4.89; 4.089; 4.870; 4.881 - Put these in order from least to greatest. Your answer​

Let the speed of the train be v km/hr and its length be l meters. The first car is moving at 45 km/hr while the second car is moving at 50 km/hr. Therefore, the speed of the train relative to the first car = (v - 45) km/hr. Similarly, the speed of the train relative to the second car = (v - 50) km/hr.

Using the formula distance = speed × time, we can calculate the distances covered by the train in passing each car. For the first car, the distance covered is l and the time taken is 36 seconds. Therefore, distance = speed × time gives us l = (v - 45) × (36/3600) km. For the second car, the distance covered is l and the time taken is 54 seconds. Therefore, distance = speed × time gives us l = (v - 50) × (54/3600) km.

Equating both these expressions for l, we get:(v - 45) × (36/3600) = (v - 50) × (54/3600)Simplifying this expression, we get v = 75 km/hr. Now we can substitute this value of v into either of the expressions for l that we derived earlier and get the length of the train. Using the first expression, we get: l = (v - 45) × (36/3600) km= (75 - 45) × (36/3600) km= 0.4 km= 400 meters Therefore, the length of the train is 400 meters. The length of the train is 400 meters. To solve this question, we first need to understand that the train passes two cars that are moving at different speeds. Using the relative speeds of the train and each car, we can set up two equations for the distances covered by the train in passing each car. Equating these expressions for the distances, we can solve for the speed of the train. Finally, substituting this value of the speed into one of the expressions for the distance covered by the train, we can find the length of the train.

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The equation of exponential regression that fits the data is given as follows:

y = 1.5(2.5)^x.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

To obtain the equation of exponential regression, we must insert the points of the data-set into a calculator.

The points are given as follows:

(1, 3.75), (4, 9.375), (3, 23.438), (4, 58.594), (5, 146.484).

Inserting these points into a calculator, the equation is given as follows:

y = 1.5(2.5)^x.

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Answer:

$29, that is the answer for this question

Therefore , the price per ticket is $12,the equation used is y=12x, the theatre made $3936 by selling 328 ticket and the relationship is proportional.

An algebraic equation is a linear equation. Each term in a linear equation is either a constant or the result of a constant plus one variable. In the case of a linear equation with two variables, the graph is a straight line.

Here,

A) From the given  we can find the price per ticket

which is => y/x

=> 60/5

=>12

Therefore the price per ticket is $12

B)The equation can be used to represent the graph is

y= 12x

C) The theater were to sell 328 tickets they would make

=> 328*12=3936

Therefore the money would they make is $3936

D)The relationship proportional as we can see from the graph

Therefore , the price per ticket is $12,the equation used is y=12x, the theatre made $3936 by selling 328 ticket and the relationship is proportional.

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The simplified form of the expression (6^2)(-3^5) is -8,748.

To simplify (6^2)(-3^5), we must first evaluate the exponents.6^2 = 36, since 6 × 6 = 36.3^5 = 243,

since 3 × 3 × 3 × 3 × 3 = 243.Now, we substitute the values into the expression:

(6^2)(-3^5) = (36)(-243)

Next, we multiply the values to obtain the simplified form:

(36)(-243) = -8,748

Therefore, (6^2)(-3^5) in its simplest form is -8,748.According to the rules of exponents, when we raise a number to an exponent, the result is the number multiplied by itself the number of times represented by the exponent.

For instance, 6^2 means 6 multiplied by itself 2 times, which is equal to 36.3^5 means 3 multiplied by itself 5 times, which is equal to 243.

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The probability that a randomly selected adult weighs between 120 and 165 lbs is approximately 0.8186.

Since the weights of adults are normally distributed with a mean of 140 lbs and a standard deviation of 25 lbs, we can use the standard normal distribution to calculate the probability.

We first need to standardize the values using the formula: z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation.

For x = 120 lbs, z = (120 - 140) / 25 = -0.8, and for x = 165 lbs, z = (165 - 140) / 25 = 1.0. We can then use a calculator to find the probability between -0.8 and 1.0, which is approximately 0.8186.

Thus, the chance of picking an adult at random who weighs between 120 and 165 lbs is roughly 0.8186.

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Part a

How many deer are younger than 15 years old?

that means

less than 15

< 15

looking at the graph

8+5=13

Part b

How many deer are in the preserve, in total?

8+5+5+2+2+2+2=26 deer

The area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

Since kite ABCD is divided into two triangles by its diagonals, we can find the area of the kite by finding the sum of the areas of these two triangles.

Let AC and BD be the diagonals of the kite, intersecting at point E. Then triangle ABE and triangle CDE are the two triangles formed by the diagonals.

The area of a triangle can be found using the formula: Area = (base x height) / 2

For triangle ABE, the base is AB and the height is the distance from E to the line containing AB. Similarly, for triangle CDE, the base is CD and the height is the distance from E to the line containing CD.

Since the diagonals of a kite are perpendicular and bisect each other, the distance from E to the line containing AB is the same as the distance from E to the line containing CD.

Therefore, the heights of the two triangles are equal.

So, we can find the area of ABCD as follows:

Area of ABCD = Area of triangle ABE + Area of triangle CDE

= (AB x height)/2 + (CD x height)/2

= (AB + CD) x height / 2

Therefore, the area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

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The state variable feedback gain vector K needs to be determined to place the closed-loop poles of the system at specified locations (-10±j*20 and -40). This can be achieved by using the pole placement method to calculate the gain matrix K.

In order to place the closed-loop poles at the desired locations, we can use the pole placement technique. The closed-loop poles represent the eigenvalues of the system matrix A - BK, where B is the input matrix and K is the gain matrix. The desired characteristic equation is given by \(s^3\) + 50\(s^2\) + 600s + 1600 = 0, corresponding to the desired pole locations.

By equating the characteristic equation to the desired polynomial, we can solve for the gain matrix K. Using the Ackermann formula, the gain matrix K can be computed as K = [k1, k2, k3], where k1, k2, and k3 are the coefficients of the polynomial that we want to achieve.

To find the coefficients k1, k2, and k3, we can equate the coefficients of the desired characteristic equation to the coefficients of the characteristic equation of the system. By comparing the coefficients, we obtain a set of equations that can be solved to determine the values of k1, k2, and k3.

After obtaining the values of k1, k2, and k3, the gain matrix K can be constructed, and the closed-loop poles of the system can be moved to the desired locations (-10±j*20 and -40). This ensures that the system response meets the specified performance requirements.

In conclusion, the state variable feedback gain vector K can be determined by solving a set of equations derived from the desired characteristic equation. By choosing appropriate values for K, the closed-loop poles of the system can be placed at the desired locations, achieving the desired performance for the system.

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Answer:

x = 5

Step-by-step explanation:

The diagram shows that the rhombus is split into two isosceles triangles, LKM and NMK.  

Thus, the three angles in triangle LKM are 110, (8x - 5), and (8x - 5).

Thus, we can solve for x by setting the sum of the measures of the three angles in triangle LKM equal to 180:

(8x - 5) + (8x - 5) + 110 = 180

(8x + 8x) + (-5 - 5 + 110) = 180

16x + 100 = 180

16x = 80

x = 5

Thus, x = 5

Optional step:

We can check that we've correctly solved for x by plugging in 5 for x in (8x - 5) twice for both angles, adding the result to 110, and seeing if we get 180 on both sides of the equation:

(8(5) - 5) + (8(5) - 5) + 110 = 180

(40 - 5) + (40 - 5) + 110 = 180

35 + 35 + 110 = 180

70 + 110 = 180

180 = 180

Thus, x = 5 is correct.

Answer:

3 & 5

Step-by-step explanation:

The value of point estimate is 101.5 and value of margin of error is 10.9 gram if the Lindsey purchased a random sample of 25 tomatoes at the farmers market.

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

\(\rm MOE = Z\times \dfrac{s}{\sqrt{n}}\)

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            n is the number of samples.

Let's suppose m is a point estimate and ME is the margin of error.

The structure of the confidence interval is:

(m—ME, m + ME)

The given confidence interval is (90.6, 112.4)

Then, m—ME = 90.6 ..... (1)

m + ME = 112.4 ..... (2)

After solving equation (1) and (2) we get:

m = 101.5

ME = 10.9 grams

Thus, the value of point estimate is 101.5 and value of margin of error is 10.9 gram if the Lindsey purchased a random sample of 25 tomatoes at the farmers market.

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A more valuable statement is produced when x and y are used as factors rather than as words.

Given,

Kate only uses the variables x and y once in her algebraic expression. She uses x and y as factors in the first expression that she creates. Then she creates another expression using the terms x and y.

We have to write a comparison between two expressions if x and y both are negative integers;

Here,

x and y are factors in her first expression;

xy

The terms x and y are written in her second expression;

x + y

Given that both x and y are negative integers, then;

-x × -y = xy  ............... 1

-x + (-y) = - x - y

= - (x + y)  .............. 2

Because of this, the value of the x and y factors is higher than when x and y are terms.

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1/4 or .75

6 divided by 4 equal 1/4 or .75

The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

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Answer:

Step-by-step explanation:

Given function:

a)  g(2)

b)  g(t - 2)

c)  g(t) - g(2)

Explanation

Step 1

let x represents the year

let y represents the hours of electricity generated ( in millons)

then, we have two coordinates of the function

Answer:

A

Step-by-step explanation:

Additive inverse is (5/3) and multiplicative inverse is (-3/5). Their product is (-1)

Inverse means the opposite of something.

In this case the opposite of -5/3 is 5/3.

So the answer is: 5/3

Answer:

3 pi 9

Step-by-step explanation:

Answer:

The image is inserted below.

Step-by-step explanation:

The blue line is the line that passes through the point (1,-1) which is marked as A on the graph.

The green line is the new line you need to graph that is parallel to the original line and has a slope of 1.

The Remainder is 3 and the Quotient is 2141.

Therefore,

The given Divisor = 4 and Dividend = 8567

4 ÷ 8567

= 2141.75

The Quotient is 2141 and the Remainder is 3

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B. Square, A quadrilateral with four congruent sides and four congruent angles is a Square.

A square is a quadrilateral with four congruent sides and four congruent angles (right angles). All sides of a square are equal in length, and all angles are right angles (90 degrees). This makes it a special type of rectangle and a special type of rhombus.

In a rhombus, all four sides are equal in length. A square is also a special type of rhombus in which all four sides are equal and it is also a special type of rectangle with four congruent sides and four congruent angles is a rhombus.

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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 relationship between the sides MN, MS, and MQ in the given regular heptagon is \(\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}\)

The area to be planted with flowers is approximately 923.558 m²

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

\(A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )\)

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

\(\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}\)

\(s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69\)

\(The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52\)

The area of the heptagon MNSRQPO is therefore;

\(A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94\)

\(MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08\)

By sine rule, we have

\(\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}\)

\(sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})\)

\(\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}\)

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

\(Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}\)

The area of the of the garden plated with flowers, \(A_{req}\), is given as follows;

\(A_{req}\) = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

\(A_{req}\)= 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, \(A_{req}\) ≈ 923.558 m²

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The probability that the spinner lands on orange is P ( O ) = 1/4 = 25 %

We have,

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

The total number of sides for the spinner = 4

Since the spinner is divided into 4 equal sections, each section has an equal chance of being landed on

Therefore, the probability of spinning orange is 1 out of 4, or 1/4, which is equivalent to 25%

We can express this probability as:

P(orange) = 1/4

Hence , the probability that Josh spins orange is 1/4 or 25%

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Answer:

x = 1 ± 4\(\sqrt{3}\)

Step-by-step explanation:

(x − 1)² - 4 = 44

(x - 1)² = (x - 1) (x - 1) = x² - x - x + 1 = x² - 2x + 1

x² - 2x + 1 - 4 = 44

x² - 2x - 3 = 44

x² - 2x - 47 = 0

Use the quadratic formula to find the solutions.

\(\frac{-b± \sqrt{b^{2}-4(ac) } }{2a}\)

We get the answer

x = 1 ± 4\(\sqrt{3}\)

So, the answer is x = 1 ± 4\(\sqrt{3}\)