Find the slope of the line

The probability of getting 3 is P(A) = 1/216. The probability that sum being 3 is 1 / 216.

When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. A dice can show a minimum of one and a maximum of six dots, for a total of six sides, giving it a total of 6 * 6 * 6 = 216 possible outcomes.

:When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. The probability can be calculated as follows:

Let A be the event that the sum is 3. The number of ways to get 3 is 1, i.e., (1, 1, 1). The total number of possible outcomes is 6³,

since each die can have 6 possible outcomes.

Therefore, the probability of getting 3 is P(A) = 1/216.

In conclusion, the probability that sum being 3 is 1 / 216.

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The population is growing as the births are more than deaths in an year.

Increases in a population's or a dispersed group's membership are referred to as population growth.

Given:

To find: Is population growing or shrinking?

Finding:

Hence the population is growing as the births are more than deaths in an year.

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The angle of inclination that the line segment A makes with the positive x-axis is 45° (option C).

To determine the angle of inclination that the line segment A makes with the positive x-axis, we can use the slope of the line. The slope is given by the formula:

slope = (change in y)/(change in x)

In this case, the change in y is 7 - 4 = 3, and the change in x is 3 - 0 = 3. Thus, the slope of the line is:

slope = 3/3 = 1

The angle of inclination θ can be found using the inverse tangent function:

θ = tan^(-1)(slope)

Substituting the slope value of 1 into the equation, we have:

θ = tan^(-1)(1) ≈ 45°

Therefore, the angle of inclination that the line segment A makes with the positive x-axis is 45°.

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A = {x|x ∈ U and is an even positive integer}

The universal set(U) consists of only positive integers.

Given,  A = {x|x ∈ U and x is an odd positive integer}.

That means the set A contains all those elements which belongs to the universal set and should be a positive odd number.

refers to the complement of A. It means that it will contain all those elements that belong to U but does not belong to A.

All  the positive odd integer is made up of two types of number ,i.e, positive and negative number.

So,this set will contain all the element belonging to U and should be an even positive integer.

Therefore,Ac = {x|x ∈ U and is an even positive integer}.

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Answer:D:Ac = {x|x ∈ U and is an even positive integer}

Step-by-step explanation:

edge 2022

Answer:

see below

Step-by-step explanation:

12. sqrt(15^2+12^2)=3sqrt(41) or around 19

13. 45 45 90 triangle means the hypotenuse is sqrt(2) times bigger, so it's 90sqrt(2) or around 127

14. 8 and 6 - divide by 2

4 and 3 - use pythagorean triple 3 4 5

multiply 5 and 2 to get to the hypotenuse being 10

subtract the original amount

8+6-10=4

15. sqrt(200+125^2)=25sqrt(89) or around 236

Answer:

83,900

Step-by-step explanation:

100/33560 = 250/x

There are 2 options to solve. You can cross multiply:

100x = 33560*250

100x = 8,390,000 Divide by 100

x = 83,900

I also see that you start with 100 naira and want to see the value at 250 naira.

250 is 2.5 times 100. If you take the original 33560 fr and multiply that by 2.5, you will get 83,900.

The bar height for the price range of less than $5,000 will increase by 200.

In the given histogram, the x-axis represents the car prices ranging from $0 to $40,000, while the y-axis represents the number of cars sold over 10 years, ranging from 0 to 700.

Based on the provided information, we can observe that between the price ranges of $20,000 and $30,000, the bar height exceeds the maximum y-axis value of 700. Similarly, between the price ranges of $5,000 and $10,000, and $40,000 and $45,000, the bar height is indicated as 200.

If the car salesman decides to include cars with prices less than $5,000 and projects selling 200 of them over the next 10 years, the distribution will be affected as follows:

The bar representing the price range of less than $5,000 will increase in height by 200, indicating the projected sale of those additional cars. This means that the histogram will show a higher number of cars sold in the lower price range, reflecting the demand from students and the inclusion of more affordable cars in the sales strategy. This modification will result in a redistribution of the bars, with an additional bar added to represent the projected sales of cars below $5,000.

Overall, the distribution in the histogram will be affected by an increase in the bar height for the price range of less than $5,000 by 200 units, indicating the projected sale of those additional affordable cars over the next 10 years.

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The inequality that represents the hours which Lisa can work is t+b≥20, 21t+16b≥195

Given that,

Lisa has two jobs to help pay for her education. She earns $21 per hour as an instructor and $16 per hour as a delivery person. Lisa can only work up to 20 hours per week due to her class and study schedule, but she has to make at least $195 each week.

We have to find which inequality system best describes this situation if T is the amount of tutoring hours Lisa works and D is the number of delivery hours she works.

The inequality we get ,

t+b≥20

21t+16b≥195

Therefore, the inequality are t+b≥20, 21t+16b≥195

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The statement you provided mentions two separate events involving different companies lower rates

1. Hertz runs a sale: Hertz, a car rental company, is having a sale. This implies that they are offering in  discounted prices or promotional deals on their rental services.

2. Avis buys new cars and Budget lowers rates: Avis, another car rental company, is purchasing that  new cars to add to their fleet. On the other hand, Budget, yet another car rental   the company, is reducing their rental rates.

These events indicate of independent actions taken by the respective companies and are not directly connected to each other.

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Answer:

y = -3

Step-by-step explanation:

There isn’t a slope since the line is flat.

the function f(x) that satisfies the given conditions is:

f(x) = x^2 + x^3 + 2x^4 + 7

We need to find a function f whose second derivative is given by 4 + 6x + 24x^2, and that satisfies f(0) = 3 and f(1) = 11.

Integrating the second derivative, we get:

f'(x) = ∫(4 + 6x + 24x^2)dx = 4x + 3x^2 + 8x^3 + C1

where C1 is an arbitrary constant of integration.

Using the initial condition f(0) = 3, we get:

f'(0) = C1 = 0

Substituting this back into the expression for f'(x), we get:

f'(x) = 4x + 3x^2 + 8x^3

Integrating f'(x), we get:

f(x) = ∫(4x + 3x^2 + 8x^3)dx = x^2 + x^3 + 2x^4 + C2

where C2 is an arbitrary constant of integration.

Using the second initial condition f(1) = 11, we get:

f(1) = 1 + 1 + 2 + C2 = 11

C2 = 7

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The average quantity of juice that is consumed per person in this country is given as 3.84

We have the following data with which to answer this question

The consumption of juice = 1.92 billion

The population of the country = 500 million

The question wants us to calculate the amount of drink that the persons would consume on average in this nation.

we have average = quantity consumed / total number of persons

This would give us

average = 1.92 billion / 500 million

= 1, 920, 000, 000 / 500, 000 ,000

= 3.84

Hence the amount of juice that is consumed per person in this country is given as 3.84

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Given :

Three trolley tours leave from the same stop at 9:00 am.

Tour A returns to the stop every 75 minutes, Tour B returns every 60 minutes, and Tour C returns every 40 minutes.

To Find :

In how many hours will all three tours return to the stop at the same time.

Solution :

We know, they will return to the stop at the same time is the L.C.M of three i.e 75, 60 and 40 minutes.

So, their L.C.M is :

L.C.M = 600 minutes.

Now, 600 minutes = 600÷60 hours = 10 hours.

Therefore, they will all meet at stop in 10 hours.

Hence, this is the required solution.

Answer:

Step-by-step explanation:

boody boody

If A is a subset of B, it does not necessarily mean that A is a proper subset of B. The union of any set A and its complement is indeed the universal set.

1. False: If A is a subset of B, it does not necessarily mean that A is a proper subset of B. A proper subset is a subset that contains some, but not all, elements of the superset. In other words, if A is a proper subset of B, it means that there exists at least one element in B that is not in A. However, if A is simply a subset of B, it is possible for A and B to have the same elements, making them equal sets.

For example, let's consider two sets:

A = {1, 2}

B = {1, 2, 3}

In this case, A is a subset of B because every element in A (1 and 2) is also in B. However, A is not a proper subset of B since there are no elements in B that are not in A. Therefore, statement 1 is false.

2. True: The union of any set A and its complement is indeed the universal set. The complement of a set A, denoted as A', consists of all elements that are not in A but are in the universal set U. When we take the union of A and its complement, we are effectively combining all elements from A and all elements not in A.

Let's consider a set A and its complement A' within a universal set U. The union of A and A' is denoted as A ∪ A' and can be represented as U. This is because every element in the universal set U is either in A or not in A (in A').

For example, let's consider the following sets:

U = {1, 2, 3, 4, 5}

A = {1, 2}

The complement of A, A', would be {3, 4, 5}. The union of A and A' (A ∪ A') is {1, 2} ∪ {3, 4, 5}, which is equal to U: {1, 2, 3, 4, 5}. Thus, the union of any set A and its complement is indeed the universal set. Therefore, statement 2 is true.

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The nearest hundredth, we get:

C ≈ 12.56 feet.

Circle circumference (or perimeter) = 2R

where R denotes the circle's radius. 3.14 is the approximate (up to two decimal points) value of the mathematical constant. Again, Pi () is a special mathematical constant that represents the circumference to diameter ratio of any circle.

The circumference of a circle is calculated as follows:

C = 2πr

where C is the circumference, (pi) is a constant close to 3.14, and r is the radius of the circle.

When the given values are substituted, the following results are obtained:

C = 2(3.14)(2) \s= 12.56

We get the following when we round to the nearest hundredth:

C ≈ 12.56 feet.

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Answer:

x = 7

Step-by-step explanation:

Since, both the polygons are similar, therefore their corresponding sides would be in proportion.

\( \therefore \: \frac{30}{4 + 3x} = \frac{36}{30} \\ \\ \therefore \: \frac{30}{4 + 3x} = \frac{6}{5} \\ \\ 6(4 + 3x) = 30 \times 5 \\ \\ 24 + 18x = 150 \\ \\ 18x = 150 - 24 \\ \\ 18x = 126 \\ \\ x = \frac{126}{18} \\ \\ x = 7\)

Answer:

425 ft³

Step-by-step explanation

Find the volume of the entire figure, if the part wasn't cut out

It would be 11 x 8 x 5 = 440

Now do 5 x 1 x 3 = 15

440 - 15 = 425

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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The given expression written in the simplest radical form is 3√5

From the question, we are to write the given expression in the simplest radical form

The given expression is 45^(1/2)

From one of the laws of indices, we have that

\(x^{y/n} = \sqrt[n]{x^{y} }\)

Thus,

Applying this rule, the given expression can be written as

√45

Now, we will express the given radical expression in the simplest radical form

Expressing in simplest radical form

√45

= √(9 × 5)

= √9 × √5

= 3 × √5

= 3√5

Hence, the given expression written in the simplest radical form is 3√5

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Answer:

SA= 119 cm²

Step-by-step explanation:

the solution contain of four steps

The equation of the curve that passes through the point (4,9) and has a slope of 6√x at each point is y = 4x × (3/2) - 23.

To find the curve in the xy-plane that passes through the point (4,9) and has a slope of 6√x at each point, we can use calculus to integrate the slope function to find the corresponding equation of the curve.

Let's denote the equation of the curve as y = f(x), where f(x) is the function we want to find.

Given that the slope at each point is 6√x, we can express this as:

dy/dx = 6√x

To find the function f(x), we integrate both sides of the equation with respect to x:

∫ dy/dx dx = ∫ 6√x dx

Integrating both sides:

∫ dy = ∫ 6√x dx

y = 6 ∫ √x dx

Using the power rule of integration:

y = 6 × (2/3) × x × (3/2) + C

where C is the constant of integration.

Now, we can substitute the given point (4,9) to find the specific value of the constant C:

9 = 6 × (2/3) × 4 × (3/2) + C

Simplifying the equation:

9 = 6 ×(2/3) × 8 + C

9 = 4 * 8 + C

9 = 32 + C

C = 9 - 32

C = -23

Substituting the value of C back into the equation:

y = 6 × (2/3) × x × (3/2) - 23

Simplifying further:

y = 4x × (3/2) - 23

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The vector field F → = r a ( -y i → + x j → ) has no z-component and is independent of z, indicating that it lies entirely in the xy-plane and does not vary along the z-axis.

The vector field is given by:

F → = r a ( -y i → + x j → )

where \(r = \sqrt{(x^2 + y^2)}\) and a is a constant.

We can rewrite this vector field in terms of its components:

F → = ( r a ( -y ) , r a x )

To show that the vector field F → has no z-component and is independent of z, we can take the partial derivatives with respect to z:

∂ F x / ∂ z = 0

∂ F y / ∂ z = 0

Both partial derivatives are zero, which means that the vector field F → does not depend on z and has no z-component. Therefore, it is independent of z.

This indicates that the vector field F → lies entirely in the xy-plane and does not vary along the z-axis. Its magnitude and direction depend on the values of x and y, as determined by the expressions \(r = \sqrt{(x^2 + y^2)}\)) and the constant vector a.

In summary, the vector field F → = r a ( -y i → + x j → ) has no z-component and is independent of z, indicating that it lies entirely in the xy-plane and does not vary along the z-axis.

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The coupon which gives Hideki a better deal is Coupon 2: as the total cost is: $27

The total cost of coupon 1 will be; $28.8

The total cost of coupon 2 will be; $27

For Coupon 1; Buy 1 get one 40% off.

Total cost = $18 + 60% ($18)

Total cost = $18 + $10.8.

Total cost = $28.8

For Coupon 2; 25% off entire purchase

Total cost = 75% ($18 + $18)

Total cost = 75% ($36)

Total cost = $27

:D Your Welcome!

enlarging the capacity of the dock to handle two boats at a time can help in achieving the goal of minimizing customer waiting time and approaching an average time in the system close to 10 minutes.

Enlarging the capacity of the dock to handle two boats at a time can be a good way of achieving the goal of having the customer's average time in the system as close to 10 minutes as possible, but not exceeding 10 minutes. Let's analyze the statements provided:

Both channels will be empty approximately ______% of the time.
Enlarging the capacity to handle two boats at a time means that both channels can be utilized simultaneously.

If we assume that boat arrivals follow a random and evenly distributed pattern, the probability of both channels being empty at the same time is the product of the probabilities of each channel being empty.

If the arrival rate of boats is within the capacity of the dock, it is likely that both channels will be empty a significant portion of the time. The specific percentage will depend on the arrival rate and other factors.

When customers do show up, they ______ likely to have to wait for 10 minutes.
By enlarging the capacity and having two boats being served simultaneously, the waiting time for customers is expected to be reduced compared to when only one boat can be served at a time.

This means that customers are less likely to have to wait for the full 10 minutes.

On the whole, the expansion _______ be the best way of achieving their goal.
Based on the information provided, enlarging the capacity of the dock to handle two boats at a time seems like a reasonable approach to achieve the goal of having the customer's average time in the system as close to 10 minutes as possible.

However, without specific data on boat arrival rates, service times, and other factors, it is not possible to determine definitively if it is the best way.

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The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot.

So the volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.

The quantity of cubic feet can be multiplied by 29.9220779 to get the conversion to quarts. For instance, if you have a container with a 2 cubic foot volume, the quantity of quarts in that container would be:2 cubic feet multiplied by the US liquid quart density of 29.9220779 gives 59.8441558 US quarts. The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.

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When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are statistically significant.

In statistical analysis, we use hypothesis testing to determine whether the results of a sample are likely to be representative of the population as a whole. If the results are statistically significant, we can infer that there is a low probability that the observed differences between the sample and the population occurred by chance alone.

This allows us to generalize the findings from the sample to the larger population with a reasonable degree of confidence.

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The magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

The value of the net electrostatic force on the 5.0-nC

charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0),

charge Q2 = −1.0 nC is at (0, 0.10 m), and

charge Q3 = 5.0 nC is at (0, 0) can be calculated as follows:

Given data,Charge Q1 = 6.0 nC is at (0.30 m, 0),

Charge Q2 = -1.0 nC is at (0, 0.10 m),

Charge Q3 = 5.0 nC is at (0, 0)

The formula to find out the force on the third charge Q3 is:

                      F = k * |Q1 * Q3| / r1^2 + k * |Q2 * Q3| / r2^2

Here, k = 8.99 × 10^9 N·m^2/C^2, Q1 = 6.0 nC, Q2 = -1.0 nC, Q3 = 5.0 nC

For the third charge Q3, the distance from Q1 is:

                                r1 = √(0.3^2 + 0^2) = 0.3 m

And the distance from Q2 is: r2 = √(0^2 + 0.1^2) = 0.1 m

Substituting all the given values in the formula:

                               F = 8.99 × 10^9 * [ (6.0 × 10^-9 * 5.0 × 10^-9) / 0.3^2 ] + 8.99 × 10^9 * [ (-1.0 × 10^-9 * 5.0 × 10^-9) / 0.1^2 ]F = 6.21 N

Therefore, the magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

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