The zoo charges $4 admission fee along with a $2 charge for each exhibit you visit.​

The area of the circle in terms of pi, with a diameter of 9.6 meters, is 23.04π square meters.

The diameter of a circle is twice the radius, so if the diameter is 9.6 meters, then the radius is half of that, or:

r = 9.6 / 2 = 4.8 meters

The area of a circle is given by the formula:

A = πr²

Substituting in the value of r, we get:

A = π(4.8)²

Simplifying the expression by squaring 4.8, we get:

A = π(23.04)

So the area of the circle is:

A = 23.04π square meters

Therefore, the area of the circle in terms of pi, with a diameter of 9.6 meters, is 23.04π square meters.

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In the context of rubiks cube solving the rate at which one can solve a rubiks cube is determined by the number of cubes solved and the time taken

In this question we were told that moira solved a rubiks cube in 3 minutes 30 seconds

Let us convert time total time to seconds

3 minutes 30  in seconds = 3*60+ 30 = 180+30 = 210 seconds

Hence  Moira rate  = 1 rubiks cube/210 seconds

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Answer: 15 years

Step-by-step explanation:

6000 x 1.05^x = 12000

1.05^x=2

log(1.05^x)=log(2)(Take log of both sides)

x*(log(1.05))=log(2)

x= log(2)

log(1.05)

x=14.206699

15 years

Answer:

(x² - 8x + 16) = (x-4) (x-4)

Step-by-step explanation:

We have to factorize the given expression

(x²-8x+16)

(x² - 8x + 16 ) = x² - 2(4x) + 4²

                    = ( x-4)²

[As we know (a-b)² = a² + b² - 2ab]

so (x² - 8x + 16) = (x-4) (x-4) is the factored form of the given expression.

Here we need to see which factored expression is equivalent to the polynomial x^2 - 8x + 16.

We will find that the correct option is: (x - 4)^2

Now let's see how to get this.

Remember the expansion:

(x + a)^2 = x^2 + 2*a*x + a^2

In our polynomial x^2 - 8x + 16 we can see that the second term is negative, thus we must have something like:

(x - a)^2 = x^2 - 2*a*x + a^2

Also the constant digit is 16, then:

a^2 = 16

a = √16 = 4

Thus the polynomial is: (x - 4)^2

Expanding this we get:

(x - 4)^2 = x^2 - 2*4*x + 16 = x^2 - 8*x + 16

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A polygon is a closed figure that has three or more sides. It is a two-dimensional geometric shape formed by connecting line segments. Polygons are classified based on the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and so on.

A polygon is a fundamental concept in geometry, representing a closed figure formed by connecting straight line segments. The word "polygon" originates from the Greek words "poly" meaning "many" and "gonia" meaning "angle." A polygon must have three or more sides, which are line segments that intersect at their endpoints.

The sides of a polygon do not cross each other and are not curved. Each side of a polygon connects two consecutive vertices (corner points). Polygons are classified based on the number of sides they possess, ranging from triangles (3 sides) to quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), and so on.

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Answer:

it is the 4th and 5th

Step-by-step explanation:

by following the laws of BODMAS

Brackets

of

Division

Multiplication

Addition

Subtraction

(5×6)+2=5×6+2

(30)+2=30+2

32=32

5×6+2=2+5×6

30+2=2+30

32=32

\(\large{\underline {\underline {\frak {SolutioN:-}}}}\)

➝ -4 × (-2) [2 × (-6)+ 3×(2×6-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-8) ]

➝ -4 × (-2) [2 × (-6) + 3 × (4) ]

➝ -4 × (-2) [2 × (-6) + 12 ]

➝ -4 × (-2) [(-12) + 12 ]

➝ -4 × (-2) [0]

➝ -4 × 0

➝ 0

Answer:

-4*-2

Step-by-step explanation:

the multiple of both side is 4*2*,26+*32*--=6 44

If this group of kids started with 120 marbles in total, then they can play 14 game

Initial number of marbles = 120

Lost at every game = 5

Stolen by a squirrel = 3

Left = less than 10

Let the number of games be x

then lost marbles = 5x

stolen marbles = 3x

Inequality:

120 - 5x - 3x < 10

120 - 8x < 10

110 < 8x

x > 110/8

x > 13 rounded down

Since there should be more than 0 left, another inequality for it:

120 - 8x > 0

120 > 8x

x < 15

So 13 < x < 15, which leaves us with 14

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Answer:

B

Step-by-step explanation:

We know that 4×6=24.

Now using the radical rule, we can simplify to find 2 √ 6.

Answer:

(-3.2)^0 = 1

Step-by-step explanation:

Anything to the power of 0 equals 1.

Answer:

1

Step-by-step explanation:

Any number raised to a power of 0 is equal to 1.

Answer:

Look below.

Step-by-step explanation:

1 pound=16 ounces

If each cereal box contains 18 then that means that one box has 1 pound and 2 ounces. We need about 72 ounces to reach 4 pounds.

72/18=4 ------->  4 boxes of cereal.

The simplified form of the expression -8/2 ÷ 6/-3 is 4.

To simplify the expression, we need to perform the division and simplify the resulting fraction. We can rewrite the expression as (-8/2) / (6/-3).

First, simplify the numerator (-8/2) to -4. Then, simplify the denominator (6/-3) to -2.

Now, we have -4 / -2. To divide fractions, we multiply the numerator of the first fraction by the reciprocal of the second fraction. In this case, we have (-4) * (-1/2), which simplifies to 4/2.

Finally, simplify the fraction 4/2 by dividing both the numerator and denominator by their greatest common divisor, which is 2. This gives us the simplified form of 4/2, which is 2.

Therefore, the simplified form of -8/2 ÷ 6/-3 is 4.

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Answer:

7.87 i b think

Step-by-step explanation:

Answer:

74% is greater

Explanation:

14/19 as a percent is 73%

74% > 73%

The alternating series test is a technique for demonstrating convergence of an alternating series when its terms (1) become smaller in absolute value and (2) get closer to zero in the limit.

The Leibniz test, often referred to as the alternating series test, is a form of series test used to ascertain whether two alternate series are converging. Remember that the test cannot determine whether the series diverges. There are three conditions that must be met for the Alternating Series Test: The series needs to switch up. For large n, the words must become less significant. The nth term must equal zero. The second prerequisite appears superfluous. Another test must be used to demonstrate that a series diverges. The ideal plan is to use the Divergence Test to check for divergence in an alternating series first. You've reached your conclusion if the terms do not converge to zero.

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The exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

The exterior angle adjacent to the largest interior angle in a triangle is equal to the sum of the other two interior angles.

Let's call the measures of the angles in the triangle x, x, and 2x. Then,

x + x + 2x = 180 degrees,

so 4x = 180 degrees, and

x = 45 degrees.

The largest interior angle is 2x, or 90 degrees. The exterior angle that is adjacent to this angle is equal to 180 degrees minus the interior angle, which is 180 - 90 = 90 degrees.

So the exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

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Answer:

Can you tell me what they are looking for in the question?

Roger Federer's record-tying run of five consecutive Wimbledon Championships was ended in 2008 when he was defeated in the final by Rafael Nadal.

Swiss tennis player Roger Federer, born in Basel, Switzerland, on August 8, 1981, dominated the sport in the early 21st century with his superb all-around performance.

At Wimbledon 2008, Federer made an effort to beat Borg's mark and become the first male player to win six straight Wimbledon championships in the Open Era.

Federer's 41-match winning streak was snapped at Wimbledon when Nadal upset him in his most successful major.

Roger federer's run of 5 consecutive wimbledon championships, a record tied with bjorn borg, was halted when he was defeated in the final in 2008 by Rafael Nadal

The following year, Federer repeated the feat, and in 2010, Nadal once again won the double.

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Answer:

\(s^2Y(s)+38Y(s)=g(s)\)

Step-by-step explanation:

Given the second order differential equation with initial condition.

\(y''+36y=g(t); \ y(0)=0, \ y'(0)=0, \ and \ y''(0)=1\)

Take the Laplace transform of each side of the equation.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

\(\boxed{\left\begin{array}{ccc}\text{\underline{Laplace Transforms of DE's:}}\\\\L\{y''\}=s^2Y(s)-sy(0)-y'(0)\\\\\ L\{y'\}=sY(s)-y(0) \\\\ L\{y\}=Y(s)\end{array}\right}\)

Taking the Laplace transform of the DE.

\(y''+36y=g(t); \ y(0)=0, \ y'(0)=0, \ and \ y''(0)=1\\\\\Longrightarrow L\{y''\}+38L\{y\}=L\{g(t)\}\\\\\Longrightarrow s^2Y(s)-s(0)-0+38Y(s)=g(s)\\\\\Longrightarrow \boxed{\boxed{s^2Y(s)+38Y(s)=g(s)}}\)

Thus, the Laplace transform has been applied.

Sum of two opposite angles in a Cyclic Quadiratral is 180°

\(\\ \sf\longmapsto 110+<CDE=180\)

\(\\ \sf\longmapsto <CDE=180-110\)

\(\\ \sf\longmapsto <CDE=70°\)

Answer:

let <CDE be x:

\({ \tt{110 \degree + x = 180\degree}} \\ \\ { \tt{x = 180 \degree - 110 \degree}} \\ \\ { \tt{x = 70 \degree}}\)

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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The length of the curve y = ln(sin(x)) for 6π ≤ x ≤ 2π is approximately 4.857 units.

To find the length of the curve, we can use the arc length formula:

L = ∫√(1 + (dy/dx)²) dx

First, let's find the derivative of y = ln(sin(x)). Taking the derivative, we have:

dy/dx = (1/sin(x)) * cos(x) = cot(x)

Next, we can compute the integral:

L = ∫√(1 + cot²(x)) dx

Since we are given the limits of integration as 6π and 2π, we evaluate the integral within this range:

L = ∫(6π to 2π) √(1 + cot²(x)) dx

Using numerical methods or a computer algebra system, we find that the approximate value of L is 4.857 units.The length of the curve y = ln(sin(x)) for 6π ≤ x ≤ 2π is approximately 4.857 units.

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The evaluated lateral surface area is 261.8 square meters, under the condition that the base length is 20 m and height is 13 m.

The lateral surface area of a cylinder is given by the formula 2πrh
Here,
r = radius of the base
h = height of the cylinder.
For the given case, the base length is 20 m and height is 13 m. Then the base length is stated  instead of the radius, we have  to evaluate the radius first.
The radius of a cylinder can be found applying the formula r = l/2π
Here,
l = base length.
So, staging l = 20 m
, we get
r = 20/(2π)
≈ 3.18 m
Now that we have received the radius and height, we can evaluate the lateral surface area applying the formula mentioned above.
Staging
r = 3.18 m
h = 13 m,
we get:
Lateral surface area
= 2πrh
≈ 261.8 m²
Then, the lateral surface area of the given cylinder is approximately 261.8 square meters.
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8k - 9(4k + 4) = 8k - 36k - 36 = -28k - 36

Let's rewrite in the simplest term,

→ 8k - 9(4k + 4)

→ 8k - 36k - 36

→ [-28k - 36]

The simplest term is -28k - 36.

To find the volume of the solid obtained by rotating the region bounded by the curves y = x³, x = 0, and x = 1 rotated around the y = −2, we can use the method of cylindrical shells.

The method of cylindrical shells involves integrating the volume of thin cylindrical shells that make up the solid. Here are the steps to follow:

Step 1: Draw a rough sketch of the region and the axis of rotation. The region is bounded by y = x³, x = 0, and x = 1, and is rotated around the line y = −2.

Step 2: For a given value of y, find the corresponding x-values of the curves that bound the region. In this case, the bounds are x = 0 and x = y¹/³

Step 3: The radius of the cylindrical shell is the distance between the axis of rotation and the curve. In this case, the radius is y + 2.

Step 4: The height of the cylindrical shell is the difference between the x-values of the curves at a given y-value. In this case, the height is x = y¹/³

Step 5: The volume of the cylindrical shell is given by the formula: V = 2πrh, where r is the radius and h is the height.

Step 6: Integrate the volume of the cylindrical shells over the range of y-values that span the region, which is from y = 0 to y = 1. The integral to evaluate is:

V = ∫(y=0 to y=1) 2π(y + 2)(y¹/³)) dy

Step 7: Simplify and evaluate the integral using standard techniques of integration, such as u-substitution. The result will be the volume of the solid.

After integrating and simplifying the integral, we get:

V = (32/5)π

Therefore, the volume of the solid obtained by rotating the region bounded by the curves y = x^3, x = 0, and x = 1 around the y = −2 is (32/5)π cubic units.

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Answer:

Answer: Level 1 - 50,000

Level 2 - 52,500

Level 3 - 55,125

Level 4 - 57,881

Level 5 - 60,775

Step-by-step explanation:

Level 1 population will be  50,000

Level 2 population will be  52,500

Level 3 population will be  55,125

Level 4 population will be  57,881

Level 5 population will be  60,775

What is a product?

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. Product can meet are the quantities that are included, and the outcome of the operation, or the final response.

The zombies would be 50,000 * 5% if Gavin were level 1, and 50,000 * (5% * 2) if Gavin were level 2, which would be equivalent to 50,000 * 10%. Gavin calculates the number of zombies by multiplying the player's stage by 5%, which equals 50,000 * 5%x Initial Density of Zombie.

The population of the 2 level is

50000 + (50000 * 5%)

50000 + 2500 = 52500

The population of 3 levels is

52500 + (52500 * 5%)

= 55,125

The population of 4 levels is

55,125 + (55,125 * 5% )

=  57,881

The population of 5 level is

57,881 + ( 57,881 + 5%)

=   60,775

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Answer:

3,-10...........................

Answer:

vertex = (3, - 8 )

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

y = x² - 6x + 1 ← is in standard form

with a = 1 and b = - 6 , thus

\(x_{vertex}\) = - \(\frac{-6}{2}\) = 3

Substitute x = 3 into the function for y

y = 3² - 6(3) + 1 = 9 - 18 + 1 = - 8

vertex = (3, - 8 )

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours