25 PTS: Given: △PQR, Area of △PQR = 50


m∠Q=90°, m∠P=36° Find: PR

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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Answer:

Step-by-step explanation:

just listen to your teacher and you will be good at subjects

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

The variance of the score for younger women is 0.6875 while that of the older women is 1.4844.

From the complete question, the mean will be:

= (8 + 6 + 6 + 7 + 8 + 7 + 8 + 8) / 8

= 7.25

The variance will be:

= (8 - 7.25)² + (6 - 7.25)² + (6 - 7.25)² + (7 - 7.25)² + (8 - 7.25)² + (7 - 7.25)² + (8 - 7.25)² - (8 - 7.25)² / 8

= 0.6875

The mean of the older women will be:

= (7 + 5 + 8 + 5 + 7 + 6 + 8 + 5) / 8

= 6.375

The variance will be gotten by subtracting the mean from each value and doing it exactly as above. This will be 1.4844.

Lastly, since the variance for younger women is less than that of the older women, the score for younger women is less consistent.

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Answer:

21

Step-by-step explanation:

PEMDAS

Answer:

21

Step-by-step explanation:

remember pedmas.

parenthesis

exponents

division

multiplication

addition

subtraction

(7-4) = 3

5*3 = 15

15*2 = 30

30/3 = 10

10 + 11 = 21

Have a nice day!    :-)

Step-by-step explanation:

a = k/m    or       ma = k    

using 4 and 9     4* 9 = k = 36

then the equation becomes:

    ma = 36    

  using a = 6

      6 * m = 36     shows m = 6 kg

Answer:

43.7 x 0.25 is 10.925

Step-by-step explanation:

To multiply decimals, we can use the following steps:

1. Multiply the numbers as if they were whole numbers, ignoring the decimal points.

2. Count the total number of decimal places in the factors being multiplied. This will be the number of decimal places in the product.

3. Place the decimal point in the product so that it has the same number of decimal places as the total counted in step 2.

Using these steps, we can find the product of 43.7 and 0.25 as follows:

1. 437 x 25 = 10925

2. There are two decimal places in 43.7 and two decimal places in 0.25, so there are a total of four decimal places in the factors being multiplied.

3. Place the decimal point in the product so that it has four decimal places: 10.925

Therefore, the value of 43.7 x 0.25 is 10.925.

The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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Answer:

D

Step-by-step explanation:

Answer:

Between 0 and 1 there is 12, between 1 and 2 there is 112=3/2, and so on. In fact, there are infinitely many fractions between any two whole numbers. Let's see why. Between 0 and 1 there are also 13, 14, 15, and any number that can be written as 1n where n is some whole number.
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Answer:

False

Step-by-step explanation:

In an equation with a variable, whatever you to to one side of the equation you must do to the other side. I am 100% positive on this answer by the way

Answer:

n ≤ 1 or n ≥ 7

Step-by-step explanation:

solve each part separately

86n + 13 ≤ 99 ( subtract 13 from both sides )

86n ≤ 86 ( divide both sides by 86 )

n ≤ 1

n + 90 ≥ 97 ( subtract 90 from both sides )

n ≥ 7

solution is n ≤ 1 or n ≥ 7

Answer:

Total area of pyramid = 113.57 sq units

Step-by-step explanation:

Given that

Pyramid has a regular hexagonal with side, a = 4 units

Slant height = 6 units

To find: Total Area of pyramid = ?

Solution:

Total area of pyramid = Area of hexagon + Area of each triangular face

Area of hexagon is given as:

\(A = 6 \times \dfrac{\sqrt3}{4}a^2\\\Rightarrow A = 6 \times \dfrac{\sqrt3}{4}4^2\\\\\Rightarrow A = 41.57\ sq\ units\)

There are 6 triangular faces with base = 4 units and height as 6 units.

Area of 6 triangular faces:

\(6 \times \dfrac{1}{2} \times Base\times Height\\\Rightarrow 6 \times \dfrac{1}{2} \times 4\times 6\\\\\Rightarrow 72\ sq\ units\)

Total area of pyramid = 41.57 + 72 = 113.57 sq units

The angle that the ramp makes with the ground is approximately 28.07 degrees.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
The sin of the angle θ is the ratio of the opposite side (height of the ramp) to the adjacent side (length of the inclined portion of the ramp):

Sin(θ) = 8/17

We can use a calculator to find the inverse sin of this ratio to get the angle θ:

θ = sin⁻¹(8/17)

θ ≈ 28.07 degrees

Therefore, the angle that the ramp makes with the ground is approximately 28.07 degrees.

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Answer:

Step-by-step explanation:

sp = 504

gain = 12%

in this case

sp =100%+12%=504

112%=504

1%=504/112 =4.5

100%=450

so cost =$450

Hope im correct, if i am im glad to be of service.

we would expect m to be positive.

In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.

Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.

If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.

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Answer:

143/220= 0.65 so 65%

Step-by-step explanation:

Answer:

65%

Step-by-step explanation:

Cross, multiply and divide method has saved my life with these problems, heres how to do it.

Set up like this:

143 x

------- = -------

220 100

Multiply 143 by 100, then divide that by 220.

x= 65, so she has read 65%

tip: you can use a calculator

Hope you could understand.

If you have any query, feel free to ask.

2nd X..

I hope that this is correct

Answer:

3rd

Step-by-step explanation:

If you know about linear eq. it's just a simple rule no worry

The value of x, y and z in the system equation is (1, 2, 3).

The solution of the equation can be determined by using Cramer's rule as follows;

[-5    -6      0] = [ -17]

[-3     -5     5]    [2   ]

[-6    -5      1]     [-13 ]

The determinant of the matrix is calculate as;

Δ = -5 (-5 + 25) + 6(-3 + 30) + 0(15 + 30)

Δ = 62

The x-determinant of the matrix is calculated as follows;

Δx = -17(-5 + 25) + 6(2 + 65) + 0

Δx = 62

The y-determinant of the matrix is calculated as follows;

Δy = -5(2 + 65) + 17(-3 + 30) + 0

Δy = 124

The z-determinant of the matrix is calculated as follows;

Δz = -5(65 + 10) + 6 (39 + 12) - 17(15 - 30)

Δz =  186

The value of x, y and z is calculated as follows;

x = Δx/Δ = 62/62 = 1

y = Δy/Δ = 124/62 = 2

z = Δz/Δ = 186/62 = 3

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The equation for the first option would be

Where "x" is the number of copies and y the cost.

The second equation will be

If we graph both equations we have

As we can see, they will be equal in terms of cost with 2 copies. The cost will be 50.

We can see it at the intersection of the two graphs! we can also do it with algebra, if the costs are equal (same "y") we can say

The number of copies is 2.

Answer:

A unit rate is a comparison of a number to one indifferent unit. It is written as a fraction.

YOU Divide to simplify and always include units

Step-by-step explanation:

Answer:i think its the second one

Step-by-step explanation:

Answer: 4 out of 13

Step-by-step explanation:

Total letters in "MASSACHUSSETT " = 13

Number of S = 4

Probability of an event = \(\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\)

The probability of selecting the  letter S = \(\dfrac4{13}\)  [already in lowest term as gcd(4,13)=1]

Hence, the probability of selecting the  letter S = 4 out of 13.

Answer:

329 degrees F

Step-by-step explanation:

If you plug in your known variables into the calculator, you would get the answer 329 for F. You plug in 165 as C in the equation to find your answer.

Answer:

Refer to the step-by-step explanation.

Step-by-step explanation:

Come up with a monomial expression and solve it.

A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.

Here are a few examples of an monomial expression:

\(\hrulefill\)

Let's work with the monomial expression, 3x²y³z.

To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.

Plug these values into the expression:

3x²y³z

=> 3(3)²(2)³(1)

=> 3(9)(8)(1)

=> 27(8)(1)

=> 216(1)

=> 216

Thus, the expression is solved.

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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