Find the difference between the area and perimeter of a shape that consists of a quarter circle in the corner of two squares as shown. A= 4.5 yds
Round to the nearest tenth if necessary

Part a

The domain is the set of x-values, which is \((-\infty, \infty)\)

Part b

The range is the set of y-values, which is \((-\infty, -2]\)

Part c

The x-intercepts is when y=0, which there are none of.

Part d

The y-intercept is when x=0, which is at (0, -2).

Answer:

the answer is two

Step-by-step explanation:

The equation is

The figure is similar to a parallelogram , with a base length equivalent to the circumference of the circle and a height equivalent to the radius of the circle

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the radius of the circle be represented as r

Now , the equation will be

The circumference of the circle C = 2πr

And , the circle is divided into 24 sectors and it is placed side-by-side

The figure formed is in the shape of a parallelogram

The base length of the parallelogram = circumference of the circle

And ,

Height of the parallelogram = radius of the circle r

Hence , the base length is the circumference and height is the radius of the circle

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Answer:

Inverse of  \(- 5 x - 4 =\) \(\frac{x + 4}{5}\)

Step-by-step explanation:

Let y = -5x-4

Swap y and x

x = -5y -4

Solve for y

x+4 = -5y

\(y=- \frac{x + 4}{5}\)  which is the inverse

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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Answer:

Each song costs $2 and each album costs $10.

Step-by-step explanation:

Since a website allows users to download individual songs or whole albums, and all songs cost the same price to download and all albums cost the same price to download, and Karim pays $ 30 to download 5 songs and 2 albums while Kimberlyn pays $ 26 for download 3 songs and 2 albums, to determine what is the cost to download 1 song and the cost to download 1 album, the following calculations must be made:

5X + 2Y = 30

3X + 2Y = 26

(30 - 26) / (5 - 3) = X

4/2 = X

2 = X

Therefore, each song has a cost of $ 2.

Thus, to know the cost of each album (knowing that both downloaded the same amount, that is, 2), the following calculation must be performed:

5x2 + 2Y = 30

10 + 2Y = 30

2Y = 30 - 10

2Y = 20

Y = 20/2

Y = 10

Therefore, each album has a cost of $ 10.

Answer:

Step-by-step explanation:

m= movie time

m=36+55=19 minutes

9514 1404 393

Answer:

  j-k = 13/6

Step-by-step explanation:

The quadratic formula tells you the two solutions are ...

  x = (-b/(2a)) ±√(b² -4ac)/(2a)

The difference between these solutions is ...

  j-k = √(b² -4ac)/a

  j-k = √((-7)² -4(6)(-5))/6 = √(49 +120)/6 = √169/6

  j-k = 13/6

Answer:

D= [-4,-1) U (2,4)

R = [-3,5)

The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.

In the question given 4 coordinates,

U(1 , -3)

V(4 , -3)

T(1 , -4)

W(5 , -4)

the reflection across x-axis

U(1 , -3) →U' (1, 3)

V(4 , -3) → V'(4 , 3)

T(1 , -4) → T'(1 , 4)

W(5 , -4) → W'(5 , 4)

so  after the reflection across the x axis the coordinates of the vertices becomes ,

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)

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Answer:

8 po yan po sagot ko .. correct me if I wrong

The value of x, considering the Pythagorean Theorem, is given as follows:

x = 9.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The sides for the problem are given as follows:

15 and 8 (segment of 8 is the radius, which is the distance from the center to a point on the circumference of the circle).

Hence the hypotenuse is obtained as follows:

h² = 15² + 8²

h² = 289

h = 17.

Hence the value of x is obtained as follows:

x = 17 - 8

x = 9.

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When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.

A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.

However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.

While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.

Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.

So, correct option is B.

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The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.

In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:

Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)

Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)

Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8

Total sugar consumed = 22/8 + 1/4

Total sugar consumed = (22 + 2)/8

Total sugar consumed = 24/8

Total sugar consumed = 3 units of sugar.

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Answer:

The probability that a skid of 50 DVD players will contain at least 3 defective units is 0.9487.

Step-by-step explanation:

We are given that Avery and Bradly work at a large electronics manufacturer that produces DVD players. The defective rate on the assembly line has gone up 12% and a skid of 50 DVD players has been selected by the manager.

Let X = Number of defective units of DVD players

The above situation can be represented through the binomial distribution;

\(P(X = r) = \binom{n}{r}\times p^{2} \times (1-p)^{n-r}; x= 0,1,2,3,....\)

where, n = number of samples (trials) taken = 50 DVD players

            r = number of success = at least 3 defective units

           p = probability of success which in our question is the probability

                 of defective rate, i.e; p = 12%

So, X ~ Binom(n = 50, p = 0.12)

Now, the probability that a skid of 50 DVD players will contain at least 3 defective units is given by = P(X \(\geq\) 3)

P(X \(\geq\) 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2)

= \(1 - [ \binom{50}{0}\times 0.12^{0} \times (1-0.12)^{50-0}]-[ \binom{50}{1}\times 0.12^{1} \times (1-0.12)^{50-1}]-[ \binom{50}{2}\times 0.12^{2} \times (1-0.12)^{50-2}]\)

= \(1 - [ 1 \times 1 \times 0.88^{50}]-[50 \times 0.12^{1} \times 0.88^{49}]-[ 1225 \times 0.12^{2} \times 0.88^{48}]\)

= 0.9487

Hence, the probability that a skid of 50 DVD players will contain at least 3 defective units is 0.9487.

Answer:

0.0806

Step-by-step explanation:

From the given information:

Number of toss = 50

The probability of having a head = 1/2 = 0.5

The Probability of 8th head occur on 12th toss can be computed as :

Pr(8th head occur on 12th toss) = Pr(7 heads in 11 toss) × P(8th head on 12th toss)

Pr(8th head occur on 12th toss) =  C(11,7) × 0.5⁷ × (1 - 0.5)⁴ * 0.5

Pr(8th head occur on 12th toss) = \(\dfrac{11!}{7!(11-7)!}\) × 0.5⁷ × (1 - 0.5)⁴ × 0.5

Pr(8th head occur on 12th toss) =  0.0806

Answer:

The probability of 8th heads,

That is occurred on 12th toss.

Step-by-step explanation:

A coin is tossed 50 times.

There are two possible outcomes of occurring a head or tail.

Probability of occurring head = no.of head/ possible outcomes

                                                    = 1/2

Total number of tossing a coin= 50 times

Probability of 8th heads occurs on 12th toss:

                                                         12C8 (1/2)8 (1/2)9 (1/2)10 (1/2)11 (1/2)12

                                 =         12C8  (1/2)8+9+10+11+12

                                                    = 12C8  (1/2)50

                                  = 12C8   / 250

                                                       = 495 / 1125899906842624

                                  = 4396.48317752 x 10-16

This is the probability of 8th heads,

That is occurred on 12th toss.

If the ratio of a basketball players completed free throws to attempted free throws is 9 to 12. If she attempted 20 free throws, the number of  free throws she completed is 27 free throws.

Given data:

Attempted free throws = 9 to 12

Free throws = 20

Formulate

9/12= 20/x

Cross-multiply

9x = 20× 12

9x = 240

Divide both side by 9x

x = 240/9

x = 26.6

x = 27 free throws (Approximately)

Therefore the free throws is 27.

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Answer:

x          y

9         0

8         2

5         8

Step-by-step explanation:

(9, 0) , (8, 2) , and (5, 8) --> all three points satisfy the equation 2x + y = 18.

Answer:

Plug the equation into a graphing calculator, and you'll get these:

(9, 0) , (8, 2) , and (5, 8)

With the help of percentage increase information, we conclude that,  Americans spent approximately $1,141.31 on summer vacation in 2014.

What is percenatge increase?

Percentage increase is a measure of how much a value has increased in comparison to the original value, expressed as a percentage.

To find what Americans spent in 2014, we need to use the percentage increase and the 2015 amount.

Let X be the amount spent in 2014.

We know that the increase from 2014 to 2015 is 3.4%, which can be expressed as:

3.4% = 0.034 (as a decimal)

We also know that the amount spent in 2015 is $1,180.

Using this information, we can set up an equation:

X + 0.034X = 1180

Simplifying the left side:

1.034X = 1180

Dividing both sides by 1.034:

X = 1141.31

So Americans spent approximately $1,141.31 on summer vacation in 2014.

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If the point you end up at is coordinate (0.25, 0) then you would have ran one full lap around the track.

1. The given track is a circular track with a radius of 0.25 miles, and the center of the track is at (0, 0).

2. If you end up at the point (0.25, 0), then you would have ran one full lap around the track. This is because the coordinates of the point you end up at, (0.25, 0), are the same as the coordinates of the circumference of the track, which is located 0.25 miles from the center of the track.

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1. An equation that represents "the amount of tax on an item of price p",

t = p x X / 100

2. Marta does pay on an item whose price is $20, $1.6

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Tax rate = 8%

1. Let's assume that the sales tax rate is X%.

Then, the equation that represents the amount of tax (t) Marta pays on an item whose price is p can be written as:

t = p x X / 100

2. If the price of the item is $20, the amount of tax Marta pays can be calculated as follows:

t = $20 x X / 100

t = $20 x 8 / 100

t = $1.6

So, Marta pays $1.6 in sales tax on an item whose price is $100.

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The in this case, the distance covered by the car would be 120 miles. The equation Distance = Speed * Time allows us to determine the distance covered by an object when the speed and time taken are known.

To determine distance, we can rearrange the formula for speed:

Speed = Distance / Time. By multiplying both sides of the equation by Time, we can isolate Distance.

Distance = Speed * Time

The formula indicates that distance is equal to the product of speed and time. By multiplying the rate at which an object moves (speed) by the duration of travel (time), we can determine the total distance covered during that period.

The equation Distance = Speed * Time represents the relationship between distance, speed, and time.

It states that the distance covered is equal to the product of the speed at which an object is moving and the time it takes to travel that distance.

For example, if a car is traveling at a constant speed of 60 miles per hour for 2 hours, the distance it would cover can be calculated as follows:

Distance = 60 miles/hour * 2 hours = 120 miles.

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The 1 in y = 1/7x+1, is the y-intercept. Its coordinates are (0,1). 1/7 means you are going up 1 and to the right 7, since it's positive.

On a graph, it looks like the graph above.

Answer:

x - 4 yards.

Step-by-step explanation:

Given:

Area of rectangle = 3x^2 - 12x square yards

Width = 3x yards

To find:

Length of rectangle

Solution:

The area of a rectangle is equal to the product of its length and width.

Area of rectangle = Length * Width

Substituting the given values, we get:

3x^2 - 12x = Length * 3x

Length =( 3x^2 - 12x )3x

Length = x-4

Therefore, the length of the rectangle is x - 4 yards.

Answer: The length of the rectangle is x - 4 yards.

Step-by-step explanation:

We can create an equation to solve this word problem, where the variable L = length.

3x  ×  L  = \(3x^2 - 12x\)

We need to solve for the variable L, to find the length of the rectangle.

First lets factor the right side of the equation to make it easier to divide with.

3x  ×  L  = \(3x^2 - 12x\)

We can factor out 3x from the right side of the equation.

3x  ×  L  = 3x(x - 4)

Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.

3x ×  L  = 3x(x - 4)

/3x           /3x

L = x - 4

The length of the rectangle is x - 4 yards.

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

ANSWER

EXPLANATION

The area of a sector is given as:

where r = radius of the circle

θ = angle of the sector

From the question, we do not have the radius, but we have the diameter of the circle.

The diameter of a circle is twice its radius, which means that:

Therefore, the area of the sector is:

The gallons of ice cream 4 machines can make is 650 gallons.

Two ice cream machines make a total of 320 gallons in a certain amount of time.

Working together for the same length of time, the number of gallons of ice creams 4 machine can make can be calculated as follows:

Therefore,

If 2 ice cream machine = 320 gallons

4 ice cream machine = ?

cross multiply

Hence,

gallons of ice cream made by 4 machines = 320 × 4 / 2

gallons of ice cream made by 4 machines = 1280 / 2\

Therefore,

gallons of ice cream made by 4 machines = 640 gallons

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The total cost for the family of four is $944

Cost denotes the amount of money that a company or a person spends on the creation or production or acquiring of goods or services.

Here the family needs the service if transportation.

The cost of adult is $280. Out of four members , two are under 3years. This means the total cost for adult is 2 × 280 = $560

The cost of under 3 is ⅔ of the cost of adult.

= ⅔ × 280= $192

The cost of the two under 3 = 2 × $192 = $384

therefore the total cost for the family is $560 +$384 = $944

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Hi!

I can help you with joy!

Answer:

The line has a slope of 3.

Hope it helps.

If you have any queries, please ask.

~Misty~

Answer:

It should be 3

Step-by-step explanation:

A line parallel to this one would have a slope of 3. where m is the slope and b is the y intercept. In this case, the equation y=3x+5 is already in slope intercept form, which means the slope is 3.

Answer: Third Choice. (2, 0)

Step-by-step explanation:

STEP ONE: Look over the given choice.

When the value of y is 0, the value of x would be the x-intercept.

The given choice are the following:

As we can see from the choices, the first two do not have the value of y as 0, therefore, they can be automatically neglected. Then, we are left with two choices left.

STEP TWO: Substitute the remaining values into the given equation

Given point = (2, 0)

3y + 4x = 8

3 (0) + 4 (2) = 8

0 + 8 = 8

8 = 8 \(\boxed {TRUE}\)

Given point = (8/3, 0)

3y + 4x = 8

3 (0) + 4 (8/3) = 8

0 + 32 / 3 = 8

32/3 ≠ 8 \(\boxed {FALSE}\)

Therefore, the ordered pair that represents the x-intercept is (2, 0).

Hope this helps!! :)

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