You deposit $500 into an account that earns a 5% interest rate that compounds quarterly. You leave the money in the account for 1 year. How much money will you have in the account after 1 year?

The model best fits the given situation is exponential.

Option D is the correct answer.

We have,

The given situation describes a situation where the height of a tree is increasing at a constant rate (2 feet) per year.

This type of growth is typically modeled by an exponential function, where the variable (in this case, the number of years) is in the exponent.

In an exponential model, the quantity being measured (in this case, the height of the tree) grows or decays at an exponential rate over time.

Thus,

The model best fits the given situation is exponential.

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The true equations for the given value of x are C, D and E

3x = 5

x = 5/3

x = 1.667

Substituting x=1.667 in the equations given in the option

The equations C, D and E are true for the value of x in the equation given.

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Answer:

3

Step-by-step explanation:

since 1 is one and 2 is 2

Hello !

1 + 2 = 3

Have a good day !

Answer:

The point U' is (-6, -2).

Step-by-step explanation:

The reflection of point U over the x-axis is the point U' with the same x-coordinate but a y-coordinate that is the opposite of U's y-coordinate. Since the y-coordinate of point U is 3, the y-coordinate of the reflected point U' will be -3. Therefore, the coordinates of U' are (-2, -3).

The graph should show U at the point (2, 3) and U' at the point (2, -3) after being reflected over the x-axis.

Check the picture below.

Answer:

C, 36 3/4

Step-by-step explanation:

Multiply 8 3/4 *4 1/5

In which direction and by how many units should f(x) be shifted to match g(x): A. Left by 4 units.

In Mathematics and Geometry, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Based on the information provided about the parent quadratic function f(x), we can logically deduce that it is given by this equation;

f(x) = x²

Next, we would create a quadratic function for g(x) by using the data points provided in the table above;

g(x) = x² + 8x + 16

g(x) = x² + 4x + 4x + 16

g(x) = x(x + 4) + 4(x + 4)

g(x) = (x + 4)(x + 4)

g(x) = (x + 4)²

Therefore, the parent quadratic function must be shifted left by 4 units to create g(x).

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Answer:

[tex]\huge\boxed{\sf y=\frac{9}{5} x + 2}[/tex]

Step-by-step explanation:

Point = (x,y) = (-5, -7)

So,

x = -5, y = -7

Where m is slope and b is y-intercept.

Along with the already given point, let us take any other point of the line.

Point 1 = (x₁,y₁) = (-5,-7)

Point 2 = (x₂,y₂) = (0,2)

So,

x₁ = -5

y₁ = -7

x₂ = 0

y₂ = 2

[tex]\displaystyle Slope = \frac{y_2-y_1}{x_2-x_1} \\\\Slope = \frac{2-(-7)}{0-(-5)} \\\\Slope = \frac{2+7}{0+5} \\\\\boxed{Slope = \frac{9}{5} }[/tex]

Here, x = 0 when y = 2.

So,

Put slope and y-intercept in general form of slope-intercept equation.

So,

[tex]\displaystyle y=\frac{9}{5} x + 2\\\\\rule[225]{225}{2}[/tex]

Answer:

3³-8*3 = 3

Step-by-step explanation:

Use order of operations:

P -> Parentheses

E -> Exponents

M -> Multiplication (left to right)

D -> Division (left to right)

A -> Addition (left to right)

S -> Subtraction (left to right)

3³=27 is done first because of the exponent. Next, we would do 8*3=24 because that has multiplication. Finally, we do 27-24=3 because of subtracting being the last step in PEMDAS.

Therefore, the final answer is 3

a. The mass of the apple is approximately 33.879 grams.

b. The volume of the apple increases by approximately 1.454 cubic inches during the five-week period.

a. To find the mass of the apple, we need to calculate its volume first. The circumference of the apple can be used to determine its radius.

The formula for the circumference of a circle is C = 2πr,

where C is the circumference and r is the radius.

Rearranging the formula, we have r = C / (2π).

Plugging in the given circumference of 6 inches.

we get r = 6 / (2π) ≈ 0.955 inches.

Now, we need to convert the radius from inches to centimeters since the density is given in grams per cubic centimeter.

Since 1 inch is approximately 2.54 centimeters, the radius in centimeters is [tex]0.955 \times 2.54[/tex]  ≈ 2.427 cm.

Next, we can calculate the volume of the apple using the formula for the volume of a sphere: V = (4/3)πr³.

Plugging in the radius in centimeters, we get

V ≈ (4/3)π(2.427)³ ≈ 73.682 cm³.

Finally, we can find the mass of the apple by multiplying the volume by the density:

mass = volume [tex]\times[/tex] density

= 73.682 cm³ [tex]\times[/tex] 0.46 g/cm³

≈ 33.879 grams.

Therefore, the mass of the apple is approximately 33.879 grams.  

b. The volume of a sphere increases with the cube of its radius.

Since the radius increases by 1/8 inch per week for five weeks, the change in radius would be[tex](1/8) \times 5 = 5/8 inch.[/tex]

Now, let's calculate the change in volume during the five-week period. The formula for the volume of a sphere is V = (4/3)πr³.

Initially, the radius was 0.955 inches.

After five weeks, the radius would be 0.955 + 5/8 inches.

To compare the change in volume, we can calculate the new volume and find the difference:

Change in Volume = New Volume - Initial Volume

Initial Volume = (4/3)π(0.955)³

New Volume = (4/3)π(0.955 + 5/8)³

By subtracting the initial volume from the new volume, we can determine how the volume changes during the five-week period.

Please note that the exact calculation will depend on the precise values used for π and the measurements provided.

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The experimental group consists of the volunteers who receive the bottle of solution with ingredients intended to minimize wrinkles among women aged 40 to 45.

In the given situation, the experimental group refers to the group of participants who receive the bottle of solution that is specifically formulated to minimize wrinkles among women.

The research team is experimenting to test the effectiveness of the product in reducing wrinkles. To do this, they divided the participants into two groups. One group is given a bottle of the solution that contains ingredients intended to lessen wrinkles, while the other group is given a similar bottle of the solution but without any ingredients targeted at reducing wrinkles.

The purpose of the experiment is to compare the outcomes between these two groups and determine whether the solution with the specific wrinkle-reducing ingredients has any effect on minimizing wrinkles among women aged 40 to 45.

The experimental group, in this case, is the group of volunteers who receive the bottle of solution with the ingredients intended to lessen wrinkles. They are the group that is exposed to the independent variable, which in this case is the wrinkle-reducing solution. The research team will monitor and evaluate the effects of the solution on this group to determine its effectiveness in minimizing wrinkles.

Meanwhile, the control group is the group of participants who receive the bottle of solution without any ingredients aimed at reducing wrinkles. The control group serves as a baseline for comparison, allowing the research team to assess the specific impact of the wrinkle-reducing ingredients in the experimental group.

Therefore, in this scenario, the experimental group consists of the volunteers who receive the bottle of solution with ingredients intended to minimize wrinkles among women aged 40 to 45.

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sinθ = t/o

cosθ = m/o

tanθ = t/m

cscθ = o/t

secθ = o/m

cotθ = m/t

Answer:

[tex]\huge\boxed{\sf x = 12}[/tex]

Step-by-step explanation:

Let the smaller number be x and greater number be y.

y = 7 + 2x ----------------(1)

x + y = 43 ----------------(2)

Put Eq. (1) in Eq. (2)

x + 7 + 2x = 43

x + 2x + 7 = 43

3x + 7 = 43

3x = 43 - 7

3x = 36

x = 36/3

Put x = 12 in Eq. (1)

y = 7 + 2(12)

y = 7 + 24

[tex]\rule[225]{225}{2}[/tex]

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

We first need to understand the logistic formula used for modeling population growth. The formula is:
P'(t) = rP(t)(1 - P(t)/K),

where P'(t) represents the rate of change of the population, P(t) is the population at time t, r is the intrinsic growth rate, and K is the carrying capacity of the environment.

(a) To calculate P'(0), we need the values for r, P(0), and K. P(0) refers to the initial population.

(c) The assumption made in the computation is that the population grows continuously and the rate is proportional to both the population size and the remaining capacity for growth.

To verify this assumption, we can plug in the given values and compare the result with the actual data. If the difference is within 1%, the assumption holds true.

Please provide the required values for r, P(0), and K to proceed with the calculations.

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1. The velocity of the object is 3 m/s.

2. The object is moving in positive direction.

3. The total distance travelled is 5√10.

1. The velocity of the object is

= displacement / time

= 12/ 4

= 3 m/s

2. The object is moving in positive direction.

3. The total distance travelled

= √225+ 25

= √250

= 5√10

4. The displacement is

= 1/2 x base x height

= 1/2 x 5 x 15

= 37.5 m

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Saving for a down payment was worth it for Isabel. It reduces the total amount paid for the car by lowering the loan amount, resulting in less interest paid over time.

When evaluating whether saving for a down payment on a car was worth it for Isabel, we need to consider the difference in the total amount paid for the car in two scenarios: with a down payment and without a down payment. Let's analyze the two scenarios to make a judgment.

Scenario 1: With a down payment

In this scenario, Isabel saved up and made a down payment on the car. As a result, her monthly loan payment fits within her budget. By making a down payment, she reduces the principal amount borrowed and, subsequently, the interest charged on the loan.

The benefits of saving for a down payment include:

Lower loan amount: By making a down payment, Isabel reduces the total amount borrowed from the lender.

Reduced interest: With a lower loan amount, the interest charged on the loan is also reduced.

Shorter loan term: A down payment can help Isabel secure a shorter loan term, reducing the overall interest paid over time.

Scenario 2: Without a down payment

In this scenario, Isabel does not make a down payment and finances the entire purchase price of the car. As a result, her monthly loan payment may be higher, as she is borrowing a larger sum and potentially paying more interest over the loan term.

The drawbacks of not saving for a down payment include:

Higher loan amount: Without a down payment, the entire purchase price is financed, leading to a higher loan amount.

Increased interest: With a higher loan amount, more interest may accumulate over the loan term, resulting in a higher total cost of the car.

By comparing the two scenarios, we can assess the impact on the total amount paid for the car. Generally, having a down payment reduces the loan amount, decreases interest charges, and may result in a shorter loan term. This, in turn, can lead to substantial savings in the long run.

To determine the exact difference in the total amount paid for the car in each scenario, we would need specific details such as the purchase price of the car, the interest rate, and the loan term. With these figures, we could calculate the total cost of the car, including interest, in both scenarios and compare the results. Based on this analysis, we can then determine if saving for a down payment was worth it for Isabel.

In conclusion, saving for a down payment on a car can offer financial benefits such as lower loan amounts, reduced interest charges, and potentially shorter loan terms. Considering the potential cost savings and improved financial stability, it is generally advisable for Isabel to save for a down payment, making it worth the effort and consideration.

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Question

The down payment makes the monthly loan payment fit into Isabel's budget. Besides this benefit, do you think saving for a down payment on the car was worth it for Isabel? Use each monthly payment with and without a down payment) to find the difference of the total amount paid for the car in each scenario to justify your answer.

Answer:

To factor the polynomial y = x³ + 2x² - 5x - 6 by dividing by (x + 1), we can use synthetic division:

-1  |   1   2   -5   -6

        |_______-1___-1___6

        | 1   1   -6   0

The result of the synthetic division is: x² + x - 6.

Therefore, we can write the polynomial as:

y = (x + 1)(x² + x - 6)

To factor it completely, we can factor the quadratic expression x² + x - 6:

y = (x + 1)(x + 3)(x - 2)

Therefore, the polynomial function y = x³ + 2x² - 5x - 6 can be factored completely as y = (x + 1)(x + 3)(x - 2).

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The value of ∂x/∂s is  4s^2 * t^6.

To find ∂x/∂s, we need to differentiate x with respect to s while treating t as a constant. Let's begin by substituting the given expressions for x, y, and z into the function f(x, y, z):

f(x, y, z) = (x^2)(y^3) + z^3

Substituting x, y, and z:

f(s, t) = ((s^2)(t^3))^2 * (s*t)^3 + ((s^2)*t)^3

Expanding the expression:

f(s, t) = (s^4 * t^6) * (s^3 * t^3) + (s^6 * t^3)

Now, let's differentiate x with respect to s:

∂x/∂s = ∂/∂s [(s^2)(t^3)]^2

Using the chain rule, we can differentiate each term separately:

∂x/∂s = 2 * (s^2 * t^3)^1 * ∂/∂s [(s^2)(t^3)]

Differentiating (s^2)(t^3) with respect to s:

∂/∂s [(s^2)(t^3)] = 2s * t^3

Substituting back into the expression for ∂x/∂s:

∂x/∂s = 2 * (s^2 * t^3)^1 * 2s * t^3

Simplifying:

∂x/∂s = 4s^2 * t^6

Therefore, ∂x/∂s = 4s^2 * t^6.

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Hello !

(9 + x)/2 = (7 + 3 + x)/3

3(9 + x) =2(7 + 3 + x)

27 + 3x = 14 + 6 + 2x

27 + 3x = 20 + 2x

27 - 20 = 2x - 3x

7 = -x

x = -7

you can check it works for the 2 averages

1. The graph of y=-2x² + 8  in the domain x ∈ [-3, 3] is attached

2. The name is a quadratic graph

3. The range is y ≤ 8

4, The equation of the axes of symmetry is x = 0

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

y =-2x² + 8

And the domain is given as x ∈ [-3, 3]

The above function is a quadratic function that has the following features

a = -2, b = 8 and c = 0

Next, we plot the graph using a graphing tool by taking note of the above features

The graph of the function is added as an attachment

Recall that

y =-2x² + 8

The above has a degree of 2

So, the name of the graph is a quadratic graph

From the graph, the maximum is 8

This means that the highest output value is 8

So, we have the range to be y ≤ 8

This is the line that divides the graph into equal parts

From the graph, the equation of the axes of symmetry is x = 0

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Answer:

Option C. 5.5

Step-by-step explanation:

To solve for x in the equation:

[tex]\sf\implies\dfrac{3x - 4}{14} = \dfrac{9}{10}[/tex]

We need to isolate x on one side of the equation.

First, we simplify the left side by solving the division:

[tex]\sf\implies\dfrac{(3x - 4)}{14} = \dfrac{9}{10}[/tex]

Next, we cross-multiply to eliminate the fractions:

[tex]\sf\implies 10(3x - 4) = 14(9)[/tex]

[tex]\sf\implies 30x - 40 = 126[/tex]

Now, we isolate x by adding 40 to both sides of the equation:

[tex]\sf\implies 30x = 166[/tex]

Finally, we solve for x by dividing both sides of the equation by 30:

[tex]\sf\implies x = \dfrac{166}{30}[/tex]

[tex]\sf\implies x = 5.533[/tex]

Therefore, the value of x is approximately 5.533. Thus, the correct option is C. 5.5.

Chi-Chiribi! EmergerOrpheus at your service. Hope it helps!

[Top Question] Answer: A. |-6| + |3|

Step-by-step explanation:

       First, we realize they are both on the same y-axis as they both have y-values of 4. This means that we can "ignore" the y-value and focus on the x-value. To find the distance between these two points, we will find the absolute value of the x-values and add them together. This gives us answer option A;

                   A. |-6| + |3|

[Bottom Question] Answer: 36 [tex]\frac{3}{4}[/tex] units²

Step-by-step explanation:

       To find the area of a parallelogram, we multiply the base by the height. I will change 8 [tex]\frac{3}{4}[/tex] into 8.75 and 4 [tex]\frac{1}{5}[/tex] into 4.2 to make multiplying with a calculator easier.

A = bh

A = (8.75 units)(4.2 units)

A = 36.75 units² = 36 [tex]\frac{3}{4}[/tex] units²

The breakeven point is 890 units and Molander Corporation's margin of safety is $3,600 in dollars and 14.42% as a percentage of its sales.

To find the breakeven point:

Breakeven Point = Fixed Expenses / Contribution Margin per unit

Contribution Margin per unit = Selling Price per unit - Variable Expense per unit

= $24 - $14

= $10

Breakeven Point = $8,900 / $10

= 890 units

The breakeven point is 890 units.

To calculate the margin of safety:

Margin of Safety = Actual Sales - Breakeven Point

Actual Sales = Unit Sales per month

= 1,040 units

Margin of Safety = 1,040 units - 890 units

= 150 units

Margin of Safety in dollars = Margin of Safety × Selling Price per unit

= 150 units × $24

= $3,600

Margin of Safety as a percentage of sales = (Margin of Safety / Actual Sales) × 100

= (150 units / 1,040 units) * 100

= 14.42% (rounded to 2 decimal places)

Therefore, Molander Corporation's margin of safety is $3,600 in dollars and 14.42% as a percentage of its sales.

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Answer:

[tex]\huge\boxed{\sf Solution\ Set: \{x | x > 8/3\}}[/tex]

Step-by-step explanation:

4x - 7 < 7x - 15

-7 < 7x - 4x - 15

-7 < 3x - 15

-7 + 15 < 3x

8 < 3x

8/3 < x

[tex]\rule[225]{225}{2}[/tex]

Answer:

This is how you simplify it.

Answer:

Step-by-step explanation:

(3x⁵)^3
= {3x}^(15)     (According to rule)

Answer = (3x)^(15)  

After 15 years, the amount in Hank's savings account, with no additional deposits or withdrawals, will be approximately $1,044.50.

To calculate the amount in Hank's savings account after 15 years with monthly compounding interest, we can use the formula for compound interest:

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

Where:

A = the future value of the account

P = the principal amount (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case:

P = $850

r = 1.2% = 0.012 (as a decimal)

n = 12 (monthly compounding)

t = 15 years

Plugging in the values into the formula, we get:

A = 850(1 + 0.012/12)^(12*15)

A = 850(1.001)^180

A ≈ 850 * 1.228824

A ≈ $1,044.50 (rounded to the nearest cent)

Therefore, after 15 years, the amount in Hank's savings account, with no additional deposits or withdrawals, will be approximately $1,044.50.

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a. To find the sum of 2 (a rational number) and (-2 + √3), we add them together:

2 + (-2 + √3) = 0 + √3 = √3

The sum is √3. Since √3 is an irrational number, the sum is irrational.

b. The expression -2 + √3 cannot be rational because a rational number can be expressed as the ratio of two integers, while √3 is an irrational number. If -2 + √3 were rational, it could be expressed as a fraction a/b, where a and b are integers. However, we know that √3 is irrational, so it cannot be written as a fraction of two integers. Therefore, -2 + √3 cannot be rational.

The value of x that satisfies the equation -8 + 5(2x + 1) = -(7x + 9) + x is x = 3/4.

To solve the equation -8 + 5(2x + 1) = -(7x + 9) + x, we will simplify the expression step by step and solve for the value of x.

Distribute 5 to the terms within the parentheses: -8 + 10x + 5 = -(7x + 9) + x

Combine like terms on both sides of the equation: -8 + 5 + 10x = -7x - 9 + x

Simplifying further, we have: -3 + 10x = -6x - 9

To eliminate the negative sign on the right side of the equation, we can multiply every term by -1: -3 + 10x = -6x - 9 * -1

This simplifies to: -3 + 10x = -6x + 9

Next, we want to isolate the x terms on one side of the equation and the constant terms on the other side. We can do this by adding 6x to both sides: -3 + 10x + 6x = -6x + 9 + 6x

Simplifying further: 16x - 3 = 9

To isolate the x term, we need to eliminate the constant term on the left side. We can do this by adding 3 to both sides: 16x - 3 + 3 = 9 + 3

Simplifying further: 16x = 12

Finally, we solve for x by dividing both sides of the equation by 16: (16x)/16 = 12/16

The equation simplifies to: x = 3/4

Therefore, the value of x that satisfies the equation -8 + 5(2x + 1) = -(7x + 9) + x is x = 3/4.

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The box plot which correctly shows displays the given data is the box plot where the whisker ranges from 1 to 6 and the box ranges from 2.5 to 4 with a line at 3.

Given a data set,

0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 6

Box shows the interquartile range.

Starting line of the box is first quartile, middle line is the median and the ending line is the third quartile.

There are 13 data points.

Here median = middle point = 7th point = 3

So the middle line of the box is at 3.

Median divides data plot in to two : 0, 1, 2, 3, 3, 3 and 3, 3, 3, 5, 5, 6.

First quartile is the median of the data points 0, 1, 2, 3, 3, 3.

First quartile, Q1 = average of middle two elements = (2 + 3) / 2 = 2.5

Third quartile is the median of the data points 3, 3, 3, 5, 5, 6.

Third quartile, Q3 = (3 + 5) / 2 = 4

IQR = Q3 - Q1 = 1.5

So the box ranges from 2.5 to 4 with a line at 3.

Now, we have to find the extension of whiskers, that is minimum and maximum value.

Lower whisker = Q1 - 1.5 (IQR) = 0.25

No values less than 0.25 is on the line.

Upper whisker = Q3 + 1.5 (IQR) = 6.25

No values greater than 6.25 will be on the line.

From the data, 0 belong as an outlier outside the whisker.

So whisker ranges from 1 to 6.

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