What is the meaning of "[tex]r_{i} \circ r_{j} =r_{i+j}[/tex] for all [tex]i[/tex] and [tex]j[/tex]"?

Answer:

6 units

Step-by-step explanation:

(8, 10 ) → (8, 4 )

since the x- coordinates of each point are the same, both 8

then this is a vertical straight line

the difference is then the absolute value of the difference in the y- coordinates, that is

| 10 - 4 | = | 6 | = 6

or

| 4 - 10 | = | - 6 | = | 6 | = 6

There are 260 students who attend Juniper Middle School. The average daily unexcused absences increased by 25% from September to October.

a. Let's assume that the total number of students at Juniper Middle School is "x."

Given that 55% of the students are in the 8th grade, we can write:

0.55x = number of 8th grade students

And since the remaining 117 students are in 7th grade, we can write:

x - 0.55x = 117

0.45x = 117

x = 260

Therefore, there are 260 students who attend Juniper Middle School.

b. To find the percent change from September to October, we can use the formula:

percent change = ((new value - old value) / old value) x 100%

Substituting the given values, we get:

percent change = ((6 - 4.8) / 4.8) x 100%

percent change = (1.2 / 4.8) x 100%

percent change = 25%

Therefore, the average daily unexcused absences increased by 25% from September to October.

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The surface area of the rectangular prism is 72 square meters.

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional figure that consists of six rectangular faces. It is a polyhedron with two identical and parallel bases, which are rectangles, and four rectangular lateral faces. The height of the prism is the perpendicular distance between the two bases. The volume of a rectangular prism is given by the formula V = l × w × h, where l, w, and h are the length, width, and height of the prism, respectively. The surface area of a rectangular prism is given by the formula SA = 2lw + 2lh + 2wh, where l, w, and h have the same meanings as in the volume formula. Rectangular prisms are commonly encountered in everyday life, such as in the shape of boxes, rooms, and buildings.

The surface area of a rectangular prism can be found by adding up the area of all its faces.

Area of blue rectangles:

= 2 x (length x width)

= 2 x (2.4m x 2m)

= 9.6m²

Area of green rectangles:

= 2 x (length x width)

= 2 x (2.4m x 3m)

= 14.4m²

Area of yellow rectangles:

= 2 x (length x width)

= 2 x (2m x 3m)

= 12m²

Total surface area = sum of all face areas

= (2 x blue rectangles) + (2 x green rectangles) + (2 x yellow rectangles)

= 2(9.6m²) + 2(14.4m²) + 2(12m²)

= 19.2m² + 28.8m² + 24m²

= 72m²

Therefore, the surface area of the rectangular prism is 72 square meters.

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The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.

To design a program in Raptor that prompts the user to enter a person's weight in pounds and height in inches, and then calculates and displays their body mass index (BMI), we can follow these steps:

Start by opening Raptor and creating a new program.

Add three input symbols to prompt the user for their weight, height, and a constant value for BMI. Label each input symbol accordingly.

Add three assignment statements to assign the input values to variables. We can use the labels we assigned to the input symbols as variable names to make the code more readable.

Add two calculation statements to calculate the person's BMI using the formula [tex]BMI = (weight in pounds * 703) / (height in inches)^2.[/tex]Assign the result to the BMI variable.

Add three output symbols to display the person's weight, height, and BMI. We can concatenate strings with the variable values to make the output more informative.

Finally, save the program and run it to test it with different input values.

Here's what the program would look like:

Start

// Prompt the user for weight, height, and BMI

Input "Enter weight in pounds:", weight

Input "Enter height in inches:", height

Input "BMI:", bmi_constant

// Calculate BMI

Set weight_in_kg = weight / 2.205 // Convert weight to kilograms

Set height_in_m = height / 39.37 // Convert height to meters

[tex]Set bmi = weight_in_kg / (height_in_m ^ 2)[/tex] // Calculate BMI

// Display results

Output "Weight: " + weight + " lbs"

Output "Height: " + height + " in"

Output "BMI: " + bmi

Stop

When the program is run, it will prompt the user to enter their weight, height, and a constant value for BMI. It will then calculate the person's BMI using the formula, convert the weight to kilograms and the height to meters, and display the results along with the original weight and height values. The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.

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Answer:

75 degrees

Step-by-step explanation:

Since angle ABD = angle ABC + angle CBD, and we know each of those, we can add them to get the answer.

30+45=75 degrees.

Answer: the movie streaming service offers 80 children's movies

Step-by-step explanation:

     $5.05                                     15

+    $9.05                                     20

+  $13.05                                     25

+  $17.05                                      30

+  $21.05                                 +   35

   $65.25                                  125      

NUMBER OF CUPS SOLD :-125

TOTAL PROFIT:- $65.25

Answer:

a machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate in pounds

per hour does the machine makes nails?

Answer:

2 (x + 8) + 5x.

Step-by-step explanation:

This question is to find the algebraic expression given by words. Call the unknown number x. Then the sum of it and eight is x + 8. Two sets of it means 2 (x + 8). Now that added to five times the number is 2 (x + 8) + 5x. Then, the answer is: 2 (x + 8) + 5x.

To solve this problem, we can use similar triangles. Let's call the height of the building "h". Then, we have two similar triangles: one formed by Ruby, the tree, and the top of the tree; and the other formed by Ruby, the building, and the top of the building.

We know that the height of the tree is 20 feet, and the distance from the tree to Ruby is 31 feet. We also know that the distance from Ruby to the building is 190 feet.

Using these values, we can set up a proportion:

h / (190 + 31) = 20 / 31

Simplifying the proportion, we get:

h / 221 = 20 / 31

Multiplying both sides by 221, we get:

h = (20 / 31) * 221

h ≈ 143.23

Therefore, the height of the building is approximately 143 feet. Rounded to the nearest foot, the height of the building is 143 feet.

Answer:

17,242 cm³

Step-by-step explanation:

Step 1:

Volume of square prism = (area of base) * height

Volume of square prism = (25 * 30) * 25

Volume of square prism = 750 * 25

Volume of square prism = 18,750 cm³

Step 2:

Volume of cylinder = (area of base) * height

Volume of cylinder = (π * (8/2)²) * 30

Volume of cylinder = 16π * 30

Volume of cylinder = 480π

Volume of cylinder ≈ 1,508 cm³

Step 3:

Volume of composite = (Volume of square prism) − (Volume of cylinder)

Volume of composite = 18,750 cm³ − 1,508 cm³

Volume of composite = 17,242 cm³

The substitutions that would be most helpful in evaluating the integral are:

1. C (x = 8 secθ)

2. B (x = 8 sinθ)

3. A (x = 8 tanθ)

4. B (x = 8 sinθ)

5. A (x = 8 tanθ)

For problem 1, the substitution x = 8 secθ will be useful because it will transform the integral into a form that can be solved using the substitution u = tanθ.

For problem 2, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a trigonometric function that can be integrated using standard techniques.

For problem 3, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using integration by parts.

For problem 4, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = cosθ.

For problem 5, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = secθ.

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Answer:

$40+99=136  For 1 week

For 3 weeks it would be $120

Answer:

Step-by-step explanation:

[tex]A=\pi r^2=\pi \times 5^2=25\pi[/tex]

Solution: [tex]A=25\pi[/tex] units²

This means that the lowest goal (LCD) is 72 and that the total of 1/8 and 1/9 stated with one common denominator = 72 is 17/72.

The denominator of a fraction, which represents many spaced evenly out parts are utilized to split an object, is the smallest amount inside the fraction. The fraction is divided by it. The denominator in this situation is 4, suggesting there are four parts altogether.

The fractions mentioned have 8 and 9 as their denominators. Multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80, while multiples of 9 include 9, 18, 27, 36, 45, 54, 63, 72, and 81.

It is evident that 72 will be the first common number of 8 and 9. Hence, for 1/8 and 1/9, its least common factor (LCD) is 72.

We must express every fraction with denominator 72 in order to sum the fraction with a common denominator:

1/8 Equals 9/72 (with multiplying both the numerator and the denominator by 9)

1/9 Equals 8/72 (with multiplying both the denominator and the numerator by 8)

We can now combine the fractions:

1/8 plus 1/9 = 9/72 plus 8/72

= 17/72

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Answer: The answer is -10 :)

Step-by-step explanation:

12)f(x)=2x-6

=》f(3)=2(3)-6

=》6-6=0

f(×)=2x-6

f(0)=-6

=》f(-2)=2(-2)-6

=》-4-6

=-10

13)h(3)=6(3)+2

=》18+2

=20

h(0)=0+2

h=2

(-2)=6(-2)+2

=》-12+2

=-10

Answer: 1.0

Step-by-step explanation:

sohcahtoa means you use sine.

sin(37) = 0.6/x

xsin(37) = 0.6

x = 0.6/sin(37)

x = 0.996

x = 1.0

If I had $14 to spend, the park that I will choose based on the information will be park D where 6 rides cost $16.50

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, if I had $14 to spend, the park that I will choose based on the information will be park D where 6 rides cost $16.50. This is because it's the cheapest.

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The cost per boxed lunch is $9.46.

Answer:

13487 ft³

Step-by-step explanation:

Volume of a Cylinder: 2πr²*h

π = 3.14

r = 9 ft

h = 53 ft

Volume = 2(3.14)(9)²*53 = 13486.86 ft³

Rounded to nearest whole number

Volume of the Cylindrical Water tank is 13487 ft³

Answer:

25%

Step-by-step explanation:

If the cost price could be 100

Then there's A/Q

One-fourth is always 100/4 = 25%

Answer: Formula

Step-by-step explanation:

Stocks x per share = return

Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.

We have,

Purchase price per share: $50

Number of shares purchased: 200

Total purchase cost (excluding loan interest):

Purchase price per share * Number of shares purchased

= $50 * 200

= $10,000

Loan amount: $5,000

Loan interest rate: 10%

Interest paid on the loan:

Loan amount * Interest rate

= $5,000 * 10%

= $500

Total purchase cost (including loan interest):

Total purchase cost + Loan interest

= $10,000 + $500

= $10,500

Selling price per share: $60

Total revenue from selling the stock:

Selling price per share * Number of shares sold

= $60 * 200

= $12,000

Return on investment (ROI):

(Total revenue - Total purchase cost) / Total purchase cost

ROI = ($12,000 - $10,500) / $10,500

Simplifying the expression:

ROI = $1,500 / $10,500

ROI = 0.1429 (approximately)

To express the ROI as a percentage:

ROI as a percentage = 0.1429 * 100 = 14.29%

Therefore,

Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.

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The complete question:

Trey purchases 200 shares of Turner stock for $50 per share.

Trey pays $5,000 in cash and borrows $5,000 from his broker at 10 percent interest to complete the purchase.

One year later, Trey sells the stock for $60 per share.

Trey's return, if the stock paid no dividends during the year, is?

The parameter to describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled is x = 36, p = 0.96 and n = 36. So, the right choice for answer is option (c).

A binomial experiment is an experiment using a fixed number of independent trials with only two outcomes. These experiments'outcomes are defined as either success or failure. The following requirements for experiment are :

Water Quantity in a bottle = 20 ounces

According to bottling company, the percentage of bottle with correct amount = 96% = 0.96

so, probability of success, p = 0.96

Probability for 36 bottles has all bottles properly filled, that is x = 36. Now, looking the all choice, we conclude option(c) is correct choice.

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Answer:

gradient= rise \ run

and cuz line is coming downward

it will be negative

so your answer is

- 5\6

Step-by-step explanation:

3y is not a constant for it has a variable.

However, (2+8) = (10) is a constant

Answer:

70 gold and bronze

Step-by-step explanation:

Add gold at 20 percent and bronze at 50 percent to get 70 percent gold and bronze.

Answer:

Minimum--> 250

Q1--> 255

Q2--> (Median): 307

Q3--> 433

Maximum-->507

Step-by-step explanation:

To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.

First, we need to sort the data set in ascending order:

{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }

Minimum: 250

Maximum: 507

To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.

Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.

Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.

Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.

After 5 hours, there will be 700 gallons of water still in the pool.

Given that, the pool has 1,200 gallons of water and can drain 100 gallons an hour.

After 5 hours, the total amount of water drained from the pool will be 100 gallons per hour times 5 hours, or 500 gallons.

= 100 gallons × 5

= 500 gallons

To find out how much water will still be in the pool, we need to subtract the amount of water drained from the original amount "y":

This forms an equation.

Amount of water still in the pool = original amount - water drained from the pool.

y = 1,200 gallons - 500 gallons

y = 700 gallons

Therefore, 700 gallons of water is still in the pool.

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1. The function that will directly calculate the final price on an item is " a * 0.455".

2. The percentage that is actually being saved by the custumer is 54.5%.

The final price of an item after the discount and coupon can be calculated using the following function:

Final price = a * (1 - 0.35) * (1 - 0.30)

Final price = a * 0.455

This function first applies the 35% discount, which reduces the original price (a) to 65% of its value. Then, it applies the 30% coupon to the discounted price, which reduces it to 70% of its value.

Original price = $100

Sale price (35% off) = $100 * (1 - 0.35)

Sale price (35% off) = $65

Final price = $65 * (1 - 0.30)

Final price = $45.50

Savings = $100 - $45.50

Savings = $54.50

Percentage saved:

= (Savings / Original price) * 100%

= ($54.50 / $100) * 100%

= 54.5%

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