alice, bob, and carol play a game in which each of them chooses a real number between $0$ and $1.$ the winner of the game is the one whose number is between the numbers chosen by the other two players. alice announces that she will choose her number uniformly at random from all the numbers between $0$ and $1,$ and bob announces that he will choose his number uniformly at random from all the numbers between $\tfrac{1}{2}$ and $\tfrac{2}{3}.$ given this information carol will choose (in simplest form) to maximize her chance of winning. find .

Answer:

Va=4r³π

Step-by-step explanation:

Vb=(4/3)r³π, Vc=r²πh, h is the height of the cylindrical container.

h=12r.

So now the volume of the cylinder is:

Vc=r²π*12r=12r³π.

There are 6 balls so their total volume is:

6*Vb=6*(4/3)*r³*π=(24/3)*r³π=8r³π.

Now we subtract the volume of 6 balls from the volume of the cylinder to get the volume of air Va inside the cylinder:

Va=Vc-6*Vb=12r³π-8r³π=4r³π.

So the volume of air inside of the cylinder is Va=4r³π

Hope This Helps!

Answer:

Volume of air = 4πr³ (units cubed)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]   [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Model the squash ball as a sphere.

Assuming the six squash balls are packaged in a cylindrical container where each ball is one on top of the other, the height of the container is 6 times the height of a squash ball.  

The height of a squash ball is its diameter, which is twice its radius.  

Therefore, the height of the cylinder is 12 times the radius of the squash ball, and the radius of the cylinder is the radius of the squash ball.

Therefore:

[tex]\begin{aligned}\textsf{Volume of the cylinder}&=\pi r^2 \cdot 12 r\\&=12 \pi r^3\end{aligned}[/tex]

where r is the radius of the sphere (squash ball).

To find the volume of air inside the container, subtract 6 times the volume of a sphere from the volume of the cylinder.

[tex]\begin{aligned}\textsf{Volume of air}&=\textsf{Volume of cylinder}-\textsf{6 volume of sphere}\\&=12\pi r^3-6\left(\dfrac{4}{3} \pi r^3\right)\\&=12\pi r^3-8\pi r^3\\&=4\pi r^3\;\; \sf units \; cubed\end{aligned}[/tex]

The area of the circle having a radius of 10 ft will be 100π.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that the radius of the circle is 10 ft. The area of the circle is calculated by the formula written as below,

Area of the circle = πr²

Substitute the value of the radius in the formula and calculate the area of the circle.

Area of the circle = πr²

Area of the circle = π x ( 10 ) ²

Area of the circle = 100π square ft

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Answer:

Step-by-step explanation 0% because there is more red markers

Answer: (Don't read this if this is a test)

Step-by-step explanation: I might get this wrong because I was kind of confused too (sorry if I am!)

Hello! The first thing you would want to do for these kinds of questions is to write the probability of a green, blue, or red marker being picked as a fraction.  To do this, add 12 + 4 + 20 which is 36.

The probability of picking a green marker - 12/36, partially simplified = 3/9

The probability of picking a blue marker - 4/36, simplified = 1/9

The probability of picking a red marker - 20/36, simplified = 5/9

G - 3/9
B = 1/9
R = 5/9

You know that the probability of picking a blue marker is 1/9.  Once you know this, you can figure out the new probability of picking a red marker since the blue marker won't be replaced.  The answer is 4/35.  Multiply 1/9 by 4/35 to find the probability of picking one after the other and you will get 4/315.  

Answer:

lesser number: 9

greater number:41

Step-by-step explanation:

Given: a+b=50

Use the word problem to create equation: 5a-4=b

We can solve for either variables, we'll solve for b(greater number) first:

a=50-b

Plug a into other equation:

5(50-b)-4=b

250-5b-4=b

246-5b=b

246=6b

b=41

Plug what we found for b into equation to solve for a(lesser number):

a+41=50

a=9

Verify:

5(9)-4=41 ?

45-4=41

41=41 Checks out.

Hope this helps.

The conditional probability that the couple gives the correct answer if the husband and wife agree is p = .6 and if husband wife don't agree is p=0.5, and statement B is the better strategy.

Option B, have them both consider the question, and then either give the common answer if they agree or, if they disagree, flip a coin to determine which answer to give is the better strategy.

c.) The conditional probability that the couple gives the correct answer if the husband and wife agree is p = .6.

d.) The conditional probability that the couple gives the correct answer if the husband and wife disagree is 0.5. This is because in this case, they must flip a coin to decide which answer to give.

Since the probability of both parties giving the correct answer is p = .6, but the probability of either party giving the correct answer is only 0.5,

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Here b is =0, According to the Zero Product Property, if ab=0, then either a=0 or b=0 (or both). If and only if one or more of the factors in a product are zero, the product is zero. This is very helpful when attempting to solve quadratic problems.

The product of two nonzero items is not zero, according to the algebraic definition of the zero product property. In other terms, the following claim:

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Answer:

The work done by the constant unit force vector in moving the object 17 units in the positive x-axis direction is equal to the magnitude of the force multiplied by the displacement in the direction of the force. Since the force makes an angle of 30 degrees with the x-axis, the magnitude of the displacement in the direction of the force is equal to the displacement in the x-axis direction multiplied by the cosine of 30 degrees. Therefore, the work done is equal to the magnitude of the force multiplied by 17 multiplied by the cosine of 30 degrees. hope this helped

The pair of variables "laptop price ($) and memory capacity (GB)" are two different scales of measure.

What is the variable?

A variable is a quantity that may be changed according to the mathematical problem. The generic letters which are used in many algebraic expressions and equations are x, y, z. In other words, a variable is a symbol for a number where the value is not known. For example, x + 5 = 10. Here “x” is a variable.

This is because "laptop price" is measured in dollars, which is a monetary unit, and "memory capacity" is measured in GB (gigabytes), which is a unit of data storage.

These are two different types of measurement and cannot be directly compared.

On the other hand, "a number of goals scored" and "penalty minutes" are both measures of performance in a sport and can be directly compared.

"Height" and "IQ" are both measures of human characteristics, although they are different in nature, but they can also be compared.

"lipstick shades" and "brands of athletic shoes" are both consumer products, but they are not directly related and cannot be compared.

Hence, The pair of variables "laptop price ($) and memory capacity (GB)" are two different scales of measure.

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Answer:

$139,200

Step-by-step explanation:

To find the total cost of the subsidized loan, we need to calculate the total amount of interest that will be added to the loan over the 10-year repayment period. We can use the formula for simple interest:

I = Prt

Where:

I = Interest

P = Principal (the original loan amount)

r = Interest rate (expressed as a decimal)

t = Time (in years)

In this case:

I = 80,000 * 0.074 * 10 = 59,200

The total cost of the loan would be the sum of the principal and the interest:

80,000 + 59,200 = $139,200

So the total cost of the subsidized loan is $139,200.

The sample proportion based on the question that we have here is 0.85

What is sample proportion?

The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.

P=X/N, where X represents the number of successes and N represents the sample size, yields the sample proportion.

Hence from the question, we see that 85% of the passengers booked for flights actually show up.  hence the proportion is 0.85.

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The value of the expression: (5 + √3)/(2- √3) = 13 +7√3

The given surd to be rationalized is (5 + √3)/(2- √3)

Using a²-b² = (a+b)(a-b)

You can rewrite the value 1 in many ways as 2/2, 16/16, or 1 = (5 + √3)/(2-+√3)

Multiplying by 1 but in the form 1 = (2 + √3)/(2- √3) given

(5 + √3)/(2- √3) * (2 + √3)/(2-+√3)

⇒ (5 + √3)(2+√3) / [2² - (3√2)²]

Simplifying the surd to have

(10+ (5 + √3 + 2√3 + 3)/4-1

Therefore this gives 13 + 7√3

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Correct question:

How do you simplify  (5 + √3)/(2- √3)?

Answer:

4x + 7y = 27

Step-by-step explanation:

The slope-intercept form of the equation of a line is

y = mx + b

Here m = slope which is the rate of change of the y-value with respect to x and b is the y-intercept which is the y-value where the line crosses the x-axis. It is therefore the value of y when x = 0

We are given slope = -4/7

So equation of line is
y = (-4/7)x + b

To find b, notice that the given point is (5, 1) which indicates that at this point x = 5, y = 1

If we plug in x = 5 in the equation we should get a y0value of 1

We can rewrite y = (-4/7)x + b as

(-4/7)x + b  = y  

Substitute x=5 and y = 1

(-4/7)(5) + b = 1

-20/7  + b = 1

b = 1 + 20/7

b = 27/7

So the equation of the line in slope intercept form is

[tex]\quad y=-\dfrac{4}{7}x+\dfrac{27}{7} \cdots (1)[/tex]

The standard form of a line equation is
Ax + By = C

We can convert equation (1) to standard form by tweaking it

The function that best models the number of game consoles sold in millions since 2009 is g(x) = (25.5)(0.6)ˣ.

The correct option is B.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and sx is the time period.

Given:

The graph shows the number of game consoles sold in millions since 2009.

Let the function is,

g(x) = abˣ.

And graph passes through two points (0, 25.5) and (1, 15.3).

So,

when x = 0 then g(x) = 25.5.

That means, a = 25.5

And, when x = 1 then g(x) = 15.3.

That means,

15.3 = (25.5)b.

b = 0.6

Therefore, the function is g(x) = (25.5)(0.6)ˣ.

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A rule for a histogram that decides into endpoint convention class intervals subjects is placed if their value is on the boundary between two intervals.

Endpoints are defined as physical devices that connect to and exchange information with a computer network.

There are some examples of endpoints:

They are mobile devices, desktop computers, virtual machines, embedded devices, and servers.

Internet-of-Things devices like cameras, lighting, refrigerators, security systems, smart speakers, and thermostats are also examples of endpoints.

When a device connects to a network, the flow of information between, for instance, a laptop and a network, is much like a conversation between two people over the phone.

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Yes, xk/yk converges to x/y. This can be proven mathematically using the definition of a limit.

If xk converges to x and yk converges to y, then the limit of xk/yk as k approaches infinity is equal to the limit of x/y. This can be expressed algebraically as limk→∞xk/yk = limk→∞x/y, which is equal to x/y. Thus, xk/yk converges to x/y.

To calculate this, we can take a sequence of xk an yk values, and divide every xk by its corresponding yk. For example, if xk = {2, 4, 8, 16, 32} and yk = {1, 2, 4, 8, 16}, then the sequence xk/yk = {2/1, 4/2, 8/4, 16/8, 32/16} = {2, 2, 2, 2, 2}. This sequence converges to 2, which is equal to x/y. Therefore, xk/yk converges to x/y.

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Answer:

True

Step-by-step explanation:

An obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees. An obtuse angle is also called a reflex angle. A reflex angle is formed when the arms of an angle point in opposite directions. The degree of an obtuse angle is between 91 and 179 degrees. Therefore, it's true.

Hope it helps! :)

Answer:

True

Step-by-step explanation:

An obtuse angle measures more than 90 degrees and 180 degrees. So 179 is greater than 90 degrees and less than 180 degrees.

The measure of angle ∠B is 44°.

What is the measure of all angles in a triangle?

A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.

We have given,  

Triangle ΔABC,

and angles ∠ACB = 90°, ∠CAB= 46°, and ∠ABC = ?

We know that the sum of all angles in the triangle is 180°.

So,

∠ACB + ∠CAB + ∠ABC = 180°

90° + 46° + ∠ABC = 180°,

136 + ∠ABC = 180°,

∠ABC = 180° - 136

∠ABC = 44°,

Hence, the measure of angle ∠B is 44°.

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The required solution of the equations is given as (2, 3, 0).

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
So we are given a system,
3x -2y + 3z = 0
-3x-5y-5z = -21

Substitute x =2, and we get the system,
-2y + 3z = -6
-5y -5z = -15

Multiply equation 1 by -5 and equation 2 by 2 we get the system,
10y - 15z = 30
-10y -10z = -30

Adding the above equations,
z = 0

Now,
-2y = -6
y = 3

Thus, the required solution of the equations is given as (2, 3, 0).

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Answer:

226.1 [tex]in^{2}[/tex]

Step-by-step explanation:

x = 5/2 is a zero of the function f(x) = 2x³ - 5x² - 6x + 15.

What is a function?

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each part of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: x = 5/2 is a zero of the function f(x) = 2x³ - 5x² - 6x + 15,

f(x) = 2x³ - 5x² - 6x + 15

When we f(x) = 2x³ - 5x² - 6x + 15 by x-5/2 we get

Remainder = -10

Quotient = 2x² - 6

Divisor = x - 5/2

2x³ - 5x² - 6x + 15 = 2x² - 6 - 10/(x - 5/2)

Hence, x = 5/2 is a zero of the function f(x) = 2x³ - 5x² - 6x + 15.

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From the given data, using perimeter of rectangle, Length(L) = 6 × 11 - 7 of the rectangular field.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. P = x+x+y+y, where P is the perimeter.

Let length of the rectangular field = L

Width of rectangular field = W

Given,

length of a rectangular field is 7 feet less than six times its width

perimeter is 140 feet,

According to the question,

L = 6W - 7

Perimeter of the rectangle = 2 (L + W)

140 = 2 (6W - 7 + W)

140 = 2 (7W - 7)

70 = 7 W - 7

77 = 7 W

W = 11

L = 6 × 11 - 7

Length = 59

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The range of the function y = -2x² + 12x - 13 will be [5, -∞). Then the correct option is A.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The domain means all the possible values of x and the range means all the possible values of y.

The equation is given below.

y = -2x² + 12x - 13

Convert the equation into a vertex form, then we have

y = -2x² + 12x - 13

y = -2x² + 12x - 18 + 18 - 13

y = -2(x² - 6x + 9) + 18 - 13

y = -2(x - 3)² + 5

The range of the function y = -2x² + 12x - 13 will be [5, -∞). Then the correct option is A.

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Answer:

2356

Step-by-step explanation:

Using exponential function, The total number of foxes that will remain after 4 years is 1534.

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

We employ the exponential function because...

In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.

Using exponential function,

P(t) = A . b^t

Formulate: 3746 based on the provided conditions. (1 - 20%) ⁴

Analyze the following formula or expression: 1534.3616

he total number of foxes that will remain after 4 years is 1534

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Answer: 133.5

Step-by-step explanation:

Add the weights together and, for some reason, you get 133.5

Answer:

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

Add the four numbers together to get the total weight:

It doesn't match any options, please double check if they are (or given weights) correct.

Answer:

375 square units

Step-by-step explanation:

Area = (1/2) h (a+b)

=1/2 × 10 (49+26)

= 5 × 75

= 375 square units

hope it helps you <3

The parent function is the simplest form of the type of function in the graph is g(x) = 1/x

What is graph ?

In mathematics, a graph is a collection of points, called vertices, and lines, called edges, that connect the vertices. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, and more. Graphs are one of the most fundamental concepts in mathematics, and they are used to model many real-world problems and situations.

The transformation from the first equation to the second one can be found by finding a, h and k for each equation.

y = a / x-h   +   k

Find  a, h and k for

g(x)= 1/x

a = 1

h=0

k = 0

The horizontal shift depends on the value of h and The horizontal shift is described as :

f(x) = f(x+h)  The graph is shifted to the left h units

f(x) = f(x-h) The graph is shifted to the right h units.

Horizontal shift depends on the value of k and The horizontal shift is described as :

f(x) = f(x+k)  The graph is shifted to up k units

f(x) = f(x-k) The graph is shifted down k units.

Vertical shift : none.

The sign of a describes the reflection across the x-axis. −a means the graph is reflected across the x-axis.

Reflection about the x-axis: None

To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.

Parent Function: g(x) = 1/x

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: None

Hence, The parent function is the simplest form of the type of function g(x) = 1/x .

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