Compare the two parking garages.

Garage A
charges $5
plus $2
for every hour.
Garage B
charges $4.50
an hour, with no flat fee.

The area of the ripple is increasing by 5654.86 square cm per second

From the question, we have the following parameters that can be used in our computation:

Ripple = Circular

Radius = 30 cm

Rate of increasing = 30 cm/seconds

The area of a circle is

A = πr²

Differentiate the area with respect to radius to get the rate at which the area of the ripple is increasing

So, we have

A' = 2πr r'

Where

r' = 30 cm/s

r = 30

So, we have

A' = 2π * 30 * 30

Evaluate

A' = 5654.86

Hence, the area is increasing by 5654.86 square cm per second

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Answer:

60

Step-by-step explanation:

Area of a trapezoid is found with the formula, A=(a+b)h/2. To find the area of a trapezoid, you need to know the lengths of the two parallel sides (the "bases") and the height. Add the lengths of the two bases together, and then multiply by the height. Finally, divide by 2 to get the area of the trapezoid.

Answer:

The graph is constant from (-oo,-2)U(4,oo).

The graph is increasing from (-2,4).

The graph never decreases.

Step-by-step explanation:

Take the x values from when the line is constant (not rising or falling), increasing (rising), and decreasing (falling).

oo means infinity

The graph is constant from (-oo,-2)U(4,oo).

The graph is increasing from (-2,4).

The graph never decreases.

Answer: 11/20

Step-by-step explanation:

1/4 = 5/20

3/5 = 12/20

3/10 = 6/20

5/10 + 12/20 - 6/20 = 11/20

The most appropriate size for this set of data is 62.

Option B is the correct answer.

We have,

To determine the appropriate bin size for a histogram, we need to find the range of the data and divide it by the number of bins we want to use.

So,

Range = maximum value - minimum value

Range = 317 - 255

Range = 62

To determine the number of bins, we can use the "2-to-20 Rule" which suggests using between 2 and 20 bins depending on the size of the data set.

Since we have 14 data points, a bin size of 10 (Option A) or 1 (Option D) would be too small or too large respectively.

A bin size of 2 (Option C) may be appropriate for larger data sets, but for this particular data set, a bin size of 62 (Option B) is most appropriate.

Therefore,

The most appropriate size for this set of data is 62.

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Hello!

x⁴ + 13x² + 36

= x⁴ + 9x² + 4x² + 36

= (x⁴ + 9x²) + (4x² + 36)

= x²(x² + 9) + 4(x² + 9)

= (x² + 4)(x² + 9)

The positive integer for the trigonometric equation is k = 2

Given data ,

There is exactly one real x ∈ (0, π/2) such that (tan²x/2)(cot⁴x+1) ( csc²x+tan²x)=1

On simplifying , we get

(tan²x/2)(cot⁴x+1)(csc²x+tan²x) = 1

(sin²x/cos²x)(cos⁴x/sin⁴x + 1)(1/sin²x + sin²x/cos²x) = 1

(sin²x/cos²x)(1/cos⁴x + sin⁴x/cos⁴x + 1/sin²x + sin⁴x/cos²x) = 1

(sin²x/cos²x)((1+sin⁴x)/cos⁴x + 1/sin²x + sin⁴x/cos²x) = 1

(sin⁶x + sin⁴x cos²x + cos⁶x)/(sin²x cos⁴x) = 1

On further simplification of the trigonometric relation , we get

(sin²x + cos²x)²/(sin²x cos⁴x) = 1

(1/cos⁴x) + (2/sin²x cos²x) + (1/sin⁴x) = 1

Multiplying both sides by sin⁴x cos⁴x, we get:

sin⁴x + 2 cos²x + cos⁴x = sin⁴x cos⁴x

Simplifying further, we get:

cos⁴x - 2 cos²x + sin⁴x = 0

Let y = cos²x. Then, the above equation becomes:

y² - 2y + (1 - y)² = 0

Expanding and simplifying, we get:

y² - 2y + 1 = 0

This is a quadratic equation with solutions y = 1 and y = 1/2. Since x is in the interval (0, π/2), we can take y = cos²x = 1/2.

Now, we have cos²x = 1/2 and sin²x = 1 - cos²x = 1/2. Therefore, we can write:

cos²(2019x) = cos²x⁴ = (cos²x)²² = (1/2)²² = 2⁻⁴

sinⁿx = (sin²x)^(n/2) = (1/2)^(n/2)

So, we need to find the positive integer k such that cos²(2019x) = sinᵏx. Substituting the values of cos²x and sin²x, we get:

2⁻⁴ = (1/2)^(k/2)

2⁻⁴ = 2^(-2k)

-4 = -2k

k = 2

Hence , the positive integer k is 2

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The number with the least value is n - p, and the number with the greatest value is p - n

From the question, we have the following parameters that can be used in our computation:

The number line (see attachment)

From the number line, we have

n = -0.8

p = 0.4

Calculating the difference and sum expressions, we have

n - p = - 0.8 - 0.4 = -1.2

n + p = - 0.8 + 0.4 = -0.4

p - n = 0.4 + 0.8 = 1.2

From the above, we have

Least = n - p

Highest = p - n

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The required area of the given figure is  19.68 in².

Given that,

length of first diagonal = p = 16.4 in.

length of 2nd diagonal = q = 2.4 in.

Since, the given figure is nothing but rhombus,

And a parallelogram is a particular instance of a rhombus and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus

And we know that area  of a rhombus = (p q)/2

Where p and q are diagonals of the given rhombus

Therefore,

Area = 16.4 x 2.4/2

        =  19.68 in²

So the area of given rhombus is 19.68 in².

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The expression that is equivalent to the given expression -4x² + 2x − 5 (1+x) is -4x²  - 3x − 5

From the question, we have the following parameters that can be used in our computation:

-4x² + 2x − 5 (1+x)

Open the brackets

So, we have

-4x² + 2x − 5 (1+x) = -4x² + 2x − 5 - 5x

Collect the like tsrms

So, we have

-4x² + 2x − 5 (1+x) = -4x² + 2x  - 5x − 5

Evaluate the like terms

This gives

-4x² + 2x − 5 (1+x) = -4x²  - 3x − 5

Hence, the expression that is equivalent to the given expression is -4x²  - 3x − 5

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Answer:

A = 280

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 12 + 16 = 28 and h = 20 , then

A = [tex]\frac{1}{2}[/tex] × 28 × 20 = 14 × 20 = 280

The break-even revenue for the retail business is Br. 6000.

Let x represent the retail company's revenue.

Since the margin is 25%, the cost of goods sold (CGS) = 75% of revenue.

Sales costs =  5% of sales.

CGS + selling costs + fixed costs = total cost.

Total cost = 0.75x + 0.05x + 1200

Total expense = 0.8x + 1200

Since the break-even point is when the company is neither earning a profit nor a loss, we must put the total cost equal to the revenue in order to determine the break-even revenue.

0.8x + 1200 = x

Simplifying the equation:

0.2x = 1200

x = 1200/0.2

x = 6000

Therefore, the break-even revenue for the retail business is Br. 6000.

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The value of x is 50 and FTD = 130°

Both of the angles in the diagram must have the same measure because are vertical, then:

3x - 20 = 2x + 30

3x - 2x = 30 + 20

x = 50

That is the value of x.

And we can see that FTD = 2x + 30 = 2*50  + 30 = 130

That is the measure.

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Answer:

101.5 m

Step-by-step explanation:

Let man 1 be the man whose angle of elevation is 30°.

Let man 2 be the man whose angle of elevation is 20°.

We can model the given scenario as a right triangle with the height of the tower as the triangle's height (100 m), and the distance between the base of the tower and man 2 as the base of the triangle.

As the angle of elevation for man 1 is greater than the angle of elevation for man 2, the position of man 1 is between the base of the tower and man 2.

Let "a" be the distance between man 1 and the base of the tower.

Let "b" be the distance between man 2 and the base of the tower.

Therefore, we have 2 right triangles (see attached diagram):

The distance between the two men is b - a.

We can calculate the values of a and b by using the tangent trigonometric ratio, since we have the side opposite the angle and wish to find the side adjacent the angle.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

Using the tan ratio, create an equation for a:

[tex]\tan 30^{\circ}=\dfrac{100}{a}[/tex]

[tex]a=\dfrac{100}{\tan 30^{\circ}}[/tex]

Using the tan ratio, create an equation for b:

[tex]\tan 20^{\circ}=\dfrac{100}{b}[/tex]

[tex]b=\dfrac{100}{\tan 20^{\circ}}[/tex]

As the distance between the two men is b - a:

[tex]\begin{aligned}\textsf{Distance between the men}&=b-a\\\\&=\dfrac{100}{\tan 20^{\circ}}-\dfrac{100}{\tan 30^{\circ}}\\\\& = 274.747741...-173.205080...\\\\&=101.542661...\\\\&=101.5\; \sf m\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the distance between the two men is 101.5 meters, to the nearest tenth.

The area of the polygon is 696

A polygon is any closed curve consisting of a set of line segments connected such that no two segments cross.

The area of a polygon is is expressed as

A = 1/2 × p × a

where p is the perimeter and a is the apothem

perimeter = n × s

where n is the number of side and s is the side length.

P = 8 × 12 = 96

A = 1/2 × 96 × 14.5

A = 1392/2

A = 696

Therefore the area of the polygon is 696

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The exponential function that represents this situation is f(x) = 42 * (0.85)ˣ

From the question, we have the following parameters that can be used in our computation:

Inital growth, a = 42

Rate of decrease, r = 15%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 - r)ˣ

Substitute the known values in the above equation, so, we have the following representation

f(x) = 42 * (1 - 15%)ˣ

So, we have

f(x) = 42 * (0.85)ˣ

Hence, the function is f(x) = 42 * (0.85)ˣ

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Question

Growth was worth $42 at tje beggining of the day. event every hour stock goes down by 15%. Write the exponential function that represents this situation.

Answer: B.

Step by step:

B is the best definition of it,

To determine whether a triangle is right, acute, or obtuse, you could use the Pythagorean theorem.

To tell if a triangle is proper, acute, or obtuse, you could compare the price of c² with the price of a² + b²:

If a² + b² = c², it is a right triangle.

If c² is larger, it is an obtuse triangle.

If c² is smaller, it's miles an acute triangle

According to the Pythagorean theorem, the sum of the squares on the legs of a proper triangle is equal to the square on the hypotenuse. This theorem may be written as an equation pertaining to the lengths of the perimeters a, b, and the hypotenuse c, often called the Pythagorean equation: a²+b²=c²

Using this method, you may remedy the following issues:

8 in, 10 feet, 16 in, 18 feet, 15 in, 23 toes, 30 ft

a = eight in, b = 15 in, c = 17 in

a² + b² = sixty four + 225 = 289

c² = 289

a² + b² = c²

Therefore, it's miles a proper triangle.

6 feet,17 in, 15ft

A = 6 ft, b = 17 in, c = 15 ft

a² + b² = 36 + 289 = 325

c² = 225

a² + b² > c²

Therefore, it is an acute triangle.

10 feet, eight feet, 29 in, 20 in

a = 10 feet, b = 20 in, c = 29 in

a² + b² = a hundred + 400 = 500

c² = 841

a² + b² < c²

Therefore, it is an obtuse triangle.

26 ft, 29 yd, 24 ft, 21 yd, 23 yd

a = 26 ft, b = 21 yd, c = 29 yd

a² + b² = 676 + 441 = 1117

c² = 841

a² + b² > c²

Therefore, it is an acute triangle.

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The correct question is;

How can I tell if a triangle is right, acute, or obtuse?

• If a² + b² = c², it is a ____ triangle.

.If c² is larger, it is a ____ triangle.

• If c² is smaller, it is a _____ triangle.

Use the Pythagorean Theorem to determine if each triangle is right, obtuse, or acute.

"8 in, 10 feet, 16 in, 18 feet, 15 in, 23 toes, 30 ft

 6 feet,17 in, 15ft

10 feet, eight feet, 29 in, 20 in

26 ft, 29 yd, 24 ft, 21 yd, 23 yd"

The correct equation for f(x) is D. f(x) = 3x² + 1.

To determine which equation represents the function f(x) when f(2) = 13, we need to substitute x = 2 into each equation and check which one gives the result of 13.

Let's test each option:

A. f(x) = x² + 8

f(2) = (2)² + 8 = 4 + 8 = 12 (not equal to 13)

B. f(x) = x + x²

f(2) = (2) + (2)² = 2 + 4 = 6 (not equal to 13)

C. f(x) = 2x³ + 5

f(2) = 2(2)³ + 5 = 2(8) + 5 = 16 + 5 = 21 (not equal to 13)

D. f(x) = 3x² + 1

f(2) = 3(2)² + 1 = 3(4) + 1 = 12 + 1 = 13 (equal to 13)

Among the given options, only option D, f(x) = 3x² + 1, gives f(2) = 13. Therefore, the correct equation for f(x) is D. f(x) = 3x² + 1.

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Step-by-step explanation:

Area of hole =  pi r^2 = 49 pi

Entire area covered by tire = pi 17^2 = 289 pi

  liklihood of 'hitting' the hole  =   49 pi / 289 pi = 49/289

The complete polynomial is f(x) = 2x³ + 15x² - 6 if n = 3 and a = 15

From the question, we have the following parameters that can be used in our computation:

f(x) = 2xⁿ + ax² - 6 is divided by (x+3), the remainder is 129

This means that

f(-3) = 129

So, we have

f(-3) = 2(-3)ⁿ + a(-3)² - 6

Evaluate

f(-3) = 2(-3)ⁿ + 9a - 6

Recall that

f(-3) = 129

So, we have

2(-3)ⁿ + 9a - 6 = 129

Subtract -6 from both sides

2(-3)ⁿ + 9a = 135

Assume n = 3

So, we have

2(-3)³ + 9a = 135

This gives

2/27 + 9a = 135

So, we have

9a = 135 - 2/27

Evaluate

9a = 3643/27

So, we have

a = 3643/243

a = 15

This means that

n = 3 and a = 15

So, the complete polynomial is f(x) = 2x³ + 15x² - 6

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1. f(x) = 665.12 (1.013[tex])^{1.39x[/tex]

2. g(x) = 14.15x + 659.5

3. The exponential function best fits the data.

To find the exponential function that best fits the given data, we can use the exponential regression feature on a graphing calculator or a statistical software. Using a graphing calculator, we obtain the exponential function:

f(x) = 665.12 (1.013[tex])^{1.39x[/tex]

To find the linear function that best fits the data, we can use the linear regression feature on a graphing calculator or a statistical software. Using a graphing calculator, we obtain the linear function:

g(x) = 14.15x + 659.5

To determine which equation best fits the data, we can compare the correlation coefficient (r) of each regression model. The closer r is to 1, the better the fit of the model.

For the exponential function, r = 0.5642.

For the linear function, r = 0.1082.

Since the correlation coefficient for the exponential function is closer to 1 than that of the linear function, we can conclude that the exponential function best fits the data.

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Therefore, the exponential function that best fits the data is y = 463.30 × 1.06×.

The equation for an exponential function is y = ab^x, where a and b are constants. To find the constants, we can use exponential regression.

We can rearrange the equation to get ln(y) = ln(a) + ln(b)x, which is a linear equation. To solve for a and b, we can use least squares regression to solve the system of equations.

Let's define our variables:

ln(y1) = ln(a) + ln(b) × x1

ln(y2) = ln(a) + ln(b) × x2

ln(y3) = ln(a) + ln(b) × x3

ln(y4) = ln(a) + ln(b) × x4

ln(y5) = ln(a) + ln(b) × x5

ln(y6) = ln(a) + ln(b) × x6

We can now solve the system of equations to find a and b. We will use the following values:

x1 = 1, y1 = 672

x2 = 2, y2 = 689

x3 = 3, y3 = 685

x4 = 4, y4 = 660

x5 = 5, y5 = 719

x6 = 6, y6 = 736

We can now calculate the ln of each y value:

ln(y1) = ln(672) = 6.38

ln(y2) = ln(689) = 6.41

ln(y3) = ln(685) = 6.40

ln(y4) = ln(660) = 6.34

ln(y5) = ln(719) = 6.46

ln(y6) = ln(736) = 6.48

We can now solve the system of equations by using least squares regression:

ln(a) + ln(b)×1 = 6.38

ln(a) + ln(b)×2 = 6.41

ln(a) + ln(b)×3 = 6.40

ln(a) + ln(b)×4 = 6.34

ln(a) + ln(b)×5 = 6.46

ln(a) + ln(b)×6 = 6.48

We can solve the system of equations using a calculator, or by using an online tool such as Wolfram Alpha. Solving the system of equations gives us the following values:

ln(a) = 6.09

ln(b) = 0.06

We can now calculate a and b:

a = [tex]e^{6.09[/tex] = 463.30

b = [tex]e^{0.06[/tex] = 1.06

Therefore, the exponential function that best fits the data is y = 463.30 × 1.06×.

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Answer:

ice creams bars cost 1 dollar

Step-by-step explanation:

Let ice cream bars = b

Let ice cream cones = c

10b+6c = 13

6b+10c = 11

Multiply the top equation by 5.

5(10b+6c = 13)

50b + 30c = 65

Multiply the second equation by -3

-3(6b+10c = 11)

-18b -30c = -33

We can add these together to eliminate the ice cream cones

50b + 30c = 65

-18b -30c = -33

----------------------------

32b = 32

Divide by 32

b = 1

The bars cost 1 dollar

Step-by-step explanation:

the area of a parallelogram is

baseline × height

in our case

7.7 × 2 = 15.4

and just in case, remember, as the side and height lengths are in m (meters), the area result is in m² (square meters).

Sara's score is 10.5; Hamza's score is 2.5; Luna's score is 8. The inequality for Mario's score is M ≥ 23 - X - Y - K - Z.

c) Let H be Hamza's score. Then we have the equation H + 4.5 = 7. Solving for H, we get:

H = 7 - 4.5 = 2.5

Therefore, Hamza's score is 2.5.

d) Let L be Luna's score. Then we have the equation L - 4 = 4. Solving for L, we get:

L = 4 + 4 = 8

Therefore, Luna's score is 8.

e) Let M be Mario's score. Then we have the inequality:

X + Y + K + Z + M ≥ 23

We can rearrange this inequality as:

M ≥ 23 - X - Y - K - Z

This represents the minimum score that Mario needs to achieve in order for the sum of all scores to be at least 23. Since we don't know the values of X, Y, K, and Z, we can't determine a specific value for M.

However, we can graph this inequality on a coordinate plane to see the possible values of M that satisfy the inequality.

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A 95% confidence interval for the mean price for all the TI-84 Plus calculators being sold on Amazon.(91.44, 155.44)

A confidence interval, in statistics is defined as the probability that a population parameter will fall between a set of values for a certain proportion of times. Analysts often use confidence intervals that contain either 95% or 99% of expected observations.

Now, the empirical rule is the formula:

CI = μ ± nσ

Where:

μ is mean

σ is standard deviation

n is number of standard deviations from the mean

A confidence level of 95% is 2 standard deviations from the mean

Thus:

CI = 123.44 ± 2(16)

CI = (91.44, 155.44)

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We can write the inequality as: 5N + 45 < 60

The solution of the inequality is: N < 3

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4

Let N represent the number of gigabytes she can use to stay within her budget.

Bao pays a flat rate of $40.50 a month. That is constant: $45

$5.00 per gigabyte. For N gigabyte, we have: $5 * N = 5N

She wants to keep her bill under $60.00. This means the total is less than 60 (< 60)

Thus, we can write the inequality as:

5N + 45 < 60

We can solve the inequality by making N the subject. That is:

5N + 45 < 60

5N < 60 - 45

5N < 15

N < 15/5

N < 3

This implies Bao must use less than 3 gigabytes to stay within her budget

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