Number 2 I need help on the whole thing 10 questions

Answer:

It is C

Step-by-step explanation:

Answer:

m = -1/2

Step-by-step explanation:

m = slope = rise/run

rise +1

run -2

rise/run = 1/-2

=

-1/2

To prove that n^3 + 2n is divisible by 3 for all integers n using mathematical induction, we need to show that it holds for the base case (n = 0) and then demonstrate that if it holds for any arbitrary integer k, it also holds for k + 1.

**Base Case (n = 0):**

When n = 0, we have 0^3 + 2(0) = 0 + 0 = 0. Since 0 is divisible by any integer, including 3, the base case is satisfied.

**Inductive Step:**

Assume that for some arbitrary integer k, k^3 + 2k is divisible by 3.

Now, we need to prove that it holds for k + 1, which means showing that (k + 1)^3 + 2(k + 1) is also divisible by 3.

Expanding (k + 1)^3 using the binomial theorem, we get:

(k + 1)^3 = k^3 + 3k^2 + 3k + 1

Substituting this back into (k + 1)^3 + 2(k + 1), we have:

(k + 1)^3 + 2(k + 1) = k^3 + 3k^2 + 3k + 1 + 2k + 2

                               = k^3 + 3k^2 + 5k + 3

Now, we can rewrite this expression as:

k^3 + 2k + 3k^2 + 3k + 3

Using the assumption that k^3 + 2k is divisible by 3 (inductive hypothesis), we can express this as a multiple of 3:

3m + 3k^2 + 3k + 3 = 3(m + k^2 + k + 1)

Since (m + k^2 + k + 1) is an integer, we have shown that (k + 1)^3 + 2(k + 1) is divisible by 3.

By satisfying the base case and demonstrating the inductive step, we have proven that n^3 + 2n is divisible by 3 for all integers n using mathematical induction.

we have proven that n³ + 2n is divisible by 3 for all integers n by mathematical induction.

To prove that the expression n³ + 2n is divisible by 3 for all integers n, we will use mathematical induction.

Let's first verify the statement for the base case, which is n = 0.

When n = 0, we have

0³ + 2(0) = 0 + 0 = 0,

which is divisible by 3 since 0 divided by any non-zero number is always 0 with no remainder.

Assume that the statement holds true for some arbitrary integer \(k\), where k is a non-negative integer. That is, assume that \(k^3 + 2k\) is divisible by 3.

We need to prove that the statement also holds true for k+1. That is, we need to show that (k+1)³ + 2(k+1) is divisible by 3.

Expanding (k+1)³ + 2(k+1), we get:

(k+1)³ + 2(k+1) = k³ + 3k² + 3k + 1 + 2k + 2

= k³ + 3k² + 5k + 3.

Now, let's express (k+1)³ + 2(k+1) in terms of our inductive hypothesis:

k³ + 3k² + 5k + 3 = (k³ + 2k) + (3k² + 3k + 3).

By our inductive hypothesis, we know that k³ + 2k is divisible by 3. Therefore, we can write k^3 + 2k as 3m for some integer m.

Substituting this back into our expression, we have:

(k³ + 2k) + (3k² + 3k + 3) = 3m + 3(k² + k + 1)

= 3(m + k² + k + 1)

The expression 3(m + k² + k + 1) is a multiple of 3 since it can be written as 3(m + k² + k + 1). Therefore, we have shown that (k+1)³ + 2(k+1) is divisible by 3.

By completing the base case and the inductive step, we have proven that n³ + 2n is divisible by 3 for all integers n by mathematical induction.

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The equation x² y² = 4 corresponds to a hyperbola when only considering x and y as variables. When considering x, y, and z as variables, the equation corresponds to a two-sheeted hyperboloid.

a) When only x and y are the variables being considered, the equation x² y² = 4 corresponds to a circle in the xy-plane. The circle has a center at the origin (0,0) and a radius of 2.

b) If x, y, and z are the only variables being considered, the equation x² y² = 4 still represents a circle in the xy-plane, but it becomes a cylinder along the z-axis. This cylinder has a center on the z-axis and a radius of 2, extending infinitely along the z-axis.

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(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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Answer:

67°

Step-by-step explanation:

TYAJSJSHSSNDNDBSBSBSBBSD

It would be helpful if you could provide the system of equations so that I can provide a specific answer to your question. However, I will provide a general explanation of how to determine the general solution of a system of equations using the method of elimination and how to find the solution that satisfies given initial conditions.The method of elimination is a technique used to solve a system of linear equations by eliminating one of the variables.

The general steps for using the method of elimination are as follows:

Step 1: Rewrite the equations in standard form, if necessary. Standard form means that the terms are arranged in the order of ax + by = c.

Step 2: Choose a variable to eliminate. Choose the variable that has the same coefficient in both equations. If one equation has a negative coefficient, multiply the entire equation by -1.

Step 3: Add or subtract the equations to eliminate the chosen variable. Add the equations if the coefficients have different signs, and subtract the equations if the coefficients have the same sign. This will result in an equation with one variable.

Step 4: Solve for the remaining variable

.Step 5: Substitute the value of the solved variable into one of the original equations to find the value of the other variable.

Step 6: Write the solution as an ordered pair (x, y).To find the general solution of a system of equations, you will need to solve for both variables.

The general solution will be a set of equations that can be used to solve for any values of x and y. To find a solution that satisfies given initial conditions, you will need to substitute the values of the initial conditions into the general solution and solve for the constants that appear in the solution. This will result in a specific solution that satisfies the given conditions.

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Answer:

£4

Step-by-step explanation:

Let's assume that the normal price of the toy is x.

If the normal price is reduced by 20%, it means that the sale price is 80% of the normal price, or 0.8x.

We know that the sale price is £3.20, so we can set up an equation:

0.8x = 3.20

To solve for x, we can divide both sides by 0.8:

x = 3.20 ÷ 0.8

x = 4

Therefore, the normal price of the toy is £4.

Answer: 7

Step-by-step explanation: 6/2 is 3, 3+4 is 7

Answer: 8?

Step-by-step explanation: because 6/2 has 4 extra so I guess you add those and get "8"

We can write (15 + 45) as a product of 2 factors using GCF and the distributive property 15(1 + 3).

We are given the following expression-

15 + 45

Now, we can factorize 15 into prime factors as follows -

= 3 × 5 (15 × 1)

Similarly, we can factorize 45 into prime factors as follows -

= 3 × 3 × 5 (15 × 3)

Thus, the greatest common factor of 15 and 45 is 15, so we can

= 15 × 1 = 15 and 15 × 3 is 45

Hence, we can write (15 + 45) as 15(1 + 3).

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20 units is the measure of the length of IK.

A line is defined as the distance between two points. Given the following parameters

IK =5x

IJ = 4

JK =4x

If the point J is on IK, hence;

IK = IJ + JK

Substitute the given parameters to have:

5x = 4 + 4x

5x - 4x = 4

x = 4

Determine the length of IK

IK = 5x = 5(4)

IK = 20

Hence the measure of the length of IK is 20 units
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Complete question

Point J is on line segment IK.Given IK =5x, IJ = 4 and JK =4x, determine the numerical length of IK

The tree diagram would be best for a probability calculation with two or more “and” statements, option (c) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

A probability calculation can be computed using multiple models, each of which is dependent on the given parameters. A graphical model, such as a tree diagram, or an analytical model, such as the systematic list model, can be used.

Tree diagram models are useful for visually showing complex probabilities and aiding solution visualization.

Thus, the tree diagram would be best for a probability calculation with two or more “and” statements option (c) is correct.

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The estimated demand at the 33rd percentile of the associated distribution is approximately 83 attendees.

To estimate the demand at the 33rd percentile of the associated distribution, we can use the properties of the normal distribution.

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% falls within two standard deviations.

Given that the mean of the distribution is 90 and the standard deviation is 16, we can calculate the z-score corresponding to the 33rd percentile using the standard normal distribution table or a calculator.

The z-score is calculated as:

z = (X - μ) / σ

where X is the value we want to find, μ is the mean, and σ is the standard deviation.

Substituting the given values, we have:

z = (X - 90) / 16

For the z-score corresponding to the 33rd percentile, we need to find the z-value such that the area to the left of it is 0.33. From the standard normal distribution table, we find that the z-score closest to 0.33 is approximately -0.44.

Now we can solve for X:

-0.44 = (X - 90) / 16

Solving for X, we get:

X = -0.44 * 16 + 90

X ≈ 83.04

Therefore, the estimated demand at the 33rd percentile of the associated distribution is approximately 83 attendees.

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Answer:

the  mean and standard error of the mean are 200 and 2 respectively.

Step-by-step explanation:

Given that ;

the sample size n = 81

population mean μ = 200

standard deviation of the infinite population σ = 18

A population  is the whole set of values, or individuals you are interested in, from an experimental study.

The value of population characteristics such as the  Population mean (μ), standard deviation (σ) are said to be known as the population distribution.

From the given information above;

The sample size is large and hence based on the central limit theorem the mean of all the means is same as the population mean 200.

i.e

\(\mu = \bar \mu_x\) = 200

∴ The mean = 200

and the standard error of the mean can be determined via the relation:

\(\mathbf{standard \ error \ of \ mean = \dfrac{\sigma}{\sqrt {n}}}\)

\(\mathbf{standard \ error \ of \ mean = \dfrac{18}{\sqrt {81}}}\)

\(\mathbf{standard \ error \ of \ mean = \dfrac{18}{9}}\)

\(\mathbf{standard \ error \ of \ mean =2}\)

Therefore ; the  mean and standard error of the mean are 200 and 2 respectively.

Answer:

=2/25+23/25

=25/25

=1 i think its the ans

Answer:

1500p

Step-by-step explanation:

The spinner A has 4 possible values, and the spinner B has 3 possible values, so the total number of possibilities for both spinners is the product of these number of possibilities:

4 * 3 = 12

From these 12 possible pair of values, the ones that give a sum of 7 are:

(6,1), (4,3) and (2,5).

We have 3 cases where the sum is 7, so the probability of having a sum of 7 is 3/12 = 25%. Therefore, the probability of not having a sum of 7 is 75%

To find the expected value, we multiply the probability of each case by the value it would give. If the player wins, the school loses 10p (the player paid 20p and earned 30p), and if the player loses, the school wins 20p. So the expected value of 120 games is:

120 * (0.25 * (-10) + 0.75 * (20)) = 1500p

Answer:

Step-by-step explanation:

Options B and D are correct as they are equal to 1728

Answer:

Step-by-step explanation:

Answer:

1- Because the degree is two, we either have two real roots or two complex roots

The roots are non-real because the discriminant is < 0

2x^2  + 4x +  7  = 0   subtract 7 from both sides

2x^2  +  4x  = -7

2 (x ^2 + 2x)  = -7    divide both sides by 2

x^2 + 2x   =  -7/2

Take 1/2 of 2  = 1.....square it  =  1   add it to both sides

x^2 + 2x + 1  =  -7/2 + 1   factor the left, simplify the right

(x + 1) ^2  =  -5/2       take both roots

x + 1  =  ± √[ -5/2 ]    subtract 1  and simplify the right

x  = ± √[5/2] i    - 1  .

2- (a) The graph is shown below.

(b)

x-intercept = (1, 0)

y-intercept = (0, -3)

Step-by-step explanation:

Given:

The function is given as: (a)

In order to plot the graph, we need to find some points on it. We also need to find the maximum and minimum of the function.

Let us find the maximum and minimum of the function. The maxima or minima occurs when the derivative of the function is 0.

Differentiating the function with respect to 'x', we get:

Now, equating  to 0, we solve for 'x'. This gives,

Now, let us find the 'y' values for the above 'x' values

When

So, the point of maxima is (-1.33, -1.8) and point of minima is (0, -3). Mark these two points on the graph.

Let us take another random point for 'x'. Let

. Mark the point (-1, -2) on the graph.

Now, let . The value of 'y' is:

. Mark the point (1, 0) on the graph.

Now, draw a smooth curve passing through all of these points with a maximum curve at (-1.33, -1.8) and minimum curve at (0, -3).

The graph is shown below.

(b)

The x-intercept is at the point when 'y' value is 0. So, the point on the graph is (1, 0).

The y-intercept is at the point when 'x' value is 0. So, the point on the graph is (0, -3).

Answer:

x(x+2) is the answer

Step-by-step explanation:

x²+2x

x(x+2)

The circumference is 160 feet for a length of 40 feet. The perimeter is 200 feet for a length of 50 feet. The circumference is 240 feet for a length of 60 feet.

A rectangular region with a 1200 square foot area will have a different perimeter depending on how long it is. The perimeter will be 160 feet if the area is 40 feet long. The length of 40 feet is multiplied by four to get a final measurement of 160 feet. In a similar manner, if the area is 50 feet long, the perimeter will be 200 feet.

The length of 50 feet is multiplied by four to get a final result of 200 feet. Finally, the perimeter will be 240 feet if the area is 60 feet long. The length of 60 feet is multiplied by four to get a final measurement of 240 feet. A rectangular region with an area of 1200 square feet will therefore have a different perimeter depending on its length, with a length of 40 feet resulting in a perimeter of 160 feet, a length of 50 feet resulting in a perimeter of 200 feet, and a length of 60 feet resulting in a perimeter of 240 feet.

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Given:

Of the 50 students in the cafeteria, 7 have red hair.

Total number of students = 750

To find:

The proportion that could be used to predict the number of students who have red hair.

Solution:

Let x represent the number of students who have red hair.

The ratio of student having red hair to the total number of students are

\(Ratio_1=\dfrac{7}{50}\)

\(Ratio_2=\dfrac{x}{750}\)

The number of students having red hair is proportional to the total number of students. So, the above ratios are equal.

\(\dfrac{x}{750}=\dfrac{7}{50}\)

Multiply both sides by 750.

\(\dfrac{x}{750}\times 750=\dfrac{7}{50}\times 750\)

\(x=7\times 15\)

\(x=105\)

Therefore, the required equation is \(\dfrac{x}{750}=\dfrac{7}{50}\) and the number of students who have red hair is 105.

Answer:

A: Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3}

Step-by-step explanation:

C = {(9, 1) (8, -3) (7, 5) (-5, 3)}

The domain is the inputs

Domain: { -5,7,8,9}

The range is the output

Range{ -3,1,3,5}

This is a functions since there is no input that goes to multiple outputs

To find the angle of elevation from the base to the top of the mountain, we can use the tangent function. Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle.tanθ = opposite / adjacent In this case, the opposite side is the vertical height of the mountain.

Which is 1500 feet, and the adjacent side is the distance from the base to the top of the mountain, which is 3000 feet.tanθ = 1500 / 3000Simplifying the above expression,tanθ = 1/2Now, we need to find the angle whose tangent is 1/2. We can use the inverse tangent (or arctan) function to do this. arctan(1/2) ≈ 26.57 degrees Therefore, the angle of elevation from the base to the top of the mountain is approximately 26.57 degrees.

In summary, data markers are used in charts to represent individual data points. They are often used in combination with other chart elements, such as axes, gridlines, and legends, to help viewers understand the data being presented. The column, bar, area, dot, pie slice, or other symbol in a chart that represents a single data point is a data marker. Data markers provide you with a visual representation of the data in a chart. For example, in a column chart, each column represents a single data point.

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DEF will be 2.68

EF will be .67

Answer:

The equation of the line is:

\(y=-x+5\)

Step-by-step explanation:

Given the points

Finding the slope between the points

\(\left(x_1,\:y_1\right)=\left(-3,\:8\right),\:\left(x_2,\:y_2\right)=\left(4,\:1\right)\)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{1-8}{4-\left(-3\right)}\)

\(m=-1\)

Using the point-slope form of the line equation

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope

substituting the values m = -1 and the point (-3, 8)

\(y-y_1=m\left(x-x_1\right)\)

\(y-8=-1\cdot \left(x-\left(-3\right)\right)\)

\(y-8=-\left(x+3\right)\)

Add 8 to both sides

\(y-8+8=-\left(x+3\right)+8\)

\(y=-x+5\)

Therefore, the equation of the line is:

\(y=-x+5\)

Answer:

25% off

Step-by-step explanation:

18 of 24 is 75% and that means there 25% left so that’s the awnser

Answer:the answer is c

Step-by-step explanation: I got it right on edge btw I got you guys

Answer:

its c

Step-by-step explanation:

;3

Answer:

11.25 miles

Step-by-step explanation:

To figure out how many miles John will travel in 1/2 an hour, we can use the following formula:

distance = rate x time

We know the rate, which is the number of miles John can travel per hour. We can find this by dividing the total distance by the total time:

rate = distance / time

rate = 45 miles / 2 hours

rate = 22.5 miles per hour

Now we can use this rate and the given time of 1/2 an hour to find the distance:

distance = rate x time

distance = 22.5 miles per hour x 1/2 hour

distance = 11.25 miles

Therefore, John will travel 11.25 miles in 1/2 an hour at this rate.

The equation that represent the relationship of the coffees is 3x + 5y = 68.

At a coffee shop, two sizes of coffee are sold. A medium coffee costs $3, and a large coffee costs $5.

The equation that represent the relationship between the number of medium coffees sold, x, and the number of large coffees sold, y, in an hour where sales totalled $68 is as follows:

where

Therefore, the equation is as follows:

3x + 5y = 68

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