A pair of dice is rolled, and the number that appears uppermost on each die is observed. Find the probability of the event that the sum of the two numbers is at most 4.

Answer:

0, 1, 1/2

Step-by-step explanation:

First you would have to make them have the same denominators.

The lowest one they share is 24.

What ever you do to the bottom you have to do to the bottom.

1/6, times each by 4.

1 * 4 = 4

6 * 4 = 24

4/24.

Now you have to do the same thnig for 5/8.

But times it by 3, since 8 times 3 is 24.

5 * 3 = 15

8 * 3 = 24

15/24

Now subtract.

15 - 4 = 11/24

the difference is close to one half.

4/24 = 1/6 is close to 0.

15/24 = 5/8 is close to 1.

Answer:

i need the points

Step-by-step explanation:

the maximum and minimum values of f(x,y) on the ellipse occur at approximately (±0.445, ±0.364) and (±0.364, ±0.445), respectively.

To find the points on the ellipse 3x^2 + 2y^2 = 1 where f(x,y) = xy has its extreme values, we can use the method of Lagrange multipliers.

We want to find the points (x, y) on the ellipse where the gradient of f(x,y) is parallel to the gradient of the constraint function g(x,y) = 3x^2 + 2y^2 - 1. The gradient of f(x,y) is <y, x>, and the gradient of g(x,y) is <6x, 4y>. Thus, we need to solve the system of equations:

y = λ(6x)

x = λ(4y)

3x^2 + 2y^2 = 1

From the second equation, we get λ = x/(4y). Substituting into the first equation, we get y = (3/8)x^2. Substituting into the third equation, we get:

3x^2 + 2[(3/8)x^2]^2 = 1

3x^2 + (27/32)x^4 = 1

Multiplying both sides by 32, we get:

96x^2 + 27x^4 - 32 = 0

This is a quartic equation in x^2, which can be solved using standard methods. We can also note that the function f(x,y) = xy is symmetric with respect to the line y = x, so any extreme values on one side of this line will have a corresponding extreme value on the other side.

Therefore, the maximum and minimum values of f(x,y) on the ellipse occur at approximately (±0.445, ±0.364) and (±0.364, ±0.445), respectively.

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To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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SOLUTION

We want to solve

To do this, change the mixed fraction into improper fraction.

We say, 2 multiplied by 12, then plus 1. We write the result as the numerator over the denominator which is 2. That is

We then multiply by 4, we have

Hence the answer is 50

Answer:

$112.80

Step-by-step explanation:

If he earns $0.235 per pack, and there are 480 packs, then our equation is:

0.235 x 480 = $112.80

The amount of money earned by Eddie for packing and sealing packs of 480 pens is $112.8

The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.

According to the given question.

Amount of money charged by Eddie for packing and sealing a pack of pens = $0.235

Therefore,

The amount of money charged by Eddie for packing and sealing packs of 480 pens

= 480 × $0.235

= $112.8

Hence, the amount of money earned by Eddie for packing and sealing packs of 480 pens is $112.8

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Answer:

D is the answer

Step-by-step explanation:

Well 35 dollar one time fee

plus 15 per hour

If used 1 hour 15+35=50

Answer:

A

Step-by-step explanation:

The price of renting a boat goes up 15 per hour, which is the rate of change.

Section A shows a decreasing speed, section B and D exhibit a constant speed, and section C displays an increasing speed as time continues. By analyzing the movements of the orange line on the graph.

In section A of the graph, the speed is decreasing as time is increasing. The description mentions that the orange line starts near the top of the vertical axis and goes down as time increases.

This downward movement indicates a decrease in speed. As time progresses, the speed is getting slower, resulting in a negative slope for section A of the graph.

In section B, the speed levels out as time continues. This implies that there is no significant change in speed as time increases. The orange line remains relatively constant, indicating a constant speed. This section is characterized by a horizontal line on the graph.

Moving on to section C, the speed is increasing as time continues. The description mentions that the orange line moves up the vertical axis as time increases. This upward movement signifies an increase in speed. As time progresses, the speed is getting faster, resulting in a positive slope for section C of the graph.

Finally, in section D, the speed levels out as time continues. Similar to section B, there is no significant change in speed as time increases. The orange line remains relatively constant, indicating a constant speed. This section is also characterized by a horizontal line on the graph.

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This question is about probability. The answer for this question is 34,09%.

Suppose there was survey that state that the number of hours spent per week on house hold course of adult has mean 26,3 and standard deviatiador 7,4 and, sample are 46.

First, we need to know the base formula for probability given a mean and standard deviation.

First we need to know the z-score with this formula:

z-score =( x -μ )/ δ

Where:

X = individual data

μ = population mean

δ = population standard deviation.

But in this case, we were asked about the probabilty mean of 46 people. Then, we can use this formula :

Z-score =(x- μ) / (δ /√n)

Where :

X = sample mean

μ = population mean

δ = population standard deviation

Then we can find the z-score in z-table value.

Given :

X = 26,75

μ = 26,3

δ = 7,4

n = 46

Question :

Probability mean more than 26,75

Answer :

Z-score = (x- μ) / (δ /√n)

Z-score = (26,75 - 26,3)/ (7,4/√46)

Z-score = (0,45)/ (1,09)

Z-score = 0,4128

if we look in z-score table, we get number 0,6591.The probability that the mean hours spent per week on household chores by a sample of 46 adults will be more than 26.75 is 1 substract by the value of z-score ,

So, the probability mean for working adult more than 26,75 is 1 - 0,6591 = 0,3409 = 34,09%

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Answer:

52.6 degrees

Step-by-step explanation:

tan^-1(72/55)

Angle of elevation is equals to 52°7'(approximately).

" Angle of elevation is the angle between the horizontal plane and  line of sight from the point of observation."

Formula used

In a right angled triangle,

tanθ = ( opposite side) / adjacent side)

According to the question,

As shown in diagram

Height of the building (AB) = 72m

Distance between base of the building and point of observation

(BC)= 55m

Angle of elevation = θ

Substitute the value in the formula we have,

 tanθ = AB / BC

          = 72 / 55

⇒ θ = tan⁻¹ (72 /55)

      = tan ⁻¹(1.3091)

      = 52° 7' (approximately)

Hence, angle of elevation is equals to 52°7'(approximately).

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Given:

The scores on a standardized test are normally distributed with a mean of 115 and standard deviation of 10.

Required:

What test score is 0.8 standard deviations below the mean?

Explanation:

Answer:

answered the question.

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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a. The equation for the tangent line of each of these points are y + 2 = 4(x - 1) and y = 4x - 6, respectively

b.  There are no points on the curve where the tangent line is vertical.

(a) To find all points on the curve whose x-coordinate is 1, we can substitute x = 1 into the equation and solve for y.

Substituting x = 1, we get:

y² - y = 6

This is a quadratic equation in y, which we can solve using the quadratic formula:

y = (1 ± √(1 + 24))/2

y = (1 ± 5)/2

So, we have two possible values of y: y = 3 and y = -2.

Therefore, the points on the curve whose x-coordinate is 1 are (1, 3) and (1, -2).

To find the equation of the tangent line at each of these points, we can use the formula:

y - y0 = f'(x0)(x - x0)

where (x0, y0) is the point of tangency and f'(x0) is the derivative of the function at that point.

For (1, 3):

First, we need to find the derivative of the function at x = 1:

dy/dx = (3x²y - 2y² - 2xy)/(-x² + 2xy)

At x = 1 and y = 3, we have:

dy/dx = (3(1)²(3) - 2(3)² - 2(1)(3))/(-1² + 2(1)(3))

dy/dx = -3/5

So, the equation of the tangent line at (1, 3) is:

y - 3 = (-3/5)(x - 1)

y = (-3/5)x + 18/5

For (1, -2):

Again, we need to find the derivative of the function at x = 1:

dy/dx = (3x²y - 2y² - 2xy)/(-x² + 2xy)

At x = 1 and y = -2, we have:

dy/dx = (3(1)²(-2) - 2(-2)² - 2(1)(-2))/(-1² + 2(1)(-2))

dy/dx = 4

So, the equation of the tangent line at (1, -2) is:

y + 2 = 4(x - 1)

y = 4x - 6

b) To find the x-coordinate of each point on the curve where the tangent line is vertical, we need to find where dy/dx is undefined, which occurs when the denominator of the expression for dy/dx is equal to zero:

2xy - 3x² = 0

x(2y - 3x) = 0

So either x = 0 or y = 3x/2. If x = 0, then the corresponding y-value is given by the equation 0y^2 - 0 = 6, which has no real solutions. So we focus on the case where y = 3x/2:

xy² - x³y = 6 becomes (3x/2)x² - x²(3x/2) = 6, which simplifies to x⁴ - 4x³+ 8x = 0.

Factoring out x, we get

x(x₃ - 4x₂ + 8) = 0.

The cubic factor has no real roots, so the only solution is x = 0. Substituting this into the original equation, we get y² = -6, which also has no real solutions. Therefore, there are no points on the curve where the tangent line is vertical.

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Answer:

Step-by-step explanation:

The standard deviation of a data set is represented by the following equation:

Therefore, for the given sample:

For each data point, find the square of its distance to the mean.

Now, solving for the standard deviation:

The equation of the line will be (assuming the y-intercept equal to zero):

y = 2.5*x

We know that we have a linear equation of the form:

y = a*x + b

Such that we know that the line passes through (-3, -7.5), notice that the proposed equation is:

y = 0.5*x

If you evaluate that in -3, you get:

y = 0.5*-3 = -1.5

So this line does not pass through (-3, -7.5).

If we assume that b = 0 in the linear equation, then we can find the value of a as:

-7.5  =  a*-3

a = 7.5/3 = 2.5

Then the linear equation is:

y = 2.5*x

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The function f(x) from the composite function is f(x) = 4x - 9

From the question, we have the following parameters that can be used in our computation:

The composite function, f(5a)=20a -9

Express properly

So, we have

f(5a) = 20a - 9

Express 20a as the product of 5a and 4

So, we have

f(5a) = 4 * 5a - 9

Let x = 5a

So, we substitute x for 5a in the above equation, and, we have the following representation

f(x) = 4x - 9

Hence, the function f(x) is f(x) = 4x - 9

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Answer:

3^x+15=3 i think this is what you are looking for

Step-by-step explanation:

The first part of the question asks whether the series (-1)^(n)(sqrt(n^2 + 2n – n)) is convergent or divergent. The second part asks about the series 4/3 + 6 and its convergence or divergence.

For the first series, we can simplify the expression inside the square root as n^2 + n. Taking the square root, we have sqrt(n^2 + n) = n*sqrt(1 + 1/n). As n approaches infinity, 1/n approaches 0, and sqrt(1 + 1/n) approaches 1. Therefore, the series becomes (-1)^n * n, which is an alternating series. For an alternating series (-1)^n * a_n, where a_n is a positive sequence that decreases to zero, the series converges if the limit of a_n approaches zero. In this case, the limit of n is infinity, which does not approach zero, so the series is divergent. Regarding the second series, 4/3 + 6 is a finite series and therefore convergent.

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You put 5 points not 100, just saying, haha.

The probability that a standard normal variable z is greater than 1.61 is 0.0549.

This is derived from the standard normal table which gives the area under the normal curve between -∞ and the given value.

This area is equal to the probability of the variable falling between -∞ and the given value. For a standard normal variable, the area between -∞ and 1.61 is 0.9451, which is the probability of the variable falling between -∞ and 1.61.

The area between 1.61 and ∞ is 0.0549, which is the probability of the variable falling between 1.61 and ∞.

Therefore, the probability of z being greater than 1.61 is 0.0549.

Complete Question:

Given that z is a standard normal variable, what is the probability that z is greater than 1.61?

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The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Answer:

The correct answer would be D, Right Five Units :)

Step-by-step explanation:

I hope this helps, if it doesn't then just message me and ill be more than happy to help :)

Answer:

D   right 5 units

Step-by-step explanation:

(x-5)   shifts the values 5 units to the right

Answer:

x=6/5 and x=-(1/2)

Step-by-step explanation:

\(f(x) = 10x^3-37x^2+15x+18\\f(x) = \frac{(5x-6)(2x+1)(x-3)}{(x-3)}\\ f(x) = (5x-6)(2x+1)\)

To find the zeros, we set f(x) = 0 for both factors

\(5x-6=0\\5x=6\\x=6/5\)

\(2x+1=0\\2x=-1\\x=-1/2\)

Therefore the zero's of f(x) are x = 6/5 and x= -(1/2)

Being Respectful, Practicing Empathy, Being Open-Minded, Remaining Patient

Attitude is an individual's way of perceiving and responding to their environment. It is a state of mind that influences how people think, feel, and behave. Attitudes are shaped by experiences, beliefs, and values, and they can be positive or negative, depending on the situation.

1. Being Respectful: A positive attitude helps to foster respect between yourself and those you meet. Respect is the foundation of any successful relationship, and having a positive attitude can help ensure that respect is maintained in the face of any potential conflicts.

2. Practicing Empathy: Having a positive attitude allows you to practice empathy and understanding of the people around you. Taking the time to understand the perspectives of others can help to prevent misunderstandings and conflicts.

3. Being Open-Minded: A positive attitude allows you to remain open-minded and flexible in any situation. This can help to stave off interpersonal conflicts by allowing you to better understand the needs and wants of those around you.

4. Remaining Patient: A positive attitude can help you remain patient and understanding of people in your life. Being patient in the face of any potential conflicts can help to resolve issues in a peaceful manner and prevent them from escalating.

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Answer:

x + 5 = 5×

7x - 5 = 2x

5x + 2x + x = 180

8× = 180

8 8

x = 22.5

The measure of the angles are;

X = 38 degrees

Y = 52 degrees

To determine the angles, we need to know the properties of a kite.

These properties includes;

Then, we can say that;

Y= 52 degrees

Note that the sum of the angles in a triangle is 180

Then, we get;

X + Y+ 90 = 180

X = 180 - 142

Subtract the values

X = 38 degrees

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the explicit rule of the nth term of the arithmetic

sequence is A. aₙ = 6n-8

                    B. aₙ = 6n-26

                     C. aₙ= 6n-26

                     D. aₙ =6n-14

the sequence of numbers having constant differences between two successive numbers.

the explicit formula is used for determining any term of an arithmetic sequences directly in where only the first term and differences between two consecutive terms are needed to know.

Given, -20,-14,-8,-2,...are the terms. an explicit rule for the nth term of the arithmetic sequence is given by the formula, aₙ=a₁+(n-1) d

where, a₁ is the first term, aₙ is the nth term, d is the difference between two terms, n is the number of terms.

as per question a₁= -20, d= 6

now A. aₙ = -20+6(n+2)

           aₙ = 6n-8

B. aₙ= -20+6(n-1)

 aₙ = 6n-26

C. aₙ =-20+6(n-1)

   aₙ = 6n-26

D. aₙ= -20+6(n+1)

  aₙ = 6n-14

the above are the explicit rules for the arithmetic sequence.

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The set of all x in R4 that are mapped into the zero vector by the transformation x - Ax, using the main answer obtained in step 4.

To find all x in R4 that are mapped into the zero vector by the transformation x - Ax, we need to solve the equation Ax = 0.

1. Write down the matrix A and set it equal to the zero vector:
  A = [a11 a12 a13 a14; a21 a22 a23 a24; a31 a32 a33 a34; a41 a42 a43 a44]
  0 = [0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0]

2. Solve the equation Ax = 0 by performing row operations on the augmented matrix [A|0] until it is in reduced row echelon form.
  Use techniques such as row swapping, row scaling, and row addition to eliminate variables and simplify the matrix.

3. Once you have the reduced row echelon form of [A|0], the variables that correspond to the pivot columns are called leading variables, and the remaining variables are called free variables.

4. Express the solutions in terms of the free variables, and write the main answer as x = (expression involving the free variables).

5. Provide an explanation of the steps you took to solve the equation Ax = 0 and find the solutions.

6. Finally, conclude your answer by stating the set of all x in R4 that are mapped into the zero vector by the transformation x - Ax, using the main answer obtained in step 4.

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The zeros of the function y = (x+12)(x-9)(x-7) are x = -12, x = 9, and x = 7.

To find the zeros of a function, we look for the values of x that make the function equal to zero. In this case, we have the function y = (x+12)(x-9)(x-7).

Setting the function equal to zero, we get:

(x+12)(x-9)(x-7) = 0

According to the zero product property, for the entire expression to equal zero, at least one of the factors must be equal to zero. So we set each factor equal to zero and solve for x:

x + 12 = 0 => x = -12

x - 9 = 0 => x = 9

x - 7 = 0 => x = 7

These values of x, namely x = -12, x = 9, and x = 7, are the solutions or zeros of the function. When x takes on these values, the function y becomes zero.

In other words, the graph of the function y = (x+12)(x-9)(x-7) will intersect the x-axis at x = -12, x = 9, and x = 7. These are the points where the function crosses or touches the x-axis.

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Answer:

105 = (5x-70)

Step-by-step explanation:

You are trying to find x so you would have to place that in to finally get to the end where x = 5