Martin incorrectly said that the slope of this graph is 3 select the correct reasoning to find the slope

Answer:

\(Expression = x + 150 +(- 26)\)

$124 higher

Step-by-step explanation:

Given

\(Deposit = \$150\)

\(Withdrawal = \$26\)

Required

Represent the situation

Determine how much higher or lower is the remaining amount

Let the initial amount in his account be represented with x

When he deposited, the balance becomes

\(Balance = x + 150\)

When he withdrew, the balance becomes

\(Balance = x + 150 + (-26)\)

Hence, the algebraic expression is

\(Expression = x + 150 +(- 26)\)

Calculating how much higher or lower

\(Balance = x + 150 + (-26)\)

Open bracket

\(Balance = x + 150 -26\)

\(Balance = x + 124\)

Recall that the initial amount in the account is x

The difference between the balance and the x is as follows

\(Difference = x + 124 - x\)

\(Difference = \$124\)

Hence, the account has a higher of $124 after both transactions

The area of Mary's rectangular garden in her backyard is 40 1/8 square feet.

To determine the area of the rectangular garden, the length and width measurements must be multiplied, according to the question.A rectangular garden is one that has four corners, each of which forms a right angle. The width and length of a rectangular garden are typically stated in feet or meters.

The formula for finding the area of a rectangular garden is simply A = LW.  A represents the area, L represents the length of the garden, and W represents the width of the garden.The solution for this question will be derived using the formula A = LW, where the length is 7 1/2 feet, and the width is 5 3/4 feet.

A = LW  =  (7 1/2 feet) * (5 3/4 feet)  =  (15/2) * (23/4) = 345/8 ft^2  =  43 1/8 ft^2. Thus, the area of Mary's rectangular garden in her backyard is 40 1/8 square feet.

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Given: f(x) = x^2/ x-8We need to find the critical numbers, the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. .Critical numbers: `x = 0, x = 16`Intervals of increasing: `(-∞, 0)`, `(8, ∞)`Intervals of decreasing: `(0, 8)`Local minima: `(0, 0)`Local maxima: `(16, 32)`

To find the critical numbers, the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema, we need to follow the steps below.Step 1: Find the derivative of f(x) using the quotient rule of differentiation.`f(x) = x^2/(x - 8)`Differentiating both the numerator and denominator we get: `f'(x) = [2x(x - 8) - x^2]/(x - 8)^2 = [-x^2 + 16x]/(x - 8)^2`Step 2: Find the critical numbers by setting `f'(x) = 0` and solving for x.`[-x^2 + 16x]/(x - 8)^2 = 0`We can see that the numerator will be zero when `x = 0 or x = 16`.But, since `(x - 8)^2 ≠ 0` for any real number x, we can ignore the denominator and we get two critical numbers: `x = 0` and `x = 16`.Step 3: Determine the intervals of increasing and decreasing of `f(x)` using the first derivative test.If `f'(x) > 0`, then `f(x)` is increasing.If `f'(x) < 0`, then `f(x)` is decreasing.If `f'(x) = 0`, then there is a local extrema at that point.The critical numbers divide the number line into three intervals: `(-∞, 0)`, `(0, 8)` and `(8, ∞)`.For `x < 0`, we can choose a test value of `-1` to get `f'(-1) > 0`, so `f(x)` is increasing on `(-∞, 0)`.For `0 < x < 8`, we can choose a test value of `1` to get `f'(1) < 0`, so `f(x)` is decreasing on `(0, 8)`.For `x > 8`, we can choose a test value of `9` to get `f'(9) > 0`, so `f(x)` is increasing on `(8, ∞)`.Step 4: Find the local extrema by finding the y-coordinate of each critical number.We need to substitute each critical number into the original function to find the y-coordinate.`f(0) = 0^2/(0 - 8) = 0``f(16) = 16^2/(16 - 8) = 256/8 = 32`Therefore, `f(x)` has a local minimum at `x = 0` and a local maximum at `x = 16`.

We have found the critical numbers, the intervals on which `f(x)` is increasing, the intervals on which `f(x)` is decreasing, and the local extrema of the function `f(x) = x^2/(x - 8)`.

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Step-by-step explanation:

i think its A

Answer:

r(-2) = -5 , r(0) = -7 , r(5) = -12

Step-by-step explanation:

Plug in the numbers for x and then solve. : )

r(-2) = - (-2) - 7

r(-2) = 2 -7

r(-2) = -5

r(0)= -0 -7

r(0)=0-7

r(0) = -7

r(5) = -5 - 7

r(5) = -12

The values of r(x) for x = - 2, 0 and 5 are obtained by Substituting the values for x in the function, hence the values are :

When x = - 2

When x = 0

When x = 5

Therefore, the required values are - 9, - 7 and - 2

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No, the presence of an effect does not necessarily imply that error variance will go away.

The presence of an effect does not necessarily imply that error variance will go away. In fact, error variance is an inherent part of any statistical model and represents the amount of variation in the response variable that is not explained by the predictor variables.

Even if a predictor variable has a significant effect on the response variable, there may still be some unexplained variation in the response that is attributable to error variance.

It is important to take into account and control for error variance in any statistical analysis, as it can affect the precision and accuracy of the estimates of the model parameters and can also influence the interpretation of the results.

One way to control for error variance is to use appropriate statistical methods, such as analysis of variance (ANOVA), regression analysis, or other modeling techniques that take into account the variability in the data.

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Answer:

BC and AD mean the same thing as BCE and CE. Image via Artoba Tours.

Answer:

the other number to get the quotient

A researcher aiming to provide an overview of the gender of respondents in their sample can best achieve this through descriptive statistics and data visualization techniques.

Descriptive statistics, such as frequency distribution, will show the number of occurrences for each gender category, helping to identify patterns and trends. Additionally, calculating the percentage of each gender category in the sample will give a clearer picture of the sample's composition.

To visually represent this information, the researcher can use graphs such as pie charts or bar graphs. Pie charts are effective in displaying proportions of each gender, while bar graphs can illustrate the frequency of each gender category. These visual aids make it easier to comprehend and interpret the data, allowing for a straightforward overview of the gender distribution within the sample.

By combining both statistical and visual methods, the researcher will provide a comprehensive and accessible representation of the gender composition in their sample.

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Answer:

2. When completing the square, add the square of half the coefficient of x to both sides of the equation.

Step-by-step explanation:

1. When completing the square, add the square of half the coefficient of x to only the x^2+bx side of the equation.

False, it is added to both sides

2. When completing the square, add the square of half the coefficient of x to both sides of the equation.

True

3. When completing the square, subtract the square of half the coefficient of x from both sides of the equation.

We add it to both sides

4. When completing the square, add half the coefficient of x to both sides of the equation.

False we add the square to both sides

Answer:

\(\huge \boxed{\mathrm{Option \ 2 }}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

When completing the square, we add the square of half the coefficient of x to both sides of the equation.

\(\Longrightarrow \ \displaystyle ( \frac{b}{2} ) ^2\)

Where b is the coefficient of x in the equation.

\(\rule[225]{225}{2}\)

Answer:

B they equations i are múltiple

Answer:

So first, we figure out the maximum the patient could be taking each day: 2 tabs every 4 hours = 12 tabs per day at the most.

The perimeter (adding up all the sides) of a rectangular piece of land is 228 feet. The length of the land is 74 feet and its width is 154 feet.

The perimeter of a closed plane figure is referred to in geometry. You might have studied perimeter calculations in school. An equilateral triangle has a 27-foot perimeter if each of its nine sides is the same length. The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeter, meters, inches, and feet.

Given,

Perimeter = 228 feet

Length = x

Width = 2x + 6

Perimeter of rectangle = Length + Width

228 = x + 2x + 6

228 = 3x + 6

228 - 6 = 3x

222 = 3x

x = 74

The length of the land is 74 feet and its width is 154 feet.

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Answer:

Y < 3x+2

Step-by-step explanation:

Alright so if you ever get stuck on something like this, Go on demos and put in (0,2) and then add in (-3,-7) and then add in the other answers to see if they match.

So your answer is:

y>3x+2

Answer:

5/4

Step-by-step explanation:

(a) The argument of z, given z = (a + ai)(b√3 + bi), is arg \(z = tan^{(-1)}\)((√3 + 1) / (√3 - 1)) and (b) The cube roots of -32 + 32√3i are 4 * [cos(-π/9) + isin(-π/9)], 4 * [cos(5π/9) + isin(5π/9)], and 4 * [cos(7π/9) + isin(7π/9)].

(a) To determine arg z, we need to find the argument (angle) of the complex number z. Given that z = (a + ai)(b√3 + bi), we can expand this expression as follows:

z = (a + ai)(b√3 + bi) = ab√3 + abi√3 + abi - ab

Simplifying further, we have:

z = ab(√3 + i√3 + i - 1)

Now, we can write z in polar form by finding its magnitude (modulus) and argument. The magnitude of z is given by:

\(|z| = \sqrt(Re(z)^2 + Im(z)^2)\)

Since z = ab(√3 + i√3 + i - 1), the real part Re(z) is ab(√3 - 1), and the imaginary part Im(z) is ab(√3 + 1). Therefore, the magnitude of z is:

\(|z| = \sqrt((ab(\sqrt3 - 1))^2 + (ab(\sqrt3 + 1))^2) = ab\sqrt(4 + 2\sqrt3)\)

To find the argument arg z, we can use the relationship:

arg z = \(tan^{(-1)}\)(Im(z) / Re(z))

Substituting the values, we have:

arg z = tan^(-1)((ab(√3 + 1)) / (ab(√3 - 1))) = \(tan^{(-1)}\)((√3 + 1) / (√3 - 1))

Therefore, the argument of z is arg z = \(tan^{(-1)}\)((√3 + 1) / (√3 - 1)).

(b) To find the cube roots of -32 + 32√3i, we can write it in polar form as:

-32 + 32√3i = 64(cosθ + isinθ)

where θ is the argument of the complex number.

The modulus (magnitude) of -32 + 32√3i is:

| -32 + 32√3i | = √((-32)^2 + (32√3)^2) = √(1024 + 3072) = √4096 = 64

The argument θ can be found using:

θ = arg (-32 + 32√3i) = \(tan^{(-1)}\)((32√3) / (-32)) = tan^(-1)(-√3) = -π/3

Now, to find the cube roots, we can use De Moivre's theorem:

\(z^{(1/3)} = |z|^{(1/3)}\)* [cos((arg z + 2kπ)/3) + isin((arg z + 2kπ)/3)]

Substituting the values, we have:

Cube root 1: \(64^{(1/3)}\) * [cos((-π/3 + 2(0)π)/3) + isin((-π/3 + 2(0)π)/3)]

Cube root 2: \(64^{(1/3)}\) * [cos((-π/3 + 2(1)π)/3) + isin((-π/3 + 2(1)π)/3)]

Cube root 3: \(64^{(1/3)}\) * [cos((-π/3 + 2(2)π)/3) + isin((-π/3 + 2(2)π)/3)]

Simplifying further, we have:

Cube root 1: 4 * [cos(-π/9) + isin(-π/9)]

Cube root 2: 4 * [cos(5π/9) + isin(5π/9)]

Cube root 3: 4 * [cos(7π/9) + isin(7π/9)]

These are the cube roots of -32 + 32√3i. To sketch them in the complex plane (Argand diagram), plot three points corresponding to the cube roots \((-32 + 32 \sqrt 3i)^{(1/3)}\) using the calculated values.

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Let's focus on the point (3,4) which is the upper left-most point of the blue figure. Draw a line through (3,4) and (1,2) which is the point we're rotating the blue figure around. This line goes through (-1,0) which is on figure C. Specifically, it is the lower right-most point of the figure. The rotation flipped things around so to speak (it's not a reflection though).

This trick of drawing a line through the rotation center only works when we are doing 180 degree rotations.

Answer: c

Step-by-step explanation:

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Rounding to the nearest whole value, we get the estimated number of observations above 118 as 2940.

To determine the number of observations expected to be below a certain value using the 68-95-99.7 Rule, we need to find the area under the normal distribution curve up to that value.

For the first scenario:

Mean (μ) = 162

Standard deviation (σ) = 11

Value to evaluate (x) = 195

We want to find the area under the curve to the left of x = 195. This corresponds to the cumulative probability of a value being less than 195 in a normal distribution.

Using a standard normal distribution table or a calculator, we can find that the cumulative probability for x = 195 is approximately 0.961. This means that about 96.1% of the observations are expected to be below 195.

To find the number of observations, we multiply the cumulative probability by the total number of observations:

Number of observations = 0.961 * 2400 = 2306.4

Rounding to the nearest single observation, we get the estimated number of observations below 195 as 2306.

For the second scenario:

Mean (μ) = 137

Standard deviation (σ) = 19

Value to evaluate (x) = 118

We want to find the area under the curve to the right of x = 118. This corresponds to the cumulative probability of a value being greater than 118 in a normal distribution.

Using the same approach, we can find that the cumulative probability for x = 118 is approximately 0.735. This means that about 73.5% of the observations are expected to be above 118.

To find the number of observations, we multiply the cumulative probability by the total number of observations:

Number of observations = 0.735 * 4000 = 2940

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You are c) a structure. A structure is a collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.

A structure is a user-defined data type that allows you to group together related data. For example, you could create a structure to store the name, age, and address of a person. The structure would have three variables, each of a different type: a string variable for the name, an integer variable for the age, and a string variable for the address.

The advantage of using a structure is that it allows you to treat the related data as a single unit. This makes it easier to manipulate the data and to pass the data to functions.

The other answer choices are incorrect. A template is a blueprint for creating a generic class or function. An array is a collection of elements of the same type. Local variables are variables that are declared within a function and that are only accessible within the function.

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Answer:

32 ounces

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

supplementary means angles that add up to 180°

one angle = 155°

other angle = 180° - 155° = 25°

A) 25°

hope this answer helps you......

The three angles of the triangle are approximately 61°, 33°, and 69°.

To find the three angles of the triangle with vertices P(2, 0), Q(0, 3), and R(3, 4), we can use the distance formula and the Law of Cosines.

First, let's calculate the lengths of the sides of the triangle:

Side PQ:
d(PQ) = √((x2 - x1)^2 + (y2 - y1)^2)
= √((0 - 2)^2 + (3 - 0)^2)
= √((-2)^2 + 3^2)
= √(4 + 9)
= √13

Side QR:
d(QR) = √((x2 - x1)^2 + (y2 - y1)^2)
= √((3 - 0)^2 + (4 - 3)^2)
= √(3^2 + 1^2)
= √(9 + 1)
= √10

Side RP:
d(RP) = √((x2 - x1)^2 + (y2 - y1)^2)
= √((2 - 3)^2 + (0 - 4)^2)
= √((-1)^2 + (-4)^2)
= √(1 + 16)
= √17

Next, let's use the Law of Cosines to find each angle:

Angle P:
cos(P) = (d(QR)^2 + d(RP)^2 - d(PQ)^2) / (2 * d(QR) * d(RP))
= (10 + 17 - 13) / (2 * √10 * √17)
= 14 / (2 * √10 * √17)
≈ 0.486

Angle Q:
cos(Q) = (d(PQ)^2 + d(RP)^2 - d(QR)^2) / (2 * d(PQ) * d(RP))
= (13 + 17 - 10) / (2 * √13 * √17)
= 20 / (2 * √13 * √17)
≈ 0.836

Angle R:
cos(R) = (d(PQ)^2 + d(QR)^2 - d(RP)^2) / (2 * d(PQ) * d(QR))
= (13 + 10 - 17) / (2 * √13 * √10)
= 6 / (2 * √13 * √10)
≈ 0.357

Finally, we can find the angles by taking the inverse cosine (arccos) of each value:

Angle P ≈ arccos(0.486) ≈ 61°
Angle Q ≈ arccos(0.836) ≈ 33°
Angle R ≈ arccos(0.357) ≈ 69°

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Answer:

34

Step-by-step explanation:

Because to find the diameter simply multiply the radius by 2

17 x 2 = 34

Hope this helps!

Step-by-step explanation:

1.(first second or third)

By simplification the quadratic function \(y = x^2 + x - 8\) in vertex form is\(y = (x + 1/2)^2 - 33/4\), and its vertex is (-1/2, -33/4).

What is the vertex form of a quadratic equation?

The standard form of a quadratic function is:

\(y = ax^2 + bx + c\)

where a, b, and c are constants and x is the variable.

The vertex form of a quadratic function is:

\(y = a(x - h)^2 + k\)

where a, h, and k are constants and (h, k) is the vertex of the parabola.

To write the quadratic function \(y = x^2 + x - 8\) in vertex form, we need to complete the square. The vertex form of a quadratic function is given by:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

So, first we need to factor out the coefficient of the x^2 term:

\(y = 1(x^2 + x) - 8\)

Now, we need to complete the square for the expression inside the parentheses:

\(y = 1(x^2 + x + 1/4 - 1/4) - 8\)

\(y = 1[(x + 1/2)^2 - 1/4] - 8\)

Finally, we can simplify and write the function in vertex form:

\(y = (x + 1/2)^2 - 33/4\)

Therefore, the quadratic function \(y = x^2 + x - 8\) in vertex form is\(y = (x + 1/2)^2 - 33/4\), and its vertex is (-1/2, -33/4).

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