The table shows the balance of a money market account over time. Write a function that represents the balance y
(in dollars) after t years.

Year, t Balance
0 $200
1 $230
2 $264.50
3 $304.18
4 $349.80
5 $402.27





































The value of a boat is $23,400. It loses 8% of its value every year. Write a function that represents the value y
(in dollars) of the boat after t years.

Answer:

x = 15.

Therefore, the width of the walkway is 15m.

Step-by-step explanation:

Let's represent the width of the walkway by "x".

We know that the total width/base of the area (including the walkway) is 300m, so we can set up the equation:

length of field + 2(width of field) + 2(width of walkway) = 300

Substituting the given values, we get:

200 + 2w + 2x = 300

Simplifying the equation, we get:

2w + 2x = 100

We also know that the area of the field is 30,000m, so we can set up the equation:

length of field x width of field = 30,000

Substituting the given values, we get:

200w = 30,000

Simplifying the equation, we get:

w = 150

Finally, we know that the total area (including the walkway) is 60,000m, so we can set up the equation:

(length of field + 2x) x (width of field + 2x) = 60,000

Substituting the values we've found so far, we get:

(200 + 2x) x (150 + 2x) = 60,000

Expanding the equation, we get:

300x^2 + 1000x - 45,000 = 0

Solving for x using the quadratic formula, we get:

x = 15 or x = -30/100

Since x can't be negative, we can discard the negative solution and conclude that x = 15.

Therefore, the width of the walkway is 15m.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x = \frac{68}{13}[/tex]

[tex]y = \frac{1}{13}[/tex]

To solve the system of equations by substitution method, we can use one equation to solve for x or y, and then substitute that expression into the other equation to solve for the other variable.

From the second equation, we have:

x - 3y = 5

Solving for x, we get:

x = 3y + 5

Now we can substitute this expression for x into the first equation and solve for y:

2x + 7y = 11

2(3y + 5) + 7y = 11

6y + 10 + 7y = 11

13y = 1

y = 1/13

Now that we have solved for y, we can substitute this value back into one of the original equations to solve for x:

x - 3y = 5

x = 3y + 5

x = 3(1/13) + 5

x = 5 6/13

Therefore, the solution to the system of equations is:

x = 5 6/13 and y = 1/13.

The amount that Nancy can save each month and put in the savings account is $10.

Savings are funds that are not used right away but are instead set aside for unforeseen expenses or future needs. It is the gap between one's earnings (income) and their outlays (expenditures) (the amount of money spent). Regular income, investment profits, tax refunds, and gifts are just a few of the several ways that people might support their savings. You may save money in a variety of ways, such as by creating a budget and eliminating wasteful spending, opening a savings account, buying stocks or bonds, and making contributions to retirement plans like 401(k)s or IRAs.

The total income earned by Nancy is:

30 + 50 + 25 + 35 = $140

The total expenses are:

40 + 60 + 30 = $130

The amount remaining after expenses is:

Savings = 140 - 130 = $10

Hence, the amount that Nancy can save each month and put in the savings account is $10.

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Step-by-step explanation:

When x -5 is a positive

   x -5  = 2

    x = 7

when x -5 is a negative

    x-5 = -2

       x = 3

The key features of the graph are (a) x-int = 5 and y-int= 5, HA; y = 0.5 and VA: x = 0.5 and hole = (-2, 7/5)

The x-intercept of a graph is the point at which the graph intersects the x-axis while the y-intercept of a graph is the point at which the graph intersects the y-axis.

From the given graph, we have the intercepts to be

x-intercept = 5 and y-intercept = 5

The horizontal asymptote of a graph is a horizontal line that the graph approaches as x approaches positive or negative infinity

While the vertical asymptote is a vertical line that the graph approaches as x approaches a certain value.

From the given graph, we have the asymptote to be

Horizontal; y = 0.5 and Vertical: x = 0.5

A hole in a graph refers to a point on the graph where the function is undefined but can be made continuous by removing the point and filling the gap with a single point.

From the given graph, we have the hole to be

Hole = (-2, 7/5)

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The slope of the line passing through (0,3) and (1,-1) is -4.

What is slope of the line?

The slope of a line is a measure of its steepness or incline. It describes how much the line rises or falls as it moves horizontally.

To find the slope of the line passing through (0,3) and (1,-1), we can use the slope formula:

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

where (x1,y1) and (x2,y2) are the coordinates of the two points.

Plugging in the given coordinates, we get:

m = (-1 - 3)/(1 - 0)

m = -4/1

m = -4

Therefore, the slope of the line passing through (0,3) and (1,-1) is -4.

The slope of a line can be positive, negative, zero, or undefined (when the line is vertical). A positive slope means that the line is increasing as it moves to the right, while a negative slope means that the line is decreasing as it moves to the right. A slope of zero means that the line is horizontal, and an undefined slope means that the line is vertical.

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Complete question is: Slope of the given line passing through (0,3) and (1,-1) is -4.

Answer: The statement that is not true is D.

Explanation:

We know that the area of the rectangle is 160 square inches. Let's assume that the length of the base is b inches. Then, the height of the rectangle would be 160/b inches (since area = base x height).

Now, we can check the given statements:

A. The base of the figure is 20 inches in length.

We do not know the length of the base, so we cannot say for sure whether this statement is true or false.

B. The formula A=b/8 could be used to determine the area.

This statement is false. The correct formula for the area of a rectangle is A = b x h.

C. The formula b=160/8 could be used to determine the length of the base.

This statement is true. We can solve for b as:

b = A/h = 160/(160/b) = 8

So, the length of the base is 8 inches.

D. The formula 160(b)(8) could be used to determine the length of the base.

This statement is false. The given formula does not make sense in the context of the problem, and it does not allow us to determine the length of the base.

Step-by-step explanation:

Step-by-step explanation:

To find the probability of Mario randomly selecting a red chip or a white chip, we need to first determine the total number of red and white chips he has.

Total number of red and white chips = 45 + 24 = 69

Therefore, the probability of Mario randomly selecting a red chip or a white chip is:

P(red or white) = (number of red chips + number of white chips) / total number of chips

P(red or white) = (45 + 24) / (45 + 12 + 24)

P(red or white) = 69 / 81

P(red or white) = 0.85

So the probability of Mario randomly selecting a red chip or a white chip is 0.85 or 85%.

Answer: 0.8519 ≈ 85%

Step-by-step explanation:

        To find the probability, we will divide wanted outcomes by total possible outcomes. See below.

[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{number of red or white chip}}{\text{total number of chips}} =\frac{45+24}{45+12+24}= \frac{69}{81}[/tex]

       = 0.8519 ≈ 85%

        The probability that Mario will randomly select a red or white chip is 0.8519 or about 85%.

Answer:

Step-by-step explanation:

The ratio for Purple People Eater can be expressed in fraction form as

✔ 3/5

.

The ratio for Purple Majesty can be expressed in fraction form as

✔ 4/7

.

To compare these fractions, rewrite them with a common denominator of

✔ 35

.

The ratio of red paint to blue paint in Purple People Eater is

✔ greater than

the ratio in Purple Majesty.

The sequence of transformation that makes the shapes congruent is rotation then transformation

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

The figures

From the figure, we have the shapes to have different orientation but same size

This means that one of the shapes is rotated to form the other

In this case, the rotation is a 90° clockwise

Followed by the rotation is a translation transformation

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(a) The total amount of the nurse's annual salary that is not taxed is $6644. (b) His annual taxable salary is $22,226.8. (c) The tax he pays annually is $5856.7.

(a) To find the total amount of the nurse's annual salary that is not taxed, we need to add up all of the non-taxable allowances:

$37 x 12 (months) = $444 for national insurance

$3000 for personal allowance

$1800 for his wife

$1400 for his children

Total non-taxable allowances = $444 + $3000 + $1800 + $1400 = $6644

Therefore, the nurse's total non-taxable salary is $6644.

(b) To find the nurse's annual taxable salary, we need to subtract his non-taxable allowances from his gross salary:

Annual taxable salary = $29,460 - 2% x $29,460 - $6644

Annual taxable salary = $29,460 - $589.2 - $6644

Annual taxable salary = $22,226.8

Therefore, the nurse's annual taxable salary is $22,226.8.

(c) To calculate the nurse's annual tax, we need to apply the income tax rates:

Tax on first $4000 at 20% = $800

Tax on remainder at 25% = 0.25 x ($22,226.8 - $4000) = $5056.7

Total annual tax = $800 + $5056.7 = $5856.7

Therefore, the nurse pays an annual tax of $5856.7.

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Complete question is attached below

The probability of choosing a password with no Y's and O's is 20/30 = 2/3, or approximately 0.667. The two probabilities are the same, so neither is greater than the other.

Probability is a measure of the likelihood or chance that an event will occur. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In mathematical terms, probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 0.5, because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

To calculate the probability of choosing a password with no Y's or no O's, we need to first count the number of valid passwords without Y's or O's and then divide it by the total number of possible passwords.

Number of valid passwords without Y's:

There are 5 choices for the first character (B, R, O, G, P), since Y is not allowed.

There are 4 choices for the second character (any of the remaining 5 letters except Y), since we cannot repeat the first letter.

So the total number of valid passwords without Y's is 5 x 4 = 20.

Number of valid passwords without O's:

There are 5 choices for the first character (Y, B, R, G, P), since O is not allowed.

There are 4 choices for the second character (any of the remaining 5 letters except O), since we cannot repeat the first letter.

So the total number of valid passwords without O's is 5 x 4 = 20.

The total number of possible passwords is the number of ways to choose 2 characters out of 6, without repetition. This is given by the formula:

6P2 = 6! / (6 - 2)! = 6 x 5 = 30

Therefore, the probability of choosing a password with no Y's is 20/30 = 2/3, or approximately 0.667.

Similarly, the probability of choosing a password with no O's is also 20/30 = 2/3, or approximately 0.667.

The two probabilities are the same, so neither is greater than the other.

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The area of the polygon is  6. 9m²

From the information given, we have that the regular polygon takes the shape of a triangle.

The formula for calculating the area of a triangle is expressed with the equation;

A = 1/2bh

Such that the parameters in the formula are;

Area of a equilateral triangle is;

= √3/4a²

Then,

= √3/4 (4)²

= √3 × 4

= 6. 9m²

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Answer: approximately 7.3 kilometers.

Step-by-step explanation:

Using the Pythagorean theorem, we can write:

x^2 = 7^2 + 2^2

x^2 = 49 + 4

x^2 = 53

Taking the square root of both sides, we get:

x = sqrt(53)

Using a calculator or estimating, we find:

x ≈ 7.3 km

So the straight-line distance between Ryan's house and Emmy's house is approximately 7.3 kilometers.

1)
a) the mean is µ = 2.5.

b)  the variance is σ² = 1.25.

c) Standard Deviation σ =  1.12

2)

a) the mean is µ = 6.40.

b)  the variance is σ² = 2.12

c) Standard Deviation σ =  1.46.

1) To find the mean (µ), we can multiply each value of x by its corresponding probability (P(x)), and then add up the products: (See attached table I)

Sum | 1 | 2.5


Therefore, the mean is µ = 2.5.

To find the variance (σ²), we need to find the squared differences between each value of x and the mean, multiply each squared difference by its corresponding probability, and then add up the products:

See table II
Sum | 1 | | 5 | 1.25

Therefore, the variance is σ² = 1.25.

Finally, to find the standard deviation (σ), we can take the square root of the variance:

σ = √(σ²) = √(1.25) ≈ 1.12.


2)
To find the mean (µ), we can multiply each value of x by its corresponding probability (P(x)), and then add up the products: See table III...


Sum | 1.00 | 6.40

Therefore, the mean is µ = 6.40/1.00 = 6.40.

To find the variance (σ^2), we need to find the squared differences between each value of x and the mean, multiply each squared difference by its corresponding probability, and then add up the products: See table IV

Sum | 1.00 | | 40.80 | 2.1200

Therefore, the variance is σ² = 2.1200.

Finally, to find the standard deviation (σ), we can take the square root of the variance:

σ = √(σ²) = √(2.1200) ≈ 1.46.

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The width of the cooling tower at the base of the structure is 100 meters, rounded to the nearest whole number.

Given that the cooling tower's walls are modeled by where the measurements are in meters and the width of the

cooling tower at the base of the structure is required, we can find the width by using the formula for the area of a

trapezoid. The area of the trapezoid represents the area of the base of the cooling tower.

Area of a trapezoid = 1/2 × (a + b) × h

where a and b are the lengths of the parallel sides of the trapezoid and h is the height or perpendicular distance

between the parallel sides.

In this case, the parallel sides of the trapezoid are not given, but we are given the height of the cooling tower, which is

100 meters. We also know that the area of the base of the cooling tower is 10,000 square meters.

Therefore, we can use the formula for the area of a trapezoid to find the sum of the lengths of the parallel sides of the

trapezoid, which will give us the width of the cooling tower at the base.

Area of a trapezoid = 1/2 × (a + b) × h

10,000 = 1/2 × (a + b) × 100

100 = (a + b)/2

200 = a + b

Width of cooling tower at the base = (a + b)/2

Width of cooling tower at the base = 200/2

Width of cooling tower at the base = 100 meters

Therefore, the width of the cooling tower at the base of the structure is 100 meters, rounded to the nearest whole number.

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The answer is A. f(x) and g(x) are closed under addition because when added, the result will be a polynomial.

Addition is denoted using the plus sign (+) or a plus symbol. Addition can be used to find the total in a group of numbers, to combine two or more numbers, or to compare two numbers.

When two polynomials f(x) and g(x) are added, the result is also a polynomial. The degree of the resultant polynomial is equal to the highest degree of the two added polynomials.

Thus, when a polynomial is added to another polynomial, the result will always be a polynomial.

This is true because when two polynomials are added, the resulting polynomial will have the same form as the two polynomials that were added.

In other words, the sum of two polynomials will have the same coefficients and powers of x as the two polynomials that were added.

Therefore, f(x) and g(x) are closed under addition because when added, the result will always be a polynomial.

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There are 75 percent of Americans consume alcoholic beverages regularly. so, the correct answer is D).

According to a 2021 survey conducted by the National Institute on Alcohol Abuse and Alcoholism, approximately 75% of adults in the United States reported that they had consumed alcohol in the past year.

However, it's important to note that this does not necessarily mean that they consume alcohol regularly. The percentage of Americans who consume alcoholic beverages regularly may vary depending on how "regularly" is defined and the specific population being studied.

So, the correct option is D).

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Answer:

  about -0.79 mg/hour

Step-by-step explanation:

You want the rate of change of the amount of medication in a patient after 4 hours if the amount after t hours is modeled by y=88/(1+e^(t+0.7)).

The rate of change is found by taking the derivative of the function with respect to time. Let u = 1+e^(t+0.7). Then du/dt = e^(t +0.7).

The function can be written ...

  y = 88/u = 88·u^-1

so its derivative is ...

  dy/dt = (-88·u^-2)·du/dt

  dy/dt = -88(e^(t +0.7))/(1 +e^(t +0.7))^2

The value of the rate of change at t=4 is ...

  dy/dt = -88(e^(4 +0.7))/(1 +e^(4 +0.7))^2 ≈ -88(109.95)/(1 +109.95)^2

  dy/dt ≈ -0.78602 ≈ -0.79 . . . . . . mg/h

The rate of change in the amount of medication is about -0.79 mg/h.

No, the triangles are not identical

Identical triangles are two triangles that have the exact same

In other words, all corresponding sides and angles are congruent (equal).

Identical triangles can be thought of as the same triangle, just in different positions or orientations in space.

The triangles are similar triangles but not identical triangles as the sides are not equal

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This method ensures that the side dish selection reflects customer preferences while incorporating an element of randomness.

Hi! To simulate choosing a side dish using 10 index cards, the manager can follow these steps:

1. Assign a number to each side dish based on the survey results.
2. Determine the probability of each side dish being chosen according to customer preferences.
3. Based on the probabilities, allocate the appropriate number of index cards to each side dish (e.g., if a dish has a 30% chance of being chosen, it would be assigned 3 out of the 10 index cards).
4. Write the side dish name or its assigned number on the allocated index cards.
5. Shuffle the index cards and randomly draw one card each week to determine the special's side dish.
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Answer:

m = 2/3

Step-by-step explanation:

Given two points on a line, we can find the slope, m, of a linear equation using the slope formula:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point and x2 and y2 are the other point.

The order of the points don't matter as long you pair the points already together (e.g., if you choose 7 as x1, you have to choose -2 as y2, and if you choose 1 as x1, you have to choose -6 as y2).

Thus, if we allow the first point to be x1 and y2 and the second point to be x2 and y2, our slope is:

[tex]m=\frac{-6-(=2)}{1-7}\\ \\m=\frac{-6+2}{-6}\\ \\m=\frac{-4}{-6}\\ \\m=\frac{2}{3}[/tex]

A rectangular pyramid is a pyramid with a rectangular base and four triangular faces that meet at a single point at the top, called the apex. It is a three-dimensional solid with five faces, including the base, and is a type of pyramid with a rectangular base.

No, we do not have enough information to find the surface area of the rectangular pyramid.

To find the surface area of a rectangular pyramid, we need to know the lengths of all four sides of the base, as well as the slant height and height of each triangular face.

In this case, we only have two sides of the rectangular base (5 ft and 7 ft) and the height of one of the triangular faces (4 ft). We do not have enough information to find the length of the other two sides of the base or the slant height and height of each triangular face.

Therefore, we cannot find the surface area of the rectangular pyramid with the given information.

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Answer:

[tex]f(t) = 4100( {2}^{ \frac{t}{2} }) [/tex]

For given triangles, Condition 3 and 6 are true.

What is a triangle's definition?

A triangle is a closed two-dimensional shape with three straight sides, three angles, and three vertices (or corners). It is formed by connecting three non-collinear points in a plane with straight lines. The sum of the interior angles of a triangle is always 180 degrees, and each exterior angle is equal to the sum of its two adjacent interior angles. Triangles can be classified based on the length of their sides and the size of their angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.

Now,

As we can see that ΔABC is rotated 90° clockwise to make

ΔDEF.

So, the angles follows these conditions

∠F=∠A

∠E=∠C

∠D=∠B

hence,

             Condition 3 and 6 are true.

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Answer:

20(x + 2) = 20x + 40 = 4(5x + 10)

The measure of DE is 8x. This was found by using the distance formula to calculate the length of the side.

Measurements are the process of comparing an unknown quantity to a known reference value in order to estimate the size, quantity, distance, weight, or other characteristics of that unknown quantity. Measurements are used in science and engineering to quantify the properties of objects, or to compare objects to each other. Measurements are also used in everyday life to help make decisions and assess the impact of changes.

To find the measure of DE, we must first calculate the length of the side. We can do this by using the distance formula. The distance formula is used to calculate the length of a line between two points in a plane. The formula is given as d = √(x2 - x1)2 + (y2 - y1)2.

For the side DE, we can use the coordinates (2x+7, 4(x-3)). The first point is (2x+7, 4(x-3)) and the second point is (2x+7, 4(x+3)). We can substitute these points into the distance formula to calculate the length of DE.

The formula becomes d = √[(2x+7 - 2x+7)2 + (4(x+3) - 4(x-3))2]

Simplifying, we get d = √[(0)2 + (8x)2]

d = √[64x2]
d = 8x

Therefore, the measure of DE is 8x.

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The expressions when factorized are x(1 + 2yz), 9x^3y^2 and 6(3x^2 − 2y) + (5ab + 6y)

Factorization of X + 2xyz:

We can factor out x from the given expression to get:

x(1 + 2yz)

Therefore, the factorization of X + 2xyz is x(1 + 2yz).

Factorization of 9x3y2:

The given expression, 9x3y2, is already in its simplest form and cannot be factorized further.

Factorization of 18x2 + 5ab − 6y:

We can use the grouping method to factorize the given expression:

(18x2 − 12y) + (5ab + 6y)

6(3x2 − 2y) + (5ab + 6y)

Therefore, the factorization of 18x2 + 5ab − 6y is 6(3x2 − 2y) + (5ab + 6y).

Factorization of 4x4 + 3x2 − x − 4:

Cannot be factorized

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