100 points please helq

The solution of the system of equations is (2, 1).

Here we have the system of equations:

y = 2x - 3

y = -x + 3

To solve the system of equations graphically, we need to graph both of these lines in the same coordinate axis and then find the point where the lines intersect.

That point will be the solution of the system.

On the image at the end you can see the graph of the system of equations, there we can see that the solution is (2, 1).

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The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.

In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.

The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.

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2x + y = -7

y= -7-2x

put this value in 2nd equation

3x=6+4(-7-2x)

3x=6-28-8x

11x= -22

x= -2

y= -7-2(-2)

y= -7+4

y= -3

Answer: slope=4

Step-by-step explanation:

[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]

[tex]Slope=\frac{4- - 4}{3-2}[/tex]

[tex]Slope=\frac{4+4}{3-2}[/tex]

[tex]Slope=4[/tex]

Yes, the number of linearly independent columns in a matrix A is equal to the number of linearly independent rows in A.

This is because the definition of linear independence states that no linear combination of a set of vectors can equal the zero vector, so if one set of vectors is linearly independent, the other set of vectors must also be linearly independent.

To explain further, the number of linearly independent vectors in a matrix A is determined by the rank of the matrix. The rank of a matrix is the number of linearly independent rows and columns in the matrix.

So if the rank of A is n, then the number of linearly independent columns and rows of A must be n. This is because if there are n linearly independent columns in the matrix, the number of linearly independent rows must also be n.

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If each basket contains the same number of eggs and there are at least 4 eggs in each basket, Jenny put 3 red eggs in each of 6 baskets, and 4 orange eggs in each of 6 baskets.

Let's call the number of eggs in each basket "x." We know that Jenny placed a total of 18 red eggs, so the number of baskets with red eggs can be represented as 18/x. Similarly, the number of baskets with orange eggs can be represented as 24/x.

Since we know that each basket contains at least 4 eggs, we can set up the inequality 4 ≤ x.

Now we can use this information to set up an equation:

18/x + 24/x = total number of baskets

Simplifying this equation, we get:

42/x = total number of baskets

But we also know that the total number of baskets is an integer (you can't have a fraction of a basket), so x must be a factor of 42.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. But we also know that each basket must contain at least 4 eggs, so we can eliminate 1, 2, and 3 as possible values of x.

Therefore, the possible values of x are 6, 7, 14, 21, and 42. But we also know that there are 18 red eggs and 24 orange eggs, so x must be a factor of both 18 and 24.

The common factors of 18 and 24 are 1, 2, 3, and 6. Therefore, the only possible value of x is 6.

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Complete question is:

Jenny places a total of 18 red Easter eggs in several green baskets and a total of 24 orange Easter eggs in some blue baskets. Each basket contains the same number of eggs and there are at least 4 eggs in each basket. How many eggs did Jenny put in each basket?

The answer to the expression 547 + 233 × 5 - 142 is 1752. To solve the expression, we must follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication, and Division (performed left to right), and Addition and Subtraction (performed left to right).

Since there are no parentheses or exponents in this expression, we start with multiplication and division. In this case, we have to multiply 233 by 5, which gives us 1165. Then, we add 547 to 1165, which gives us 1712. Finally, we subtract 142 from 1712, which gives us the final answer of 1752. Therefore, the result of the expression 547 + 233 × 5 - 142 is 1752, which can be obtained by following the order of operations and performing the arithmetic operations in the correct order.

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Answer:

11

Step-by-step explanation:

15 - (p + 1)

Let p=3

15 - (3 + 1)

Parentheses first

15 - (4)

11

Answer:

11

Step-by-step explanation:

Given that,

p = 3

So, to find the value of the expression you have to solve it by replacing p with 3.

15 - ( p + 1 )

15 - ( 3 + 1 )

15 - 4

11

By using LCM, we find that the three planets  x, y and z will be in the exact same locations again after $5400$ days.

To find the minimum positive number of days before the planets are all in the exact same locations again, we need to find the least common multiple (LCM) of the three given periods of rotation.

The prime factorization of each of the given periods of rotation is as follows

$360 =[tex]2^3 \cdot 3^2 \cdot 5$[/tex]

$450 =[tex]2 \cdot 3^2 \cdot 5^2$[/tex]

$540 =[tex]2^2 \cdot 3^3 \cdot 5$[/tex]

To find the LCM, we need to take the highest power of each prime factor that appears in any of the three factorizations. So the LCM is:

[tex]$LCM = 2^3 \cdot 3^3 \cdot 5^2 = 2^3 \cdot 27 \cdot 25 = 5400$[/tex]

Therefore, the three planets will be in the exact same locations again after $5400$ days.

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Answer: 196 Joules (J)

Step-by-step explanation:

To calculate the potential energy of the apple, we can use the formula:

Potential Energy = Mass x Gravity x Height

First, let's convert the height from kilometers to meters:

100 km = 100,000 meters

Now, let's convert the mass of the apple from grams to kilograms:

0.2 gram = 0.0002 kilograms

Using these values, we can calculate the potential energy:

Potential Energy = 0.0002 kg x 9.8 m/s^2 x 100,000 m

Potential Energy = 196 Joules (J)

Therefore, the potential energy of the apple is 196 Joules (J).

The probability of selecting 8 female students from a sample of 8 students from a student body with 60% female students is 0.2187, or 21.87%.

The probability of selecting a sample of 8 students from a student body of 60% female students is calculated using binomial probability. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of independent trials. In this case, the probability of selecting 8 students, with 60% being female students, can be calculated using the binomial probability formula.

The probability can be calculated using the following equation:
[tex]P(x=8) = (n!/((n-x)!x!)) * p^x * q^{(n-x)}[/tex]

Where:

In this case, n = 8, x = 8, p = 0.6, and q = 0.4. Plugging these values into the equation gives us a probability of 0.2187. This means that there is a 21.87% chance of selecting 8 female students out of a sample of 8 students from a student body with 60% female students.

It is important to remember that binomial probability is only used when there are two possible outcomes in each trial (i.e. success or failure). Additionally, it is important to remember that the equation only applies when the trials are independent of each other.

In conclusion, the probability of selecting 8 female students from a sample of 8 students from a student body with 60% female students is 0.2187, or 21.87%.

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The expression 3x-(4-x) is equivalent to 4x-4

The distributive property is a mathematical property that describes the relationship between multiplication and addition or subtraction. It states that when a number is multiplied by a sum or difference of two or more numbers, the result is the same as if we multiplied the number by each of the individual terms inside the parentheses and then added or subtracted the products.

To simplify the expression 3x-(4-x), we can distribute the negative sign to the second term inside the parentheses, which gives:

3x - (4 - x) = 3x - 4 + x

Now we can combine the like terms (3x and x) to get:

3x - 4 + x = 4x - 4

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The given question is incomplete, the complete question is:

Which expression is equivalent to 3x-(4-x)?

First one is 6

second one is 12

third one is -8

hope this helps

Answer:

Step-by-step explanation:

x=6

x=12

x=-8

y = -5x² + 5 is the equation of the parabola which has its vertex at (0, 5) and passes through the point (1, 0)

We know that the vertex of the parabola is (0, 5), which means that the equation for the parabola has the form:

y = a(x - 0)² + 5

where 'a' is a constant that determines the shape of the parabola. Since the parabola passes through the point (1, 0), we can substitute these values into the equation and solve for 'a':

0 = a(1 - 0)² + 5

0 = a + 5

a = -5

Therefore, the equation of the parabola is: y = -5x² + 5

This equation represents a parabola that opens downwards (since the coefficient of x² is negative), has a vertex at (0, 5), and passes through the point (1, 0).

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The percentage is 42% of the population is heterozygous for the recessive genetic disorder.

To determine the percentage of the population that is heterozygous for a recessive genetic disorder occurring in 9 percent of the population,

follow these steps:

1. Identify the frequency of the recessive allele (q) by taking the square root of the 9 percent occurrence (0.09). The square root of 0.09 is 0.3.

2. Calculate the frequency of the dominant allele (p) using the equation p = 1 - q. In this case, p = 1 - 0.3 = 0.7.

3. Determine the percentage of the population that is heterozygous using the equation 2pq. In this case, 2(0.7)(0.3) = 0.42 or 42%.

So, 42% of the population is heterozygous for the recessive genetic disorder.

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Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ

The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:

[tex]Q = mcΔT[/tex]

Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).

Using the equation, the amount of heat produced can be calculated as follows:

Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
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The number of ways to arrange N people with A and B separated is given by expression   N! - 2*(N-1)! .

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, operators, and functions that are grouped together in a meaningful way. Expressions can be as simple as a single number or variable, or they can be complex and include many different elements. They are used to represent mathematical relationships and operations, and can be evaluated or simplified using mathematical rules and techniques. Examples of expressions include:

Now,

Let the two particular people be A and B.

If we place A in a spot, there are N-1 spots left for B to be placed. Once A and B are placed, there are (N-2)! ways to place the remaining people. Therefore, the number of ways to arrange N people with A and B separated is:

(N-1) * (N-2)!

Alternatively, we can find the total number of ways to arrange N people in a line (N!) and subtract the number of ways to arrange them with A and B together.

To find the number of ways to arrange N people with A and B together, we can treat A and B as a single entity, so there are (N-1)! ways to arrange the remaining people with AB together. However, A and B can be arranged in two ways (AB or BA), so we need to multiply (N-1)! by 2.

Therefore, the number of ways to arrange N people with A and B separated is:

N! - 2*(N-1)!

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There is only one equiangular octagon that Jordan can create with side lengths as the first 8 positive integers.

To create an equiangular octagon with side lengths as the first 8 positive integers, each side must have a different length. The sum of the interior angles of an octagon is 1080 degrees, so each angle in the octagon must measure 135 degrees.

If we arrange the 8 integers in decreasing order, we can label the longest side as a and the remaining sides as b1, b2, b3, b4, b5, b6, in descending order. Then, we must have:

a + b1 + b2 = a + b2 + b3 = a + b3 + b4 = a + b4 + b5 = a + b5 + b6 = a + b6 + b1 = 135 degrees

Simplify each equation, we get:

b1 - b3 = b2 - b4 = b3 - b5 = b4 - b6 = b5 - b1 = b6 - a

Since all the side lengths are different, we can use these equations to find all possible combinations of side lengths. By inspection, we can see that there is only one set of side lengths that satisfies these conditions, namely:

a = 8

b1 = 7

b2 = 6

b3 = 5

b4 = 4

b5 = 3

b6 = 2

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Answer:

Step-by-step explanation:

First, we need to calculate the annual interest rate from the given APR.

APR = 2.25%

Daily interest rate = 2.25% / 365 = 0.00616438

Now, we can use the formula for compound interest:

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

Where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = time in years

In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.

A = 2000(1 + 0.00616438/365)^(365*4)

A = 2000(1.00616438)^1460

A = $2,388.34 (rounded to the nearest cent)

Therefore, the answer is option D) $2,388.34.

Answer:

Data Visualization Tools

Step-by-step explanation:

We can claim that after answering the above question, the  As a result, equation the correct answer is "Milwaukee is near a lake."

In mathematics, an equation is a statement that states the equality of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the sentence "2x + 3" equals the value "9". The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complex equations, regular or nonlinear, with one or more factors are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.  

Milwaukee's average high temperature in the summer is four degrees lower than other cities in its latitude since it is located next to a lake. The lake (Lake Michigan) cools the surrounding areas, notably Milwaukee, which is located on the lake's western shore. This is referred to as the "lake breeze" effect, and it is a regular occurrence in cities located near major bodies of water. As a result, the correct answer is "Milwaukee is near a lake."

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This equation fits the given data: Oy = -2x + 10. The equation creates a linear relationship between the x and y values, with each x value increasing by 1 resulting in a decrease in the y value by 2.

Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.

The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.

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This equation fits the given data: y = 1/3x + 2. The equation creates a linear relationship between the x and y values. Hence the correct option is b.

Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.

The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.

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Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.

To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.

In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:

P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)

Using a calculator or statistical software, we can evaluate this expression to find:

P(X = 7) ≈ 0.170

This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.

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Answer:

The answer to our problem is, $17.75

Step-by-step explanation:

First we need to find out what is 25% of 71

25% of 71 is 17.75. Or [tex]17\frac{3}{4}[/tex] We would need to stick to the term in decimals because of we are using money. Have you ever heard of a fraction in money my guess is no. So let’s stay with decimals. 17.75

How I got it:

25 percent * 71

= (25:100)* 71

= (25* 71):100

= 1775:100

= 17.75

Percentage solution with steps:

71 = 100% (1)

X = 25% (2)

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of bothequations have the same unit (%); we have

[tex]\frac{71}{x} = \frac{25}{100}[/tex]

X = 17.75

Thus the answer to your problem is, $17.75

If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.

Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.

Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800

Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.

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By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.

To construct a 95% CI for the population mean of a normal distribution, we can use the formula:

CI = sample mean ± z* (standard error)

Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:

standard error = population standard deviation / √sample size

In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:

standard error = 5.48 / √20 = 1.226

Now, we can use the formula for the CI:

CI = 10 ± 1.96 x 1.22

Simplifying this expression gives us:

CI = (7.59, 12.41)

This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.

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The coordinates of the image after rotating the figure 180 degrees about the origin are T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

Given that

T'(-4, 3). V'(-5, 5), W'(-2, 5). X(-1, 3)

Rotating a figure by 180 degrees is equivalent to flipping it over the horizontal and vertical axes simultaneously.

This means that the x-coordinate of each point will be negated, and the y-coordinate will be negated as well.

Therefore, to find the coordinates of the image of a point after rotating it by 180 degrees, you can use the following formula:

(x', y') = (-x, -y)

Using the above, the image is

T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

Hence, the image is T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

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Complete question

Rotate the figure 180 degrees about the origin

T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

T'(3, 4). V'(5, 5), W'(5, 2), X '(3. 1) (Th

T'(-3, 4) V(-5. 5), W'(-5, 2). X'(-3, 1)

T'(-3, -4), V'(-5, -5). W(-5, -2), X '(-3, -1)

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

Here, we will use the method of steepest descent to find the minimiser of the function f(x1, x2, x3). The steepest descent method is an iterative optimization algorithm used to find the local minimum of a function.

Step 1: Initialize the starting point (x1, x2, x3) and set the initial values.
Step 2: Compute the gradient of the function f(x1, x2, x3) with respect to each variable (x1, x2, x3). The gradient is a vector that points in the direction of the steepest increase of the function.
Step 3: Calculate the step size, which determines how far along the descent direction we move. This can be done using various techniques, such as line search or a constant step size.
Step 4: Update the current point by moving in the direction of the negative gradient (steepest descent direction) with the computed step size. The new point will be (x1_new, x2_new, x3_new).
Step 5: Check the convergence criteria. If the change in the function value or the variables is below a certain threshold, stop the iteration process. Otherwise, return to Step 2 with the updated point.
By following these steps, the method of steepest descent will help us find the minimizer of the function f(x1, x2, x3).

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