The function A = A0e
-0.0077x models the amount in pounds of a particular radioactive material
stored in a concrete vault, where x is the number of years since the material was put into the vault. If
300 pounds of the material are initially put into the vault, how many pounds will be left after 140
years

The first four terms of the sequence are -5, -3, 1 and 3

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

Expression = n(n-1)-5

Set n = 1 to 4

So, we have

f(1) = 1(1 - 1) - 5 = -5

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

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

f(4) = 4(3 - 1) - 5 =3

Hence, the first four terms are -5, -3, 1 and 3

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Receiving a large tax refund is problematic because it means overpaying taxes and missing out on the opportunity to use that money throughout the year for paying down debt, building an emergency fund, or investing.

We have,

While receiving a large tax refund each year may seem like a positive thing, it actually means that Mia and Allen are overpaying their taxes throughout the year.

This means that they are essentially giving the government an interest-free loan by allowing them to hold onto their money instead of having it available to them throughout the year to use for things like paying down debt or investing in their future.

By overpaying their taxes,

Mia and Allen are essentially missing out on the opportunity to use their money in ways that could benefit them in the long run.

Additionally, the large tax refund they receive each year may create a sense of false security, leading them to believe that they are in a better financial situation than they actually are.

Rather than receiving a large tax refund each year, it may be more beneficial for Mia and Allen to adjust their tax withholdings so that they are receiving more money in each paycheck.

This way, they can use the extra money to pay down debt, build up their emergency fund, or invest in their future, rather than giving the government an interest-free loan.

Thus,

Receiving a large tax refund is problematic because it means overpaying taxes and missing out on the opportunity to use that money throughout the year for paying down debt, building an emergency fund, or investing.

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Answer:I’m not so sure but I’m pretty sure it’s the 4th one?

Step-by-step explanation:

Answer:

Option b

Step-by-step explanation:

For x=1, y=-0.5

For x=0, y=2

For x=1, y=-7/2

Graphing the equation on the coordinate plane we get the second graph.

The density in trees per acre upon completion will be 500 trees per acre.

In this scenario, let's say the landscaping provider donates 2750 seedlings.

Density of trees per acre = Total number of trees / Total area of land

Hence, applying the formula leads us to:

Density of trees per acre = 2750 trees / 5.5 acres

The answer comes out to be roughly around 500 trees/acre. So when completed, approximately 500 trees are estimated to be present in each acre of the landscape.

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A relation is called a function when each element in the domain is paired with just one element from the A. Range

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

The incomplete definition of relation

A relation takes the form

Domain : x

Range : y

The values from the domain are then paired with the range

If these values are paired just once, then it is a function

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The equations are classified as follows

System A

consistent and independent this means that the system as a unique  solution at (3, 3)

System B

inconsistent this means that the system as a no  solution

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.

System C

consistent and dependent this means that the system as infinitely many solution

A consistent system is dependent if there are an infinitely many solutions. The two equations represent the same line when you graph them.

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Answer:

$130

Step-by-step explanation:

price of helmet =discount+ price after discount

=$13.75+$116.25

=$130

The end behavior of the given function is Both ends of the graph goes down(In the same direction),

The degree and the leading coefficient (The coefficient of the highest degree monomial) of a function shows the end behavior of its graph.

if Degree  is even and leading coefficient is negative then the end behavior of the function f(x) is,

f(x)---> -∞, as x---> -∞

f(x)---> -∞, as x---> + ∞

That is, Both ends of the graph goes down(In the same direction)

Here, the given function is f(x)=-4x⁶+6x²-52

Degree = 6(even), leading coefficient = -4 (negative)

Thus, the end behavior of the given function is Both ends of the graph goes down(In the same direction),

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The probability that (all 23 are not smokers is 0.0429

P(all 23 are not smokers 0.0429

P(exactly 6 smokers)  ≈ 0.1671

a) If 16% of the population are smokers, then the probability that an individual is not a smoker is 1-0.16=0.84.

P(all 23 are not smokers) = 0.84²³ ≈ 0.0429

b) The probability that any one individual smokes is 0.16, and the probability that any one individual does not smoke is 0.84.

P(all 23 are not smokers) = 0.84²³ ≈ 0.0429 (rounded to four decimal places).

c) Similarly, we can use the binomial distribution to find the probability of exactly 6 smokers in a sample of 23:

P(exactly 6 smokers) = (23 choose 6) * 0.16⁶ * 0.84^17 ≈ 0.1671

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Answer: 1/2

Step-by-step explanation:

The fraction equivalent of 0.5 is 1/2.

To convert it into a mixed number, we can divide the numerator by the denominator:

1 ÷ 2 = 0 with a remainder of 1

So, the mixed number is 0 1/2.

The inequality represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks is 50 ≥ 3.5x + 5

We are given that Sydney started with no money in her piggy bank and adds $3.50 each day. Destiny started with $50 in her piggy bank and spends $5 of her money each day.

We need to find the equation or inequality that represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks.

Sydney started with zero money in her piggy bank and adds $3.50 each day means 0 + 3.50 and Destiny started with $50 in her piggy bank and spends $5 of her money each day then

the inequality  becomes as ;

50 ≥ 3.5x + 5

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The volume of the sports ball is 6286.28 cm³

A sphere is round, has no edges, and is a solid shape. Examples of a sphere include; The playing ball, balloon, and even light bulbs .

A sphere is a 3-dimensional shape ,and it's therefore a solid shape.

The volume of a sphere is expressed as;

V = 4/3 πr³

where r is the radius of the sphere and v is the volume.

the radius of the sphere is half the diameter.

D = 2r

r = 23/2 = 11.5

therefore ;

V = 4/3 × 3.14 × 11.5³

V = 18858.85/3

V = 6286.28 cm³ ( 2 decimal place)

Therefore the volume of the ball is 6286.28 cm³

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0.00205 can be written in scientific notation as 2.05 x 10^-3.

Answer:

The answer is 2.05×10‐³

Step-by-step explanation:

0.00205 to scientifi notation or standard form

=2.05×10‐³

Answer:

x=9 y=-2

Step-by-step explanation:

Substitute -2 for y in x+2y=5

x+2y=5

x+(2)(-2)=5

x-4=5(add 4 to both sides)

x=9

y=-2 as stated before

x=9 y=-2

Answer: volume of the cone is 324pi cm^3

Step-by-step explanation:

the volume of the cone is derived by the formula

V= 1/3 pi r^2 h

v= volume of the cone

h= height of the cone

r= radius of the cone

V= 1/3 x pi x 9 x 9 x 12

V= 324pi cm^3

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Step-by-step explanation:

to find the volume use the formula (1/3)πr2h,

[tex]( \frac{1}{3})h\pi \: r {}^{2} \\ \frac{1}{ 3} \times \pi \times 9 \times 9 \times 12 \\ \frac{1}{3} \times 972\pi \: cm \\ = 324\pi \: cm {}^{3} [/tex]

The numbers as an integer or not are:

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

7/10 - yes or no

-6/1 - yes or no

-30.18 - yes or no

7 - yes or no

-76 - yes or no

integers are numbers without decimal point (including 0)

Using the above as a guide, we have the following:

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The values of the composite functions are f(g(2)) = 5.5, h(f⁻¹(5)) = 1, x = 5 for f(h(x)) = 7, R(4) = 4 and k(x) = 2

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

The functions f(x), g(x) and h(x)

Solving the composite functions, we have

f(g(2)) = f(3) i.e. g(2) = 3

This gives

f(g(2)) = 5.5

Next, we have

h(f⁻¹(5))

Here, we have

f⁻¹(5) = 4

So, we have

h(f⁻¹(5)) = h(4)

Evaluate

h(f⁻¹(5)) = 1

Next, we have

f(h(x)) = 7

From the graph, we have

f(0) = 7

This means that

h(x) = 0

From the table, we have

h(5) = 0

This means that

x = 5 for f(h(x)) = 7

Evaluating R(x) at x = 4. we have

R(x) = 2f(x) - 3g(x) + h(x)

This means that

R(4) = 2f(4) - 3g(4) + h(4)

So, we have

R(4) = 2 * 9 - 3 * 5 + 1

R(4) = 4

Evaluating k(x) at x = 5. we have

k(x) = h⁻¹(g(f⁻¹(x)))

This means that

k(x) = h⁻¹(g(f⁻¹(5)))

From the graph, f⁻¹(5) = 4

So, we have

k(x) = h⁻¹(g(4))

Next, we have

g(4) = 5

So, we have

k(x) = h⁻¹(5)

From the table, we have

h⁻¹(5) = 2

This means that

k(x) = 2

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The y-intercept of the line is 2.

In the equation y = 9x + 2, x and y are variables that represent the coordinates of any point on the line.

To find the Y-intercept, we need to find the value of y when x equals 0.

When x equals 0, the equation becomes:

y = 9(0) + 2

Any number multiplied by 0 is 0, so the first term drops out and we are left with:

y = 0 + 2

Which simplifies to:

y = 2

Therefore, when x equals 0, y equals 2. This means that the point (0, 2) is on the line. In other words, the line intersects the y-axis at y = 2, which is the Y-intercept of the line.

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The answer to the expression is  (x+3)/(x-1)

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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Huai's monthly payment for the community college loan is $89.72 and $235.35.

To calculate the monthly payment for each loan, we need first to calculate the total amount borrowed and the total interest paid for each loan.

For the first loan

Total amount borrowed = $3700

Total interest paid = $3700 x 0.068 x (4 + 4/12 + 3/12) = $1,271.12

Total amount repaid = $3700 + $1,271.12 = $4,971.12

To find the monthly payment, we can use the formula for a loan payment

P = (r(PV))/(1-(1+r)⁻ⁿ)

Where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan, and n is the total number of payments.

For the first loan, r = 0.068/12, PV = $3700, and n = 48 (4 years x 12 months/year). Substituting these values into the formula, we get

P = (0.068/12 * $3700)/(1-(1+0.068/12)⁻⁴⁸) = $89.72

Therefore, the monthly payment on the first loan is $89.72.

For the second loan

Total amount borrowed = $12,000

Total interest paid = $12,000 x 0.074 x (3/12) = $222.00

Total amount repaid = $12,000 + $222.00 = $12,222.00

The second loan was acquired 2 years after the first, so the total repayment period is 5 x 12 - 2 x 12 - 3 = 51 months.

Using the same formula as before, but with r = 0.074/12, PV = $12,000, and n = 51, we get

P = (0.074/12 * $12,000)/(1-(1+0.074/12)⁻⁵¹) = $235.35

Therefore, the monthly payment on the second loan is $235.35.

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Answer: 95 ft²

Step-by-step explanation:

      To solve for the surface area, we will find the area of all the sides and then add them together. We see that we have a square as the base and 4 congruent triangles.

For the square:

      A = LW

      A = (5 ft)(5 ft)

      A = 25 ft²

For one triangle:

      A = [tex]\frac{BH}{2}[/tex]

      A = [tex]\frac{(5\;ft)(7\;ft)}{2}[/tex]

      A = 17.5 ft²

For all four triangles:

      A = 17.5 ft² * 4 = 70 ft²

Total surface area by adding the triangles and square together:

       70 ft² + 25 ft² = 95 ft²

There are 60 seconds in 1 minute, so 4 minutes would be:

4 minutes * 60 seconds/minute = 240 seconds

Therefore, it takes 240 seconds to complete the administrative task.

Answer:

x=28

x=-28

Step-by-step explanation:

Solving the system of equations, the number of children, parents, and Grandparents who were in attendance are 190, 140 and 70 respectively.

Let C, P and G denotes the number of children, parents and the grandparents in the function.

We get the system of equations,

C + P + G = 400 [equation 1]

P = 2G  ⇒ G = P/2 [equation 2]

C = P + 50 [equation 3]

Substituting 2 and 3 in 1,

(P + 50) + P + (P/2) = 400

2P + P/2 = 350

5/2 P = 350

P = 140

C = P + 50 = 140 + 50 = 190

G = P/2 = 140/2 = 70

Hence the number of parents = 140, grandparents = 70 and children = 190.

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From 1970 to 2013, the price of postal stamps increased at an average yearly rate of 4.851%.

The formula for compound interest is:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where A represents the total sum, P represents the beginning sum, r represents the yearly interest rate, n is the number of times the interest is compounded annually, and t represents the number of years.

In this instance, we may consider the initial cost of postal stamps in 1970 as the principal and the rise in price as the interest. The yearly rate of rise, r, may be calculated using the formula.

Let P represent the price in 1970 ($0.06) and A represent the price in 2013 ($0.46). Let t be the duration, or 43 years, from 1970 to 2013.

Then, we can write:

[tex]A = P(1 + r)^t[/tex]

Substituting the values, we get:

[tex]0.46 = 0.06(1 + r)^{43[/tex]

Dividing both sides by 0.06, we get:

[tex]7.67 = (1 + r)^{43[/tex]

Taking the 43rd root of both sides, we get:

[tex](1 + r) = 7.67^{1/43}\\(1 + r) = 1.04851[/tex]

Subtracting 1 from both sides, we get:

r = 0.04851 = 4.851%

Therefore, the average annual rate of increase in the price of postage stamps from 1970 to 2013 is 4.851%.

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The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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Answer:

Regarding the conjecture of Serena and Jack:

Serena suggests that they can use the graph of the first rocket and shift it to find the graphs for the other two rockets. This means that the paths of the rockets are similar, and the only difference is the time of launch. Jack suggests that they need to recalculate the graphs for the other two rockets, which means that the paths of the rockets are different.

In this scenario, Serena is correct. Since the rockets are identical, they will follow the same path, but with a different time of launch. Thus, they can use the graph of the first rocket and shift it to the right to get the graph of the second rocket and shift it further to the right and up to get the graph of the third rocket.

Analyzing the equation:

The equation for the first rocket's path is h(t) = -6(t-3.7)^2 + 82.14. Assuming that the graph is a transformation from f(t) = -6t^2, the term -3.7 shifts the graph horizontally to the right by 3.7 seconds. This means that the first rocket was launched 3.7 seconds before the time t in the equation. The value t = 3.7 represents the time when the first rocket was launched.

The term 82.14 shifts the graph vertically up by 82.14 feet. This means that the initial height of the rocket is 82.14 feet above the ground. Therefore, the value h(t) = 82.14 represents the initial height of the rocket.

Equation of the second rocket:

The second rocket is launched 3 seconds after the first rocket. This means that the graph of the second rocket is a horizontal shift of the first rocket's graph by 3 seconds. Therefore, the equation of the second rocket is:

h(t) = -6(t-6.7)^2 + 82.14

This is because the launch time of the second rocket is t = 6.7 seconds (which is 3 seconds after the first rocket's launch).

Description of the third rocket's graph:

The third rocket is launched 3 seconds after the second rocket and from a 20-foot-tall platform. This means that the graph of the third rocket is a horizontal shift of the second rocket's graph by 3 seconds and a vertical shift upwards by 20 feet. Therefore, the equation of the third rocket is:

h(t) = -6(t-9.7)^2 + 102.14

This is because the launch time of the third rocket is t = 9.7 seconds (which is 3 seconds after the second rocket's launch).

Answers to the questions:

a. The third rocket is launched at approximately t = 9.7 seconds.

b. The first rocket lands when h(t) = 0. Solving -6(t-3.7)^2 + 82.14 = 0 gives t = 5.16 seconds (approximate).

c. The approximate interval during which all three rockets are in the air is from t = 6.7 seconds (when the second rocket is launched) to t = 14.46 seconds (when the first rocket lands).