Two distinguishable fair dice are rolled: Define the following events: (sum of the numbers rolled is divisible by 4] (sum of the numbers rolled is less than 4} (a) What is the total number of possible outcomes in this experiment? (b) List the outcomes in A (c) List the outcomes in B (d) Find the probability P(A) (e) Find the probability P(B) (f) Find the probability P(AU B) (g) Find the probability P(AnB) (h) Are events A and B independent?

Answer: A cubic polynomial function has the form f(x) = ax^3 + bx^2 + cx + d.

A horizontal tangent line is a line that is parallel to the x-axis and it occurs at a critical point of the function, where the derivative of the function is 0.

We know that a cubic function has 3 critical points and thus 3 derivative that could be 0, so to find the equation of the cubic function we will use these two points to find the value of a, b, c, and d.

We know that the critical points of a cubic function are found by solving f'(x) = 0, where f'(x) is the derivative of the function, so we have:

f'(x) = 3ax^2 + 2bx + c = 0

Now we can use the two points to find the value of a, b, c, and d.

We know that the point (1,-2) is on the graph of the function, so we can substitute it into the equation to find d:

f(1) = a + b + c + d = -2

And we know that the point (-1,2) is on the graph of the function, so we can substitute it into the equation to find d:

f(-1) = -a + b - c + d = 2

Now we can use these two equations to find the value of a, b, and c:

a + b + c + d = -2

-a + b - c + d = 2

2a + 2d = 0

a = -d

-a + b - c + d = 2

b - c = 4

3ax^2 + 2bx + c = 0

3(-d)x^2 + 2bx - c = 0

Now we can use these equations and the critical points to find the value of a, b, c, and d

3(-d)x^2 + 2bx - c = 0, (1,-2) => 3d+2b-c = 0

3(-d)x^2 + 2bx - c = 0, (-1,2) => 3d-2b+c = 0

b-c = 4

Solving these equations, we have:

a = -1/3

b = 1

c = -5/3

d = -2

And the equation for the function is:

f(x) = -1/3x^3 + x^2 - 5/3x - 2

We can now sketch the graph of the function by using the information that we have. The cubic function will have an vertex of symmetry at (0,-2) and two horizontal tangent lines at (1,-2) and (-1,2) .

Since a < 0, the function is concave down, so the graph will be opened downwards and will have a local minimum at (0,-2) .

It is important to note that this is one possible equation for a cubic function that has horizontal tangent lines at (1, −2) and (−1, 2), but there may be other possibilities.

Step-by-step explanation:

Using the Triangle Inequality Theorem, the range of heights his ladder should have would be greater than or = 23 feet.

The Triangle Inequality Theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

That is c >/= a + b

a = 5 feet

b = 18 feet

C >/ = 5+18 = 23 feet

Therefore, the range of heights his ladder should have would be greater than or = 23 feet.

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We have 50 cases to distribute among 8 varieties of dairy products, with a restriction of 20 cases of milk.

To find the total number of ways to place the order, you can use the binomial coefficient formula, which is often used in combinatorics to count the number of ways to choose k items from a set of n items without regard to order. In this case, you have 8 varieties of dairy products and you want to choose 50 cases in total, with no regard to the order in which you choose the cases. So, the number of ways to place the order is:

(n k) = (8 50) = 8! / (50! (8-50)!) = 8! / (50! (-42)!) = 8! / 50! = 87654321 / (50494847464544434241)

This is a very large number, and it's impractical to calculate it exactly.

To find the number of ways to place the order if they order at most 20 cases of milk, you can use a similar approach, but with a restriction on the number of cases of milk. One way to do this is to use the stars and bars method, which is a combinatorial method for counting the number of ways to distribute n identical items into k distinguishable containers, with a restriction on the number of items in some of the containers.

In this case, we have 50 cases to distribute among 8 varieties of dairy products, with a restriction of 20 cases of milk. So, the number of ways to place the order is:

(50 + 8 - 1) choose (8 - 1) = 56 choose 7 = 56! / (7! 49!) = 56555453525150 / (7654321) = 807,794,400

This is the number of ways to place the order if they order at most 20 cases of milk.

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Answer:

∠MKN and ∠OKN

Step-by-step explanation:

∠MKN and ∠OKN are supplementary because they add up to 180°

The charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s] is given by q(t) = q0 + (t)I,

The charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s] is calculated by the formula q(t) = q0 + (t)I, where q0 is the initial charge and I is the current.

The charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s] is given by q(t) = q0 + (t)I, where q0 is the initial charge and I is the current. To calculate q(t), we need to first calculate the initial charge q0 and then calculate the current I. To calculate q0, we need to integrate the current I over the time interval (0, t). To calculate q(t), we need to know q0 and I. Then, we can calculate q(t) by multiplying t by I and adding it to q0. For example, if q0 = 3 C and I = 2 A, then q(t) = 3 + (t)(2) = 3 + 2t C.

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Answer:

The answers are

False

True

True

Thank you

The angles ∠1 and ∠2 are vertical angles. Vertical angles are congruent and according to the definition of congruency, ∠1 = ∠2.

The completed table used to prove that ∠1 ≅ ∠2 is presented as follows;

Statement     [tex]{}[/tex]                                 Reasons

1. m∠1 + m∠3 = 180° [tex]{}[/tex]                     1. Linear pair angles are supplementary

m∠2 + m∠3 = 180°

2. m∠1 + m∠3 = m∠2 + m∠3 [tex]{}[/tex]       2. Substitution

3. m∠1 = m∠2[tex]{}[/tex]                                3. Subtraction property

4. ∠1 ≅ ∠2                  [tex]{}[/tex]                   4. Definition of congruency

Two angles are congruent if the measures of the each angle are equivalent.

The details of the reasons used to prove that ∠1 = ∠2, are as follows;

Linear pair angles

Linear pair angles are adjacent angles that have a common side and for which the other non common sides of the two angles, together form a straight line.

Substitution property

The substitution property of equality states that if a = b then b can replace a in any expression or equation, with the value of the new expression remaining the same as the previous expression or both sides of the new equations remain equivalent.

Subtraction property

The subtraction property of equality states that the subtraction of the same amount from two quantities that have the same amount, will result in two new quantities that remain equivalent.

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If the series JK has 12 2 I J K 30, the value of JK is 720

In order to find the value of JK, multiply the given values all through and then generate the answer in a simplified manner

JK=(12)(2)(30)

Multiply all the figures

JK = 12 X 2 X 30

JK = 720

Therefore, the correct answer is as given above. It can be concluded that the value of JK is 720 as a result of the multiplication.

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The Complete statement is : The location of proton in the atom is inside nucleus , has a charge of +1 elementary charge and the approximate mass of proton is 1.00727647 amu .

The Protons are the positively charged particles, the electrons are negatively charged particles and the neutrons have no charge.

In an atom there are equal number of protons and number of electrons . Thus the atom is electrically neutral in nature. The charge of the  proton is equal and opposite of an electron. So , proton has a unit positive charge.

The Protons are found inside the nucleus of atom , the proton carries the elementary charge of  1.00727647 amu (atomic mass units) , the charge on the proton is +1 .

The given question is incomplete , the complete question is

Answer the following questions about the Proton ,

The location of proton in the atom is  ______ , has a charge of ______ elementary charge and the approximate mass of proton is _____ amu .

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The solution for the given differential equation is  [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex].

We have given a differential equation:

[tex]\frac{d}{dx}(C_1e^{12x})[/tex]

since C1 is a constant,

=[tex]C_1\frac{d}{dx} (e^{12x})[/tex]

we know that [tex]\frac{d}{dx} (e^{ax}) = e^{ax}\frac{d}{dx} (ax)[/tex]

= [tex]C_1e^{12x}(12) = 12C_1e^{12x}[/tex]

Therefore, [tex]\frac{d}{dx}(C_1e^{12x}) = 12C_1e^{12x}[/tex]

Now, let y = [tex]C_1e^{12x}[/tex]

Therefore, [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex]

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The complete question is:

Fill in the blank. The symbol C represents a constant. [tex]\frac{d}{dx}C_1e^{12x}[/tex]= ____ Write this result as a linear first-order differential equation that is free of the symbol C1 and has the form dy/dx = f(x, y).

Answer:

D is the answer..

Step-by-step explanation:

a) The assessed value of the residential property is, proportionately, $45,806.

b) Proportionately, the market value of the property is $111,722.

Proportion refers to two ratios equated to each other.

Proportion is a fractional value, expressed as the relative size of a variable or number to another.

We represent proportions as decimals, fractions, or percentages.

The assessed value of a residential property = 41% of the market value

Residential property tax rate = 3³/₅% or 3.6% of the assessed value

Tax = $1,649

Assessed value = $45,806 ($1,649/3.6%)

Market value = $111,722 ($45,806/41%)

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The diameter of the circle whose circumference is 62.8 feet is 20 ft, thus the correct option is C.

Remember that for a circle of diameter D, the circumference is given by the formula:

C = pi*D

Where pi = 3.14

Here we know that the circumference is 62.8 feet, then we can rewrite:

62.8 feet = 3.14*D

Now we can solve that equation for D, then we will get:

D = 62.8ft/3.14 = 20ft

The diameter is 20 ft, thus, the correct option is C.

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Answer: The statement given tells us that the Acme Company manufactures widgets and that the distribution of widget weights is bell-shaped. A bell-shaped distribution is also known as a normal distribution or a Gaussian distribution. This means that the majority of the data will cluster around the mean (average) value and the farther the data is from the mean, the less common it is.

The mean weight of the widgets is given as 51 ounces, which is the average weight of all the widgets manufactured by the company. The standard deviation is given as 10 ounces, which is a measure of how spread out the data is from the mean. A smaller standard deviation means that the data is more tightly clustered around the mean, while a larger standard deviation means that the data is more spread out.

This information allows us to make some predictions about the weights of the widgets. For example, we know that approximately 68% of the widgets will weigh between 41 ounces (mean - standard deviation) and 61 ounces (mean + standard deviation). Additionally, we know that approximately 95% of the widgets will weigh between 31 ounces (mean - 2standard deviation) and 71 ounces (mean + 2standard deviation) and 99.7% of the widgets will weigh between 21 ounces (mean - 3standard deviation) and 81 ounces (mean + 3standard deviation).

It is important to note that these predictions are based on the assumption that the distribution of widget weights is indeed bell-shaped. If that assumption is not true, these predictions may not be accurate.

Step-by-step explanation:

The result of the calculation, 120, will be stored in register r7.

Factorial is a mathematical operation where a number is multiplied by all its preceding numbers until 1. For example, 5! is calculated by multiplying 5 by 4, then 4 by 3, then 3 by 2, then 2 by 1. In mathematical notation, this is expressed as:

5! = 5 * 4 * 3 * 2 * 1

= 120

In arm assembly language, we can create a loop that multiplies the number that is stored in register r0 with all of its preceding numbers until 1 is reached. The result of the calculation will be stored in register r7. For example, to calculate 5!, we can set the initial value of r0 to 5 and the initial value of r7 to 1. Then, we can create a loop that multiplies the value of r0 by the value of r7 and then decrements the value of r0. This loop will run until r0 is equal to 1. At that point, the loop will end and the result of the calculation will be stored in r7. The following example shows the code for a program to calculate 5!:

MOV R0, #5

MOV R7, #1

LOOP:

MUL R7, R0

SUB R0, #1

CMP R0, #1

BNE LOOP

The result of the calculation, 120, will be stored in register r7.

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The computer output for scenario 3-8 indicates that 83.5% of the variation in egg production can be accounted for by the linear regression of egg production on fish length, while 69.7% of the variation in fish length can be accounted for by the same linear regression.

This indicates that there is a strong and significant correlation between fish length and egg production, with egg production increasing as fish length increases. This suggests that egg production is a good predictor of fish length and vice versa, and that changes in one can be used to predict changes in the other.

However, it is worth noting that this correlation is not perfect and that there is still a considerable amount of variation in each that cannot be explained by the linear regression.

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Correct question should be:

Use Scenario 3-8. Which of the following statements can be made on the basis of the computer output?

A. 83.5% of the variation in egg production can be accounted for by the linear regression of

egg production on fish length.

B. 69.7% of the variation in egg production can be accounted for by the linear regression of

egg production on fish length.

C. 83.5% of the variation in fish length can be accounted for by the linear regression of egg

production on fish length.

D. 69.7% of the variation in fish length can be accounted for by the linear regression of egg

production on fish length.

E. 68.4% of the variation in fish length can be accounted for by the linear regression of egg

production on fish length.

1) Note that the result of the above highlighted 10 by 10 block of units in the fraction are:

10/100; and

1/ 10.

2) In decimal, that would be:

0.1

3) In part-to-part ratio it would be:

10:90

4) In Part to whole ratio 10/100

5) In whole to part, that would be:

100:10

5) In percent, that would be 10%

A part-to-whole ratio compares a part to the total of all parts. For example, if you have 100 apples and you want to know what percentage of them are red, you would express the number of red apples as a ratio of the total number of apples. In this case, 10 red apples would be expressed as a ratio of 10:100

A part-to-part ratio compares two or more quantities in terms of their relative sizes. For example, if you have 100 apples and you want to know how many more red apples than green apples you have, you would express the number of red apples and the number of green apples as a ratio of each other. In this case, if you have 30 red apples and 20 green apples, the ratio would be 30:20

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Answer:

11.6 ft

Step-by-step explanation:

    |\

    |   \

    |      \

    |         \

h   |            \    12 ft

    |               \

    |                  \

    |                     \

    |                        \

    ------------------------

              3 ft

Use the Pythagorean theorem: a² + b² = c²

(3 ft)² + h² = (12 ft)²

9 ft² + h² = 144 ft²

h² = 135 ft²

h = √(135 ft²)

h = 11.6 ft

The expression equivalent to the expression 2(3t + 4) is 6t + 8

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

2(3t + 4)

To start with, we need to open the bracket of the expression

so, we have the following representation

2 * 3t + 2* 4

Evaluate the products

6t + 8

hence, the equivalent expression is 6t + 8

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The range of the rational function:

y = 1/(x + 2) - 1

is R: (-∞, 0) U (0, ∞)

Remember that for a function y = f(x), we define the range as the set of the possible inputs of the function (the possible values of y).

In this case we have the rational function:

y = 1/(x + 2) - 1

Notice that when x approaches at -2, the function tends to positive or negative infinity (deppending if it comes from the left or right).

And then as x goes affar from -2, the absolute value decreases.

But the function never reaches the value 0, as tends to infinity or negative infintiy the functio approaches zero, but it will never be equal to zero, then the range is:

R: (-∞, 0) U (0, ∞)

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The graph shows a maximum wolf population size of 500 individuals, which occurred in 2017.

The graph depicts the magnitude of the wolf population in a certain location during the previous 25 years. The population size is shown to have changed over time, with the peak population count of 500 people happening in the year 2017. A population size of 450 people, which is a little less than the highest population level, was then reached in 2018. The year 2000 saw the lowest population size, with only 200 people living there. In 2017, there were 500 people in the population, which had grown considerably over the years. This suggests that over the past 25 years, the wolf population has been growing which occurred in 2017.

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The complete question is

based upon the data presented in the graph, which of the following best identifies the highest wolf population size which occurred in 2017?

The speed in kilometers per hour is 15.48. And the total number of hours for the trip will be 1.60 hours.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

Brice is taking a bike tour of the city. The entire tour is 24 ⁷/₁₀ kilometers long. Brice knows that his average biking rate is 4.3 meters per second.

Convert the mixed fraction number to a decimal number. Then we have

24 ⁷/₁₀ = 24 + 0.70

24 ⁷/₁₀ = 24.70 kilometers

Convert the speed into kilometers per hour. Then we have

Speed = 4.3 x 18/5

Speed = 15.48 kilometers per hour

Then the total number of hours for the trip is given as,

15.48 = 24.70 / T

T = 24.70 / 15.48

T = 1.60 hours

The speed in kilometers per hour is 15.48. And the total number of hours for the trip will be 1.60 hours.

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The unit rate of Lena's bicycle trip if she travelled 212 miles in 5 days is 42.4 miles per day

Unit rate refers to the rate of traveling in miles per day.

Number of miles Lena has ridden= 212 miles

Number of days = 5 days

Lena’s rate as a unit rate = Number of miles Lena has ridden / Number of days

= 212 miles / 5 days

= 42.4 miles per day

Hence, Lena is traveling at a unit rate of 42.4 miles per day.

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The probability that they’re will be between 33 and 45 with part time jobs in a randomly selected group of 300 is given as follows:

B. 0.736.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution in this problem are given as follows:

p = 0.13, n = 300.

Hence the mean and the standard deviation are given as follows:

Using continuity correction, the probability of X between 33 and 45 is (32.5 < X < 45.5), which is the p-value of Z when X = 45.5 subtracted by the p-value of Z when X = 32.5, hence:

X = 45.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (45.5 - 39)/5.82

Z = 1.12

Z = 1.12 has a p-value of 0.8686.

X = 32.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (32.5 - 39)/5.82

Z = -1.12

Z = -1.12 has a p-value of 0.1314

Hence:

0.8686 - 0.1314 = 0.736 (approximately).

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Answer:

If 55% of the fish in the pond are goldfish, that would be 55/100 of the total number of fish. To express this as a fraction in its simplest form, we would divide the numerator and denominator by the greatest common divisor, 5. So, 55/100 simplifies to 11/20.

10/3 of the fish in the pond are perch, which in its simplest form is already in the form of 10/3.

The rest of the fish are sticklebacks, meaning the total number of goldfish, perch, and sticklebacks must add up to 100%. Therefore, to find the ratio of sticklebacks to goldfish and perch, we can subtract the percentage of goldfish and perch from 100%.

100 - 55 - (10/3) = 100 - 55 - 10/3 = 100 - 55 - (10/3) = 100 - 55 - (10*3/3) = 100 - 55 - 10 = 35.

So the ratio of goldfish to perch to sticklebacks in this pond is 11/20: 10/3: 35/100 in its simplest form.

Step-by-step explanation:

The example of a sequence of rational numbers is 1/1, 1/2, 2/1, 1/3, 3/2, 2/3, 3/1, 1/4, 4/3, 3/5, 5/2, 2/5, 5/3, 3/4, ….

The term rational number in math is defined as  a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.

Here we have given that {xₙ} n > 0 is a sequence of reals.

Here we need to find the definition of sequence and the example for the sequence of rational numbers.

As per the given definition we all know that the rational number is the number that can be expressed as the quotient or fraction

Here first we have to identify the definition of sequence that is none other than a group of numbers in an ordered way following a pattern and it is also known as Series which means that it is a sum of the elements of the sequence.

And the example for sequence of rational number is written as 1/1, 1/2, 2/1, 1/3, 3/2, 2/3, 3/1, 1/4, 4/3, 3/5, 5/2, 2/5, 5/3, 3/4, ….

Here we have given that the value must be greater than 0, so we have taken only the positive values.

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Answer:

Step-by-step explanation:

You want to use the graph to estimate the lower and upper quartiles of the lengths of the 16 fish that Jay measured.

The lower quartile is comprised of the 1/4 of the total number of fish that are the shortest. The graph shows that 4/16 of the fish are 10 inches or less, so the lower quartile is 10 inches.

The upper quartile is comprised of the 1/4 of the total number of fish that are the longest. The graph shows that 12/16 of the fish are 25 inches or less, so 4/16 of the fish are 25 inches or more. The upper quartile is 25 inches.

The lower and upper quartiles are 10 inches and 25 inches, respectively.

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Answer:

Step-by-step explanation: 21