Amanda is framing her pool for resurfacing. The pool began with 14,340 gallons of water and it is draining at a rate of 880 gallons per hour. How long has the pool been draining if currently there are 8,840 gallons in the pool.

Amount must the owner make to have the cost of the ski lift in 5 years  is $6,711,045.22.

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

A = P(1 + r/n)\(^{nt}\)

P =5,500,000

r =4%= 0.004

n =4

t= 5 years.

Now,

A = P(1 + r/n)\(^{nt}\)

A = 5,500,000.00(1 + 0.04/4)\(^{(4)(5)}\)

A = 5,500,000.00(1 + 0.01)\(^{20}\)

A = $6,711,045.22

Hence, The total amount accrued is $6,711,045.22.

Learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ1

Answer:

Carbon-14 loses around 10% ( 0.1 in decimal form) of its mass, after one millennium.

Then if we start with a mass A of Carbon-14, after one millennium we will have a mass equal to:

A - A*0.1 = A*(0.9)

After another millennium, we will have a mass equal to:

A*(0.9) - A*(0.9)*0.1 = A*(0.9)^2

And so on, this is an exponential decay.

We already can see the pattern here, after x millenniums, the mass of carbon-14 will be:

M(x) = A*(0.9)^x

Now, in this problem we have 600 grams of carbon-14, then the equation for the mass will be:

y = M(x) = 600g*(0.9)^x

And the graph of this equation is shown below.

Answer:

S(t)=600(0.9)

Step-by-step explanation:

Losing mass at a rate of 10\%10%10, percent per millennium means the sample keeps 100\%-10\%=90\%100%−10%=90%100, percent, minus, 10, percent, equals, 90, percent of its mass each millennium.

So each millennium, the size is multiplied by 90\%90%90, percent, which is the same as a factor of 0.90.90, point, 9.

If we start with the initial mass, 600600600 grams, and keep multiplying by 0.90.90, point, 9, this function gives us the mass of the sample ttt millennia from now:

S(t)=600(0.9)^tS(t)=600(0.9)

t

The value of a for the given expression will be -3.31.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 3.6= − a/0.8 − 1.6 − 0.8 a ​ −1.6. The value of a will be calculated as below,

3.6 = − a/0.8 − 1.6 − 0.8 a ​ −1.6

3.6 + 1.6 + 1.6 = -a / 0.8  - 0.8a

6.8 = ( -a - 0.64a ) / 0.8

5.44 = -1.64a

a = -3.31

Therefore, the value of a will be -3.31.

To know more about an expression follow

https://brainly.com/question/388367

#SPJ1

Answer:

396

Step-by-step explanation:

Since a kite is a quadrilateral, it has the value of 360 total degrees.

The surface region of the cylinder will be 301.44 square inches.

Let r be the radius and h be the altitude of the cylinder. Then the surface region of the cylinder will be given as,

SA = 2πrh + 2πr² square units

The radius of the cylinder is 4 inches and the height of the cylinder is 8 inches.

Then the surface area of the cylinder is calculated as,

SA = 2πrh + 2πr²

SA = 2 x 3.14 x 4 x 8 + 2 x 3.14 x 4²

SA = 200.96 + 100.48

SA = 301.44 square inches

The surface region of the cylinder will be 301.44 square inches.

More about the surface area of the cylinder link is given below.

https://brainly.com/question/22074027

#SPJ9

Answer:

The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:

$442 * 0.9 = $397.80

The selling price of the same necklace at the competitor's store after 34% and 14% discount is:

$527 * 0.66 * 0.86 = $247.08

So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:

$397.80 - $247.08 = $150.72

To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:

($150.72 / $442) * 100 = 34.11%

Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.

Step-by-step explanation:

Answer:

(-19, -7)

Step-by-step explanation:

y=x+12

x+12+x=-26

2x=-14

x=-7

y + x = -26

y -7 = -26

y = -19

The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

for such more question on sphere

https://brainly.com/question/28228180

#SPJ11

Answer:

£50-£y or 50-y

Step-by-step explanation:

remaining = initial - taken

remaining = 50 - y

Answer:

Step-by-step explanation:

(-4 - 8)/(5 + 1)= -12/6 = -2

Option C

Answer: 0.00923521

Step-by-step explanation:

Given : The probability U.S households play video or computer games=69%=0.69

here, the probability of each U.S household play video or computer games is fixed as 0.69

Then, the probability of each U.S household not play video or computer games= 1-0.69=0.31

For independent events the probability of their intersection is product of probability of each event.

Now, the probability that none play video/computer games will be :-

\((0.31)^4=0.00923521\)

If a radius is drawn to the point of tangency of a tangent line, then the radius is basically perpendicular to the tangent line.

Given that the radius is drawn to the point of tangency of a tangent line.

We are required to fill the blank with the appropriate word.

Radius is basically the line segment which joins the center to any point on the circumference of the circle.

Tangent line is basically a line which is drawn from an outside point on the circumference of the circle.

When the radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.

Hence if a radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.

Learn more about tangent at

brainly.com/question/11738604

#SPJ4

Answer:

x=\(\frac{5}{2}\)

Step-by-step explanation:

cross multiply

8x=20

divide both sides by 8

x=\(\frac{5}{2}\)

Answer:

Step-by-step explanation:

Multiply both sides by 20

x = 20 * 1/8

x = 2 4/8

x  = 2.5

Answer:

14

Step-by-step explanation:

angle 90° is opposite the side x. angle 45° is opposite side 7√2.

x/sin 90 = (7√2)/sin 45

multiply both sides by sin 90 (sin 90 is = 1).

x = (7√2)/sin 45

 = 14

a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

Learn more about APR, visit:

brainly.com/question/13597527

#SPJ1

Answer:

72 square feet.

Step-by-step explanation:

You could do this by figuring out directly how many tiles are needed to make the border B...

It is easier to find the area of the large area and subtract the white pool

Large rectangle = 18 * 9 = 162

Small rectangle = 15 * 6 = 90       Subtract

Area of border =               72

Answer: All real numbers

Step-by-step explanation:

Let's find the critical points of the inequality.

2y2+1=

−9

5

y−6

2y2+1−(

−9

5

y−6)=

−9

5

y−6−(

−9

5

y−6)(Subtract (-9)/5y-6 from both sides)

2y2+

9

5

y+7=0

For this equation: a=2, b=1.8, c=7

2y2+1.8y+7=0

y=

−b±√b2−4ac

2a

(Use quadratic formula with a=2, b=1.8, c=7)

y=

−(1.8)±√(1.8)2−4(2)(7)

2(2)

y=

−1.8±√−52.76

4

Answer:

i think it 32214

Step-by-step explanation:

59 x 42 = 2478 x 26 = 66428. And divided by 1/2 (I'm sorry if im wrong)

If the child uses the marbles at random what is the chance that the child gets less than six red marbles is given as   0.9561. See the calculation below.

Note that we are given the following:

p = 20% = 0.20

1 - p = 1 - 0.20 = 0.80

n = 14

Utilizing the binomial formula, we have:

P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x

P(X < 6) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)+  P(x = 4) + P(x = 5)  

Plugging in the value of n, we have:

=  ((14! / 0! (14)!) * 0.200 * (0.80)14 + ((14! / 1! (13)!) * 0.201 * (0.80)13 + ((14! / 2! (12)!) * 0.202 * (0.80)12 + ((14! / 3! (11)!) * 0.203 * (0.80)11 + ((14! / 4! (10)!) * 0.204 * (0.80)10 + ((14! / 5! (9)!) * 0.205 * (0.80)9

=  0.9561

As a result, the probability that the youngster would receive less than six red marbles is provided as 0.9561 if the marbles are used at random.

Learn more about chance:
https://brainly.com/question/25870256
#SPJ1

Answer:

Step-by-step explanation:

a) Volume of small cube box = 8 in³

      side³ = 8 = 2³

Side of small box = 2 in

b)  Side of larger box = 2 + 6 = 8 in

Volume of larger box = 8*8*8 = 512 in³

c) Number of balls to be shipped in the larger box = Volume of larger box ÷ Volume of smaller box

= 512 ÷ 8

= 64 golf balls

Answer: 1 1/2

Step-by-step explanation: I took it on k12

Answer:

The answer is 1 1/2 for K12

Answer:

4

Step-by-step explanation:

(3-4)+5

-1+5

4

Step-by-step explanation:

Answer:

The total of all three raises is $1,890. Jane's raise is $1,660 (4% of $41,400), John's raise is $1,980 (4.5% of $44,000), and Jack's raise is $1,250 (3% of $39,400).

Step-by-step explanation:

volume cylinder 1 =

3.14× 3²× 5 = 3.14×45 = 141.3 in³

volume cylinder 2 =

3.14× 5²× 2 = 3.14× 50= 157 in³

the volume difference between cylinder 1 & 2 =

157 - 141.3 = 15.7 in³

A function m(t)= m₀e^(-rt) that models the mass remaining after t years is; m(t) = 27e^(-0.00043t)

The amount of sample that will remain after 4000 years is; 4.8357 mg

The number of years that it will take for only 17 mg of the sample to remain is;  1076 years

A) Using the model for radioactive decay;

m(t)= m₀e^(-rt)

where;

m₀ is initial mass

r is rate of growth

t is time

Thus, we are given;

m₀ = 27 mg

r = (In 2)/1600 = -0.00043 which shows a decrease by 0.00043

and so we have;

m(t) = 27e^(-0.00043t)

c) The amount that will remain after 4000 years is;

m(4000) = 27e^(-0.00043 * 4000)

m(4000) = 27 * 0.1791

m(4000) = 4.8357 mg

d) For 17 mg to remain;

17 = 27e^(-0.00043 * t)

17/27 = e^(-0.00043 * t)

In(17/27) = -0.00043 * t

-0.4626/-0.00043 = t

t = 1076 years

Read more about Exponential decay function at; https://brainly.com/question/27822382

#SPJ1