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The magnitude or length of AB, represented as ||AB||, is calculated using the distance formula resulting in √101.

To sketch AB, plot the initial point A(8, -4) and the terminal point B(-2, -3) on a coordinate plane. Then, draw a line segment connecting these two points. The line segment AB represents the vector AB.

To write AB in component form, subtract the x-coordinates of B from the x-coordinate of A and the y-coordinates of B from the y-coordinate of A. This gives us the vector (-2 - 8, -3 - (-4)), which simplifies to (-10, 1). Therefore, AB can be represented as the vector (-10, 1).

To find the magnitude or length of AB, we can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane. Applying the distance formula to AB, we have √((-2 - 8)² + (-3 - (-4))²). Simplifying the equation inside the square root, we get √(100 + 1), which further simplifies to √101. Thus, the magnitude or length of AB, denoted as ||AB||, is √101.

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Answer:

f(- 2) = - 20

Step-by-step explanation:

Using synthetic division

- 2 | 4    1   - 3   2

      4   - 8   14  - 22

     ------------------------

           - 7   11    - 20 ← f(- 2) = - 20

Answer:7:20

Step-by-step explanation:

Answer & Step-by-step explanation:

Let's start by defining some variables:

M = Mina's age

O = Mina's older sister's age

Y = Mina's younger sister's age

A = Mina's mother's age. We can now use the information given in the problem to set up a system of equations:

O = 2M + 3

Y = 2M - 8

A = 2Y + 10

Grandmother's age = M + O + Y + A

We can substitute the first three equations into the fourth equation to get:

Grandmother's age = M + (2M + 3) + (2M - 8) + (2(2M - 8) + 10)

Simplifying this expression, we get:

Grandmother's age = 9M + 9

Finally, we can substitute M = 7 (Mina's age) to get:

Grandmother's age = 9(7) + 9 = 72 Therefore, Mina's grandmother is 72 years old.

Answer:

Step-by-step explanation:

Function 1 is defined for all x; there's a point on the graph for every x value.  Thus the domain of Function 1 is "all real numbers."  Notice that there is no graph for y smaller than 0.  Thus, the range of Function 1 is [0, infinity).

For which x- and y-values is Function 2 defined?  We see that x can be 0 or greater, and y 0 or greater.  Thus, the domain of Function 2 is [0, infinity), and the range is [0, infinity).

Arc ED is 72 Degrees-A)CED = 72 degrees ,B)ECD = 36 degrees ,C)CDE = 144 degrees, D)CAB = 90 degrees .E)DAB = 90 degrees

The measurements of the angles in the given scenario, we need to apply the properties of angles in a circle.

Given:

- Arc ED is 72 degrees.

- CD is the diameter of the circle.

Using the properties of angles formed by a chord and an arc, we can determine the measurements of the angles as follows:

A. CED:

The angle CED is formed by the arc ED. Since arc ED is given as 72 degrees, the measurement of angle CED is also 72 degrees.

B. ECD:

Angle ECD is an inscribed angle that intercepts arc ED. By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore, angle ECD is half of 72 degrees, which is 36 degrees.

C. CDE:

Angle CDE is formed by the chord CD. It is an opposite angle to angle ECD. Since the sum of opposite angles formed by a chord is always 180 degrees, angle CDE is also 180 - 36 = 144 degrees.

D. CAB:

Angle CAB is formed by the diameter CD. When a diameter of a circle creates an angle with any other point on the circle, the angle is always a right angle (90 degrees). Therefore, angle CAB is 90 degrees.

E. DAB:

Angle DAB is an inscribed angle that intercepts arc CD. Since CD is the diameter of the circle, the intercepted arc CD is a semicircle, which has a measure of 180 degrees. By the inscribed angle theorem, angle DAB is half of 180 degrees, which is 90 degrees.

To summarize:

A. CED = 72 degrees

B. ECD = 36 degrees

C. CDE = 144 degrees

D. CAB = 90 degrees

E. DAB = 90 degrees

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Answer:

x = -1/2, 7

Step-by-step explanation:

2x^2 = 13x + 7

bring everything to one side: 2x^2 - 13x - 7 = 0

factor it out: 2x1 = 2 and -7x1 = -7.

-7x2 = -14 and 1x1 = 1

-14 + 1 = -13, so these numbers work

you end up with (2x + 1)(x - 7) = 0

solve each section:

2x + 1 = 0                         x - 7 = 0

2x = -1                              x = 7

x = -1/2                              

Answer:

Step-by-step explanation:

work with the ratios

2x/x+5 = 3/4

Cross multiply

2x *4 =3(x+5)

8x = 3x + 15 ( minus 3x from both sides)

-3x   -3x

5x = 15

Divide both sides by 5 to isolate the variable

x = 3

Answer:

x equals 1.5/ one point five

Answer:

x+2=11

Step-by-step explanation:

7(x+2)=77

x+2=77/7

x+2=11

Answer:

8

Step-by-step explanation:

pythagorean theorem

The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.

The ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.

12⅝ = 101/8 = 12.645

12.62 = 12.62

√146 = 12.0830

12.39 = 12.39

12¾ = 51/4 = 12.75

Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.

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Answer: 6/5 or 1.2

Step-by-step explanation:

Answer:

6ft = 72 in.

Step-by-step explanation:

1 foot = 12 inches

6 feet = 12 inches * 6 = 72 inches

Let s be Jim's Sister's age now

s = 2x

Answer:

x < 6

Step-by-step explanation:

2x < 12

Divide both sides by 2;

x < 6

x is less than 6

The surface area of the triangular prism with bases that are 4 cm and sides that are 4 cm is 192 cm²

Surface area of a triangular prism = 12 × base × height

= 12 × 4 cm × 4 cm

= 192 cm²

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Answer:

240

Step-by-step explanation:

4 x 2 x 3 = 24 x 10 = 240 milimeters

The amount of paint Jasmine needs to paint the surface of the storage box is 520 ml.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

Storage box:

length = l

breadth = b

height = h

The surface area of a rectangular prism = 2 (lb + bh + lh)

Now,

The storage box is in the shape of a rectangular prism with the dimensions 4 feet by 2 feet by 3 feet.

This means,

length = 4

breadth = 2

height = 3

Now,

The surface area of the storage box.

= 2 (lb + bh + lh)

= 2 (4 x 2 + 2 x 3 + 4 x 3)

= 2 (8 + 6 + 12)

= 2 x 26

= 52 ft²

Now,

If 10 milliliters of paint cover 1 square foot of the storage box.

This means,

1 ft² = 10 ml

Multiply 52 on both sides.

52 ft² = 520 ml

Thus,

520 ml of paint is needed to paint the surface area.

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Answer:

19

Step-by-step explanation:

straight line=180°

180-123=57

57/3=19

19*3=57

Answer:

x = -1

Step by step explanation:

Distribute 6

6x-12= -18

Add 12 to both sides

6x= -6

Divide both sides by 6

x= -1

Hope this helps

There are two main subtypes of quantitative data, which are discrete data and continuous data. Each subtype has different techniques for analysis.

1. Discrete data: This type of data represents whole numbers or counts that can only take specific values. Examples include the number of students in a class or the number of cars in a parking lot. Techniques used to analyze discrete data include:
  a. Frequency distribution: A summary of the number of times each value appears in the dataset.

 b. Measures of central tendency: Calculating the mean, median, and mode of the dataset to understand its central point.

 c. Measures of dispersion: Assessing the range, variance, and standard deviation to understand the spread of the data.

2. Continuous data: This type of data represents measurements that can take any value within a range, such as height, weight, or temperature. Techniques used to analyze continuous data include:

 a. Histogram: A graphical representation of the distribution of the data, using bars to represent the frequency of values within specific intervals.

  b. Probability density function: A mathematical function that describes the probability of a continuous random variable falling within a specific range.

  c. Regression analysis: A statistical method for analyzing the relationship between a dependent variable and one or more independent variables.

Both discrete and continuous data can also be analyzed using inferential statistics, such as hypothesis testing and confidence intervals, to make inferences about a population based on a sample of the data.

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Answer:

Step-by-step explanation:

\(5\frac{1}{6}=\frac{(5*6)+1}{6}=\frac{31}{6}\)

Answer:

31/6 (improper fraction).

Step-by-step explanation:

5 1/6 = (6 × 5) + 1/6 = 31/6

31/6 is the improper fraction.

Equations for common surfaces:

1. Plane: Ax + By + Cz + D = 0

2. Sphere: (x - h)² + (y - k)² + (z - l)² = r²

3. (Elliptic) Paraboloid: z = ax² + by² + c

4. Hyperbolic Paraboloid: z = ax² - by² + c

5. (Circular) Cylinder: (x - h)² + (y - k)² = r²

6. Half Cone: z = √(x² + y²)

For each surface:

1. Plane: The easiest coordinate system to express the equation is the Cartesian coordinate system (x, y, z) since the equation involves linear terms in all three variables.

2. Sphere: The Cartesian coordinate system (x, y, z) is most suitable for expressing the equation of a sphere because it directly relates to the distance between the center of the sphere and any point on its surface.

3. (Elliptic) Paraboloid: The Cartesian coordinate system (x, y, z) is most convenient for expressing the equation of a (elliptic) paraboloid because it allows a direct representation of the quadratic terms in x and y.

4. Hyperbolic Paraboloid: Similar to the (elliptic) paraboloid, the Cartesian coordinate system (x, y, z) is best suited for expressing the equation of a hyperbolic paraboloid due to its direct representation of the quadratic terms.

5. (Circular) Cylinder: The cylindrical coordinate system (ρ, φ, z) is easiest to express the equation of a (circular) cylinder because it naturally separates the radial distance from the axis (ρ) and the angle in the xy-plane (φ).

6. Half Cone: The Cartesian coordinate system (x, y, z) is most suitable for expressing the equation of a half cone since it provides a direct representation of the relationship between the coordinates and the square root of the sum of their squares.

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The average age of the interviewees in the study investigating childhood asthma is 15.2 years.

To find the average age at the interview, you need to follow these steps. Here's how you can calculate it:

First, add up all the ages of the interviewees:18 + 16 + 16 + 17 + 14 + 13 + 15 + 16 + 19 + 12 + 16 + 13 + 13 + 18 + 13 = 228Next, count the total number of interviewees in the study:

15 interviewees

Finally, divide the sum of ages by the number of interviewees: 228 ÷ 15 = 15.2

Therefore, the average age calculated in the study while investigating childhood asthma is approximately 15.2 years.

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Answer:

-2

Step-by-step explanation:

slope = (14-10)/(6-8) = -2

please give brainliest if this helped :)

Answer:

- 2

Step-by-step explanation:

Rate of change

\( =\frac{14 - 10}{6 -8 } = \frac{4}{ - 2} = - 2 \\ \)

The correct sequence of transformations that could be applied to square M to map it to square P is  a reflection over the y-axis followed by a dilation by a factor greater than 1

Reflection over the y-axis reflects the square across the y-axis, effectively switching the positions of the points on the left and right sides of the square.

This is necessary because square M is positioned along the y-axis, while square P is positioned along the x-axis.

After reflecting the square over the y-axis, we need to scale it up to match the size of square P.

Since square P is positioned along the x-axis, which is a greater distance from the origin compared to the y-axis, a dilation by a factor greater than 1 is required to enlarge the square accordingly.

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On solving the provided question we can say that by null hypothesis There is insufficient proof to conclude that student attendance has changed.

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

This is a z-test for a proportion.

\(H0:p=.34 H1:p not=.34\\\alpha=0.01 ... this is a\\2-tailed test\\critical values are +2.58, -2.58\\p=.34 (given) q=1-p=.66\\p^=.33\\z=(p^-p)/sqrt(pq/n)\\z=(.33-.34)/sqrt(.34*.66/8302)\\z=-.01/.0051961\\z=-1.92\)

1.96 does not fall in the reject region

There is insufficient proof to conclude that student attendance has changed.

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