State If The Three Side Lengths Form An Acute, Obtuse, Or Right Triangle. (2024)

Mathematics High School

Answers

Answer 1

The three side lengths form an acute, obtuse, or right triangle depending on the relationship between their squares.

To determine the type of triangle based on the side lengths, you can use the Pythagorean theorem (a² + b² = c²). If the sum of the squares of the two shorter sides is equal to the square of the longest side (a² + b² = c²), then the triangle is a right triangle. If the sum of the squares of the two shorter sides is greater than the square of the longest side (a² + b² > c²), then the triangle is an acute triangle. If the sum of the squares of the two shorter sides is less than the square of the longest side (a² + b² < c²), then the triangle is an obtuse triangle.

Make sure to first identify the longest side (c) and the two shorter sides (a and b) among the given side lengths. Then, calculate the squares of each side and compare their sums as mentioned above. This method will allow you to classify the triangle as acute, obtuse, or right.

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Related Questions

find the length of the arc.

Answers

The length of the arc is approximately 10.47 cm.

What is the length of an arc is the distance along the circumference of a circle between two points on the circle that define the arc?

The length of an arc is the distance along the circumference of a circle between two points on the circle that define the arc. To find the length of an arc, you need to know the measure of the central angle that subtends the arc and the radius of the circle.

The formula for the length of an arc is:

length of arc = (angle measure / 360) x (2πr)

where angle measure is the measure of the central angle in degrees, r is the radius of the circle, and π is the mathematical constant pi (approximately equal to 3.14).

Here's an example of how to use this formula:

Suppose you have a circle with radius 10 cm, and you want to find the length of an arc that subtends a central angle of 60 degrees. To use the formula, you would plug in the values:

angle measure = 60 degrees

r = 10 cm

length of arc = (angle measure / 360) x (2πr)

length of arc = (60 / 360) x (2π x 10)

length of arc = (1/6) x (20π)

length of arc = (10/3)π

length of arc ≈ 10.47 cm

Therefore, the length of the arc is approximately 10.47 cm.

Note that if the angle measure is given in radians instead of degrees, you would need to convert it to degrees by multiplying it by 180/π before plugging it into the formula.

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w varies directly as the square of x and inversely as p and q.

If w = 12 when x = 4, p = 2 and q = 20,

find w when x = 3, p= 8 and q = 5. b. 9 d. 5 21.

Answers

The formula for this problem is: w = kx^2/(pq), where k is the constant of proportionality. To solve for k, we can substitute the given values of w, x, p, and q into the formula and solve for k. The value of w when x = 3, p = 8, and q = 5 is approximately 3.375.

12 = k(4^2)/(2*20)
12 = k(16/40)
12 = k(2/5)
k = (12*5)/2 = 30

Now that we know k, we can use the same formula to find w when x = 3, p = 8, and q = 5:

w = 30(3^2)/(8*5) = 27/4

To simplify this fraction, we can divide both the numerator and denominator by 1/4:

w = (27/4)/(1/4) = 27

Therefore, the answer is 27.

Given that w varies directly as the square of x and inversely as p and q, we can express this relationship using the equation:

w = k * (x^2) / (p * q)

where k is the constant of variation.

First, let's find the value of k using the given values w = 12, x = 4, p = 2, and q = 20:

12 = k * (4^2) / (2 * 20)

Now, solve for k:

k = 12 * (2 * 20) / (4^2)
k = 240 / 16
k = 15

Now that we have the value of k, we can find w when x = 3, p = 8, and q = 5:

w = 15 * (3^2) / (8 * 5)

w = 15 * 9 / 40
w = 135 / 40
w = 3.375

So, the value of w when x = 3, p = 8, and q = 5 is approximately 3.375.

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-4(-7m-10m-4)-2m−4(−7m−10m−4)−2m simplest term

Answers

Simplifying the given expression, we get -4(-7m-10m-4)-2m−4(−7m−10m−4)−2m = 120m - 16.

To simplify the given expression, we need to apply the order of operations or BEDMAS rule, which stands for Brackets, Exponents, Division and Multiplication, Addition and Subtraction. We start by simplifying the expressions inside the brackets first.

-4(-7m-10m-4) can be simplified as follows:

= -4(-17m - 4) (combining like terms)

= 68m + 16 (distributing the negative sign)

Similarly, -4(−7m−10m−4) can be simplified as:

= -4(-17m - 4) (combining like terms)

= 68m + 16 (distributing the negative sign)

Substituting these values in the original expression, we get:

-4(-7m-10m-4)-2m−4(−7m−10m−4)−2m

= (68m + 16) - 2m - (68m + 16) - 2m

= 120m - 16

Therefore, the simplest form of the given expression is 120m - 16.

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I need to pass this before summer help!!!

Answers

Where is the question I don’t see one

In order for me to help you pass this before summer I would need a question/problem to solve

In the problem below -- do you use the leg rule or the altitude rule to solve?

EF = 10

HF = X

GF = 5

Find x

Answers

We used the leg rule to find the value of x and the value of x is 2.5

The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.

hypotenuse/leg1 = leg1/part1

Here, hypotenuse = EF = 10

leg1 = GF = 5

part1 = HF = x

putting values in formula

10 / 5 = 5 / x

10x = 5*5

10x = 25

x = 25 / 10

x = 2.5

Therefore, We used the leg rule to find the value of x and the value of x is 2.5

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Given question is incomplete, the complete question is below

In the problem below -- do you use the leg rule or the altitude rule to solve?

EF = 10

HF = x

GF = 5

Find x

La toya thinks of a number that is greater than 100and less than 110 she can make her number with the same number of hundreds and ones whatsblatoya number

Answers

La Toya's number is 105. It falls within the range of being greater than 100 and less than 110. The number is composed of the same number of hundreds and ones, which is one hundred and five.

1. To find La Toya's number, we need to consider the given conditions. The number should be greater than 100 and less than 110, narrowing down the possibilities to a range of nine numbers. Since the number must have the same number of hundreds and ones, we know that the hundreds digit must be equal to the ones digit.

2. Looking at the numbers within the specified range, we can determine that only one number satisfies these conditions: 105. It has a hundreds digit of 1 and an ones digit of 5, fulfilling the requirement of having the same number of hundreds and ones. Therefore, La Toya's number is 105.

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Q has coordinates (0,0). R has coordinates (3,0). Find the midpoint of QR.

Answers

To find the midpoint of the line segment QR, which has coordinates (0,0) and (3,0), we can use the midpoint formula. The midpoint of QR is (1.5,0).

Explanation:

The midpoint formula gives us a way to find the coordinates of the midpoint of a line segment when we know the coordinates of its endpoints. The formula is:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Answers

The table below is best modeled by an exponential function. The exponential function that models the table is y = (1)(2)^x or y = 2^x.

This means that the y-values increase by a constant factor as the x-values increase by a constant amount.

To see why this is the case, we can look at the ratio of consecutive y-values in the table. For example, when x increases from -1 to 0, y increases from 0.5 to 1. The ratio of these y-values is 1/0.5 = 2. Similarly, when x increases from 0 to 1, y increases from 1 to 2. The ratio of these y-values is also 2. In fact, for any pair of consecutive y-values in the table, the ratio is always 2. This shows that the y-values increase by a factor of 2 every time the x-values increase by 1.

An exponential function has the form y = ab^x, where a and b are constants. In this case, we can see that b = 2, since that is the factor by which the y-values increase. To find a, we can use any point in the table. For example, when x = 0, y = 1. Substituting these values into the equation, we get:

1 = a(2)^0

1 = a(1)

a = 1

Therefore, the exponential function that models the table is y = (1)(2)^x or y = 2^x.

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Im not sure about the answer tried it many times

Answers

The function is not decreasing on intervals 1 and 4.

Interval 1 is increasing and interval 4 is neither increasing nor decreasing.

Hope this helps!

Which set of ordered pairs does not represent a function?

10 Points

{(0,8), (5,4), 10,0), (15,4), (20,8)}

{(1,10), (3,18), (5,26), (7,34), (9,42)}

{(2,10), (3,20), (4,15), (5,5), (6,25)}

{(9,1), (6,2), (3,3), (6,4),

Answers

The set of ordered pairs that does not represent a function is set {(9,1), (6,2), (3,3), (6,4)}. Therefore, the correct option is option 4.

A function is defined as a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. For a set of ordered pairs to represent a function, no two ordered pairs can have the same x-value with different y-values. In other words, in order for a set of ordered pairs to represent a function, each input (the first number in each pair) can only correspond to one output (the second number in each pair).

In option 4, we have two ordered pairs with the same x-value, (6,2) and (6,4), but with different y-values. This violates the definition of a function, so option 4 does not represent a function.

Hence, the set of ordered pairs which is not a function is option 4: {(9,1), (6,2), (3,3), (6,4)}.

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what is closet to the lateral surface area of a cylinder with a height of 12 inches and a radius of 3 inches

Answers

The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height. Plugging in the given values, we get:

Lateral surface area = 2π(3)(12) = 72π
Rounded to the nearest whole number, the lateral surface area of the cylinder is 226.

To find the lateral surface area of a cylinder, you can use the formula:

Lateral Surface Area (LSA) = 2 × π × radius × height

Given that the height of the cylinder is 12 inches and the radius is 3 inches, you can plug these values into the formula:

LSA = 2 × π × 3 × 12

LSA = 6 × π × 12

LSA ≈ 6 × 3.14 × 12

LSA ≈ 226.08 square inches

So, the lateral surface area of the cylinder is closest to 226.08 square inches.

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lve the system of equations by finding the reduced row-echelon form of the augmented matrix

for the system of

uations.

(1, - 1, -4)

(1, - 4, - 10)

(11, - 10, -41)

d. (11, - 1, - 10)

Answers

The question asks to solve a system of equations by finding the reduced row-echelon form of the augmented matrix.

The solution is provided as the row-reduced form of the augmented matrix, which can be used to determine the values of the variables in the original system of equations.

To solve the system of equations by finding the reduced row-echelon form of the augmented matrix, we first construct the augmented matrix by combining the coefficients of the variables with the constants on the right-hand side of each equation.

Then, we apply a sequence of elementary row operations to the matrix to reduce it to row-echelon form, and then to reduced row-echelon form. The result is the row-reduced form of the augmented matrix, which provides the solution to the system of equations.

Using this method to solve the given system of equations with augmented matrix (1, -1, -4 | 0), (1, -4, -10 | 0), (11, -10, -41 | 0), we can perform row operations to reduce the matrix to the row-reduced form (1, 0, -1 | 0), (0, 1, -3 | 0), (0, 0, 0 | 0). This row-reduced form corresponds to the system of equations x - z = 0, y - 3z = 0, 0 = 0. Therefore, we have x = z, y = 3z, and z can be any real number. The solution to the system of equations is given as (x, y, z) = (z, 3z, z), or equivalently, as (11t, -t, 10t), where t is any real number.

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(b) Express (1/root3) to the power of 7

in the form where b and c are integers.

Answers

(1/root3) to the power of 7 can be expressed as 3^(-4) * root3^7 where b = -4 and c = 7. To express (1/root3) to the power of 7 in the form where b and c are integers, we need to rationalize the denominator first.

(1/root3) = (1/root3) * (root3/root3) = root3/3
So, (1/root3) to the power of 7 = (root3/3)^7
Using the exponent rule, we can rewrite this as:
(root3)^7 / (3)^7
Simplifying, we get:
(3^3 * root3^7) / 3^7
= 3^(-4) * root3^7
Therefore, b = -4 and c = 7.
So, (1/root3) to the power of 7 can be expressed as 3^(-4) * root3^7 where b = -4 and c = 7.
To express (1/√3) to the power of 7 in the form b√c, where b and c are integers, you can follow these steps:
1. Raise (1/√3) to the power of 7: (1/√3)^7
2. Rewrite the expression as (√3)^(-7) since 1 to any power remains 1.
3. Apply the power to the square root: (√3)^(-7) = 1/((√3)^7)
4. Recognize that (√3)^7 = (√3)^6 × √3 = (3^3) × √3 = 27√3
5. Replace the expression in the denominator: 1/(27√3)
Now we have the expression in the form 1/(27√3), which is equivalent to b√c with b = 1 and c = 27.
Your answer: 1/√27

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John is developing a scale model of the solar system for science class where the 1,392,000 km diameter sun is scaled to 1.0 m and given that 1 astronomical unit,

AU, equals 1.5 x 10% km. Determine the scaled distance of Mercury from the sun.

A:28 m

B: 39 m

C: 42 m

D:51 m

Answers

To determine the scaled distance of Mercury from the sun, we first need to find the actual distance of Mercury from the sun in astronomical units.

According to the question, 1 AU is equal to 1.5 x 10^8 km.

The actual distance of Mercury from the sun is 0.39 AU (this information is typically given in textbooks or online resources).

To scale this distance to the model, we can use the ratio of the diameter of the sun to its scaled size:

1,392,000 km / 1.0 m = x km / scaled distance of Mercury

Solving for x:

x = (scaled distance of Mercury) x 1.392 x 10^6

Now we can set up a proportion:

0.39 AU / 1.5 x 10^8 km = x km / scaled distance of Mercury

Solving for x:

x = (0.39 AU / 1.5 x 10^8 km) x (scaled distance of Mercury)

Setting the two expressions for x equal to each other:

(scaled distance of Mercury) x 1.392 x 10^6 = (0.39 AU / 1.5 x 10^8 km) x (scaled distance of Mercury)

Simplifying:

(scaled distance of Mercury) = (0.39 AU / 1.5 x 10^8 km) x (1.0 m / 1.392 x 10^6 km)

Plugging in the values and simplifying:

(scaled distance of Mercury) = 0.0026 m

Therefore, the scaled distance of Mercury from the sun is 2.6 mm.

None of the answer choices match this result, so the question may have been written incorrectly or there may be a mistake in the calculations.

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A consignment shop is a store that sells used items that people bring in a consignment shop owner bought a used dress from a woman for $30 he put a dress on sale for $50 by what percent did he mark up the price of the dress?

Answers

The consignment shop owner marked up the price of the dress by 66.67%.

The markup percentage can be calculated by dividing the difference between the selling price and the cost price by the cost price and then multiplying the result by 100 to get a percentage. In this case, the difference between the selling price ($50) and the cost price ($30) is $20. Dividing $20 by $30 gives us 0.6667, which when multiplied by 100 gives us 66.67%. Therefore, the consignment shop owner marked up the price of the dress by 66.67%.

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The bag contains 14 plastic marbles, 9 wooden marbles, 15 glass marbles, and 5 metal marbles.

a. What is the probability if Monica picks a plastic marble, replaces it then picks a wooden marble?

Answers

The probability that Monica picks a plastic marble and wooden marble is 266/1849

What is probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is is 1 and it's equivalent to 100% in percentage.

Percentage = sample space /total outcome

total outcome = 14+9+15 = 43

probability that she picks a plastic = 14/43

probability that she picks wooden = 9/43

Probability of picking a plastic and a wooden marble = 14/43 × 9/43

= 266/1849

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You have 1000000 small cubes. Each cube measures 1 inch on a side. If you used the cubes to make one big cube, what would be the side length of the big cube?

Answers

Therefore, if we used 1,000,000 small cubes to make one big cube, the side length of the big cube would be 100 inches.

To solve this problem, we need to understand the concept of volume and the relationship between the volume of small cubes and the volume of a big cube.

The volume of a cube is calculated by multiplying its length, width, and height together. In this case, each small cube measures 1 inch on a side, so its volume is 1 x 1 x 1 = 1 cubic inch.

To find the side length of the big cube, we need to determine how many small cubes would be needed to create it. Since we have 1,000,000 small cubes, we can calculate the total volume of all the small cubes by multiplying the volume of one small cube (1 cubic inch) by the number of small cubes we have (1,000,000).

1 x 1,000,000 = 1,000,000 cubic inches

Now we need to find the side length of a cube with a volume of 1,000,000 cubic inches. To do this, we can use the formula for the volume of a cube:
Volume of big cube = (Side length)^3

We can rearrange this formula to solve for the side length:
Side length = (Volume of big cube)^(1/3)

Plugging in the volume we calculated earlier, we get:
Side length = (1,000,000)^(1/3)

Using a calculator, we find that the side length of the big cube would be approximately 100 inches.

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A pizza parlor is considering adding taco pizza and Hawaiian pizza to its

menu. It surveyed a group of potential customers to find out what they

thought, and the results of the survey are shown in the bar graph below, with

the percentage of respondents favoring the addition of each pizza shown

above the corresponding bar.

What should we add to our menu?

70°

60%

50%

66%

40%

37%

10%

Taco

pizza

Hawaiian

pizza

If the pizza parlor can make a maximum of 135 pizzas a day, how many

should they expect will be taco pizzas?

Answers

The pizza parlor should expect to make approximately 89 taco pizzas per day. To determine how many taco pizzas the pizza parlor should expect to make, we need to look at the percentage of respondents who favored the addition of taco pizza in the survey.

According to the bar graph, 66% of respondents favored the addition of taco pizza.
To find out how many pizzas the pizza parlor should expect to make, we need to multiply the percentage by the total number of pizzas they can make in a day (135):
66% of 135 = 0.66 x 135 = 89.1
Therefore, the pizza parlor should expect to make approximately 89 taco pizzas per day.
Based on the survey results, 66% of respondents favor adding taco pizza to the menu, while 37% favor adding Hawaiian pizza. Since the majority of customers prefer taco pizza, it would be a good choice to add to the menu.
If the pizza parlor can make a maximum of 135 pizzas a day and 66% of customers prefer taco pizza, they should expect to make approximately 89 taco pizzas per day (0.66 x 135 ≈ 89).

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What is the value of ? 4 1/2 – 1 3/4?

Answers

The value of 4 1/2 - 1 3/4 is 2 3/4. mixed fraction for 9.875

When calculating the value of 4 1/2 - 1 3/4, you should follow these step:

1. Convert both mixed numbers into improper fractions. 4 1/2 = (4 x 2 + 1)/2 = 9/2 1 3/4 = (1 x 4 + 3)/4 = 7/4

2. Find a common denominator, which in this case is 4.

3. Convert the fractions to equivalent fractions with the common denominator: 9/2 = 18/4

4. Subtract the fractions: 18/4 - 7/4 = 11/4 5.

If needed, convert the result back into a mixed number:

11/4 = 2 3/4

The value of 4 1/2 - 1 3/4 is 11/4, which can be expressed as a mixed number: 2 3/4.

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The graph of a function is shown.

Which function is represented by the graph?

O 1(x) :

≥ 0

O 1%) =

x 2 0

O 10%) =:

x > 0

Nx)=

• 0

Answers

The graph shown represents the function f(x) = 3, x ≥ 0. This is a constant function, meaning that the output of the function is the same for all values of x that are greater than or equal to zero.

In this case, the output is always 3. The function is defined only for non-negative values of x, as indicated by the vertical line on the graph at x = 0.

The graph of the function is a horizontal line that passes through the point (0,3) on the y-axis. This indicates that the output of the function is always 3, regardless of the input. The function f(x) = 3 is an example of a step function, which has a constant output for different intervals of the input. In this case, the interval is [0,∞), meaning that the function is defined for all non-negative real numbers.

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When Ramona went to bed, the temperature was 12°F. When she woke up,

the temperature was -5F. Explain how a temperature of 0°F relates to these

two temperatures.

HELP PLEASE ;(

Answers

A temperature of 0°F is 29 degrees Fahrenheit colder than the initial temperature of 12°F and 5 degrees Fahrenheit colder than the final temperature of -5°F.

Relation of -5°F and 12°F to 0°F.

The temperature difference between Ramona going to bed and waking up can be found by subtracting the initial temperature of 12°F from the final temperature of -5°F:

-5°F - 12°F = -17°F

This means that the temperature dropped by 17 degrees Fahrenheit overnight.

To relate this to a temperature of 0°F, we can see that the temperature dropped by 17°F from 12°F to -5°F. Therefore, if the temperature continued to drop at the same rate, it would reach 0°F when the initial temperature is increased by 17°F:

12°F + 17°F = 29°F

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Each set of measures is the angle measures of a triangle. Find the measure of the missing angle in each triangle.

30, 40,

50, 60,

30, 60,

30, 120,

Answers

Thus, the missing angle is 180 - (30 + 40) = 110 degrees.
In the second triangle, the missing angle is 180 - (50 + 60) = 70 degrees.
In the third triangle, the missing angle is 180 - (30 + 60) = 90 degrees.
In the fourth triangle, the missing angle is 180 - (30 + 120) = 30 degrees.

The missing angle in the first triangle can be found by subtracting the sum of the other two angles from 180 degrees.
Understanding the angles in a triangle is important in various fields such as mathematics, engineering, architecture, and design. The sum of the three interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles. Finding missing angles in triangles is a basic problem-solving skill that requires an understanding of angles and their relationships. Triangles with specific angle measures have their own names and classifications, such as acute, right, obtuse, isosceles, and equilateral triangles, which have different properties and characteristics.

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In an experiment, the probability that event A occurs is 5/9 the probability that event B occurs is 5/7 and the probability that events A and B both occur is 4/9. What is the probability that A occurs given that B occurs? Simplify any fractions.

Answers

To find the probability that event A occurs given that event B occurs, we can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

Given information:

P(A) = 5/9

P(B) = 5/7

P(A and B) = 4/9

Now, let's substitute the values into the formula:

P(A|B) = (P(A and B)) / P(B) = (4/9) / (5/7)

To divide fractions, we can multiply the numerator by the reciprocal of the denominator:

P(A|B) = (4/9) * (7/5)

Multiplying the numerators and denominators:

P(A|B) = (4 * 7) / (9 * 5) = 28/45

Therefore, the probability that event A occurs given that event B occurs is 28/45.

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Abram's monthly liabilities equal $2,400 and hi monthly assets are $6,800. what is his debt-to-income, expressed as a percent? round. to hte nearest whole number

Answers

Abram's debt-to-income ratio is 26% according to the information provided.

Abram's debt-to-income ratio can be calculated as follows:

Debt-to-Income Ratio = (Monthly Liabilities / Monthly Income) x 100%

Since we are not given Abram's monthly income directly, we can calculate it by adding his monthly liabilities to his monthly assets:

Monthly Income = Monthly Liabilities + Monthly Assets

= $2,400 + $6,800

= $9,200

Now, we can substitute these values into the formula for debt-to-income ratio:

Debt-to-Income Ratio = (Monthly Liabilities / Monthly Income) x 100%

= ($2,400 / $9,200) x 100%

= 26.09%

Rounded to the nearest whole number, Abram's debt-to-income ratio is 26%.

This means that Abram's monthly liabilities represent about 26% of his monthly income. In general, a lower debt-to-income ratio is considered better, as it indicates that a person has more disposable income to save or invest after paying their debts. A higher ratio may suggest that a person is overextended and may have difficulty managing their debt payments.

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How do i solve this problem?

The room is 18 feet long and 12 feet wide at the cost of $13.25 per square yard, What will be the cost for wall-to-wall carpeting?

Answers

The cost for wall-to-wall carpeting would be $318.00.

How to calculate the area of the room?

First, we need to calculate the area of the room to determine the amount of carpet needed. The area of the room is:

$18 \text{ ft} \times 12 \text{ ft} = 216 \text{ ft}^2$

To convert this to square yards, we divide by 9:

$\frac{216 \text{ ft}^2}{9} = 24 \text{ yd}^2$

So we need 24 square yards of carpeting.

The cost of carpeting per square yard is $13.25$. Therefore, the total cost of wall-to-wall carpeting for the room is:

$24 \text{ yd}^2 \times $13.25/\text{yd}^2 = $318$

So the cost for wall-to-wall carpeting would be $318.00.

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A multiple choice exam has 7 questions with 4 answer choices per problem. How many different ways can the exam be answered?

Answers

there are 16,384 different ways the exam can be answered.For each question on the exam, there are 4 answer choices. This means that for each question, there are 4 possible ways to answer.

Since there are 7 questions in total, we multiply the number of possibilities for each question to get the total number of ways the exam can be answered.

To determine the number of different ways the exam can be answered, we need to calculate the total number of possible combinations for each question and then multiply them together.

For each question, there are 4 answer choices. Therefore, for each question, there are 4 possible ways to answer.

Since there are 7 questions in total, we multiply the number of possibilities for each question:

4 * 4 * 4 * 4 * 4 * 4 * 4 = 4^7

Using exponentiation, we find that 4^7 equals 16,384.

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A diver's height above the surface of the water

when diving can be modeled by the equation

h=-16t²-8t + 120, where h is the diver's

height above the water's surface measured in feet,

and it is the time in seconds. How long will it take

for the diver to reach the surface of the water?

A 8 seconds

B 3 seconds

2.5 seconds

D 0.4 seconds

Answers

To find how long it will take for the diver to reach the surface of the water, we need to solve the equation h = -16t² - 8t + 120 for t when h = 0 (the surface of the water).

0 = -16t² - 8t + 120

We can solve this quadratic equation using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a = -16, b = -8, and c = 120. Plugging in these values:

t = (8 ± √((-8)² - 4(-16)(120))) / 2(-16)

t = (8 ± √(64 + 7680)) / -32

t = (8 ± √7744) / -32

t = (8 ± 88) / -32

Now we have two possible solutions:
t = (8 + 88) / -32 = 96 / -32 = -3 (discard this solution as time cannot be negative)
t = (8 - 88) / -32 = -80 / -32 = 2.5 seconds

So, it will take the diver 2.5 seconds to reach the surface of the water. Your answer is 2.5 seconds.

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Using complete sentences explain which function as the greatest y-intercept.

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The y-intercept of a function is the point where the graph of the function intersects with the y-axis. In other words, it is the value of the function when the input or x-value is equal to 0.

To determine which function has the greatest y-intercept, we need to evaluate each function at x=0 and compare their y-values. The function with the largest y-value at x=0 will have the greatest y-intercept.

For example, if we have two functions f(x) and g(x), we can evaluate them at x=0 as follows:

f(0) = 5

g(0) = 7

In this case, g(x) has the greatest y-intercept since its y-value at x=0 is larger than that of f(x). Therefore, we can say that the function g(x) has the greatest y-intercept.

In summary, to determine which function has the greatest y-intercept, we need to evaluate each function at x=0 and compare their y-values. The function with the largest y-value at x=0 will have the greatest y-intercept.

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The ice cream shop has chocolate, strawberry and vanilla soft serve. They have 5 different topping choices. What is the probability of randomly selecting strawberry ice cream with chocolate sprinkles?

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The probability of randomly selecting strawberry ice cream with chocolate sprinkles from an ice cream shop with chocolate, strawberry, and vanilla soft serve and 5 different topping choices is 1/15 or approximately 0.067.

To calculate the probability, we use the product rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities. Here, the probability of selecting strawberry ice cream is 1/3 since there are three flavors to choose from. Similarly, the probability of selecting chocolate sprinkles is 1/5 since there are five toppings to choose from. Thus, the probability of selecting strawberry ice cream with chocolate sprinkles is the product of these two probabilities, which is (1/3) * (1/5) = 1/15 or approximately 0.067.

Therefore, the probability of randomly selecting strawberry ice cream with chocolate sprinkles is 1/15 or approximately 0.067. This means that for every 15 ice cream orders that customers place, on average, one will be for strawberry ice cream with chocolate sprinkles. The product rule of probability is a useful tool to calculate the probability of two independent events occurring together. By multiplying the individual probabilities of the events, we can determine the likelihood of both events happening simultaneously.

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Mrs. Mayerson read 11 books last month. 14 of the books had 278 pages each. If all the books had a total of 5,000 pages, how many pages did each of the remaining books have? K Write an equation to solve

Answers

Let x represent the number of pages in each of the remaining books. We can write an equation to represent the total number of pages Mrs. Mayerson read:

11 books (total) - 14 books with 278 pages = 11 - 14 = -3 remaining books

Since there are actually 3 remaining books, we can rewrite the equation as:

14 books * 278 pages + 3 books * x pages = 5,000 pages

Now, we can solve the equation:

(14 * 278) + (3 * x) = 5,000

3,892 + 3x = 5,000

Subtract 3,892 from both sides:

3x = 1,108

Now, divide both sides by 3:

x = 369

So, each of the remaining books had 369 pages.

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