A student deposited money into a savings account. The following equation models the amount of money in the account, A(1), after t years. A(1)-1575 (1.045) a. State the initial amount of money deposited into the account. b. Determine the annual interest rate being paid on the account. C. Use the equation to find the amount of money, to the nearest dollar, in the account after 15 years. d. How many years, to the nearest whole year, will it take for the account to have at least $4000?

Complete question :

On their first dive, researchers explore a part of the ocean floor that is 60 feet below sea level. This depth can be represented by the integer -60. On their second dive, researchers explore a deeper depth. Write an inequality that represents the possible depth, d, of the researchers' second dive.

Answer:

d < - 60

Step-by-step explanation:

Depth explored during first dive = 60 feets below sea level = - 60 feets

The depth, d explored during second dive is deeper Than that explored during first dive

The inequality representing depth on second,

This means they the depth exceeds 60 feets below sea level. And hence. Deeper than - 60

Therefore, the depth will be values less Than - 60

Hence, d < - 60

Answer: 7,833

Step-by-step explanation:

Answer:

$18.5

Step-by-step explanation:

You just add up all the costs and divide them by two and then you would get your answer

Answer:

1)

Triangle formula:

A = 1/2bh

A = 1/2(3)(5.9)

A = 8.85

2)

Parallelogram Area:

A = bh

A = (8.9)(6)

A = 53.4

Answer:

324

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

The profit function is; P(x) = -0.01·x² + 3.2·x + 150

What is a profit?

Profit is the amount gained following a business transaction, which is the difference between the amount received as payment for doing a business transaction, within a specified period, known as the revenue and the amount amount spent or invested in doing the business, including the fixed and variable expenses, which is the cost of the business.

The cost and the revenue functions, obtained from a similar question on the internet are;

The cost function is; C(x) = 150 + 5.8·x

The profit function is; R(x) = 9·x - 0.01·x²

The profit function, P(x), is therefore; P(x) = 9·x - 0.01·x² - (150 + 5.8·x) = -0.01·x² + 3.2·x + 150

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Answer:

18 is 3 more than 9- false

18 is 3 times as much as 6 - true

9 is 3 times as much as 27- false

9 is 3 more than 6 - true

On a 7-question multiple-choice test, with 4 answer choices for each question, we need to determine the probability of getting at least one question wrong.

To calculate the probability of getting at least one question wrong, we can consider the complementary probability, which is the probability of getting all questions correct and subtract it from 1.

The probability of getting a single question correct is 1/4, since there are 4 answer choices for each question. Therefore, the probability of getting all 7 questions correct is (1/4) * (1/4) * (1/4) * (1/4) * (1/4) * (1/4) * (1/4) = [tex](1/4)^7[/tex].

To find the probability of getting at least one question wrong, we subtract the probability of getting all questions correct from 1:

P(at least one question wrong) = 1 - P(all questions correct).

Substituting the probability of getting all questions correct, we have:

P(at least one question wrong) = 1 - [tex](1/4)^7[/tex]

Calculating this expression, the probability of getting at least one question wrong is approximately 0.99999, which is essentially equal to 1

Therefore, on a 7-question multiple-choice test with 4 answer choices for each question, the probability of getting at least one question wrong is extremely high, nearly 1. This means that it is highly likely that a test taker will get at least one question wrong on such a test.

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The probability that Astronaut Joe, who is currently on Zorgon, will be affected by the impact is 0.667%.

To determine the probability that Astronaut Joe will be affected by the impact of the asteroid on planet Zorgon, we need to consider the area of the blast zone in relation to the total area of the planet.

An asteroid is heading for the planet Zorgon with a diameter of 2600 miles. When it hits, it will create a blast zone that extends 150 miles in all directions from the point of impact.

What is the probability that Astronaut Joe, who is currently on Zorgon, will be affected by this impact?

The total surface area of Zorgon is given by:2 * 3.14 * (1,300 miles)2 = 10.6 million sq Miles

The blast zone covers an area of:3.14 * (150 miles)2 = 70,685 sq Miles

To calculate the probability that Astronaut Joe will be affected by the impact, we divide the area of the blast zone by the total surface area of the planet.

That is,70,685 / 10.6 million = 0.00667 = 0.667%.

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Answer:

x = 20

y = 7.2

Step-by-step explanation:

12/x = 9/15

9x = 180

x = 20

12/x= y/12

12/20 = y/12

144 = 20y

y = 7.2

y = 20

Answer:

6

Step-by-step explanation:

No. of people going to beach = 46 .

Using Unitary Method ,

9 people can go in one van .

1 person can go in 1/9

46 people can go in 1/9 * 46 = 5.1

Since vans can't be in fraction , 1 extra van for 1 person is need that is for 46th person .

So total number of vans = 5 + 1 = 6

Answer:

3500 dandelions

Step-by-step explanation:

To start you must multiply the number of dandelions by the growth rate to find the number of dandelions grown each day:

2,000 * 0.025 = 50

Then you multiply the number of dandelions by 30 for each day:

50 * 30= 1500

Lastly, you add the dandelions grown in 30 days to the original for your answer.

Answer:

Polymer to be mixed with water to produce 350 gallons of a 0.5% solution is  1.75 gallons.

Step-by-step explanation:

Solution weight-age   100% = 350 gallons

Polymer weight-age = 0.5 %  = ?

Water weight-age = 99.5 % = ?

100 =99.5 w + 0.5 p

350 = ?      + ?

Using ratios

100          350

0.5           p

Applying the cross product rule

p = 350 *0.5/100= 1.75 gallons

Polymer to be mixed with water to produce 350 gallons of a 0.5% solution is  1.75 gallons

Using ratios

100          350

99.5           w

Applying the cross product rule

w = 350*99.5 /100= 348.25 gallons

Water to be mixed with water to produce 350 gallons of a 0.5% solution is  348.25 gallons

Answer:

8

Step-by-step explanation:

Because i wanted extra points.

To find the slope of the line, we need to put the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Step 1: Divide both sides of the equation by 3 to get y by itself on one side of the equation.

3y = 9x + 18

y = 3x + 6

Step 2: Compare the equation to the slope-intercept form y = mx + b, and we can see that the slope is 3.

Therefore, the slope of the line is 3.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

{48, 64, 81}

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

1 out of the 6 cards is 4

Answer:

1

Step-by-step explanation:

Answer:

Uh i dont really get it

Step-by-step explanation:

best of luck though

Answer:

3861.75

Step-by-step explanation:

i hope its the good answer

Answer:  its 4x(3+2)-6÷ 1=14

Step-by-step explanation: in the picture

Answer:

hmmm I think u need to talk to ur teacher

Answer:

Large number=12

Smaller number=6

Step-by-step explanation:

Let the two numbers be x and y

x+y=18

x-y=6

Given [tex]v=4i-j[/tex], and [tex]w=3i+2j\\[/tex], the angle between v and w is 47.7°.

To find the angle between vectors v and w, we can use the dot product formula:

v · w = |v| |w| cos(θ)

where v · w represents the dot product of v and w, |v| and |w| represent the magnitudes of vectors v and w, and θ represents the angle between the vectors.

First, let's calculate the magnitudes of vectors v and w:

|v| = √(4² + (-1)²) = √(16 + 1) = √17

|w| = √(3² + 2²) = √(9 + 4) = √13

Next, let's calculate the dot product of v and w:

v · w = (4)(3) + (-1)(2) = 12 - 2 = 10

Now, we can substitute the values into the dot product formula to find the angle θ:

10 = (√17)(√13) cos(θ)

cos(θ) = 10 / (√17)(√13)

cos(θ) = 10 / (√(17 * 13))

cos(θ) = 10 / (√221)

θ = cos⁻¹ (0.6717)

θ = 47.7°.

Therefore, the angle between vectors v and w is approximately 47.7° .

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Answer:

a = 12.

Step-by-step explanation:

Sum of n terms = n/2[2a + d(n-1)]

For 25 terms

S25 = 12.5(2a + 24d)

S25 = 25a + 300d

For 4 terms

S4 = 2(2a + 3d)

So:

S25 = 15*2(2a + 3d)

S25 = 60a + 90d

25a + 300d = 60a + 90d

35a =  210d

a = 6d

Take  a to be 12 and d to be 2:

25th term = 12.5(2*12 + 24 * 2) = 900

4th term = 2(24 + 6) = 60

900 = 15 * 60 so a = 12.

Answer:

B

Step-by-step explanation:

The average rate of change in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a , b ] = [ 15, 35 ]

and f(b) = f(35) = 400 ← from graph

f(a) = f(15) = 200 ← from graph

Then average rate of change is

[tex]\frac{400-200}{35-15}[/tex] = [tex]\frac{200}{20}[/tex] = 10 m/ s → B

Answer: Where is the rest of the question?

Step-by-step explanation:

Let's denote the length of the table as "x" feet. According to the problem, the width is 2 feet less than the length, so the width can be represented as "x - 2" feet. The area of the table is given as 20 square feet.

The formula for the area of a rectangle is length times width. Therefore, we can set up the equation:

Length × Width = Area

x(x - 2) = 20

Expanding the equation, we get:

x^2 - 2x = 20

Rearranging the equation in quadratic form:

x^2 - 2x - 20 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -2, and c = -20. Plugging these values into the quadratic formula, we get:

x = (-(-2) ± √((-2)^2 - 4(1)(-20))) / (2(1))

Simplifying further:

x = (2 ± √(4 + 80)) / 2

x = (2 ± √84) / 2

x = (2 ± 2√21) / 2

Simplifying the expression inside the square root:

x = (1 ± √21)

So the possible values for x are 1 + √21 and 1 - √21.

Since the length cannot be negative, we take the positive value:

x = 1 + √21

Now we can find the width by substituting this value of x into the expression for width:

Width = x - 2

Width = (1 + √21) - 2

Width = -1 + √21

Therefore, the dimensions of the table are approximately 1 + √21 feet for the length and -1 + √21 feet for the width.

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Solution: Given, Abigail (A) and Balan (B) want to share a pizza of size

1. Both agents have the same utility function u(x) = 2 for pizza, Abigail discounts with 8A = 1/2. Balan discounts with 88 1/2 Abigail moves first.

We have to calculate the Rubinstein solution of the bargaining problem. Bargaining Solution Using Rubinstein's alternating offers model, the bargaining solution is:

Take x as the size of the pizza that Abigail gets.

Hence, Balan gets 1 - x.

The possible utility that they get are:

Abigail: 2x(1/2) + 0(1/2) = x

Balan: 2(1 - x)(88 1/2) + 0(11 1/2) = 177 - 177x The minimum utility that they both need to be satisfied is:

minimum value = 2 x 177/2 = 177

The bargaining range is [0,1], thus there are infinite pairs that satisfy the minimum utility requirement. However, Rubinstein assumes that the final solution should be somewhere between both parties' ideal points, so we can restrict the bargaining range to [1/2, 1]. Abigail gets x and Balan gets 1 - x. Now, we have to see what happens if Balan rejects this offer.

When Balan rejects, the bargaining range is [0, x) for Abigail and (x, 1] for Balan. In this range,

Abigail's ideal point is 2x(1/2) + 0(1/2) = x and

Balan's ideal point is 2(1 - x)(88 1/2) + 0(11 1/2) = 177 - 177x.

The bargaining range is again restricted to [1/2, 1]. When Balan rejects, the bargaining range is [0, x) for Abigail and (x, 1] for Balan. In this range, Abigail's ideal point is 2x(1/2) + 0(1/2) = x and Balan's ideal point is 2(1 - x)(88 1/2) + 0(11 1/2) = 177 - 177x.The bargaining range is again restricted to [1/2, x) and (x, 1].

Now, if Abigail rejects, then the bargaining range is (0, x) for Abigail and [x, 1] for Balan. In this range, Abigail's ideal point is 2x(88 1/2) + 0(11 1/2) = 177x and Balan's ideal point is 2(1 - x)(1/2) + 0(1/2) = 1 - x. The bargaining range is again restricted to (1/2, x) and (x, 1/2 + 1/176). In the next step, if Balan rejects, then the bargaining range is [0, x) for Abigail and (x, 1] for Balan. In this range, Abigail's ideal point is 2x(1/2) + 0(1/2) = x and Balan's ideal point is 2(1 - x)(1/2) + 0(1/2) = 1 - x. The bargaining range is again restricted to [1/2, x) and (x, 1/2 + 1/176).

Repeating the steps,

the solution is: x = 2/3, 177 - 177x = 59.

After calculating the Rubinstein solution of the bargaining problem, we can see that Abigail gets 2/3 of the pizza and Balan gets 1/3 of the pizza. There are two reasons why Abigail gets a larger share of the pizza: Abigail moves first, so she has an advantage because she can propose a deal that is more favorable to her. This is why the bargaining range is initially restricted to [1/2, 1]. Abigail has a lower discount rate than Balan, so she is willing to wait longer for a deal. This means that Abigail can drive a harder bargain because she has a higher reservation utility.

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The regression model estimates the portfolio return closest to 13.79% when the benchmark return is 14%.

The analyst performed a regression analysis using the benchmark returns as the explanatory variable and the portfolio returns as the dependent variable. The y-intercept of the regression line is 0.013, indicating that when the benchmark return is zero, the estimated portfolio return is 0.013%. The slope coefficient of the benchmark returns is 0.892, meaning that for every 1% increase in the benchmark return, the estimated portfolio return increases by 0.892%.

To estimate the portfolio return when the benchmark return is 14%, we plug the value of 14 into the regression model. The estimated portfolio return is calculated as follows: 0.013 + 0.892 * 14 = 13.79%.

Therefore, based on the regression analysis, the model estimates that the portfolio return would be closest to 13.79% when the benchmark return is 14%.

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