Mr. Bearfield deposited $3,500 in a new investment account. -The investment pays 8% interest compounded annually on this account. -Mr. Bearfield did not make any additional deposits or withdrawals. What is the balance of the account at the end of three years?

The expression that can be used to find the percent of change between the gym's membership in 2012 and the current membership is ((Current Value - Initial Value) / Initial Value) \(\times\) 100.

To find the percent of change between the gym's membership in 2012 and the current membership, we can use the following expression:

Percent of change = ((Current Value - Initial Value) / Initial Value) \(\times\) 100

In this case, the initial value is 9,300 (membership in 2012), and the current value is 2,800 (current membership).

Substituting these values into the expression, we get:

Percent of change = ((2,800 - 9,300) / 9,300) \(\times\)100

Simplifying the expression further, we have:

Percent of change = (-6,500 / 9,300) \(\times\) 100

Therefore, the expression that can be used to find the percent of change between the gym's membership in 2012 and the current membership is ((Current Value - Initial Value) / Initial Value) \(\times\)100. This formula calculates the relative difference between the initial and current values and expresses it as a percentage.

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Answer:

D

Step-by-step explanation:

everything that should happen at x+4 happens now at x. that is what that means.

so, the graph shifts 4 units to the left.

Answer:

x = 78

Step-by-step explanation:

(x-8) + 20 = 90

x - 8 = 90 - 20

x - 8 = 70

x = 70 + 8

x = 78

Check:

(78-8) + 20 = 90

70 + 20 = 90

The exponential growth model is given by the equation y = 2000(1.06)ˣ

An equation is an expression showing the relationship between numbers and variables.

An exponential function is in the form:

y = abˣ

a is the initial value and b is the multiplication factor. if b > 1, it is an exponential growth whereas if b < 1, it is an exponential decay.

A Exponential growth model initial value 2,000 growth rate 6%, hence a = 2000, b = 100% + 6% = 1.06

The exponential model becomes y = 2000(1.06)ˣ

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The calculations are shown below -

a) the ball is 16 feet off the ground at the start of its flight.

b) the ball is in the air for 2 seconds or 4 seconds, to the nearest second.

c) the ball is at its highest point, 12 feet off the ground.

The problems can be solved using the concept of parabolic pathway.

Projectile trajectory is referred to as a parabolic route. Find out what a parabolic route is, about projectiles, beginning velocities, and how to calculate one for a projectile using examples.

a.) A function's point of intersection with the y-axis is known as its y-intercept. The y-intercept in this scenario is (0, 16). In other words, the ball is 16 feet off the ground when it first takes off at t=0, or s(t) = 16.

b.) Finding the value of t at s(t) = 0 will allow us to determine how long the ball has been in the air. By making s(t) = 0 and figuring out t, we can do this:

s(t) = - 4t² + 16t

or, 0 = - 4t² + 16t

or, 4t² - 16t = 0

or, (2t - 4)(2t - 4) = 0

or, t = 2 t = 4

So, the ball is in the air for 2 seconds or 4 seconds, to the nearest second.

c.) A parabolic function's vertex is the point on the curve that is either highest or lowest, and it appears whenever the function reaches its maximum or minimum. The vertex's coordinates are (h, k), where h denotes the x-coordinate and k the y-coordinate. The vertex in this instance is (2, 12). This indicates that the ball is 12 feet off the ground at

t = 2 seconds, when it is at its highest point.

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Isaac will get approximately 9.46 quetzals for his 100 reais.

Given:

Spot rate on the GTQ/₡ cross rate: GTQ 10.5799 = ₡1.00

To find the Brazilian reais/Guatemalan quetzal cross rate:

GTQ/R$ = 1 / (GTQ/₡)

GTQ/R$ = 1 / 10.5799

GTQ/R$ = 0.09461

Therefore, the Brazilian reais/Guatemalan quetzal cross rate is approximately 0.0946.

To calculate how many quetzals Isaac will get for his reais, we need to multiply the number of reais by the cross rate.

Let's assume Isaac has 100 reais:

Quetzals = Reais * GTQ/R$

Quetzals = 100 * 0.0946

Quetzals = 9.46

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Answer:

f=2 and f=11/8

Step-by-step explanation:

Let's solve your equation step-by-step.

f(−4)=−8

Step 1: Simplify both sides of the equation.

−4f=−8

Step 2: Divide both sides by -4.

−4f

−4

=

−8

−4

f=2

Let's solve your equation step-by-step.

f(−8)=−11

Step 1: Simplify both sides of the equation.

−8f=−11

Step 2: Divide both sides by -8.

−8f

−8

=−11/−8

f=11/8

Answer:

Step-by-step explanation:

Answer:

1 is 35 and 2 is 42 and 3 i think is 65

Step-by-step explanation:

Answer:

1. 42875 cube root is expresed as \(\sqrt[3]{42875}\) = 35

2. 74088 cube root is expresed as \(\sqrt[3]{74088}\) = 42

3. 274625cube root is expresed as \(\sqrt[3]{274625}\) = 65

Answer:

\(\displaystyle y=-\frac{a}{b}x+\frac{c}{b}\)

Step-by-step explanation:

The equation of the line, expressed in slope-intercept form is:

\(y=mx+y_o\)

Where m the slope and yo the y-intercept.

Since we are given the line in standard form:

ax+by=c

To find the slope-intercept form, we just solve it for y:

\(\boxed{\displaystyle y=-\frac{a}{b}x+\frac{c}{b}}\)

Comparing the last equation with the slope-intercept form:

\(\displaystyle m=-\frac{a}{b}\)

\(\displaystyle y_o=\frac{c}{b}\)

Answer:

ax + by = c

-ax     -ax

by=ax+c

then dived both sides by b to get y by itself

y= a/bx +c

Step-by-step explanation:

Answer:

450 meters is 0.45 kilometers.

Answer:

It traveled 600,000 miles in one day

The quadratic equation that models the data in the table is y = -0.6x² + 2x + 6.

To determine which quadratic equation models the data in the table where x represents the time in seconds and y is the height of the ball in feet, we will plug the values from the table into each equation and see which one consistently gives the correct heights.

1. y = -0.6x² + 2x + 6

When x=0: y = -0.6(0)² + 2(0) + 6 = 6 (matches the table)

When x=1: y = -0.6(1)² + 2(1) + 6 = 7.4 (matches the table)

When x=2: y = -0.6(2)² + 2(2) + 6 = 7.6 (matches the table)

When x=3: y = -0.6(3)² + 2(3) + 6 = 6.6 (matches the table)

When x=5: y = -0.6(5)² + 2(5) + 6 = 1 (matches the table)

All the values match the table, so the quadratic equation that models the data in the table is y = -0.6x² + 2x + 6.

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Answer:

-6

Step-by-step explanation:

To determine the minimum thickness of the iron, we need to calculate the diffusion flux of hydrogen through the iron and equate it to the maximum allowed hydrogen loss.

The diffusion flux (J) of hydrogen through a material can be calculated using Fick's first law of diffusion:

J = -D * (∆C/∆x)

Where:

J is the diffusion flux

D is the diffusion coefficient of hydrogen in iron

∆C is the difference in hydrogen concentration across the thickness (∆C = C1 - C2)

∆x is the thickness of the iron

We are given:

Maximum allowed hydrogen loss = 50 g/cm²/year

Temperature (T) = 400 °C (673 K)

Hydrogen concentration at surface 1 (C1) = 0.05 H atom per unit cell

Hydrogen concentration at surface 2 (C2) = 0.001 H atom per unit cell

First, we need to convert the hydrogen concentrations into a common unit. The atomic mass of hydrogen (H) is approximately 1 g/mol. The number of atoms in a unit cell for BCC iron is 2.

Concentration in g/cm³:

C1 = (0.05 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.025 g/cm³

C2 = (0.001 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.0005 g/cm³

Now, we can calculate the difference in hydrogen concentration across the thickness:

∆C = C1 - C2 = 0.025 g/cm³ - 0.0005 g/cm³ = 0.0245 g/cm³

Next, we need to determine the diffusion coefficient of hydrogen in iron at 400 °C. The diffusion coefficient can be estimated using the following equation:

D = D0 * exp(-Q/RT)

Where:

D0 is the pre-exponential factor

Q is the activation energy for diffusion

R is the gas constant (8.314 J/(mol·K))

T is the temperature in Kelvin

For hydrogen diffusion in iron, typical values are:

D0 = 5 x 10^-7 cm²/s

Q = 40,000 J/mol

Plugging in the values:

D = (5 x 10^-7 cm²/s) * exp(-40000 J/mol / (8.314 J/(mol·K) * 673 K))

D ≈ 2.70 x 10^-12 cm²/s

Now, we can substitute the values into Fick's first law of diffusion and solve for the thickness (∆x):

J = -D * (∆C/∆x)

Rearranging the equation:

∆x = -D * (∆C/J)

Substituting the given values:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year))

Converting the year unit to seconds:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year)) * (1 year / 3.1536 x 10^7 s)

Calculating:

∆x ≈ -0.000347 cm ≈ 3.47 μm

The negative sign indicates that the thickness (∆x) is measured in the opposite direction of the hydrogen diffusion. Thus, the minimum thickness of the iron required to limit the hydrogen loss to no more than 50 g per year through each square cent.

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Answer:

Yes

Step-by-step explanation:

Yes, since the relationship between the denominators can be expressed as x(4) = y, then you must apply this to the numerators as well. If you multiply 2 by 4 the result is 8, which aligns with the 2nd ratio - in fraction form.

I hope this helped a bunch! Tell me if you need any further assistance...

( :

Answer:

Yes

Step-by-step explanation:

2/3 and 8/12 are equal because of a multiplying factor. To get from 2 to 8, you'd have to multiply by 4. And to get from 3 to 12 you would have to multiply by 4 as well. So that means they are equal because both the numerator and denominator are multiplied by 4.

Using a system of equations, it is found that the simplified equation is y = 6x - 5.

Last year, Ada was x - 1 years old and Bill was y - 1 years old.

Bill was 6 times as old as Ada, hence:

\(y - 1 = 6(x - 1)\)

\(y - 1 = 6x - 6\)

\(y = 6x - 6 + 1\)

\(y = 6x - 5\)

The simplified equation is y = 6x - 5.

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Answer:

-4×-1

Step-by-step explanation:

first answer: -4x-1

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

Answer:

The area is about 25/2 inches^2

Step-by-step explanation:

You are given an isoceles triangle; the sides equal to each other are radiuses of the circle G.  They are both 5 inches in length.  

The angle between the two equal sides is equal to 88 degrees.

To find the height of the triangle, draw a line perpendicular to  GH and solve for the lengths of the sides.  

sin(88) = x/5

5sin88 is about 5 it is (4.99695)

Multiply the side length GH (5) and the solved height and divide by two;

The area is about 25/2 inches^2

The probability of being a senior is the total number of seniors divided by the total number of students.

The probability of a student walking given that they are seniors can be calculated using Bayes' theorem. Bayes' theorem is a formula that relates conditional probabilities to their inverses. The formula is: P(A|B) = P(B|A) P(A) / P(B)where P(A|B) is the probability of event A given that event B has occurred. In this case, A is "walking" and B is "senior." P(B|A) is the probability of being a senior given that the student is walking, P(A) is the probability of walking, and P(B) is the probability of being a senior. We can also represent the above formula in the form of a tree diagram, where P(walk | senior) is one branch of the tree.

The probability of being a senior is represented by the root of the tree, while the probability of walking is represented by a branch from the root. The probability of walking given that the student is a senior is calculated by dividing the probability of a senior walking by the probability of being a senior. The probability of walking can be calculated by adding up the probabilities of walking for each grade level and dividing by the total number of students.

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Answer:

B

Step-by-step explanation:

To find the value of z such that the area to the right of z is 0.5, we can use the standard normal distribution table (also known as the z-table). The z-table provides the cumulative probability to the left of a given z-value.

Since the area to the right of z is 0.5, the area to the left of z is also 0.5. We need to find the z-value that corresponds to a cumulative probability of 0.5 (or 50%).

Referring to the z-table, we find that a cumulative probability of 0.5 corresponds to a z-value of 0. This means that the area to the left of 0 is 0.5, and therefore, the area to the right of 0 is also 0.5.

Thus, the value of z when the area to the right of z is 0.5 is 0.

Therefore, the correct option is b. 0.0000.

Answer:

Approximately 626,000 square miles (1,000,000 km²) in size

So, if Octavio scores 10 points higher than the class mean on the midterm, we may anticipate that he will score final = a + b * (x + 10) points higher on the final.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

Given the regression equation for predicting final-exam score from midterm-exam score:

final = a + b * midterm

where a and b are the regression coefficients, we can use the class mean midterm score x as a reference point to predict the final exam score for a student who scored 10 points above the class mean on the midterm.

First, we need to find the class mean midterm score, which can be represented as x:

x = mean(midterm_scores)

Next, we find the predicted final exam score for the class mean midterm score:

final = a + b * x

Finally, we find the predicted final exam score for a student who scored 10 points above the class mean midterm score:

final = a + b * (x + 10)

So, if Octavio scores 10 points above the class mean on the midterm, we can predict that he will score final = a + b * (x + 10) points above the class mean on the final.

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If a scale model of the plane is 40.6 cm long, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.

To determine the scale factor used to create the model, we need to divide the length of the actual airplane by the length of the model airplane:

58 m / 40.6 cm

To perform this calculation, we need to convert the units so that they match. We can convert 58 m to cm by multiplying by 100:

58 m = 58 × 100 cm = 5800 cm

Now we can divide:

5800 cm / 40.6 cm = 142.857...

Rounding to the nearest thousandth, we get:

142.857... ≈ 142.857

Therefore, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.

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Answer:

y = 1 or y = 27

Step-by-step explanation:

so first transpose -27 to the left side of the equation to make a quadratic equation.

y² - 28y + 27 = 0.....product = 27 , sum = -28 , factors = -1 , -27

( y² - y) ( -27y + 27)=0

y ( y - 1) - 27( y - 1)=0

( y - 1) ( y - 27)=0

y - 1 = 0 or y - 27 = 0

y = 1 or y = 27

Answer:

f(x) = sin(x)

Step-by-step explanation:

sin(x) = 0 for x = n×pi, n>=0

sin(x) = 1 for pi/2 and so on

so, clearly that graph is a pure sine wave.

The argument needs to be rewritten because it is not clear what the eight forms referred to are, and the argument's validity cannot be determined without proper identification of these forms.

Without knowing what the eight forms are, it is not possible to accurately determine if the argument is an instance of one of these forms or if it is invalid. The question mentions "eight forms" but does not provide any context or definition of these forms. It is important to identify and understand the specific forms being referred to in order to assess the validity of the argument. Without this information, it is not possible to provide a proper evaluation of the argument's validity.

Therefore, the argument needs to be rewritten to clearly state the eight forms being referred to and provide adequate context for proper evaluation.

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The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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Perimeter of the soccer field is 306 meters.

A shape's perimeter  is defined as the total length of its bounds. The perimeter of a shape is determined by summing all sides and side lengths that enclose the shape. It is measured in linear measurement units such as centimeters, meters, inches, and feet.

Given,

Length of the soccer field = 98 meters

Width of the soccer field = 55 meters wide

Perimeter of rectangle = 2(Length + Width)

Perimeter of soccer field = 2(98 + 55)

Perimeter of soccer field = 2(153)

Perimeter of soccer field = 306 meters

Hence, 306 meters is the perimeter of the soccer field.

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