If point M is 2 units to the left of point N and 4 units above point N, what is the slope of

the line between the two points

If two random variables, Y1 and Y2, are independent, the condition that needs to be satisfied is that the joint probability distribution of Y1 and Y2 factors into the product of their individual probability distributions.

Mathematically, for independent random variables Y1 and Y2, the condition can be expressed as:

P(Y1 = y1, Y2 = y2) = P(Y1 = y1) * P(Y2 = y2)

This means that the probability of both events Y1 = y1 and Y2 = y2 occurring together is equal to the product of the probabilities of each event occurring individually.

In simpler terms, knowing the outcome or value of one random variable does not provide any information about the outcome or value of the other random variable if they are independent. They do not influence each other's probability distributions.

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The z-score corresponding to Anastasia's test score is -0.5. This indicates that her score is 0.5 standard deviations below the mean.

To calculate the z-score corresponding to Anastasia's test score of 110, we can use the formula:

z = (x - mean) / standard deviation

where x is Anastasia's score, mean is the mean of the test scores (120), and standard deviation is the standard deviation of the test scores (20).

Substituting the values into the formula, we get:

z = (110 - 120) / 20 = -0.5

Therefore, the z-score corresponding to Anastasia's test score is -0.5. This indicates that her score is 0.5 standard deviations below the mean. A negative z-score implies that her score is below the mean, while a positive z-score would indicate a score above the mean. In this case, Anastasia's z-score of -0.5 suggests that her score is below average relative to the distribution of scores on the standardized test.

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Answer: A. 0

Step-by-step explanation: To determine the number of solutions for the system of equations x - y = 7 and y = sqrt(3x + 3) - 2, we can substitute y in the first equation with the expression for y in the second equation, giving us x - (sqrt(3x + 3) - 2) = 7. Simplifying this equation, we get sqrt(3x + 3) = -x + 9.

Since the square root of a number is always non-negative, we can conclude that there are no solutions to this system of equations. Therefore, the answer is A. 0.

- Lizzy ˚ʚ♡ɞ˚

Answer:

3/4

Step-by-step explanation:

The fraction of 75 is 3/4

And its the simplest form

Answer:

The first choice, second choice, fifth choice are correct

Step-by-step explanation:

To get the first and second choices, you just need to count the number of boxes. For the fifth choice, you can see that the side lengths have been cut in half from the pre-image to image

The value of h(a -4) is -a² + 8a - 8

A function can be defined as an expression or rule that explains the relationship between a dependent and an independent variable.

Given the functions;

To determine  h(a-4), we substitute the value of x as a - 4 in the h(x) function, we have;

h(a - 4) =- (a - 4)² + 8

expand the bracket

h(a - 4) = - ( a - 4)(a - 4) + 8

h(a - 4) = - (a²- 4a - 4a + 16) + 8

collect like terms

h(a - 4) = - a² + 8a -16 + 8

h(a - 4) = -a² + 8a - 8

Thus, the value of h(a -4) is -a² + 8a - 8

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The opposite side of the right triangle (x) is approximately 6.888 inches long.

To solve this problem, we can use the trigonometric ratio for the sine function, which is opposite/hypotenuse. We have the hypotenuse as 12 inches and the opposite angle as 35 degrees, so we can set up the equation:

sin(35) = opposite/12

To solve for the opposite, we can multiply both sides by 12:

opposite = 12 * sin(35)

sin(35) as approximately 0.574:

opposite = 12 * 0.574

opposite ≈ 6.888

Therefore, the opposite side of the right triangle (x) is approximately 6.888 inches long.

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Answer:

3 , 2.96 , 1/5 (0.2)  
3.48 , 3 , 1/4 (0.25)

Step-by-step explanation:

descending order

Answer:

Hope this helped!!!

Step-by-step explanation:

If Jamie spins the spinner 60 times, we can predict 20 red, 10 blue, 20 green, and 10 yellow outcomes

First, calculate the probability of each color by dividing the frequency by 30 spins.

Red: 10/30 = 1/3

Blue: 5/30 = 1/6

Green: 10/30 = 1/3

Yellow: 5/30 = 1/6

Now, predict the frequency of each color if Jamie spins the spinner 60 times.

Red: (1/3) * 60 = 20

Blue: (1/6) * 60 = 10

Green: (1/3) * 60 = 20

Yellow: (1/6) * 60 = 10

So, if Jamie spins the spinner 60 times, we can predict 20 red, 10 blue, 20 green, and 10 yellow outcomes

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The Complete Question:

Jamie spun a spinner with 4 colors - red, blue, green, and yellow - 30 times and recorded the frequency of each result in the table below. Use the table to determine the probability of each color and predict the frequency of each color if Jamie spins the spinner 60 times.

Table:

Red - 10

Blue - 5

Green - 10

Yellow - 5

I Hope This Helps You

y=2x-20/5-3

y+3=2x-20/5

5(y+3)=2x-20

5y+15=2x-20

2x-5y-35=0

The numbers between 3 and 4 are 15/5, 16/5, 17/5, 18/5, 19/5 and 20/5.

Given,

The numbers 3 and 4.

We have to find the whole number between 3 and 4.

So, the number between 3 and 4 will be a rational number.

Between any two given rational numbers, we can discover any number of rational numbers.

To continue, we multiply and divide the rational numbers by an appropriate number to make their denominators identical.

If the denominators are already the same, we choose the numbers based on how many reasonable ones can be discovered.

So, lets find the rational number between 3 and 4 by multiplying and dividing with 5.

That is,

3 × 5/5 = 15/5

4 × 5/5 = 20/5

So the numbers between 3 and 4 are 15/5, 16/5, 17/5, 18/5, 19/5 and 20/5.

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The quadrilateral with no pair of parallel sides is trapezium

Given data ,

A = a quadrilateral with no pair of parallel sides

This type of quadrilateral is called a trapezium. In some countries, a trapezium is defined as having exactly one pair of parallel sides, while in other countries, a trapezium is defined as having at least one pair of parallel sides.

In any case, a quadrilateral with no pair of parallel sides is not considered a trapezium. Instead, it is known as a general quadrilateral.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

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He can invite 7 friends.Because he had $40. He will spent for each person $5.25.

In mathematics, a relationship between two expression that are not equal to each other is called inequality.The word inequality mean not being equal ,especially in status, rights and opportunities.

A statement is a declarative statement that is true or false but both not.A statement is also called proposition.It may contain symbols and  words.

he has total money = $40

 cost of burger        =$4.50

 cost of soda           =$0.75

 Let, he will spend for each person

 4.50+0.75=$5.25

so, he can invite=40/5.25

                          =7.619

he can invite 7 friends.

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Answer:

4√3

Step-by-step explanation:

Hello!

This is a 30° 60° 90° because it has a 90° angle, a 30° angle, and the missing angle is 60° (sum of angles in a triangle is 180°). This triangle has special properties.

In a 30°-60°-90° triangle, the leg opposite 30° is always half the hypotenuse.

This means that the hypotenuse would be 2 times 4, or 8.

The leg opposite to 60° in a right triangle of this sort is the length of a leg multiplied by √3.

So the measure of x is 4√3.

An image is attached for your reference.

The value of side labeled x using Trigonometric ratio is  \({4}{\sqrt 3}\).unit.

Given:

Angle = 30

Perpendicular or opposite side= 4

Using Trigonometric ratio

tan 30 = Opposite side / Adjacent side

Substituting Opposite side= 4 and Adjacent side = 4 in above ratio

So, tan 30 = 4 / x

As, the value of tan 30 = \(\dfrac{1}{\sqrt 3}\) then

tan 30 = 4 / x

\(\dfrac{1}{\sqrt 3}\)  = \(\dfrac{4}{x}\)

solving for x

x = \({4}{\sqrt 3}\)

Thus, the value of x is \({4}{\sqrt 3}\).

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Answer:

x=10

Step-by-step explanation:

To solve for x, you need to draw an imaginary line connecting the right end of side x to the left side with length 15. This forms a triangle with side lengths 6 and 8, and hypotenuse x. Using the Pythagorean Theorem to solve for x, we get 6^2 + 8^2 = x^2, 36 + 64 = 100, \(\sqrt{100}\) = 10.

Answer:

It's 10

Step-by-step explanation:

C^2=A^2+B^2blank

C=√(A^2+B^2)

If c is x and a and b are the side lengths the we can use Pythagoras's theorem to calculate the length of the line. A=6 B=8 and in the end when you calculate all that doohickey stuff you get x=10

The connected sum operation does not have an inverse as it destroys information about the original spaces.

A simple intuitive reason for this is that if one connects two spaces, the operation doesn't have any way of determining which space is the "original" one, and which one is the "newly added" one.

The connected sum of two spaces X and Y is defined as follows: take a copy of X, a copy of Y, remove an open ball from each of them, and then glue the resulting two spaces together along the open balls' boundaries. This is denoted by $X \# Y$.The connected sum operation does not have an inverse, which can be rigorously proved as follows:

Similarly, $Z$ is orientable if and only if both $X$ and $Y$ are orientable.

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Answer:

100

Step-by-step explanation:

Hey there!

First, to find the cost of one apple, 50 ÷ 25, which equals 2.

At this point, i am not very sure if you meant to say 75 apples, or $75 apples, so I am just going to give both solutions.

If you meant 75 apples: 75 x 2 = $150

If you meant $75 apples: $75 ÷ 2 = 37.5

Since it isn't realistic to buy 37 apples and one half, round it to 37 apples.

Hope this helps!

Have a great day!

Answer:

about .24 mile per hour

1 mile is 5280 foot

Step-by-step explanation:

The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.

By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.

Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

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If \(x^(3/3) = y^(2/2)\), then \(x^3\) can be determined by simplifying the exponents.

To solve the given equation, we need to simplify the exponents on both sides.

Using the property of exponentiation, when we raise a power to another power, we multiply the exponents.

In this case, x^(3/3) can be simplified as x^(1), since 3/3 equals 1. Similarly, y^(2/2) simplifies to \(y^(1).\)

Therefore, the given equation \(x^(3/3) = y^(2/2)\) simplifies to \(x^1 = y^1.\)

Since any number raised to the power of 1 is equal to the number itself, we have x^1 = x and y^1 = y.

Hence, x^3 can be written as \(x^1 x^1 x^1 = x x x = x^3.\)

Therefore, x^3 is the answer to be filled in the space provided.

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The difference in the values of the two cars when they are each 7 years old is equal to $6,000.

In order to determine the difference in the values of the two cars, we would have to write an equation that models the price of the cars after a length of time, by using the data points shown in the graph above.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For Car A, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (9 - 12)/(4 - 2)

Slope, m = -3/2

Slope, m = -1.5

At point (4, 9), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y - 9 = -1.5(x - 4)

y = -1.5x + 15

In 7 seven years, the value of Car A is given by:

y = -1.5x + 15

y = -1.5(7) + 15

y = $4,500

Note: The negative sign indicates that the value of the car is depreciating.

For Car B, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (10 - 18)/(5 - 1)

Slope, m = -8/4

Slope, m = -2

At point (5, 1), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - 1 = -2(x - 5)

y = -2x + 11

In 7 seven years, the value of Car B is given by:

y = -2x + 11

y = -2(7) + 3.5

y = $10,500

Now, we can determine the difference as follows:

Difference = $10,500 - $4,500

Difference = $6,000.

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The area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To solve this problem, we can use the formula for the volume of a hexagonal prism:

V = (3√3/2) * a^2 * h

where V is the volume, a is the length of one side of the hexagonal base, and h is the height of the prism.

We are given that the height of the prism is 4 units and the volume is 98 units^3. Plugging these values into the formula, we can solve for the length of one side of the base:

98 = (3√3/2) * a^2 * 4
a^2 = 98 / (12√3)
a ≈ 2.95

Now that we know the length of one side of the base, we can find the area of the hexagon by using the formula:

A = (3√3/2) * a^2

where A is the area of one of the bases. Plugging in the value we found for a, we get:

A = (3√3/2) * (2.95)^2
A ≈ 7.39

Therefore, the area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

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Answer: 1. 33 , 2. 21 , 3. $5.00 , 4. 39.

Step-by-step explanation:

4. Let the original number of baseball trading cards in Tim's possession be

x

An equation to arrive at the number will be:

x

+

9

2

=

24

This is because half the collection AFTER adding

9

new cards is

24

(the other half was eaten by his dog).

Multiply both sides by

2

.

x

+

9

=

48

Subtract

9

from both sides.

x

=

39

Answer:

The right answer is:

(a) 0.4866

(b) 10.3972

Step-by-step explanation:

Let X be the number of days,

X is \(exp(\lambda)\),

⇒ \(\lambda =\frac{1}{15}\)

now,

⇒ \(F_x(x) = P(X \leq x)\)

              \(=1-e^{-\lambda x}\)

              \(=1-e^{-\frac{x}{15} }\)

or,

\(x>0\)

(a)

⇒ \(P(X<10)=F_x(10)\)

                      \(=1-e^{\frac{10}{15} }\)

                      \(=1-e^{\frac{2}{3} }\)

                      \(=0.4866\)

(b)

If the medium be m, then

\(P(X=m) = \frac{1}{2}\)

                 \(=2^{-1}\)

⇒\(1-e^{-\frac{m}{15} } = \frac{1}{2}\)

        \(e^{-\frac{m}{15} } = 2^{-1}\)

             \(m= 15\ ln2\)

                 \(=10.3972\)  

I believe the answers b

Answer:

Correct answer is A. Multiply the first equation by 2 and the second equation by 3.

Step-by-step explanation:

slope=7

Explanation

the slope of a line ( or segment) is given by

so

Step 1

Let

now,replace in the formula

therefore, the slope is 7

I hope this helps you

Answer:

highest: $1,438

lowest: $1,062

Step-by-step explanation:

The highest and lowest points are adding $188 and subtracting $188 from her brother's amount.

So, to find the highest point, add $188 to $1,250, which is $1,438.

To find the lowest point, subtract $188 from $1,250, which is $1,062.

Hope this helps ;)

When the sine function  sinθ = 0.5126 then the angle θ  is 30.001°

Given sinθ = 0.5126

We have to find the value of θ or the angle θ.

We know that the sine function is a ratio of opposite side and hypotenuse.

As given value sinθ = 0.5126

To find θ value, we take sin⁻¹ on both sides of the equation.

sin⁻¹(sinθ)=sin⁻¹(0.5126)

On left side the sine and its inverse will be cancelled and left with angle θ.

Now θ = sin⁻¹(0.5126)

To find the value of sin⁻¹(0.5126), you can use the inverse sine function or arcsin function.

θ = 30.001°

Hence, when the sine function  sinθ = 0.5126 then the angle θ  is 30.001°

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