Need help With This Math problem​

$7,008 is the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7%.

percentage, a relative value indicating hundredth parts of any quantity.

The formula to calculate the future value of an investment with simple interest is:

FV = P(1 + rt)

where FV is the future value, P is the principal amount, r is the annual interest rate expressed as a decimal, and t is the time period in years.

P = $6,525

r = 0.037

t = 2 years

Plugging these values into the formula, we get:

FV = $6,525(1 + 0.037×2)

FV = $6,525(1.074)

FV = $7,008.

Therefore, the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7% is $7,008.

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The centroid of the region is at the point (0, 2/5).

To find the centroid of the region bounded by the curves y=2-x² and y=x, we first need to find the limits of integration and the expressions for the x-coordinate and y-coordinate of the centroid.

The curves intersect at (1,1) and (-1,1), so we will integrate over the interval [-1,1].

To find the x-coordinate of the centroid, we need to evaluate the following integral:

x' = (1/A) ∫[a,b] xf(x) dx

where;

A = ∫[a,b] (f(x) - g(x)) dx

In this case, f(x) = 2 - x² and g(x) = x, so

A = ∫[-1,1] (2 - x² - x) dx

= [2x - (1/3)x³ - (1/2)x²] | from -1 to 1

= (4/3)

Now we can evaluate the x-coordinate of the centroid:

x' = (1/A)∫[-1,1] x*(2-x²-x) dx

= (1/(4/3))∫[-1,1] (2x - x³ - x²) dx

= (3/4) [(x²/2) - (1/4)x⁴ - (1/3)x³] | from -1 to 1

= 0

So the x-coordinate of the centroid is 0.

To find the y-coordinate of the centroid, we need to evaluate the following integral:

y' = (1/A) ∫[a,b] (1/2) [f(x)² - g(x)²] dx

y' = (1/(4/3)) ∫[-1,1] (1/2)[(2-x²)² - x²] dx

= (3/4)[(8/15)x⁵ - (2/3)x³ + (1/2)x] | from -1 to 1

= (2/5)

So the y-coordinate of the centroid is 2/5.

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A function is a relationship between a few different inputs and an output, where each input can only lead to one possible outcome.

(i) The exponential function that models the decay of the substance is given by:

[tex]N(t) = Noe^(-0.088t)[/tex]

(ii) If [tex]400g[/tex] of the substance is present at to, then  [tex]No = 400g[/tex] . Therefore, the amount of the substance remaining after 3 days is:

[tex]N(3) = 400e^(-0.0883) = 309.21g[/tex]  (rounded to two decimal places)

(iii) The rate of change of the amount of the substance after 3 days is given by:

 [tex]dN/dt = -0.088N(3) = -0.088309.21 = -27.21 g/day[/tex] (rounded to two decimal places)

(iv) To find the number of days it takes for half of the original [tex]400g[/tex] of the substance to remain, we need to solve the equation:

[tex]N(t) = 0.5No[/tex]

[tex]0.5No = Noe^(-0.088t)[/tex]

[tex]0.5 = e^(-0.088t)[/tex]

[tex]ln(0.5) = -0.088t[/tex]

[tex]t = ln(0.5)/(-0.088) = 7.89 days[/tex] (rounded to two decimal places)

Therefore, after  [tex]7.89[/tex] days, half of the original  [tex]400g[/tex] of the substance will remain.

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Answer: 94%

Step-by-step explanation: there are 16 .4's in 6.4 and if he missed by .4 then he got 15/16 which equals 94%

Answer:

Step-by-step explanation:

To calculate the present value (PV) and future value (FV) of the cash flow stream, we can use the following steps:

Calculate the present value of each cash flow using the formula:

PV = CF / (1 + r)^n

where CF is the cash flow, r is the annual interest rate, and n is the number of years until the cash flow is received.

For the first three cash flows of $150 at the end of each of the next 3 years, assuming a starting point of Year 0, we have:

PV1 = $150 / (1 + 0.11)^1 = $134.59 (Year 1)

PV2 = $150 / (1 + 0.11)^2 = $120.75 (Year 2)

PV3 = $150 / (1 + 0.11)^3 = $107.99 (Year 3)

For the cash flow of $250 at the end of Year 4:

PV4 = $250 / (1 + 0.11)^4 = $165.14

For the cash flow of $300 at the end of Year 5:

PV5 = $300 / (1 + 0.11)^5 = $179.34

For the cash flow of $500 at the end of Year 6:

PV6 = $500 / (1 + 0.11)^6 = $277.12

Add up the present values of each cash flow to find the present value of the entire stream:

PV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6

PV = $134.59 + $120.75 + $107.99 + $165.14 + $179.34 + $277.12

PV = $985.93

Therefore, the present value of the cash flow stream is $985.93.

To find the future value of the cash flow stream, we can simply add up the cash flows and then apply the future value formula:

FV = CF x [(1 + r)^n - 1] / r

where CF is the sum of the cash flows, r is the annual interest rate, and n is the number of years from the present until the future value is calculated.

CF = $150 x 3 + $250 + $300 + $500 = $1,100

n = 6 (assuming a starting point of Year 0)

FV = $1,100 x [(1 + 0.11)^6 - 1] / 0.11

FV = $2,525.72

Therefore, the future value of the cash flow stream is $2,525.72.

Answer:

Step-by-step explanation:

The formula for Sn of a geometric series with first term a and common ratio r is:

Sn = a((1-r^n)/(1-r))

In this case, the first term a is $1,000, the common ratio r is 1.02 (since she's depositing 2% more each year), and n is 30 (since we're looking for the amount deposited after 30 years).

Plugging in these values, we get:

Sn = 1000((1-1.02^30)/(1-1.02))

Sn ≈ $87,453

Therefore, the answer is D. $87,453.

Answer:

Step-by-step explanation:

The simple interest can be calculated using the formula:

I = P * r * t

where:

P = principal amount = $575

r = annual interest rate = 6.5% = 0.065

t = time period = 10 years

I = 575 * 0.065 * 10

I = $373.75

The new balance can be found by adding the interest to the principal:

New balance = Principal + Interest

New balance = $575 + $373.75

New balance = $948.75

Rounded to the nearest cent, the new balance is $948.75.

The data transfer rate per second​ is found as: 24 KB / sec.

Data transfer:  5760 KB

Time : 240 seconds

Rate per second​ = Data transfer / Time

Rate per second​ = 5760/ 240

Rate per second​ = 24

Thus, the data transfer rate per second​ is found as: 24 KB / sec.

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When polygon ABCD is dilated by a factor of 2. Then,

Point A′ is at  (-2, -2) and point D′ is at (4, -2).

A reference point needed to scale a dilation of such a figure correctly is the centre of dilatation.

A fixed point there in plane around whereby all points are enlarged or contracted is the centre of a dilation. The centre, which may be found within, outside, or on a figure, is the only unchanging.

Thus,  A' will occur at :(2 × (-1), 2 × (-1)) = (-2, -2)

D' will occur at (2 × 2, 2 × (-1)) = (4, -2).

Thus, when polygon ABCD is dilated by a factor of 2. Then,

Point A′ is at  (-2, -2) and point D′ is at (4, -2).

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The complete question is-

In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation.

Point A′ is at

(2 , 1)

(-2, -2)

(1 , -2)

( -2 , 2)

and point D′ is at

(-2 , 2)

(4 , -2)

(4 , 2)

(-2 , 2)

There are 509 tourists only visited the LEGOLAND (of these three).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, To find the number of tourists who only visited LEGOLAND, we need to subtract the tourists who visited LEGOLAND and another theme park from the total number of tourists who visited LEGOLAND.

Calculation:

First, we can find the total number of tourists who visited LEGOLAND:

Total = Tourists who visited only LEGOLAND + Tourists who visited LEGOLAND and another park

Hence, Total = (Total visitors to LEGOLAND) - (Tourists who did not visit any of the parks)

Total = 1,033 - (256 + 267 + 75 + 93 - 52 - 82 - 33)

Total = 1033 - 260

Total = 509

Hence, There are 509 tourists only visited the LEGOLAND (of these three).

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The answer to this question is as follows equation  As a result, each recipient will get $1,350.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.  

We must divide the total sum by three in order to distribute the funds among the three recipients equally. Let x represent the total sum that will be given to each recipient.

x = 4,050 / 3

x = 1,350

As a result, each recipient will get $1,350.

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The height of the pole is 336 feet.

The 24 foot shrub has a 6 foot shadow . The height of the pole that has an 84 foot shadow is as follows:

Hence. let's use proportion to find the height of the pole.

Therefore,

let

h = height of the pole

Hence,

24  /h = 6 / 84

cross multiply

6h = 84 × 24

6h = 2016

divide both sides by 6

h = 2016 / 6

h = 336 ft

Therefore,

height of the pole = 336 ft

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True; the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.

From the question, we have the following parameters that can be used in our computation:

f(x) = 7.5x

The point is given as

(x, y) = (-1/5, -3/2)

To determine whether the point (-1/5, -3/2) lies on the graph of f(x) = 7.5x, we can substitute x = -1/5 into the equation and see if it gives us y = -3/2.

f(x) = 7.5x

By substitution, we have

f(-1/5) = 7.5(-1/5)

Evaluate

f(-1/5) = -1.5

Express as fraction

f(-1/5) = -3/2

So, the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.

Hence, the statement is false.

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Complete question

True or False. The point (-1/5, -3/2) lies on the graph of f(x).

Where f(x) = 7.5x

Answer: Marginal cost is the added cost to produce an additional good or the increase in production costs generated by the production of additional product units

Step-by-step explanation:  It is calculated by taking the total change in the cost of producing more goods and dividing that by the change in the number of goods produced.

Answer:

So it's basically the cost added by producing one extra unit of a product or service. I hoped this helped and if you need a better explanation let me know!

Given- The rectangle that represents the base of right rectangular prism

To find - The volume of the prism.

Explanation- we know that the volume of the right rectangular prism is product of area of rectangle and the height

Area of rectangle is [tex](lb)[/tex]

length (l) = 4.2

breadth = 3

area = 4.2×3=12.6

Volume of prism = 12.6 × height =12.6×6=75.6

Hence the volume of the prism is 75.6 in^3

Final answer - The correct option is D.

Answer:

Side PQ is the same as RQ

Angle QRS is the same as QPS

Step-by-step explanation:

Step-by-step explanation:

this (outside) angle of depression is equal to the inner angle at P.

because the line of sight from the helicopter to P is like the diagonal in a rectangle spring the rectangle into 2 equal right-angled triangles (one of just rotated by 180° of the other).

so, the angle at P is 30°.

1400 ft = sin(30)×radius

radius being the line of sight from the helicopter to P.

we need to calculate the radius, because we need it for d :

d = cos(30)×radius

radius = 1400/sin(30) = 2800 ft

d = cos(30)×2800 = 2,424.871131... ft ≈ 2,425 ft

The prove that triangle ABE is congruent to triangle CDE is given below

Generally, To prove that triangle ABE is congruent to triangle CDE, we need to show that they have the same size and shape.

First, we can see that angle AED and angle CEB are opposite angles and therefore congruent, since AB || DC.

Also, since line AB = line DC, we know that segment AE is congruent to segment CE and segment BE is congruent to segment DE.

Using these congruent sides and the congruent angle, we can apply the Side-Angle-Side (SAS) congruence criterion to conclude that triangle ABE is congruent to triangle CDE.

Therefore, we have proven that triangle ABE is congruent to triangle CDE.

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Answer:

There is a direct relationship, in which the value of the division of the circumference by the diameter is a constant. This constant is know as Pi.

Answer: -3,9

Step-by-step explanation: plug in -3 for x which gives u 9

As a result, for purchases of $9500, the salesperson gets a royalty of $285.

Commission, also known as a sales bonus, is paid to employees in accordance with the amount of sales they make. Statement generation is offered without charge by SumUp Bills. Frequently, a fee is calculated as a percentage of the sale's value.

To find the commission that the salesperson receives for $9500 in sales, we can use the formula:

commission = rate x sales

where rate is the commission rate as a decimal, and sales is the amount of sales.

In this case, the rate is 3% or 0.03, and the sales is $9500.When these numbers are added to the algorithm, we obtain:

commission = 0.03 x $9500

Simplifying this expression, we get:

commission = $285

Therefore, the salesperson receives a commission of $285 for $9500 in sales.

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Answer:

Step-by-step explanation:

[tex]7 \times 3 + 2 = 23 [/tex]

[tex]2 \times 3 + 2 = 8[/tex]

[tex] \frac{23}{8}[/tex]

so if want to have improper fraction this is the answer but to get proper fraction i am continuing

[8 \div 23 \sqrt[23]{80} to get the correct answer.you can get a mixed fraction too when you multiply 8 how many times you will get 23 8×2=16=2whole number 16 as the numerator and 8 as the denominator

Answer:

300.20

Step-by-step explanation:

because it was a nice guesss

Answer: The atmospheric pressure decreases with altitude. This is because as we move higher above the earth's surface, there is less air above us and therefore less weight pushing down on us. Therefore, the correct answer is:

C. An altitude of 7 km above sea level

At an altitude of 7 km above sea level, a person would experience the least atmospheric pressure because they would be furthest from the earth's surface and there would be very little air above them. This is why the air pressure in the Earth's upper atmosphere is much lower than at the surface of the Earth.

Step-by-step explanation:

The value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Measure of arc ML=76 Degrees and

Measure of Angle JLK = 54 Degrees

We have to find the value of x

O is the centre of the circle.

As we see the figure angle L is corresponding to 54 degrees.

x=54

Hence, the value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.

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Answer:x=-4,-2

Step-by-step explanation:it is

240 more residents have an occupation in industry than have an occupation in government. The solution has been obtained by using arithmetic operations.

It is believed that the four fundamental operations, often referred to as "arithmetic operations", can describe all real numbers. The four mathematical operations that produce the quotient, product, sum, and difference are divide, multiply, add, and subtract.

We are given a graph determining the types of occupations of the 1,200 residents of a town.

Percentage of residents having occupation in government is:

100% - 25% - 15% - 25% - 30% = 5%

Number of residents having occupation in industry is as follows:

25% of 1200 = 300

Similarly, number of residents having occupation in government is:

5% of 1200 = 60

Number of more residents that have occupation in industry than have an occupation in government is:

300 - 60 = 240

Hence, 240 more residents have an occupation in industry than have an occupation in government.

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The circle graph was missing in the question which has been attached below.

Answer:

Approximately 13%

Step-by-step explanation:

Troy meant to make 15, but only made 13, meaning that he was off by 2. To find the percent error here, we will divide how off Troy was by the amount Troy meant to make:

2/15=0.133333333, or approximately 13% (multiply the decimal by 100 to find the percent, then round to the nearest integer.)

The graph of the piecewise function is added as an attachment

Let c(x) be the cost of an automotive ad with x lines.

For the first 4 lines, the cost is $34, so:

c(x) = 34, for 1 ≤ x ≤ 4

For each additional line beyond the first 4, the cost is $3.50, so:

c(x) = 34 + 3.50(x - 4), for x > 4

When these two cases are put together, we get the piecewise function:

c(x) = 34, for 1 ≤ x ≤ 4

c(x) = 34 + $3.50(x - 4), for x > 4

This function represents the cost of an automotive ad as a piecewise function that depends on the number of lines in the ad.

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