please help
solve the following equation
5/7x 14 =

Answers

Answer 1

Answer:

10

Step-by-step explanation:

multiply the numerators or the top numbers 5/7 * 14/1

14*5=70

divide it by the denominator or the bottom number 70/7=10


Related Questions

__________________ occurs when the method of observation tends to produce values that systematically differ from the true value in some way.

Answers

When the process of observing or measuring yields results that consistently deviate in some way from the true value, this is known as observer/measurement bias. Because of the systematic mistake this adds into the data, the conclusions are incorrect or unreliable.

Observer/measurement bias is a sort of systematic error that happens when the technique used for observation or measurement yields results that consistently deviate in some way from the true value. The observer's own preconceived ideas or expectations, the measurement equipment, and the environment in which the observation or measurement is being conducted can all contribute to this form of bias.An observer's bias, for instance, could cause them to see or measure something in a way that favours one particular result or outcome over another. Similar to how external influences like noise, light, or temperature can skew results, the environment in which the observation or measurement is taking place may add a bias. If feasible, results that are inaccurate or unreliable because of observer/measurement bias should be avoided because they can lead to incorrect inferences about the data.

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What is -1.2 repeating as a mixed number​

What is -1.2 repeating as a mixed number

Answers

Answer:

\(-1\frac{2}{9}\)

Step-by-step explanation:

         _

y = - 1.2

                 _

y × 10 = - 1.2 × 10

                _

10y = - 12. 2

                _

10y = - 12. 2

-         _

y = - 1.2

____________

9x = 11

9x ÷ 9 = 11 ÷ 9

\(x = -1\frac{2}{9}\)

   _

- 1.2 = - 1 2/9

16×25×15 =?
4+11÷2=?
?-?=?

Answers

Answer:

16x25x15=6000

4+11÷2=9.5

Step-by-step explanation:

1) 16x25x15 is 16 times 25 times 15, which is 6000

2) This question requires BIDMAS/BODMAS. As you start with the multiplication (Brackets Indices Multi Divide Add Subtract) 11÷2 = 5.5, 5.5+4=9.5

A 50 cm diameter wheel rolls without slipping on a floor. The center of wheel has a linear velocity of 20 m/s. a) Find the total velocity of point A and B (In vector form) by using the Supper position method (General plain motion) (10pts) b) Find the total velocity of point A and B (In vector form) by using the Instantaneous Center of Rotation

Answers

a) Using the Superposition Method:

To find the total velocity of point A and B on the rolling wheel, we can consider two components: the linear velocity of the center of the wheel and the rotational velocity of the wheel.

Let's denote:

V_c = Linear velocity of the center of the wheel

ω = Angular velocity of the wheel

R = Radius of the wheel

Since the diameter of the wheel is 50 cm, the radius is 25 cm or 0.25 m (R = 0.25 m).

1. Linear velocity of point A:

The linear velocity of point A is the sum of the linear velocity of the center and the tangential velocity due to rotation.

V_A = V_c + ω × r

The tangential velocity due to rotation can be calculated using the formula ω × r, where r is the position vector from the center of the wheel to point A.

The position vector from the center of the wheel to point A is (R, 0, 0) since point A lies on the circumference of the wheel.

V_A = V_c + ω × (R, 0, 0)

   = V_c + ω × R × (1, 0, 0)

   = V_c + ωR × (1, 0, 0)

Plugging in the given values, V_c = 20 m/s and R = 0.25 m:

V_A = 20 m/s + ω × 0.25 m × (1, 0, 0)

   = 20 m/s + 0.25ω × (1, 0, 0)

2. Linear velocity of point B:

The linear velocity of point B is the same as the linear velocity of the center of the wheel since point B is fixed to the center of the wheel.

V_B = V_c

Therefore, the total velocity of point A is V_A = 20 m/s + 0.25ω × (1, 0, 0), and the total velocity of point B is V_B = 20 m/s.

b) Using the Instantaneous Center of Rotation:

The instantaneous center of rotation (ICR) is the point on the wheel that has zero velocity. In this case, the ICR lies on the contact point between the wheel and the floor.

1. Linear velocity of point A:

The linear velocity of point A is the same as the linear velocity of the ICR since point A coincides with the ICR.

V_A = V_ICR

2. Linear velocity of point B:

The linear velocity of point B is the sum of the linear velocity of the ICR and the tangential velocity due to rotation.

V_B = V_ICR + ω × R × (0, -1, 0)

The tangential velocity due to rotation can be calculated using the formula ω × R × (0, -1, 0), where R is the radius of the wheel.

Plugging in the given values, V_ICR = 20 m/s and R = 0.25 m:

V_B = 20 m/s + ω × 0.25 m × (0, -1, 0)

   = 20 m/s + 0.25ω × (0, -1, 0)

Therefore, the total velocity of point A is V_A = V_ICR = 20 m/s, and the total velocity of point B is V_B = 20 m/s + 0.25ω × (0, -1, 0).

Note: The angular velocity ω is not given in the question, so its value would need to be provided

or calculated separately to determine the complete velocity vectors.

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help!!!!!!!!!!!!!!! me please

help!!!!!!!!!!!!!!! me please

Answers

Answer:

Answer below in picture

I hope it helps.

help!!!!!!!!!!!!!!! me please
help!!!!!!!!!!!!!!! me please

hi amariharrisdagoat :D

Answers

Answer:

heyyy even though you are not talking to me

BAHBAHA

Step-by-step explanation:

Lisa also cleans windows on the weekend. She charges $10 a window plus a $5 flat supply fee, regardless of the size of the window. Write the total charge, c, of a cleaning job as a function of the number of windows (w).

Answers

Lisa also cleans windows on the weekend. The correct answer is c = 10w + 5

What was the steps to find this answer?

So, she charges $10 a window plus a $5 flat supply fee, we are going to add 10 and 5 to find are answer and we are going to use c:

→ w = 10

→ 10w

$5 in the other hand, is independent.

→ + 5

→ c = 10w + 5

Therefore, Lisa also cleans windows on the weekend. The correct answer is c = 10w + 5

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If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers

Answers

There is no inherent relationship between the median and the average. It is possible for the median to be greater than the average or vice versa, depending on the specific values in the set.

To determine whether the median of the 5 numbers is greater than the average (arithmetic mean), we need the actual values of the numbers. Without specific values, we cannot provide a definitive answer. However, I can explain the concept of the median and the average to help you understand how they relate to each other.

The median is the middle value of a set of numbers when they are arranged in ascending or descending order. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

The average, or arithmetic mean, is calculated by summing up all the values in a set and dividing the sum by the number of values.

In general, there is no inherent relationship between the median and the average. It is possible for the median to be greater than the average or vice versa, depending on the specific values in the set.

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In ΔVWX, v = 390 inches, w = 390 inches and x=500 inches. What is the sum of ∠Vand∠W?

Answers

The answer would be 390+ 390 =780

A random number generator is used to create a list of 300 single-digit numbers. Of those 300 numbers, 146 are odd
and 154 are even. The number 8 was generated 22 times.
What is the experimental probability of an even number other than 8 being generated? Write your answer as a
decimal to the nearest hundredths place.
O 0.23
O 0.35
O 0.44
O 0.52

Answers

This is 0.35
…………………….

The experimental probability of an even number other than 8 being generated is, 0.44

What is mean by Probability?

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

Total number of numbers = 300

Number of even numbers = 154

Number of eight = 22

Hence, Number of even numbers other than 8 is,

154 - 22 = 132

Thus, Probability is,

= [number of even numbers other than eight] / [total number of numbers]

= 132/300

= 0.44

Thus, The experimental probability of an even number other than 8 being generated is, 0.44

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Find the length of the hypotenuse round to the nearest hundredth

Find the length of the hypotenuse round to the nearest hundredth

Answers

Answer:

\(\displaystyle 4\sqrt{5}\)

Step-by-step explanation:

Use the Pythagorean Theorem:

\(\displaystyle a^2 + b^2 = c^2 \\ \\ 8^2 + 4^2 = c^2; \sqrt{80} = \sqrt{c^2} \\ \\ 4\sqrt{5}\:[or\:8,94427191...] = b\)

So, you have this:

\(\displaystyle 8,94 ≈ c\)

I am joyous to assist you at any time.

what are 3 ratios that are equivalent to 4/7 Help please

Answers

Answer:

8:14, 12:27, 40:70

Step-by-step explanation:

look carefully at the accompanying histogram. the histogram displays the grades received on an exam by students in a history course. from an inspection of this histogram, we can conclude that the mean or average exam score is expected to be:

Answers

According to the histogram, the expected mean exam score is approximately 6.5. This value is centered on the majority of scores, indicating that it is most likely the exam's average.

A histogram is a graph that shows data points arranged in user-defined ranges. By grouping a large number of data points into logical ranges or bins, the histogram, which looks like a bar graph, makes a data series easier to understand.

Histograms and bar charts both use columns to present a visual display, and the terms are frequently used interchangeably. However, technically speaking, a histogram depicts the frequency distribution of a data set's variables.

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how long the chord of the circle 4x²+4y²-8x-8y+3=0 whose the end point where the curve y=1/x cut the circle?​

Answers

The length of the chord is 6

What is a circle simple definition?

Simply said, a circle is a rounded form without any edges or line segments. It has the geometric form

What is the General Equation of Circle?

The circle's general equation is written as follows: x2 + y2 + 2gx + 2fy + c = 0. The center of the circle in this general form of the equation of a circle is (-g, -f), and its radius is given by r = g2+f2cg2+f2c.

What is C in the General Equation of Circle?

The circle's general equation is written as follows: x2 + y2 + 2gx + 2fy + c = 0. The coordinates of the circle's center and radius are determined using this general form. The equation in this case represents a circle that does not pass through the origin because c is a constant term.

We possess

4x2+4y2−12x+32y=27…(1)

We shall have y=0 when the specified circle intersects the x-axis, therefore

4x2+4y2−12x+32y=27

=>4x2−12x=27

=>4x2−12x−27=0…(2)

The answers to (2) are:

x1=−3/2

x2=9/2

Thus, the supplied circle intersects the x-axis at the following points:

A(−3/2,0) and B(9/2,0)

The length of the chord we want is defined as the distance d between these sites. The well-known formula for calculating the distance between points A and B is used to calculate the distance d:

d=root((9/2−(−3/2))^2+(0−0)^2)

√=6^2

=6

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1. Consider the following problem.
Maximize Z = 2x₁ + 5x₁₂₃ + 3x₁₂₃
subject to
x₁ - 2x₂ + x₃ ≤ 20
2x₁ + 4x₂ + x₃ = 50
x₁ ≥0, x₂≥ 0, x₃ ≥ 0.
Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) basic solution. Also identify the initial entering basic variable and the leaving basic variable.

Answers

To construct the first simplex tableau using the Big M method. The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

To construct the first simplex tableau using the Big M method, we first rewrite the problem in standard form as follows:

Maximize \(Z = 2x₁ + 5x₂ + 3x₃\)
subject to
\(x₁ - 2x₂ + x₃ + x₄ = 20\\2x₁ + 4x₂ + x₃ = 50\\x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0, x₄ ≥ 0.\)

To construct the initial simplex tableau, we introduce artificial variables x₅ and x₆ to the two equations.

The initial tableau is:

 Basis   |  x₁   |  x₂   |  x₃   |  x₄   |  x₅   |  x₆   |   RHS  
----------------------------------------------------------------------
    x₅    |   1    |   2    |   1    |   0    |   1    |   0    |   20    
    x₆    |   2    |   4    |   1    |   0    |   0    |   1    |   50    
----------------------------------------------------------------------
    -Z    |  -2    |  -5    |  -3    |   0    |   0    |   0    |   0    

The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

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Using the Big M method, the complete first simplex tableau for the given linear programming problem is constructed as follows:

┌─────────────┬──────┬───────┬───────┬─────┬─────┬─────┬─────────────┐

│     BV      │  x₁  │   x₂  │   x₃  │ s₁  │ s₂  │ a₁  │      RHS    │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│      Z      │  2   │   5   │   3   │  0  │  0  │  0  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   x₁ - 2x₂  │  1   │  -2   │   1   │ -1  │  0  │  0  │     20      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   2x₁ + 4x₂ │  2   │   4   │   1   │  0  │ -1  │  0  │     50      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₁      │  1   │   0   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₂      │  0   │   1   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₃      │  0   │   0   │   1   │  0  │  0  │ -M  │      0      │

└─────────────┴──────┴───────┴───────┴─────┴─────┴─────┴─────────────┘

The initial (artificial) basic solution is x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, a₁ = 0. The initial entering basic variable is x₁, which has the most positive coefficient in the objective row. The leaving basic variable is s₁, determined by selecting the row with the smallest positive ratio of the right-hand side (RHS) to the entering column's coefficient. In this case, the ratio for the second row (20/1) is the smallest, so s₁ leaves the basis.

To construct the complete first simplex tableau using the Big M method, we first convert the given problem into standard form by introducing slack variables (s₁, s₂) for the inequalities and an artificial variable (a₁) for the equality constraint. We assign a large positive value (M) to the coefficients of the artificial variables in the objective row.

The first row represents the objective function, where the coefficients of the decision variables x₁, x₁₂₃ are taken directly from the given problem. The slack variables and the artificial variable (a₁) have coefficients of 0 since they don't appear in the objective function.

The subsequent rows represent the constraints. Each row corresponds to one constraint, where the coefficients of the decision variables, slack variables, and the artificial variable are taken from the original problem. The right-hand side (RHS) values are also copied accordingly.

The initial (artificial) basic solution is obtained by setting the decision variables to 0, the slack variables and the artificial variable to the right-hand side values. In this case, x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, and a₁ = 0.

The initial entering basic variable is determined by selecting the most positive coefficient in the objective row, which is x₁ in this case. The leaving basic variable is determined by finding the smallest positive ratio of the RHS to the entering column's coefficient. Since the ratio for the second row (20/1) is the smallest, s₁ leaves the basis.

The resulting tableau serves as the starting point for applying the simplex method to solve the linear programming problem iteratively.

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Is it possible to find the maxima or minima for the following function? y=4x 2
Yes No QUESTION 8 Is it possible to find the maxima or minima for the following question? y=3x Yes No QUESTION 9 What is the value of y, at the maxima/minima of this function? y=−3x 2
+6x 6 −6 3 1

Answers

For the function y = 4x^2, it is possible to find the maximum or minimum. the value of y at the maxima/minima of the function y = -3x^2 + 6x is 3.

The function represents a quadratic equation with a positive coefficient (4) in front of the x^2 term. This indicates that the parabola opens upward, which means it has a minimum point.

For the function y = 3x, it is not possible to find the maximum or minimum because it represents a linear equation. Linear equations do not have maxima or minima since they have a constant slope and continue indefinitely.

For the function y = -3x^2 + 6x, we can find the maxima or minima by finding the vertex of the parabola. The vertex can be found using the formula x = -b/(2a), where a and b are coefficients of the quadratic equation.

In this case, the coefficient of x^2 is -3, and the coefficient of x is 6. Plugging these values into the formula, we have:

x = -6 / (2 * -3) = 1

To find the value of y at the vertex, we substitute x = 1 into the equation:

y = -3(1)^2 + 6(1) = -3 + 6 = 3

Therefore, the value of y at the maxima/minima of the function y = -3x^2 + 6x is 3.

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Find the 68th multiple of 89, if the 69th multiple is 6141.

Answers

Answer:

6141 - 89 = The 68th multiple (6052)

Combine the like terms to create an equivalent expression 10k + 4k

Answers

Answer:

14k

Step-by-step explanation:

add 10 and 4 because they both have k

which of the following has a graph that is a straight line (70 POINTS HURRY PLSSS)

which of the following has a graph that is a straight line (70 POINTS HURRY PLSSS)

Answers

Answer:

A answer 1

Step-by-step explanation:

that's my best guess and I'm 99.9% sure it's right. sorry if I'm wrong I wish you luck):

Answer:

A) Equation 1

Step-by-step explanation:

A) Equation 1 is representing the straight lineB) Equation 2 - square root functionC) Equation 3 - quadratic functionD) Equation 4 - cubic function

Correct choice is A

Peter set up the iron board to iron his shirt. 3 If m 3 is 65°, what is the measure of its vertical angle? OA. 155° OB. 65 OC. 25° OD. 115°​

Peter set up the iron board to iron his shirt. 3 If m 3 is 65, what is the measure of its vertical angle?

Answers

Answer:

the same  65 degrees

Step-by-step explanation:

Geometry help needed! I need the work shown! I can give brainliest when it lets me! <3

⦁ What is the length of AB, written in simplest radical form?

⦁ What is the perimeter of the triangle?

Geometry help needed! I need the work shown! I can give brainliest when it lets me! &lt;3 What is the

Answers

Answer:

length of AB = 3\(\sqrt{3}\)

perimeter = 2\(\sqrt{5}\)+3\(\sqrt{3}\)+\(\sqrt{7}\) = 12.314

Step-by-step explanation:

length \(\sqrt{(2\sqrt{5})^{2} +\sqrt{7}^{2} }\)= \(\sqrt{27}\) = \(3\sqrt{3}\)

perimeter 2\(\sqrt{5}\)+3\(\sqrt{3}\)+\(\sqrt{7}\) = 12.314

6. suppose that x is an exponential random variable with mean 1. give another random variable that is negatively correlated with x and that is also exponential with mean 1.

Answers

If we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

Let Y = 2 - X, where X is an exponential random variable with mean 1.

To show that Y is negatively correlated with X, we need to show that Cov(X,Y) < 0.

Cov(X,Y) = E[XY] - E[X]E[Y]

Since X and Y are both exponentially distributed with mean 1, we have:

E[X] = 1, E[Y] = 2 - E[X] = 1

E[XY] = E[X(2-X)] = 2E[X] - E[X^2] = 2 - Var(X)

Var(X) = E[X^2] - (E[X])^2 = 1 - 1^2 = 0

Therefore, Var(X) = 0, which means that E[XY] = 2, and Cov(X,Y) = E[XY] - E[X]E[Y] = 2 - 1*1 = 1 > 0.

Since Cov(X,Y) > 0, we know that Y is positively correlated with X. To find a random variable that is negatively correlated with X, we can use Y = 3 - X instead.

Therefore, if we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

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Twenty-four is ___% of 80

Answers

Answer:

30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

i really don't have a method for this, just try a number you think is close, go up, or down depending on the number

40= -1/3(9x+30)+2

Pls solve this in steps and explain

Answers

Answer:

-1/3 x 9x -1/3 x 30 + 2

-3x -10 +2

-3x - 8

Step-by-step explanation:

this is a distributive type of problem you distribute the -1/3 to the 9x and the 30 by distribute i mean multiply. if you dont know how to multiply this use the calculator but you multiply it by the 2 pairs of numbers in the parenthesis and then you just add the 2

Hope the answer helped!!!!!!
40= -1/3(9x+30)+2Pls solve this in steps and explain

PLEASE HELP ASAP!!!!!!!!!!!!!

PLEASE HELP ASAP!!!!!!!!!!!!!

Answers

The response is written as (x,y)

To translate means to just move.

Answer:

A. Coordinates are (-1,-1)

b. Coordinates are (-1,-2)

c. coordinates are (3,-2)

d. coordinates are (3,2)

Step-by-step explanation:

You would begin by bringing each point down 4 and to the right 5. Then plot the new points. These are your new values.

Screenshot:

PLEASE HELP ASAP!!!!!!!!!!!!!

if a test has a mean of 24 and a standard deviation of 4, what percent of students in the class would have earned a score between 20 and 28?

Answers

approximately 68% of the students in the class would have earned a score between 20 and 28.

we will be using the mean and standard deviation to determine the percentage of students who scored between 20 and 28.
The mean score of the test is 24, and the standard deviation is 4. To determine the percentage of students scoring within this range, we will apply the empirical rule, which states that in a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean
- Approximately 95% of the data falls within two standard deviations of the mean
- Approximately 99.7% of the data falls within three standard deviations of the mean
Since we want to find the percentage of students who scored between 20 and 28, we are looking at a range that is one standard deviation below and one standard deviation above the mean (24 - 4 = 20 and 24 + 4 = 28). This range represents approximately 68% of the data.

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GUYS PLEASE HELP ASAP

GUYS PLEASE HELP ASAP

Answers

Answer:

A

Step-by-step explanation:

When each input value has one and only one output value, that relation is a function.

Una compañía de renta de carros. Si renta un auto chico su cuenta se divide en dos partes: $300 por día, $2 por kilometro recorrido, supón que rentas el auto por un día. 1.- si rentas el auto por un día y recorres 50 kilómetros, ¿Cuál es el precio de renta? 2.- determina una función que relacione el precio de renta con los kilómetros recorridos 3.- Si rentas el auto por un día ¿Cuántos kilómetros podrás recorrer si deseas que el precio de renta sea de $500? 4.- La función determinada en el puntos es: A) Constante B) Lineal C) Racional D)Trascendente

Answers

Si alquilas el auto por un día y recorres 50 kilómetros, el precio del alquiler es de $400

Si rentas un auto por un día y recorres 50 kilómetros, el precio de renta será

$300 por día + $2 por kilómetro recorrido * 50 kilómetros

= $300 + $100 = $400.

La función que relaciona el precio de renta con los kilómetros recorridos se puede expresar como

P = 300 + 2K,

donde P es el precio de renta en dólares y K es la cantidad de kilómetros recorridos.

Si rentas un auto por un día y deseas que el precio de renta sea de $500, podemos utilizar la función determinada en el punto 2 para calcular la cantidad de kilómetros que puedes recorrer.

Reemplazando P = 500 en la función, tenemos

500 = 300 + 2K, entonces 200 = 2K, entonces K = 100.

Por lo tanto, puedes recorrer 100 kilómetros si deseas que el precio de renta sea de $500.

La función determinada en el punto 2 es lineal, ya que relaciona una variable dependiente (el precio de renta) con una variable independiente (los kilómetros recorridos) de manera lineal. Por lo tanto, la respuesta es is Lineal.

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Use the histogram betow to answer the following questons. a) How many people were surveyed? b) How many people purchased four soft drinks? c) What is the modal class? d) How many soft driniss were pur

Answers

a) The number of people surveyed can be determined by adding up the frequency of all the bars on the histogram. The total frequency of all the bars on the histogram is 40 + 26 + 16 + 7 + 4 + 2 + 1 = 96, which means 96 people were surveyed.

b) Looking at the bar that corresponds to a purchase of 4 soft drinks, the frequency is 7. Therefore, 7 people purchased four soft drinks.

c) The modal class is the class with the highest frequency. In this case, the class with the highest frequency is the class corresponding to a purchase of 1 soft drink. Therefore, the modal class is 0.5-1.5 soft drinks.

d) The total number of soft drinks purchased can be determined by adding up the number of soft drinks for each bar and multiplying by the frequency.

For example, for the class corresponding to a purchase of 1 soft drink, there were 1 × 40 = 40 soft drinks purchased. Similarly, for the class corresponding to a purchase of 2 soft drinks, there were 2 × 26 = 52 soft drinks purchased.

Continuing in this way, we can find the total number of soft drinks purchased to be 40 + 52 + 48 + 35 + 16 + 6 + 2 = 199. 199 soft drinks were purchased.

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The probability that a rental car will be stolen is. 4. if 3500 cars are rented, what is the approximate poisson probability that 2 or fewer will be stolen?

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Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.

What is the Poisson distribution?

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

x is the number of successese = 2.71828 is the Euler number\(\mu\) is the mean in the given interval.

The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:

\(\mu = 3500 \times 0.0004 = 1.4\)

The probability that 2 or fewer cars will be stolen is:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466\)

\(P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452\)

\(P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417\)

Then:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335\)

0.8335 = 83.35% probability that 2 or fewer will be stolen.

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