Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.

(a) The distribution of Y is P(Y = y) = (12^y * e^-12)/y!

(b) E(Y) = 12.

The random variable X is distributed as Bernoulli(p). Given X = x the random variable Y ~ Poisson(12) for 1> 0.

(a) The distribution of Y ~ Poisson(12) is given by:
P(Y = y) = (12^y * e^-12)/y!

(b) The expected value of a Poisson distribution is simply the mean, which in this case is 12. Therefore, E(Y) = 12.

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For the inequality y ≤ -2/3x + 6 the graph is plotted with the points (0, 6) and (9, 0).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The inequality y ≤ -2/3x + 6 is already in slope-intercept form (y = mx + b), where the slope is -2/3 and the y-intercept is 6.

To find some possible solutions for this inequality, we can choose any value of x and then solve for y.

Let's choose x = 0 -

y ≤ -2/3(0) + 6

y ≤ 6

So when x = 0, any y value less than or equal to 6 will satisfy the inequality.

This gives us the solution set -

{(x, y) | y ≤ 6}

Now choose a value of y to find another point that satisfies the inequality. Let's choose y = 0 -

0 ≤ -2/3x + 6

2/3x ≤ 6

x ≤ (6 × 2)/3

x ≤ 9

So when y = 0, any x value less than or equal to 0 will satisfy the inequality.

Therefore, some possible solutions for the inequality y ≤ -2/3x + 6 are -

(0, 6) and (9, 0).

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The value of the scale factor is 3. And the value of the variables 'v' and 'w' will be 36 and 96, respectively.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The scale factor is given as,

SF = 162 / 54

SF = 3

Then the equation is given as,

v / (72 + v) = 1/3

Simplify the equation, then we have

3v = 72 + v

2v = 72

v = 36

Then the other equation is given as,

48 / (48 + w) = 1/3

144 = 48 + w

w = 96

The value of the scale factor is 3. And the value of the variables 'v' and 'w' will be 36 and 96, respectively.

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Fluff-ball can run at a speed of 4 meters per second.

Speed is a measure of how fast an object is moving. It is typically measured in units of distance per unit time, such as meters per second (m/s) or miles per hour (mph). Speed is a scalar quantity, meaning it has magnitude but no direction.

Fluff-ball can run at a speed of 4 meters per second.

This is because speed is equal to distance divided by time, and in this case the distance is 20 meters and the time is 5 seconds:

Speed = distance/time = 20 meters/5 seconds = 4 meters per second.

Therefore, Fluff-ball can run at a speed of 4 meters per second.

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Answer:

The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle. The area of the inner circle is pi multiplied by the square of the radius, or 3.14 * (125.6/2)^2, which equals 19644.8. The area of the outer circle is pi multiplied by the square of the radius, or 3.14 * (125.6)^2, which equals 49766.56. Subtracting the inner circle’s area from the outer circle's area, the area of the shaded region is 30121.76, rounded to the nearest hundredth

Step-by-step explanation:

The equation 7y = 4x - 7.

An equation is a statement that asserts the equality of two mathematical expressions. It contains an equals sign (=) and typically has variables, constants, and mathematical operations on both sides.

Equations are used in many areas of mathematics, science, and engineering to represent relationships between variables and to solve problems. In algebra, equations are often used to solve for the values of variables that make the equation true.

We have;

y = 4/7x - 1

Multiplying through by 7

7y = 4x - 7

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Answer:

60

Step-by-step explanation:

850-250=600

600/10=60

60

Answer:

she must save $60 each week to have enought money to purchase the iPhone 10

Step-by-step explanation:

Because 850-250=600

                 600/10=60                

Earthquake in Turkey was 1000 times much stronger, compared to a magnitude 5​ earthquake

The Richter scale (also known as the Richter magnitude scale) assigns  magnitude numbers to quantify the energy released by an earthquake. Developed by Charles Richter in the 1930s, the Richter scale is a base 10 logarithmic scale that defines magnitude as the logarithm of the ratio of  seismic wave amplitudes to smaller amplitudes.

As measured by seismographs, an earthquake measuring 5.0 on the Richter scale has 10 times more shaking amplitude than a 4.0 earthquake.

Given,

Magnitude 6 is 10² = 100 times greater than magnitude 4.

Magnitude 4 is 10 times greater than magnitude 4.

By the above data, 1 digit greater magnitude means 10 times powerful.

Earthquake on turkey is of 8 magnitude

∵ Difference of 8 magnitude and 5 magnitude = 8 - 5 = 3

∴ 8 magnitude earthquake is 1000 times greater.

Hence, 1000 times much stronger was earthquake in Turkey, compared to a magnitude 5​ earthquake.

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The domain of the function y = log(6 + 5x) is (-6/5, ∞).

To find the domain of the given function, y = log(6 + 5x), we need to determine the values of x for which the function is defined.

Step 1: The logarithmic function is only defined for positive values of the argument. So, we need to set the argument of the logarithm greater than zero:
6 + 5x > 0

Step 2: Solve for x:
5x > -6
x > -6/5

Step 3: The domain of the function is the set of all x values that satisfy the inequality. So, the domain is:
{x | x > -6/5}

In interval notation, the domain can be written as:
(-6/5, ∞)

Therefore, the domain of the function y = log(6 + 5x) is (-6/5, ∞).

Answer: The domain of the function y = log(6 + 5x) is (-6/5, ∞).

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The probability that a randomly selected student is female or a physics major would be 0.65.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring needs to be 1.

The probability that a randomly selected student is female or a physics major can be calculated:

P(PM or F) = P(PM) + P(F) - P(PMF)

Where P(PM or F) = Probability of student selected is Physics Major or Female needed to find.

P(PM) = Probability of student selected is Physics Major

P(PM) = Number of Physics Major / Total number of students in the Physics class

P(PM)  = 14 / 40 = 0.35

P(F) = Probability of student selected is Female = Number of female students in the Physics class / Total number students in the Physics class = 18 / 40 = 0.45

P(PMF) = Probability of student selected is Physics Major and Female  = 6 / 40 = 0.15

Substituting the values into equation (1);

P(PM or F) = 0.35 + 0.45 - 0.15

P(PM or F) = 0.65

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The matrix \( A \) is not diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R}) \), because there does not exist a basis of \( \mathbb{R}^{3} \) consisting of eigenvectors of \( A \).

The matrix \(A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & -1 & 1\end{array}\right] \) is diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R}) \) if and only if there exists a basis of \( \mathbb{R}^{3} \) consisting of eigenvectors of \( A \).

To determine if \( A \) is diagonalizable, we need to find the eigenvalues and eigenvectors of \( A \).

The characteristic polynomial of \( A \) is given by:

\(\det(A-\lambda I)=\left|\begin{array}{ccc}1-\lambda & 0 & 0 \\ 0 & 1-\lambda & 1 \\ 0 & -1 & 1-\lambda\end{array}\right|=(1-\lambda)^{3} \)

The eigenvalues of \( A \) are the roots of the characteristic polynomial, which are \( \lambda=1 \) with multiplicity 3.

To find the eigenvectors of \( A \), we need to solve the equation \( (A-\lambda I)x=0 \) for each eigenvalue.

For \( \lambda=1 \), we have:

\( (A-1I)x=0 \)

\(\left[\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{array}\right]x=0 \)

The solution to this equation is the eigenspace of \( \lambda=1 \), which is spanned by the eigenvector \( x=\left[\begin{array}{c}1 \\ 0 \\ 0\end{array}\right] \).

Since the eigenspace of \( \lambda=1 \) has dimension 1, there is only one linearly independent eigenvector for this eigenvalue. Therefore, the matrix \( A \) is not diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R}) \), because there does not exist a basis of \( \mathbb{R}^{3} \) consisting of eigenvectors of \( A \).

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The coordinates of the point that partitions the segment BA into a ratio of 3 to 2 is (-1, 0).

Directed line segments are line segments which has an initial point and the terminal point along with the direction.

Given a directed line segment BA.

The coordinates of A are (-5, -2) and the coordinates of B are (5, 3).

Let P be the required point which partitions the segment BA in to 3 : 2.

P would be at a 3/5 along the line from B to A.

Write the components of the segment using the end points.

Components = < (x₂ − x₁),(y₂ − y₁) >

                      = < (-5 - 5) , (-2 - 3) >

                      = < -10, -5 >

Components of BP = < 3/5 (-10, -5) >

                                = < -6, -3 >

Coordinates of P = Coordinates of initial point + component of BP.

                             = (5 + -6, 3 + -3)

                             = (-1, 0)

Hence the required coordinates is (-1, 0).

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You would receive $13.50 if you cashed in 135 dimes. That's the equivalent of 1,350 pennies.
If you cashed in 135 dimes, you would receive 1,350 pennies.

This is because each dime is worth 0.1 dollars, or 10 pennies. So, to find the total number of pennies you would receive, you can simply multiply the number of dimes by the number of pennies in each dime:
135 dimes * 10 pennies/dime = 1,350 pennies
So, you would receive 1,350 pennies if you cashed in 135 dimes.

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Answer:

The y-intercept is 1

at the point (0,1)

Step-by-step explanation:

The y-intercept is the point at which a graph crosses the y-axis.

The area of the given isosceles trapezoid is 120 square units.

An isosceles trapezoid is a quadrilateral formed by a trapezium whose base angles are equal due to which the left and right sides are also equal in length.

In the given question,

Length of left/right side = 10

Length of bigger base = 21

Length of smaller base = 9

If we join the edges of the smaller base to the bigger base in such a way that we get 2 right-angled triangles formed by the legs of the trapezoid and the base,

we can say that the length of the base would be

=(bigger base-smaller base)/2

=(21-9)/2

=6

and we know that the length of the legs is 10

So to the Pythagorean theorem,

the height of the trapezoid would be

h=√(10² - 6²) = √64 = 8

Now that we know all the variables, we can easily calculate the area of the trapezoid by the formula

= height × (bigger base+smaller base)/2

= 8 ×(21+9)/2

= 4 × (30)

= 120 square units

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To make the trinomial y2 - 18y a perfect square, we need to add a constant that is equal to (18/2)^2 = 81.

This is because a perfect square trinomial is in the form (x + a)^2 = x^2 + 2ax + a^2. In this case, x = y and 2a = -18, so a = -9 and a^2 = 81. So, the trinomial becomes y2 - 18y + 81, which is a perfect square.

To factor the trinomial, we can use the formula (x + a)^2 = x^2 + 2ax + a^2, where x = y and a = -9. So, the trinomial y2 - 18y + 81 can be factored as (y - 9)^2.

Therefore, the proper constant to add to the binomial y2 - 18y to make it a perfect square trinomial is 81, and the factored form of the trinomial is (y - 9)^2.

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Answer:

33 degrees

Step-by-step explanation:

Angles BFG + GFC = 90

5r +68 + 8r +113 =90

1

Collect like terms

13r + 181 = 90

Subract 181 from both sides

13r = 90-181

13r = - 91

r = - 7

Now insert the value of r into BFG (5r +68)

5r + 68 = 5(-7) +68

= -35 + 68

=33

Check your answer by inserting the value of r into 8r +113

8r + 113 =8(-7) +113

-56+113= 57

The two angles 33 and 57 must add up to 90, a rt angle

The system of equations according to the given instructions are x + (1/2)y = -5; 2y - 12 = x

The sum of one number and half another is negative five. Twelve less than twice the second number yields the first number.

Let x represent the first number and y represent the second number.

System:

x + (1/2)y = -5
2y - 12 = x

The system of equations that represents this situation is:
x + (1/2)y = -5
2y - 12 = x

Where x represents the first number and y represents the second number.

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Answer: Your welcome!

Step-by-step explanation:

Expanded form: 7.4 x 10-4 cm

Exponential form: 7.4E-4 cm

Expanded form is when a number is written as the sum of its digits multiplied by their respective powers of 10. In this case, the number is 7.4 x 10-4, which means that 7.4 is multiplied by 10 to the power of -4.

Exponential form is when a number is written as a base number times a power of 10. In this case, the number is 7.4E-4, which means that 7.4 is multiplied by 10 to the power of -4.

To restrict the domain of the function f so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. This means that for every value of x in the restricted domain, there is exactly one value of f(x).

Once we have restricted the domain, we can find the inverse function f-1 by switching the x and y values in the original function and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.

For example, consider the function f(x) = x^2. This function is not one-to-one because for every value of x, there are two values of f(x) (one positive and one negative). However, if we restrict the domain to x ≥ 0, the function becomes one-to-one and we can find the inverse function.

The restricted function is f(x) = x^2 for x ≥ 0. The inverse function is f-1(x) = √x for x ≥ 0. The domain of f is x ≥ 0 and the range is f(x) ≥ 0. The domain of f-1 is x ≥ 0 and the range is f-1(x) ≥ 0.

In general, to restrict the domain of a function so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. Once we have restricted the domain, we can find the inverse function by switching the x and y values and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.

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Answer:

Step-by-step explanation:

1 hour = 60 minutes, so ratio is

20:60 = 1:3

∴ n = 1

793 people in the country said that they like country music if 23% of the people surveyed prefer country music.

The given data is as follows:

percentage of people prefer music = 23%

People did not like country music = 2653

Let us assume make this equation has equal properties,

0.23x = people who like country music

We know that 2,653 people did not like music. We can write this equation as:

x - 0.23x = 2653

0.77x = 2653

x = 2565 / 0.77

x = 3446.75

Taking the x value approximately, we get the x value as,

x = 3447

Now we can substitute the x value in the above equation, we get,

0.23x = 0.23(3447)

= 792.81

Therefore we can conclude that 793 people in the country said that they like country music.

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The two real solutions of the equation are:

z=32.5/18 ± √(81+32.5z)/18

The equation 18z2-65z-72=0 can be solved by completing the square. We start by taking half of the coefficient of the squared term and squaring it:

(18/2)2 = (9)2 = 81

We then add 81 to both sides of the equation to complete the square:

18z2-65z-72+81=0+81

18z2-65z+9=81

Now, we take half of the coefficient of the z-term, subtract it from both sides of the equation, and add it in the parentheses:

18z2-(65/2)z+(65/2)z+9=81+(65/2)z

(18z-32.5)2=81+32.5z

We now have a perfect square on the left side, so we can simplify:

(18z-32.5)2=81+32.5z

18z-32.5=±√(81+32.5z)

18z=32.5±√(81+32.5z)

z=32.5/18 ± √(81+32.5z)/18

Therefore, the two real solutions of the equation are:

z=32.5/18 ± √(81+32.5z)/18

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By applying Two-Variable Linear Equation it can be concluded that the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.

Two-Variable Linear Equation is a form of relation equal to the algebraic form which has two variables and both are raised to the power of one.

We will use this concept to calculate the amount of each type of investment.

The total amount invested is $10,000, with some going to bonds and some going to certificates of deposit (CDs). According to the question, the amount invested in bonds is to exceed that in CDs by $3,000. We can write this as an equation:

$10,000 = x + y  , where:

x = the amount invested in bonds

y = the amount invested in CDs

We are also told that x = y + $3,000. We can substitute this into the first equation:

$10,000 = x + y

              = y + $3,000 + y

              = 2y + $3,000

         2y = $7,000

           y = $3,500

Now we can substitute this back into the equation for x:

x = y + $3,000

  = $3,500 + $3,000

  = $6,500

So the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.

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By answering the above question, we may infer that Ling will thus require equation 42 feet of wallpaper border to install at the top of the three walls.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Three walls, each 14 feet long and 12 feet tall, are being wallpapered by Ling. Just the top of the wall will be covered by the border. As a result, each wall requires a 14-foot-long wallpaper border.

The length of the border on each of the three walls must be added together to determine the overall length of wallpaper border required. So:

Whole wallpaper border length is one wall's border length times the number of walls.

Overall wallpaper border length is 14 feet multiplied by 3 walls.

42 feet is the total length of the wallpaper border.

Ling will thus require 42 feet of wallpaper border to install at the top of the three walls.

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For the given function f(x) = (x - 4)² - 3, the following statements are correct -

B: relative minimum at (4,-3).

C: decreasing interval from (-∞, 4).

E: increasing interval is (4, ∞).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the relative maximum and minimum of the function, we need to find its critical points by setting the derivative of the function equal to zero -

f(x) = (x - 4)² - 3

f'(x) = 2(x - 4)

2(x - 4) = 0

x = 4

So, the only critical point of the function is x = 4.

Plug in the value of x = 4 in the equation -

(4 - 4)² - 3

0 - 3

-3

Since f''(4) is positive, the critical point at x = 4 is a relative minimum.

Therefore, the function has a relative minimum at (4, -3).

To find the increasing and decreasing intervals, we can look at the sign of the first derivative -

f'(x) = 2(x - 4)

For x < 4, f'(x) is negative, meaning that f(x) is decreasing on the interval (-∞, 4).

For x > 4, f'(x) is positive, meaning that f(x) is increasing on the interval (4, ∞).

Therefore, the decreasing interval is (-∞, 4), and the increasing interval is (4, ∞).

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→ the lenght = 13 square units

→ the width = 2 square units

→ the area of the rectangle = 13×2 = 26 square units

→ the area of the triangle = 26 : 2 = 13 square units

Answer:

Step-by-step explanation:

you would copy and paste another triangle on top to form a rectangle. That would make the rectangle's length 13 units and its width 2 units. the area of a rectangle is found by A=length x width which in this case is 26 units^2. A single triangle's area is 1/2 the area of the rectangle making it 26/2 which is 13.

So the area of the triangle is 13 units^2.

you multiply x by y and then multiply 5 to the power of 67 to then come to an answer of 500000000000x

1. A person should choose one family pizza.

2. The area of two medium pizza < area of 1 large pizza.

3. The area of two medium pizza is 1413.8 square cm and the area of one large pizza is 1661.9 square cm.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

I would one family pizza.

I would choose one family because the total area of two medium pizzas is less than the area of a family pizza.

This means that the two medium pizzas will have less pizza to share between the same number of people, so everyone will get a smaller slice of pizza.

To calculate the areas of the pizzas, we need to use the formula for the area of a circle -

Area of a circle = π × (radius)²

For the family pizza with a diameter of 46 cm, the radius is 23 cm. Therefore, the area of the family pizza is -

Area of family pizza = π × (23 cm)² ≈ 1661.9 square cm

For two medium pizzas with a diameter of 30 cm, the radius is 15 cm. Therefore, the area of each medium pizza is -

Area of each medium pizza = π × (15 cm)² ≈ 706.9 square cm

The total area of two medium pizzas is -

Total area of two medium pizzas = 2 × (Area of each medium pizza) ≈ 1413.8 square cm

Since the total area of two medium pizzas is less than the area of the family pizza, it means that two medium pizzas have less pizza to share between the same number of people.

Therefore, choosing one family pizza would be a better option.

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A family pizza or two medium?

* Each medium pizza is 30 cm in diameter

* The family pizza has only a diameter of 46 cm

1. What do you choose?

2. Why?

3. Please conclude your facts