Find the slope
y = -5x - 2

Each payment should be $948.86, rounded to two decimal places

A sinking fund is a financial account or a reserve fund created by setting aside money periodically over a certain period of time to accumulate a sum of money needed to replace an asset or to repay a debt.

Compounding refers to the process of earning interest or investment returns on both the principal amount and the accumulated interest or returns from previous periods. In other words, compounding involves reinvesting the interest or returns earned on an investment, rather than withdrawing them, so that the investment grows at an increasing rate over time.

In the given question,

To determine the size of each payment that needs to be made at the end of every 2 months, we can use the formula for the future value of an annuity:

FV = Pmt x [(1 + r)^n - 1] / r

where FV is the future value, Pmt is the payment amount, r is the interest rate per period, and n is the total number of periods.

In this case, we know that the future value of the sinking fund should be $61,000, the interest rate per 2-month period is 5.9%/6 = 0.983%, and the total number of periods is 9 years x 12 months/year / 2 months/period = 54 periods.

Substituting these values into the formula, we get:

$61,000 = Pmt x [(1 + 0.00983)^54 - 1] / 0.00983

Solving for Pmt, we get:

Pmt = $61,000 x 0.00983 / [(1 + 0.00983)^54 - 1]

= $61,000 x 0.00983 / 0.6346

= $948.86

Therefore, each payment should be $948.86, rounded to two decimal places. .

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ST is having a length of 3 units.

A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway.

As per the given data:

R is the midpoint of QS:
QR = RS

RS = 6

QT = 15

S is between Q and T

QT = 15

QS + ST = 15

QR + RS + ST = 15

6 + 6 + ST = 15

ST = 3

The length of ST = 3.

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Answer:

55 cards

Step-by-step explanation:

Based on the proportionate ratios of 1:6, the number of overs bowled if 120 balls are bowled is 20.

Proportion describes two ratios equated to each other.

Proportional values are like fractional values and can be depicted in percentages or fractions.

The ratio of one over and balls bowled = 1:6

This implies that for every 6 balls being bowled, one goes over.

Proportionately, for 120 balls bowled, the number of overs will be = 20 (120/6 x 1)

Thus, if one over consists of 6 balls being bowled, proportionately, the number of overs bowled if 120 balls are bowled is 20.

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Answer:

To calculate the monthly payment for an installment loan, we can use the formula:

M = P * r * (1 + r)^n / [(1 + r)^n - 1]

where:

M = monthly payment

P = principal (amount borrowed)

r = monthly interest rate (annual interest rate divided by 12)

n = total number of payments

In this case, Adolfo borrowed $6,800, and the loan is to be repaid in 24 monthly payments at an 18% APR. First, we need to calculate the monthly interest rate:

r = 18% / 12 = 0.015

Next, we can substitute the given values into the formula:

M = 6,800 * 0.015 * (1 + 0.015)^24 / [(1 + 0.015)^24 - 1]

M ≈ $342.03

Therefore, the monthly payment for Adolfo's installment loan is approximately $342.03.

Step-by-step explanation:

Answer:$342.03.

Step-by-step explanation:

In response to the query, we have that So, depending on the precise equation choice of five positive numbers, the data range might be 5, 6, or 7.

In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific programme typically correspond. An illustration would be 2x - 4 = 2.

The five positive integers will be denoted as a, b, c, d, and e.

We know that c must equal 5, since the median is 5.

The three integers we now have add up to 15 (a + b + c = 15).

We may write the equation as follows since the mean is 5:

(a + b + c + d + e)/5 = 5

a + b + 18 = 25

a + b = 7

a = 1, b = 6, c = 5, d = 8, e = 8

a = 2, b = 5, c = 5, d = 8, e = 8

a = 3, b = 4, c = 5, d = 8, e = 8

Range = 8 - 1 = 7

Range = 8 - 2 = 6

Range = 8 - 3 = 5

So, depending on the precise choice of five positive numbers, the data range might be 5, 6, or 7.

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Answer:

-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,

Answer:

A. the graph of the function does not form a straight line.

Step-by-step explanation:

The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

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1. The decrease in the balance would be $11.25 2. The interest on the average daily balance would be $28.77. 3. The total interest paid would be $214,960. 4. The payment would be $1,978.

Interest refers to the amount of money that is charged or earned for the use of borrowed money. It is a fee paid by a borrower to a lender for the use of funds, or a payment received by a depositor from a bank for the use of their money.

Interest rates are typically expressed as a percentage of the principal amount and can be fixed or variable, depending on the terms of the loan or investment. The interest rate charged on a loan is determined by a number of factors, including the creditworthiness of the borrower, the length of the loan, and prevailing market conditions.

1. The decrease in the balance would be $11.25.

Calculation:

Minimum payment = 2.5% of $450 = $11.25

New balance after paying the minimum = $450 - $11.25 = $438.75

The decrease in the balance would be $450 - $438.75 = $11.25.

2. The interest on the average daily balance would be $28.77.

Calculation:

The balance for the first 14 days of the month = $2000

The balance for the last 16 days of the month = $1400

Average daily balance = (14 * 2000 + 16 * 1400) / 30 = $1666.67

Interest for the month = 0.23 / 12 * $1666.67 = $28.77

3. The total interest paid would be $214,960.

Calculation:

No. of payments = 30 * 12 = 360

Total amount paid = $876 * 360 = $315,360

Total interest paid = $315,360 - $125,000 = $190,360

4. The payment would be $1,978.

Calculation:

Monthly interest rate = 7.3% / 12 = 0.6083%

Number of payments = 30 * 12 = 360

Payment = $275,000 * 0.006083 / (1 - (1 + 0.006083)^-360) = $1,977.54 (rounded to nearest dollar: $1,978)

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The slope-intercept form of the equation of the line through (5, 0) and perpendicular to y = -5/3x is y = 3/5x - 3.

What is the slope-intercept form of a linear equation, and how can we determine the equation of a line perpendicular to another line?

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. This form is useful for graphing lines and solving problems involving linear relationships.

To determine the equation of a line perpendicular to another line, we use the fact that the slopes of perpendicular lines are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

Calculate the slope-intercept form:

We are given that the line we are looking for passes through the point (5, 0) and is perpendicular to the line y = -5/3x. To find the equation of the line, we need to determine its slope and y-intercept.

The slope of the given line is -5/3, so the slope of the line perpendicular to it is:

-1/(-5/3) = 3/5

Therefore, the slope of the line we are looking for is 3/5.

Next, we can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. We can substitute m = 3/5 and (x1, y1) = (5, 0) to get:

y - 0 = 3/5(x - 5)

Simplifying this equation, we get:

y = 3/5x - 3

which is the slope-intercept form of the equation of the line we were looking for.

Therefore, the slope-intercept form of the equation of the line through (5, 0) and perpendicular to y = -5/3x is y = 3/5x - 3.

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Answer:

Step-by-step explanation:

The diameter of the circle is twice the length of the radius, so we can write:

2r = d

where r is the radius and d is the diameter.

Substituting the given diameter of 11 4/5 ft, we get:

2r = 11 4/5 ft

To find the length of the radius, we can divide both sides by 2:

r = (11 4/5) / 2

r = 5 9/10 ft

We also know that the length of the radius is z + 3.6, so we can set up the equation:

z + 3.6 = 5 9/10

Subtracting 3.6 from both sides, we get:

z = 5 9/10 - 3.6

z = 2 3/10

Therefore, the value of z is 2 3/10 or 2.3 as a decimal.

Answer: The correct answer is 2.3

Step-by-step explanation: Answer confirmed correct on test so no worries

Barbara's weekly average for the four-week period is 65 minutes.

What is the average?

The average, also known as the arithmetic mean, is a measure of central tendency that represents the typical value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing the sum by the total number of numbers.

To find Barbara's weekly average for the four-week period, we need to add up her weekly totals and divide the sum by 4 (since there are four weeks in the period):

Average = (48 + 115 + 62 + 35) / 4

= 260 / 4

= 65

Therefore, Barbara's weekly average for the four-week period is 65 minutes.

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The monthly payments on the original loan are $899.33.

percentage, a relative value indicating hundredth parts of any quantity.

To find the monthly payments on the original loan, we can use the formula for the monthly payment of an amortized loan:

M = P (r/12)(1 + r/12)ⁿ/ ((1 + r/12)ⁿ - 1)

where M is monthly payment, P is principal, r is monthly interest rate, n is total number of payments

For the original loan, P = $150,000, r = 0.06/12 = 0.005, and n = 45 years x 12 months/year = 540 months.

Substituting these values into the formula, we get:

M = 150,000(0.005)(1 + 0.005)⁵⁴⁰ / ((1 + 0.005)⁵⁴⁰- 1)

= 899.33

Therefore, the monthly payments on the original loan are $899.33.

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The height at the point A is 10 ft.

In math, subtraction is when you take one number away from another number.

In other words, the subtraction of two from five gives you an answer of three.

Subtraction is typically the second operation in arithmetic, after addition.

Given that, a ferris wheel has a center that is 38 feet above the ground and a radius of 28 feet, there is A point on the wheel, we need to find the distance of this point from the ground,

To find the same, we will simply subtract the radius of the wheel from the distance of the center of the wheel,

Therefore,

The distance of the point A from the ground = 38 - 28 = 10 ft

Hence, the height at the point A is 10 ft.

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The area of the shaded region in factored form is 9x^2(9 - 4π)

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

Square length = 9x

Radius of circle = 6x

The area of the square is given by (side length)^2.

Since the square has 9x as a side length, its area is:

Area 1 = (9x)^2 = 81x^2

For the circle, we have

Area 2 = π(6x)^2

Area 2 = 36πx^2

The area of the shaded region is the area of the original square minus the area of the circle, which is:

Shaded = 81x^2 - 36πx^2

Factorize

Shaded = 9x^2(9 - 4π)

Hence, the area is 9x^2(9 - 4π)

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Answer: less then

Step-by-step explanation: Less than means subtraction, whereas more than means addition. · Saying twice a number means that you are multiplying that number by 2.

The surface area of the cone is 96π square centimeters (or approximately 301.59 square centimeters if we use a decimal approximation for π).

Calculating a cone's surface area is as follows:

SA = πr² + πrℓ

where l is the cone's slant height and r is the base's radius.

The radius and slant height in this instance are 6 cm and 10 cm, respectively. Therefore:

SA = π(6²) + π(6)(10)

= 36π + 60π

= 96π

The cone's surface area is 96 square centimetres, or roughly 301.59 square centimetres if we round to the nearest decimal.

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SA = 2π(1.3)² + 1.3π(3.8) is the equation that calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown.

The correct equation to calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder is:

SA = 2πr(h + r)

where r is the radius of the cylinder (which is half of the diameter), and h is the height of the cylinder.

In this case, the radius is 1.3 centimeters (half of the diameter of 2.6 centimeters), and the height is 3.8 centimeters. Therefore, the correct equation to calculate the surface area (amount of wrapping paper needed) is:

SA = 2π(1.3)(3.8 + 1.3)

SA = 2π(1.3)(5.1)

SA ≈ 41.82 square centimeters

So, the amount of wrapping paper needed to completely cover the cylinder is approximately 41.82 square centimeters.

Identify the relevant measurements of the cylinder: In this case, the problem states that the cylinder has a diameter of 2.6 centimeters and a height of 3.8 centimeters.

Calculate the radius of the cylinder: The radius of the cylinder is half of its diameter. So, divide the diameter by 2: 2.6/2 = 1.3 centimeters. Therefore, the radius of the cylinder is 1.3 centimeters.

Use the formula for the surface area of a cylinder: The formula for the surface area of a cylinder is SA = 2πr(h + r), where r is the radius of the cylinder and h is its height. Plug in the values for r and h: SA = 2π(1.3)² + 1.3π(3.8).

Thus, SA = 2π(1.3)² + 1.3π(3.8) is the equation that alculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown.

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Answer:

19107

Step-by-step explanation:

First, we need to find the common difference (d), which we can find by subtracting two consecutive terms.  Thus, we can do d = 1 - (-3) = 4.

Now, we need to know how many terms are in the arithmetic series.  We can find the number using nth term formula, which is

[tex]a_{n}=a_{1}+(n-1)*d[/tex], where a1 is the first term, n is the term position (e.g., 1st, 2nd).

Although we don't know the term position of 389, we can still plug it into the formula and solving for n will reveal it's term number and the total number of sums in the sequence:

[tex]389=-3+(n-1)*4\\392=(n-1)*4\\392=4n-4\\396=4n\\99=n[/tex]

Now, we can find the sum using the sum formula, which is

[tex]S_{n}=n/2*(a_{1}+a_{n})[/tex]

Sn can become S99 since there are 99 terms and we can let an = a99, which we know is 389.

Now, we must solve for S99:

[tex]S_{99}=\frac{99}{2}*(-3+389)\\ S_{99}=\frac{99}{2}*(386)\\ S_{99}=19107[/tex]

Answer:

-3, 1

Step-by-step explanation:

these are points where the curve cuts the x-axis

at this point the value of y=0

Answer:

1/360

Step-by-step explanation:

A full circle corresponds to a central angle of 360°.

A 1° angle corresponds to 1/360 of a full circle.

Answer:

1/360

Step-by-step explanation:

1° angle corresponds to 1/360 of a whole circle

Answer:

Step-by-step explanation:

Step-by-step explanation:

To graph the relationship between the number of pencils and the number of boxes, we can plot some points that satisfy the equation p = 144b.

We can choose any values of b and calculate the corresponding values of p using the equation. For example:

When b = 0, p = 144(0) = 0. So one point on the graph is (0, 0).

When b = 1, p = 144(1) = 144. So another point on the graph is (1, 144).

When b = 2, p = 144(2) = 288. So another point on the graph is (2, 288).

We can continue this process to find more points, or we can notice that the equation p = 144b represents a linear relationship between p and b with a slope of 144. This means that every time we increase b by 1, we increase p by 144.

We can use this information to graph the equation by starting at the y-intercept (0, 0) and then moving up 144 units for each unit we move to the right. This gives us a straight line with a slope of 144 passing through the origin.

The graph of the equation p = 144b looks like this:

|

| .

| .

| .

| .

| .

| .

| .

----------------------------------

0 1 2 3 4 b

The horizontal axis represents the number of boxes (b), and the vertical axis represents the number of pencils (p). Each dot on the graph represents a point that satisfies the equation p = 144b.

The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

A linear function is a polynomial of degree 1, or a mathematical expression that describes a relation between two variables. It is often written in the form y = mx + b, where m is the slope, x is the independent variable, and b is the y-intercept.

The factored form of a linear equation is the same as the standard form of the equation, with the exception that the coefficients of the variables are each expressed as a product of their prime factors. In the case of y=3x+12, the factored form is (3x+12). The zero of the function (also known as the root of the equation) is the value of the variable that will result in a value of 0 for the equation. To find the zero of the function, we need to set the equation equal to 0 and solve for the value of x. When we set y=0, we get 3x+12=0, which can be solved to get x=-4. Therefore, the zero of the function is -4.

The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

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To find out how many 18-24 year olds only hung out with friends last Friday night, we need to subtract the number of people who engaged in other combinations of activities from the total number of people surveyed:

Total surveyed = 520

Watched TV only = 172 - 38 - 36 - 38 = 60

Ate pizza only = 156 - 38 - 36 - 40 = 42

Watched TV and ate pizza = 38

Did not do any of these three activities = 63

Therefore, the number of 18-24 year olds who only hung out with friends last Friday night can be calculated as follows:

Only hung out with friends = Total surveyed - (Watched TV only + Ate pizza only + Watched TV and ate pizza + Did not do any of these three activities)

Only hung out with friends = 520 - (60 + 42 + 38 + 63)

Only hung out with friends = 217

The coordinate notation for a clockwise rotation of 180° about the origin include the following: (x, y) → (-x, -y).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Generally speaking, the mapping rule for the rotation of a geometric figure about the origin by 180° is given by this mathematical expression:

(x, y) → (-x, -y)

Where:

In conclusion, the transformation rule (x, y) → (-x, -y) is used for the rotation of a geometric figure about the origin in a clockwise direction.

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The explicit formula of the function s(n) is s(n) = 2n

The domain and the range of h(n)

Given that

h(n) is the number of houses

The possible values of n and h(n) are whole numbers

So, we have

The values of h(5) and h(11)

Based on the patterns in the sequence, we have

h(n) = n

So, we have

h(5) = 5

h(11) = 11

The explicit function of h(n)

In (b), we have

h(n) = n

The values of s(4) and s(7)

Given that

s(n) is the number of segments

Based on the patterns in the sequence, we have

s(n) = 2n

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

Above, we have

s(n) = 2n

The above equation is a proportional equation

This means that

The growth pattern of s(n) is linear, with a constant rate of change

The explicit function of s(n)

Above, we have

s(n) = 2n

Hence, the explicit of s(n) is s(n) = 2n

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