Select the correct answer.
Which graph represents this system of inequalities?
ý <-2x + 4
y < x + 3
x<3

The weakest correlation is represented by the value of c. 0.11.

The weakest correlation is represented by the value that is closest to zero, as it indicates a weaker relationship between the variables. In this case, the answer is: c. 0.11

A correlation coefficient of 0.11 is closer to zero than the other options provided, indicating a weaker correlation compared to the rest. The negative values (-0.75 and -0.27) represent negative correlations, but their magnitudes are larger than 0.11, making them stronger correlations (although still considered weak in general). The positive value of 0.54 represents a moderate positive correlation.

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The solution to the equation is x = 2 and x = -1.

We have,

To solve the equation 1 - 1/x - 2/x = 0, we can simplify it by multiplying through by x² to eliminate the fractions:

x² - x - 2 = 0

Now, we can factor the quadratic equation:

(x - 2)(x + 1) = 0

Setting each factor equal to zero and solving for x:

x - 2 = 0

x = 2

x + 1 = 0

x = -1

The solutions to the equation are x = 2 and x = -1.

Thus,

The solution to the equation is x = 2 and x = -1.

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The solutions to the quadratic equation are x = 2 and x = -1.

To solve the equation 1 - 1/x - 2/x² = 0, we can first multiply the entire equation by x² to eliminate the fractions:

x² - x - 2 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.

Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 1, b = -1, and c = -2. Plugging these values into the quadratic formula, we get:

x = (-(-1) ± √((-1)² - 4(1)(-2))) / (2(1))

x = (1 ± √(1 + 8)) / 2

x = (1 ± √9) / 2

x = (1 ± 3) / 2

This gives us two possible solutions:

x₁ = (1 + 3) / 2 = 4 / 2 = 2

x₂ = (1 - 3) / 2 = -2 / 2 = -1

Therefore, the solutions to the quadratic equation are x = 2 and x = -1.

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Answer:

Step-by-step explanation:

area of triangle = 1/2 * base * height = 1/2 * 9 = 9/2

area  of semicircle = 22/7 * {3 root 2 / 2}^2 = 22/7 *18 / 4 = 22/7 *9/2 = 198/14=99/7

area of figure =  99/7 + 9 /2 =18.6mm2

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Answer:

area of figure= area of semi circle + area of triangle

area of semi circle= 1/2πr²

1/2×3.14×2.12×2.12

1/2×14.11

= 7.06

area of triangle = 1/2×base×height

but I am going to use the Pythagoras theorem to find the its height

= hypotenus² = base²+height²

3²=2.12²+h²

9=4.5+h²

9-4.5=h²

√4.5=√h²

h= 2.12

so area of triangle= 1/2×4.24×2.12

=4.5

area of figure = 70.6+4.5

= 75.1mm²

hope it helps even if its not correct just wanted to try

Answer:

Step-by-step explanation:

To find the explicit formula for the given sequence, we can use the recursive formula and keep substituting until we get a general formula.

a₁ = 4

a₂ = a₁ - 4 = 4 - 4 = 0

a₃ = a₂ - 4 = 0 - 4 = -4

a₄ = a₃ - 4 = -4 - 4 = -8

a₅ = a₄ - 4 = -8 - 4 = -12

a₆ = a₅ - 4 = -12 - 4 = -16

We can see that the sequence is decreasing by 4 each time, and we can write the general formula as:

aₙ = 4 - 4(n - 1)

Simplifying the formula, we get:

aₙ = -4n + 8

Therefore, the explicit formula for the given sequence is aₙ = -4n + 8.

Therefore, the given equation is true and we have successfully proved that the first side is equal to the second side.

Given, A + (AB) = A + B

First we take LHS, then expand using distributive property:

A + (AB) = A + B

=> A + AB = A + B

=> AB = B

Subtracting B from both the sides we get:

AB - B = 0

=> B (A - 1) = 0

So, either B = 0 or (A - 1) = 0.

If B = 0, then both sides are equal as 0 equals 0.

If (A - 1) = 0, then A = 1.

Substituting A = 1, the given equation is rewritten as:(1 + B) = 1 + B => 1 + B = 1 + B

Thus, both sides are equal.

Hence, we can say that the first side is equal to the second side.

Proof: A + (AB) = A + B(1 + B) = 1 + B [As we have proved it in above steps]

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O sin(0.0005) ≈ 0.0005. The line tangent to the graph of f(x) = sin x at (0,0) is y = x.

The line y = x touches the graph of f(x) = sin x at exactly one point, (0,0). This means that the point (0,0) is on the line y = x and the slope of the line y = x is equal to the derivative of the function f(x) = sin x evaluated at x = 0. The slope of the line y = x is 1, so the derivative of f(x) = sin x evaluated at x = 0 is 1.

The line y = x is the best straight line approximation to the graph of f(x) = sin x for x near 0. This is because the first derivative of sin x evaluated at x = 0 is 1, which is the same as the slope of the line y = x. Therefore, the tangent line to the graph of f(x) = sin x at (0,0) is y = x.

Finally, O sin(0.0005) ≈ 0.0005. This is because sin x is approximately equal to x for small values of x. When x = 0.0005, sin x is approximately equal to 0.0005. Therefore, O sin(0.0005) ≈ 0.0005.

In summary, the line tangent to the graph of f(x) = sin x at (0,0) is y = x. The line y = x touches the graph of f(x) = sin x at exactly one point, (0,0). The line y = x is the best straight line approximation to the graph of f(x) = sin x for x near 0. O sin(0.0005) ≈ 0.0005.

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Answer:

10

Step-by-step explanation:

pythagorean theorem

6^2+8^2=d^2

d=10

Identify the function to integrate and the limits of integration, check if the function is elementary, apply the appropriate integration technique, check its validity by differentiating it, substitute them into the antiderivative and evaluate the expression to find the definite integral.

Evaluating integrals involves finding the antiderivative of a function, which is also known as the indefinite integral. Here are the steps to evaluate an integral:

1. Identify the function to integrate and the limits of integration, if any.

2. Check if the function is elementary, meaning that it can be expressed as a combination of basic functions such as polynomials, trigonometric functions, exponential functions, and logarithmic functions. If the function is not elementary, more advanced techniques may be required to evaluate the integral.

3. Apply the appropriate integration technique based on the form of the function to integrate. Some common techniques include u-substitution, integration by parts, trigonometric substitution, and partial fraction decomposition.

4. Once the antiderivative is found, check its validity by differentiating it to make sure it matches the original function.

5. If there were any limits of integration, substitute them into the antiderivative and evaluate the expression to find the definite integral.

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Answer:

(f - g)(x) = (x+3) – ( x² –2)

= (x+3) + ( - x²+2)

= – x²+x +5

(f -g)(3t) = - (3t)² + (3t)+5

= - 9t²+3t+5

I hope I helped you^_^

The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3), and the minima of the given function at the point (-3, -12), and maxima at point (3,2).

A graph can be defined as a pictorial representation or a diagram of any function that represents data or values.

According to the given graph,

We can see that the function is decreasing at the interval (-∞, -3), then the function is increasing at the interval (-3, -1), then the function is decreasing at the interval (-1, 1), the function is increasing at the interval (1, 3), and the function is decreasing at the interval (3, ∞).

The function is decreasing at the interval (-∞, -3) ∪ (-1, 1) ∪ (3, ∞), and the function is increasing at the interval (-3, -1) ∪ (1, 3).

Thus, the minima of the given function at the point (-3, -12), and maxima at point (3,2).

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The distribution of X is (6,11).

Suppose the time it takes your daughter Lizzie to eat an apple is uniformly distributed between 6 and 11 minutes.

Let X represent the time it takes Lizzie to eat an apple.

The distribution of X can be described as follows,

X ~ Uniform(6, 11) which means the time it takes Lizzie to eat an apple, represented by the random variable X, follows a uniform distribution with a minimum value of 6 minutes and a maximum value of 11 minutes. In this distribution, every time interval between 6 and 11 minutes has an equal probability of occurring.

The distribution of X which represents the time it takes Lizzie to eat an apple is uniformly distributed between 6 and 11 minutes.

Therefore, we can write X ~ Uniform(6,11).

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Answer:

Step-by-step explanation: false

It is true that if BD bisects ∠ABC, then D lies in the interior of ∠ABC

There are three types of triangle and they are

Isosceles triangle in which two sides and two angles are same.

Equilateral triangle in which all the sides and angles are equal.

Scalene triangle in which none of the sides and angles are equal.

According to the given question

If BD bisects ∠ABC, then D lies in the interior of ∠ABC and it is true.

If we draw any line from the vertex B which passes through inside the given triangle then it lies in the interior of \(\angle B\).

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The slope of the line is 2 and Jan runs 2 laps for every minute.

The slope of the line is defined as the change in the y-coordinate with respect to the x- coordinate and the formula for slope is given by

Where (x₁, y₁) and (x₂, y₂) are points where the line passes through.

Here we have

The graph shows the number of laps that Jan runs  

From the graph,

The line that represents the situation will pass through (2, 4) and (5, 10)

Using the formula, Slope (m) = (y₂ - y₁) / (x₂ - x)  

Slope of the line = [10 - 4]/[5 - 2 ] = 6/3 = 2

This means that Jan runs 2 laps for every 1 minute  

Therefore,

The slope of the line is 2 and Jan runs 2 laps for every minute.

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False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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Answer:

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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The following are the steps to solve this problem using the Gram-Schmidt process:Step 1:Find the orthogonal basis for span{x, y, 2}.

Step 2:Normalize each vector found in step 1 to get an orthonormal basis for the subspace.Step 1:Find the orthogonal basis for span{x, y, 2}.Take x, y, and 2 as the starting vectors of the orthogonal basis. We'll begin with x and then move on to y and 2.Orthogonalizing x: $v_1 = x = \begin{bmatrix}4\\4\\3.5\\7\\-3\\1\\-0.5\end{bmatrix}$$u_1 = v_1 = x = \begin{bmatrix}4\\4\\3.5\\7\\-3\\1\\-0.5\end{bmatrix}$Orthogonalizing y: $v_2 = y - \frac{\langle y, u_1\rangle}{\lVert u_1\rVert^2}u_1 = y - \frac{(y^Tu_1)}{(u_1^Tu_1)}u_1 = y - \frac{1}{69}\begin{bmatrix}41\\30\\-35\\4\\15\\-10\\-10\end{bmatrix} = \begin{bmatrix}-\frac{43}{23}\\-\frac{10}{23}\\\frac{40}{23}\\\frac{257}{23}\\-\frac{183}{23}\\\frac{76}{23}\\\frac{46}{23}\end{bmatrix}$$u_2 = \frac{v_2}{\lVert v_2\rVert} = \begin{bmatrix}-\frac{43}{506}\\-\frac{10}{506}\\\frac{40}{506}\\\frac{257}{506}\\-\frac{183}{506}\\\frac{76}{506}\\\frac{46}{506}\end{bmatrix}$Orthogonalizing 2: $v_3 = 2 - \frac{\langle 2, u_1\rangle}{\lVert u_1\rVert^2}u_1 - \frac{\langle 2, u_2\rangle}{\lVert u_2\rVert^2}u_2 = 2 - \frac{2^Tu_1}{u_1^Tu_1}u_1 - \frac{2^Tu_2}{u_2^Tu_2}u_2 = \begin{bmatrix}\frac{245}{69}\\-\frac{280}{69}\\-\frac{1007}{138}\\\frac{2680}{69}\\-\frac{68}{23}\\\frac{136}{69}\\-\frac{258}{138}\end{bmatrix}$$u_3 = \frac{v_3}{\lVert v_3\rVert} = \begin{bmatrix}\frac{49}{138}\\-\frac{56}{69}\\-\frac{161}{138}\\\frac{536}{69}\\-\frac{34}{23}\\\frac{17}{69}\\-\frac{43}{138}\end{bmatrix}$

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Answer:

x = 36 degrees

y = 48 degrees

Step-by-step explanation:

The two given triangles are congruent

Hence, we can say that the interior angles are equal

We shall use the angle markings on each of the triangles

Using the markings, we can see that y is 48 degrees

Now, let us find the last angle measure of the first triangle

Mathematically, the sum of angles in a triangle is 180

Thus;

108 + 48 + A = 180

A = 180 - 48 - 108

A = 180 - 156 = 24

Now, the measure 2x-y is equal to this;

Hence;

2x -y = 24

2x = 24 + y

we have that y = 48

2x = 24 + 48

2x = 72

x = 72/2

x = 36 degrees

a. Probability that there are minor fraudulent activities in fewer than 2 out of 100 transactions is 0.1761

b. Using the table, we get the value of probability that there are serious fraudulent activities in fewer than 2 out of 100 transactions  0.9695.

When it comes to fraud detection, it is a necessary tool for banks and credit card companies to help fight fraudulent credit card transactions.

Fraudulent activities have been detected by a fraud detection firm at a rate of 1.31 percent in minor cases and 0.87 percent in serious cases.

To solve this question, we must follow the steps below:

We have to use the binomial distribution formula for solving this question.

The formula for the binomial distribution is: \(P (x) = C (n, x) * p^x * q^(n-x)\)

Where, n = number of trials,

x = number of successes,

p = probability of success,

and q = probability of failure.

Here, for minor fraudulent activities, probability of success,

p = 0.0131;

probability of failure,

q = 1 - 0.0131

= 0.9869;

n = 100.

Thus, for part a, we have to find P (x < 2) = P (0) + P (1).

Now, using the formula mentioned above: \(P (0) = C (100, 0) * (0.0131)^0 * (0.9869)^(100-0) = 0.8581\)

\(P (1) = C (100, 1) * (0.0131)^1 * (0.9869)^(100-1)\)

\(= 0.3172P (x < 2) = P (0) + P (1) = 0.8581 + 0.3172 = 1.1753\)

We can't have a probability greater than 1, so this answer doesn't make sense.

Thus, we have to find 1 - P (x > 1) = 1 - [P (2) + P (3) + ... + P (100)].

We can use the cumulative binomial distribution table to calculate this probability.

We have n = 100 and p = 0.0131. Using the table, we get the value of 0.1761.

b. Probability that there are serious fraudulent activities in fewer than 2 out of 100 transactions is 0.9695.

We will be solving this part using a similar approach as we used in part

a. Probability of success,

p = 0.0087; probability of failure, q = 1 - 0.0087 = 0.9913;

n = 100.

Now, for part b, we have to find P (x < 2) = P (0) + P (1).

Using the formula mentioned above:

\(P (0) = C (100, 0) * (0.0087)^0 * (0.9913)^(100-0)\)

\(= 0.9131P (1)\)

\(= C (100, 1) * (0.0087)^1 * (0.9913)^(100-1)\)

\(= 0.0839P (x < 2)\)

= P (0) + P (1)

= 0.9131 + 0.0839

= 0.9970

We can use the cumulative binomial distribution table to calculate \(1 - P (x > 1) = 1 - [P (2) + P (3) + ... + P (100)].\)

We have n = 100 and p = 0.0087.

Using the table, we get the value of 0.9695.

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Step-by-step explanation:

To make your answer concrete, suppose there will be 30 guests and the genie will tell you either x-bar= 5 cans or M=3 cans. Which of these two measures would best help you determine how many can you should have on hand?

In linear equation the solution set of the equations x = 1/2, y = -3.

What in mathematics is a linear equation?

Multiply both sides of the equation by a

coefficient -  2(4x - 3y ) = 11 × 2

                     3 ( 10x + 2y ) = ( - 1 ) × 3

apply multiplicative distribution law

8x - 6y = 11 × 2

3( 10x + 2y ) = (-1) × 3

calculate the first terms

8x - 6y = 22

3( 10x + 2y ) = ( -1) × 3

remove the parentheses

8x - 6y = 22

30x + 6y = -3

add up the two equation

8x - 6y + ( 30x + 6y ) = 22 + ( -3)

remove parentheses  - 8x - 6y + 30x + 6y = 22 -3

cancel the unknown variables - 8x + 30x = 22 -3

combine like terms - 38x = 22 - 3

calculate the sum or difference - 38x = 19

reduce the greatest common factor on both

sides of equation - 2x = 1

divide both sides of the equation by the coefficient of variable - x = 1/2

substitute one unknown quantity into the elimination 8 * 1/2 - 6y = 22

reduce the expression to the lowest term 4-6y = 22

reduce the greatest common factor on both sides of the equation

2 - 3y = 11

Rearrange unknown terms to the left side of the equation - 2 - 3y = 11

calculate the sum or difference  -3y = 9

reduce the greatest common factor on both sides of the equation   -y = 3

divide both sides of the equation by the coefficient of variable   y = -3

the solution set of the equations

x = 1/2

y = -3

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The length of the rectangular flower whose area is 60 sq. meters garden is 10 meters.

Let's assume the width of the rectangular flower garden is x meters. According to the given information, the length is 4 meters more than the width, so the length can be represented as (x + 4) meters.

The area of a rectangle is calculated by multiplying its length and width. In this case, we know that the area is 60 square meters, so we can set up the following equation:

Area = Length × Width 60 = (x + 4) × x

Expanding the equation, we get: 60 = x² + 4x

Rearranging the equation to the standard quadratic form, we have

x² + 4x - 60 = 0

x² + 10x - 6x - 60 = 0

x(x + 10) - 6(x+ 10) = 0

(x - 6)(x+ 10) = 0

x - 6 = 0 or x + 10 = 0

x = 6 or x = -10

we find that the solutions are x = 6 and x = -10. Since the width cannot be negative, we discard the negative value.

Therefore, the width of the garden is 6 meters.

The length, we can substitute the width value into the expression for the length:

Length = Width + 4 = 6 + 4 = 10 meters.

Hence, the length of the garden is 10 meters.

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Answer:

87.50%

Step-by-step explanation:

You have to find the difference between the two numbers and divide the result by the first number which is 32. Multiply the answer by 100 to get the answer as a percentage!

Answer:32% of 60 = 87.5

Step-by-step explanation:

Answer:

(a)5 and 8

(b)5 and 5

(c) 7 and 5

(d)6 and 2

(e)6 and -2

Step-by-step explanation:

(a)a negative integer

We consider the integers 5 and 8

Difference = 5-8 =-3

3 is a negative integer.

(b)Zero

We consider the integers 5 and 5

Difference = 5-5 =0

(c) an integer smaller than both the integer.

We consider the integers 7 and 5

Difference = 7-5 =2

2 is smaller than both integers.

(d) an integer smaller than only one of the integers.

We consider the integers 6 and 2

Difference =6-2=4

4 is smaller than only 6.

(e)an integer greater than both the integers

We consider the integers 6 and -2

Difference =6-(-2)=6+2=8

8 is greater than both 6 and -2.

Answer:

Last year sale = $14200Increase = 57% x $14200 Increase = 0.57 x 14200 Increase = $8094

$8094

Step-by-step explanation:

Answer:

8094.00 I think. I'm on this question, and it says to round to 100th. I'm not sure why, because it just says 00, and they usualy do not ask you to round if theirs no decimals.

Step-by-step explanation:

Based on the line of best fit, the approximate maximum depth of a lake that has 31 miles of shoreline is; 142.968 ft

The line of best fit is defined as a straight line which is drawn to pass through a set of plotted data points to give the best and most approximate relationship that exists between such data points.

Now, we are given a table of values that shows the total shoreline in miles which will be represented on the x-axis and then the maximum depth of several area lakes which will be represented on the y-axis.

However, when the geologist found the graph, she arrived at an equation of best fit as;

y = 4.26x + 10.908.

Thus, for 31 miles of shoreline, the approximate maximum depth is;

Approximate maximum depth = 4.26(31) + 10.908.

Approximate maximum depth = 142.968 ft

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Answer:

143 feet

Step-by-step explanation:

its technically 142 and change but edmentum rounds up

Step-by-step explanation:

the correct answer is option a 6a-7