One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared.
answer choices
- Observational Study
- Experiment

A statement which best describes how the graph of h is different from the graph of g include the following: A. The graph of h is the graph of g vertically shifted up 1 unit.

In Mathematics, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

In Mathematics, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

In this scenario, the function g(x) = x² is translated upward by 1 units to produce h(x) = g(x) + 1.

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Answer:

68%

Step-by-step explanation:

So we had 34 filets and 16 steaks.

We can add these two together to find the total amount of items sold.

[tex]34 + 16 = 50[/tex]

So 50 total, but we're dealing with filets which is at 34

A percentage can be found by dividing 50 and 34

[tex]34\div 50[/tex]

Giving us 0.68, also known as 68%

The transformation that is needed in order to obtain the graph of​ h(x) from the graph of​ f(x) is D. Vertical translation

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

f(x) = |x|

h(x) = |x| + 3

Using the above as a guide, we have the following:

h(x) = f(x) + 3

This means that the function f(x) is translated 3 units up to get the function h(x)

See attachnent for the graph

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Kareem make muffin using a ratio of 3. 5 cup of flour for every 1. 75 cup of sugar. If he ha 3. 5 cup of sugar, flour doe he need to make the muffin is 7 cups.

The ratio that Kareem uses to make the muffin is 3.5 cups of flour for every 1.75 cups of sugar .

let the number of cups of flour be "y" and

the number of cups of sugar be "x" .

So , y ∝ x ,

y = k*x , where k is the constant of proportionality .

From the given data ,

3.5 = k*1.75

k = 3.5/1.75

k = 2 .

we have to find the cups of flour that Kareem needs , if he has 3.5 cups of sugar .

the equation becomes ,

y = 2*3.5

y = 7

Therefore , Kareem needs 7 cups of flour .

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.

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The values of the x component of d1 is 6.5, the y component of d1 is 23 the x component of d2 is 2.6 and the y component of d2 is 9.2

Given that,

d1 +d2 = 7.0d3,   (1)

d1-d2 = 3.0d3    (2)

and d3= 1.3i +4.6j         (3)

Adding equation 1 and equation 2

d1 +d2 +d1 -d2 = 7 d3 + 3 d3

2d1 = 10 d3

d1 = 5d3

and we also have that  d3= 1.3i +4.6j    

substitute the given d3 in  d1 = 5d3

therefore , d1 = 5(1.3i +4.6j)

d1 = 6.5i + 23 j

here the x component of d1 is 6.5

subtract 2 from 1

d1+d2-d1+d2 = 7d3-3d3

2d2 = 4d3

d2 = 2d3

d2 = 2(1.3i +4.6j)

     = 2.6 i + 9.2j

here the x component of d2 = 2.6

the y component of d2 = 9.2

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The correct option is option D. That is, R'(4,1). The RST coordinates of the given point is: (4,1).

The midpoint is the spot that is in the center of a line that connects two locations. The two reference points that make up a line's endpoints are where it finds its middle. At the halfway point, the line that links these two locations is evenly divided in half. Additionally, if a line is drawn to split the line that links these two points, the midway point is achieved. The midpoint formula may be used to determine the midpoint between two locations when we know their coordinates. The midpoint formula may be used to determine the coordinates of the other endpoint if we know the midpoint's coordinates as well as those of the other endpoint. RST coordinate is (4,1).

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By looking at the frequency of each value, we can see how many individuals had a score of X = 5, which is 4 individuals.

Frequency distribution is a way of organizing data by counting how many times each value appears in a set of data.

In this specific frequency distribution, the value of X = 5 appears once. The frequency, F, for X = 5 is 4, which means that 4 individuals had a score of 5.

This information can be found by looking at the row where X = 5. The frequency distribution allows us to see a pattern in the data, in this case, the frequency of scores.

By analyzing the frequency distribution, we can see that there are more individuals with scores of 2 and 4 compared to those with scores of 3 and 5.

Therefore option (d) is correct.

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The expressions for (h - g)(x) and (h . g)(x) are -x - 8 and  (x - 5)(2x + 3)

While the function (h + g) (-1) is -5

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

g (x) = 2x+3

h(x) = x - 5

This means that

(h - g)(x) = x - 5 - 2x - 3

Evaluate

(h - g)(x) = -x - 8

Also, we have

(h . g)(x) = (x - 5)(2x + 3)

Lastly, we have

(h + g)(-1) = (x - 5) + (2x + 3)

So, we have the following equation

(h + g)(-1) = ((-1) - 5) + (2(-1) + 3)

Evaluate

(h + g)(-1) = -5

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The quotient of the given division expression is 183.25

The division is multiplying one number by any other number to produce a different number. Consequently, the dividend is the number that is divided in this instance. A number's divisor is the one that divides the given number. The quotient is the sum of the two numbers we arrive at as a result. A number is called a "remainder" when a divisor produces a result that does not divide a given number entirely.

formula for dividing

Dividend Divisor = Quotient is how division is performed.

You may alternatively write the expression above as:

Dividends times quotients is a divisor.

In this instance, the divisional symbol is "." However, sometimes, the symbol "/" is used instead, as in

Divisor / Dividend = Quotient

733 ÷  4= 183.25

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(b)  The value of f^(-1) is g.

(c)  The value of f ◦ f ◦ f = f ◦ (f ◦ f) is f((f ◦ f)(x)) = f((x * (x-1))*((x * (x-1)) - 1)).

According to the question

(a) To prove that f is bijective, we need to show that it is both injective (one-to-one) and surjective (onto).

Injectivity: Let x, y ∈ a such that f(x) = f(y). Then, x * (x-1) = y * (y-1). Multiplying both sides by x-1, we get x = y, meaning that f is injective.

Surjectivity: Let z ∈ a. Then, z = z * (z-1) / (z-1), which means that there exists an x ∈ a such that f(x) = z. This shows that f is surjective.

Therefore, f is bijective.

(b) To find the inverse of f, we need to find a function g: a → a such that f(g(x)) = x and g(f(x)) = x for all x ∈ a.

Consider the function g: a → a defined by g(x) = x / (x-1) for all x ∈ a.

Let x ∈ a. Then, f(g(x)) = f(x / (x-1)) = (x / (x-1)) * ((x / (x-1)) - 1) = x. Similarly, g(f(x)) = g(x * (x-1)) = x * (x-1) / (x * (x-1) - 1) = x. This shows that f and g are inverses.

Therefore, f^(-1) = g.

(c) To find f ◦ f ◦ f, we first evaluate f ◦ f and then evaluate f of the result.

Let x ∈ a. Then, (f ◦ f)(x) = f(f(x)) = f(x * (x-1)) = (x * (x-1)) * ((x * (x-1)) - 1). Hence, f ◦ f ◦ f = f ◦ (f ◦ f) = f((f ◦ f)(x)) = f((x * (x-1)) * ((x * (x-1)) - 1)).

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The equation that correctly solves the given equation for t is C) t = (100 - G) / 4

To solve for t in the equation G = -4t + 100, we need to isolate t on one side of the equation. To do this, we start by subtracting 100 from both sides:

G - 100 = -4t + 100 - 100

Simplifying the right side:

G - 100 = -4t

Finally, dividing both sides by -4:

t = (100 - G) / -4

So, option C) t = (100 - G) / 4 correctly represents the equation for t in terms of G.

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Your question is incomplete but most probably the full question was:

A swimming pool is being drained. The number of gallons of water in the pool changes with time t according to the equation G = -4t + 100.

Which equation correctly solves the given equation for t?

A) t = 4G - 100

B) t = -4G + 100

C) t =

100 - G

4

D) t =

G - 100

4

The correct option representing the domain of the relation is given as follows:

{−3, −1, 0, 2, 4}

The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, representing the number of years.

The values of x are the values of x for which there is a dot, hence they are given as follows:

Meaning that the fourth option represents the correct option.

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The answer is cos(B/2) = 2√5 / 5

Half angle formula of cosine: cos B/2 = ±√[(1 + cos B) / 2]

Given: The positive value of cos 1/2 B in the simplest radical form with a rational denominator, if cos B = 3/5:

Regarding applying the cosine half-angle formula:

cos²(B/2) = (1 + cos B) / 2

put value of cos B =3/5 (given)

cos²(B/2) = (1 + 3/5) / 2

on simplifying

cos²(B/2) = (8/5) / 2

cos²(B/2) = 4/5

on taking under root we get

cos(B/2) = 2/√5

use a rational denominator and the simplest radical form hence, cos(B/2) = 2√5 / 5

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An estimate of the real height of the lamp post is 9m.

The first step is to determine the scale of the drawing. The scale can be determined by dividing the height of the lamp post by the height of the car. The height of the lamp post when measured with a ruler is 10.8 cm and the height of the car is 1.8cm

here, we have,

Scale = length of the lamp post / height of the car

10.8 / 1.8 = 6

Now, multiply the scale by the width of the car.

The real height of the lamp post = 6 x 1.5 = 9m

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The symbol for the common normal CDF is. The function represents the CDF of the standard normal distribution.

What is CDF?

The probability function that X will have a value less than or equal to x is known as the Cumulative Distribution Function (CDF) of a real-valued random variable X, evaluated at x. It is employed to describe a table's random variables' probability distribution. And using these data, we can quickly make a CDF plot in an Excel spreadsheet.

So, CDF determines the cumulative probability for the specified value. Under specific circumstances, it is used to compare the probability between values and to ascertain the probability of a random variable. For continuous distribution functions, CDF provides the area under the probability density function up to the specified value, and for discrete distribution functions, it provides the probability values up to what we specify.

F(x)=P(X≤x)=x∫−∞f(t)dt, for x∈R, In other words, integrating the pdf yields the cdf for a continuous random variable. It should be noted that the Fundamental Theorem of Calculus implies that cdf differentiation can be used to determine the pdf of a continuous random variable.

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Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²

We can start by evaluating each bracketed expression first:

{(67)3} = 67 * 67 * 67 = 42,949,769

{(67)2} = 67 * 67 = 4489

Next, we evaluate the first part of the expression:

(67)3 * 2 = 42,949,769 * 2 = 85,899,538

Next, we evaluate the second part of the expression:

(67)2 * (67)2 = 4489 * 4489 = 20,067,961

Finally, we divide the result of the first part by the result of the second part:

85,899,538 / 20,067,961 = 4.286766

To express this result as a power of 2, we find the nearest power of 2 and write it in exponential form:

2² = 4

Thus, Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²

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Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²

We can start by evaluating each bracketed expression first:

{(67)³} = 67 * 67 * 67 = 42,949,769

{(67)²} = 67 * 67 = 4489

Next, we evaluate the first part of the expression:

(67)³ * 2 = 42,949,769 * 2 = 85,899,538

Next, we evaluate the second part of the expression:

(67)² * (67)² = 4489 * 4489 = 20,067,961

Finally, we divide the result of the first part by the result of the second part:

85,899,538 / 20,067,961 = 4.286766

To express this result as a power of 2, we find the nearest power of 2 and write it in exponential form:

2² = 4

Thus, Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²

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A matrix consisting entirely of zeros is called a zero matrix, or an all-zero matrix.

It is denoted with the symbol O and can be written in a matrix form, such as O = [0 0 0 0] where the number of columns and rows depends on the size of the matrix. A zero matrix is a matrix which has all its elements equal to zero. It has a number of special properties that make it useful in linear algebra. For instance, the sum of any two zero matrices is a zero matrix, and any scalar multiple of a zero matrix is a zero matrix. Additionally, the product of two zero matrices is a zero matrix, and the product of a zero matrix and an identity matrix is a zero matrix. These properties make it useful in solving systems of linear equations where all the coefficients are zero. Finally, the inverse of a zero matrix does not exist since its determinant is zero.

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The functions that are solutions of the differential equation y" - 4y' -21y = 0 is -Option E: y(x) = [tex]e^{-3x}[/tex] Option F: y(x) = [tex]e^{7x}[/tex]

A differential equation is any equation that has one or more terms and one or more derivatives of the dependent variable with respect to the independent variable.

The given differential equation is y" - 4y' -21 = 0

This can be written as characteristic equation -

m² - 4m - 21 = 0

m² - 7m + 3m - 21 = 0

m(m - 7) + 3(m - 7) = 0

(m + 3)(m - 7) = 0

m = -3 and m = 7

The general solution is given by

[tex]y = (C1 + xC2)e^{-3x}[/tex]

[tex]y = C1 e^{-3x} + C2 xe^{-3x}[/tex]

[tex]y = (C1 + xC2)e^{7x}[/tex]

[tex]y = C1 e^{7x} + C2 xe^{7x}[/tex]

So, now the solutions are y = [tex]e^{-3x}[/tex], [tex]y = xe^{-3x}[/tex], [tex]y = e^{7x}[/tex]and [tex]y = xe^{7x}.[/tex]

Therefore, the solutions are y = [tex]e^{-3x}[/tex] and [tex]y = e^{7x}[/tex]

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The possible locations of point P are  (-7, -1) and (-7, -11)

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

M = (-7, -6)

Also, we have"

P = 5 units from M

And

P = same x coordinate as point m.

This means that

P = (-7, y)

5 units from (-7, -6) is calculated as

(-7, -6 + 5) and (-7, -6 - 5)

Evaluate

(-7, -1) and (-7, -11)

Hence, the possible location is (-7, -1) and (-7, -11)

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Percent of the square will be shaded is 96.9%. Option A -96. 9%

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used.

Percent is from the Latin adverbial phrase per centum meaning “by the hundred.”

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step 1 : 50%

step 2 : 50% + 25% = 75%

step 3 : 50% + 25% + 12.5% = 87.5%

step 4 : 50% + 25% + 12.5% + 6.25% = 93.75%

step 5 : 50% + 25% + 12.5% + 6.25% + 3.125% = 96.9%

Thus, percent of the square will be shaded is 96.9%. Option A -96. 9%

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Percent of the square that will be shaded is 96.9%. Option A -96. 9%

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used.

Percent is from the Latin adverbial phrase per centum meaning “by the hundred.”

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step 1 : 50%

step 2 : 50% + 25% = 75%

step 3 : 50% + 25% + 12.5% = 87.5%

step 4 : 50% + 25% + 12.5% + 6.25% = 93.75%

step 5 : 50% + 25% + 12.5% + 6.25% + 3.125% = 96.9%

Thus, the percentage of the square will be shaded is 96.9%. Option A -96. 9%

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The algebraic expression is (x² - 4x - 21)/4(x - 7) , we need to find the simplified value of it . Therefore , the simplified form is (x + 3)/4 .

What is simplification?

Rules are typically rewritten to achieve this simplicity. Systems for computer algebra use them in a methodical way. Associative operations, such as addition and multiplication, can be challenging. It is common practice to approach associativity by assuming that addition and multiplication can have any number of operands, such that the symbol for a + b + c is "+." (a, b, c). It follows that a + (b + c) and (a + b) + c are both condensed to "+"(a, b, c), which is shown as a + b + c.

In the question ,it is given that ,

the algebraic expression is (x² - 4x - 21)/4(x - 7) ,

we need to find the simplified value of it .

we first simplify the

numerator

that is x² - 4x - 21 ,

By using the split the

middle term method ,

we get ,

= x² - 7x  3x - 21

= x(x - 7)  3(x - 7)

= (x  3)(x - 7)

Writing the simplified numerator in the expression ,

we get ,

= (x  3)(x - 7)/4(x - 7)

cancelling out the common term (x-7) , we get

= (x  3)/4

Therefore , the simplified form is (x + 3)/4  . It is important to take into account different classes of rewriting rules. The easiest are formulas like E E 0 or sin(0) 0 that always make the expression smaller.

Complete question

What is the simplified form of the expression  

(x² - 4x - 21)/4(x - 7) ?

(a) (x+3)/4

(b) (x-3)/4

(c) (x+3)/(x-7)

       (d) (x-3)/(x-7)

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The value of the expression (1 - 1/2) × (1 - 1/3) × (1 - 1/4)...(1 - 1/20) will be 1/20.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (1 - 1/2) × (1 - 1/3) × (1 - 1/4)...(1 - 1/20)

Simplify the expression, then we have

⇒ (1 - 1/2) × (1 - 1/3) × (1 - 1/4)...(1 - 1/20)

⇒ (1/2) × (2/3) × (3/4)...(19/20)

⇒ 1 / 20

The value of the expression (1 - 1/2) × (1 - 1/3) × (1 - 1/4)...(1 - 1/20) will be 1/20.

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The slope of the secant line over the interval [3, t] for the curve Q(t) = t² is given by the formula m = (t² - 9) / (t - 3).

The slope of a line is a measure of how steep the line is. It tells us how much the line is rising or falling as we move from left to right.

The secant line is a line that passes through two points on a curve. In this case, the curve is Q(t) = t².

To find the slope of the secant line over the interval [3, t], we need to find the slope of the line that passes through the points (3, 9) and (t, t²).

The slope of the line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

So, using this formula, we can find the slope of the secant line over the interval [3, t]:

m = (t² - 9) / (t - 3)

This formula gives us the exact slope of the secant line over the interval [3, t]. We can simplify it if needed, but the answer will always be in exact form.

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The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.

A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.

Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.

It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.

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Therefore , the solution of the given problem of percentage comes out to be 32 liters after 60% increased.

Any value that may be expressed as a fraction of 100 is referred to as a percentage in mathematics. The acronyms "pct.," "pct," or "pc" are also occasionally used. However, the "%" symbol is typically used to denote it. The proportional amount has no dimensions and is flat. Percentages can be viewed as fractions because their numerator is 100. To indicate that a number is a percent, it needs to be followed by the percent symbol (%).

Here,

Given:

=> 20 liters is the given volume

It is increased by 60% ,

then the final volume is :

=> 20 + 60/100 *20

=> 20 + 0.6*20

=> 20 + 12

=> 32 liters

Therefore , the solution of the given problem of percentage comes out to be 32 liters after 60% increased.

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The sum of interior angle in 12-gon is 1800°, in 102-gon is 18000°, in 90-gon is 15840° and 36-gon is 6120° and measure of interior angle in 12-gon is 150°, in 102-gon is 176.5°, in 90-gon is 176° and 36-gon is 170°

A polygon is a two-dimensional geometric shape consisting of straight lines and having three or more sides. The sides of a polygon are line segments that connect its vertices, or corners, and the vertices are where the sides meet. The most common types of polyggon include triangles, squares, rectangles, and hexagons. There are also many types of irregular polygon, which have sides of different lengths or angles, as well as regular polygon, which have equal sides and equal interior angles.

The sum of the interior angles and the measure of the interior angle of a regular polygon can be found using the formula:

Sum of interior angles = (n-2) * 180°

Measure of interior angle = Sum of interior angles / n

Where n is the number of sides of the polygon.

For a 12-gon:

Sum of interior angles = (12-2) * 180° = 1800°

Measure of interior angle = 1800° / 12 = 150°

For a 102-gon:

Sum of interior angles = (102-2) * 180° = 18000°

Measure of interior angle = 18000° / 102 = 176.5°

For a 90-gon:

Sum of interior angles = (90-2) * 180° = 15840°

Measure of interior angle = 15840° / 90 = 176°

For a 36-gon:

Sum of interior angles = (36-2) * 180° = 6120°

Measure of interior angle = 6120° / 36 = 170°

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The equation x - 3 = 2 when evaluated is x = 5

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

x - 3 equal to 2.

Express the equation properly

So, we have the following representation

x - 3 = 2

Add 3 to both sides of the equation

This gives

x - 3 + 3 = 2 + 3

Evaluate the like terms

x = 5

Hence, the solution is x = 5

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Complete question

What is x - 3 equal to 2.

Evaluate

Rounding to the nearest dollar, Joshua would have $4,129 more in his account than Josiah after 18 years.

To find the amount of money in the account after 18 years,

We can use the formula:

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

where A is the amount of money in the account,

P is the principal amount ($750),

r is the interest rate (3% or 25%),

n is the number of times the interest is compounded per year (4 or 1), and t is the number of years (18).

For Joshua's account:

A = 750 * (1 + 0.03/4)^(4 * 18)

= 750 * (1.0075)^72

= $1417.15

For Josiah's account:

A = 750 * (1 + 0.25)^18 = 750 * (1.25)^18

= $5547.01

The difference in the amount of money in the two accounts will be

=$5547.01 - $1417.15 = $4129.86.

For more questions on Compound Interest

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