If the length and width of a rectangle are 11 cm and 10 cm, then find its perimeter. OA. 420 cm OB. 21 cm OC. 42 cm OD. 110 cm​

The equation is  [tex]g(x) = -\frac{1}{16} (x - 1)^2 + 2[/tex]  Graphing this equation below, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.

To graph function g, we need to find its equation that satisfies the given properties. We know that the y-intercept of g is less than that of f, so we can choose it to be 1. Also, the parabola of g opens downwards and its vertex is between the two x-intercepts, which are at x = -2 and x = 4. We can use these points to find the equation of the parabola in the standard form: g(x) = a(x - h)² + k. Using the fact that g(0) = 1 and the x-intercepts, we can solve for a, h, and k. The resulting equation is:

[tex]g(x) = -\frac{1}{16} (x - 1)^2 + 2[/tex]

Graphing this equation, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

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Therefore, there are approximately 889 faculty members at the college.

Ratio is a mathematical concept that expresses the relationship between two or more quantities or values. It is a way to compare the size of two numbers, by dividing one number by the other. The result of this division is a numerical expression of the relative size of the two numbers.

Ratios are often expressed as a fraction or a colon (:) between the two numbers. For example, if there are 4 red balls and 6 blue balls in a bag, the ratio of red balls to blue balls can be expressed as 4/6 or 4:6. This means that for every 4 red balls in the bag, there are 6 blue balls.

Ratios are commonly used in various fields, such as finance, statistics, and science, to compare different values and make meaningful interpretations.

To solve this problem, we need to use the ratio between faculty members and students, which is given as 1:18. This means that for every one faculty member, there are 18 students.

If there are 16000 students in the college, we can find the number of faculty members by dividing the number of students by the ratio of students to faculty members:

Number of faculty members = 16000 / 18

This gives us 888.888, but since we are asked to round to the nearest whole number, we should round up to 889. Therefore, there are approximately 889 faculty members at the college.

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Answer:

Step-by-step explanation:

7k+8=71

7k=71-8

7k=63

k=63/7

k=9

-9=3-y

-9+3=y

-6=y

y=-6

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Salut! Comment allez-vous? Comment s'est passée ta journée?

Answer :

Angle A = 19.6°

Step-by-step explanation :

According to the question It is given that,

Angle A = x

Angle B = 5x

Angle C = 4x - 16

We will apply angle sum property in the question.

Angle sum property states that sum of all the angles of triangle is 180°

[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180

[tex]\: :\implies [/tex] x + 5x + 4x - 16 = 180

[tex]\: :\implies [/tex] 10x - 16 = 180

[tex]\: :\implies [/tex] 10x = 180 + 16

[tex]\: :\implies [/tex] 10x = 196

[tex]\: :\implies [/tex] x = 196/10

[tex]\: :\implies [/tex] x = 19.6

Hence,

Angle A = x

[tex]\: :\implies [/tex] 19.6 °

Angle B = 5x5 × 19.6

[tex]\: :\implies [/tex] 98

Angle c = 4x - 16

[tex]\: :\implies [/tex] 4 × 19.6 - 16

[tex]\: :\implies [/tex] 78.4 - 16

[tex]\: :\implies [/tex] 62. 4

We must also check our answer.

Sum of all angles = 180°

[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180

[tex]\: :\implies [/tex] 19.6 + 98 + 62.4 = 180

[tex]\: :\implies [/tex] 117.6 + 62.4 = 180

[tex]\: :\implies [/tex] 180 = 180

Hence, Verified.

Therefore, The Measure of Angle A is 19.6°

Answer:

angle A = 19.6°

Explanation:

angle ABC + angle ACB + angle BAC = 180°

5x + (4x - 16)° + x = 180°

Simplifying:

5x + x + (4x + -16) = 180

Reorder the terms:

5x + x + (-16 + 4x) = 180

Remove parenthesis around (-16 + 4x)

5x + x + -16 + 4x = 180

Reorder the terms:

-16 + 5x + x + 4x = 180

Combine like terms: 5x + x = 6x

-16 + 6x + 4x = 180

Combine like terms: 6x + 4x = 10x

-16 + 10x = 180

Solving

-16 + 10x = 180

Solving for variable 'x'.

Add '16' to each side of the equation

-16 + 16 + 10x = 180 + 16

Combine like terms: -16 + 16 = 0

0 + 10x = 180 + 16

10x = 180 + 16

Combine like terms: 180 + 16 = 196

10x = 196

Divide each side by '10'

x = 19.6

The measure of angle A is 19.6°

The program that would be run in the MARIE Simulator to get the desired output is given below:

The MARIE Program with the given requirements is as follows

ORG 33610

InputStore ID_LAST_DIGIT

Load ID_LAST_DIGIT

Loop:

 Output

 Add ONEStore ID_LAST_DIGIT

  Load ID_LAST_DIGIT

  Subt TEN

Skipcond

800Jump

Loop:

 HaltI

 D_LAST_DIGIT:

 DEC 0ONE:

 DEC 1TEN:

 DEC 10

END

The program starts at 33610.

Input your last university ID digit (e.g., 5)

The program will show numbers from the input to 10.

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The domain of function A and function B are compared by the statement of Option A: The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1.

What is a function?

A function is a fundamental concept in mathematics that relates a set of inputs (also known as the domain) to a corresponding set of outputs (sometimes referred to as the codomain). For each input, there exists exactly one output, and the output can be linked to its corresponding input in a unique manner.

The domain of a function refers to the set of all possible input values for which the function can produce an output.

In Function A, the domain consists of all real numbers greater than 0, since it is a logarithmic function that can take any positive number as an input.

In contrast, the domain of Function B includes all real numbers greater than or equal to 1, since it is a square root function that begins at (1,0) and continues to infinity.

This means that any number greater than or equal to 1 can be used as an input to produce a corresponding output.

It is essential to define the domain of a function accurately to ensure that the function is well-defined and to avoid potential errors or ambiguities in mathematical computations.

Therefore, the correct statement is A.

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The expression of total amount paid in the first 12 months for the big screen TV is C. [tex]\frac{62*(1 - 1.04^{12})}{(1-1.04)}[/tex]

To find the expression of the total amount paid in the first 12 months, we can use the formula for the sum of a geometric series which states: S = a(1-r^n) / (1-r)

Data:

First term (a) is $62

Common ratio (r) is 1.04

We have 12 terms (n) in the series.

Substituting the values, we get:

[tex]S = 62*(1 - 1.04^{12}) / (1-1.04)\\S = 62 * 15.0258054642\\S = 931.59993878\\S = $931.60[/tex]

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The angle SWY is 59°.

What is points of tangency?

Points of tangency is a point When a line is tangent to a circle.

It intersects the circle at exactly one point.

This point is always perpendicular to the radius of the circle which passes through it which means that the tangent line and the radius form a right angle.

The measure of an arc is equal to the measure of the central angle which delete it. This means that if you know the measure of an arc.

We can find the measure of the central angle that subtends it.

If we assume that point Y is on the tangent line and is between point W and point S, then angle SWY is an inscribed angle that intercepts arc WS. In a circle, the measure of an inscribed angle that intercepts an arc is half the measure of the arc.

So, if the measure of arc WS is 118 degrees, then the measure of angle SWY is half of 118 degrees, which is 59 degrees.

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The science class had a higher average of 85 compared to te math's average of 81

Maths class

The function si given as

f(x) = 0.5x + 80

After completing test 2, we have

f(2) = 0.5 * 2 + 80

f(2) = 81

Science class

The function si given as

The table

The equation of the table is

g(x) = 2x + 81

After completing test 2, we have

g(2) = 2(2) + 81

g(2) = 85

This means that the science class had a higher average

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Answer:

Let's call the speed of the bus on the winding road "s". Then we know that the bus traveled at a speed of "s + 20" on the level road. We also know that the time spent on the winding road was 4 hours, so the distance traveled on the winding road is:

distance = speed × time = s × 4

Similarly, the distance traveled on the level road is:

distance = speed × time = (s + 20) × 4

Since the entire trip was 400 miles, we can write:

4s + 4(s + 20) = 400

Simplifying this equation, we get:

8s + 80 = 400

8s = 320

s = 40

Therefore, the speed of the bus on the winding road was 40 mph, and the speed on the level road was 40 + 20 = 60 mph.

To check that this solution is correct, we can calculate the distance traveled on each road:

distance on winding road = 40 × 4 = 160 miles

distance on level road = 60 × 4 = 240 miles

The total distance traveled is indeed 160 + 240 = 400 miles, so our solution is correct.

Therefore, the average speed on the level road was 60 miles per hour.

Okay, here are the steps to solve this problem:

* There are 100 politicians total

* 35 support RK

* 20 support both RK and JS

* So 35 + 20 = 55 support RK in some way

* That means the remaining 100 - 55 = 45 politicians support JS

* So 45 politicians support JS

In summary:

RK supporters: 35

Both RK and JS: 20

Remaining JS supporters: 45

Total politicians: 100

So the answer is:

45 politicians support JS

Let me know if this helps explain the problem and solution. I can provide more details if needed.

Step-by-step explanation:

(x-3)(x-1 +2i)(x-1-2i)        The imaginary roots always come in pairs :   1+- 2i

Answer:

The matrix with row 1 showing 6 and 3 and 10, row 2 showing 8 and 9 and 9, row 3 showing 4 and 7 and 12 can be used to accurately represent the data.

The following matrix that can be used to accurately represent the data is the matrix:

[tex]\left[\begin{array}{ccc}6&3&10\\8&9&9\\4&7&12\end{array}\right][/tex]

A matrix is a collection of numbers, encompassed by brackets.

The numbers are known as matrix elements or entries. The components are organized in rows (horizontal) or columns (vertical), which determine the matrix's size (dimension or order).

As per the question, the entry in row i and column j represents the number of type j clubs offered by school i.

The matrix that can be used to accurately represent the data is the matrix:

[tex]\left[\begin{array}{ccc}6&3&10\\8&9&9\\4&7&12\end{array}\right][/tex]

This is because the rows represent the three different schools, and the columns represent the number of each of the types of clubs they offer.

The given data matches the entries in this matrix, so it can be used to accurately represent the data.

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The 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

A z-score calculates how many standard deviations an observation is from the mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative.

For the 3-year-old boy, the z-score is:

z = (43 - 38) / 2 = 2.5

The z-score for the 10-year-old girl is:

z = (57 - 54.5) / 2.5 = 1

The 3-year-old boy has a higher z-score than the 10-year-old girl, indicating that he is more unusually tall for his age and gender. This is due to his height, which is higher than the average for his age group 38 inches .

Therefore, the 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

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Answer:

Let's call the number we're looking for "x".

The problem states that the quotient of x and 8 is added to 1/2, and the result is 7/8. We can write this as an equation:

x/8 + 1/2 = 7/8

To solve for x, we need to isolate it on one side of the equation.

First, we can simplify the left side of the equation by finding a common denominator of 8:

8(x/8 + 1/2) = 8(7/8)

x + 4 = 7

Next, we can isolate x by subtracting 4 from both sides:

x = 3

Therefore, the number we're looking for is 3.

Answer: 7

Step-by-step explanation:

The answer of the given question based on the image transformation is , (a) reflection over line BC⎯.

Reflection is a transformation in which a figure or an object is flipped across a line or a plane. The line or plane across which  figure is flipped is called line or plane of reflection. In two-dimensional geometry, a reflection can be thought of as a "flip" of the figure over the line of reflection. Any point on the figure that lies on the line of reflection will remain fixed, while all other points will be reflected across the line.

The pre-image ABC was transformed to create image A′B′C′ through a reflection over line BC⎯.

To visualize this transformation, imagine folding the original figure over line BC⎯, so that point A maps to point A′, point B maps to point B′, and point C maps to point C′. The resulting image is the reflection of the original figure over line BC⎯.

The other options listed (90° clockwise rotation around point C, translation up, and translation down) would create different images, but not the image A′B′C′ shown in the diagram.

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Answer:

40

Step-by-step explanation:

In order to find your answer, you would need to multiply -5, by -8 which equals 40.

:)

-5(-8) = 40

Because both the 5 and 8 being multiplied are negative, the commutative multiplication property states that the product should be positive. Since 5*8=40, -5*-8=40

Answer:

Step-by-step explanation:

You take items out of a square root if you have a pair of numbers or if you know the square root.  

[tex]\sqrt{48b^{7} }[/tex]=[tex]\sqrt{4*4*3*bbbbbbb}[/tex]

So I know the [tex]\sqrt{4}[/tex]=2 so i can take both out so outside the root will be 2*2 and inside the root will be 3

Now for the b's for every pair there are, you can take that out.  There are 3 pairs of b's so b³ is outside and one b is left inside.

Answer:

4b³[tex]\sqrt{3b}[/tex]

Answer:

Step-by-step explanation:

substitute:

2(5) + 3(3-5) + 3²     Do PEMDAS  order (parenthesis, exponent, mult/div, add/sub

2(5) + 3(-2) +3²

2(5) + 3(-2) + 9

10 + 3(-2) +9

10-6+9

4+9

13

The average rate of change of a beach ball thrown according to the function[tex]f(x) = 12x - 4.8x^2[/tex] over the interval 0 < x < 2 is -9.6 feet per second.

To find the average rate of change, we need to find the height of the ball at x = 0 and x = 2, and then find the change in height over the time interval.

At x = 0, the height of the ball is:

[tex]f(0) = 12(0) - 4.8(0)^2 = 0[/tex]

At x = 2, the height of the ball is:

[tex]f(2) = 12(2) - 4.8(2)^2 = -19.2[/tex]

The change in height over the time interval 0 < x < 2 is:

-19.2 - 0 = -19.2

Therefore, -19.2/2 = -9.6 feet per second is the average rate of change over the range 0 x 2.

The average change throughout the range of 0 x 2 is therefore -9.6 feet per second.

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Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}[/tex]

Answer:

its 32 square units

Step-by-step explanation:

The Shape is a rectangle. Area of a rectangle is Length x Width

8 x 4 = 32

Answer:

32 Square units

Step-by-step explanation:

You can see that there are 8 spaces of width by using the graph. And 4 spaces of height. So, assuming each space is 1 Square unit. All you have to do is 8×4 which is 32.

Answer:

Step-by-step explanation:

The formula for continuous compound interest is:

A = P(1 + r/100)^t

where A is the amount after t years, P is the principal, r is the annual interest rate as a decimal, and t is the time in years.

In this case, we have P = $380, r = 0.08 (8%), and t = 8 years. Plugging in these values, we get:

A = 380 x (1+8/100)^8

A= 380 x (1+0.08)^8

A=380 x (1.08)^8

A= 380 x 1.8509..

A= $703.35

Therefore, the amount in the account after eight years, rounded to the nearest cent, is  $703.35.

Using the figure the missing sides are

A rectangle is a type of quadrilateral that has four right angles and two pairs of opposite sides that are parallel and equal in length. Some of the properties of a rectangle will b used to find the value of the missing sides as follows

∠ BCD = 90 degrees (All four angles are right angles (90 degrees)).

∠ ABD = 6 degrees (alternate angles are equal)

∠ CBE = 90 - 6  = 84 degrees

∠ ADE = ∠ CBE = 84 degrees (alternate angles are equal)

∠ AEB = ∠ DEC (vertical angles)

∠ DEC = 180 - 6 - 6= 168 degrees (Diagonals are equal, isosceles triangle)

∠ DEA = 180 - ∠ DEC (Linear pair theorem)

∠ DEA = 180 - 168 = 12 degrees

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Answer: the answer is B

Step-by-step explanation:

Part A: For Sky View School: The median is 50. The mean is 50.8. For Riverside School: The median is 20.5. The mean is 9.93. Part B: The variability is For Sky View School: 1,298.16. For Riverside School: 477.0.

Interquartile Range, or IQR, is a measure of a dataset's variability or spread. It is determined by subtracting the dataset's third quartile (Q3) from its first quartile (Q1), where the quartiles divide the dataset into four equally sized segments. When compared to the range, the IQR contains the median 50% of the data and is less impacted by extreme values or dataset outliers. As a result, IQR is a valuable metric for describing a dataset's central tendency and variability.

Part A: The measure of the center is obtained by determining the mean and median for each school.

For Sky View School:

The median is (50 + 50) / 2 = 50.

The mean is 762 / 15 = 50.8.

For Riverside School:

The median is (20 + 21) / 2 = 20.5.

The mean is 139 / 14 = 9.93.

Part B:

The measure of variability is determined using IQR:

For Sky View School:

The range is 96 - 12 = 84.

IQR:

The 25th percentile is the 4th value when the data is arranged in ascending order, which is 20. The 75th percentile is the 12th value, which is 60. So the IQR is 60 - 20 = 40.

Variance is:

Square of mean = -38.8, -33.8, -28.8, -25.8, -25.8, -25.8, -23.8, -20.8, -9.8, -7.8, 11.2, 11.2, 14.2, 21.2, and 45.2.

Now summation of the square of mean is:

19,472.4

Now, dividing by 15 we have:

19,472.4 / 15 = variance of 1,298.16.

For Riverside School:

The range is 25 - 2 = 23.

The 25th percentile is the 4th value when the data is arranged in ascending order, which is 5. The 75th percentile is the 11th value, which is 21. So the IQR is 21 - 5 = 16.

The deviations from the mean are: -19.7, -9.7, -9.7, -9.7, -9.7, -9.7, -9.7, -9.7, 0.3, 0.3, 10.3, 20.3, 20.3, 20.3, 27.3.

The sum of squared deviations is 6678.7.

Variance = 6678.7 / 14 = 477.0

Part C:

If you are interested in a larger class size, Riverside School is a better choice because it has a higher maximum class size (57) compared to Sky View School (69).

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Answer:

Step-by-step explanation:

assuming that every square is 1 unit, the distance from the store to home should be 5 units, I hope this helped

Answer:

[tex] \frac{10}{3} = 10 \div 3 = 3 \frac{1}{3} [/tex]

Answer: Mixed Number Form: 3[tex]\frac{1}{3}[/tex]

Decimal Form: 3.3 repeating

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