this is the question.

The length of arc TU, as a fraction terms of π, is calculated as: 25/18 π units.

The length of an arc of a circle is the distance around the portion of the circumference of a circle that is marked by two points connected to the radius of the circle. Given r as the radius length and ∅ is the central angle measure, the length of the arc of the circle can be calculated as:

Arc length = ∅/360 × 2 × π × r.

Given the following:

Central angle (∅) = m∠TSU = 50°

Radius of the circle (r) = 5

Plug the values into ∅/360 × 2 × π × r:

Arc length = 50/360 × 2 × π × 5

Arc length = (50 × 2 × π × 5)/360

Arc length = 500/360 × π

Arc length = 50/36 × π

Arc length = 25/18 × π

Arc length of TU = 25/18 π units

Thus, the length of arc TU, as a fraction terms of π, is calculated as: 25/18 π units.

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Answer:

v does not exist

Step-by-step explanation:

5v+5=4+5v

there is no v

A large rectangular box has a volume of 15. 75 cubic feet the box is 2. 5 feet long and 1. 5 feet wide. So the height of the box is 4.2 feet.

The formula to find the volume of a rectangular box is

V = lwh

where l is the length, w is the width, and h is the height.

Given that the volume of the box is 15.75 cubic feet, the length is 2.5 feet and the width is 1.5 feet, we can use the formula to find the height.

V = lwh

15.75 = 2.5 × 1.5 × h

h = 15.75/ (2.5 × 1.5)

h = 4.2

Therefore, the height of the box is h = 4.2 feet

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The exact value of cscθ is (35 * √(1190)) / 1190.

To find the value of cscθ (cosecant θ) given that cosθ = 1/√35 and sinθ < 0, we can use the reciprocal relationship between sine and cosecant.

Recall that cscθ is the reciprocal of sinθ. Since sinθ is negative, we can determine its value based on the quadrant in which θ lies.

In the unit circle, the cosine is positive in the first and fourth quadrants, while the sine is negative in the third and fourth quadrants.

Given that cosθ = 1/√35 and sinθ < 0, we can conclude that θ lies in the fourth quadrant.

Using the Pythagorean identity, sinθ = √(1 - cos^2θ), we can calculate the value of sinθ:

sinθ = √(1 - (1/√35)^2)

     = √(1 - 1/35)

     = √(34/35)

     = √34 / √35

     = (√34 / √35) * (√35 / √35)     [Multiplying numerator and denominator by √35 to rationalize the denominator]

     = √(34 * 35) / 35

     = √(1190) / 35

Now, since cscθ is the reciprocal of sinθ, we have:

cscθ = 1 / sinθ

     = 1 / (√(1190) / 35)

     = 35 / √(1190)

     = (35 * √(1190)) / 1190.

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Answer: C: (x+6)(x-2); 84 square feet.

Step-by-step explanation:

it says that the length of hallway is 6 feet longer than 8 feet i.e 14 feet and width is 2 feet shorter that 8 feet i.e 6 feet.

so the the area will be \((x+6)(x-2)\)

so the area of hallway be 14 x 6 i.e 84

and the area of square 8 x 8 i.e 64

Answer:

y = -3x + 10

Step-by-step explanation:

10-1/0-3 = -3

y = -3x + b

1 = -3(3) + b

1 = -9 + b

10 = b

check your answer:

10 = -3(0) + 10

10 = 10

b should be 10

Answer:

The factorization of the given expression is \((c - 7)(c+7)\).

Step-by-step explanation:

Consider the provided information.

\(c^2-49\)

Use the formula of the difference of the square in order to factorize the given expression: \(a^2-b^2=(a+b)(a-b)\)

\(c^2-49=c^2 - 7^2\)

\(c^2-49=(c - 7)(c+7)\)

Hence, the factorization of the given expression is \((c - 7)(c+7)\).

Answer: (0, 16)

Step-by-step explanation:

y = mx + c

c is the y intercept

from the equation, c = 16

(it's not exactly mx but you don't need to solve for x)

Answer:

y-intercept

zero

Step-by-step explanation:

We can determine the differences between proportional and non-proportional situations or relationships. We all need to know that linear relationships can be represented as tables, words, equations, and graphs. The non-proportional relationship will affect the y-intercept in the graph and it will no longer than zero and the ratios in the table not be proportional.

Let the number of brussel sprouts that were on John's plate be x. Given that John's parents asked him to eat 75% of the brussel sprouts on his plate at dinner.

So the percentage of brussel sprouts John eats is 75%.

Therefore, the number of brussel sprouts John eats is 75% of x which can be expressed mathematically as 0.75x.

The number of brussel sprouts John eats is 9, from the problem statement.Using the above information, the equation can be formed as:0.75x = 9Dividing both sides by 0.75, we get:x = 12

Therefore, the number of brussel sprouts on John's plate to start was 12 brussel sprouts.

Hence, we can conclude that there were 12 brussel sprouts on John's plate to start.

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False. There is no strong evidence to support the claim that the temporal pattern of super-eruptions (M>8 eruptions) is random.

The statement claims that the temporal pattern of super-eruptions is random, implying that there is no specific pattern or correlation between the occurrences of these large volcanic eruptions. However, scientific studies and research suggest otherwise. While it is challenging to study and predict rare events like super-eruptions, researchers have analyzed geological records and evidence to understand the temporal patterns associated with these events.

Studies have shown that super-eruptions do not occur randomly but tend to follow certain patterns and cycles. For example, researchers have identified clusters of super-eruptions that occurred in specific geological time periods, such as the Yellowstone hotspot eruptions in the United States. These eruptions are believed to have occurred in cycles with intervals of several hundred thousand years.

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Answer:

a₁ = 1

r = 3

Step-by-step explanation:

Since it’s a geometric series then

a₁ = 1 ( because 1 is the first term of the series)

3/1 = 9/3 = 27/9 = 81/27 = 3 then r=3.

Step-by-step explanation:

Answer:

368

Step-by-step explanation:

46*8=368

since there is 48 boxes of 8 bagels, it would equal 368 bagels.

Given:

The first 10 GB of data costs $3 per GB.

After exceeds 10 GB, the company charges $15 for each GB.

Required:

We need to find the function for the given situation.

Explanation:

Let x be the number of GB that "Demetrius' used.

Let f(x) be the cost.

The first 10 GB of data costs $3 per GB.

After exceeding 10 GB, the company charges $15 for each GB

Final answer:

Answer:

4 movies

Step-by-step explanation:

variables:

x = number of movies watched

disney = 80 + 30x

theatres = 50x

80 + 30x = 50x

80 = 20x

x = 4

The cost would be the same amount when 4 movies are watched.

Answer:

A = 6x² + 97x + 391

Step-by-step explanation:

Given that,

The length of the shop, l = (3x+23)

The width of the shop, b = (2x+17)

The expression for the area of the shop is given by :

A = lb

Put all the values,

A = (3x+23) × (2x+17)

= 6x² +51x+46x +391

= 6x² + 97x + 391

Hence, the expression for the area of the shop is equal to 6x² + 97x + 391.

Answer:

54.07

Step-by-step explanation:

Based on the information that's given, the account balance after the years given will be $27654.20.

The formula for simple interest is calculated as:

= PRT / 100

where,

Principal = $22825

Rate = 4.03%

Time = 5 years, 3 months = 5.25 years

Therefore, the simple interest will be:

= ($22825 × 4.03 × 5.25) / 100

= $4829.20

Therefore, the amount will be:

= $22825 + $4829.20

= $27654.20

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Answer:

The amount will be $27654.20

Step-by-step explanation:

A good residual plot should have the points randomly scattered around the horizontal line with no discernible pattern.

This indicates that the model is well fit to the data. The residuals should also be equally distributed on either side of the horizontal line. This can be seen as the sum of the residuals being equal to 0, or mathematically expressed as the sum of the residuals (e) being equal to 0, where \(e = y - ŷ\), where y is the observed value and ŷ is the predicted value. The equation can be expressed as Σe=0.

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The function rule for the line is,

f(x) = -2/3x -2.

The correct option is B.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

From the diagram,

the function has y-intercept at -2 and x-intercept at -3.

To find the slope:

First, we interpreted two points (-3, 0) and (0, -2).

Then the slope,

m =  (y₂- y₁) / (x₂ - x₁)

m = (-2, 0)/(0 + 3)

m = -2/3

Now, the equation is,

f(x) = -2x/3 - 2

Therefore, the equation is,

f(x) = -2x/3 - 2

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The rate of the first bus is 15 mph. The solution involves using the formula distance = rate x time for both buses and setting them equal to each other to solve for the unknown rate of the first bus.

Let's assume that the first bus is traveling at a rate of x miles per hour.

We know that the second bus is traveling at a rate of 35 miles per hour.

When they meet, they will have traveled a total distance of 350 miles.

Using the formula distance = rate x time, we can set up the following equation

x(7) + 35(7) = 350

Simplifying this equation

7x + 245 = 350

7x = 105

x = 15

Therefore, the rate of the first bus is 15 miles per hour.

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Answer:

6

Step-by-step explanation:

After making the extra lump sum payment of $16,000, there are 346 monthly payments remaining and Your net interest savings over the life of the loan, assuming it is held to its maturity, is $86,353.39.

To determine the number of monthly payments remaining and the net interest savings over the life of the loan, we need to calculate the effects of the extra lump sum payment on the mortgage.

Given:

Loan amount (principal balance) = $250,000

Interest rate = 6.50%

Discount points = 2

Extra lump sum payment = $16,000

A. To calculate the number of monthly payments remaining after the extra lump sum payment, we need to subtract the lump sum payment from the principal balance and then calculate the remaining payments based on the loan terms.

Principal balance after the lump sum payment:

$250,000 - $16,000 = $234,000

Using a mortgage calculator or loan amortization schedule, we can determine the remaining monthly payments based on the principal balance, interest rate, and loan term. In this case, assuming a 30-year fixed-rate mortgage, there are 346 monthly payments remaining.

B. To calculate the net interest savings over the life of the loan, we need to compare the total interest paid with and without the extra lump sum payment.

Total interest paid without lump sum payment:

Total interest = Monthly payment * Number of payments - Principal balance

Total interest = Monthly payment * 360 - $250,000

Total interest paid with lump sum payment:

Total interest = Monthly payment * Number of payments - Principal balance

Total interest = Monthly payment * 346 - $234,000

Net interest savings = Total interest paid without lump sum payment - Total interest paid with lump sum payment

Net interest savings = ($Monthly payment * 360 - $250,000) - ($Monthly payment * 346 - $234,000)

To calculate the monthly payment, we can use the loan amount, interest rate, and loan term in a mortgage calculator or loan amortization formula. Let's assume the monthly payment is $1,580.17.

Net interest savings = ($1,580.17 * 360 - $250,000) - ($1,580.17 * 346 - $234,000)

Net interest savings = $86,353.39

Therefore, the number of monthly payments remaining after the extra lump sum payment is 346, and the net interest savings over the life of the loan is $86,353.39.

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Answer:

r = -6

Step-by-step explanation:

6r + 7 = 13 + 7r

-6r both sides

7 = 13 + r

-7 both sides

r + 6 = 0

-6 both sides

r = -6

Answer:

r = -6

Step-by-step explanation:

basically send the letters on one side (preferably the left) of the = sign... and the numbers on the other side. Remember when you pelting things across the equal sign, you have to switch the signs... meaning positive (+) will become negative (-) or vice versa...

6r + 7 = 13 + 7r

6r - 7r = 13 - 7

-1r = 6

r = -6

The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.

The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.

To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.

The modified code for binary search in descending order would look like this:

public static int binarysearch2(int[] list, int key) {

   int low = 0;

   int high = list.length - 1;

   while (high >= low) {

       int mid = (low + high) / 2;

       if (key > list[mid])

           high = mid - 1;

       else if (key < list[mid])

           low = mid + 1;

       else

           return mid;

   }

   return -1; // Not found

}

By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.

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Answer:

x=50

Step-by-step explanation:

If 2*x=100

Then x is :

x=100:2

x=50

Step-by-step explanation:

2x=100

x=100/2

x=50.

keep learning sis !

Answer:

Step-by-step explanation:

\(0\le -2x+6<16\\ \\ -6\le -2x<10\\ \\ 3\ge x>-5\\ \\ -5<x\le 3\\ \\ \text{So the line should go from -5 to 3 with a hollow dot at -5 and a solid dot at 3}\)

The equation of the line that is parallel to the given line and passes through the point (-2, 2) is y = (1/5)x + 12/5.

To find the equation of the line that is parallel to the given line and passes through the point (-2, 2), we need to first determine the slope of the given line. The slope of a line is defined as the change in y divided by the change in x between any two points on the line. We can use the coordinates (-5, -4) and (0, -3) to find the slope of the given line as follows:

slope = (change in y) / (change in x)

= (-3 - (-4)) / (0 - (-5))

= 1/5

Now that we know the slope of the given line, we can use it to find the equation of the line that is parallel to it and passes through the point (-2, 2). Parallel lines have the same slope, so the equation of the new line will have the same slope as the given line. We can use the point-slope form of the equation of a line to find the equation of the new line as follows:

y - y₁ = m(x - x₁)

where y₁ and x₁ are the coordinates of the given point, and m is the slope of the given line. Plugging in the values we have, we get:

y - 2 = (1/5)(x - (-2))

y - 2 = (1/5)(x + 2)

y - 2 = (1/5)x + 2/5

This is the equation of the line that is parallel to the given line and passes through the point (-2, 2). We can simplify it further by adding 2 to both sides to get:

y = (1/5)x + 2/5 + 2

y = (1/5)x + 12/5

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Complete Question:

On a coordinate plane, a line goes through (- 5, - 4) and (0, - 3). A point is at (- 2, 2).What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?

Answer: The answers are in the steps please look carefully.

Step-by-step explanation:

In this given situation, the length of RS plus the length of ST will equal to the length of RT because RS and ST lies on RT. We are given that  RS is equal to 2x + 10  and  ST is equal to  x- 4 , this means that 2x + 10 plus x-4 will equal to 21 because the whole length of RT is 21.

A. Equation:   (2x + 10 ) +(x -4) = 21  

Now solve the equation for x.

2x + 10 + x -4 = 21   First combine like terms on the left side.

3x + 6 = 21     Subtract 6 from both sides  

    -6     -6

3x = 15     Divide both sides by 3

x = 5    

The value of x is 5.  

The length of RS is 2x +10  so since we know the value of x input it into the expression and solve for the real length.

2(5) + 10

10 + 10  = 20

ST is   also x -4  so input  the value for x and solve for the real length.

5 - 4 = 1    

x = 5 , RS = 20 , ST = 1

B. The same applies to B.  

RS plus ST has to Equal to RT.

We know the length of  RS is 3x -16 and the length of ST is 4x -8  so it has to equal 60.

Equation: ( 3x -16) + (4x - 8) = 60    Solve for x  

    3x - 16 + 4x -8 = 60

    7x - 24 = 60  

         +24    +24    

     7x = 84

x=  12  

Input 12 in for x and solve for the real lengths

RS = 3(12) - 16

RS = 36 - 16

RS = 20

ST= 4(12) - 8

ST= 48 - 8

ST= 40

x = 12, RS = 20, ST = 40

Answer:

65%

Step-by-step explanation:

You have to do 13 divided by 20 and get 0.65 and then multiply by 100

and get 65