10. Which is the bigger portion, ½ of a 12 inch pizza, or % of a 9 inch pizza? Give a reason for your
answer.

Answer:

1.             0             10             20           30            40            50

             10             14             18            22            26            30

2. (the immage)

3. Yes this is a liner equation

Step-by-step explanation:

The value of k for the given differential equation is exact is,

⇒ k = 12

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

Given that;

The given differential equation is,

⇒ (y³ + kxy⁴ - 2x) dx + (3xy² + 24x²y³) dy = 0

And, The given differential equation is exact.

Now, We know that;

For the differential equation M dx + N dy = 0;

The condition of exactness is,

⇒ dM / dy = dN / dx  .. (i)

Here, We have;

M = y³ + kxy⁴ - 2x

N = 3xy² + 24x²y³

Hence, We get;

M = y³ + kxy⁴ - 2x

dM / dy = 3y² + 4kxy³

N = 3xy² + 24x²y³

dN / dx = 3y² + 48xy³

From (i);

⇒ dM / dy = dN / dx

⇒ 3y² + 4kxy³ = 3y² + 48xy³

⇒ 4kxy³ = 48xy³

⇒ 4k = 48

⇒ k = 48/4

⇒ k = 12

Thus, The value of k = 12

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6. The probability that Flight A will have a full flight is 0.4163.

7. The probability that all passengers who show up will have a seat on the flight is 0.5731.

8. The probability that Flight B will have exactly 68 customers show up is 0.0904.

9. The probability that all passengers that show up will have a seat on the flight is 0.9707.

6. If the airline chooses not to oversell flight A and sells exactly 96 tickets, the probability that it will have a full flight can be calculated using the binomial distribution. Let X be the number of passengers who show up for the flight.

Then, X follows a binomial distribution with n = 96 and p = 0.97 (since the probability that a passenger shows up is 1 - 0.03 = 0.97). Thus, the probability that all 96 passengers show up is:

P(X = 96) = (96 choose 96) × [tex]0.97^{96}[/tex] × [tex]0.03^0[/tex] = 0.4163

So, the probability that Flight A will have a full flight is 0.4163.

7. If the airline oversells Flight A with 99 tickets sold, the probability that all passengers who show up will have a seat on the flight (i.e. 3 or more no-shows) can be calculated using the binomial distribution again. Let Y be the number of no-shows for the flight. Then, Y follows a binomial distribution with n = 99 and p = 0.03. We want to find the probability that Y is greater than or equal to 3 (i.e. there are 3 or more no-shows), which can be calculated as:

P(Y >= 3) = 1 - P(Y <= 2) = 1 - ((99 choose 0) × [tex]0.03^0[/tex] × [tex]0.97^{99}[/tex] + (99 choose 1) × [tex]0.03^1[/tex] × [tex]0.97^{98}[/tex] + (99 choose 2) × [tex]0.03^2[/tex] × [tex]0.97^{97}[/tex]) = 0.5731

So, the probability that all passengers who show up will have a seat on the flight is 0.5731.

8. If the airline oversells Flight B with 70 tickets sold, the probability that the flight will have exactly 68 customers show up can be calculated using the binomial distribution with n = 70 and p = 0.98 (since the probability that a customer shows up is 1 - 0.02 = 0.98). Let Z be the number of customers who show up for the flight. Then, the probability that exactly 68 customers show up is:

P(Z = 68) = (70 choose 68) × [tex]0.98^{68}[/tex] × 0.02² = 0.0904

So, the probability that Flight B will have exactly 68 customers show up is 0.0904.

9. If the airline oversells Flight B with 72 tickets sold, the probability that all passengers who show up will have a seat on the flight can be calculated using the binomial distribution again. Let W be the number of no-shows for the flight. Then, W follows a binomial distribution with n = 72 and p = 0.02. We want to find the probability that W is less than or equal to 3, which can be calculated as:

P(W <= 3) = (72 choose 0) × [tex]0.02^0[/tex] × [tex]0.98^{72}[/tex] + (72 choose 1) × [tex]0.02^1[/tex] × [tex]0.98^{71}[/tex] + (72 choose 2) × [tex]0.02^2[/tex] × [tex]0.98^{70}[/tex] + (72 choose 3) × [tex]0.02^3[/tex] × [tex]0.98^{69}[/tex] = 0.9707.

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Answer: The actual roots of f(x) = 2x² + 2x - 24 are -3 and 4.

Step-by-step explanation:

The derivation of the critical radius(r*) as  and critical saturation(S*) as  is explained below .

To derive the critical saturation ratio (S*) and critical radius (r*),

We  use calculus to find the maximum value of the saturation ratio for a given radius on the Kohler curve.

First, let us consider the equation for the saturation ratio, S, as a function of radius, r:

that is : S = 1 + ar²/3b  ;

where a and b are constants.

Next, we find the derivative of S with respect to r:

On differentiating Curve "S" with respect to "r" ;

⇒ dS/dr = 2ar/3b  ;

Equating the derivative = 0 , we can find the critical points:

⇒ dS/dr = 0 = 2ar/3b  ;

On Solving for r, we have ;

⇒ r* = √(3b/a)

Next , to find the critical saturation ratio(S*) , we substitute r* back into the original equation for S:

⇒ S* = 1 + ar²/3b = 1 + a×(3b/a)/3b = 1 + √(4a³/27b)

Therefore , the critical saturation ratio and critical radius are written as r* = √(3b/a)  and  S* = 1 + √(4a³/27b)  .

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The given question is incomplete , the complete question is

Using your calculus skills derive the equations for the critical saturation ratio and the critical radius. (Hint: the critical point on the Kohler curve represents a maximum value).

The equations you should end up with are as follows:

r* = √(3b/a) and S* = 1 + √(4a³/27b) Where r* is the critical radius and S* is the critical saturation ratio .

Answer:

1.48

1 minute and 48 seconds

P(a purple marble then a white marble) is 6/105 ⇒ 1st answer

* Lets explain how to solve the problem

- There are 2 green marbles

- There are 7 blue marbles

- There are 3 white marbles

- There are 4 purple marbles

- Once a marble is drawn, it is NOT replaced

- We need to find P(a purple marble then a white marble)

* At first lets find the total number of marbles by adding all color

∵ There are 2 green , 4 purple , 3 white and 7 blue

∴ The total number of marbles = 2 + 4 + 3 + 7 = 16

∴ There are  16 marbles in the bag

∵ Probability = number of events/number of all outcomes

∵ There are 4 purple marbles

∴ The probability of chosen a purple marble is P(purple) = 4/15

∵ Once a marble is drawn, it is NOT replaced

∴ The total number of marbles = 15 - 1 = 14 marbles

∵ The number of white marbles is 3

∴ The probability of chosen a white marble is P(white) = 3/14

∵ P(a purple marble then a white marble) = P(purple) . P(white)

∵ P(purple) = 4/15

∵ P(white) = 3/14

∴ P(a purple marble then a white marble) = (4/15)(3/14) = 6/105

* P(a purple marble then a white marble) is 6/105

An equation connecting y and x.​is given as y = 15/x

What is inverse variation?

In Maths, inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases

y∞1/x

This implies that y=k/x            where k is a constant

5 = k/3

Making k the subject of the relation

therefore, k = 15

The equation connecting y and x would be y = 15/x

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Answer:12

Step-by-step explanation:

n*11=4*33

n=4*33/11=3*4=12

The largest total number of people who attended 3 matches on the day was 17, 000 people.

The largest total number of people who attended 3 matches on the day would be the sum of the largest rounded attendance numbers for each match:

Match 1: 5,000

Match 2: 8,000

Match 3: 4,000

Rounding each attendance number to the nearest 1,000 gives us:

Match 1: 5,000

Match 2: 8,000

Match 3: 4,000

Adding these rounded numbers together gives us:

5,000 + 8,000 + 4,000 = 17,000

Therefore, the largest total number of people who attended the three matches on the day was 17,000.

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The full question is:

Match 1 - 5, 000 people

Match 2 - 8, 000 people

Match 3 - 4, 000 people

This was the attendance at 3 football matches one day, each round to the three nearest 1,000. what's the largest total number of people who attended 3 matches on the day

3.5 kilograms is 3500 grams

Answer: 3500

Step-by-step explanation: one kilogram is 1000 gram so multiply 3.5 x 1000

The function's two zeros are: x = -1 and x = 6.

In mathematics, a function is a set of ordered pairs (input, output), where each input is associated with exactly one output. The input is commonly referred to as the independent variable, and the output is referred to as the dependent variable. A function can be represented algebraically, graphically, or verbally. Algebraically, a function is often represented by an equation that defines the relationship between the independent variable and the dependent variable. For example, the equation y = 2x + 1 defines a linear function, where x is the independent variable and y is the dependent variable.

Here,

The zeros of a function are the values of the independent variable for which the function equals zero. To determine all zeros for the function f(x) = (2x + 2)(x - 6), we need to find the solutions to the equation f(x) = 0.

To do this, we can set the two factors equal to zero and solve for x:

2x + 2 = 0

x = -1

x - 6 = 0

x = 6

These are the two zeros of the function: x = -1 and x = 6.

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Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

No, it is not possible to have a function f defined on [2,4] that is continuous and has an unbounded range. This is because of the Extreme Value Theorem, which states that a continuous function on a closed interval must have a maximum and minimum value within that interval. If the range of f is unbounded, then there is no maximum or minimum value, which contradicts the Extreme Value Theorem. Therefore, it is not possible to have such a function.

If we modify the condition to allow for an unbounded range in only one direction (either unbounded from above or unbounded from below), then it is possible to have a function that is continuous on [2,4] with an unbounded range.

For example, consider the function f(x) = 1/(x-4) defined on the interval [2,4]. This function is continuous on [2,4] and has an unbounded range in the negative direction, as f(x) approaches negative infinity as x approaches 4 from the left.

Another example is the function g(x) = x^2 defined on the interval [2,4]. This function is continuous on [2,4] and has an unbounded range in the positive direction, as g(x) approaches infinity as x approaches 4 from the right.

So, it is possible to have a continuous function on [2,4] with an unbounded range in one direction, but not in both directions simultaneously.

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Answer:

Step-by-step explanation:

EVALUATE

n(m ^5+m−n) divided by

m(m−n)

​

EXPAND

m^2mn Divided by

mn-n^2+nm^5

Answer: The value of the limit of the function may not be equal to the value of the function evaluated at a particular x-value. In other words, just because a function takes on a certain value at a particular x-value doesn't mean that the limit of the function at that x-value is equal to that value. To determine the limit of the function, you may need to use different methods such as L'Hopital's Rule or other limit laws. Additionally, it's important to keep in mind that the limit of the function may not exist, in which case it wouldn't be equal to any specific value.

Step-by-step explanation:

If we consider between mean and median in case of better measure of the center, median is likely to be the better measurement.

The list of values given here is 25, 29, 23, 26, 25, 27, 10, 26, 23, 23, 26.

First we are making or rearranging it in ascending/ descending order.

10, 23, 23, 23, 25, 25, 26, 26, 26, 27, 29.

Mean will be  the average of the given set.

Median will be the exact middle number or the average of the two middle entries.

Mean = 23.9

Median = 25

If we consider the range of data and how it is distributed, you can see it ranges from 10 to 29.

But the problem is that, after 10, the second least value is 23 and rest of the values are nearer also.

There is a clear gap between the values of other data points and the first data entry 10.

As mean is the average of every data, this 10 can directly influence the value of mean and cannot gave us an approximation of center.

Imagine that if the last entry is somewhat very big number, then the mean will surely slant to the higher number as it is the sum average of the given set of data.

But median is then also the exact middle number and not influenced by the range of the given data.

Mean and median can be the same in certain cases but when we approximate the measurement of center more than mean, median will likely to give better answer.

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Yes, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row. This is because each flip of a fair coin is an independent event and has an equal chance of landing on either heads or tails.

The probability of getting heads on a single coin flip is 0.5 (or 1/2), and the same is true for getting tails on a single coin flip. The probability of getting three heads in a row is calculated by multiplying the probability of getting heads on each of the three flips together, which is"

(1/2) x (1/2) x (1/2) = 1/8.

Similarly, the probability of getting three tails in a row is also:

(1/2) x (1/2) x (1/2) = 1/8.

Therefore, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row, both of which are 1/8.

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Let G be the number of general seats sold.

Let R be the number of reserved seats sold.

The total number of seats sold is G + R = 1139

Since general seats costs $2 each, 2G is the total receipts from general tickets sales.

Since reserve seats costs $3.50 each, 3.5R is the total receipts from reserved ticket sales.

The total receipts is 2G + 3.5R = 2716

We now have two equations in two unknowns and can solve for G and R.

The area of the polygon is 42 metres squared.

The figure is a composite figure. The area of the figure is the sum of the area of the individual shapes.

Therefore,

area of the figure = area of the rectangle + area of trapezium

Hence,

area of the rectangle = lw

where

Therefore,

area of the rectangle = 6 × 4

area of the rectangle = 24 m²

area of trapezium = 1  /2 (a + b)h

area of trapezium = 1 / 2 (4 + 8)3

area of trapezium = 1 / 2 (36)

area of trapezium = 18 m²

Therefore,

area of the figure = 18 + 24

area of the figure = 42 m²

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Answer:

[tex]x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}[/tex]

Step-by-step explanation:

First, multiply out the set of parentheses and simplify the resulting quadratic expression.

[tex]4(x - 1)(3x - 1) = 0[/tex]

[tex]4(3x^2-x-3x+1) = 0[/tex]

[tex]4(3x^2-4x+1) = 0[/tex]

Then, factor out a 3 from the parentheses to get rid of the coefficient on the quadratic's first term.

[tex]4(3(x^2-\dfrac{4}{3}x+\dfrac{1}{3})) = 0[/tex]

[tex]12(x^2-\dfrac{4}{3}x+\dfrac{1}{3}) = 0[/tex]

Finally, complete the square.

[tex]12\left(x^2-\dfrac{4}{3}x + \left(\dfrac{-\dfrac{4}{3}}{2}\right)^2\right) = 12\left(-\dfrac{1}{3}\right) + 12\left(\dfrac{-\dfrac{4}{3}}{2}\right)^2[/tex]

[tex]12\left(x^2-\dfrac{4}{3}x + \dfrac{4}{9}\right) = -4 + \dfrac{16}{3}[/tex]

[tex]12\left(x - \dfrac{2}{3}\right)^2 = \dfrac{4}{3}[/tex]

[tex]\left(x - \dfrac{2}{3}\right)^2 = \dfrac{1}{9}[/tex]

↓ take the square root of both sides

[tex]x - \dfrac{2}{3}\right = \pm \sqrt{\dfrac{1}{9}}[/tex]

[tex]x = \dfrac{2}{3} \pm \sqrt{\dfrac{1}{9}}[/tex]

[tex]x = \dfrac{2}{3} \pm\dfrac{1}{3}[/tex]

↓ split into two equations

[tex]x = \dfrac{2}{3} + \dfrac{1}{3} \ \ \ \text{OR} \ \ \ x = \dfrac{2}{3} - \dfrac{1}{3}[/tex]

[tex]\boxed{x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}}[/tex]

Step-by-step explanation:

Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.

so, in our case,

27² = 16² + x²

729 = 256 + x²

473 = x²

x = sqrt(473)

473 = 11×43 and has therefore no squared factors.

therefore, it cannot be further simplified.

AB dotted line segment correctly represents the perpendicular bisector of line segment XY

A line is an infinitely long object with no width, depth, or curvature.

A perpendicular bisector can be defined as a line segment which bisects another line segment at 90 degrees.

In other words, a perpendicular bisector intersects another line segment at 90° and divides it into two equal parts.

In the given figure the XY is a straight line.

The perpendicular bisector to this line is AB.

Hence, AB dotted line segment correctly represents the perpendicular bisector of line segment XY

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The scales in the ratio of 1 : n are:

a) 1 : 80

c) 1 : 80000

d) 1 : 100000

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

a)

5 cm and 4 m

1 m = 100 cm

So,

4 m = 4 x 100 cm

4 m = 400 cm

Ratio.

= 5 cm : 4 m

= 5 cm : 400 cm

= 1 : 80

c)

5 cm and 4 km

1 km = 100000 cm

So,

4 km = 400000 cm

Ratio.

= 5 cm : 400000 cm

= 1 : 80000

d)

4 cm and 5 km

1 km = 100000 cm

So,

5 km = 500000 cm

Ratio.

= 5 cm : 500000 cm

= 1 : 100000

Thus,

The scales in the ratio of 1 : n are:

1 : 80

1 : 80000

1 : 100000

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Answer:

Tennis, a game of skill and grace,

A dance upon a court of green.

Racquets are partners in this space,

A symphony of motion seen.Each stroke a crescendo to the ear,

A harmony of speed and spin.

The ball, a fleeting, flashing sphere,

A fleeting moment to win.The court is life, a battlefield,

Of challenges and victories.

A test of strength, both heart and mind,

Of courage, skills, and agility.The net, a barrier, divides,

Two opponents in their quest.

A symbol of the tension that resides,

In every match, every test.But when the final point is served,

And winner takes the day.

The court transforms, a stage, preserved,

For celebration in its way.

Step-by-step explanation:

The total distance driven by Ryan is given as follows:

20.5 miles.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

Considering that 12 minutes = 12/60 = 0.2 hours, the distance for the first customer was of:

40 = d/0.2

d = 40 x 0.2

d = 8 miles.

Considering that 15 minutes = 15/60 = 0.25 hours, the distance for the second customer was of:

50 = d/0.25

d = 0.25 x 50

d = 12.5 miles.

Hence the total distance was of:

8 + 12.5 = 20.5 miles.

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The relative change in tuition tells us the tuition in 2016/17 decreased by 9.99 %.

The indicator's value in the earlier period is used to calculate the relative change, which expresses the absolute change as a percentage. Additionally, indicators that are expressed as percentages, such as the unemployment rate, are subject to the concepts of absolute and relative change.

Given:

The tuition in University if Washington in 2015-16 = 10,203

and, The tuition in University if Washington in 2016-17 = 9,183

so, the relative change is

= (10203 - 9183)/ 10203

= 1020/ 10203

= 0.0999

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The probability of finding gold in that land is 0.8.

Given is that a mining company buys a piece of land in Peru. The studies determined the following prior probabilities -

We can write the probability of finding gold in that land as -

P{E} = P(find good quality gold) + P(find poor quality gold)=0.30

P{E} = 0.5 + 0.3

P{E} = 0.8

Therefore, the probability of finding gold in that land is 0.8.

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{QUESTION IN ENGLISH -

A mining company buys a piece of land in

Peru. The studies determined the following

prior probabilities:

to.

P(find good quality gold)=0.50

b. P(find poor quality gold)=0.30

C. P(find no gold)=0.20

Calculate the probability of finding gold in that}

The population after 68 years from now is 160, 000.

A relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

Given:

10000 is the initial population

2 is the rate at which the population grows

68/17 is the number of periods that the population grows

Now, using Exponential function the population can be represented as

= 10000 x [tex]2^{(68/17)}[/tex]

= 10000 x [tex]2^{(4)}[/tex]

= 10000 x 16

= 160, 000

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the standard matrix of T. T: R2→R2 is [ 0 1 ]

                                                               [ 1  0]

We must locate the pictures of the standard basis vectors of R2 under T and translate those images into columns of a 2x2 matrix in order to get the standard matrix of T.

Let's start by thinking about the reflection along the line x2 - x1. The point (x1, x2) is mapped to the point via this reflection (x2, x1).

We apply T to the first standard basis vector, e1 = (1,0), to determine its image:

T(e1) = (0,1) (0,1)

We also use T: to determine the image of the second standard basis vector, e2 = (0,1).

T(e2) = (1,0) (1,0)

Hence, (0,1) and (1,0) are the images of the standard basis vectors,  These photos can now be expressed as columns in a matrix:

[0 1]

[1 0]

This is the standard matrix of T.

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