Write an equation of the line that passes through the given points (-6,2) (1,0)

Answer: Slope intercept form: y = \(\frac{1}{6} x\) - 4

Step-by-step explanation:

The general solution of the differential equation is given as

\(y = y_h + y_py = C/x^2 + C2\)

where C and C2 are constants.

General solution of the homogeneous equation.

2xy' + y = 0

On dividing by y and rearranging

dy/dx = -y/2x

Integrating both sides

ln(y) = -ln(2)ln(x) + ln(C1)

where C1 is the constant of integration. Rewriting

y =\(C/x^2\),

where C = ±\(e^{(C1/2ln2)}\) is the constant of integration. Therefore, the general solution of the homogeneous equation is

\(y_h = C/x^2\)

where C is a constant.

Assume the particular solution of the given equation.

2xy' + y = 2√x

Assume the particular solution to be of the form

\(y_p = v(x)√x\)

where v(x) is the unknown function of x. Substitute the assumed solution in the differential equation and solve for v(x).Differentiate\(y_p\) w.r.t x,

\(y'_p = v'√x + v/(2√x)\)

Substitute the above equations into the given differential equation

\(2xy' + y = 2√x2x(v'√x + v/(2√x)) + v(x)√x = 2√x\)

On simplification

\(2xv'√x = 0, and v/(2√x) + v(x)√x = 1\)

On solving the above equations

v(x) = C2/√x,

where C2 is a constant of integration. Therefore, the particular solution of the differential equation is

\(y_p = v(x)√xy_p = C2\)

The general solution of the differential equation is given as

\(y = y_h + y_py = C/x^2 + C2\)

where C and C2 are constants.

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The formula for the height of the banner in terms of the side length of the cardboard square, the height of the grandstand, and the distances from the person's eye level to the grandstand and the ground.

Mathematically, we can write this as:

(height of banner) / (distance from eye level to top of grandstand) = (side length of cardboard square) / (distance from eye level to bottom of square)

So, the distance from the eye level to the top of the grandstand is "s + h". We also know the distance from the person's eye level to the bottom of the square, which is "d₂ - d₁".

Putting all of this together, we can write:

(height of banner) / (s + h) = s / (d₂ - d₁)

To solve for the height of the banner, we can cross-multiply and simplify:

(height of banner) = (s² / (d₂ - d₁)) * (1 + h/s)

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Complete Question:

Zach wants to order a banner that will hang over the side of his baseball stadium grandstand and reach the ground. And then he needs to find the height for the banner so he uses a cardboard square to line up the top and bottom of the grandstand. Then he measures the distance from the grandstand and from the ground to his eye level.

Find height of the banner.

The tank currently contains 44 gallons of water, and 36 more gallons are needed to fill it completely.

a. The fish tank that holds 80 gallons of water is 55% full, which means it contains:

44 gallons = 80 gallons × 0.55

b. To find out how many more gallons are needed to fill the tank, we can subtract the current amount of water in the tank from its full capacity:

80 gallons - 44 gallons = 36 gallons

Therefore, the tank currently contains 44 gallons of water, and 36 more gallons are needed to fill it completely.

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Answer:

True

Step-by-step explanation:

1) Add up the cost of all items.

11+4.50+2.95=18.45

2) Compare with 18.

18.45>18

Therefore, Abdurrahman got what he asked for.

Answer:

Its vertical.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Slope (m) is equal to the change in the y-coordinate divided by the change in the x-coordinate.

The change in y= 6

The change in x= 3

6/3 =2

Answer:

b. 8

Step-by-step explanation:

the point asked has coordinates (100;8) (weight;calories)

Answer:

Step-by-step explanation:

Applying the midpoint formula to the points (a, 0) and (0, a) looks like this:

\(M=(\frac{a+0}{2},\frac{0+a}{2})\) which simplifies to

\(M=(\frac{a}{2},\frac{a}{2})\)

Answer:

0.50 or about half a year longer.

Step-by-step explanation:

We can write an equation to model bot investments.

Oliver invested $970 in an account paying an interest rate of 7.5% compounded continuously.

Recall that continuous compound is given by the equation:

\(A = Pe^{rt}\)

Where A is the amount afterwards, P is the principal amount, r is the rate, and t is the time in years.

Since the initial investment is $970 at a rate of 7.5%:

\(A = 970e^{0.075t}\)

Carson invested $970 in an account paying an interest rate of 7.375% compounded annually.

Recall that compound interest is given by the equation:

\(\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}\)

Where A is the amount afterwards, P is the principal amount, r is the rate, n is the number of times compounded per year, and t is the time in years.

Since the initial investment is $970 at a rate of 7.375% compounded annually:

\(\displaystyle A = 970\left(1+\frac{0.07375}{1}\right)^{(1)t}=970(1.07375)^t\)

When Oliver's money doubles, he will have $1,940 afterwards. Hence:

\(1940= 970e^{0.075t}\)

Solve for t:

\(\displaystyle 2 = e^{0.075t}\)

Take the natural log of both sides:

\(\ln\left (2\right) = \ln\left(e^{0.075t}\right)\)

Simplify:

\(\ln(2) = 0.075t\Rightarrow \displaystyle t = \frac{\ln(2)}{0.075}\text{ years}\)

When Carson's money doubles, he will have $1,940 afterwards. Hence:

\(\displaystyle 1940=970(1.07375)^t\)

Solve for t:

\(2=(1.07375)^t\)

Take the natural log of both sides:

\(\ln(2)=\ln\left((1.07375)^t\right)\)

Simplify:

\(\ln(2)=t\ln\left((1.07375)\right)\)

Hence:

\(\displaystyle t = \frac{\ln(2)}{\ln(1.07375)}\)

Then it will take Carson's money:

\(\displaystyle \Delta t = \frac{\ln(2)}{\ln(1.07375)}-\frac{\ln(2)}{0.075}=0.4991\approx 0.50\)

About 0.50 or half a year longer to double than Oliver's money.

Step-by-step explanation:

Hi there!

From above question;

A cuboid has a length of 25cm, a width of 5cm and height of (x-2)cm.

Length (l) = 25cm

width (b) = 5cm

height (h) = (x-2)cm.

a).

Volume= l*b*h

V = 25*5*(x-2)

V = 125(x-2)

V = 125x - 250 → Answer

b).

(i)

V = 750cm³

V = 125x - 250

750 = 125x - 250..........(i)

(ii)

The equation (i) is: 750 = 125x - 250

or, 125x = 750+250

or, 125x = 1000

or, X = 1000/125

Therefore, X= 8cm.

(iii)

Height (h) = x-2

= 8-2

= 6

Therefore, height is 6cm.

Hope it helps!

If the target behavior is recorded whenever it occurs at any point within the scoring interval, the measurement procedure used is called continuous recording or event recording. This method involves observing and recording each instance of the behavior without considering its duration or intensity.

Continuous recording is typically used when the target behavior is discrete and occurs relatively infrequently or has a short duration. With this measurement procedure, each occurrence of the behavior is recorded as a separate event, regardless of when it starts or ends within the scoring interval. Examples of behaviors that can be measured using continuous recording include vocalizations, hand clapping, or instances of aggression.

Continuous recording provides a comprehensive account of the frequency or rate at which the behavior occurs, allowing for a detailed analysis of its occurrence patterns. This method is particularly useful when a precise count of behavior instances is needed and when the duration or intensity of the behavior is not a focus of measurement.

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Answer:

125 degrees

Step-by-step explanation:

Answer:

7.8 miles.

Step-by-step explanation:

5.2 x 1.5 = 7.8

The interest rates implied by the given combinations are: a. 4.39%. b. 5.19%. c. 0%. a.  The value of the 3.6% perpetuity is approximately £64.29. b. The value of the 2.1% perpetuity is approximately £37.50. a. The investment would be worth approximately $1,073,741.82 today. b. Approximately $3,839.28 was invested in 1901.

To find the interest rate implied by the given combinations of present and future values, we can use the formula for the interest rate:

Interest Rate = ((Future Value / Present Value)^(1 / Years)) - 1

a. Present Value = $340

  Years = 12

  Future Value = $611

Interest Rate = (($611 / $\(340)^(1 / 12)) - 1\)

Interest Rate ≈ 0.0439 or 4.39%

b. Present Value = $153

  Years = 5

  Future Value = $225

Interest Rate = (($225 /\($153)^(1 / 5)) - 1\)

Interest Rate ≈ 0.0519 or 5.19%

c. Present Value = $240

  Years = 8

  Future Value = $240

Interest Rate = (($240 / $\(240)^(1 / 8)) - 1\)

Interest Rate = 0 or 0%

Therefore, the interest rates implied by the given combinations are:

a. 4.39%

b. 5.19%

c. 0%

Regarding the perpetuities:

a. The value of a 3.6% perpetuity if the long-term interest rate is 5.6% can be calculated using the formula:

Value = Cash Flow / Interest Rate

Value = £3.6 / 0.056

Value ≈ £64.29

Therefore, the value of the 3.6% perpetuity is approximately £64.29.

b. The value of a 2.1% perpetuity can be calculated in the same way:

Value = £2.1 / 0.056

Value ≈ £37.50

Therefore, the value of the 2.1% perpetuity is approximately £37.50.

Regarding the stock market investment:

a. To calculate the value of a $1,000 investment in 1901 with a compound growth rate of 5% until 2019, we can use the formula:

Value = Present Value * (1 + Growth Rate)^Years

Value = $1,000 * (1 + 0.05)^(2019 - 1901)

Value ≈ $1,073,741.82

Therefore, the investment would be worth approximately $1,073,741.82 today.

b. To calculate the initial investment if it has grown to $1 million, we rearrange the formula:

Present Value = Future Value / (1 + Growth Rate)^Years

Present Value = $1,000,000 / \((1 + 0.05)^(2019 - 1901)\)

Present Value ≈ $3,839.28

Therefore, approximately $3,839.28 was invested in 1901.

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The standard normal random variable, denoted as z, represents a normally distributed variable with a mean of 0 and a standard deviation of 1. To calculate the probabilities given in your question, we use the standard normal table (also known as the z-table).

(a) P(Z > 0.70) = 0.7196

This probability represents the area to the right of z = 0.70 under the standard normal curve. By looking up the value 0.70 in the z-table, we find that the corresponding area is approximately 0.7580. Therefore, the probability P(Z > 0.70) is approximately 0.7580.

(b) P(-2 ≤ Z ≤ 2) = 0.4024

This probability represents the area between z = -2 and z = 2 under the standard normal curve. By looking up the values -2 and 2 in the z-table, we find that the corresponding areas are approximately 0.0228 and 0.9772, respectively. Therefore, the probability P(-2 ≤ Z ≤ 2) is approximately 0.9772 - 0.0228 = 0.9544.

(c) P(-2 < Z < 2) = 0.9544

This probability represents the area between z = -2 and z = 2 under the standard normal curve, excluding the endpoints. By subtracting the areas of the tails (0.0228 and 0.0228) from the probability calculated in part (b), we get 0.9544.

Note: It seems there might be a typographical error in part (b) of your question where you mentioned P(-20 ≤ z ≤ 20) = 0.4024. The probability for such a wide range would be extremely close to 1, not 0.4024.

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Answer:

150

Step-by-step explanation:

Let there are 'x' girls. According to the given chart, 30% of the total girls participitated in basketball. As well as, we are provided with the statement '45 girls participated in basketball'

=> 30% of x = 45

=> 30/100 × x = 45

=> x = 45 x 100/30

=> x = 150

if you are looking for the missing angle then C=58*

if you are looking for the missing sides then you might need to ask someone else

The length of this rectangular room is equal to 9 meters.

The breadth of this rectangular room is equal to 5 meters.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = xy

Where:

If length would become 3 meters less and breadth would become 1 meter more, we have the following expressions;

y = x - 3

x = y + 1

45 = xy

When the rectangle turns to a square, all of the side lengths become equal;

y + 1 = x - 3

x = y + 4

From the area of a rectangle formula, we have:

45 = (y + 4)y

45 = y² + 4y

y² + 4y - 45 = 0

y² + 9y - 5y - 45 = 0

y(y + 9) - 5(y + 9) = 0

y = 5 or -9 meters.

For the length, we have:

x = y + 4

x = 5 + 4

x = 9 meters.

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Answer:

in your equation it says (y=32x) which 32 will mean how much he is charging for each skateboard, x will be how many he sells, and y would be how much he makes from selling them. So if he sold 2 skateboards you would do

Step-by-step explanation:

For the standard normal distribution , the probability will be 0.0401 which means option a is the correct choice.

A standard deviation (or σ) is a degree of ways dispersed the records is when it comes to the mean. Low general deviation approach records are clustered across the mean, and excessive general deviation suggests records are extra unfold out.

Using a standard normal table the area to the right of z = 1.75 is given by

P(z > 1.75) = .0401

Therefore, the correct option is a.

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Answer:

It has to be 40° or 55°, I think.

sorry if wrong.

After using the linear regression we would have the value for a and b. a and b represent the slope (a) of a line and the y-intercept (b).

To find the values of the equation we must round the results of the linear regression to the nearest integer

a would be equal to -2 as the number -1.96341463 is nearer to -2 than -1.

b would be equal to 19 as the number 19.09756098 is nearer to 19 than 20.

The final equation would be:

y= -2x + 19

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Based on the nature of the variable and the ability to assign numerical values and perform mathematical operations, it is clear that the variable "distances between cities" is quantitative.

The variable "distances between cities" represents the measurements of distances, which are inherently quantitative in nature. Distances can be measured using standard units, such as miles, kilometers, or any other unit of length. These units allow for numerical comparisons and calculations.

Quantitative variables are those that can be measured or expressed numerically. In the case of distances between cities, we can assign numerical values to represent the distances. For example, we can say City A is 100 miles away from City B, or City C is 500 kilometers away from City D.

Furthermore, quantitative variables can be subjected to mathematical operations like addition, subtraction, multiplication, and division. For instance, we can add or subtract distances to calculate the total distance traveled or find the difference between two cities' distances.

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Answer:

C

Step-by-step explanation:

The system of equations, are y = 4x-1 and y = -x+5

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given are tables for points of a system of equations,

1) consider two points, (-1, -5) and (0, -1)

Slope = -1+5 / 0+1 = 4 / 1 = 4

Therefore, y = 4x + c

Put y = -1, x = 0

-1 = c

Therefore, y = 4x-1

This is the first equation of the system of equations,

Since, in option is c this equation is given therefore, second equation is

y = -x+5

Hence, the system of equations, are y = 4x-1 and y = -x+5

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The null hypothesis (H _0 ) is a statement that assumes there is no significant difference or effect in the population. In this case, the null hypothesis states that the variance of the production line is equal to or greater than 25. It serves as the starting point for the hypothesis test.

a. The null hypothesis (\(H_0\)) in this case would be that the variance of the production line is equal to or greater than 25.

b. The alternative hypothesis (\(H_1\) or \(H_a\)) would be that the variance of the production line is less than 25.

c. To compute the test statistic, we can use the chi-square distribution. The test statistic, denoted as \(\chi^2\), is calculated as:

\(\chi^2 = \frac{{(n - 1) \cdot s^2}}{{\sigma_0^2}}\)

where \(n\) is the sample size, \(s^2\) is the sample variance, and \(\sigma_0^2\) is the hypothesized variance under the null hypothesis.

d. The rejection region is the range of values for the test statistic that leads to rejecting the null hypothesis. In this case, since we are testing whether the variance is less than 25, the rejection region will be in the lower tail of the chi-square distribution. The specific numerical value depends on the degrees of freedom and the significance level chosen for the test.

e. To draw a conclusion, we compare the test statistic (\(\chi^2\)) to the critical value from the chi-square distribution corresponding to the chosen significance level. If the test statistic falls within the rejection region, we reject the null hypothesis. Otherwise, if the test statistic does not fall within the rejection region, we fail to reject the null hypothesis.

f. In terms of the problem situation, if we reject the null hypothesis, it would provide evidence that the variance of the production line is indeed less than 25. On the other hand, if we fail to reject the null hypothesis, we would not have sufficient evidence to conclude that the variance is less than 25.

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