in the land of oz, 20% of the residents are members of the lollipop guild (80% are not members), and 75% of the residents have a home in emerald city (25% live outside the city). suppose that lollipop guild membership is independent of having a home in emerald city. what is the probability that a randomly selected resident from the land of oz is a member of the lollipop guild and has a home in emerald city?

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x - 9.9 = 2.1

+ 9.9 to both sides

x = 12

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Answer:

X = 12

Step-by-step explanation:

X - 9.9 = 2.1

Add 9.9 to both sides

X - 9.9 + 9.9 = 2.1 + 9.9

Simplify

X = 12

The Angular speed of the tires is approximately 150.72 radians per minute.

The angular speed of the tires in radians per minute, we need to convert the given rate from revolutions per minute to radians per minute.

The relationship between revolutions and radians is as follows: 1 revolution = 2π radians.

Given that the tires are rotating at a rate of 24 revolutions per minute, we can calculate the angular speed as follows:

Angular speed (in radians per minute) = 24 revolutions/minute × 2π radians/revolution.

Angular speed = 48π radians/minute.

Therefore, the angular speed of the tires is 48π radians per minute.

To further simplify this value, we can use an approximation for the value of π, such as 3.14:

Angular speed ≈ 48 × 3.14 radians/minute.

Angular speed ≈ 150.72 radians/minute.

the angular speed of the tires is approximately 150.72 radians per minute.

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The statements that must be true about the figure are

AB is bisected by EF,CD is bisected by AB, AE = 1/2 AB, EF = 1/2 ED,

FD = EB.

AB is bisected by EF: This statement is true because point E is the midpoint of AB, meaning it divides AB into two equal parts, and EF is a line connecting the midpoints of the sides. Therefore, EF bisects AB.

CD is bisected by AB: This statement is also true because point F is the midpoint of CD, meaning it divides CD into two equal parts, and AB is a line connecting the midpoints of the sides. Therefore, AB bisects CD.

AE = 1/2 AB: This statement is true because E is the midpoint of AB, which means AE and EB are equal in length. Since E is the midpoint, AE is half the length of AB.

EF = 1/2 ED: This statement is true because F is the midpoint of CD, and EF is a line connecting the midpoints of the sides. Therefore, EF is half the length of CD, and ED is twice the length of EF.

FD = EB: This statement is true because F is the midpoint of CD, meaning FD and EB are equal in length.

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Equation of a line in slope-intercept form

where m is the slope and b is the y-intercept.

The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:

This line passes through (2,5) and (6,1), then its slope is:

Substituting with the point (2, 5) and m = -1 into the general equation and solving for b:

Substituting with m = -1 and b = 7 into the general equation, the equation of this line is:

Answer

90*

Step-by-step explanation:

Answer:

s = 30

Step-by-step explanation:

The three angles lie on a line.

The sum of angles on a line are supplementary, meaning they add up to 180 degrees.

Answer:

1/3

Step-by-step explanation:

DE/AB = EF/BC = FD/CA

15/45 = 9/27 = 8/24 = 1/3

hope this will help u

Answer:

look at the screenshot

Step-by-step explanation:

Answer:

6z plus 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-5/3)(-5/3)= 25/9= 2 7/9

In the multiple regression equation, the symbol b represents the partial slope.

In multiple regression analysis, the goal is to examine the relationship between a dependent variable (Y) and multiple independent variables (X1, X2, X3, etc.). The multiple regression equation can be expressed as:

Y = b0 + b1*X1 + b2*X2 + b3*X3 + ...

In this equation, the symbol b is used to represent the regression coefficients or slopes associated with each independent variable. Specifically, each b coefficient represents the change in the dependent variable (Y) associated with a one-unit change in the corresponding independent variable, while holding all other independent variables constant. Therefore, b is the partial slope of the specific independent variable, indicating the direction and magnitude of the relationship between that independent variable and the dependent variable.

Option A, "partial slope," correctly describes the role of the symbol b in the multiple regression equation. The slope of X and Y (Option B) refers to the simple regression coefficient in a simple linear regression equation with only one independent variable. Option C mentions the beta slope of X and Z, which is not a standard terminology. Option D, Y-intercept, represents the value of Y when all independent variables are set to zero, and it is denoted by b0 in the multiple regression equation.

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The proportion of operations that lasted less than 118 minutes is approximately 0.16.

To find the proportion of operations that lasted less than 118 minutes, we need to calculate the area under the normal distribution curve up to that point. Given the average duration of 130 minutes and a standard deviation of 12 minutes, we can use z-scores to determine the proportion.

First, we calculate the z-score using the formula z = (x - μ) / σ, where x is the given value (118 minutes), μ is the mean (130 minutes), and σ is the standard deviation (12 minutes). Substituting the values, we have z = (118 - 130) / 12 = -1.

Using a standard normal distribution table or calculator, we find that the proportion of values less than -1 is approximately 0.1587. However, since we're interested in the proportion of values less than 118 minutes, we take the area to the left of -1 and subtract it from 0.5 (the area under the entire curve).

Therefore, the estimated proportion of operations that lasted less than 118 minutes is approximately 0.5 - 0.1587 = 0.3413, which is approximately 0.16.

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Answer: (228.7, 241.3)

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

-15=-30x

-15/-30=0.5

Answer:

£45.84375

Step-by-step explanation:

To top up the tank he needs:

1200 - 450 = 750 liters

Since the price of oil is 81.5p per liter and he gets a 7.5% discount, the discount per liter is:

81.5 x 7.5/100 = 6.1125p

Since he needs 750 liters, the discount in total is:

6.1125 x 750 = 4584.375p

Since 1p = £0.01

The discount he gets in £ is:

4584.375 x 0.01 = £45.84375

Answer:

7

Step-by-step explanation:

as a fraction it would be 7/1 but it is a half so it goes in evenly

Answer:

7

Step-by-step explanation:

Lets turn 3 1/2 to an improper fraction.

3*2=6

6 + 1 = 7

7/2

Because dividing by 1/2 means multiplying by 2, the answer is 7.

The polynomial is Prime.

To identify the factors:

Therefore, the polynomial is Prime.

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Answer:

Bolded below are the answers

Step-by-step explanation:

4568 ÷ 8

(4000 ÷ 8) + (560 ÷ 8) + (8 ÷ 8)

500 + 70 + 1

571

Hope this helps!

Answer:

4568 ÷ 8

= (4,000 ÷ 8) + (560 ÷ 8) + (8÷8)

= 500 + 70 + 1

= 571

Step-by-step explanation:

The distance from y to the plane is:

distance = |47| / √30

= 47 / √30 (approximate value)

To find the distance from point y to the plane in ℝ³ spanned by u₁ and u₂, we can use the formula for the distance between a point and a plane. The formula is:

distance = |(y - p) · n| / ||n||

where y is the given point, p is a point on the plane, n is the normal vector to the plane, · denotes the dot product, and ||n|| represents the magnitude of the normal vector.

First, let's find the normal vector n by taking the cross product of u₁ and u₂:

n = u₁ x u₂

Calculating the cross product:

n = (-3, -5, 1) x (-1, 1, 2)

= (-32 - (-51), -12 - 1(-3), (-11 - (-31))

= (-1, -5, 2)

Now, let's choose a point on the plane. Since the plane is spanned by u₁ and u₂, any linear combination of u₁ and u₂ will lie on the plane. Let's choose the origin (0, 0, 0) as the point on the plane (p).

Using the formula, the distance from y to the plane is:

distance = |(y - p) · n| / ||n||

= |(6, -9, 4) · (-1, -5, 2)| / ||(-1, -5, 2)||

Calculating the dot product:

(6, -9, 4) · (-1, -5, 2) = 6*(-1) + (-9)(-5) + 42

= -6 + 45 + 8

= 47

Calculating the magnitude of the normal vector:

||(-1, -5, 2)|| = √((-1)^2 + (-5)^2 + 2^2)

= √(1 + 25 + 4)

= √30

Therefore, the distance from y to the plane is:

distance = |47| / √30

= 47 / √30 (approximate value)

Please note that the approximate value depends on the specific decimal approximation used for √30.

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The arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

In mathematics, an expression or mathematical expression is a combination of terms both variables and constants. For example -

2x + 4y + 5z

4y + 2x

Given are the expressions as given in the questions.

{a} -

5 - 9 = - 4

{b} -

8 - 8 = 0

{c} -

- 1 + 12 = 11

{d} -

- 12 + 12 = 0

{e} -

- 2 + 4 + 3

5

{f} -

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

Therefore, the arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

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{Complete question -

Calculate the following:

a) 5-9

b) 8-8

c) -1 + 12

d) -12 + 12

e) -2 +4+3

f) -4-3+2-1}

Answer:

heptagon

Step-by-step explanation:

\(-7,5 + 4,2 = -3.3\)

\(-0,9 \cdot 2,7 = -2.43\)

Answer:

Step-by-step explanation:

Answer:

x = 132

Step-by-step explanation:

Solve by raising both sides to the multiplicative inverse of the exponent.

\(((x-7)^{\frac{2}{3} } )^{\frac{3}{2} } =25^{\frac{3}{2} }\)

x - 7 = 125

x = 132

(i) For X ~ Laplace(0,1):

E(X) = 0, Var(X) = 2.

(ii) If X ~ Laplace(0,1) and Y = bX + μ:

Y ~ Laplace(μ, b).

(iii) For W ~ Laplace(2,8):

E(W) can be approximated numerically.

Var(W) = 128.

(i) If X ~ Laplace(0,1), we need to find the expected value (E(X)) and variance (Var(X)).

The Laplace(0,1) distribution has μ = 0 and b = 1. Substituting these values into the PDF, we have:

fX(x) = (1/2) * exp(-|x|)

To find E(X), we integrate x * fX(x) over the entire range of X:

E(X) = ∫x * fX(x) dx = ∫x * [(1/2) * exp(-|x|)] dx

Since the Laplace distribution is symmetric about the mean (μ = 0), the integral of an odd function over a symmetric range is zero. Therefore, E(X) = 0 for X ~ Laplace(0,1).

To find Var(X), we use the formula:

Var(X) = E(X^2) - [E(X)]^2

First, let's find E(X^2):

E(X^2) = ∫x^2 * fX(x) dx = ∫x^2 * [(1/2) * exp(-|x|)] dx

Using the symmetry of the Laplace distribution, we can simplify the integral:

E(X^2) = 2 * ∫x^2 * [(1/2) * exp(-x)] dx (integral from 0 to ∞)

Solving this integral, we get:

E(X^2) = 2

Now, substitute the values into the variance formula:

Var(X) = E(X^2) - [E(X)]^2 = 2 - 0 = 2

Therefore, for X ~ Laplace(0,1), E(X) = 0 and Var(X) = 2.

(ii) To show that Y = bX + μ follows a Laplace(μ, b) distribution, we need to find the probability density function (PDF) of Y.

Using the transformation method, let's express X in terms of Y:

X = (Y - μ)/b

Now, calculate the derivative of X with respect to Y:

dX/dY = 1/b

The absolute value of the derivative is |dX/dY| = 1/b.

To find the PDF of Y, substitute the expression for X and the derivative into the Laplace(0,1) PDF:

fY(y) = fX((y-μ)/b) * |dX/dY| = (1/2) * exp(-|(y-μ)/b|) * (1/b)

Simplifying this expression, we get:

fY(y) = 1/(2b) * exp(-|y-μ|/b)

This is the PDF of a Laplace(μ, b) distribution, thus showing that Y ~ Laplace(μ, b).

(iii) For W ~ Laplace(2,8), we need to find E(W) and Var(W).

The PDF of W is given by:

fW(w) = (1/16) * exp(-|w-2|/8)

To find E(W), we integrate w * fW(w) over the entire range of W:

E(W) = ∫w * fW(w) dw = ∫w * [(1/16) * exp(-|w-2|/8)] dw

This integral can be challenging to solve analytically. However, we can approximate the expected value using numerical methods or software.

To find Var(W), we can use the property that the variance of the Laplace distribution is given by 2b^2, where b is the scale parameter.

Var(W) = 2 * b^2

= 2 * (8^2)

= 2 * 64

= 128

Therefore, Var(W) = 128 for W ~ Laplace(2,8).

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Answer:

15

Step-by-step explanation:

Answer:

slope = 3

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (9, 27 )

m = \(\frac{27-3}{9-1}\) = \(\frac{24}{8}\) = 3

\(\mathbb{FINAL\:ANSWER:}\)

\(\huge\boxed{\sf\:Slope=3}}\)

\(\mathbb{SOLUTION\:WITH\:STEPS:}\)

Hi! Hope you are having a nice day!

We are given 2 points that the line passes through, so we can use the slope formula and find the slope.

Slope Formula:

\(\displaystyle\frac{y2-y1}{x2-x1}\)

\(\displaystyle\frac{27-3}{9-1}\)

\(\displaystyle\frac{24}{8}\)

The fraction can be reduced:

\(\displaystyle\frac{3}{1}\)

which is the same as

\(3\)

Hope you could understand everything.

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