A rectangular room is 5 meters longer than it is wide, and its perimeter is 30 meters. Find the dimension of the room

7π/12 lies in the second quadrant, so we expect cos(7π/12) to be negative.

Recall that

\(\cos^2x=\dfrac{1+\cos(2x)}2\)

which tells us

\(\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1+\cos\left(\frac{7\pi}6\right)}2}\)

Now,

\(\cos\left(\dfrac{7\pi}6\right)=-\cos\left(\dfrac\pi6\right)=-\dfrac{\sqrt3}2\)

and so

\(\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1-\frac{\sqrt3}2}2}=\boxed{-\dfrac{\sqrt{2-\sqrt3}}2}\)

Answer:

A negative correlation means that there is an inverse relationship between two variables - when one variable decreases, the other increases. The vice versa is a negative correlation too, in which one variable increases and the other decreases.

Step-by-step explanation:

The false statement from the stem-and-leaf plot is given as follows:

b. The data for Paul’s group has two modes.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The mode of a data-set is the data-set that appears the most times in a data-set.

Hence, for Paul's group, the mode is given as follows:

44.

As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.

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Answer:

1/4+6

Step-by-step explanation:

Answer:

\(y=80-\frac{8x}{7}\)

Step-by-step explanation:

15). Given equation is,

     \(\frac{x}{7}+ \frac{y}{8}=10\)

     Multiply the equation by 8,

     \(8(\frac{x}{7}+ \frac{y}{8})=10\times 8\)

     \(\frac{8x}{7}+y=80\)

     Subtract \(\frac{8x}{7}\) from both the sides of the equation,

     \(\frac{8x}{7}+y-\frac{8x}{7}=80-\frac{8x}{7}\)

     \(y=80-\frac{8x}{7}\)

     Therefore, value of the variable 'y' will be,

     \(y=80-\frac{8x}{7}\)

First, we need to know that the diagram is symmetric so

the information is given also say that

P(Z > b) = .0768.

the value of b =1.5 we can see the value of b in the graph

a is equal to b but with the opposite sign so

a=-1.5

in order to calculate the are of C

the area of C is 0.43 because

P(Zb)=0.0768

the area C = 0.5- 0.0768=0.43

the can know P(Z>a) because

P(Zb)

the total value of the graph is 1

P(Z>a) = 1-P(Z1-0.0758= 0.92

P(Z>a)=0.92

What is the area of C? 0.43

What is P(Z > a)? 0.92

What is the value of b? 1.5

Answer:

A and D

Step-by-step explanation:

0.45 - 0.23 = 0.22

0.45(8) = 3.60

Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

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Answer: 13, remainder : 3

Step-by-step explanation:

The quotient and remainder of 55 divided by 4 are 13 and 3 respectively.

We have to given that,

To find the quotient and remainder of 55 divided by 4.

We can divide it,

⇒ 55 ÷ 4

4 ) 55 ( 13

  - 4

 -------

    15

  - 12

 ---------

       3

Hence, We get;

After divide,

Quotient = 13

Remainder = 3

Therefore, the quotient and remainder of 55 divided by 4 are 13 and 3 respectively.

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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The standard form of the equation of circle 8 · x + 32 · y + y² = - 263 - x² is the polynomial (x + 4)² + (y + 16)² = 3².

In this question we find the equation of a circle in general form, whose form is:

A · x² + B · y² + C · x + D · y + E = 0

Where A, B, C, D, E are real coefficients.

And we need rewrite it into its standard form, whose definition is:

(x - h)² + (y - k)² = r²

Where:

Now we proceed to derive the equation of the circle in standard form by means of algebra properties:

8 · x + 32 · y + y² = - 263 - x²

x² + y² + 8 · x + 32 · y + 263 = 0

(x² + 8 · x) + (y² + 32 · y) + 263 = 0

(x² + 8 · x + 16) + (y² + 32 · y + 247) = 0

(x² + 8 · x + 16) + (y² + 32 · y + 256) = 9

(x + 4)² + (y + 16)² = 3²

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Answer:

21

Step-by-step explanation:

\(\huge\purple{Hi!}\)

The area of a regular polygon is one-half the product of its apothem and its perimeter.

Given statement solution is :- The actual length of the part is 3751/64 inches.

To find the length of the actual part, you can use the scale factor and the length of the part on the drawing. The formula for finding the actual length is:

Actual Length = Length on Drawing × Scale Factor

In this case, the length on the drawing is given as 3 7/8 inches, and the scale factor is given as 15 ¹/8. Let's calculate the actual length:

Length on Drawing = 3 7/8 inches = (3 × 8 + 7) / 8 = 31/8 inches

Scale Factor = 15 ¹/8

Now we can substitute the values into the formula:

Actual Length = (31/8 inches) × (15 ¹/8)

To perform the multiplication, we can convert the mixed fraction into an improper fraction:

15 ¹/8 = (15 × 8 + 1) / 8 = 121/8

Now we can multiply the fractions:

Actual Length = (31/8) × (121/8)

To multiply fractions, we multiply the numerators together and the denominators together:

Actual Length = (31 × 121) / (8 × 8)

Actual Length = 3751 / 64

Therefore, the actual length of the part is 3751/64 inches.

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Answer:

238

Step-by-step explanation:

299+428-62-106-126-195

727-62-106-126-195

665-106-126-195

559-126-195

433-195

238

Answer:

= 40

Step-by-step explanation:

Calculate within the parentheses:

28 - [10 + (3 + 1) * 2]

= 10

Calculate within the parentheses:

[10 + (3 + 1) * 2]

= 18

Subtract (Left to right):

= 28 - 18

Simplify:

= 4 * 10

Simpliy:

= 40

The expression that represents the correct factorization of the polynomial 8x³  +  125 is (2x + 5) (4x²  -  10x  +  25)

The given polynomial expression is:

8x³  +  125

The expression 8x³  +  125 can be rewritten as (2x)³ + 5³

Applying the sum of cubes formula

\(x^3+y^3=(x+y)(x^2-xy+y^2)\)

(2x)³ + 5³  =  (2x  + 5)( ((2x)² - 2x(5) + 5²)

8x³  +  125 = (2x + 5) (4x²  -  10x  +  25)

Therefore, the expression that represents the correct factorization of the polynomial 8x³  +  125 is (2x + 5) (4x²  -  10x  +  25)

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We have that Supplementary Angles are those angles whose sum is 180 degrees.

If we have For example, msupplementary angles.

mTherefore, the answer is Supplementary Angles.

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Step-by-step explanation:

i hope it's helpful!........

The given shape is a kite, by definition. By definition of a kite, there will be two pairs of adjacent congruent sides. Also note, as it has 4 angles, it's total interior angle measurements will = 360°.

∴ the measurements of B & D can be found by subtracting the measurements for C and A & dividing by 2:

[360 - (32 + 102)]/2 = 113°

m∠B & m∠D would therefore = 113°

Answer:

p=45°, q=45°, s=112.5°

Step-by-step explanation:

Because the triangle is an isosceles right triangle, \(p=q=45^{\circ}\).

In the top triangle, because of the isosceles triangle, the other two angles are each 67.5°.

Therefore, because angles that add to form a straight angle add to 180°, s=112.5°.

Answer:

What is this...?

Step-by-step explanation:

Answer: i think it the sencond one

The measure of arc ILR is 223 degrees

The sum of angle on a straight line is 180 degrees

Given the following parameter

∠ICR = (3x + 5)°, and

∠RCL = (x – 1)°.

Taking the sum:

3x + 5 + x - 1 = 180

4x + 4 = 180

4x = 176

x = 176/4

x = 44

arc ILR = 180 + arcRL
arc ILR = 180 + 44 - 1

arc ILR = 223 degrees

Hence the measure of arc ILR is 223 degrees

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Answer:

E &F

Step-by-step explanation:

The rules of a 30-60-90 Triangle is E, and F is just a different value of numbers (but the same ratio).

Answer:

Top Left

I sincerely hope this is right and that you get g really good mark ;)