5. The hourly garage at BWI Airport costs $4 an hour with a maximum cost of $22 a day. The equation (ℎ)= { 4 , 0<ℎ≤1 8 , 1<ℎ≤2 12 , 2<ℎ≤3 16 , 3<ℎ≤4 20 , 4<ℎ≤5 22 , 5<ℎ≤24 represents the cost of parking for ℎ hours. a. How much does it cost to park for 45 minutes? b. How much does it cost to park for 2 hours? c. How long could you have parked if it cost you $16? d. List the domain and range for this situation.

The area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.

To find the area of the surface obtained by rotating the circle

[tex]x^2 + y^2 = r^2[/tex] about the line y = r, we can use the method of cylindrical shells.

The circle [tex]x^2 + y^2 = r^2[/tex] is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.

When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.

Consider a small strip on the circle at a distance y from the line y = r.

This small strip is at a distance r - y from the y-axis.

The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).

The width of this strip is the change in x, which we can denote as dx.

The area of this small strip is then given by the product of its length and width, which is 2πy dx.

Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):

Total Surface Area = ∫[from -r to r] 2πy dx

Now, we need to express y in terms of x using the equation of the circle [tex]x^2 + y^2 = r^2:\\y^2 = r^2 - x^2[/tex]

y = ±√(r² - x²)

Since we are considering the upper half of the circle, we take the positive square root:

y = √(r² - x²)

Now, we can rewrite the integral with respect to x:

Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx

To solve this integral, we can make a trigonometric substitution:

Let x = r sin(θ), then dx = r cos(θ) dθ.

When x = -r, θ = -π/2, and when x = r, θ = π/2.

Now the integral becomes:

Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ

Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ

Now, we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

√(1 - sin²(θ)) = cos(θ)

Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ

Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2

Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ

Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]

Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]

Since sin(π) = 0 and sin(-π) = 0:

Total Surface Area = 2πr² [(π/2 - (-π/2))/4]

Total Surface Area = 2πr² (π/2)

Total Surface Area = π²r²

So, the area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.

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Answer:

Refer to the image attached. If you have ANY questions about what I did/how I did it, please ask in the comments. I will be happy to help you understand! :)

Step-by-step explanation:

The value of GI, given that GH = 2x - 9 , HI = 14 , and GT = 3x - 8 will be 31.

An algebraic equation is formed by comparing two algebraic expressions to one another.

In G-H-I, GH = 2x - 9, HI = 14 , and GT = 3x - 8

If G-H-I is a line and GH, HI and GT lies between G to I

To find G to I ⇒ GI = GH + HI = GT

GI = 2x - 9 + 14 = 3x - 8

2x + 5 = 3x - 8

2x - 3x = -8 - 5

-x = -13

x = 13

Substituting x in GT = 3x - 8; GI = GT

GI = 3(13) - 8

GI = 39 - 8

GI = 31

Using algebraic expressions, if x is 13 then, 3x - 8 or 2x - 9 will be GI = 31

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The degree of the polynomial  [tex]2xA^2 5xA^2A^37[/tex] is 9

A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.

The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).

Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]

The polynomial has a degree of 6.

This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.

As per question, polynomial is: [tex]2xA^2 5xA^2A^37[/tex]

The total sum of power is: 1+2+1+2+3=9

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Answer:

To find the sale price of the suit, we need to first calculate the discount. The discount is equal to the original price multiplied by the discount rate, which in this case is $280 * 30% = $84.

Then we subtract the discount from the original price to find the sale price: $280 - $84 = $196.

So the sale price of the suit is $196.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

32% is the same as 0.32

0.23 is the same as 23%

Does there seem to be a pattern in the population estimates of the bugs on this tree is the query or the question .

Variation is the difference in an individual's genetic make-up that causes a population's members to have different physical characteristics. Variation can be shown in an individual's physical characteristics, fertility, metabolism, and method of reproduction. A variation is a relationship between a set of values for one variable and another set of values. direct change. If m is a nonzero constant and b = 0, the function y = mx (commonly written y = kx) that results from the equation y = mx + b is known as a direct variation.

given

the population of the bugs

b is the no. of bugs = 50 . [tex]3^{t}[/tex]

t is the no. of weeks they first counted

so this question explains

the range of population estimates

Is there a trend in the variation of estimates

Does there seem to be a pattern in the population estimates of the bugs on this tree is the query or the question .

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Answer:

The surface area of this cuboid is 420 square inches.

Step-by-step explanation:

All we have to do is calculate each rectangle. For the width, we have 10 x 5 which is 50. Then we multiply it by 2 because we have two of those sides. Then we get 100. Then we have 11 x 5 which is 55. We multiply that by 2 and we get 110. Then we do that to the final two sides and we get 220. So the final answer if we add them all up is 420 square inches.

Answer: no question=no answer

Step-by-step explanation:

The portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of sport hours is 72 degrees.

Therefore the answer is 72°.

To calculate the portion of walking in degrees, we first need to find the total amount of time spent walking. In this case, it is 10 hours.

Next, we need to find the total amount of time spent on all sports, which is 50 hours.

Now we can calculate the portion of walking by taking the amount of time spent walking (10 hours) and dividing it by the total amount of time spent on sports (50 hours).

This gives us the fraction of time spent walking which is

10/50

= 1/5

Finally, we can convert this fraction to degrees by multiplying it by 360 (the number of degrees in a full circle).

So the portion of walking in degrees is

(1/5) × 360

= 72 degrees

--The question is incomplete, complete question is given below--

"Calculate the portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of sport hours."

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a) 7 examples are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

b) Fabric Larry will have left after using [tex]2\frac{2}{3}[/tex] yard out of [tex]5\frac{5}{6}[/tex] yard to make a bag for his computer is: [tex]3\frac{3}{6} yard[/tex]

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

7 examples of mathematical expression are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

For the second part of the question:

Larry had 5 3/6 yards of fabric. He used 2 2/3 yards to make a bag for his computer. Write an expression that will show how much of the fabric Larry will have left.

The mathematical expression that represents the amount of fabric Larry has left is:

5 3/6 - 2 2/3 = 2 7/18

You can simplify this further:

2 7/18 = 2 1/6

The amount of fabric Larry will have left is 2 1/6 yards.

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Direct variation is represented by this situation and she earn $900

if she works 12 hours.

Direct variation describes a relationship whereby one measure directly affects the other when the first one changes. This is completely opposed by inverse variation. Learn the definitions of direct and inverse variations in this article, along with some instances that have been solved.

When x is not equal to 0, y = kx is the equation that describes the linear function known as direct variation. An equation of the form xy = k, where x is not equal to zero and k is a nonzero real number constant, describes the nonlinear function known as inverse variation.

5 hours  = earns $ 375

1 hours = 375/5 = earns $ 75

12 hours  = 75  12 = earns $ 900

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Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

The half of the planet facing the Sun experiences daylight, while the half facing away from the Sun experiences darkness. This cycle repeats itself every 24 hours, resulting in the day and night cycle that we experience.

Earth's rotation causes day and night by rotating on its axis, with half of the planet facing the Sun and the other half facing away from the Sun. This cycle of daylight and darkness lasts for  creating the day and night cycle that we observe.Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

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Answer:

Step-by-step explanation:

Answer: Y = 1/3x^2 - 4x + 12

Step-by-step explanation:

Hope this helps, sorry I don't have an explanation...

The volume of Hannah's suitcase in cubic inches is: C: 7938.

The volume can be determine using this formula

Volume = Length × Width × Depth

Where:

Length = 27 inches

Width = 21 inches

Depth = 14 inches

Let plug in the formula

Volume = 27 inches × 21 inches × 14 inches

Volume = 7,938

Therefore we can conclude that the volume is 7,938.

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In two-dimensional space, only two coordinates are required to specify the location and orientation of a rigid body.

In two-dimensional space, a rigid body can only move in two directions (up/down and left/right) and rotate around a single axis. As a result, only two coordinates are needed to specify the location and orientation of a rigid body in two-dimensional space. The two coordinates needed to specify the rigid body's position are the x-coordinate and y-coordinate, which define the position of the body in the plane. The orientation of the rigid body can be determined by determining the angle between the x-axis and the body's orientation, which is referred to as the angle of rotation. The combination of these two coordinates (position and rotation) specify the full state of the rigid body in two-dimensional space.

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The domain is all values of x that makes the expression defined.

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

Given the function in the question;

y = 5√(6−2x)​

To find the domain, set the radicand greater than or equal zero and solve for x.

6 - 2x ≥ 0

Subtract 6 from both sides

6 - 6- 2x ≥ 0 - 6

-2x ≥ -6

Divide both sides by -2

-2x/-2 ≤ -6/-2

x ≤ -6/-2

x ≤ 3

Therefore, the domain is;

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

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Using substitution method to solve the system of linear equation, the girls have tp sell 700 flower arrangement.

A system of linear equations is a collection of two or more linear equations that use the same set of variables. The solution of the system is the set of values for the variables that satisfy all of the equations in the system.

To solve this problem, we have to set our variables as;

Let;

The equations can be written as;

5x + 6y = 500 ...eq(i)

x + y = 200 ...eq(ii)

From equation ii,

x = 200 - y ...eq(iii)

Put eq(iii) into eq(i)

5(200 - y) + 6y = 500

1000 - 5y + 6y = 500

1000 + y = 500

y = -500

Put y = -500 into eq(ii)

x - 500 = 200

x = 700

From the solution, it shows they couldn't sell any candy and had to sell 700 flower arrangement.

Kindly find the attached graph below

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Therefore , the solution of the given triangle comes out to be  AC = 10 units and PD = 6 units.

Triangles, which have three sides and three angles, can be made by joining any three points in a plane. They are among the earliest geometric shapes to be studied. Triangles are especially important since they may be divided into each polygon, whether it has four, five, six, or n sides.

Here,

Let AD and DC are 2x and x respectively.

We have, BC = 10 units

=> 2x =10

=> x = 10/2

=> x= 5

Now ,

=> AP + PF = 8 + y

=> 8 + y = 12

=> y =4

Therefore , the solution of the given triangle comes out to be  AC = 10 units and PD = 6 units.

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The values of p that satisfy the inequality for all[tex]$q > 0$[/tex] are

[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex]and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]

Given:[tex]$$\frac{3(pq^2 p^2q 3q^2 3pq)}{p q} > 2p^2q^2$$[/tex]

Step 1: Multiply both sides by [tex]$\frac{pq}{3}$[/tex] to get: [tex]$$pq^3 p^2q 3q^2 3pq > 2p^2q^3$$[/tex]

Step 2: Simplify the left side to get: [tex]$$3p^2q^3+3pq^3+3q^2 > 2p^2q^3$$[/tex]

Step 3: Divide both sides by [tex]$q^2$[/tex] to get: [tex]$$3p^2q+3pq+3 > 2p^2$$[/tex]

Step 4: This is a quadratic inequality in[tex]$p$[/tex]with solution[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]. Therefore, the values of p that satisfy the inequality for all  [tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]

the given inequality can be simplified to a quadratic inequality in p by multiplying both sides by[tex]$\frac{pq}{3}$[/tex], simplifying the left side, and dividing both sides by[tex]$q^2$[/tex] The solution of the quadratic inequality is

[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and

[tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]. Therefore, the values of p that satisfy the inequality for all [tex]$q > 0$[/tex] are

[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex]and

[tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex], which means that any value of p that is greater than[tex]$\frac{3+\sqrt{21}}{2}$[/tex] or less than

[tex]$-\frac{3+\sqrt{21}}{2}$[/tex]will satisfy the inequality for all [tex]$q > 0$[/tex]

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The number of hours of practice is 3 x h or 3h.

In mathematics, an expression is a sentence that contains at least one number or variable. Additionally, an expression consists of at least one mathematical operation. There is no equal to sign in an expression.

Given:

Volleyball practice is h hours long. Debbie had 3 volleyball practices last week.

Multiply the number of hours for each practice by the total number of practice to get the expression for the number of practice hours.

The mathematical operation known as multiplication is used to calculate the sum of two or more numbers.

Number of hours of practice

= hours of practice x number of practice

= 3 x h

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Answer: 25% of 40 is 40 times 25 divided by 100 which is 10 (number of children in the club)

there:)

Answer: 160 children

Step-by-step explanation: 25% times 4 is 100%. So, you'd multiply 40 by 4.

The family's monthly payment for their new minivan is $6,664.52

To calculate the monthly payment, we first need to find the total amount that the family is financing by subtracting the down payment from the total cost of the minivan: $45,000 - $12,000 = $33,000.

Then, we can use the monthly payment factor to calculate the monthly payment. The formula to do this is:

Monthly Payment = Financed Amount * Monthly Payment Factor

So in this case:

Monthly Payment = $33,000 * 0.202764 = $6,664.52

Therefore, the family's monthly payment for their new minivan is $6,664.52

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When a four-digit number is divisible by nine and is written as 3AA1, the digit A stands for 7.

A number is itself divisible by nine if the total of its digits is also divisible by nine.

Multiples in mathematics are the outcomes of multiplying an integer by a certain number. a multiple of 9 is a number that divides by nine without remainder.

By utilizing the aforementioned attribute, we can

1 + 3 + 4 + 5 = 9, 18, or 27.

4 +2A = 9, OR 18, OR 27

calculating based on sum equal to 18

2A = 18 - 4

2A = 14

A = 7

therefore 3771 is the number

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The given sequence represents the sales of a product over time. The sum of the first 6 terms is 693.75, which is calculated by multiplying each term in the sequence by its respective exponent.

The sum of the first 6 terms of the geometric sequence is calculated as follows:

[tex]a_1 = 125 \left(\frac{1}{5}\right)^{1-1} = 125 \\[/tex]

[tex]a_2 = 125 \left(\frac{1}{5}\right)^{2-1} = 25 \\[/tex]

[tex]a_3 = 125 \left(\frac{1}{5}\right)^{3-1} = 5 \\a_4 = 125 \left(\frac{1}{5}\right)^{4-1} = 1 \\a_5 = 125 \left(\frac{1}{5}\right)^{5-1} = \frac{1}{5} \\a_6 = 125 \left(\frac{1}{5}\right)^{6-1} = \frac{1}{25} \\[/tex]

Total sum = 125 + 25 + 5 + 1 +[tex]\frac{1}{5} + \frac{1}{25}[/tex] = 693.75

The geometric sequence a_n=12[tex]5\left(\frac{1}{5}\right)^{n-1}[/tex]represents the sales of a product over time, where n is the number of years after its release. The sum of the first 6 terms is calculated by multiplying each term in the sequence by its respective exponent. This gives us the following 6 terms: a_1 = 125, a_2 = 25, a_3 = 5, a_4 = 1, a_5 = 1/5, and a_6 = 1/25. The sum of these 6 terms is 693.75.

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In question 1;

The student multiplied without flipping the second expression.

In second question;

The negative should only be distributed to the numerator.

In third question,

3/2 should be remove from the x - value which make the expression undefined.

In fourth student;

Neither student is correct.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

In question 1;

The expression is,

⇒ x² + 2x - 3 / (x² - 3x - 10) ÷ (2x + 12) / (8x + 16)

= (2x³ + 16x² + 18x - 36) / (8x³ - 8x² - 128x - 100)

Cleary, The student multiplied without flipping the second expression.

In question 2;

⇒ (-2y - 2) / (y² + 2y - 8) - (y - 1) / (2 - y)

⇒ (-2y - 2) / (y² + 2y - 8) + (-y + 1) / (-2 + y)

Clearly, The negative should only be distributed to the numerator.

In Question 3;

The student make mistake is ''3/2 should be remove from the x - value which make the expression undefined.''

In fourth student;

Neither student is doing correct solution.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

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Answer:

Step-by-step explanation:

hello follow me on zepeto if this helps

16 is 33.3333% of 48. 33 is the whole number hope you get a

No matter how far it is moved away, the midline of a function stays the same. because a sinusoidal function is involved.

A function's amplitude is the distance that the graph of the function moves above and below its midline. The value of the amplitude when graphing a sine function is comparable to the value of the sine coefficient. the greatest displacement or distance that a point on a wave or vibrating body can travel in relation to its equilibrium position A wave or vibration's amplitude or peak amplitude is a gauge of how far from the central value it deviates. All amplitudes are positive numbers.

given

( A)if pendulum were pulled away from its resting position, then Amplitude is the distance from its resting position to the end where it was released.

Amplitude is the same distance it was pulled away if more distance was pulled away then Amplitude is more.

(B). The midline of function s will not change, it will same irrespective of the distance pulled away. Because it's a sinusoidal function.

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Answer:

This is how you graph it

Step-by-step explanation:

As seen in the equations above, this equation can fit into the equation y=mx+b. M = slope, where is how we will be able to plot the points. Since the slope for both is two, we would go up 2 then right 1, from the y intercept. Which is the point we will be starting at. Plot two points directly on the y-axis at (0,3) and (0,1). Then go back to the slope and go up 2 and right 1. I hope I helped!