A pentagon has sides with lengths given in terms of the variable c; Which of
expressions would represent the perimeter of the pentagon?
(1) 11c
(2) c +11
(3) 48c
(4) c2 + 24

The length of the base of the rectangle is 11.9 yards if it has a perimeter of 57.6 yards.

We can determine the length of the base of the given rectangle by using the following for the perimeter as follows;

P = 2 ( L + W )

Here L represents length, W represents width and P represents the perimeter.

Since the height of the rectangle is 16.9 yards and we have to find the length of the base, the height can be considered to be the width of the rectangle. Therefore;

57.6 = 2 ( L + 16.9 )

57.6 = 2L + 33.8

2L = 57.6 - 33.8

2L = 23.8

L = 23.8 ÷ 2

L = 11.9

Therefore; the length of the base is calculated to be 11.9 yards.

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To determine the probabilities, we need to consider the number of favorable outcomes for each situation divided by the total number of possible outcomes.

1.Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)

2. Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7%

3. Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)

4.Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)

1. Salmon chooses a composite number, a cool color (G, B, I, or V), and an A:

a) Composite numbers between 1 and 100: There are 57 composite numbers in this range.

b) Cool colors (G, B, I, or V): There are 4 cool colors.

c) The letter A: There is 1 A in "INDIANA."

Total favorable outcomes: 57 (composite numbers) * 4 (cool colors) * 1 (A) = 228

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 1 (possible letter) = 700

Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)

2. Federico chooses a prime number, a color starting with a vowel (E or I), and a consonant:

a) Prime numbers between 1 and 100: There are 25 prime numbers in this range.

b) Colors starting with a vowel (E or I): There are 2 colors starting with a vowel.

c) Consonants in "INDIANA": There are 4 consonants.

Total favorable outcomes: 25 (prime numbers) * 2 (vowel colors) * 4 (consonants) = 200

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 5 (possible letters) = 3500

Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7% (rounded to one decimal place)

3. Either chooses a number divisible by 7 or 8, any color, and a vowel:

a) Numbers divisible by 7 or 8: There are 24 numbers divisible by 7 or 8 in the range of 1 to 100.

b) Any color: There are 7 possible colors.

c) Vowels in "INDIANA": There are 3 vowels.

Total favorable outcomes: 24 (divisible numbers) * 7 (possible colors) * 3 (vowels) = 504

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 3 (possible letters) = 2100

Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)

4. Either chooses a number divisible by 5 or 4, blue or green, and L or N:

a) Numbers divisible by 5 or 4: There are 45 numbers divisible by 5 or 4 in the range of 1 to 100.

b) Blue or green colors: There are 2 possible colors (blue or green).

c) L or N in "INDIANA": There are 2 letters (L or N).

Total favorable outcomes: 45 (divisible numbers) * 2 (possible colors) * 2 (letters) = 180

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 2 (possible letters) = 1400

Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)

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Answer:

a mathematical sentence thar has an equal sign

Answer: 5/96

Step-by-step explanation:

You have to solve the following equation

After you use the quadratic formula you would get

t=2.2

That would be the final answer

t=2.2

Option a. calculate a correlation coefficient is the right response because a correlation coefficient measures the strength and direction of the relationship between two interval level variables.

This is because a correlation coefficient measures the strength and direction of the relationship between two interval level variables. It provides a numerical value that ranges from -1 to 1, where -1 indicates a strong negative correlation, 0 indicates no correlation, and 1 indicates a strong positive correlation.

A scatter plot is also useful in visualizing the relationship between two variables, but it does not provide a numerical value like the correlation coefficient. A test of significance and variance calculation are not typically used as first steps in assessing the relationship between two variables.

Hence, option a. calculate a correlation coefficient is the correct answer.

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Answer:

Step-by-step explanation:

5%×g= 5g/100

g-5g/100

Based on the given information, we cannot determine the scale of measure for the age variable in the bar chart. However, we can make some inferences based on the types of scales of measure typically used for age data.

Nominal scale: This scale is used for categorical data, where the values have no inherent order or numerical meaning. For example, if the age variable were categorized into groups like "child," "teen," "adult," and "elderly," this would be a nominal scale.

Ordinal scale: This scale is used for categorical data where the values have a natural order or ranking. For example, if the age variable was categorized into groups like "under 18," "18-24," "25-34," "35-44," and so on, this would be an ordinal scale. The values have a natural order, but the differences between the groups are not necessarily equal.

Interval scale: This scale is used for numerical data where the differences between values are meaningful and consistent, but there is no true zero point.

Ratio scale: This scale is used for bar chart with a true zero point, meaning that a value of 0 represents an absence of the attribute being measured.

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a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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Answer:

D

Step-by-step explanation:

A M function file 'tconvert.m', which can convert coordinates (x, y) into Polar from Cartesian coordinates. is:
"```matlab
function [theta, r] = tconvert(x, y)
```"

To create the M function file 'tconvert.m' that converts Cartesian coordinates (x, y) into Polar coordinates, follow these steps:

1. Open the MATLAB Editor or any text editor and create a new file named 'tconvert.m'.

2. In the file, start with the function declaration line: `function [theta, r] = tconvert(x, y)`.

3. Inside the function, write the conversion code using MATLAB's built-in functions:

  - Calculate the angle theta using `atan2(y, x)`, which returns the angle in radians.

  - Calculate the radius r using `sqrt(x^2 + y^2)`, which gives the distance from the origin.

4. End the function with the `end` keyword.

5. Save the file in a directory accessible by MATLAB.

The function 'tconvert' takes the Cartesian coordinates (x, y) as input and returns the corresponding Polar coordinates (theta, r). The angle theta represents the direction in radians, and the radius r represents the distance from the origin.

The function can be called from the MATLAB command window or from another script or function file.

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Complete question:

Write a M function file 'tconvert.m', which can convert from Cartesian coordinates (x,y) into Polar coordinates.

You have the following list of numbers:

7, 6, 3, 5, 1, 9, 8

In order to determine which of the previous numbers are prime numbers, you consider that a prime number is a number greater than 1, that ONLY can be divided by itself and 1 (to obtain a whole number).

Due to the previous definition, yuo can notice that from the list of numbers, there are three prime number: 7, 3, 5,

The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.

The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.

Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.

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The proportions equal to the ratio 9 : 5 is given by the equation A = 18 : 10 , 27 : 15 and 36 : 20

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the equation will be

A = 9 : 5

Now , the proportion equivalent to the proportion A is given by

A = 9/5   be equation (1)

Multiplying the numerator and denominator by 2 , we get

A = 18/10

So , the value of A = 18 : 10

Now , Multiplying the numerator and denominator by 3 , we get

A = 27/15

So , the value of A = 27 : 15

Now , Multiplying the numerator and denominator by 4 , we get

A = 36/20

So , the value of A = 36 : 20

Hence , the proportion is 9 : 5

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Answer:

C) 4

Step-by-step explanation:

Arcs on one side of the diameter adds upto 180°.

Therefore,

\((2 + 17x) \degree + 54 \degree + 56 \degree = 180 \degree \\ \\ (2 + 17x) \degree + 110 \degree = 180 \degree \\ \\ (2+ 17x) \degree = 180 \degree - 110 \degree\\ \\ (2 + 17x) \degree = 70 \degree \\ \\ 2 + 17x = 70 \\ 17x = 70 - 2 \\ \\ x = \frac{68}{17} \\ \\ x = 4\)

Answer:

Choice C) 4

Step-by-step explanation:

You can do this in multiple different ways but I will do it in the way I believe will be the fastest.

So since we already know everything on one side of the line, we can use that to find x. The line is 180° and since the angles are on the line we know that they will all add up to 180.

For this we will need an equation:

\(2+17x+54+56=180\)

Now we add the like terms:

\(112+17x=180\)

Subtract the 112 on both sides:

\(17x=68\)

Divide the 17 on both sides:

\(x=4\)

The given series is as follows:\[\sum\limits_{n = 1}^\infty  {\frac{{n!}}{{112^n }}} \]We need to determine whether the series is absolutely convergent, conditionally convergent or divergent.Let's proceed to solve it:Absolute Convergence:The series is said to be absolutely convergent if the series obtained

by taking the modulus of each term is convergent.If \[\sum\limits_{n = 1}^\infty  {\left| {\frac{{n!}}{{112^n }}} \right|} \] is convergent, then the series is absolutely convergent.Now,\[\sum\limits_{n = 1}^\infty  {\left| {\frac{{n!}}{{112^n }}} \right|}  = \sum\limits_{n = 1}^\infty  {\frac{{n!}}{{112^n }}} \]Use ratio test to find out whether the given series is convergent or divergent.\[L = \mathop {\lim }\limits_{n \to \infty } \

Hence, the given series is not absolutely convergent.Now, we proceed to the next part of the answer.Conditionally Convergence: A series is said to be conditionally convergent if the series is convergent but not absolutely convergent.Since we have already proved that the given series is not absolutely convergent, we cannot determine whether the given series is conditionally convergent or not.We can conclude that the given series is divergent and not absolutely convergent.

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Let the age of Gabrielle be G

and the age of Mikhail age be M

given: Gabrielle is 15 years younger than Mikhail → G = M - 15

the sum of their ages is 43 → G + M = 43

M - 15 + M = 43

2M = 43 + 15

M = 58/2

M = 29

G = 29 – 15 = 14

Mikhail is 29 years old.

First term (a1) = -7

Second term (a2) = -2

Common difference: a2 - a1 = -2-(-7) = 5

Hence, Fifth term = a1 + 4d = -7 + 4(5) = 13

Answer:

The cost is $.08 per ounce or 8 cents per ounce

Step-by-step explanation:

1 quart = 32 ounces

2 quarts = 64 pints

2 quarts costs 5.12

Take the cost and divide by the number of ounces

5.12 / 64

.08 per ounce

The cost is $.08 per ounce or 8 cents per ounce

=================================================

Explanation:

1 quart = 32 fluid ounces

2 quarts = 64 fluid ounces (multiply both sides by 2)

He paid 5.12 dollars for 64 fluid ounces, so the unit rate is 5.12/64 = 0.08 dollars per fluid ounce, or 8 cents per fluid ounce.

---------

We can think of it this way in terms of an equation

5.12 dollars = 64 fluid ounces

5.12/64 dollars = 64/64 fluid ounces ... divide both sides by 64

0.08 dollars = 1 fluid ounce

We divided both sides by 64 to turn "64 fluid ounces" into "1 fluid ounce", due to how the term "unit rate" is set up. The term "unit" means "one". Basically we're finding the cost per 1 unit, or per 1 fluid ounce.

Answer:

804 cm^2

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr^2

where r is the radius of the circle. Since we are given the diameter of the circle, which is 32 cm, we can find the radius by dividing the diameter by 2:

r = d/2 = 32/2 = 16 cm

Substituting this value into the formula for the area of a circle, we get:

A = πr^2 = π(16)^2 = 256π

To find the approximate value of this expression in square centimeters, we can use the approximation π ≈ 3.14. Therefore:

A ≈ 256(3.14) ≈ 804

Rounding this value to the nearest whole number, we get:

A ≈ 804

Therefore, the area of the circle to the nearest whole number is 804 square centimeters.

The total number of sodium atoms in 92 grams of sodium can be calculated by using Avogadro's number and the molar mass of sodium.

To find the total number of sodium atoms, we need to first calculate the number of moles of sodium in 92 grams. The molar mass of sodium (Na) is approximately 22.99 grams/mol. By dividing the given mass (92 grams) by the molar mass, we can determine the number of moles of sodium.

92 grams of sodium / 22.99 grams/mol = 4 moles of sodium

Next, we can use Avogadro's number, which is approximately 6.022 x 10²³ atoms/mol, to convert the number of moles of sodium into the total number of sodium atoms.

4 moles of sodium x (6.022 x 10^²³ atoms/mol) = 2.409 x 10²⁴ sodium atoms .Therefore, there are approximately 2.409 x 10²⁴ sodium atoms in 92 grams of sodium.

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The correct answer for the Estimate at Completion (EAC) based on the given information is not among the provided options. The calculated EAC = $319,772.19.

Given the following information calculate the EAC and select from the list below. The project is planned for 12 months PV $30000 EV $26000 AC$29000 BAC $252000.The correct answer is option A) $293,023.25.

What is EAC? EAC (Estimate at Completion) refers to the total expected cost of the project. EAC includes the actual cost incurred to date as well as the expected cost required to complete the remaining project work.

The formula for EAC is as follows:

EAC = AC + (BAC - EV) / (CPI * SPI)

EAC= Estimated Cost at Completion, BAC= Budget at Completion, AC= Actual Cost, CPI= Cost Performance Index, SPI= Schedule Performance Index, EV= Earned Value, and PV= Planned Value.

Given, PV (Planned Value) = $30000EV, (Earned Value) = $26000, AC (Actual Cost) = $29000, BAC (Budget at Completion) = $252000.

Now, calculate CPI and SPI.

CPI (Cost Performance Index) = EV / AC = 26000 / 29000 = 0.8965SPI

(Schedule Performance Index) = EV / PV = 26000 / 30000 = 0.8667

Calculate EAC using the following formula:

EAC = AC + [(BAC - EV) / (CPI * SPI)]EAC = 29000 + [(252000 - 26000) / (0.8965 * 0.8667)]

EAC = 29000 + [226000 / 0.7773]

EAC = 29000 + 290772.19

EAC = $319,772.19

Therefore, the correct answer is not in the given options.

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Given the `simplevector.h` definition, the file needs to be modified to implement the template. The updated file with modifications is given below: Updated simplevector.h file templateclass SimpleVector {private: T *aptr; int arraySize; void subError().

The `class` keyword and `template` keyword are used to declare and define a template class `SimpleVector`. The template parameter type is `T`.The implementation is defined inside the class declaration itself. Hence, `SimpleVector::` is prefixed to the function definitions.The member functions include `SimpleVector()` as a constructor, `SimpleVector(int)` as a constructor.

`SimpleVector(const SimpleVector&)` as a copy constructor, `~SimpleVector()` as a destructor, `size()` function to return the size of the array, `operator[]` function to perform subscripting, `print()` function to print the contents of the array, and a private `subError()` function to throw an exception when an index out of bounds error occurs.

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Answer: 32

Step-by-step explanation: 480 divided by 15

Answer:

At least 3 times each because 6 divided by 2 = 3.

Step-by-step explanation:

The three represents how many I think it will land on and plus that would mean 50/50 change it can land on tails and heads each 3 times.

Answer:

Step-by-step explanation:

Probability is expressed as

Number of favorable outcomes/total number of possible outcomes

From the information given,

Total number of outcomes = 16

Starting from 1, the multiples of 3 between 1 and 16 are 3, 6, 9, 12 and 15

This means that the number of favorable outcomes is 5

Therefore, the probability that the card has a multiple of 3 on it is

5/16 = 0.3125

Answer:

13

Step-by-step explanation:

Use the distance formula to determine the distance between two points.

===========================================

Work Shown:

The two given points are \((x_1,y_1) = (4,3)\) and \((x_2,y_2) = (16,8)\)

Use the distance formula

\(d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(4-16)^2+(3-8)^2}\\\\d = \sqrt{(-12)^2+(-5)^2}\\\\d = \sqrt{144+25}\\\\d = \sqrt{169}\\\\d = 13\\\\\)