The x-intercept is -4 and the y-intercept is 5. What is the slope of the line?

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

To know more about annual interest rate,

https://brainly.com/question/33696451

#SPJ11

HERE is your answer

Answer:

40 BASKETS

Step-by-step explanation:

GFTYDXRTYFCYTGXCR7CKIYFYUC7TCTCGUKCKG\

Answer:

29.666...

Step-by-step explanation:

Answer:

29. Remainder: 2/3

Step-by-step explanation:

89/3 = 29.6666.

The expression  aₙ > 0 and lim n → [∞] aₙ + 1 is true.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.

And we need to check whether the given statement is true or not.

While we looking into the given question, we have identified the following expression,

=> lim n → [∞] aₙ + 1

Here we have also know that the value of aₙ > 0.

When we equate the given expression with zero, we have get the following expression,

=> lim n → [∞] aₙ + 1 = 0

=>  lim n → [∞] aₙ = -1

Here we have given the condition that,  aₙ >0, so

=> lim n → [∞] aₙ = 0

Therefore, the expression is zero.

To know more about Expression here.

https://brainly.com/question/14083225

#SPJ4

Answer:

area = 94.2 min²

Step-by-step explanation:

area = 30 x 3.14 = 94.2 in²

Chad will purchase 0.432 gallons of red and white paint.

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups.

Given

Dimension of the door = 18 feet by 6 feet

Area of the door = 108 square feet

1 gallon of paint covers 250 square feet

Let x gallon paint covers 108 square feet

Proportion of paint to area covered

1/250 = x/108

x = 108/250

x = 0.432

Hence, 0.432 gallons of red and white paint, Chad will purchase.

Learn more about division here:

https://brainly.com/question/21416852

#SPJ1

The directionality of the alternative hypothesis and the support offered by the sample data determine whether the null hypothesis is likewise rejected at the 5% level of significance for a related one-tailed test.

When the two-tailed test rejects the null hypothesis, it means that the sample data, regardless of how we look at it, support the null hypothesis.. A one-tailed test, however, simply considers the evidence in one way. As a result, the null hypothesis should be used if the sample data only show evidence that the alternative hypothesis is true in one direction (for example, greater than).

To know more about Null hypothesis, visit,

https://brainly.com/question/4436370

#SPJ4

Answer:

65/100

Step-by-step explanation:

The number 65 stays the same all  you have to do is add the numbers up to get 100

Step-by-step explanation:

these 2 parallel lines create similar triangles.

that mags they're is one common scaling factor for the side lengths bergen the 2 triangles.

and that means they must have the same ratio.

the large triangle has the side lengths

24 + 9 = 33

32 + x

the smaller triangle has the corresponding side lengths

24

32

so, the equal ratios are

24/33 = 32/(32+x)

24(32 + x) = 32×33

32 + x = 32×33/24 = 4×11 = 44

x = 44 - 32 = 12

Answer:

54.8

Step-by-step explanation:

41+39+48+52+46+62+54+40+96+52+98+40+42+52+60 = 822

822/15= 54.8

Please mark this as Brainliest if it helped you

Answer:

9/10

Step-by-step explanation:

if he has 10 and eats 9 you divide 9 by 10

= 9/10

Arnold eats 9 / 10 fractions of the sweets.

Given that,

Arnold has a bag of 10 sweets. He eats 9 of them. What fraction of the sweets he eat is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Fraction is defined as the number of compositions that constitutes the Whole.

Here,
Arnold has a bag of 10 sweets
Total sweets = 10
Total sweets that were eaten by Arnold = 9
So,
Fraction = sweets eat / total sweet
Fraction = 9 / 10

Thus, Arnold eats 9 / 10 fractions of the sweets.


Learn more about fractions here:

brainly.com/question/10708469

#SPJ2

Answer:the answer is 60 m x 10 m

Step-by-step explanation:

The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

Learn more about distributive property here

https://brainly.com/question/12192455

#SPJ11

Step-by-step explanation:

P(b) = 7/16

P(g) = 6/16 = 1/4

the function is f(×) is square root

Answer:

m=18/3

Step-by-step explanation:

m=-7-11/-6-(-1)

Answer:

2) Gain

3) 0.39 (rounded)

Step-by-step explanation:

2)

12.16/64= 0.19

21/100= .21

12.24/72= 0.17

3)

9.25/24= .3854

if they tell you to round it, its .39, if not its .38

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

Answer:

36.9

Step-by-step explanation:

The graph of the given equation is the lower half of an ellipse with center at (0, 0) and semi-major and semi-minor axis equal to 5 units.

The equation of the ellipse is ((y-0)^2/5^2) + ((x-0)^2/5^2) = 1.

Given equation is:x = (1/5)(25 - y²)

We know that the equation of an ellipse with center (h,k) and semi-major axis a and semi-minor axis b is given by:((x−h)^2/a^2)+((y−k)^2/b^2)=1  (if a is greater than b, then the major axis is horizontal)( (x−h)^2/b^2)+((y−k)^2/a^2)=1  (if a is greater than b, then the major axis is vertical)Here, x = (1/5)(25 - y²) is given.

Therefore, x = (1/5)(5² - y²)Comparing the given equation with the standard equation of an ellipse, we get:((y-0)^2/5^2) + ((x-0)^2/5^2) = 1Here, h = 0, k = 0, a = b = 5

Know more about ellipse here:

https://brainly.com/question/27725600

#SPJ11

The differential equation which passes through the point (0,e) is

y =[(-3/4x² + 1/27)⁻³/²)].

To solve the differential equation:

dy/dx = 4xy/(ln y)⁴

We can separate the variables by writing:

(ln y)⁻⁴dy/y} = 4x dx

Integrating both sides, we get:

∫(ln y)⁻⁴ dy/y = ∫4x dx

Solving the integral on the left-hand side using the substitution

u = ln y, we get:

-1/3(ln |ln y|)⁻³| from e to y = 4x² + C

Applying the initial condition y(0) = e, we can solve for C:

-1/3(ln |ln e|)⁻³= 4(0)²+ C

C = -1/27

Therefore, the solution to the differential equation that passes through the point (0, e) is:

-1/3(ln |ln y|)⁻³ = 4x² - 1/27

Taking the natural logarithm of both sides, we get:

The solution to the differential equation dy/dx = 4xy/(ln y)⁴ which passes through the point (0,e) is:

y =  [(-3/4x² + 1/27)⁽⁻³/²⁾]

Learn more about differential equation

brainly.com/question/13426876

#SPJ11

Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.

What is division in mathematics?

Division is the process of splitting a number or an amount into equal parts.

To find the number of times Anna will need to fill the measuring cup, divide the number of cups of turnips by the size of the measuring cup:

78 cups/14 cups:

                            = 78/14

                              =5.57 measures

Hence, Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.

To learn more about the division in mathematics, visit:

https://brainly.com/question/28119824

#SPJ1

Answer:

7.5

Step-by-step explanation:

Since the triangles are congruent, corresponding sides will have the same lengths. So since line AC is 7.5, line HT must also be 7.5

Answer: $122.64

Step-by-step explanation:

5% of $116.80 is $5.84

$116.80 + $5.84 = $122.64

Answer:

-x² + 13x + 2

Step-by-step explanation:

you are on ambitious level, and you cannot answer that yourself ? that is trivial. truly. no hidden traps, just straight forward adding and simplifying. what is the problem, please ?

-7x² + 6x² = -x²

5x + 8x = 13x

-1 + 3 = 2

Answer:

3rd option

Step-by-step explanation:

Given

(- 7x² + 5x - 1) + (6x² + 8x + 3) ← remove parenthesis

= - 7x² + 5x - 1  + 6x² + 8x + 3 ← collect like terms

= - x² + 13x + 2

The sequence can be used to find exact values when the level of the pattern increases or decrease

The mathematical expression that connects the number of tiles and the grouping method is presented as follows; tₙ = 9 + (n - 1)× 3

From the given diagram, we have that the number of green tiles = 18

Grouping method 1 has 15 green colored tiles with Figure size 3

We have;

Grouping method 1

The figure size number of the shape with 15 green colored tiles = 3

Grouping method 2, figure size 4

The figure size number of the shape with 18 green colored tiles = 4

The size number of the shape with 12 green colored tiles = 2

The size number of the shape with 9 green colored tiles = 1

Therefore the sequence is an arithmetic progression having the following characteristics;

nth term, tₙ = a + (n - 1)·d

In the first term, a = 9

The common difference, d = 3

The mathematical expression that connects the grouping methods above, and gives the number of green tiles, tₙ, is tₙ = 9 + (n - 1)× 3

Where;

n = The grouping method number

The number of green tiles is given by the equation, tₙ = 9 + (n - 1)× 3

Learn more about number sequence here:

brainly.com/question/12474324

#SPJ1

the revenue function is R(x) = 102x - 0.03x²/2.

Given the marginal revenue from selling X irons as 102 - 0.06x dollars per iron, we can find the revenue function by integrating the marginal revenue function and adding a constant of integration, denoted as C.

Integrating the marginal revenue function, we have:

R(x) = ∫(102 - 0.06x) dx

Evaluating the integral, we get:

R(x) = [102x - 0.03x²/2] + C

Since the revenue at 0 irons is 0, we can substitute x = 0 into the revenue function to find the value of the constant C.

R(0) = [102(0) - 0.03(0)²/2] + C

0 = [0 - 0/2] + C

0 = 0 + C

C = 0

To know more about marginal revenue

https://brainly.com/question/33446428

#SPJ11