Ajay buys oranges in bulk for Rs. 20 each. He sells them for Rs. 45 each. Calculate the profit and the profit percentage

Triangle ABD is scalene and obtuse.

The triangle has three sides of unequal length, hence it is classified as an scalene triangle.

(it would be equilateral if all had the same length, and isosceles if two sides have the same length).

The triangle has one angle larger than 90º, hence it is classified as an obtuse triangle.

(acute with no angles of 90º or greater, right with one angle of exactly 90º).

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The test statistic (or standard score) would be 1.72.

To convert the outcome of the pulse rate data to a standard score, we would need to calculate the z-score. The formula for the z-score is: (sample mean - population mean) / (standard deviation / square root of sample size).

In this case, the sample mean is 76, the population mean (according to the report) is 72, the standard deviation is 13, and the sample size is 85. Plugging these values into the formula, we get:

(76 - 72) / (13 / sqrt(85)) = 1.72.

Therefore, the test statistic (or standard score) is 1.72. This indicates that the sample mean of 76 is 1.72 standard deviations above the population mean of 72. This information can be used to conduct a statistical test of significance and determine whether the difference between the sample mean and population mean is statistically significant.

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The coordinate of a point between A and B, such that the distance from A to point B is 3/11 of distance A to B, is 1.

Let's denote the unknown point between A and B as P, and let the distance from A to P be x. Then the distance from P to B is (11/3)x. Since the distance from A to B is 19 - (-3) = 22, we have the equation x + (11/3)x = 22(3/11), which simplifies to (14/3)x = 6, or x = 9/7. Therefore, the coordinate of point P is -3 + (9/7)(19 - (-3)) = 1.

To check our answer, we can verify that the distance from A to P is (10/7)(22) and the distance from P to B is (1/7)(22)(11), and that (10/7)(22) = (3/11)(22), which is indeed true.

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Bank B is offering a lower interest rate and will result in a lower total cost over the 20-year period. Even though the monthly payment is slightly lower with Bank B, Trevor should choose Bank B because he will save money in the long run due to the lower interest rate.

To compare the two mortgage options, Trevor needs to consider both the interest rate and the monthly payment amount.

Bank A offers a 5% interest rate with a monthly payment of $791.95. The total amount he will pay over 20 years is:

$791.95 x 12 months/year x 20 years = $190,068

Bank B offers a 4.75% interest rate with a monthly payment of $775.47. The total amount he will pay over 20 years is:

$775.47 x 12 months/year x 20 years = $186,113.60

So, in this case, Bank B is offering a lower interest rate and will result in a lower total cost over the 20-year period. Even though the monthly payment is slightly lower with Bank B, Trevor should choose Bank B because he will save money in the long run due to the lower interest rate.

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The explicit formula for the given sequence is An = 256 * (0.25)ⁿ⁻¹, where n is the term number. Using this formula, we can generate the first five terms of the sequence as follows:

A1 = 256 * (0.25)¹⁻¹ = 256 * 1 = 256
A2 = 256 * (0.25)²⁻¹ = 256 * 0.25 = 64
A3 = 256 * (0.25)³⁻¹ = 256 * 0.0625 = 16
A4 = 256 * (0.25)⁴⁻¹ = 256 * 0.015625 = 4
A5 = 256 * (0.25)⁵⁻¹ = 256 * 0.00390625 = 1

In simpler terms, the explicit formula for the given sequence is found by multiplying the first term by the common ratio raised to the power of n-1, where n is the term number. This results in a decreasing sequence as the common ratio is less than 1. The first five terms of the sequence are 256, 64, 16, 4, and 1, respectively.

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The expression that represents the length (in feet) of the world's longest glass-bottom bridge is 4.3x+550.4.

Let's denote the length of the Coiling Dragon Cliff Skywalk as y (in feet). According to the given information, we have:

y = x + 128

The length of the world's longest glass-bottom bridge is 4.3 times longer than the Coiling Dragon Cliff Skywalk, so we can write an expression for it as:

Length of the longest glass-bottom bridge = 4.3 * y

Now, we can substitute the expression for y from the first equation:

Length of the longest glass-bottom bridge = 4.3 * (x + 128)

To simplify, distribute the 4.3:

Length of the longest glass-bottom bridge = 4.3x + 550.4

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To find the height of the square pyramid, we will use the Pythagorean theorem. Given the area of the base is 64 cm² and the slant height is 9 cm, let's first find the side length of the base.

Since it's a square, the area of the base is side length squared (s²). Therefore, s² = 64 cm². Taking the square root of both sides, we get s = 8 cm.

Now, let the height be h and use the Pythagorean theorem with the side length (8 cm) and the slant height (9 cm):

h² + (s/2)² = (slant height)²
h² + (8/2)² = 9²
h² + 4² = 81
h² + 16 = 81
h² = 65

Taking the square root of both sides:

h = √65 cm ≈ 8.06 cm

The height of the pyramid is approximately 8.06 cm.

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If a number cube is rolled twice, then the probability of getting a six on the first role and then a number less than 5 on the second role is 1/9.

To find the probability of getting a six on the first roll and a number less than 5 on the second roll, we will multiply the individual probabilities of each event.

A number cube has 6 faces, so the probability of rolling a six is 1/6.

For the second roll, there are 4 numbers less than 5 (1, 2, 3, and 4), so the probability of rolling a number less than 5 is 4/6 or 2/3.

To find the combined probability, simply multiply the two probabilities: (1/6) × (2/3) = 2/18 = 1/9.

So, the probability of getting a six on the first roll and a number less than 5 on the second roll is 1/9.

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Answer:

im gooder like that

Step-by-step explanation:

3z*5=15z

15z+4z-7

19z-7  

The numerical value of Oz is approximately -1819.86.

Using the chain rule, we have:

[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt\\dz/ds = dz/dy * dy/ds[/tex]

We can calculate each term using the given equations:

dz/dx = 1

dx/dt = 2

dy/dt = 0

dz/dy = cos(y)

dy/ds = 6t

Substituting these values, we get:

[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt = 1 * 2 + cos(y) * 0 = 2\\dz/ds = dz/dy * dy/ds = cos(y) * 6t = 6t * cos(6st)[/tex]

To find дz as/Əz, we need to solve for as in terms of z and s:

z = x + sin(y) = 2t + sin(6st)

x = 2t

y = 6st - 1

Solving for s in terms of t, we get:

s = (y + 1)/(6t)

Substituting this into the equation for z, we get:

z = 2t + [tex]sin(6t(y+1)/(6t)) = 2t + sin(y+1)[/tex]

Taking the partial derivative of z with respect to as, we get:

[tex]дz/Əz = 1[/tex]

B. To find the numerical values of дz and Oz, we need to plug in the given values of x, y, s, and t into our equations. Using the given values, we get:

x = 2t = -964

y = 6st - 1 = -3617

z = x + sin(y) = -964 + sin(-3617) ≈ -964.73

Using the values of s and t, we can find:

s = (y + 1)/(6t) ≈ -0.9985

t = x/2 ≈ -482

Substituting these values into our equation for дz as/Əz, we get:

дz/Əz = 1

Therefore, the numerical value of дz is 1.

Substituting these values into our equation for dz/ds, we get:

dz/ds = 6t * cos(6st) ≈ -1819.86

Therefore, the numerical value of Oz is approximately -1819.86.

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To find dy/dx, we need to take the derivative of y with respect to x. On evaluating the value of dy/dx is [tex]-9t^{8/9}[/tex]

However, we are given x in terms of t. So first, we need to use the chain rule to find dx/dt:
x = [tex]t^{1/9}[/tex]
dx/dt = (1/9) * [tex]t^{-8/9}[/tex]

Now, we can use the chain rule again to find dy/dt:

y = 9 - t
dy/dt = -1

Finally, we can use the formula for the chain rule to find dy/dx:

dy/dx = (dy/dt) / (dx/dt)
dy/dx = (-1) / ((1/9) * [tex]t^{-8/9}[/tex]
dy/dx = [tex]-9t^{8/9}[/tex]

So, the final answer is dy/dx = [tex]-9t^{8/9}[/tex]
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Answer:

D. 4π

Step-by-step explanation:

Circumference: C = 2πr = 2π(8) = 16π

The distance = 1/4 circumference (angle is 90 degrees)

=> distance = 16π/4 = 4π

The value of integral of (198r² + 9r – 50 dr  is  (16/27)ln|11r + 2| - (2/3)ln|9r - 4| + C

Now, we can write the integrand as a sum of two fractions:

(198r² + 9r - 50) / (11r + 2)(9r - 4) = A/(11r + 2) + B/(9r - 4)

To find A and B, we need to solve for them using the method of equating coefficients:

198r² + 9r - 50 = A(9r - 4) + B(11r + 2)

Setting r = 4/9 and r = -2/11, we get two equations:

198(4/9)² + 9(4/9) - 50 = A(9(4/9) - 4) + B(11(4/9) + 2)

198(-2/11)² + 9(-2/11) - 50 = A(9(-2/11) - 4) + B(11(-2/11) + 2)

Solving these equations gives A = 16/27 and B = -2/3.

So, the integral can be written as:

∫(198r² + 9r - 50) / (11r + 2)(9r - 4) dr = ∫16/27(11r + 2)^-1 dr - ∫2/3(9r - 4)^-1 dr

Integrating each term gives:

(16/27)ln|11r + 2| - (2/3)ln|9r - 4| + C

where C is the constant of integration.

In summary, using partial fraction decomposition, we can express the given integral as a sum of two simpler integrals, which can be evaluated using the natural logarithm function.

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Step 1: Find the cost of 1 pie

1 pie = 4 cups of fruit + 1 pie crust

1 pie = 4(0.75) + 1(2.50)

1 pie = 3 + 2.50

1 pie = 5.50

Step 2: Find the amount of money a baker makes by selling 1 pie

1 pie cost = 5.50

1 pie revenue = 10.25

1 pie profit = 4.75

Step 3: Find the amount of money a baker makes by selling 10 pies

1 pie profit = 4.75

10 pies profit = 47.5

Answer: $47.50

Hope this helps!

Answer:

a = 16

b = 8z

Step-by-step explanation:

Expanding the given expression, we get:

(4y + z)^2 = (4y + z) × (4y + z)

= 16y^2 + 8yz + z^2

Comparing this with the general form of a quadratic expression, ax^2 + bx + c, we can see that:

a = 16

b = 8z

Therefore, the value of a is 16 and the value of b is 8z.

Answer:

Step-by-step explanation:

In option (a), sin(t) < 0 and cos(t) < 0, In trigonometry, the terminal point of an angle t is the point on the unit circle where the angle intersects with the circle.

The position of the terminal point determines the quadrant in which the angle lies.

To determine the quadrant, we need to look at the signs of the sine and cosine functions. In quadrant I, both sine and cosine are positive. In quadrant II, sine is positive and cosine is negative. In quadrant III, both sine and cosine are negative. In quadrant IV, sine is negative and cosine is positive.

In option (a), sin(t) < 0 and cos(t) < 0, both the sine and cosine functions are negative. This means that the terminal point lies in quadrant III.

In option (b), sin(t) > 0 and cos(t) < 0, the sine function is positive and the cosine function is negative. This means that the terminal point lies in quadrant II.

In option (c), sin(t) > 0 and cos(t) > 0, both the sine and cosine functions are positive. This means that the terminal point lies in quadrant I.

In option (d), sin(t) < 0 and cos(t) > 0, the sine function is negative and the cosine function is positive. This means that the terminal point lies in quadrant IV.

In summary, the signs of the sine and cosine functions can be used to determine the quadrant in which the terminal point lies.

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The evaluation of the triple integral ∫∫∫E 4[tex]x^{2}[/tex] + 3dV is  (38/15)ππ

To evaluate the triple integral ∫∫∫E 4x^2 + 3dV in spherical coordinates, we need to express the integrand and the volume element dV in terms of the spherical coordinates ρ, θ, and φ.

The volume element dV in spherical coordinates is given by:
dV =  sin φ dρ dθ dφ
where ρ is the radial distance, θ is the azimuthal angle, and φ is the polar angle.
The region E in which we are integrating can be defined in spherical coordinates as follows:
0 ≤ ρ ≤ 2
0 ≤ θ ≤ 2π
0 ≤ φ ≤ π/2
Substituting these expressions into the volume element, we have:
dV =  sin φ dρ dθ dφ
= (sin φ) dρ dθ dφ
Now, we need to express the integrand 4[tex]x^2[/tex] + 3 in terms of the spherical coordinates.

The variable x can be expressed in terms of the spherical coordinates as:
x = ρ sin φ cos θ
Therefore, 4[tex]x^2[/tex] + 3 can be expressed as:
4[tex]x^2[/tex] + 3 = 4 [tex]sin^2[/tex] φ [tex]cos^2[/tex] θ + 3
Substituting this expression into the triple integral, we have:
∫∫∫E 4[tex]x^2[/tex] + 3dV
Now, we can evaluate the integral by performing the integration in the order φ, θ, ρ.
= (8/15)π + 2π
= (38/15)ππ

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The maximum height of Anna's golf ball is 6.25 feet.

To find the maximum height of Anna's golf ball, we need to determine the vertex of the parabolic equation y = x - 0.04x^2. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, the coefficients a and b are:
a = -0.04
b = 1

Substituting the values into the formula:

x = -1 / (2 * -0.04)
x = -1 / (-0.08)
x = 12.5

Now, we need to find the y-coordinate of the vertex by plugging the x-coordinate back into the equation:

y = 12.5 - 0.04(12.5)^2

y = 12.5 - 0.04(156.25)

y = 12.5 - 6.25

y = 6.25

So, the maximum height of Anna's golf ball is 6.25 feet.

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For each function, all four second-order partial derivatives are f(x,y) are (x + y)2, (x + y), 3x^2y + 5xy^2, 2xy, (x + y)e^y, xe^y, sin(x/y), x^2 + y^2, 5x^3y^2 - 7xy^3 + 9x^2 +11, sin(x^2 + y^2) and 3 sin(2x) cos(5y). It is proved that f x y is equals to f y x.

f(x,y) = (x + y)2

f x x = 2, f xy = 2, f yx = 2, f y y = 2

Since f x y = fy x, the mixed partial derivatives are equal.

f(x,y) = (x + y)

f x x = 0, f x y = 1, f y x = 1, f y y = 0

Since f x y = f y x, the mixed partial derivatives are equal.

f(x, y) = 3x^2y + 5xy^2

f x x = 6y, f x y = 6x + 10y,  f y x = 6x + 10y, f y y = 10x

Since f x y = f y x, the mixed partial derivatives are equal.

f(x, y) = 2 x y

f x x = 0, f x y = 2, f y x = 2, f y y = 0

Since f x y = f y x, the mixed partial derivatives are equal.

f(x,y) = (x + y) * e^y

f x x = e^y, f x y = e^y + e^y, f y x = e^y + e^y, f y y = (x + 2y) * e^y

Since f x y = f y x, the mixed partial derivatives are equal.

f(x,y) = x * e^y

f x x = 0, f x y = e^y, fy x = e^y, f y y = x * e^y

Since fx y = fy x, the mixed partial derivatives are equal.

f(x, y) = sin(x/y)

f x x = -sin(x/y) / y^2, f x y = cos(x/y) / y^2,  f y x = cos(x/y) / y^2, f y y = -x * cos(x/y) / y^4 - sin(x/y) / y^2

Since f x  y = f y x, the mixed partial derivatives are equal.

f(x, y) = x^2 + y^2

f x x = 2, f x y = 0, f y x = 0, f y y = 2

Since f x y = f y x, the mixed partial derivatives are equal.

f(x, y) = 5x^2y^2 - 7xy + 9x^2 + 11

f x x = 10xy^2 + 18, f x y = 10x^2y - 7, f y x = 10x^2y - 7, fy y = 10x^2y^2

Since fx y = fy x, the mixed partial derivatives are equal.

f(x,y) = sin(x^2 + y^2)

fx x = 2xcos(x^2 + y^2), fx y = 2ycos(x^2 + y^2), fy x = 2ycos(x^2 + y^2), fy y = 2x * cos(x^2 + y^2)

Since fx y = fy x, the mixed partial derivatives are equal.

f(x,y) = 3sin(2x)cos(5y)

fx x = 0, fx y = -30sin(2x)sin(5y), fy x = -30sin(2x)sin(5y), fy y = 0

Since fx y = fy x, the mixed partial derivatives are equal.

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The largest box of soup will hold about 120 ounces or 221 cubic inches of soup.

Since the scale factor is 2, the volume of the largest box will be 2^3 = 8 times the volume of the smallest box. Therefore, the volume of the largest box will be 8 x 15 cubic inches = 120 cubic inches. To find the dimensions of the largest box, we need to find the cube root of 120 cubic inches, which is approximately 5.87 inches.

Since the smallest box has no shape restrictions, we can assume that the largest box will also have a rectangular shape. Therefore, a set of dimensions for the largest box could be 5.87 inches x 5.87 inches x 5.87 inches, or rounded to the nearest tenth, 5.9 inches x 5.9 inches x 5.9 inches.

This would result in a volume of approximately 221 cubic inches, which is about 120 ounces of soup.

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The radar beam moves at a pace of roughly 536.47 kilometers per hour as it scans the coastline.

Let A represent the location of the radar antenna and B represent the shoreline location that is closest to A. Let C represent the radar beam's current location on the coast and Ф represent the angle between the beam and the line AB. As a result, we obtain a right triangle ABC, where AB is equal to 4 km, and BC is the length at which the radar beam sweeps along the shore.

32 rev/min(2π/60 sec) = 3.36 radians/sec. BC = r(Ф) = (4 km)(π/4) = π km.

We may calculate the radar beam's speed down the shore by multiplying these two values:

(536.47 km/hr) = 10.54 km/sec or (3.36 rad/sec)(π km).

Hence, the of sweeping is 10.54 km/sec.

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it is 16 steps from second base to third base .we can get this answer by

solving the logic given in the question .we need to add up the number of steps

what is  add up  ?

"Add up" means to calculate the total of two or more numbers or quantities by combining them together. It involves the mathematical operation of addition, which is the process of finding the sum of two or more numbers. For example, if you add up the numbers 3, 5, and 7, t

In the given question,

To find out how many steps it is from second base to third base, we need to add up the number of steps Gavin took in each direction.

Starting at second base, he took 18 steps forward to get caught, and then took 7 steps back. This leaves him 11 steps forward from second base.

Next, he took 3 more steps forward, for a total of 14 steps forward from second base. But then he took 5 steps back, leaving him 9 steps forward from second base.

Then he took 11 more steps forward, for a total of 20 steps forward from second base. But then he took 4 steps back, leaving him 16 steps forward from second base.

Finally, he was tagged out halfway between second and third base. Since he was 16 steps forward from second base, and halfway between second and third base, we can assume that third base is 16 steps away from second base.

Therefore, it is 16 steps from second base to third base.

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The volume of the pyramid with a square base of side length 11.8 ft and a height of 5.2 ft is 240.0 cubic feet.

To find the volume of a pyramid with a square base of side length 11.8 ft and a height of 5.2 ft, you can use the following formula:

Volume = (1/3) × Base Area × Height

1: Find the base area.

The base is a square with a side length of 11.8 ft, so the area of the base is:

Base Area = Side Length × Side Length

Base Area = 11.8 ft × 11.8 ft

Base Area ≈ 139.24 square ft

2: Find the volume.

Now, use the formula to find the volume:

Volume = (1/3) × Base Area × Height

Volume = (1/3) × 139.24 sq ft × 5.2 ft

Volume ≈ 240.0368 cubic ft

3: Round your answer to the nearest tenth.

Volume ≈ 240.0 cubic ft

So, the volume of the pyramid is approximately 240.0 cubic feet.

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Answer: 6cm

Step-by-step explanation: VF=(SF)^3

let x be the height of the larger container

VF1/VF2=(SF1/SF2)^3

54/128=(4.5/X)^3

rearrange to find x

x=cube root of (4.5^3*128)/54

x=6cm

31.8 kilograms is equivalent to 31,800 grams.

The correct answer is (D) 31,800 grams.

To convert kilograms to grams, we multiply the number of kilograms by 1000. So, to convert 31.8 kilograms to grams, we can use the following formula:

31.8 kilograms x 1000 grams/kilogram = 31,800 grams

Therefore, 31.8 kilograms is equivalent to 31,800 grams.

To convert kilograms to grams, we need to multiply the number of kilograms by 1000 because there are 1000 grams in one kilogram. In this case, Eddie's dog weighs 31.8 kilograms. To find out how many grams this is, we simply multiply 31.8 by 1000, which gives us 31,800 grams. Therefore, 31.8 kilograms is equivalent to 31,800 grams. It's important to understand the basic metric system conversions, like kilograms to grams, as they are commonly used in everyday life, particularly when it comes to measuring weight. Knowing how to make these conversions can be helpful in many different situations, from cooking and baking to medical and scientific contexts.  

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1. The area of the shaded region is

2. percentage of the shaded part is 89.6%

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of the shaded part = area of the rectangle - area of unshaded part

Area of rectangle = 7× 11 = 77 unit²

area of rectangle = 1/2 bh

= 1/2 × 4 × 4

= 1/2 × 8

= 4 unit²

area of second triangle = 4 units²

area of unshaded part = 4+4 = 8 units²

area of shaded part = 77-8 = 69units²

2. percentage of the rectangle shaded = 69/77 × 100

= 6900/77 = 89.6%

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1 hour =60 minutes

Step-by-step explanation:

Let M be the time in minutes . T be temperature in Farhenheit. From 45th min to end of the hour there remains a steady temperature. after that gyms starts to cools down . For time 45≤M≤60, Temperature T=77oF.To find a) Is M a function of T ? we know that Temperature changes with respect to time . So M is independent variable and T is dependent variable . so M cannot be a function of T .

From the given graph, the roots of the quadratic equation, 0 = x² - 6x + 5, is 1 and 5. The correct option is the last option x= 1, 5

From the question, we are to determine the roots of the quadratic equation from the provided graph.

From the given information,

The given quadratic equation is

0 = x² - 6x + 5

The roots of a quadratic function are the values of x where the function equals zero. On a graph, this corresponds to the points where the graph intersects the x-axis.

From the graph, we will read the x-coordinates of the points where the graph intersects the x-axis.

From the given graph, the x-coordinates of the points where the graph intersects the x-axis are 1 and 5

Hence, the roots of the quadratic equation is 1 and 5

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The parabola has an axis of symmetry x=22, vertex at (22, 2), and opens downward.

Given the focus (22, 3) and directrix y=1, we can determine the following:

a. Axis of symmetry: Since the parabola is vertical (directrix is horizontal), the axis of symmetry will be a vertical line passing through the focus. So, x=22 is the axis of symmetry.

b. Vertex: The vertex is the midpoint between the focus and the directrix. To find the vertex, average the y-coordinates of the focus and the directrix. Vertex = (22, (3+1)/2) = (22, 2).

c. Direction: If the focus is above the directrix, the parabola opens upward. If the focus is below the directrix, the parabola opens downward. In this case, the focus (22, 3) is above the directrix y=1, so the parabola opens downward.

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The number of cells found in an average Koala is 1.30 x 10¹², under the condition that a cell is a sphere with radius 10 or 0. 001 centimeter.

Then the volume of a sphere with radius 10 cm is considered to be 4/3π(10)³ cubic cm that is approximately 4,188.79 cubic cm.
The evaluated volume of a sphere with radius 0.001 cm is 4/3π(0.001)³ cubic cm that is approximately 0.00000419 cubic cm.

Then the evaluated mass of a single cell is  found by applying the formula
mass = density x volume
In case of larger cell, the mass will be
mass = 1.1 g/cm³ x 4,188.79 cubic cm
= 4,607.67 grams

In case of  smaller cell, the mass will be

mass = 1.1 g/cm³ x 0.00000419 cubic cm
= 0.00000461 grams

As koalas measure an average of 6 kilograms or 6,000 grams², we can evaluate the number of cells in an average koala using division of the weight of the koala by the mass of a single cell

In case of larger cells
number of cells = weight of koala / mass of single cell
number of cells = 6,000 grams / 4,607.67 grams
≈ 1.30 x 10⁶ cells

For smaller cells:
number of cells = weight of koala / mass of single cell
number of cells = 6,000 grams / 0.00000461 grams

≈ 1.30 x 10¹² cells
To learn more about volume
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