The product of two consecutive integers is three less than three times their sum. Find the integers.

I got the answer "x^2-5x=0"

How can I find out the numbers??

The most expensive car that he can afford to buy is 4-door hatchback.

We have,

Car Price 2-door coupe $21,750

4-door hatchback $22,500

Compact sedan $23,000

Compact SUV $23,400

Sales tax = 6%

So, the most expensive car Dean can buy is the 4-door hatchback.

= 22500 x 0.06

= 13501350 + 22500

= 23850

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Answer:

The length of the hypotenuse is 41.

Step-by-step explanation:

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

In this case, the lengths of the legs are 9 and 40. Using the Pythagorean theorem, we can find the length of the hypotenuse:

[tex]\sf:\implies h^2 = 9^2 + 40^2[/tex]

[tex]\sf:\implies h^2 = 81 + 1600[/tex]

[tex]\sf:\implies h^2 = 1681[/tex]

Taking the square root of both sides, we get:

[tex]\sf:\implies h = \sqrt{1681}[/tex]

Simplifying the square root, we get:

[tex]\sf:\implies \boxed{\bold{\:\:h = 41\:\:}}\:\:\:\green{\checkmark}[/tex]

Therefore, the length of the hypotenuse is 41.

Greetings! ZenZebra at your service, hope it helps! <33

The least number of boxes the bakery can use is 4 boxes of 8-cupcake capacity (32 cupcakes) and 3 boxes of 5-cupcake capacity (15 cupcakes), totaling 47 cupcakes. In this arrangement, there are no empty spaces, and a total of 7 boxes are used.

To minimize the number of boxes used without empty spaces, the bakery needs to efficiently pack the 47 cupcakes into the 5-cupcake and 8-cupcake boxes.

To start, we can calculate how many 8-cupcake boxes can be filled by dividing the total cupcakes (47) by the capacity of the 8-cupcake box:

47 ÷ 8 = 5 (remainder 7).

This means that 5 boxes of 8-cupcake capacity can be filled, leaving us with 7 cupcakes.

Now we'll work with the remaining 7 cupcakes and the 5-cupcake boxes. Since one 5-cupcake box can fit 5 of the remaining cupcakes, we still have 2 cupcakes left. However, if we replace one 8-cupcake box with two 5-cupcake boxes, we can fit the remaining 2 cupcakes, effectively filling up all the boxes without empty spaces.

So, the least number of boxes the bakery can use is 4 boxes of 8-cupcake capacity (32 cupcakes) and 3 boxes of 5-cupcake capacity (15 cupcakes), totaling 47 cupcakes. In this arrangement, there are no empty spaces, and a total of 7 boxes are used.

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Angle IKH must be right angle since line IH is the diameter of the circle.

A right angle is an angle that measures exactly 90 degrees, or a quarter of a full turn.

In the given diagram, we can see that line IH is the diameter of the circle.

Also if line IH is the diameter, then the angle at the circumference formed by the lines joining the diameter of the circle must be 90 degrees.

So angle KHI + angle KIH + angle IKH = 180 (sum of angles in a triangle)

angle KHI + angle KIH + 90 = 18

Thus, angle IKH must be right angle since line IH is the diameter of the circle, and angle IBH must also be 90 degrees.

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The solution is taken by solving the linear equations. The woman will have 17 cats and 14 birds.

Let's assume that the woman has x cats and y birds.

Each cat has 4 legs, and each bird has 2 legs. Therefore, the total number of legs can be expressed as:

4x + 2y = 76

We also know that the woman owns a total of 21 pets, so we have:

x + y = 21

We can use these two equations to solve for x and y. First, we can rearrange the second equation to solve for x:

x = 21 - y

Substituting this into the first equation, we get:

4(21 - y) + 2y = 76

Expanding and simplifying, we get:

84 - 2y = 76

2y = 8

y = 4

So the woman owns 4 birds. We can use the second equation to find the number of cats:

x + 4 = 21

x = 17

Therefore, the woman owns 17 cats and 4 birds.

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To the correct number of significant figures, the area of the rectangle is 1.723 m². The correct answer is an option (C).

As per the question, we have:

The length of the rectangle = 3.24 m

The width of the rectangle = 0.532 m

To find the area of the rectangle, we can use the formula:

Area of the rectangle = length x height

Substituting the given values, we get:

Area of the rectangle = 3.24 m × 0.532 m

Area of the rectangle = 1.72368 m²

To the correct number of significant figures, the area of the rectangle is 1.723 m².

Therefore, the correct answer is an option (C).

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6 is the maximum number of tickets he can buy with $50

To determine the maximum number of tickets Jordan can buy with $50, we need to divide the total amount of money by the cost of each ticket.

$50 / $7.75 per ticket = 6.45 tickets

However, since Jordan can only buy whole tickets,

the maximum number of tickets he can buy with $50 is 6.

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The correct option is: d. No. There are no free variables since the matrix must have 5 pivots

If the equation Ax=b is consistent for every b in R, it means that the matrix A is invertible, since the solutions to the equation can be expressed as x = [tex]A^(^-^1^)[/tex]b.

An invertible matrix has full rank, which means that it has 5 pivots in this case.

If Ax=b has more than one solution for some b, then there would be two different vectors x₁ and x₂ that satisfy the equation, which implies that A(x₁ - x₂) = 0.

This means that the matrix A has a nontrivial nullspace, which contradicts the fact that A has full rank. Therefore, it is not possible for Ax=b to have more than one solution for any b in R.

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The length of the piece of cardboard is 25 inches, and the width is 15 inches.

Let's assume the width of the cardboard is x inches. Since the length of the cardboard is 10 inches longer than the width, the length would be x + 10 inches.

When squares with sides of 2 inches are cut from each corner, the width of the resulting box will be reduced by 4 inches (2 inches from each side), and the length will be reduced by 4 inches as well.

The height of the box will be 2 inches since the squares cut from the corners have a height of 2 inches.

To find the dimensions of the box, we need to determine the length, width, and height.

Width of the box = x - 4 inches

Length of the box = x + 10 - 4 = x + 6 inches

Height of the box = 2 inches

The volume of a rectangular box is given by the formula:

Volume = Length × Width × Height

We are given that the volume of the box is 462 in³, so we can set up the equation:

462 = (x + 6)(x - 4)(2)

Simplifying the equation:

231 = (x + 6)(x - 4)

Expanding and rearranging:

231 = x² + 2x - 24

Bringing all terms to one side:

x² + 2x - 24 - 231 = 0

Simplifying further:

x² + 2x - 255 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Factoring is the most efficient method in this case:

(x - 15)(x + 17) = 0

Setting each factor equal to zero:

x - 15 = 0 or x + 17 = 0

Solving for x:

x = 15 or x = -17

Since we are dealing with dimensions, a negative value does not make sense. Therefore, the width of the cardboard is 15 inches.

Using the width, we can find the length:

Length = Width + 10 = 15 + 10 = 25 inches

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Answer:

Step-by-step explanation:

To find the 48th term of the sequence, we need to determine the pattern or rule governing the sequence. From the given sequence, we can observe that each term is decreasing by 4 from the previous term. This means that the common difference between the terms is -4.

Using this information, we can write the general formula for the nth term of the sequence. The formula for the nth term of the sequence would be:

y = x + (n-1)d

where y is the nth term of the sequence, x is the first term, n is the position of the term we want to find, and d is the common difference.

Substituting the given values, we get:

x = 205

d = -4

Now we can plug in n = 48 and solve for the 48th term:

y = x + (n-1)d

y = 205 + (48-1)(-4)

y = 205 - 188

y = 17

Therefore, the 48th term of the sequence is 17.

Answer: 17

Step-by-step explanation:

1. First we find out how to get from 1 term to the next:

205 - 201 = 4,   201 - 197 = 4, and the sequence is decreasing each time so -4, -4n

2. Next we determine the difference between the sequence, and the -4 times table

205  201  197

-4      -8     -12

205 - - 4 = 201,   201 - - 8 = 209,  etc...

so the difference is positive 209 (+209)

3. Next, we use the nth term rule (-4n+209), and substitute 48 into n:

-4 x 48 + 209

-4 x 48 = -192, -192 + 209 = 17

4. So 17 is the 48th term.

The requried another dose of Robitussin would need to be taken at least 5 hours after the initial dose in order for the body to maintain the minimum effective amount of 100 mg.

Let t be the number of hours that have passed since the dose was taken, and let A(t) be the amount of Robitussin in the body at time t. We know that A(0) = 1000 mg (the initial dose), and that A(t) = 0.55 A(t-1) (the rate of decay is 55% per hour).

We want to find the value of t such that A(t) = 100 mg. We can use recursive substitution to find A(t) in terms of A(0):

A(1) = 0.55 A(0) = 0.55 * 1000 = 550

A(2) = 0.55 A(1) = 0.55 * 550 = 302.5

A(3) = 0.55 A(2) = 0.55 * 302.5 = 166.375

A(4) = 0.55 A(3) = 0.55 * 166.375 = 91.50625

A(5) = 0.55 A(4) = 0.55 * 91.50625 = 50.3284375

So, after 5 hours, the amount of Robitussin in the body drops below 100 mg.

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There are some bacteria in a dish. Every hour, each bacterium splits into 3 bacteria. Hence, in total after 3 hours, we have 27 bacteria.

Bacteria are ubiquitous, largely free-living creatures that frequently only have one biological cell. They make up a significant portion of the prokaryotic microbial kingdom. Bacteria, which tend to be a few micrometres long and were among the initial organisms that appeared on Earth, are found in the majority of its habitats.

n = the number of bacteria at a given hour

at zero hour=1 bacteria.

1 bacteria after an hour is split in to 3 bacteria.

n(1)  = 3

n(2)  = 3 x 3  = 9 bacteria

n(3)  = 9 x 3  = 27 bacteria

Hence, in total after 3 hours, we have 27 bacteria

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The solutions of the given equation in the interval [0, 2π) are:

x = π/4, 3π/4, 5π/4, 7π/4

Let's start by simplifying the given equation using the trigonometric identity:

sec²(x) - tan²(x) = 1

Rearranging, we get:

sec²(x) = tan²(x) + 1

Substituting this into the given equation, we get:

3sec²(x) - 2tan²(x) - 4 = 0

3(tan²(x) + 1) - 2tan²(x) - 4 = 0

tan²(x) = 1

Taking the square root of both sides, we get:

tan(x) = ±1

We need to solve for x in the interval [0, 2π), so we need to find all solutions of the equation tan(x) = ±1 within that interval.

When tan(x) = 1, we have x = π/4 and 5π/4, both of which are in the given interval.

When tan(x) = -1, we have x = 3π/4 and 7π/4, both of which are also in the given interval.

Therefore, the solutions of the given equation in the interval [0, 2π) are:

x = π/4, 3π/4, 5π/4, 7π/4

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The claim that the new tire is superior to current tires is the alternative hypothesis.

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Factor analysis and PCA (Principal Component Analysis) are statistical techniques used to reduce data dimensionality and identify underlying patterns.

Here's a general procedure for both methods:

1. Data collection: Gather a dataset with relevant variables for analysis.

2. Standardization: Standardize the data to ensure variables have equal weight and influence.

3. Covariance or correlation matrix: Calculate the covariance (for PCA) or correlation (for factor analysis) matrix to identify relationships between variables.

4. Eigenvalue decomposition: Perform eigenvalue decomposition on the matrix to obtain eigenvalues and eigenvectors, which represent the amount of variance explained and the direction of the principal components/factors, respectively.

5. Select principal components or factors: Choose the number of components/factors to retain based on the proportion of variance explained and the scree plot, which displays eigenvalues in descending order.

6. Rotation (for factor analysis): Apply a rotation method (e.g., varimax or promax) to the factor loading matrix to simplify interpretation and achieve a more meaningful structure.

7. Interpretation: Analyze and interpret the principal components or factors and their relationships with the original variables.

Remember that PCA and factor analysis have different assumptions and goals: PCA focuses on identifying orthogonal axes maximizing variance, while factor analysis aims to explain the correlation structure among variables using underlying latent factors.

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The first table with function y = 5+5x is completed as follows:

X = 0 1 2 3 4

Y = 5 10 15 20 25

The second table with function y= 5+5^x is completed as follows:

X= 0 1 2 3 4

y= 10 10 30 130 630

For the first table;

when X = 0 , y = 5+5(0) = 5

when X = 1, Y = 5+5(1) = 10

When X = 2, Y = 5+5(2) = 15

When X = 3, y = 5+5(3) = 20

When X = 4, y = 5+5(4) = 25

For the second table:

When X = 0, y = 5+5(^0) = 10

When X = 1, y = 5+5(^1) = 10

When X = 2, y = 5+5(^2) = 30

When X = 3, y = 5+5(^3) = 130

When X = 4, y = 5+5(^4) = 630

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There are several types of values that individuals and societies hold. Here are the differences among global values, terminal values, instrumental values, and domain-specific values:

Global values are values that are considered important across cultures and societies. These values are often seen as universal and are not specific to any particular group or society.

Global values include traits such as honesty, integrity, and respect for others. These values are considered fundamental to human interaction and are often emphasized in ethical and moral teachings.

Terminal values are values that individuals or societies hold as ultimate goals or end states. These values are often seen as the most important goals that individuals or societies can strive for.

Examples of terminal values include happiness, freedom, and world peace. These values are often deeply rooted in culture and are influenced by factors such as religion, history, and political ideology.

Instrumental values are values that individuals or societies hold as means to achieve the terminal values. These values are seen as important because they help individuals or societies achieve their ultimate goals.

Examples of instrumental values include hard work, responsibility, and self-discipline. These values are often taught through socialization and are reinforced through the rewards and punishments for responsible.

Domain-specific values are values that are specific to a particular domain or area of life. These values are often shaped by the unique demands and characteristics of the domain.

For example, in the domain of business, values such as profitability, innovation, and customer satisfaction may be considered important.

These values are often influenced by the goals and objectives of the organization, as well as the needs and desires of stakeholders such as customers, employees, and shareholders.

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To save enough money to pay for one year of school, regardless of interest earned on the savings, Yasmine should choose a plan that allows her to save $9,000 annually. This means she should opt for a savings plan that offers a high-interest rate or a low-risk investment option.

Here are a few options that Yasmine can consider:

High-yield savings account: Yasmine can open a high-yield savings account that offers a competitive interest rate. By depositing $9,000 annually into the account, she can accumulate the required funds for one year of school.

Certificate of Deposit (CD): Yasmine can invest her money in a CD with a fixed interest rate and a specific maturity period, such as one year. This way, she can ensure that her savings are protected and will grow over time.

Money market account: Yasmine can open a money market account that typically offers higher interest rates than regular savings accounts. By consistently contributing $9,000 per year, she can build up the necessary funds for her education.

Remember, it is essential for Yasmine to research and compare different savings options, considering factors such as interest rates, fees, and any potential restrictions or penalties associated with the account. Consulting with a financial advisor can also provide valuable insights tailored to Yasmine's specific financial situation and goals.

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A polygon is called non-convex if there are "dents" or indentations in it, where the internal angle is greater than 180 degrees.

In other words, a non-convex polygon is a polygon whose line segments intersect, creating an interior angle greater than 180 degrees. This is in contrast to a convex polygon, where all of the interior angles are less than 180 degrees and none of the line segments intersect.

Non-convex polygons can have a variety of shapes and sizes, and can be composed of any number of sides. However, they are generally more difficult to work with mathematically than convex polygons, and often require more advanced techniques to analyze and understand their properties.

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Answer:

14/16, 21/24, and 28/32

Step-by-step explanation:

(7 x 4) (8 x 4) = 28/32

(7 x 3) (8 x 3) = 21/24

(7 x 2) (8 x 2) = 14/16

Thus, a decision to not reject the null hypothesis should be interpreted with caution and further investigation may be needed to fully understand the underlying factors affecting student study habits at the university.

The null hypothesis in this scenario would be that the mean number of hours students study at the university (per day) is equal to or greater than 4.4 hours.

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Answer: 36

Step-by-step explanation: you would take 60-24 and that makes 36.

There are infinitely many inequalities that have b = 4 as a solution.

i.e,

b - 5 < 1

2b + 1 ≥ 9

b/2 > 1

We have,

To find inequalities that have b = 4 as one of its solutions, we need to replace b with 4 in the inequality and check if the inequality is satisfied.

For example, the inequality 2b > 6 has b = 4 as a solution because:

2(4) > 6

8 > 6

This inequality is satisfied when b = 4, so b = 4 is a solution to the inequality 2b > 6.

Similarly, the inequality b + 3 ≤ 7 has b = 4 as a solution because:

4 + 3 ≤ 7

7 ≤ 7

This inequality is satisfied when b = 4, so b = 4 is a solution to the inequality b + 3 ≤ 7.

Other examples of inequalities that have b = 4 as a solution include:

b - 5 < 1 (because 4 - 5 < 1)

2b + 1 ≥ 9 (because 2(4) + 1 ≥ 9)

b/2 > 1 (because 4/2 > 1)

Thus,

There are infinitely many inequalities that have b = 4 as a solution.

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Any ordered arrangement of a given set of objects is called a permutation. Permutations are used in various fields, including mathematics, statistics, computer science, and cryptography.

Permutations are essentially different ways of arranging objects, and they depend on the number of objects to be arranged and the order in which they are arranged. In a permutation, the order of objects matters, and the same set of objects can have different permutations. The number of permutations of a set of n distinct objects can be calculated by multiplying n by all positive integers less than n.

This is denoted by n!, which is read as n factorial. For example, the number of permutations of the set {1, 2, 3} is 3! = 3 × 2 × 1 = 6. Permutations are important in probability theory, where they are used to calculate the number of possible outcomes of an event.

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Sophia should budget the total cost calculated in step 3 to fill up her tank when she gets home.

To determine the amount Sophia should budget for refueling when she gets home, we need to consider the following terms:
Fuel efficiency:

Determine the miles per gallon (mpg) that Sophia's car gets. we can find this information in the car's manual or online.

Gas price: Find the current price per gallon of gasoline in Sophia's area. You can check local gas stations or websites that track gas prices.

Determine the fuel efficiency of Sophia's car (miles per gallon or mpg).
Calculate the total number of gallons needed to drive 291 miles by dividing 291 miles by the car's mpg.
Example:  

If Sophia's car has a fuel efficiency of 29 mpg, the calculation would be 291 miles / 29 mpg = 10 gallons.
Multiply the total number of gallons needed by the current gas price per gallon to find the total cost.

Example:  If the gas price is $3 per gallon, the calculation would be 10 gallons * $3 = $30.

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The requried, lateral area of the right prism is 4.8 cm².

To find the lateral area of a right prism, we need to find the perimeter of the base and multiply it by the height of the prism. Since the base of the prism is a parallelogram with sides of 6 cm and 20 mm, we first need to convert the length of one of the sides to the same unit as the other side.

20 mm is equal to 2 cm (since 1 cm = 10 mm), so the sides of the parallelogram are 6 cm and 2 cm.

The perimeter of the parallelogram base is the sum of the lengths of its four sides, which is:

Perimeter = 2(6 cm) + 2(2 cm) = 12 cm + 4 cm = 16 cm

Therefore, the lateral area of the right prism is:

Lateral Area = Perimeter of Base x Height

Lateral Area = 16 cm x 0.3 dm = 4.8 cm²

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The total number of hours Hong was driving is 34.5 hours, which is a mixed number in simplest form of 34 1/2 hours.

To find the total number of hours Hong was driving, we need to divide the total amount of gas used by the rate of gas consumption per hour.

Let's first convert the mixed number 3 5/6 to an improper fraction:

3 5/6 = (3 × 6 + 5) / 6 = 23/6

So, Hong used a total of 23/6 gallons of gas.

Now, we need to divide this by the rate of gas consumption per hour, which is 7/9 gallons:

(23/6) ÷ (7/9) = (23/6) × (9/7) = (23 × 3) / 2 = 34.5

Therefore, the total number of hours Hong was driving is 34.5 hours, which is a mixed number in simplest form of 34 1/2 hours.

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320 senior citizens paid for admission at the Family Fine Arts Center on that weekend evening.

Let's use the given information and these terms in our answer:
Let x represent the number of adult tickets sold, and y represent the number of senior citizen tickets sold.

We have two pieces of information that can be expressed as equations:
The total number of tickets sold: x + y = 511

The total receipts: 20x + 10y = 7020.
Now let's solve this system of equations step by step:
Solve the first equation for x:
x = 511 - y

Substitute the expression for x from Step 1 into the second equation:
20(511 - y) + 10y = 7020

Simplify the equation by distributing the 20:
10220 - 20y + 10y = 7020
Combine like terms:
-10y = -3200
Divide by -10 to find y:
y = 320.

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The sister who had less variation in her daily step count, given the box plots, would be Brenda.

To determine variation in a box plot, one can look at the length of the whiskers. Longer whiskers indicate greater variation in the data, while shorter whiskers indicate less variation.

A wider box indicates greater variation, while a narrower box indicates less variation.

We can also look at the range of the data.

Janet's range is:

= 9, 000 - 5, 000 steps

= 4, 000 steps

Brenda's range would be :

= 10, 000 - 7, 000

= 3, 000 steps

Brenda's range being lower means her variation is less.

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The quantity of pounds of fertilizer that she would use on a lawn of given area would be = 68 pounds of fertilizer.

To calculate the quantity of fertilizer that is needed for the area of lawn given, the following of carried out.

The total area of lawn that needs fertilizer = 1700 square feet

The quantity lawn that needs 2 pounds of fertilizer = 50ft²

That is;

2 pound = 50ft²

X pound = 1700ft²

make X the subject of formula;

X = 1700×2/50

= 3400/50

= 68 pounds

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