DYN
MEDICIN
r
5
In the table below, fill in the empty cell with the corresponding exact measures in radian or degrees.
Angle measure in
radians
9rt/5
3π/4
Angle measure in
degrees
20
275

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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Answer:

B

Step-by-step explanation:

A. There will be bias with this solution as parents that attend the PTO meeting will already know the school well, and are likely to sway the vote.

B. Every 5th person creates unbias, as the Headmaster can not pick who to survey from the list. Therefore, I would argue that this is the best way to survey the parents out of the provided options.

C. We can not infer that every parent waits in the pick-up line, and therefore it would be unfair to carry out the data collection knowing that you are going to miss out on parents' opinions.

D. This completely rules out all students with uneven numbered birthdays for no reason, which is an unfair way of carrying out this survey.

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:

18

Step-by-step explanation:

[tex]x^{2}[/tex] -2x + 3      x = -3

[tex](-3)^{2}[/tex] - 2(-3) + 3

9 + 6 + 3

18

Helping in the name of Jesus.

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.

Part 1) The variables are y, the total cost (dependent variable), and x the charge per day (independent variable).

Part B) A linear equation in a slope-intercept form representing the cost of the campsite is y = 15 + 20x.

A linear equation is an algebraic equation.

A linear equation is written in the form of y = mx+b, where y is the dependent variable, m is the slope and b is the y-intercept or a constant.

The fixed rental fee to reserve the camping site, b = $15

The charge per day (slope), m = $20

Let the number of days the site is rented = x

Total cost, y = 15 + 20x.

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The median would be a better measure to use for his homework grades.

What is the median?

The midway number in a set of data is known as the median. The data should first be arranged and ranked from smallest to greatest. Divide the total number of observations by two to get the midway value. The value in that location is the median if there are an odd number of observations; otherwise, round the number up.

Here, we have

Given: In his history class, Han's homework scores are:

100 100 100 100 95 100 90 100 0

The history teacher uses the mean to calculate the grade for homework.

We have to write an argument for Han.

Median would objectively fair better as a way to calculate grades. The median value doesn't rely on all of the assets that make up the dataset, unlike the mean method would.

The mean sum up every asset, which can lead to it being unreliable. The median, however, is the middle-most value within a list of numbers, which would make it a more accurate method of grading.

Overall, it would make the most sense for Han's history teacher to use the median method for grading homework.

Hence, the median would be a better measure to use for his homework grades.

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The volume of the rectangular prism is  234 cm³

The formula for calculating the volume of a rectangular prism is expressed with the equation

V = Bh

Such that the parameters are enumerated as;

From the information given, we have that;

Substitute the values into the equation

Volume = 36(6.5)

multiply the values, and expand the bracket, we get;

Volume= 234 cm³

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Answer: -20

Step-by-step explanation:

The formula is written as -2 - (-8) + (-14) + 2. Using the following addition and subtraction rules for integers will allow us to simplify this expression:

1.  To add two integers with the same sign, we add their absolute values and then assign the common sign to the sum.

2.  To add two integers with different signs, we find the difference   between their absolute values and assign the sign of the integer with the greater absolute value to the sum.

3.  To subtract an integer, we add its opposite.

Using these rules, we can simplify the given expression as follows:

-2 - (-8) + (-14) + 2

= -2 + 8 - 14 + 2      (using rule 3 for the second term)

= -6 - 14              (combining like terms)

= -20

Therefore, the value of the expression is -20.

The average speed of the Moon's orbit is  593,21 km/h

The average speed is defined as the quotient between distance and time, here we know that:

distance = 384,400 km

time = 27 days = 27*(24 hours)= 648 hours.

Then the average speed will be:

S = 384,400 km/648h

S = 593,21 km/h

That is the average speed of the Moon's orbit.

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First, write the coefficients of the polynomial in order of decreasing degree and include a placeholder for missing terms:

2 -8 -27 14 24

6

Bring down the leading coefficient:

2 -8 -27 14 24

6

2

Multiply the divisor by the result of the previous step and subtract from the corresponding coefficients:

2 -8 -27 14 24

6

2 -12

48

2 -12 21

-42

2 -12 21 -28

168

2 -12 21 -28 192

The result of the division is 2x³ - 12x² + 21x - 28 with a remainder of 192.

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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The values of  x, y, and z in the triangle are y = 7.8, z = 1.25 and x = 3.25

From the question, we have the following parameters that can be used in our computation:

the right triangle

So, we have

y^2 = 7.2^2 + 3^2

Evaluate

y = 7.8

For z, we have

3^2 = 7.2z

So, we have

z = 1.25

For x, we have

x^2 = (z + 7.2)^2 - y^2

So, we have

x^2 = (1.25 + 7.2)^2 - 7.8^2

x = 3.25

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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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To add these two mixed numbers, we first add their whole number parts and then their fractional parts separately.

Whole number parts: 10 + 13 = 23

Fractional parts: 9/12 + 9/12 = 18/12

We can simplify 18/12 by dividing both the numerator and denominator by their greatest common factor, which is 6.

18/12 = (18 ÷ 6) / (12 ÷ 6) = 3/2

Therefore, the sum of 10 9/12 and 13 9/12 is:

23 3/2 or 23 and 1/2.

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.

The answer  is ,  the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.

An integer is a whole number that can be positive, negative, or zero, but does not have any fractional or decimal parts. Integers can be represented on the number line, with zero at the center and positive integers to the right and negative integers to the left.

We  use technique called "stars and bars" to solve this problem.

Using this approach, the number of positive integers less than 1000 with a digit sum of 4 is equal to the number of ways to arrange 4 stars and 3 bars. We can choose the positions of the bars in 7 ways (i.e., there are 7 places where we can place a bar), so the total number of such arrangements is 7 choose 3 (i.e., we choose 3 places for the bars out of the 7 possible places), which is:

7 choose 3 = 7! / (3! * (7-3)!) = 35

Note that we need to subtract the number of solutions that have 0 as the first digit, since we are only looking for positive integers. We can choose the positions of the bars in 6 ways (i.e., we cannot place a bar before the first star), so the number of such arrangements is 6 choose 3, which is:

6 choose 3 = 6! / (3! * (6-3)!) = 20

Therefore, the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.

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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.

After 5 years, the amount owed on the loan will be approximately $15,792.34.

What is compounding?

Compounding refers to the process where interest is earned on both the principal amount and the accumulated interest of an investment. In other words, it is the addition of interest to the principal sum of a loan or deposit, which in turn earns interest in the following periods.

To find the amount owed after 5 years, we can use the formula for compound interest:

[tex]A = P(1 + \frac{r}{n})^{n*t}[/tex]

where:

A = the amount owed after t years

P = the principal (initial amount borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Plugging in the given values, we get:

[tex]A = $7000(1 + 0.18/1)^{1*5}[/tex]

[tex]A = $7000(1.18)^5[/tex]

A ≈ $15,792.34

Therefore, after 5 years, the amount owed on the loan will be approximately $15,792.34.

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Complete question:  Suppose Rita borrows $7000 at an interest rate of 18% compounded each year. Assume that no payments are made on the loan. find the amount owed after 5 years.

Answer:

-6

Step-by-step explanation:

Y + 8 = 2

Subtract 8 from both sides
Y = -6

The 95 percent confidence interval for the true mean metal thickness is [0.290351, 0.290649] (rounded to 4 decimal places).

Confidence level is a statistical phrase that reflects the degree of confidence or reliability associated with an estimated parameter (such as a mean or percentage) generated from a sample of data. It is frequently stated as a percentage and shows the likelihood that the real population parameter falls within a certain confidence range.

Given :

Sample mean ([tex]\mu[/tex]) = 0.2905 mm

Sample size (n) = 59

Standard deviation (σ) = 0.000586 mm

Critical value for 95% confidence level = 1.96 (rounded to two decimal places)

Now,

[tex]\text{Standard error (SE)}= \sigma /\sqrt(n)\\\\SE = 0.000586 / \sqrt(59) = 0.00007613 \;\text{(rounded to 5 decimal places)}[/tex]

Now, for confidence interval;

[tex]\text {Confidence Interval }= \mu \pm Critical \;Value * SE[/tex]

[tex]\text{Confidence Interval} = 0.2905 \pm 1.96 * 0.00007613}\\\\\text{Confidence Interval} = 0.2905 \pm 0.000149 \text{ (rounded to 6 decimal places)}[/tex]

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The expression of the given statement is 2y - 3  = -1

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. The operations of mathematics include multiplication, division, addition, and subtraction.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Let's look at how expressions are written.

The expression of the given statement is 2y - 3  = 4.

Here, let the unknown number = y

Now, product of y and 2 =  2 times  y   =   2y

Also, three less than the product   =  Product - 3

So, three less than the product  of 3 and y =  2 y - 3

Now, this above expression is equivalent to -1.

⇒2 y - 3  = -1

Hence the expression of the given statement is 2y - 3  = -1

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The sentence "Three less than the product of 2 and a number is 4" can be translated into the equation: 2x - 3 = 4

A mathematical statement that demonstrates the equivalence of two expressions is known as an equation.

It has two sides that are divided by the equals sign (=).

Variables, constants, coefficients, operators, and functions can all be used in the expressions on either side of the equation.

Here, x represents the unknown number that we are trying to solve for. The expression "the product of 2 and a number" is represented by 2x, and "three less than" is represented by the subtraction of 3 from that product. This expression is set equal to 4, which is the result given in the original sentence.

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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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Answer:

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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The function that is represented by the graph is y = - [tex]\frac{1}{x}[/tex] + 1, Option C.

Graph functions are mathematical functions that are plotted on a graph, with the input values on the horizontal axis and the corresponding output values on the vertical axis.

They are a visual representation of how the output values of the function change as the input values change.

The function is y = -(1/x) + 1 might be identifies as transformation of the reciprocal function y = 1/x.

we can start by identifying any coordinated we see for both curved lines.
The first curved line has (-1, 2)

The second curved line has (1, 0)

We can cross check if we can find y using the function y = - [tex]\frac{1}{x}[/tex] + 1,

x = -1  therefore

y = (-1/(-1)) + 1 = 2. 2 matches matches the y coordinate (-1, 2).

x = 1 therefore,

y = (-1/1) + 1 = 0. 0 matches the y coordinate (1, 0).

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Answer:

Based on the description, Rhett's drawing of his house is a rectangular prism. A rectangular prism is a three-dimensional figure that has six faces, where each face is a rectangle. In a rectangular prism, opposite faces are congruent and parallel, and adjacent faces meet at right angles.

Answer:

Option C

Step-by-step explanation:

f(x) can be factorised and re-written as (2x+3)(x-2)

g(x) can be re-written as (x+2)(x-2)

On dividing f(x) by g(x): (x-2) cancels out

Quotient: (2x+3)/(x+2)