Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual simple interest rate of 11%. After 14 years, the interest earned on the account was $3,080. How much money did Mike's grandmother deposit in the account?

For a call that is under six minutes, the cost is $0.70, the cost of a 14-minute call is $2.62 and the cost of a 9-minute call is $1.90.

For a call that is under six minutes, the cost is $0.70.

This is because the rate schedule specifies that for m ≤ 6 minutes, the cost is a flat rate of $0.70.

For a 14-minute call, we can apply the second part of the rate schedule. Since 14 > 6 and 14 is an integer, the formula to calculate the cost becomes:

c(m) = 0.70 + 0.24(m - 6)

Plugging in m = 14:

c(14) = 0.70 + 0.24(14 - 6)

c(14) = 0.70 + 0.24(8)

c(14) = 0.70 + 1.92

c(14) = 2.62

Therefore, the cost of a 14-minute call is $2.62.

c. For a 9-minute call, we again apply the second part of the rate schedule. Since 9 > 6 and 9 is not an integer, the formula becomes:

c(m) = 0.70 + 0.24([m - 6] + 1)

Plugging in m = 9:

c(9) = 0.70 + 0.24([9 - 6] + 1)

c(9) = 0.70 + 0.24(4 + 1)

c(9) = 0.70 + 0.24(5)

c(9) = 0.70 + 1.20

c(9) = 1.90

Therefore, the cost of a 9-minute call is $1.90.

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Answer:

x=4

Step-by-step explanation:

2x+3=11

2x+3-3=11-3

2x=8

x=4

2x+3=11

2(4)+3=11

8+3=11

11=11

Answer:

x =4

Step-by-step explanation:

\(2x +3=11\\\\Collect \:like\:terms\\2x =11-3\\\\Subtract\\2x =8\\\\Divide\:both\:sides\:of\:the\:equation\:by\:2\\\frac{2x}{2} =\frac{8}{2} \\\\x = 4\)

The period of the function is 4π, and the amplitude is 2.

Given data ,

Let the function be represented as f ( x ) = y

Now , the value of f ( x ) is

y = 2sin ( 1/2 )x

To find the period and amplitude of the function y = 2sin((1/2)x), we can use the standard form of a sine function: y = Asin(Bx).

In this case, the amplitude (A) is 2.

The amplitude represents the maximum displacement from the midpoint of the sinusoidal function.

To find the period, we can use the formula:

Period = (2π) / |B|.

B = 1/2.

Period = (2π) / |1/2|

P = (2π) / (1/2) = 2π * 2/1 = 4π

Hence , the period of the function is 4π, and the amplitude is 2.

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Answer:

63

Step-by-step explanation:

180 -  143 = 37

80 + 37 + x = 180

117 + x = 180

x = 63

The purpose of data is to provide information and insights that can be used to make informed decisions, draw conclusions, and gain knowledge about a particular subject or phenomenon.

Data plays a crucial role in various fields, including science, business, research, healthcare, and everyday life.One primary purpose of data is to describe and understand the world around us.

By collecting and analyzing data, we can identify patterns, trends, and relationships that exist within a dataset. This helps us gain a deeper understanding of complex systems and phenomena.

For example, in scientific research, data is used to study the behavior of natural processes, investigate the effects of interventions, and formulate theories and models.

Data also serves as a foundation for making informed decisions. By examining relevant data, individuals and organizations can assess the potential outcomes of different choices and select the most optimal course of action.

Data-driven decision-making enables organizations to improve efficiency, identify opportunities, mitigate risks, and enhance overall performance. In fields like marketing and finance, data is extensively used for market research, customer segmentation, trend analysis, and financial forecasting.

Furthermore, data is crucial for monitoring and evaluating performance. By collecting data over time, organizations can track progress, measure outcomes, and identify areas for improvement. Data-driven monitoring allows for evidence-based assessments and adjustments to strategies or interventions.

Overall, the purpose of data is to provide reliable information that can be used to enhance understanding, support decision-making, and drive progress in various domains. It empowers individuals and organizations with the ability to derive insights, solve problems, and make meaningful contributions to society.

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Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

Answer:

A = 2000(2)60/80

A = 2000(2)600/60

Step-by-step explanation: i wish it is help you

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5

We have to given that;

the terminal side of theta in standard position contains the point (6,-8)

Hence, For given condition we get;

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

Here, x = 6, y = - 8

Hence, We get;

r = √x² + y²

r  = √6² + 8²

r = √36 + 64

r = √100

r = 10

So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

cos θ = x / r

cos θ = 6 / 10

cos θ =  3 / 5

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What is the sum of the geometric series Σ2

Σ(3)

rounded to the nearest whole number?

Answer: O2

Using the perimeter formula, fence needed to enclose a rectangular field is 240 m, to enclose a rectangular vegetable garden is 40 m, rope needed to fence a rectangular lot is 494 m. The area of the vegetable garden is 75 m^2.

The length of fence/rope that will be needed to enclose the rectangular field or a rectangular vegetable garden can be determined by calculating the perimeter of the rectangle.

Perimeter of the rectangle (P) = 2(Length + Width)

Fence needed to enclose a rectangular field when L = 20 m and W = 100 m

P = 2(20 + 100) = 2(120) = 240 m

Fence needed to enclose a rectangular vegetable garden when L = 15 m and W = 5 m

P = 2(15 + 5) = 2(20) = 40 m

Area of the rectangle = L x W = 15 x 5 = 75 m^2

Rope needed to enclose a rectangular lot when L = 150 m and W = 97 m

P = 2(150 + 97) = 2(247) = 494 m

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Answer:

\(6 \times 12.5 = 75\)

The total price in shoe sales equals $709.96

10% of $709.96 is $71 after rounding up.

$71 plus $75=$146

answer-$146

Answer:

Step-by-step explanation:

Answer:

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Step-by-step explanation:

The best interpretation for the expression 85h + 75 is;

The charge for each hour worked is $85

The initial charge before commencement of work per hour is $75

The general formula of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, the slope may also be called the rate of change of the output with the input while the y-intercept represents the initial value or the value of the output when the input is zero.

Now, we are given the equation for total bill as;

T = 85h + 75

where h is number of hours worked

Thus;

The charge for each hour worked is $85

The initial charge will be $75 before commencement of work per hour.

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The given linear equation, 5x - 8 = 11 - 7x + 12x , has no solution

From the question, we are to solve the given linear equation.

From the given information,

The given linear equation is

5x - 8 = 11 - 7x + 12x

To solve the linear equation, we would determine the value of the unknown variable.

In the given equation, the unknown variable is x. Thus, we would solve for x.

Solving for x

5x - 8 = 11 - 7x + 12x

Simplify

5x - 8 = 11 + 5x

Add 8 to both sides of the equation

5x - 8 + 8 = 11 + 8 + 5x

5x = 19 + 5x

Subtract 5x from both sides

5x - 5x = 19 + 5x - 5x

0 = 19

Hence, no solution

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Answer:

62•4=248

\(63^{4} =2^{24}\)

Step-by-step explanation:

I didn't know which one you needed so here's both.

Answer:

1265 kg of protein

Step-by-step explanation:

If 55kg is eaten in one day then in 23 days there will be x kgs.

To find 'x':

55 x 23 = 1265

The expression that models the number of people attending concert 1 is given as follows:

512/6.

The number of people attending concert 1 is obtained applying the proportions in the context of the problem.

From the bar model, the fractions corresponding to each concert are given as follows:

The total number of people is given as follows:

512.

Hence the expression that models the number of people attending concert 1 is given as follows:

512/6.

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Answer:

890 1/2 or  890.5

Step-by-step explanation:

Answer:

890.5 ft²

Step-by-step explanation:

Formula to find rectangular area

    Area = A = L × W

So put values

R 1        A 1 = 24.5 ×  18 = 441

R 2      A 2 = 14.5  × 18.5 = 268.25

R 3      A 3 = 12.5 ×  14.5 = 181.25

Add them up

441 + 268.25 + 181.25 = 890.5

Earth's diameter is 0.0092 times less than the sun's diameter.

The Diameter of Earth = 1.3 * 10⁴ km

The Diameter of Moon = 3.5 * 10³ km

Let the diameter of sun be x km

According to the question

The diameter of the sun is 400 times that of the moon.

x = 400 * 3.5 * 10³ km

= 14 * 10⁵ km

The Diameter of earth / diameter of sun

=  1.3 * 10⁴ / 14 * 10⁵

= 0.0092

Hence, The diameter of the Earth is 0.0092 times that of the Sun.

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Answer:

84

hope this helps you!

Answer:

96

Step-by-step explanation:

Answer:

13.2 + 0.292X = Y

Step-by-step explanation:

Given that, according to the National Center for Education Statistics, there were 13.2 million undergraduate students enrolled in degree-granting postsecondary institutions in Fall 2000, while in Fall 2014, the enrollment was 17.3 million students, assuming this relationship grows linearly, a linear function that models the undergraduate enrollment in postsecondary institutions X years after 2000 would be carried out as follows:

2014-2000 = 14

17.3 - 13.2 = 4.1

4.1 / 14 = 0.292

Thus, each year 292,000 new students are enrolled in postsecondary institutions. Therefore, the function that determines what is requested would be the following:

13.2 + 0.292X = Y

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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P(x) = I(x3 - 6x2 + 21x - 54) is the degree 3 polynomial with real coefficients factorization having zeros 3, 3 - 3i, and 3 + 3i and a lead coefficient of I.

In mathematics, a number or another mathematical entity is factored, or represented as the sum of many factors, usually smaller or less complex variables of the same kind. For instance, the polynomial x2 - 4 can be factored into the number 15, which is multiplied as 3 5. In mathematics, the term "factorization" describes the division of a number through smaller amounts that are then multiplied together to create the initial number. A number is divided into one or more components through the process of factorization. As an illustration, 12 is increased by 3 and 4.

Real values in the polynomial require that the conjugate of 3 - 3i also be zero. In other words, 3 plus 3i, the complex conjugate, also contains a zero.

The polynomial can now be factored using the zero product property:

P(x) = I(x-3)(x-3/+3i)(x - 3 - 3i)

Adding up the variables results in:

P(x) is defined as I(x - 3)((x - 3) + 3i)((x - 3) - 3i)).

P(x) = I(x-3)(x-3/+3i)(x - 3 - 3i)

P(x) = I(x - 3)((x - 3)^2 - (3i)^2)

P(x) = I(x - 3)((x - 3)^2 + 9)

P(x) is equal to I(x3 - 6x2 + 21x - 54).

As a result, P(x) = I(x3 - 6x2 + 21x - 54) is the degree 3 polynomial with real coefficients having zeros 3, 3 - 3i, and 3 + 3i and a lead coefficient of I.

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Answer: 5 : 3, 10: 6, 25: 15

Step-by-step explanation: We know from our original ratio that for every 5 peanuts, we have 3 cashews. Therefore 5:3, to get to 6 from 3, we have to double it, and whatever we do to the last number, we have to do to the first, so we get 10:6. We can continue this process for 15:9, 20:12, 25:15

Answer:

I can't see the picture.

Step-by-step explanation:

The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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Answer:

(5+5)x2-12 = 8

Step-by-step explanation:

5+5=10, 10×2= 20-12 = 8