If E and F are mutually exclusive events, which of the following must be true?
a. P(EF) P(E)
b. P(EUF) P(E) + P(F) - P(En F)
d. E and F are independent
e. none of these

A scaled function is a dilated function

The function g(x) is: \(\mathbf{g(x) = \frac 12x^2}\)

Function f is given as:

\(\mathbf{f(x) = x^2}\)

Function g is a scaled version of f(x).

So, we have:

\(\mathbf{g(x) = kx^2}\) --- where k is the scale

The graph of g(x) passes through (4,8).

So, we have:

\(\mathbf{8 = k \times 4^2}\)

\(\mathbf{8 = k \times 16}\)

Divide both sides by 16

\(\mathbf{\frac 12 = k }\)

So, we have:

\(\mathbf{k = \frac 12 }\)

Substitute \(\mathbf{k = \frac 12 }\) in \(\mathbf{g(x) = kx^2}\)

\(\mathbf{g(x) = \frac 12x^2}\)

Hence, the function g(x) is: \(\mathbf{g(x) = \frac 12x^2}\)

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Answer:

no solutions

Step-by-step explanation:

Hi there!

We're given this system of equations:

x+y=3

4y=-4x-4

and we need to solve it (find the point where the lines intersect, as these are linear equations)

let's solve this system by substitution, where we will set one variable equal to an expression containing the other variable, substitute that expression to solve for the variable the expression contains, and then use the value of the solved variable to find the value of the first variable

we'll use the second equation (4y=-4x-4), as there is already only one variable on one side of the equation. Every number is multiplied by 4, so we'll divide both sides by 4

y=-x-1

now we have y set as an expression containing x

substitute -x-1 as y in x+y=3 to solve for x

x+-x-1=3

combine like terms

-1=3

This statement is untrue, meaning that the lines x+y=3 and 4y=-4x-4 won't intersect.

Therefore the answer is no solutions

Hope this helps! :)

The graph below shows the two equations graphed; they are parallel, which means they will never intersect. If they don't intersect, there's no common solution

P + 127 = 550        P = 423

Answer:

P = 423  

P + 127 = 550

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

it's multiplied by 2 as you go to triangle 2

Answer:

x = 8

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

\(\frac{5}{10}\) = \(\frac{4}{x}\) ( cross- multiply )

5x = 40 ( divide both sides by 5 )

x = 8

Angles in standard position with their terminal side in quadrant II have measures between 90 and 180 degrees.

Therefore, the angles that have their terminal side in quadrant II are

120 degrees

135 degrees

150 degrees

165 degrees

So, all of the above angles apply.

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Answer:

x = 7 m and x = −7 m

Step-by-step explanation:

Its a modulus problem

concept

|x|  = x when x>=0

|x| = -x when x < 0

____________________________________

Now given

|x| − 2 = 5

adding 2 both sides

|x| − 2  + 2 = 5 + 2

|x|  = 7

now

x = 7  when x >= 0

x = -7 when x<0

Thus, correct answer is x = 7 m and x = −7 m

The side length of the square game board with an area of 113 (in)² is approximately 10.63 in.

The area of any two-dimensional figure is the space occupied within its boundary.

The area of a square with side length a, is calculated using the formula, A = a² square units.

In the question, we are asked to find the approximate side length of a square game board with an area of 113 (in)².

Since the game board is square in shape, we can apply the formula for the area of a square.

We assume the side length to be a in.

By the formula for the area of a square, we can calculate the area of the square game board to be a² (in)².

But, the area of the square game board is given to be 113 (in)².

Thus, we get an equation:

a² = 113,

or, a = √113,

or, a = 10.63014581273465,

or, a ≈ 10.63.

Thus, the side length of the square game board with an area of 113 (in)² is approximately 10.63 in.

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Answer:

Its C

Step-by-step explanation:

The y starts at negative 3 and it is going up by 1 and over 2

Hope this Helped

Answer:

C. y = 1/2x - 3

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope:  

1

2

y-intercept:  

(

0

,

−

3

)

x

y

0

−

3

6

0

Answer: 2/3

Step-by-step explanation:

You can do cross multiplication 12 x 2 = 24 and 3 x 8 = 24

The error in the system of inequalities represented by the graph is that the inequality symbol is incorrect for the blue boundary line.

What informs the description?

The error in the system of inequalities represented by the graph is that the inequality symbol is incorrect for the blue boundary line. The blue boundary line is a dashed line, which represents a "less than" or "greater than" inequality. However, the inequality symbol used is "=". The correct inequality symbol for the blue boundary line should be "<" or ">", depending on which side of the line the solution is on.

The correct system of inequalities would be:

y > -2x + 2 (if the solution is on the side above the blue line)

or

y < -2x + 2 (if the solution is on the side below the blue line)

Additionally, there is an error in the representation of the red boundary line, it should be y=0.5x+1 not y=5 or 2.

There is also an error on the representation of x and y, it should be x>= 1505+1.

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Answer:

42

Step-by-step explanation:

it is stated that the triangle are similar so their side lengths must be proportional, we can use this to find the missing side length

AB/XY = BC/YZ write this with the side lengths

3/21 = 6/? cross multiply expressions

3? = 126 divide both sides by 3

? = 42

Answer: The solutions of the absolute value equation are given by:

x = -41 and x = 49.

What is the absolute value function?

The absolute value function is defined by:

|x| = x, x >= 0.

|x| = -x, x < 0.

The absolute value function measures the distance of a point x to the origin, that is, the distance to x = 0. From this, we get that |x| = a can mean either that:

x = a, or;

x = -a.

In this problem, the equation is given by:

Hence:

0.2|x - 4| = 9

|x - 4| = 45

The first possible solution is:

x - 4 = 45

x = 49.

The second possible solution is:

-x + 4 = 45

-x = 41

x = -41.

Hence the solutions are x = -41 and x = 49.

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Step-by-step explanation:

we do not have any information about the measures of the other angles or the lengths of the sides in this triangle, we cannot determine the value of CobB.

The given triangle is not fully specified, so it is impossible to determine the value of CobB. We need additional information such as the lengths of the sides or measures of other angles in the triangle.

In general, to find the measure of an angle in a triangle, we can use thethe fact that the sum of the measures of the angles in a triangle is always 180 degrees. If we know the measures of two angles in the triangle, we can subtract their sum from 180 to find the measure of the third angle.

However, since we do not have any information about the measures of the other angles or the lengths of the sides in this triangle, we cannot determine the value of CobB.

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Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

Answer:

2°

Step-by-step explanation:

because all they days had the same temperature, with no escalation it will stay as 2°

The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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The line which passes through (-4,2) and (-5,0) has a slope of 2.

Let,

\((x_{1},y_{1})\) = (-4,2)

\((x_{2},y_{2})\) = (-5,0)

If the points are equal to each other, their x-coordinates are equal to each other:

\(x_{1}\)=-4

\(x_{2}\)=-5

If the points are equal to each other, their y-coordinates are equal to each other:

\(y_{1}\)=2

\(y_{2}\)=0

The slope, m is the steepness of a line and it is measured as the ratio of the change in vertical distance, rise over the change in horizontal distance, run.

The slope of the line, m:

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

m=(0-2)/(-5-(-4))

m=(-2)/(-1)

m=2

The slope of the line for the two points is 2.

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The measures of the corresponding inscribed angles, and then add those angles together to find the measure of angle L. Therefore, the measure of angle L is 64 degrees.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. In other words, if we have an angle whose vertex is on the circumference of a circle, and whose sides intersect two points on the circumference, then the measure of the angle is half the measure of the arc between those two points.

In this problem, we are given the measures of two arcs, DR and SV, and we want to find the measure of angle L. We can start by using the Inscribed Angle Theorem to find the measures of the corresponding inscribed angles. Let's call these angles A and B, where A is the inscribed angle that intercepts arc DR, and B is the inscribed angle that intercepts arc SV.

Using the Inscribed Angle Theorem, we can find that m∠A=12m⌢DR=12(34∘)=17∘m∠B=12m⌢SV=12(94∘)=47∘

To find the measure of angle L, we simply add angles A and B together: m∠L=m∠A+m∠B=17∘+47∘=64∘

Therefore, the measure of angle L is 64 degrees.

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The standard deviation is usually presented in conjunction with the mean in the description of a continuous variable to provide information about both the central tendency and the variability of the dataset.

In statistical analysis, the standard deviation is a measure of the spread or dispersion of a dataset. It quantifies how much the values in a dataset deviate from the mean or average value. When describing a continuous variable, the standard deviation is typically presented alongside the mean to provide a comprehensive understanding of the distribution of the variable.

The mean represents the central tendency or average value of the dataset, while the standard deviation provides information about the variability or spread around the mean. By considering both the mean and the standard deviation together, you can gain insights into both the central value and the degree of dispersion of the variable.

For example, let's say we have a continuous variable that represents the heights of a group of individuals. The mean height tells us the average height of the group, while the standard deviation indicates how much the heights of individuals vary around that average. A large standard deviation suggests that the heights are more spread out and less concentrated around the mean, while a small standard deviation indicates that the heights are more tightly clustered around the mean.

Therefore, when describing a continuous variable, presenting the standard deviation along with the mean provides a more complete picture of the dataset's central tendency and variability.

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A = P ( 1 + r )^t

Given A = $2000 , r = 3% = 0.03

so, after 2 years t = 2

A = 2000 * ( 1 + 0.03)^2 = $2,121.8

so, the total after 2 years = $2,121.8

==============================================================

How much money should be invested today to accumulate to $10,000 in 10 years at 4.5% compounded monthly? (Simplify your answer. Round to the nearest cent as needed)

so, A = $10,000

r = 4.5% = 0.045

t = 10 years = 10 * 12 = 120 months

So, A = P (1 + r/n)^t ,,, n = 12

10,000 = P ( 1 + 0.045/12)^120

10,000 = P * 1.567

P = 10,000/1.567 = 6,381.65 ( to the nearest cent )

so, the money should be invested = $6,381.65

Answer:

Step-by-step explanation:

The first step is to get the given equation to look like the answers provided.

y = - 2/3 x - 1                     multiply by 3

3y = -2x - 3                       add 2x to both sides

3y +2x   = - 3        

Only the answer on the lower left looks the left side of the above equation.

2x + 3y = - 24 is your answer.

The p- value for the given sample and favored sample to determine the proportion is equal to 0.04135 which is statistically significantly , reject null hypothesis and accept alternative hypothesis.

As given in the question,

Sample size of people 'n' = 100

Number of favored candidates = 60

Success value 'p'  = 60/100

                              = 0.60

1 - p = 1 - 0.60

      = 0.40

Null hypothesis : H₀ > 50%

Alternative hypothesis : H₁ ≤ 50%

Test statistic :

Proportion of the population:

z = (p - \(\^{p}\) ) / √ p ( 1- p)/n

  = ( 0.60 - 0.50)/ √ 0.60(0.40)/100

 = 0.10/ √0.0024

 = 0.10/0.049

 = 2.04

p - value using table is equal to 0.04135

Significant level is 0.05

0.04135 < 0.05 .

Here conclusion is statistically significant, reject null hypothesis and accept alternative hypothesis.

Therefore, the p- value for the given sample and favored sample is equal to 0.04135 which is statistically significantly , reject null hypothesis and accept alternative hypothesis.

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Answer: bro just look it up fr fr

Step-by-step explanation:

The interquartile range of the given dataset is 12.5. This measure represents the spread of the middle 50% of the data, providing a robust measure of variability that is not affected by extreme values or outliers.

To find the interquartile range (IQR) of a dataset, we first need to determine the values of the first quartile (Q1) and the third quartile (Q3). The IQR is then calculated as the difference between Q3 and Q1.

Arrange the data in ascending order:

43, 46, 47, 51, 51, 52, 54, 54, 55, 56, 60, 61, 62, 64, 69, 70.

Determine the position of Q1 and Q3:

Q1 is the median of the lower half of the dataset, and Q3 is the median of the upper half.

The dataset contains 16 observations, so the median (Q2) will be the average of the 8th and 9th values, which are 54 and 55.

Q2 = (54 + 55) / 2 = 54.5

For Q1, we consider the first 8 values: 43, 46, 47, 51, 51, 52, 54, 54. Since there are an even number of values, the median will be the average of the 4th and 5th values, which are 47 and 51.

Q1 = (47 + 51) / 2 = 49.

For Q3, we consider the last 8 values: 55, 56, 60, 61, 62, 64, 69, 70. Again, the median will be the average of the 4th and 5th values, which are 61 and 62.

Q3 = (61 + 62) / 2 = 61.5.

Calculate the IQR:

IQR = Q3 - Q1 = 61.5 - 49 = 12.5.

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It is possible to use a relational operator and math operators in the same expression.

In programming, you can use relational operators (e.g., <, >, ==, !=) and math operators (e.g., +, -, *, /) together in the same expression. This is often used in conditional statements or loops to compare calculated values.

For example, consider the following expression:

`if (2 * 3) > (4 + 1)`

In this expression, we have math operators (*) and (+) and a relational operator (>). The math operations are evaluated first, resulting in:

`if (6) > (5)`

Then, the relational operator (>) is evaluated, and the expression becomes:

`if True`

The expression is true because 6 is greater than 5.

It is possible to use both relational operators and math operators in the same expression, which can be useful in various programming situations such as conditional statements or loops.

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Answer:

Step-by-step explanation:

The perimeter of the square whose diagonal is 10 centimeters using the diagonal formula is 28.28 centimeters.

To find the perimeter of a square with a diagonal of 10 centimeters, we need to use the Pythagorean theorem. According to the theorem, the diagonal of a square can be calculated as the square root of twice the square of one of its sides, which is represented by the formula:

diagonal = √(2) × side

where the side is the length of one side of the square.

We know that the diagonal of our square is 10 centimeters, so we can solve for the length of one side by rearranging the formula as follows:

side = diagonal / √(2)

side = 10 / √(2)

side ≈ 7.07 centimeters

Now that we know the length of one side, we can find the perimeter of the square by multiplying the length of one side by 4, which is the number of sides in a square:

perimeter = 4 × side

perimeter ≈ 28.28 centimeters

Therefore, the perimeter of the square with a diagonal of 10 centimeters is approximately 28.28 centimeters.

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