What is the independent and dependent variable in this statement, types of pizza or number of votes

The probability that in a given ten-minute interval, 15 cars arrive at the booth, and 10 of these are japanese imports = 0.0002

We know that the conditions for the Poisson distribution.

1) The occurrence of one event does not affect the probability another event will occur. i.e., the events are independent events.

2) The average rate i.e., the ratio events per time period is constant.

3) Two events cannot occur at the same time.

and the formula for the Poisson distribution is:

\(P(X = k)=\frac{e^{-\lambda}\times {\lambda}^k}{k!}\)

Here, the cars arrive at a toll booth according to a Poisson process at a rate of 3 arrivals per minute.

We need to find the probability tthat in a given ten-minute interval, 15 cars arrive at the booth, and 10 of these are japanese imports.

Here, we need to multiply the Binomial probability of 10 out of 15 cars being Japanese with the Poisson probability of 15 cars arriving in a 10 minute period.

The Binomial probability of 10 out of 15 cars would be:

P₁(x = 10) = ¹⁵C₁₀ (0.6)¹⁰ (0.4)¹⁵⁻¹⁰

P₁ = 0.18594

And the Poisson probability of 15 cars arriving in a 10 minute period.

So we use λ = 30.

P₂(X = 15) = \(\frac{e^{-30}\times {30}^{15}}{15!}\)

P₂ = 0.0010

So, the required probability would be:

P = P₁ × P₂

P =  0.18594 ×  0.001

P = 0.00018594

P= 0.0002

Therefore, the required probability is 0.0002

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The complete question is:

Cars arrive at a toll booth according to a Poisson process at a rate of 3 arrivals per minute.

b) Of the cars arriving at the both, it is known that over the long run 60% are Japanese imports. What is the probability that in a given ten-minute interval. 15 cars arrive at the booth, and 10 of these are Japanese imports? State your assumptions clearly.

The perimeter be 410 then the maximum area be \($A=\left(\frac{410-3 x}{2}\right) * x$$\).

A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.

Let the perimeter be p = 410

The perimeter of the fence is:

p = 2(x + y + 5 + y) + x

p = 2x + 2y + 10 + 2y + x

Collect like terms

p = 2x + x + 2y + 2y + 10

p = 3x + 4y + 10

Where, p = 410, then

3x + 4y + 10 = 410

\($$\begin{aligned}& 4 y=410-10-3 x \\& 4 y=400-3 x\end{aligned}$$\)

simplifying the equation, we get

\($y=\frac{400-3 x}{4}$$\)

The area (A) of the fence is:

\($$\begin{aligned}& A=(y+y+5) * x \\& A=(2 y+5) * x\end{aligned}$$\)

Substitute: \($y=\frac{400-3 x}{4}$\)

\($$\begin{aligned}& A=\left(2 * \frac{400-3 x}{4}+5\right) * x \\& A=\left(\frac{400-3 x}{2}+5\right) * x\end{aligned}$$\)

simplifying the equation, we get

\($A=\left(\frac{400-3 x+10}{2}\right) * x$$\)

\($A=\left(\frac{410-3 x}{2}\right) * x$$\)

\($A=\frac{410 x-3 x^2}{2}$$\)

A = 205x - 1.5 x²

Differentiate both sides, we get

A' = 205-3 x

simplifying the equation, we get

205 - 3x = 0

3x = 205

Therefore, the maximum area be \($A=\left(\frac{410-3 x}{2}\right) * x$$\).

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The relationship between the ratios of sin x° and cos yº is that they are reciprocals. The correct answer is option c. The ratios of sin x° and cos yº are reciprocals of each other.

In trigonometry, sin x° represents the ratio of the length of the side opposite the angle x° to the length of the hypotenuse in a right triangle. Similarly, cos yº represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Since the hypotenuse is the same in both cases, the ratios sin x° and cos yº are related as reciprocals. This means that if sin x° is equal to 12/13, then cos yº will be equal to 13/12. The reciprocals of the ratios have an inverse relationship, where the numerator of one ratio becomes the denominator of the other and vice versa.

It's important to note that the signs of the ratios can vary depending on the quadrant in which the angles x° and yº are located. However, the reciprocal relationship remains the same regardless of the signs.

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Step-by-step explanation:

(a)→ Given numbers are 7/-13 and -8/15

LCM of 13 and 15 = 195

7/-13

= -7/13

= (-7/13)×(15/15)

= (-7×15)/(13×15)

= -105/195

and

-8/15

= (-8/15)×(13/13)

= (-8×13)/(15×13)

⇛ -104/195

So,

-105/195 < -104/195

-7/13 < -8/15

(b)→ Given numbers are 5/8 and -9/14

We know that

Negative numbers are always less than positive numbers

5/8 > -9/14

(c).→Given numbers are -11/16 and 13/-16 = -13/16

-11/16 >-13/16

(d)→Given numbers are -9/-13 = 9/13 and

36/52 = 9/13

Both are same

-9/-13 = 36/52

Answer:65miles

Step-by-step explanation:

Let the needed miles be x

(67+62+59+47+x)/5=60

235+x=60×5

235+x=300

x=300-235

x=65miles

Answer:

B

Step-by-step explanation:

The equation is

y<=-x+1.

We test all and figure that B is correct.

-2<=-3+1

-2<=-2.

Correct!

So the answer is B

Hope this helps ;D

Answer:

Step-by-step explanation:

the answer is bee

Answer:

Step-by-step explanation:

In order to be 98% confident that the proportion of women wearing shoes that are too small for their feet is within 3 percentage points of the true proportion, a sample size needs to be determined.

To determine the necessary sample size, we can use the formula for sample size calculation in estimating proportions. The formula is:

n = (Z^2 * p * q) / E^2

Where:

- n is the required sample size

- Z is the Z-score corresponding to the desired level of confidence (98% confidence corresponds to a Z-score of approximately 2.33)

- p is the estimated proportion (in this case, it is 0.80)

- q is 1 - p (the complement of the estimated proportion)

- E is the desired margin of error (in this case, it is 0.03)

Substituting the values into the formula:

n = (2.33^2 * 0.80 * 0.20) / 0.03^2

Calculating this expression gives us the required sample size. Rounding up to the nearest whole number, the sample size necessary to achieve the desired confidence level and margin of error is approximately 682. Therefore, a sample size of at least 682 women would be needed to meet the specified requirements.

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Answer:  The slope-intercept form is y = -2x + 10

Step-by-step explanation:

Step 1: The y-intercept is the point where x=0, so that is (0,10)

Step 2: Use the points (-2,14) and (-1,12) to find the slope

Slope (m) = ΔY/ΔX = -2/1 = -2

Step 3: The slope-intercept form is:

y = mx+b

y = (step 2 value) x + (step 1 value)

y = -2x+10

Please remember to vote this as Brainliest if I earned it!

Answer:

y-intercept: 5

slope: -1

equation: y = -x + 5

Step-by-step explanation:

The y-intercept is when x is 0, and it is shown on the table as 5.

The slope can be found by doing \(y_1-y_2/x_1-x_2\), which is 6-5/-1-0 = 1/-1 = -1.

The equation is y = mx + b, so we can write it as y = -x + 5

The number that is not equal to the others is d.

a. 0.84% is equal to 0.0084 in decimal form.

b. (0.21)(0.04) is equal to 0.0084.

c. 8.4 * \(10^-^2\) is equal to 0.084. This is the same as 8.4 divided by 100, which is 0.084.

d. This is the number that is not equal to the others. We don't have the value of d.

e. 21/25 * \(10^-^2\) is equal to 0.0084. When we divide 21 by 25 and multiply the result by \(10^-^2\), we get 0.0084.

To summarize, all of the given numbers (a, b, c, and e) are equal to 0.0084 except for d, which doesn't have a specified value. Therefore, d is the number that is not equal to the others.

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red: y = 4.

black: y = -2x + 4.

blue: x = -4.

green: y = x - 1.

Answer:

D. 29

Step-by-step explanation:

just did the test and got it correct. Edmentum, Plato.

Answer:

8x^3y

Step-by-step explanation:

The area of a rectangle is length * width.

area = 4x^2y * 2x =

= 4 * 2 * x^2 * x * y

area = 8x^3y

Answer:

First Problem. 17x , 17 + x, and 7x + 10x

Second Problem. 2 + 12y, 2x1 + 2x6y

Step-by-step explanation:

Given:

The mass function is:

\(m(v)=4.5v\)

where v is the volume in cubic centimeters.

The force function is:

\(F(m)=800m\)

To find:

The composite function can be used to find the force of the object based on its volume.

Solution:

The composite function can be used to find the force of the object based on its volume is:

\(F(m(v))=F(4.5v)\)              \([\because m(v)=4.5v]\)

\(F(m(v))=800(4.5v)\)              \([\because F(m)=800m]\)

\(F(m(v))=3600v\)

Therefore, the correct option is D.

Answer: F(m(v)) = 3,600v

Step-by-step explanation:DDDD

Answer:

3

Step-by-step explanation:

I'm sure if that shoe fits

Answer:

All 3

Step-by-step explanation:

Brainliest please

Answer:

Not sure, is there a problem or only the rant? lol. I'd appreciate my first brainliest though.

Step-by-step explanation:

The indefinite integral of (53 + 8/7) dx is (53 + 8/7)x + C. To evaluate the definite integral ∫[(+5x – 5) dx] over the interval [a, b], we need to substitute the limits of integration into the antiderivative and calculate the difference.

Let's find the antiderivative of the integrand (+5x – 5):

∫[(+5x – 5) dx] =\((5/2)x^2 - 5x + C\)

Now, let's substitute the limits of integration [a, b] into the antiderivative:

∫[(+5x – 5) dx] evaluated from a to b =\([(5/2)b^2 - 5b] - [(5/2)a^2 - 5a]\)

=\((5/2)b^2 - 5b - (5/2)a^2 + 5a\)

Therefore, the value of the definite integral ∫[(+5x – 5) dx] over the interval [a, b] is \((5/2)b^2 - 5b - (5/2)a^2 + 5a.\)

To solve the integral ∫[-5(ln(x))] dx using integration by substitution, let's perform the substitution u = ln(x).

Taking the derivative of u with respect to x, we have:

\(du/dx = 1/x\)

Rearranging, we get dx = x du.

Substituting these into the integral, we have:

∫[-5(ln(x))] dx = ∫[-5u] (x du) = -5 ∫u du \(= -5(u^2/2) + C = -5(ln^2(x)/2) + C\)

Therefore, the indefinite integral of -5(ln(x)) dx is \(-5(ln^2(x)/2) + C.\)

The indefinite integral of (53 + 8/7) dx can be evaluated as follows:

∫[(53 + 8/7) dx] = 53x + (8/7)x + C = (53 + 8/7)x + C

Therefore, the indefinite integral of (53 + 8/7) dx is (53 + 8/7)x + C.

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To find the total differential of the function w = e^y * cos(x) * z^2, we can take the partial derivatives with respect to each variable (x, y, and z) and multiply them by the corresponding differentials (dx, dy, and dz).

The total differential can be expressed as:

dw = (∂w/∂x) dx + (∂w/∂y) dy + (∂w/∂z) dz

Let's calculate the partial derivatives:

∂w/∂x =   \(-e^{y} * sin(x) * z^{2}\)

∂w/∂y =  \(e^{y} * cos(x) * z^{2}\)

∂w/∂z =  \(2e^{y} *cos (x)* z\)

Now, let's substitute these partial derivatives into the total differential expression:

\(dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y}* cos(x) * z^{2} ) dy + 2e^{y} *cos (x)*z) dz\)

Therefore, the total differential of the function w = e^y * cos(x) * z^2 is given by:

\(dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y} * cos(x) * z^{2} ) dy + ( 2e^{y} * cos(x) * z) dz\)

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Answer:

hope this helped :D

Step-by-step explanation:

-3x + 7 = -2

-3x + 7 - 7 = -2 -7

-3x = -9

-3x divided by -3 = -9 divided by -3

x= 3

Answer:

3

Step-by-step explanation:

Step 1:

- 3x + 7 = - 2       Equation

Step 2:

- 3x = - 9           Subtract 7 on both sides

Step 3:

x = - 9 ÷ - 3        Divide

Answer:

x = 3

Hope This Helps :)

after following the sequence "I walk 6 steps at a rate of 1 step per second then stand still for 4 seconds then turn around and walk back at a rate of 2 steps per second," you will end up back at your starting point having walked a total of 6 steps forward and 6 steps backward. The entire process will take a total of 6 seconds for the initial forward walk, 4 seconds of standing still, and 3 seconds for the walk back, which adds up to 13 seconds in total.

Based on the information provided, you walk 6 steps at a rate of 1 step per second, then stand still for 4 seconds, and finally turn around and walk back at a rate of 2 steps per second.

Let's break this down step by step:

1. Walking 6 steps at a rate of 1 step per second:
  - Since you are walking at a rate of 1 step per second, it will take you 6 seconds to complete the 6 steps. This is because 1 step per second multiplied by 6 seconds equals 6 steps.
  - Therefore, during this time, you will have walked a total of 6 steps.

2. Standing still for 4 seconds:
  - Since you are standing still, you won't be taking any steps during these 4 seconds.
  - Therefore, the number of steps you will have taken remains at 6.

3. Walking back at a rate of 2 steps per second:
  - Now, you are walking back at a rate of 2 steps per second.
  - Since you walked a total of 6 steps in the previous step, it will take half the time to walk back, as the rate is now double.
  - So, it will take you 3 seconds to complete the 6 steps back to your starting point.

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Step-by-step explanation:

Simply input 3 for x in the equation.

\(x^{3} -2x^2+3x-12\\(3)^{3} -2(3)^2+3(3)-12\\27-18+9-12\\Final answer = 6\)

Answer:

Answer is 2

Step-by-step explanation:

F(x)=x3-2X2+3x-12

F(3)=3X3-2X2+3X3-12

=9-4+9-12

=18-4-12

=18-16

=2

I Hope you Understood

Using proportions, it is found that the scale of dilation is of \(\frac{3}{4}\).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The length of LM changed from 12 to 9, hence:

\(\frac{9}{12} = \frac{3}{4}\).

The length of MN changed from 8 to 6, hence:

\(\frac{6}{8} = \frac{3}{4}\).

Thus, the scale of dilation is of \(\frac{3}{4}\).

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The system of equations that satisfies the solution (3, -4) is:

4x + 1y = 8

2x - 3y = -17

To create a system of equations where the solution is (3, -4), we can assign arbitrary values to the coefficients of the equations. Let's use the following values:

Equation 1: 4x + 1y = 8

Equation 2: 2x - 3y = -17

By plugging in the values (3, -4) into these equations, we can find the missing coefficients:

Equation 1: 4(3) + 1(-4) = 12 - 4 = 8

Equation 2: 2(3) - 3(-4) = 6 + 12 = 18 - 17 = -17

Therefore, the system of equations that satisfies the solution (3, -4) is:

4x + 1y = 8

2x - 3y = -17

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In this case, Christopher divides the athletes into groups of varsity and junior varsity, which creates the strata. The type of sampling used in this scenario is stratified sampling.

Stratified sampling is a sampling method where the population is divided into homogeneous subgroups or strata, and individuals are randomly selected from each stratum in proportion to their representation in the population. In this case, Christopher divides the athletes into groups of varsity and junior varsity, which creates the strata.

By randomly selecting a proportionate number of individuals from each group, Christopher ensures that both varsity and junior varsity athletes are represented in the sample, maintaining the proportional representation of each group in the population. This method allows for more accurate and representative results by capturing the characteristics of both groups separately.


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The line of the equation should be y = 20x + 320 and travelers will spend about $620 billion in the year 2008. So, the option c is correct.

In the given question, we have to write an equation for the line of best fit and then predict how much money travelers will spend in 2008.

The graph of the question is given below:

From the graph the points are (1.5, 350) and (4, 400)

As we know that the formula of the equation of line is:

y-y(1) = {y(2)-y(1)}/{x(2)-x(1)} (x-x(1))

x(1) = 1.5, y(1) = 350, x(2) = 4 and y(2) = 400

Now putting the values

y-350 = (400-350)/(4-1.5) (x-1.5)

y-350 = 50/2.5 (x-1.5)

y-350 = 20(x-1.5)

y-350 = 20x-30

Add 350 on both side, we get

y = 20x + 320

So, the line of the equation should be y = 20x + 320.

So that travelers will spend about $620 billion in the year 2008.

Hence, the option c is correct.

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The values in the difference are interpreted as:

option (c): A positive difference means that the commute by public transportation takes longer, and a negative difference means that the commute by car takes longer.

What is meant by the difference between the two values?

Finding the difference between two numbers is a type of subtraction. Subtract the smaller of the two numbers from the larger of the two numbers to find the difference between them. The difference between the two numbers is the sum's product. It is not necessarily positive when two positive rational numbers differ from one another. The sequence in which the numbers are subtracted will affect the result as subtraction is not a commutative feature.

Let us look at the table.

For the 1st employee,

The time taken by car = 20 minutes

The time is taken by public transportation = 25 minutes

Difference = 25 - 20 = 5 minutes

So the difference is obtained when the time taken by car is subtracted from the time taken by public transportation.

Now the difference is positive because the time taken by public transportation is more.

A negative difference is obtained when the time taken by the car is more.

Therefore the values in the difference are interpreted as:

option (c): A positive difference means that the commute by public transportation takes longer, and a negative difference means that the commute by car takes longer.

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Answer:

In general, the number of valence electrons is the same within a column and increases from left to right within a row. Group 1 elements have just one valence electron and group 18 elements have eight, except for helium, which has only two electrons total.

Step-by-step explanation: