Find the area. Simplify your answer.
x-5
6

It will take approximately 8.53 years for the car to be worth $10,000, assuming a constant annual depreciation rate of 12%.

To model the depreciation of Manny's car, we can use the method for exponential decay:

\(y = a(1 - r)^t\)

Wherein:

In this situation, we've:

Substituting those values into the method, we get:

 \($10,000 = $28,750(1 - 0.12)^t\)

Dividing each aspects by $28,750, we get:

\(0.3478 = (0.88)^t\)

Taking the logarithm of both facets (base 10), we get:

\(log(0.3478) = t*log(0.88)\)

Solving for t, we get:

\(t = log(0.3478)/log(0.88)\)

= 8.53 (rounded to two decimal locations)

Consequently, it'll take approximately 8.53 years for the car to be worth $10,000.

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Answer:

8.26 years

Step-by-step explanation:

To model the depreciation of the car over time, we can use an exponential decay function in the form:

\(\large{\boxed{V(t) = V_0(1 - r)^t}\)

where:

Given values:

Substitute these values into the formula and solve for t:

\(V(t) = V_0(1 - r)^t\)

\(10000=28750(1-0.12)^t\)

\(10000=28750(0.88)^t\)

\(\dfrac{10000}{28750}=(0.88)^t\)

\(\dfrac{8}{23}=(0.88)^t\)

\(\ln \left(\dfrac{8}{23}\right)=\ln (0.88)^t\)

\(\ln \left(\dfrac{8}{23}\right)=t\ln (0.88)\)

\(t=\dfrac{\ln \left(\dfrac{8}{23}\right)}{\ln (0.88)}\)

\(t=8.2611657...\)

Therefore, the car will be worth $10,000 after approximately 8.26 years, or about 8 years and 3 months.

Note: After 8 years, the car will be worth $10,339.49. After 9 years, the car will be worth $9,098.75. So the value of the car will reach $10,000 during the 9th year. Therefore, rounding up to 9 years may be more appropriate if the answer should be in whole years.

The relationship between the dates of spread and the number of people infected can vary depending on various factors such as the infectiousness of the disease, the effectiveness of containment measures, population density, and individual behaviors.

However, there is a general rule that can describe the relationship:As the dates of spread progress, the number of infected individuals tends to increase initially, reaching a peak, and then gradually decreasing over time.

This pattern is often referred to as the epidemic curve or the epidemiological curve. In the early stages of an outbreak, the number of cases may grow rapidly as the disease spreads through a susceptible population. This rapid increase is often influenced by factors such as the contagiousness of the disease, population density, and social interactions.

As containment measures, such as vaccination campaigns, public health interventions, and behavioral changes, are implemented, the rate of new infections may start to decline. This can lead to a peak in the number of cases, after which the curve gradually decreases as the disease is brought under control and fewer susceptible individuals remain.

It's important to note that the specific shape, duration, and magnitude of the epidemic curve can vary significantly depending on the disease and the effectiveness of the response measures implemented. Additionally, emerging variants, changes in behavior, and other factors can impact the trajectory of the epidemic curve.

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Using the z-distribution, as we are working with a proportion, the minimum sample size required to ensure a 90% confidence interval for p to within 0.02 is of 1692.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

The margin of error is of:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In this problem:

Then, solving for n:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.02 = 1.645\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.02\sqrt{n} = 1.645(0.5)\)

\(\sqrt{n} = \frac{1.645(0.5)}{0.02}\)

\((\sqrt{n})^2 = \left(\frac{1.645(0.5)}{0.02}\right)^2\)

\(n = 1691.3\)

Rounding up, a sample size of 1692 is needed.

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The years where the spending will be more than $89 billion are: after 2009, i.e., 5 years after 2004, as found by basic algebra.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.

Given: y = 14.4x + 17,

where: x = number of years after 2004

y = amount spent by businesses

To find: number of years where spending

$89 billion.

Finding:

We are given: y = 89, for which, we have to find the x, i.e., the number of years.

By basic algebra, substituting the value of y and solving for x:

89 = 14.4x + 17

72 = 14.4x

x = 5

Hence, The years where the spending will be more than $89 billion are: after 2009, i.e., 5 years after 2004, as found by basic algebra.

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Answer:

Each piece is 1.25m

Step-by-step explanation:

If you divide 12 1/2 by 10 you would get 1.25

Answer:

\( 1\frac{1} {4} \: m\)

Step-by-step explanation:

Length of wire = 12½ m = 12.5 m

Number of pieces = 10

Length of each piece = 12.5/10= 1.25 m \( =1\frac{1} {4} \: m\)

The time it will take for your account balance to reach $10,000 is given as follows:

t = 10.8 years.

The balance of an account after t years, using continuous compounding, is given as follows:

A(t) = A(0)e^(kt).

In which:

The parameters for this problem are given as follows:

A(0) = 6500, k = 0.04.

Hence the time needed for a balance of $10,000 is obtained as follows:

10000 = 6500e^(0.04t)

e^(0.04t) = 10000/6500

0.04t = ln(10000/6500) -> ln is the inverse operation of the exponential

t = ln(10000/6500)/0.04

t = 10.8 years.

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Answer:

± (1 ÷ 9)

Step-by-step explanation:

Data provided in the question

Since  3 is added to the absolute value and -9

The result is 4

Now this information should be transformed in a mathematical equation

Let us assume be x so the product of the number and -9 be -9x

Fo rthe absolute value we use the mode. Thus the required expression is:

3 + |-9x|

Given that the result is 4

So, it would be

3 + |-9x| = 4

Now Solving the above equation which is given below:

|-9x| = 4-3

|-9x| = 1

here we will remove the mode by introducing ± sign which is shown below:

-9x = ± 1

-9x = 1 or -9x = -1

x = -1/9

or

x = \(\frac{1}{9}\)

Therefore, the value of x is ± (1 ÷ 9).

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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Answer:

Please select all of the things below that were the main issues the Anti Federalists

had with the US Constitution.

Select 3 correct answer(s)

A-They felt that the states did nothing to protect peoples' rights

B-They felt that the state had too much power

C-Many people felt that the representatives of the convention in Philadelphia had

overstepped its authority and that the articles should have been amended

D-They were concerned in giving the national government more power

E-They felt that the Constitution did nothing to protect the peoples' rights

Please hurry I’m soo stressed!!!!!!!

Step-by-step explanation:

1 Which of these objects are made from magnetic materials?

a copper pipe

b plastic paper clip

c steel nail

d glass bottle

e iron bar

g nickel coins

frubber tyre

Answer:

umm uh

Step-by-step explanation mmu hu

The total interest on the loan and monthly payments are $64,000 and $ 1,333.3 respectively

The formula for calculating the simple interest is expressed as:

I = PRT

Get the interest;

I = 16,000 * 0.8 * 5

I = $64000

Amount after 5 years = 16000 + 64000

Amount after 5 years  = $80,000

Monthly payment  = 80000/60months

Monthly payment = $1,333.33

Hence the total interest on the loan and monthly payment are $64,000 and $ 1,333.3 respectively

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Answer:

Step-by-step explanation:

Let the side of the square base be x

h be the height of the box

Volume V = x²h

13500 = x²h

h = 13500/x² ..... 1

Surface area =  x² + 2xh + 2xh

Surface area S =  x² + 4xh  ...... 2

Substitute 1 into 2;

From 2; S =  x² + 4xh

S = x² + 4x(13500/x²)

S = x² + 54000/x

To minimize the amount of material used; dS/dx = 0

dS/dx = 2x - 54000/x²

0 = 2x - 54000/x²

0 = 2x³ - 54000

2x³ = 54000

x³ = 27000

x = ∛27000

x = 30cm

Since V = x²h

13500 = 30²h

h = 13500/900

h = 15cm

Hence the dimensions of the box that minimize the amount of material used is 30cm by 30cm by 15cm

Answer:

165 minutes

Step-by-step explanation:

To solve for the number of minutes that Joaquin played for, we can use this expression:

(let 'a' represent how much time passed from the time Joaquin started playing basketball until the time he arrived at home)

Subtracting 1:10 from each side:

1:10 - 1:10 cancels out to 0, while 3:35 - 1:10 is equal to 2:25.

So, the expression is now:

So, 2 hours and 25 minutes passed.

If we know that 1 hour is equivalent to 60 minutes, we can use this expression to solve for however many minutes are in 2 hours:

Now we need to add on the number of minutes and the time it took him to get home:

Therefore, 165 minutes passed from the time Joaquin started playing basketball until the time he arrived at home.

The entrepreneur's revenue is  $2325x, entrepreneur's cost is $33,750 + $1700x and entrepreneur's profit from x sold-out performances is  $625x - $33,750

The entrepreneur's revenue from x sold-out performances is given by the formula:

Revenue = (Price per Performance) x (Number of Performances)

Revenue = $2325 x x

Revenue = $2325x

The entrepreneur's cost from x sold-out performances is given by the formula:

Cost = Overhead + (Production Cost per Performance) x (Number of Performances)

Cost = $33,750 + $1700x

The entrepreneur's profit from x sold-out performances is the revenue minus the cost:

Profit = Revenue - Cost

Profit = $2325x - ($33,750 + $1700x)

Profit = $625x - $33,750

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For

We got to use the middle part, because it is for values

So

For

We got to use the bottom one, since it is for values

So

If the circle is dilated by a factor of 2, the equation of the circle is: C. (x + 3)² + (y - 2)² = 18.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

By critically observing the graph of this circle, we have the following parameters:

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-3))² + (y - 2)² = 3²

(x + 3)² + (y - 2)² = 9.

By dilating with a scale factor of 2, we have:

(x + 3)² + (y - 2)² = (9 × 2)

(x + 3)² + (y - 2)² = 18

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The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Answer:

7/11 or

7

--

11

Step-by-step explanation:

Hope this helps :)

Answer:

B [-4, + ∞)

Step-by-step explanation:

Minimum Y min = -4 {From the graph}

Honestly, it's hard to explain, sorry

Answer:

f(x)=-3/2x+3

Step-by-step explanation:

y intercept is 3, slope is -3/2

f(x)=-3/2x+3

Take 2 points

Slope:-

\(\\ \rm\Rrightarrow m=\dfrac{0-3}{2-0}=\dfrac{-3}{2}\)

Equation of line in point slope form

\(\\ \rm\Rrightarrow y-3=-3/2x\)

\(\\ \rm\Rrightarrow y=-3/2x+3\)

Using the z-score, mean and sample mean, the standard deviation of the sample is 7.57

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

The formula is given as;

z = x - μ / σ

Substituting the values into the formula;

-2.13 = 19.3 - 29 / σ

Cross multiply both sides;

-2.13σ = 19.3 - 29

-2.13σ = -9.7

Divide both sides by the coefficient;

-2.13σ / -2.13 = -9.7 / -2.13

σ = 7.57

The standard deviation is 7.57

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Answer:

  all real numbers

Step-by-step explanation:

Both a(x) and b(x) are polynomials. The set of polynomials is closed on multiplication, so (b•a)(x) will also be a polynomial. All polynomials are defined for all real numbers. The domain is the set of input values (x) for which the function is defined.

The domain of (b•a)(x) is all real numbers.

Answer:

Slope: 1/3 ---- y-intercept: (0,-3)

Step-by-step explanation:

The number of years the interest was compounded quarterly is given by the equation b = 9.098 years

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after b years be A = $ 26,725.00

The number of years be = b

The number of times the interest is applies n = 4 ( quarterly )

Let the principal amount be P = $ 7,000

A = P ( 1 + r/n )ⁿᵇ

Substituting the values in the equation , we get

t = ln ( A/P ) / n [ ln ( 1 + r/n ) ]

t = b = n ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.15/4 ) ] )

On simplifying the equation , we get

b = ln ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.0375 ) ] )

b = ln ( 3.81785714 ) / 4 [ ln ( 1.0375 ) ]

On further simplification , we get

b = 9.098 years

Hence , the number of years the interest was applied is 9 years 1 months

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Answer:

180 in²

Step-by-step explanation:

base b = 2 ft = 2*12 in = 24 in

height h = 15 in

Area = bh/2 = 24 * 15/2 = 180 in²

The area of a 135 slice of pizza be,

⇒ 6,782.41 inches²

We have to given that;

Recently they had a lunch special for a Personal Pie with a radius of 4 inches .

Since, WE know that;

Area of circle is,

A = πr²

Where, r is radius of circle

Here, Radius of circle = 4 inches

Hence, Area of pizza is,

⇒ A = 3.14 x 4²

⇒ A = 50.24 inches²

Hence, the area of a 135 slice of pizza be,

⇒ 50.24 × 135

⇒ 6,782.41 inches²

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Answer:

see the attachment photo!

Answer:

The answer is circle.

Step-by-step explanation:

For all the rest of the shapes, we use certain base x height formulas.  Square uses base x height along with parallelograms and trapezoids. For a triangle, we use \(\frac{base x height}{2}\). Though, for a circle, we use the formula  \(\pi r^{2}\) where r= radius.

Answer:

It's y = 3x + 1 :)