given a certain population, assume the probability that a person is taller than x inches is 1/2. suppose two persons are chosen at random, one after another, without replacement. however, you can assume the population is large enough (say, infinite), so that the probability of being taller than x inches for a randomly chosen person remains 1/2, even when we are drawing from a population reduced in size by one. (a) (10 points) suppose we know that at least one person is taller than x. what is the probability that the other person is shorter than x? (b) (10 points) suppose we know that the person chosen second is taller than x. what is the probability that the first person chosen is shorter than x?

The function f(x) is 3/x³ if f'(x) is 1/x²

Given that,

f'(x) is 1/x²

To find : f(x)

Differentiation is the opposite of integration. In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:: y = x2 => dy/dx = 2x. So, ∫ (dy/dx) dx = ∫ 2x dx = x2 together represent the integration of the function with respect to the  x.

f(x) ---> differentiation  ------> f'(x)

f'(x)---> integration ------> f(x)

f(x) = ∫ f'(x)

f(x) = ∫ 1/x²

f(x) = 3/x³

Therefore, function f(x) is is 3/x³ if f'(x) is 1/x² .

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The factors of the equation 3x^2+2x-21=0 are (3x - 7) (x + 3) = 0 and x = -3 and x = 7/3.

All related terms should be combined and moved to one side of the equation. Moving all of the components to one side of an equation while maintaining the x2 term positive is the first step in factoring an equation. The x2 terms, x terms, and constants (integer terms) must all be added to or subtracted from one another, and they must all be moved to one side of the equation so that nothing is left on the other. You may just write "0" on the other side of the equal sign if that side has no more words.

Given that the equation is 3x^2 + 2x -21 = 0

Using the method of expansion to solve the quadratic equation we have:

3x^2 + 2x -21 = 0

Multiply (a)(c) and find its prime factors:

(3)(21) = 63

Prime factors: 7, 9

Using the factors deduce the middle term:

3x^2 + 9x - 7x -21 = 0

Take the common in the first two and the last two terms:

3x(x + 3) -7(x+3) = 0

(3x - 7) (x + 3) = 0

Equate to 0:

(x + 3) = 0

x = -3

(3x - 7) = 0

x= 7/3

Hence, the factors of the equation 3x^2+2x-21=0 are (3x - 7) (x + 3) = 0 and x = -3 and x = 7/3.

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The value of y if (1, y, −9) is perpendicular to vector v is  38/5.

Given vector v = 2i - 5j - 4k and vector c = 1i + yj - 9k

In the question, we are told that we need to find y if vector v and vector c are perpendicular. So, if two vectors are perpendicular their dot product is zero

So,  vector v.vector c = 0

(2i - 5j - 4k ).(i + yj - 9k)  = 0

                    2(1) - 5(y) - 4(-9) = 0

                           2 - 5y + 36 = 0

                                    5y = 38

                                      y = 38/5

Hence, the value of y is 38/5.

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The domain of y = sin x is the set of all real numbers.

The sine function, represented by y = sin x, is defined for all real numbers, meaning that any real number can be plugged into the function as the input (x) and will produce a valid output (y). Therefore, the domain of y = sin x is the set of all real numbers.

If a paper company needs to ship paper to a late printing business. 12 small boxes were shipped and 8 large boxes were shipped.

Using a system of equations to represent the problem.

Let x represent the number of small boxes shipped

Let  y represent the number of large boxes shipped.

We know that:

x + y = 20 (the total number of boxes shipped)

8x + 21y = 264 (the combined volume of all boxes )

Solving the first equation for y: y = 20 - x

Substituting this expression for y into the second equation:

8x + 21(20 - x) = 264

8x + 420 - 21x = 264

-13x = -156

x = 12 (small boxes)

So,

y = 20 - x

y = 20 -12

y = 8 (Large boxes)

Therefore 12 small boxes were shipped and 8 large boxes were shipped.

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The surface area of the whole solid will be 144 square inches.

The surface area of a three-dimensional object is the total area of all its faces. In real-life we use the concept of surface areas of different objects when we want to wrap something, paint something, and eventually while building things to get the best possible design.

The surface area will be calculated as:-

SA = SA of cuboid + SA of cube

SA = 6 x ( 11 x 2 ) + 6 x 2

SA = 132 + 12

SA = 144 square inches

Therefore, the surface area of the whole solid will be 144 square inches.

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Answer: The last option.

Step-by-step explanation:

         The statement that can be used to prove that vertical angles ∠1 and ∠3 are congruent is;

             m∠1 + m∠2 = m∠2 + m∠3

       This is because we know that m∠1 + m∠2 is a straight line and that m∠2 + m∠3 is a straight line. Straight lines are equal to 180 degrees, so the vertical angles must be congruent.

Answer:

Green: 5; White: 2; Blue: 3; Red: 2; Total: 12

A) 8/12

i) 5/12 and 3/11

ii) 10/12

Hope this helps!

Step-by-step explanation:

a) The probability that it is either green or a blue marble is 2/3

b) The probability that first draw will be a green and the second draw, a blue marble is 3/44

c) The probability that neither is a red marble is 15/22

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

A man has twelve identical marbles in his pockets consisting of five green, two white, three blue and two red

Now , the probability is

a)

The probability that it is either green or a blue marble is P(green or blue) = P(green) + P(blue)

P(green) + P(blue) = 5/12 + 3/12

P(green) + P(blue) = 8/12 = 2/3

Therefore , the probability is 2/3

b)

The probability that first draw will be a green and the second draw, a blue marble is P(green and blue) = P(green) x P(blue | green)

P(green) x P(blue | green) = (5/12) x (3/11)

P(green) x P(blue | green) = 15/132

c)

The probability that neither is a red marble is P(neither draw is red) = P(non-red on first draw) x P(non-red on second draw | non-red on first draw)

P ( neither red ) = ( 5/6 ) ( 9/11 )

P ( neither red ) = 15/22

Hence , the probability is solved

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A line pae through the point (-2, -3) and (1, -9). Then the equation of the line is 2x + y + 7 = 0.

These are the specified parameters:

Passes through the points (-2, -3) and (1, -9).

With, x₁ = -2 and y₁ = -3

         x₂ = 1 and y₂ = -9

The equation of the line

[tex]\begin{aligned} \frac{y-y_1}{y_2-y_1} & = \frac{x-x_1}{x_2-x_1} \\ \frac{y-(-3)}{-9-(-3)} & = \frac{x-(-2)}{1-(-2)} \\ \frac{y+3}{-6} & = \frac{x+2}{3} \\ 3(y+3) & = -6(x+2)\\ 3y + 9 & = -6x - 12\\ 6x + 3y + 9 + 12 & = 0\\ 6x + 3y + 21& = 0\\ 2x + y + 7 & = 0\end{aligned}[/tex]

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Answer:

The percentage error in x can be calculated as follows:

Percentage error = (Estimated value - Actual value) / Actual value * 100

Let x be the actual value and y be the estimated value such that y > x.

Percentage error = (y - x) / x * 100

This formula calculates the absolute error in terms of a percentage of the actual value.

The vector vec{a} = (1.5, -1) points into the second quadrant.

To determine this, we look at the signs of the components of the vector. Since the x-component is positive (1.5) and the y-component is negative (-1), the vector is in the quadrant with positive x-values and negative y-values, which is the second quadrant.

The plane is divided into four infinite areas known as quadrants, each of which is bounded by two half-axes, using two-dimensional Cartesian axes. Roman numerals I (where the signs of the (x; y) coordinates are I (+; +), II (-; +), III (-;-), and IV (+;-) are frequently used to identify these.

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The equation 120(b - 0.75) = 60 can you use to find the amount of money, b, smart start normally charges for a blue ribbon

Ms. Avila ordered 120 blue ribbons from the smart start school supplier.

Smart start reduced the price of each blue ribbon by $0.75.

The total came to $60.

To express the problem in equation we have to read the question carefully and write the equation according to question.

Let the price of 1 blue ribbon = b

If he reduce the price by 0.75, then the price of blue ribbon = (b - 0.75)

She buy total blue ribbons = 120

So the price of 120 blue ribbons = 120(b - 0.75)

But the total cost is $60.

So the equation is:

120(b - 0.75) = 60

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To determine the cosine of an angle, use the Cos Theta Formula in mathematics.The Answer is 3.

If arctan(2)=, then let the angle be.In this case, tan = 2.

We get =63.43 when we plug the value into the arctan(x) graph.

We do this by using the x=2 line and examining where it crosses the arctan graph (x).

To determine the cosine of an angle, use the Cos Theta Formula in mathematics.

The symbol for it is Cos(), and it has the following form:

adjacent/hypotenuse = cos().

f(θ) = tan(θ) = 3

Note that

tan (x+y ) = tan x +tan y/1-tan x tan y

Note that tan(π) = 0.

Therefore

f(θ + π) = tan(θ+π)

           = (tanθ + tan π)/(1 -tanθ tan π)

           = 3/1 = 3

Answer is 3.

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Answer:

Salvador has traveled 584 - 396 = 188 kilometers so far.

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2 }[/tex] - [tex]\frac{1}{4}[/tex]

[tex]\frac{2}{4}[/tex] - [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{1}{2}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{4}[/tex]

Answer:

[tex]14400i[/tex]

Step-by-step explanation:

(50 + 72i)^2 = 7200i - 2684

(50 - 72i)^2 = -7200i - 2684

= 7200i - 2684 - -7200i - 2684

= 7200i - 2684 + 7200i + 2684

= 14400i - 2684 + 2684

= [tex]14400i[/tex]

The greatest common factor of y²(2y - 1)  , 3(2y - 1) is 2y.

Given expressions,

y²(2y - 1)  , 3(2y - 1)

y²(2y - 1) = 2y³ - y

= 2 x y x y x y - y

3(2y - 1)

= 6y - 1

= 2 x 3 x y - 1

This way, you can find the elements that are shared by both terms.

2y(2y)(-y)(-3).

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The measure of arc FQ is given as follows:

155º.

The measure of arc FQ is obtained applying the two secant theorem in the context of this problem.

From the theorem we have that the angle of 40º represents half the difference between the angle measures of arcs FQ and TR = 75º.

Applying the two secant theorem, the angle measure of arc FQ is given as follows:

(FQ - 75)/2 = 40

FQ - 75 = 80

FQ = 75 + 80

FQ = 155º.

Meaning that the last option represents the correct option in the context of this problem.

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(a) The domain of the function-

[tex]g(t)=sin(e^{-t})[/tex]

is (-∞,∞)

(b) the domain of the given function -

[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)

The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The domain is indicated by the fact that the fraction's denominator is not equal to zero and by the fact that the digit under the square root bracket is positive. (For a function that has fractional values.)

(a) The domain of the function-

[tex]g(t)=sin(e^{-t})[/tex]

is (-∞,∞)

(b) the domain of the function -

[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)

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Step-by-step explanation:

What we have is...

[tex]4(-4.6+w) = 22.24[/tex]

What we'll first do is distribute the 4 into the -4.6 and w

-18.4+4w = 22.24

Next we add 18.4 to both sides to get rid of it on the right side

4W = 22.24+ 18.4

4W = 40.64

Last thing to get W alone, we will divide both sides by 4

W = 10.16

Answer:

2300000

Step-by-step explanation:

The probability of exactly 2 packages being delivered to the correct houses is, [tex]\frac{24}{24}[/tex] = [tex]\frac{1}{1}[/tex] or 100%.

The total number of ways to deliver the packages to the 4 houses is 4! = 24.

To find the number of ways that exactly 2 packages are delivered to the correct houses, we first choose which 2 houses will receive the correct packages, which can be done in 4 choose 2 = 6 ways.

Then, for each of the two remaining houses, we can choose which of the two remaining packages to deliver to that house in 2 ways. So, the total number of ways to deliver exactly 2 packages to the correct houses is    6×2×2 = 24.

the probability of exactly 2 packages being delivered to the correct

houses are, [tex]\frac{24}{24}[/tex] = [tex]\frac{1}{1}[/tex] or 100%

Therefore, the probability of exactly 2 packages being delivered to the correct houses is,  [tex]\frac{24}{24}[/tex] = [tex]\frac{1}{1}[/tex] or 100%.

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Answer:

a

Step-by-step explanation:

Answer:

a. a student who was not absent during unit should score about 98

Applying the two-tangents theorem, the value of x is: 5.

The Two-Tangents Theorem says that if a single point outside a circle is used to draw two tangent lines, they will have the same length.

Since point J is formed by the two tangents, KJ and MJ, therefore:

KJ = MJ

Substitute:

4x + 7 = 7x - 8, find x

Combine like terms:

4x - 7x = -7 - 8

-3x = -15

-3x/-3 = -15/-3

x = 5

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The rate of change of the radius when the radius is 2 is approximately 4 / (π³ * 2⁵).

         V = (1/6) * π³ * r⁶

         dV/dt = (1/6) * π³ * 6 * r⁵ * dr/dt

          dV/dt = 4

       4 = (1/6) * π³ * 6 * 2⁵ * dr/dt

       dr/dt = 4 / ((1/6) * π³ * 6 * 2⁵) = 4 / (π³ * 2⁵)

So the rate of change of the radius when the radius is 2 is approximately  with this one: dr/dt = 4 / (π³ * 2⁵).

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Answer: x/4+2=5

Step-by-step explanation:

Answer:

x = 1/a

Step-by-step explanation:

To solve 7ax + 8ax = 9ax + 6 for x, we can start by combining like terms on both sides of the equation:

7ax + 8ax = 9ax + 6

becomes

15ax = 9ax + 6

Next, we can subtract 9ax from both sides of the equation:

15ax - 9ax = 9ax + 6 - 9ax

becomes

6ax = 6

Finally, we can divide both sides of the equation by 6a to find the value of x:

6ax / 6a = 6 / 6a

becomes

x = 1/a

So, the solution for x is x = 1/a.

According to the scatter plot below, when x = 5, the value of y is 1.

A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed. A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables). With a particular confidence interval, a scatter plot might imply several types of relationships between variables. Weight and height, for example, would be on the y-axis, whereas height would be on the x-axis. Positive (increasing), negative (falling), or null correlations exist (uncorrelated).

Here,

Based on the scatter plot below, when x=5 then value of y is 1.

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Answer: Graph A is your answer

Step-by-step explanation:

Graph A becuase since it makes the same bobble-heads each hour and in 2 hours it made 120 then it makes 60 an hour. So 60x5 is 300 so Graph shows the relationship between the amount of time the machine runs and the number of bobble-head toys built.

The volume of the cylinder is 1413 cubic cm. Then the mass of the carbon will be 2741.22 grams.

The density is the ratio of mass to volume of any substance. Let m be the mass of the object and v be the volume of the object.

Then the density D will be

D = m / v g/cm³

The volume of the cylinder is given as,

V = (π/4) d²h

V = (π/4) x 10² x 18

V = 1413 cm³

Then the mass of the carbon is given as,

1.94 = m / 1413

m = 2741.22 grams

The mass of the carbon will be 2741.22 grams.

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