Find the median and mode of the data.
3, 4 1/4, 3 3/4, 5, 2 1/2, 8 2/3, 2 1/2
The median is
and the mode is

The diameter of the pizza is 8.96 inches then we get the largest slice of the pizza.

Given, we are offered one slice from a round pizza and the perimeter of the slice is 16 inches.

so, the largest slice in the pizza will have an angle of 90° at the center.

Now, Perimeter of the slice = length of the arc + 2 × radius

16 = 1/4×2πr + 2r

16 = πr/2 + 2r

16 = 3.57r

r = 4.48

So, the diameter of the pizza is 8.96 inches.

Hence, the diameter of the pizza is 8.96 inches then we get the largest slice of the pizza.

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Answer:

30+6p

Step-by-step explanation:

6 times p + 6times5

6p+30

According to the question, the region is bounded by the curve with the given data as \(x = y^{3} , x=1, y=0.\)

To compute the volume of the solid, use the disk method. The given object is rotated along the horizontal axis with the disk cross sectional area and the volume can be written as:

\(v=\int\limits^a_b {\pi x^{2} } \, dx\)

As per question, when x = 1 then the value of y is: y = 1

Now, substituting calculated values in the expression:

\(v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx\)

Substitute the value of the variable 'x':

Therefore, the expression can be written as:

\(v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx=\int\limits^0_1 {\pi (y^{3}) ^{2} } \, dx=\frac{\pi }{7}=0.448\)

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Answer:

Slant height of the pyramid = 11.66 m

Step-by-step explanation:

A squad pyramid has a volume of

V = ⅓ × (area of base) × (vertical height)

Area of the pyramid's square base = 144 m²

Volume = 384 m³

384 = ⅓ × 144 × (vertical height)

Vertical height = (3×384)/(144) = 8 m

But, the slant height of the square based pyramid forms a right angled triangle with the vertical height of the pyramid and the distance from the centre of the base of the pyramid to an edge of the pyramid.

The distance from the centre of the base of the pyramid to an edge of the pyramid = half of the length of the diagonal of the square base of the pyramid.

The diagonal of the square base of the pyramid also forms a right angled triangle with two sides of the square base of the pyramid.

Area of the square base of the pyramid = 144 m²

Area of a square = (side length)²

Side length = √(Area of the square) = √144 = 12 m

Using Pythagoras theorem,

(Length of the diagonal)² = 12² + 12² = 288

Length of the diagonal = (12√2) m

Half of the length of the diagonal of the square base = 6√2 m

Using Pythagoras theorem further

(Slant height of the pyramid)² = (vertical height of the pyramid)² + (Half of the length of the diagonal of the square base)²

(Slant height of the pyramid)² = 8² + (6√2)² = 64 + 72 = 136

Slant height of the pyramid = √136 = 11.66 m

Hope this Helps!!!

Answer:

7/2

Step-by-step explanation:

Answer:

65.97

Step-by-step explanation:

Don't really know how to explain how to do this, but Omni Calculator is very helpful.

Hope that this helps!

For events A and B to be independent, the condition that must be true is:
P(A ∩ B) = x * y

The correct condition that must be true if events A and B are independent is:

P(A ∩ B) = P(A) x P(B).

where P(A) is the probability of event A, P(B) is the probability of event B, and P(A ∩ B) is the probability of both events A and B occurring together.

In other words, if events A and B are independent, then the probability of both events occurring together is equal to the product of their individual probabilities.

When two events A and B are independent, the following condition must be true:
P(A ∩ B) = P(A) * P(B)
In your case, the probability of event A is x, and the probability of event B is y.

Therefore, the correct answer is:

P(A ∩ B) = x*y

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x<4 is the solution of the inequality 5 x < 20

A number system is defined as a system of writing to express numbers.

The given inequality is  5 x < 20

We have to solve for x

Divide both sides by 5

x<20/5

Divide numerator and denominator by 5

x<4

The graph of x<4 is given in the attachment.

Hence, x<4 is the solution of the inequality 5 x < 20

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Teresa needs to buy two new tires for her mountain bike.

With a budget of $120, she will likely spend within $25 of that amount.

To help her find the best deal, Teresa should first research what type of mountain bike tire she needs. She can look at the bike's current tires to determine the size, or she can look up the bike model and size online. She should then research prices at a variety of local bike shops and online retailers to compare costs.

Once she finds the best price, Teresa should look for discounts and coupon codes that she can use to reduce the cost of her tires. She should also make sure she is aware of any extra costs, such as shipping and taxes.

With some research and savvy shopping, Teresa should be able to find two mountain bike tires that fit within her budget of $120 and that will keep her bike running smoothly.

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Answer:

No

Step-by-step explanation:

There is no numerator, no denominator, no division symbol because it is not a legal fraction. The denominator can never be zero in any fraction.

Answer:

A

Step-by-step explanation:

Given a parabola in standard form, y = ax² + bx + c ( a ≠ 0 ), then

minimum/ maximum value is the y- coordinate of the vertex.

The x- coordinate of the vertex is

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

y = x² - \(\frac{5}{3}\) x + \(\frac{31}{36}\) ← is in standard form

with a = 1 and b = - \(\frac{5}{3}\) , thus

\(\frac{x}{vertex}\) = - \(\frac{-\frac{5}{3} }{2}\) = \(\frac{5}{6}\)

Substitute this value into y

y = (\(\frac{5}{6}\) )² - \(\frac{5}{3}\) (\(\frac{5}{6}\) ) + \(\frac{31}{36}\)

   = \(\frac{25}{36}\) - \(\frac{25}{18}\) + \(\frac{31}{36}\) = \(\frac{1}{6}\)

Since a > 1 then the vertex is a minimum, thus

minimum value = \(\frac{1}{6}\) → A

Answer:

The perimeter is 56.6 ft

Step-by-step explanation:

  7.7 * 6 + 5.2 * 2

= 46.2 + 10.4

= 56.6 ft

Answer:

Step-by-step explanation:

It is asking for the "mode" which is the data element you see the most, therefore it is 2.

according to question the correct answer is:

dy/dx = (3cos(lnx) - 2sin(lnx)) / x

To find the derivative of y = 2cos(lnx) + 3sin(lnx), we use the chain rule and the product rule:

dy/dx = [d/dx(2cos(lnx))] + [d/dx(3sin(lnx))]

= [-2sin(lnx) / x] + [3cos(lnx) / x]

= (3cos(lnx) - 2sin(lnx)) / x

what is derivative?

The derivative is a fundamental concept in calculus that measures how a function changes as its input changes. In other words, it's the rate at which the output of a function changes with respect to its input.

The derivative of a function y = f(x) is denoted by f'(x) or dy/dx, and it gives the slope of the tangent line to the graph of f(x) at any point x. Geometrically, the derivative represents the instantaneous rate of change of the function at a given point.

The derivative can be calculated using various rules and formulas, including the power rule, product rule, quotient rule, chain rule, and trigonometric rules, among others.

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The standard normal distribution has the largest variance.

The variance of a normal distribution determines the spread or dispersion of the data.

A larger variance indicates a wider spread of values around the mean. The standard normal distribution is a specific case of the normal distribution with a mean of 0 and a variance of 1. Since the variance is fixed at 1 for the standard normal distribution, it has the largest variance compared to any other normal density with different variances.

The variance of a normal distribution measures how much the data values deviate from the mean.

It is calculated as the average of the squared differences between each data point and the mean. A higher variance implies a greater dispersion of values, indicating a wider range of possible outcomes.

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Answer:

f(8) = 9

Step-by-step explanation:

f(x)=(x-5)^2

Let x = 8

f(8)=(8-5)^2

     = 3^2

     = 9

Answer:

The first option

Step-by-step explanation:

You do 1.68/3 and get .56

meaning that each can in the 3 pack is .56 cents

Next do 2.45/5 to get .49

meaning that each can in the 5 pack is .49 cents

which means that the 5 cans is a better buy

One ton of cooling is equal to 12,000 British Thermal Units (BTUs) per hour.

In the context of air conditioning and refrigeration systems, a ton is a unit of measurement used to describe the cooling capacity of the system. One ton of cooling is equal to 12,000 British Thermal Units (BTUs) per hour.

Therefore, to convert BTUs to tons, you simply need to divide the number of BTUs by 12,000. For example:

24,000 BTUs = 2 tons (24,000 / 12,000)

36,000 BTUs = 3 tons (36,000 / 12,000)

48,000 BTUs = 4 tons (48,000 / 12,000)

60,000 BTUs = 5 tons (60,000 / 12,000)

This conversion is useful when selecting the appropriate size air conditioning or refrigeration system for a given space, as the size of the system will depend on the cooling load required to keep the space at a comfortable temperature.

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The value of x is 12.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

We are given a triangle with the angles (8x-1), (3x +9) and (3x + 4)

Since we know that the sum of the interior angles of a triangle is 180 degrees.

Therefore,

(8x-1) + (3x +9) + (3x + 4) = 180

8x + 6x + 12 = 180

14x + 12 = 180

14x = 168

x = 12

Hence, the value of x is 12.

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In any group of two or more people, there are always two who have the same number of friends within the group.

Suppose we have a group of n people. Each person can have between 0 and n-1 friends within the group. If someone has 0 friends, then everyone else must have at least 1 friend. Similarly, if someone has n-1 friends, then everyone else must have at most n-2 friends.

Therefore, there are only n-1 possible numbers of friends that a person can have within the group. But we have n people, so by the pigeonhole principle, at least two people must have the same number of friends within the group.

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The equivalent equation solved for h is \(\frac{P}{mg} = h\)

From the question, we are to determine the equivalent equation solved for h

From the given information,

The amount of potential energy, P, is modeled by the equation

P = mgh

To determine the equivalent equation solved for h, we will make h the subject of the equation,

From,

P = mgh

Divide both sides of the equation by mg

That is,

\(\frac{P}{mg} = \frac{mgh}{mg}\)

∴ \(\frac{P}{mg} = h\)

Hence, the equivalent equation solved for h is \(\frac{P}{mg} = h\)

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Answer

B

Step-by-step explanation:

Edge 2022

Answer:

\(y = \frac{11}{3}x + -\frac{4}{3}\)

Step-by-step explanation:

\(y = mx + b\\m = \frac{-5 - 6}{-1 - 2} = \frac{-11}{-3} = \frac{11}{3} \\\\y = \frac{11}{3}x + b\\6 = \frac{11}{3}(2) + b\\6 = \frac{22}{3} + b \\6 - \frac{22}{3} = b \\b = -\frac{4}{3}\\\\y = \frac{11}{3}x + -\frac{4}{3}\)

Volume = base area x tall

base area = π x (1.8in)²

base area = 10.179 in²

Volume = 10.179 in² x 6.7 in

Volume = 68.198 in³

the volume is 68.198 in³

Answer:

(-9,-6)

Step-by-step explanation:

(-8 + - 10) ÷ 2 = - 9 = x axis value

(-10 + - 2) ÷ 2 = - 6 = y axis value

Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

For a function, f(x) = 1 + 3x , the computed value of lim h→0 [f(5 + h) − f(5)]/h is equals to the three.

In Mathematics, the limit of a function is a value of the function as the input of the function tries approaches some number. Function limits are used to define continuity, integrals, and derivatives. Mathematically, let f(x) be a function and L be limit of function, f(x) at x a exist if and only if lim f(x) = lim f(x) = L

x→a⁻ x→a⁺

We have, f(x) = 1+3x and will compute lim h→0 [f(5 + h) − f(5)]/h . Firstly, determine the value of function at x = 5 , x = 5+h.

So, f(5) = 1+ 3×5 = 16 and f(5+ h) = 1+3(5+h)

= 16+ 3h

Now, lim [ f(5 + h) − f(5)]/ h

h→0

= lim [(16 + 3h) − (16) ]/ h

h→0

= lim [ 16 + 3h - 16 ]/ h

h→0

= lim [ 3h/ h ] = lim [ 3h¹h⁻¹ ]

h→0 h→0

= lim [ 3h¹⁻¹ ] = lim [ 3h⁰ ]

h→0 h→0

= lim 3 (1) = 3 ( since, x⁰ = 1 )

h→0

Hence, the required limit value is 3.

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Answer:

5 Months

Step-by-step explanation:

For Avas its 50 dollars times 5 months which equals 250 plus the 100 dollar fee makes 350

For Mark its 60 times 5 equals 300 plus the 50 dollar fee makes also 350

Answer:the correct answer would be 5 months

Step-by-step explanation:

This vector function removes an item from a vector is erase (option c).

The vector function that removes an item from a vector in most programming languages, including C++, is typically called "erase." The erase function is used to remove elements from a vector based on a specified position or range.

The erase function can take different forms depending on the programming language and vector implementation. For example, in C++, the erase function is a member function of the vector class and can be used in the following ways:

vector.erase(position) - Removes the element at the specified position.

vector.erase(first, last) - Removes elements in the range defined by the iterators 'first' and 'last'.

Using the erase function allows you to remove elements from a vector and adjust the size of the vector accordingly. The correct option is c.

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