the smallest trophy and see how much Tristen use in the final trophy:

135 + 31

= 166 legos

So we need to use 166 legos to build the final trophy.

Answer:

he already used 355 so 166

Step-by-step explanation:

Answer:

\(x \leq -4\)

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

Therefore , the solution of the given problem of unitary method comes out to be $3.5 is the average price.

After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.

Here,

Given :

subscription for 8 months

She paid $28 and Holly wanted to find the price, p

Price for one month is :

=> 28/8

=> $3.5

Therefore , the solution of the given problem of unitary method comes out to be $3.5 is the average price.

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The complete question is "Holly bought a magazine subscription for a year. She paid $27. Holly wanted to find the price, p, of the subscription each month. She created the model shown to help find this price. 27 р |р |р |р |р |р |р |р | Р | Р |р | p What was the price of the subscription each month? F $39.00 G $2.25 H $324.00 3 $22.50​"

Answer:

So when you  are round here is a trick or easy way to round, if 1-4 then round down. If it is 5-9 then round up.

Step-by-step explanation:

It might take time but when rounding you mostly round Depending on if your question saw round to the nearest tens or ones.

Plan A lasts for 0.5 hours, and Plan B lasts for 0.75 hours based on the given information and the solution to the System of equations.

To determine the duration of each workout plan, let's assume that both Plan A and Plan B have a fixed duration. Let's denote the duration of Plan A as "x" hours and the duration of Plan B as "y" hours.

From the given information, we can form the following equations:

On Wednesday:

5 clients did Plan A, so the total duration for Plan A is 5x hours.

6 clients did Plan B, so the total duration for Plan B is 6y hours.

The total training duration on Wednesday is 7 hours, so we have the equation: 5x + 6y = 7   ... Equation (1)

On Thursday:

3 clients did Plan A, so the total duration for Plan A is 3x hours.

2 clients did Plan B, so the total duration for Plan B is 2y hours.

The total training duration on Thursday is 3 hours, so we have the equation: 3x + 2y = 3   ... Equation (2)

We now have a system of equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.

Multiplying Equation (1) by 2 and Equation (2) by 5 to eliminate the y variable, we get:

10x + 12y = 14   ... Equation (3)

15x + 10y = 15   ... Equation (4)

Multiplying Equation (3) by 3 and Equation (4) by 2 to create a new system of equations:

30x + 36y = 42   ... Equation (5)

30x + 20y = 30   ... Equation (6)

Subtracting Equation (6) from Equation (5), we can eliminate the x variable:

(30x + 36y) - (30x + 20y) = 42 - 30

16y = 12

y = 12/16

y = 0.75

Substituting the value of y into Equation (2), we can solve for x:

3x + 2(0.75) = 3

3x + 1.5 = 3

3x = 3 - 1.5

3x = 1.5

x = 1.5/3

x = 0.5

Therefore, the duration of Plan A is 0.5 hours, and the duration of Plan B is 0.75 hours.

Plan A lasts for 0.5 hours, and Plan B lasts for 0.75 hours based on the given information and the solution to the system of equations.

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Answer:

Step-by-step explanation:

With replacement

(1/10)^4

1/10000

0.0001

Without replacement

(1/10)(1/9)(1/8)(1/7)

1/5040

0.00019841269

\(\begin{align}\sf\:\Phi_1 &= \iint_{S_1} (-2u^6\cos(v) - 2u^3\sin(v)) \, du \, dv \\ &= \int_{0}^{1} \int_{0}^{2\pi} (-2u^6\cos(v) - 2u^3\sin(v)) \, dv \, du \end{align} \\\)

The difference between 126 1/4 and 78 7/12 is 143/3 or 47 2/3.

To find the difference between the numbers simplify means;

to subtract 78 7/12 from 126 1/4 .

126 1/4 - 78 7/12

First, convert the mixed fractions into improper fractions.

( 126 × 4 + 1 )/4 - ( 78 × 12 + 7) /12

505/4 - 943/12

Multiply first term by 3/3 which is the same as 1.

( 505/4 × 3/3 ) - 943/12

1515/12 - 943/12

( 1515 - 943) / 12

572 / 12

143/3 or 47 2/3.

Therefore, the difference is 143/3 or 47 2/3.

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The essays that she can review in 1 hour would be; 2 2/3.

A fraction represents a part of a number or any number of equal parts.

We are given that English teacher reviewed 2 /3 of an essay in 1/ 4 of an hour.

Thus, Fraction of the essay reviewed = 2/3

Amount of time used = 1/4

Therefore, the fraction of essay for an hour can be calculated as;

= Fraction of the essay reviewed / Amount of time used

= 2/3 ÷ 1/4

= 2/3 × 4

= 8/3

= 2 2/3

Hence, She will review 2 2/3 essay.

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Answer:

Step-by-step explanation:

A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings

Commission = 612.50 shillings

B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:

2,450.00 shillings = X - X * 2% = X - 0.02 X --->

------> 0.98 X = 2,450.00 shillings

------>X= 2,450.00 / 0.98

------> X = 2,500.00  shillings

NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings

NEW COMMISSION = 625 shillings

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

Step-by-step explanation:

Let r(y)=x.

\(x=\frac{2}{3}(4y-5)\\\\\frac{3}[2}x=4y-5\\\\\frac{3}{2}x+5=4y\\\\y=\frac{3}{8}x+\frac{5}{4}\\\\r^{-1}(x)=\frac{3}{8}x+\frac{5}{4}\)

Answer:

-3 < y ≤ 3

Step-by-step explanation:

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

When two straight lines or rays intersect at a shared endpoint, an angle is generated. The exact value of cosine(7π/8) is 0.912939.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

The given angle can be written in degree form as,

(7π/8) radian = (7π/8) × (180/π) = 157.5°

The exact value of cosine(7π/8) can be written as,

Cosine (7π/8) = Cosine(157.5°) = 0.912939

Hence, The exact value of cosine(7π/8) is 0.912939.

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Answer:

D. -sqrt(2+sqrt(2))/2

Step-by-step explanation:

Took the test and this was the correct answer

Answer: 4/7

Step-by-step explanation:

pretty simple, 1/7 and 3/7 both has a denominator of "7", so the seven stays the same. (While writing this I made a chart to see where I put everything)

Write:

 1/7 = (denominator 7)

+ 3/7 = (denominator 7)

Now we start doing the math, what goes into 7? 7x1 so 1 x 3 = 3

know we go up to the numerator, 7x1=7, so 1 x 1 = 1

add 3 + 1 and that adds up to 4

so your answer is 4/7, hope it helps

To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.

The general form of the polar equation for a conic with focus at the pole is given by:

r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)

Where:

- r is the distance from the origin (pole) to a point on the conic.

- e is the eccentricity.

- d is the distance from the pole to the directrix.

- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.

- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.

In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.

Substituting these values into the general equation, we get:

r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)

Simplifying further:

r =\(\frac{6}{1+2\cos(\theta)}\)

Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:

r =\(\frac{6}{1+2\cos(\theta)}.\)

This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.

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The rectangle \(R\) is the set

\(R = \{(x,y) \mid 0 \le x \le 2 \text{ and } -1 \le y \le 1\}\)

The average value of \(f(x,y)\) over \(R\) is the ratio of the integral of \(f\) over \(R\) to the area of \(R\).

\(f_{\rm ave} = \dfrac{\displaystyle \iint_R f(x,y) \, dA}{\displaystyle \iint_R dA}\)

The rectangle is 2-by-2, so its area is

\(\displaystyle \iint_R dA = 2\times2 = 4\)

Integrate \(f\).

\(\displaystyle \iint_R xy^2 \, dA = \int_{-1}^1 \int_0^2 xy^2 \, dx \, dy \\\\ ~~~~~~~~ = 2 \int_{-1}^1 y^2 \, dy \\\\ ~~~~~~~~ = 4 \int_0^1 y^2 \, dy = \frac43\)

Then the average value of \(f\) is

\(f_{\rm ave} = \dfrac{\frac43}4 = \boxed{\dfrac13}\)