Find the expected​ frequency,
Ei​,
for the given values of n and
pi.
n=170​,
pi=0.21

To find the PDF (Probability Density Function) of the duration of the trip, we need to determine the distribution of the speed and calculate the corresponding duration.

Given that the speed of John Slow is uniformly distributed between 30 and 60 miles per hour, we have a continuous uniform distribution over this interval.

The duration of the trip can be calculated by dividing the distance (180 miles) by the speed (v) since speed = distance/time, rearranging the equation gives time = distance/speed.

Let's denote the duration of the trip as T. We can express T in terms of the speed (v) as follows:

T = 180 miles / v

To find the PDF of T, we need to determine the probability density function of v. Since v is uniformly distributed between 30 and 60 mph, its PDF is a constant over this interval.

The width of the interval is (60 - 30) = 30 mph, and since it is a uniform distribution, the height of the PDF is 1/30 mph^(-1) to ensure the total area under the PDF equals 1.

Therefore, the PDF of T is given by:

PDF(T) = PDF(v) * |dt/dv|

Since v = 180/T, we can differentiate this equation with respect to T to find |dt/dv|:

|dt/dv| = |-180/T²|

Substituting the PDF of v and |dt/dv| into the PDF of T:

PDF(T) = (1/30 mph^(-1)) * |-180/T²|

Simplifying further, we have:

PDF(T) = 6/T² mph^(-1)

Therefore, the PDF of the duration of the trip is 6/T² mph^(-1).

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Answer:

a

Step-by-step explanation:

Answer:  B. False, the solution set is Ø.

Explanation:

If the elimination method leads to 0 = -2, then that's a false statement. This then has a chain reaction to cause the original system to be inconsistent, meaning there aren't any solutions.

We consider the solution set to be the empty set, denoted with the special symbol of Ø which unfortunately looks like the number 0, but they're different symbols.

Perhaps better notation is to write a pair of curly braces with nothing inside them. So you'd write {   }  to indicate the empty set.

Answer:

Below!

Step-by step explanation:

We know that:

Solution of Question A:

Percent of children: Total children/Total attendance

Hence, the percent of children is about 27%.

Solution of Question B:

Percent of women: Total women/Total attendance

Hence, the percent of women is 56.67%.

Solution of Question C:

Percent of men: Total men/Total attendance

Hence, the percent of men is about 17%

Hoped this helped.

\(BrainiacUser1357\)

Answer:

its b

Step-by-step explanation:

18 times 20 = 360 and  subtract 6 = 354.

The approximate length of each side of the box is 18 inch.

The distance between the center of the sphere and any plane passing through it is known as the circumference. Any large circle that passes through a point known as a pole is called a meridian. The shortest path between any two points on a sphere called a geodesic. The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.

The circumference of a circle or other curved geometric object refers to its length. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.

Given,

Circumference of circle = 56.5

c = π diameter

diameter = 3.14 × 56.5

diameter = 18

The approximate length of each side of the box is 18 inch.

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The standard deviation of the given data can be calculated using the formula for the population standard deviation:

Standard deviation = √[∑(X - μ)² * f / N]

where X is the data value, μ is the mean, f is the frequency, and N is the total number of observations.

Given the data:

X: 3 4 5 6 7 8 9

f: 37 8 10 12 4 3 2

Assumed mean (μ) = 6

To calculate the standard deviation, we need to calculate the squared difference between each data value and the mean, multiply it by the frequency, and sum up these values. Then divide the sum by the total number of observations (N) and take the square root of the result.

Let's calculate it step by step:

(X - μ)² * f:

(3 - 6)² * 37 = 111

(4 - 6)² * 8 = 32

(5 - 6)² * 10 = 10

(6 - 6)² * 12 = 0

(7 - 6)² * 4 = 4

(8 - 6)² * 3 = 12

(9 - 6)² * 2 = 18

Sum of (X - μ)² * f = 187

Now divide the sum by the total number of observations (N = 37 + 8 + 10 + 12 + 4 + 3 + 2 = 76) and take the square root of the result:

Standard deviation = √(187 / 76) ≈ 1.82

Therefore, the standard deviation of the given data is approximately 1.82.

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Answer:634/8= 79.25

Step-by-step explanation:

Answer:

79 R 2

Step-by-step explanation:

I think maybe not but I dunno

Explanation:

Concept:

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

Hence,

From the graph below,

We can see that the graph cuts the x-axis at two points

Therefore,

The zeroes of the graph are

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

(a)The optimal order quantity is  4609 units.

(b)The time between orders is  1.98 months.

To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.

Optimal Order Quantity:

The formula for the EOQ is given by:

EOQ = √[(2DS) / H]

Where:

D = Annual demand

S = Cost per order

H = Holding cost per unit per year

calculate the annual demand (D) using the 2020

sales numbers provided:

D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774

= 9559 units

To calculate the cost per order (S) and the holding cost per unit per year (H).

The cost per order (S) is given as $500.

The holding cost per unit per year (H)  calculated as follows:

H = Carrying cost percentage × Unit value

= 0.30 × $3

= $0.90

substitute these values into the EOQ formula:

EOQ = √[(2 × 9559 × $500) / $0.90]

= √[19118000 / $0.90]

≈ √21242222.22

≈ 4608.71

Approximate Time Between Orders:

To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.

Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:

Working days in a year = 360 - 7 = 353 days

Approximate time between orders = Working days in a year / Number of orders per year

= 353 / (9559 / 4609)

= 0.165 years

Converting this time to months:

Approximate time between orders (months) = 0.165 × 12

= 1.98 months

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For a relative frequency table by rows 4-column table with 2 rows about the breakfast choices of boys and girls. The conclusion is of table is represented by option(b).

We have provided the following information about relative frequency table by rows, tables by row, 4 columns and 2 rows.

Now, we represent the above information into tabular form,

Eat cereal do not eat cereal Total

boys 68.3% 31.7% 100%

girls 69.1% 30.9% 100%

Now, we have to draw conclusion about the relative frequency of these results. From the table, the percentage of girls and boys who eat cereal is exceed from the not. Thus, we cannot say if a person eat cereal for breakfast, then he is a boy. Similarly we cannot know about gender of a person by eats cereal. The right conclusion is that if i am a girl in this group, i am more likely to eat cereal for breakfast than not. Hence, required option is option (b).

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Complete question:

relative frequency table by rows 4-column table with 2 rows. column 1 has entries boys, girls. column 2 is labeled eat cereal with entries 68.3 percent, 69.1 percent. column 3 is labeled do not eat cereal with entries 31.7 percent, 30.9 percent. column 4 is labeled total with entries 100 percent, 100 percent. What conclusion can you draw about the relative frequency of these results?

a) If you are a boy in this group, you are more likely not to eat cereal for breakfast than to eat cereal.

b) If you are a girl in this group, you are more likely to eat cereal for breakfast than not.

c) If you eat cereal for breakfast, you are a boy.

d) Knowing if a person eats cereal will help determine gender.

Answer:

B. If you are a girl in this group, you are more likely to eat cereal for breakfast than not.

Step-by-step explanation:

Edge 2023

Katy's house is about 8.1 miles from Camilla's house, measured in a straight line.

we apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we have:

H^2 = west distance^2 + north distance^2

H^2 = 4.6^2 + 6.7^2

H^2 = 21.16 + 44.89

He^2 = 66.05

We take the square root of both sides, we get:

hypotenuse = 8.13

We then can say that  Katy's house is about 8.1 miles from Camilla's house, measured in a straight line.

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Answer:  13

Step-by-step explanation:

See attached graph.

A third point (18,20) may be added to the two given points to form a right triangle with sides 5 and 12.  The distance, x, between the original two points is given by x^2 = 5^2 + 12^2

x^2 = 25 + 144

X^2 = 169

x = 13

The Laplace transform of the given differential equation yields Y(s) = (2 + 4s) / (2s^3 + 6s^2 + 9s). The solution y(t) will contain exponential functions of the form e^(αt) * cos(βt) and e^(αt) * sin(βt) due to the complex roots of the denominator of Y(s). The solution y(t) is obtained by inverse Laplace transforming Y(s) = (s(s^2 + 4s + 8))/(2s + 1), resulting in y(t) = -1 + 2e^(-t/2) + te^(-t/2).

a. To derive Y(s), we take the Laplace transform of the given differential equation. The Laplace transform of a function f(t) is defined as:

Taking the Laplace transform of the differential equation, we have:

Using the linearity property of the Laplace transform, we split it into three separate transforms:

Taking the Laplace transforms of the derivatives and the cosine function:

Substituting the initial conditions y(0) = 0 and dy/dt(0) = 2:

Rearranging the terms:

Multiplying through by s to eliminate the fraction:

Now, solving for Y(s):

b. To determine what functions of time will appear in the solution y(t) without solving for y(t), we find the roots of the denominator of Y(s).

We factor the denominator:

The quadratic term, 2s^2 + 6s + 9, has no real roots since the discriminant is negative. Therefore, the functions of time that will appear in the solution y(t) are exponential functions of the form e^(αt) * cos(βt) and e^(αt) * sin(βt), where α and β are complex numbers.

c. Let Y(s) = (s(s^2 + 4s + 8))/(2s + 1).

We rewrite Y(s) as:

Now, we use partial fraction decomposition to separate Y(s) into simpler fractions:

Multiplying both sides by the common denominator:

Expanding and equating coefficients:

Matching the coefficients of like powers of s:

s^3: 1 = 4A + 2B + C

s^2: 4 = 4A + 2B + C

s^1: 4 = A + 5B + 4C

s^0: 0 = A + 2B + 4C

Solving the system of equations, we find A = -1, B = 2, and C = 1.

Therefore, Y(s) can be expressed as:

Now, we take the inverse Laplace transform of Y(s) to find y(t):

Using the properties of the inverse Laplace transform, we obtain:

Therefore, the solution to the differential equation with the given initial conditions is:

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Answer:

Part A - Angle d is 29º

Part B - Angle e is 61º

Part C - Angle f is 95º

Part D - the box represents a 90º angle

Step-by-step explanation:

Angle d is 29º because of the vertical angles theorem

Angle e is 61º because if you take into account that it tells you one of the angles is 90º, you'll add d, which is 29º, to that in order to get 119. Then you'll subtract 119 from 180, as all the angles in a triangle must have a sum of 180º degrees. The result should be 61º

Although it looks rather acute, f should be 95 degrees because it's a supplementary angle with 85º, meaning you subtract 85 from 180

The box in the triangle is just a symbol indicating a 90º angle

Answer:

3

Step-by-step explanation:

The graph that has the slope that best represents the unit rate of 4 miles per hour is: graph B.

For any proportional relationship, we can find the slope of the graph by using any point on the line of the graph. The slope of the graph is also the unit rate, Therefore, picking a point on the line, (x, y), we have:

Slope (m) = y/x.

Number of miles Tyrell walks (y) = 12 miles

Time spent working (x) = 3 hours

The unit rate or slope = y/x = 12/3

Slope/unit rate (m) = 4 miles per hour.

From the graphs given, only graph B has the same unit rate/slope as 4, when we use the point, (5, 20).

Slope of graph B = 20/5 = 4.

Therefore, the graph that has the slope that best represents the unit rate of 4 miles per hour is: graph B.

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Answer:

\(\frac{3}{8}\)

Step-by-step explanation:

Possibilities (G for girls and B for boys):

GGG

GGB

GBG

GBB

BGG

BGB

BBG

BBB

Answer:

1/4

Step-by-step explanation:

There are a total of four possibilities,

- Three girls

- Three boys

- Two girls and One boy

- Two boys and One girl

and only one of those options are 2 boys and 1 girl

Answer:

\(x\leq 1\)

Alternative forms:

\(x\in\left(-\infty,\left.\ 1\right]\right.\)

Step-by-step explanation:

\(-3(x+1)\geq -6\)

Apply the Distributive Property

\(-3x-3\geq -6\)

Rearrange variables to the left side of the equation

\(-3x\geq -6+3\)

Calculate the sum or difference

\(-3x\geq -3\)

Divide both sides of the inequality by the coefficient of variable

\(x\leq \frac{-3}{-3}\)

Determine the sign for multiplication or division

\(x\leq \frac{3}{3}\)

Cross out the common factor

\(x\leq 1\)

I hope this helps you

:)

wait

am writing answer Step-by-step explanation:

Answer:

23 miles per gallon

Step-by-step explanation:

92/4=23

Answer and Step-by-step explanation:

Ok, so all we have to do is input the values into the equation.

We are told Adam bought 2 mechanical pencils and 8 spiral notebooks, which cost $13

and that

Kia bought 3 mechanical pencils and 5 spiral notebooks, which cost $12.50.

Adam: 2p + 8n = 13

Kia:     3p + 5n = 12.5

This is the answer.

#teamtrees #WAP (Water And Plant)

Answer: Adam: 2p + 8n = 13

Kia:     3p + 5n = 12.5

Step-by-step explanation:

Answer:

13n^2 + 2n + 7

Step-by-step explanation:

(6+8n2−9n) + (1+5n2+11n)

6+8n2−9n + 1+5n2+11n

7 + 13n^2 - 9n + 11n

7 + 13n^2 + 2n

In Standard Form

13n^2 + 2n + 7

The quotient of (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1) is 2x² + x – 3.

A quotient is a quantity produced by the division of two numbers.

The quotient is most frequently encountered as two numbers, or two variables, divided by a horizontal line. The words "dividend" and "divisor" refer to each individual part, while the word "quotient" refers to the whole.

For example when 8 is divided by 2, the result obtained is 3. Thus, the quotient is 4.

To determine the quotient when (2x4 – 3x3 – 3x2 + 7x - 3) is divided by (x2 - 2x + 1), we'll apply the long division method as shown below:

              2x² + x – 3

x² - 2x + 1|2x⁴ – 3x² – 3x² + 7x - 3

              –(2x⁴ – 2x³ + 2x²)

                 x³ – 5x² + 7x – 3

              –(x³ – 2x² + x)

             –3x² + 6x – 3

            –(3x² + 6x – 3)

                    0

Thus, the quotient is 2x² + x – 3.

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Answer:

shshjshshsbs

Step-by-step explanation:

shzjshsjjsisjs

If 64 to the x equals 9, then 8 to the x equals 3.

This can be solved by using the rules of logarithms.

First, we can rewrite the equation 64 to the x equals 9 as log64⁹ = x.

Next, we can use the rule of logarithms that states \(log_ab = \frac{log_cb}{log_ca}\).

Using this rule, we can rewrite the equation as log₈9 / log₈64 = x.

Simplifying the equation, we get log₈9 / 2 = x.

Finally, we can use the rule of logarithms that states alogₐb = b to rewrite the equation as 8log₈9 / 2 = 8ˣ.

Simplifying the equation, we get 3 = 8ˣ.

Therefore, if 64 to the x equals 9, then 8 to the x equals 3.

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Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).

A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.

By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).

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Answer:

10 sides,that is, a decagon or 10gon

Step-by-step explanation:

If the exterior angle is 36° then numbers of sides=

\(36 = \frac{360}{n} \)

Therefore

n=360°÷36°=10

Answer:

Step-by-step explanation:

The sum of the measures of the exterior angles in a convex polygon is 360°.And each exterior angle measure 36 degrees so Number of side will be 10.

360 : 36 = 10