Find the gradient of the line segment between the points (-5,-2) and (4,3).
Give your answer in its simplest form.

Answer: 53,643.95

Step-by-step explanation:

50,000 + 3,000 + 600 + 40 + 3 + .9 + .05

Answer:

8/10 = 4/5

Step-by-step explanation:

Substituting y back in terms of x, we have x = Py = P⎡⎣⎢⎢ 3e^(-3t) ⎤⎦⎥⎥ = ⎡⎣⎢⎢ 3e^(-t) ⎤⎦⎥⎥ 3e^(3t). Thus, the solution to the system is x(t) = ⎡⎣⎢⎢ 3e^(-t) ⎤⎦⎥⎥ 3e^(-2t).

The solution to the system dx/dt = ⎡⎣⎢⎢ -3 3 ⎤⎦⎥⎥ -6 3 x, with x(0) = ⎡⎣⎢⎢ 3 ⎤⎦⎥⎥ 3, is x(t) = ⎡⎣⎢⎢ 3e^(-t) ⎤⎦⎥⎥ 3e^(-2t).

To find the solution, we can first diagonalize the coefficient matrix [-3 3; -6 3]. Diagonalization involves finding the eigenvalues and eigenvectors of the matrix.

The eigenvalues of this matrix are -3 and 3, with corresponding eigenvectors [1; -2] and [1; 1].

We can then form the matrix P using the eigenvectors as columns: P = ⎡⎣⎢⎢ 1 1 ⎤⎦⎥⎥. The inverse of P, denoted P^(-1), is equal to the transpose of P: P^(-1) = ⎡⎣⎢⎢ 1 1 ⎤⎦⎥⎥.

Next, we can find the matrix D, which is a diagonal matrix containing the eigenvalues: D = ⎡⎣⎢⎢ -3 0 ⎤⎦⎥⎥.

Using these matrices, we can rewrite the original system as d/dt(Px) = DPx. Multiplying both sides by P^(-1) gives d/dt(P^(-1)(Px)) = D(P^(-1)(Px)). Simplifying, we have d/dt(P^(-1)x) = D(P^(-1)x).

By letting y = P^(-1)x, the system becomes dy/dt = Dy, which is a decoupled system of equations. Solving each equation independently gives y_1 = 3e^(-3t) and y_2 = 3e^(3t).

Finally, substituting y back in terms of x, we have x = Py = P⎡⎣⎢⎢ 3e^(-3t) ⎤⎦⎥⎥ = ⎡⎣⎢⎢ 3e^(-t) ⎤⎦⎥⎥ 3e^(3t). Thus, the solution to the system is x(t) = ⎡⎣⎢⎢ 3e^(-t) ⎤⎦⎥⎥ 3e^(-2t).

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The outer layer in a data set of plague amounts refers to outliers or extreme values. The presence of outliers in a data set can have a significant effect on the measures of central tendency, particularly the mean and median.

Outliers are data points that fall significantly far from the majority of the data, either higher or lower. The mean is calculated by adding together all the values and dividing by the total number of values, and outliers can significantly affect this calculation.

On the other hand, the median only considers the position of the middle value, making it more resistant to the impact of outliers. Therefore, it is important to identify the outer layer or outliers in a data set of plague amounts to understand their impact on the measures of central tendency, particularly the mean.

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An interval can be defined as a set of real numbers. The interval (44-47), (48-51), and (56-59) will have frequencies of 3, 4, and 1.

A collection of real numbers between two specified values known as the interval's endpoints is referred to as an interval.

The data set given to us is 42, 43, 46, 47, 47, 48, 49, 50, 51, 53, 55, 55, 59. Therefore, the frequency can be written as,

Thus, the interval (44-47), (48-51), and (56-59) will have frequencies of 3, 4, and 1.

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Answer:

3 4 1

Step-by-step explanation:

I took the assignment and got it right

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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The school building is 36ft tall.

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Chris is 6 feet tall and he casts a shadow that is 5 feet long

He measures that the shadow cast by the school building is 30 feet long

We can say the ratios will be same  6/h = 5/30

h =6 × 6 = 36 ft

Hence the school building is 36ft tall.

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x≥ 0 , everthing to the right of the y-axis

y≥ 0 , everthing above the x-axis

So far you are in quadrant I of the x-y plane

y ≤ 3 , everthing from the above, but also below the horizontal line y = 3

lastly y ≤ -x + 5

sketch a line leaning 45° to the left with a y-intercept of 5, shade in everthing below that line

My diagram has a simple trapezoid consisting of a

rectangle with a right-angled triangle attached

now our Objective Function is

C = -5x + 3y , which is a line with slope 5/3

letting that line go through the origin, let it slide parallel to itself over the shaded region until you reach the farthest point from the origin.

On my diagram that looks like (5,0)

Answer:

Step-by-step explanation:

I think is x-1

It is because you need to find f(1) and the formula of x-1 when x is greater and equal to 1.

Answer:

The answer to the question provided is possibly 2.

Step-by-step explanation:

\( \: \: \: \: \: \: \: \: \: \: \: \: 3y + 77 = 2y + 79 \\ \frac{ - 2y \: \: \: \: \: \: = - 2y}{1y + 77 = 79} \\ \frac{ \: \: \: \: \: \: \: \: - 77 = - 77}{ \frac{1y}{1} = \frac{2}{1} } \\ \\ y = 2\)

Answer:

a) x^3y2

b) 6x^2y^3

Step-by-step explanation:

because 3 x's and 2 y's are being multiplied.

You can put a hidden exponent of 1 to each variable without an exponent, and the value will remain the same.

Merely add the exponents of the values with the same base number, or coefficient. —> like terms

X^1 times X^1 times X^1 is X^3, and Y^1 times Y^1 is Y^2.

Our final answer is X^3 Y^2.

Like the first expression, we can add a hidden exponent to each VARIABLE, not number.

2 times 3 is 6, and X^1 times X^1 is X^2, and Y^1 times Y^1 times Y^1 is Y^3.

Our final answer is 6X^2 Y^3.

There is a 95% chance that the true mean of the population lies within the interval of [29.12, 40.88]. In other words, if we were to take many samples from the population and calculate their means, 95% of those means would fall within this interval.

Without additional information about the distribution of the data, it's difficult to provide an exact interval. However, we can use the standard normal distribution and the given values of "u" and "o" to approximate the interval.

Assuming a normal distribution, 95% of the data falls within 1.96 standard deviations of the mean. Therefore, the interval for the amount of data that appears within 95% of the mean would be:

u ± (1.96 * o)

= 35 ± (1.96 * 3)

= 35 ± 5.88

= [29.12, 40.88]

This means that there is a 95% chance that the true mean of the population lies within the interval of [29.12, 40.88]. In other words, if we were to take many samples from the population and calculate their means, 95% of those means would fall within this interval.

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There are 120 ways in which 5  riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways \(^nN_r = \frac{n!}{(n-r)!}\),

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways \(^nN_r = \frac{n!}{(n-r)!}\),

Now,

Substituting values,

We get,

\(^5N_5 = \frac{5!}{(5-5)!}\)

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5  riders and 5 horses can be arranged.

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Answer:

D. 9, 40, 41

Step-by-step explanation:

We can use Pythagorean theorem (a²+b²=c²) to answer this question by squaring the smallest 2 lengths then seeing if it equals the square of the 3rd length.

2²+3² = 4+9 = 13 ≠ 4²

12²+15² = 144+225 = 369 ≠ 20²

8²+9² = 64+81 = 145 ≠ 10²

9²+40² = 81+1600 = 1681 = 41²

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's evaluate ~

\(\qquad \tt \dashrightarrow \:(6 \times 1000) + (1 \times 10) + (8 \times \frac{1}{1} ) + (9 \times \frac{1}{10} ) + \frac{4}{100} \)

\(\qquad \tt \dashrightarrow \:6000 + 10 + 8 + \frac{9}{10} + \frac{4}{100} \)

\(\qquad \tt \dashrightarrow \: \dfrac{600000 + 1000 + 800 + 90 + 4}{100} \)

\(\qquad \tt \dashrightarrow \: \dfrac{601894}{100} \)

or

\(\qquad \tt \dashrightarrow \:{6018.94}{} \)

Answer: (6, -6)

Step-by-step explanation:

so midpoint =(\(\frac{X1+X2}{2}\),\(\frac{Y1+Y2}{2}\))

for x co ordinate

\(\frac{-2+X2}{2}\)=2

-2+X=4            (X2=x co ordinate point for b, can be written as just x now)

X=6

x co ordinate of B= 6

y co ordinates of y

\(\frac{-8+Y2}{2}\)=-7

-8+Y=-14

Y=-6

co ordinates B (6,-6)

for proof/extra explanation (NOT necessary for working):

\(\frac{Y1+Y2}{2}\)

=\(\frac{(-2)+6, (-8)+(-6)}{2}\)

=\(\frac{4, -14}{2}\)

=(2,-7)

which is the midpoint M

Answer:

Below

Step-by-step explanation:

Radians =  degrees * pi /180

Radians * 180/pi   =  degrees

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Step-by-step explanation:

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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Answer:

After the December 7, 1941, Japanese attack on the American naval fleet at Pearl Harbor, Hawaii, the U.S. was thrust into World War II (1939-45), and everyday life across the country was dramatically altered. Food, gas and clothing were rationed. Communities conducted scrap metal drives. To help build the armaments necessary to win the war, women found employment as electricians, welders and riveters in defense plants. Japanese Americans had their rights as citizens stripped from them. People in the U.S. grew increasingly dependent on radio reports for news of the fighting overseas. And, while popular entertainment served to demonize the nation’s enemies, it also was viewed as an escapist outlet that allowed Americans brief respites from war worries.

Step-by-step explanation:

The two negatives cancel out when we divide or multiply. Think of negative as opposite. Having two opposites cancel.

The slash means fraction and it also means division

6/7 = 6 divided by 7

6/7 = six sevenths

So that allows us to go from fraction to decimal form 6/7 = 0.857 approximately after using your calculator or long division.

Answer:

\(tan 56 = \frac{26}{x}\)

Step-by-step explanation:

\(tangent = \frac{opposite}{adjacent}\)

Side z is the hypotenuse, since it is opposite the right angle.

Side x is the adjacent, since it is next to the angle you are solving for.

The side measuring 26 is the opposite, since it is opposite the angle you are solving for.

Step-by-step explanation:

\(tan = \frac{opposite}{adjacent} \)

tan(tetha) = DC/1 ( here 1 bc as they said, an arc circe w/ radius (OB) 1

The sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

A random sample is drawn from a population with mean μ=73 and standard deviation σ=6.1. To determine if the sampling distribution of the sample mean with n=18 and n=46 is normally distributed, we need to calculate the standard error for each sample size.

For n=18:
The standard error (SE) is calculated using the formula:

     SE = σ / √n
SE = 6.1 / √18

          ≈ 1.441 (rounded to 3 decimal places)

For n=46:
SE = 6.1 / √46 ≈ 0.901 (rounded to 3 decimal places)

To determine if the sampling distribution of the sample mean is normally distributed, we need to consider the Central Limit Theorem (CLT). According to the CLT, when the sample size is sufficiently large (typically n > 30), the sampling distribution of the sample mean tends to be approximately normally distributed, regardless of the shape of the population distribution.

Since both n=18 and n=46 are larger than 30, we can conclude that the sampling distribution of the sample mean with these sample sizes is approximately normally distributed.

Therefore, the sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

The sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

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Both Julia and William placed the same number of cakes, which is the highest among all four. Julia and William placed the most cakes with 5 each.

To determine who placed the most cakes, we need to calculate the number of cakes each person placed and compare the results.

Given:

Total cakes = 25

Jessica's portion = 0.24 * 25 = 6 cakes

Justin's portion = 9 cakes

Julia's portion = 20% * 25 = 0.20 * 25 = 5 cakes

To find William's portion, we subtract the total number of cakes placed by the other three from the total:

William's portion = Total cakes - (Jessica's portion + Justin's portion + Julia's portion)

William's portion = 25 - (6 + 9 + 5) = 5 cakes

Now let's compare the number of cakes placed by each person:

Jessica: 6 cakes

Justin: 9 cakes

Julia: 5 cakes

William: 5 cakes

Both Julia and William placed the same number of cakes, which is the highest among all four. Therefore, Julia and William placed the most cakes with 5 each.

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Using the method of undetermined coefficients, a particular solution of differential equation for y was found to be yp(t) is (t^3/9 + 2t^2/5 + Bt + C) e^(5t).

For the differential equation y″−10y′+25y=1.5e5t^2+1, we can start by finding the complementary solution by solving the characteristic equation r^2 - 10r + 25 = 0 which gives r = 5 (with multiplicity 2). Therefore, the complementary solution is yc(t) = c1 e^(5t) + c2 t e^(5t).

Now, we can find the particular solution by assuming a solution of the form yp(t) = A(t) e^(5t). Taking the first and second derivatives of yp(t), we have

yp'(t) = A'(t) e^(5t) + 5A(t) e^(5t)

yp''(t) = A''(t) e^(5t) + 10A'(t) e^(5t) + 25A(t) e^(5t)

Substituting yp(t) and its derivatives into the original differential equation, we get

( A''(t) e^(5t) + 10A'(t) e^(5t) + 25A(t) e^(5t)) - 10 ( A'(t) e^(5t) + 5A(t) e^(5t)) + 25A(t) e^(5t) = 1.5e^(5t)t^2 + 1

Simplifying and collecting like terms, we get

A''(t) = 3e^(-5t) t^2 + e^(-5t)

A'(t) = -3e^(-5t) t^3/3 - e^(-5t) t + B

A(t) = e^(-5t) t^3/9 + e^(-5t) t^2/5 + Bt + C

where B and C are constants of integration. Therefore, the particular solution is

yp(t) = A(t) e^(5t) = (t^3/9 + 2t^2/5 + Bt + C) e^(5t)

where B and C are constants that can be determined using the initial/boundary conditions if given.

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Polynomials are expressions. The solution of the division can be written as \(4x^2-27x+167-\dfrac{996}{x+6}\).

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

The division of the polynomial  (4x³-3x²+5x+6) when divided by (x+6), can be done in the following manner,

\(\dfrac{4x^3-3x^2+5x+6}{x+6}\)

\(=4x^2+\dfrac{-27x^2+5x+6}{x+6}\)

\(=4x^2-27x+\dfrac{167x+6}{x+6}\)

\(=4x^2-27x+167+\dfrac{-996}{x+6}\\\\\\=4x^2-27x+167-\dfrac{996}{x+6}\)

Hence, the solution of the division can be written as \(4x^2-27x+167-\dfrac{996}{x+6}\).

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Answer:

Step-by-step explanation:

OPT D ON EDG 2023

Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.