Solve. Write your answer in interval notation.
|x + 6| ≥ 3x − 2

Graph if possible. Not necessary tho.

Using visual interpretation of the plot trend, the scatter plot shows positive correlation.

A positive correlation is depicted by a positive slope or trend line on a scatter plot. The trend of the scatter plot slopes upward which establishes a positive association.

If the slope is otherwise negative, such that the trend line slopes downward, then we have a negative association or relationship.

Therefore, the scatter plot shows positive relationship.

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The area of the polygon in the question is: option B - 59 square inches.

Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. He wants to create a home plate for his house. The figure is in the form of a polygon. In order to calculate the area of the polygon, we must first determine the dimensions of the polygon. The figure is made up of two triangles and a square. Pentagon with a square measuring 7 inches by 4 inches and two triangles with heights of 6 inches and 5 inches. The area of a polygon can be found by adding the areas of its individual parts. As a result, we must first determine the area of the square and then the areas of the two triangles. After we've found all of the individual areas, we can add them together to get the polygon's overall area. Given that the square is 7 by 4 inches, the area of the square is calculated as:

7*4 = 28 square inches.

For triangles, area = (1/2) base x height.

Since we only have the height of the triangles, we must first determine the length of their bases. To accomplish so, we must subtract the length of the square from the length of the polygon, which is 6 + 5 = 11 inches.

As a result, the base of the triangle is equal to 11 - 4 = 7 inches for the first triangle and 11 - 7 = 4 inches for the second triangle.

The first triangle's area is 1/2 * 6 * 7 = 21 square inches, while the second triangle's area is 1/2 * 5 * 4 = 10 square inches.

As a result, the area of the polygon is the sum of the areas of the square and the two triangles, or

28 + 21 + 10 = 59 square inches.

Therefore, the correct answer is option B.

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Answer:

YZ DIVIDED BY XY (YZ/XY)

Step-by-step explanation:

By using trigonometry, XZ is the hypotenuse, and XY and YZ are the opposite and adjacent sides.

The tangent of an angle is the opposite over the adjacent.

so it is yz/xy

Answer:

A (0,6)  B (6, 1)  C (2,2)

Step-by-step explanation:

A (4, 4)

  [-4, 2]

Subtract 4 - 4 = 0 and then add 4+2 since both of them are positive. Do it for all of the coordinates

Image Coordinates:

A----->A¹(0,6)

B----->B¹(2,3)

C----->C¹(-2,4)

The marginal product of capital (MPK) for the production function is option (a) \(\frac{1}{2} \frac{AKL^{1/2}}{K}\)

A production function is a mathematical equation that describes the relationship between the inputs used in the production of a good or service and the output that is produced.

Given the production function \(Y = AK^{1/2} L^{1/2}\), where Y represents output, K represents capital, and L represents labor, we need to find the marginal product of capital (MPK).

As we all know that the marginal product of capital (MPC) is the additional output produced by using one additional unit of capital, while holding all other inputs constant.

To find MPK, we take the derivative of the production function with respect to K:

∂Y/∂K = \((1/2)AK^{-1/2}L^{1/2}\)

Simplifying this expression, we get:

MPK = ∂Y/∂K = \(\frac{1}{2} \frac{AKL^{1/2}}{K}\)

Therefore, the correct answer is (a) \(\frac{1}{2} \frac{AKL^{1/2}}{K}\)

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Complete Question:

What is the marginal product of capital (MPK) for the production function \(Y = AK^{1/2} L^{1/2}\)?

a) \(\frac{1}{2} \frac{AKL^{1/2}}{K}\)

b) \(\frac{1}{2} \frac{AKL^{1/2}}{L}\)

c) \(\frac{1}{3} \frac{AL^{1/2} L^{1/2}}{K}\)

d) \(\frac{1}{2} \frac{AL^{1/2} L^{1/2}}{K}\)

Answer:

c) m <2 =m <3

Step-by-step explanation:

since the angles 2 and 3 are equal then they should be alternate angles

then c and d are parallel lines

The given equation is:

qt = a + bt + cd

To estimate the intercept of the trend line in the third quarter, we need to substitute the values into the equation. Here, t represents the quarter number.

The variable d is a dummy variable that takes the value 1 in the second quarter and 0 otherwise. Therefore, in the third quarter, d will be 0.

The results of the estimation are not provided, so we cannot directly determine the values of a, b, or c. However, we can determine the intercept by plugging in the values of the coefficients based on the given options.

Let's go through each option:

Option 1: 24.50 - Incorrect

Option 2: 22.50 - Correct

Option 3: 2.00 - Incorrect

Option 4: 24.36 - Incorrect

Option 5: None of the above

Based on the given options, the correct estimated intercept of the trend line in the third quarter is 22.50.

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The given statement, "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is False.

Explanation: Null space is a linear algebra term used to refer to the set of all vectors that are mapped to the null vector. The solution of Ax=0 is also referred to as the null space or kernel of A. Since the matrix is of size 4x4 and non-zero, it must have at least one non-zero eigenvalue. Any non-zero vector multiplied by this non-zero eigenvalue will result in a non-zero vector, even if it is in the nullspace of the matrix. Because of this, a non-zero 4 x 4 matrix's nullspace can have four or fewer linearly independent vectors.

Hence, the statement "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is false.

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Answer:

\(y=3\)

Step-by-step explanation:

The slope of a line is given as \(m=\frac{\Delta y}{\Delta x}\), where \(\Delta y\) is change in y-value and \(\Delta x\) is change in x-value for any two points the line passes through.

Using the points (0, 3) and (4, 3) as given in the problem, we have:

\(m=\frac{0}{-4}=0\). Therefore, the slope of this line is 0.

In slope-intercept form, we have \(y=mx+b\). Since we've found out that \(m=0\) the entire term \(mx\) will be equal to 0 and we are left with \(y=b\), where \(b\) is the y-intercept. We can plug in the coordinates of any point the line passes through to find this value:

Using the point (4, 3) as given in the problem:

\(3=0(4)+b,\\3=0+b,\\b=3\)

Thus, the equation of our line is \(y=0x+3,\\\boxed{y=3}\)

Answer:

t = 6 km/hour

And, J would be 4 km per hour

Step-by-step explanation:

Let us assume the speed of Tom be T

And, the Speed of Jim  be J

Given that  

T - J = 2 km /hr ...........(i)

After 3 hours distance between them  = 30 km

As they are walking in the opposite direction

Thus,  

Net speed =T + J

L ÷ (T+J) = 3

30 ÷ (T+J) = 3

T +J =10 ..............(2)

After solving these two equations

2T = 12

t = 6 km/hour

And, J would be 4 km per hour

Answer:

b=11/10

Step-by-step explanation:

plug in 11 for "a" and solve for "b"

the height of the triangle formed by the diagonal and base of the TV screen.

The height of the TV is approximately 15.6 inches.

(26 inches / √2) = 18.8 inches

(18.8 inches * √2) = 26 inches

Height = (26 inches / 18.8 inches) * 18.8 inches

Height = 15.6 inches

Step 1: Calculate the hypotenuse of the triangle formed by the diagonal and base of the TV screen.

Hypotenuse = diagonal / √2

Hypotenuse = 26 inches / √2

Hypotenuse = 18.8 inches

Step 2: Calculate the diagonal of the triangle formed by the hypotenuse and base of the TV screen.

Diagonal = hypotenuse * √2

Diagonal = 18.8 inches * √2

Diagonal = 26 inches

Step 3: Calculate the height of the triangle formed by the diagonal and base of the TV screen.

Height = diagonal / base

Height = 26 inches / 18.8 inches

Height = 15.6 inches

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Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.

Answer:

-3 ⅛

Step-by-step explanation:

The time it takes for the beanbag to reach the ground is t = 1 second.

What is quadratic equation ?

A quadratic equation is a expression of the form ax^{2} + bx + c = 0, where x is the variable, and a, b, and c are constants. It is a type of second-degree polynomial equation, which can be solved using various methods, including factoring, completing the square, and using the quadratic formula

We know that the beanbag will touch the ground when its height, h, equals zero. Therefore, we can set the equation for h equal to zero and solve for t:

h = -16t² + 14t + 2

0 = -16t²  + 14t + 2 (substitute h=0)

0 = -8t²  + 7t + 1 (divide both sides by 2)

0 = (t-1)(-8t-1) (factor the quadratic)

So, either t - 1 = 0 or -8t - 1 = 0. Solving for t in each case, we get:

t - 1 = 0 => t = 1

-8t - 1 = 0 => t = -1/8

The negative value of t doesn't make sense in this context, since time cannot be negative. Therefore, the time it takes for the beanbag to reach the ground is t = 1 second.

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Answer:

The outlier in this graph is (4, 55)

Step-by-step explanation:

Outliers can be seen graphically when we first draw a line of best fit. When we draw the line of best fit it connects through the middle of the string of points near the top of our graph. We can see that any given point on the graph is either on the line of best fit or very close to it. This can be said about all points but one... the point (4,55). This point lies far away from the line we've created and can be identified as an outlier for this reason.

Waiting time representing 8th percentile = 299.09 days.

Find values on the left of the mean in this negative Z score table. Table entries for z represent the area under the bell curve to the left of z.

Negative scores in the z-table correspond to the values which are less than the mean.

Let X be the random variable representing the waiting time.

Here the mean(\mu) = 203 days

Standard deviation (\sigma) = 25.7 days

For calculating the 8th percentile, we need to find the z- score having an area of 0.08.

By the Z-score table, we have Z= -3.7

Now, Using the formula X=Z\sigma +\mu

X = (-3.7)*(25.7)+204

X = 299.09 days

Therefore, Waiting time representing the 8th percentile = 299.09 days.

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After solving the given expression the values for x will be equal to x = 1 and x = 13.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given information in the question,

The given equation is,

(x - 7)² = 36

x - 7 = √36

x = ±6

Then the values for x will be,

x1 = 6 + 7 = 17

x2 = -6 + 7 = -1

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Answer:

55

Step-by-step explanation:

40+y+30+y=180

40+2y+30=180

70+2y=180

2y=110

y=55

Checking: 55+40+(55+30) = 55+40+55+30 = 180

The function to find paycheck amount is P = (S - 50)/0.05, where P is Paycheck amount and S is the amount he saves.

The amount Horatio saves is found by taking 5% of his paycheck and adding $50 to it.

This means that the function that can be used to find the amount of his paycheck given the amount he saves can be written as follows:

Paycheck amount = (Amount saved - $50)/0.05

Where, Amount saved = Amount Horatio saves in his paycheck.

Note that the 5% savings in Horatio's paycheck is calculated as a percentage of the paycheck.

Therefore, the amount he saves increases as his paycheck increases and decreases when his paycheck decreases.

Variable definition:

Paycheck amount = P

Amount saved = S

Savings percentage = 5% = 0.05

Fixed amount Horatio saves = $50

In summary, the formula used to find the amount of Horatio's paycheck given the amount he saves is

P = (S - 50)/0.05.

The variables in the formula are P for paycheck amount, S for the amount he saves, 0.05 for the savings percentage, and $50 for the fixed amount he saves.

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Answer:

The function is neither odd nor even.

Step-by-step explanation:

Hope this helps! :D

Answer:

100

Step-by-step explanation:

it is 50 when he sees it in a horizontal line so double it to see how much it is if it where straight

Answer:

n=2

Step-by-step explanation:

Answer:  n = 2

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

The degrees of freedom for a chi-square goodness-of-fit test are calculated as the number of categories minus 1.

Suppose we wish to determine if an ordinary-looking six-sided die is fair, or balanced, meaning that each face has a probability of 1/6

of arrival on top when the die is tossed. We could toss the die dozens, maybe hundreds, of times and compare the actual number of times each face arrival on top to the scheduled number, which would be 1/6

of the total number of tosses. We would not expect each number to be exactly 1/6 of the total, but it should be close.

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The Riemann zeta-function is defined for all complex numbers x with real part greater than 1, that is, the domain of ζ is {x ∈ C : Re(x) > 1}.

However, the zeta function can be analytically extended to a meromorphic function on the whole complex plane except for a simple pole at x = 1, where it has a limit of infinity.

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The number of games that will be played in the first round will be 14 games.

It should be noted that the appropriate function to use in this scenario will be:

= (n - 1) × 2

where n = total number of people participating.

Therefore, this will be:

= (n - 1) × 2

= (8 - 1) × 2

= 7 × 2

= 14

Therefore, the number of games that will be played in the first round will be 14 games.

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Answer:

Jemima is wrong because perimeter is sum of all sides and the perimeter of this figure would be the outer sides of it and not the inner sides.

Answer:

See below.

Step-by-step explanation:

She is wrong because  3 times the perimeter  of one triangle is the sum of 9 sides of the triangles.

In the shape  we see that some of the sides of the triangles are 'shared' and dare not part of the perimeter of the shape,  - the perimeter is only the length of 5 sides of a triangle.

So the perimeter is less than the sum of the sides of the 3  triangles.

The area of one tile in Chanita's pattern is 21 square units.

To determine the area of one tile in Chanita's pattern, we are given that the area is equal to 21 square units. Since the tile is described as triangular, we can infer that it is a right-angled triangle. The area of a triangle can be calculated using the formula: Area = (base × height) / 2. In this case, the given area is 21 square units.

Since we don't have specific values for the base and height, we cannot calculate them directly. However, we can conclude that the base and height must be such that their product equals 42 (2 times the given area). Therefore, the area of one tile in Chanita's pattern is 21 square units.

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