The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes. nothing ​(Simplify your answer. Round to three decimal places as​ needed.)

Answer:

m∠A = 9°

Step-by-step explanation:

\( \sin 7A = \cos 3A \\ \\ \sin 7A = \sin(90 \degree - 3A) \\ \\ 7A = 90 \degree - 3A\\ \\ 7A + 3A= 90 \degree \\ \\ 10A= 90 \degree \\ \\ A = \frac{90 \degree}{10} \\ \\ m \angle A =9 \degree\)

Willard should interpret the 95% prediction interval for percent potassium when nitrogen is 18 ppm as a range of values within which the true value of percent potassium is likely to fall with a 95% probability.

Specifically, the prediction interval (0.87%, 1.02%) suggests that if Willard were to measure the percent potassium in a large number of soil samples with a nitrogen level of 18 ppm and calculate the prediction interval for each sample, then 95% of the prediction intervals would contain the true value of percent potassium.

The lower and upper limits of the prediction interval correspond to the lower and upper bounds of the plausible range for percent potassium, given the observed nitrogen level. In this case, the interval (0.87%, 1.02%) indicates that Willard can be 95% confident that the true value of percent potassium for a soil sample with nitrogen level 18 ppm falls between 0.87% and 1.02%. However, it is important to note that the prediction interval is based on statistical assumptions and may not capture all sources of uncertainty or variability in the data. Therefore, it is important to interpret the prediction interval with caution and in the context of the specific statistical model and assumptions used to derive it.

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Answer:

O y = -5x + 7

Step-by-step explanation:

\(5x + y = -2 \\y = -5x - 2\)

the slope of this line is -5 so the slope of a parallel line will also have to be -5

put it in point slope form:

y - - 3 = -5(x - 2)

y + 3 = -5x + 10

y = -5x + 7

42 adult tickets and 421 children tickets were purchased for the field trip, based on the given information that the total cost of the tickets was $995 and the children tickets cost $11 while the adult tickets cost $13, and the number of children tickets purchased was one more than ten times the number of adults tickets purchased.

Let's use variables to represent the unknown quantities in the problem:

Let x be the number of adult tickets purchased

Then the number of children tickets purchased is 10x + 1 (since it is one more than ten times the number of adults tickets purchased)

Using these variables, we can set up an equation based on the total cost of the tickets:

13x + 11(10x + 1) = 995

Simplifying and solving for x, we get:

23x + 11 = 995

23x = 984

x = 42.7826087 (rounded to 9 decimal places)

Since we can't purchase a fraction of a ticket, we'll round x down to the nearest whole number, which means 42 adult tickets were purchased. Then the number of children tickets purchased is:

10x + 1 = 10(42) + 1 = 421

So, 42 adult tickets and 421 children tickets were purchased.

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Answer:

numerator is 1

denominator is 25

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The mass of water vapor (g) / mass of dry air (kg) is the humidity measure of  the mixing ratio

The mixing ratio is defined as the mass of water vapor in grams divided by the mass of dry air in kilograms in a mixture of air and water vapor. It is a useful parameter for meteorologists and atmospheric scientists to describe the amount of water vapor in the atmosphere, particularly in the upper atmosphere where the relative humidity may be very low.

Relative humidity is the ratio of the partial pressure of water vapor in the air to the equilibrium vapor pressure at a given temperature and pressure, expressed as a percentage. Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. Absolute humidity is the mass of water vapor per unit volume of moist air.

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Answer:

27mph

Step-by-step explanation:

Let's assume the speed of the first car is x mph. Since the second car is traveling 6 mph slower, its speed would be (x - 6) mph.

To find out how far each car has traveled, we can use the formula: distance = speed × time.

For the first car:

Distance traveled by the first car = speed of the first car × time

d₁ = x mph × (4 hours + 20 minutes)

Since we need to work with a single unit of time, let's convert 20 minutes to hours:

20 minutes = 20/60 = 1/3 hours

Substituting the values:

d₁ = x mph × (4 + 1/3) hours

d₁ = x mph × (13/3) hours

d₁ = (13x/3) miles

For the second car:

Distance traveled by the second car = speed of the second car × time

d₂ = (x - 6) mph × (4 hours + 20 minutes)

d₂ = (x - 6) mph × (13/3) hours

d₂ = (13/3)(x - 6) miles

Since they are traveling in opposite directions, the sum of their distances is equal to the total distance between them:

d₁ + d₂ = 260 miles

Substituting the expressions for d₁ and d₂:

(13x/3) + (13/3)(x - 6) = 260

To simplify the equation, let's multiply both sides by 3 to get rid of the denominators:

13x + 13(x - 6) = 780

13x + 13x - 78 = 780

26x - 78 = 780

26x = 780 + 78

26x = 858

x = 858/26

x ≈ 33

The speed of the first car is approximately 33 mph. Substituting this value back into the equation for the speed of the second car:

Speed of the second car = x - 6 ≈ 33 - 6 ≈ 27 mph

Therefore, the first car is traveling at approximately 33 mph, and the second car is traveling at approximately 27 mph.

The distance between the planes after 20 minutes = 15496.8

What is Distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

1st planes = 570mph at a bearing of s 62e plane

2nd planes = 525 mph at a bearing of n 18e plane

Coverting 20 minutes into hour = 0.3333 hours

speed of 1st plane = 570mph

Distance travelled by plane after 0.3333 hours= 570*0.3333 hours

= 189.981

speed of 2st plane = 525mph

Distance travelled by plane after 0.3333 hours= 525*0.3333 hours

= 174.982

Angle made by both plane between their is 62 + 18 = 80° ≅ 90°

Distance between both the planes

= \(\sqrt{(189.981)^{2} + (174.982)^{2} }\)

= \(\sqrt{36092.78 + 30618.700}\)

= \(\sqrt{66711.48}\)

= 258.28 hours

Converting hours into minutes

=15496.8

The distance between the planes after 20 minutes = 15496.8

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Given:

Side lengths of triangle are (6.2v-5.5) cm, (8.5v-6.7) cm, and (6.6w+7.6) cm.

To find:

The expression which represents the perimeter of the given triangle.

Solution:

We know that perimeter of a triangle is the sum of all sides of a triangle. So,

\(Perimeter=(6.2v-5.5)+(8.5v-6.7)+(6.6w+7.6)\)

On combining like terms, we get

\(Perimeter=(6.2v+8.5v)+6.6w+(-5.5-6.7+7.6)\)

\(Perimeter=14.7v+6.6w+(-4.6)\)

\(Perimeter=14.7v+6.6w-4.6\)

Therefore, the perimeter of the triangle is \(14.7v+6.6w-4.6\).

Answer:

A

Step-by-step explanation:

The reflection line remained and you can see that the direction changed of the shape and the vertex pointing down on the right is pointing up on the left

In the given stem-and-leaf plot, we can conclude that there are at least 5 outliers

The number of outliers in the given stem-and-leaf plot can be determined by identifying values that are significantly higher or lower than the majority of the data.

To find the number of outliers in the stem-and-leaf plot, we need to analyze the data distribution and identify values that deviate significantly from the rest of the scores.

Looking at the stem-and-leaf plot, we observe that the majority of the scores are concentrated between 20 and 90. The numbers 2, 3, 4, 5, 6, 7, 8, 9, and 10 represent the tens digit of the scores, while the leaves represent the ones digit.

Upon examining the plot, we notice that there are a few values that stand out from the rest. These values are 00, 01677, 6899, 233569999, and 01268. Outliers are typically defined as values that fall outside the "typical" range of the data, and these values appear to deviate significantly from the majority of the scores.

To determine the exact number of outliers, we need to apply specific criteria. One common method is to use the 1.5 × IQR (interquartile range) rule. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of the data. Any values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR are considered outliers.

In this case, we don't have the exact raw data to calculate the quartiles and IQR. However, based on visual inspection of the stem-and-leaf plot, we can still identify the values mentioned earlier as outliers due to their significant deviation from the majority of the scores.

Therefore, in the given stem-and-leaf plot, we can conclude that there are at least 5 outliers

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Answer:

yes cause its in a form of y=mx+b

Step-by-step explanation:

Answer:

linear

Step-by-step explanation:

I got to K-12 and this was correct

Answer:

Step-by-step explanation:

[G/K] divides m!, and [H/K] divides (m - 1)!.

Let G be a group with a subgroup H ≤ G, and let K = ker(λ).

We aim to show that G/K is isomorphic to a subgroup of Sym(G/H), where Sym(G/H) denotes the symmetric group on the set of cosets G/H.

To establish this, we define a map from G/K to Sym(G/H) as follows:

ϕ: G/K → Sym(G/H)

ϕ(gK) = λ(g) for all g ∈ G

In other words, for each coset gK in G/K,

we assign the left multiplication by g as a permutation on the cosets of G/H.

We need to verify that ϕ is a well-defined homomorphism, injective, and surjective.

1. Well-defined:

Suppose gK = hK, i.e., g and h represent the same coset of H.

Then g\(h^{(-1)\) ∈ K (by the definition of K).

We have:

ϕ(gK) = λ(g) and ϕ(hK) = λ(h)

Since g\(h^{(-1)\) ∈ K = ker(λ),

λ(g\(h^{(-1)\)) = e, the identity element of Sym(G/H).

Therefore, ϕ(gK) = λ(g) = λ(h) = ϕ(hK).

Thus, ϕ is well-defined.

2. Homomorphism: For any g, h ∈ G, we have:

ϕ((gK)(hK)) = ϕ((gh)K)

                 = λ(gh)

                 = λ(g)∘λ(h)

                 = ϕ(gK)∘ϕ(hK)

Therefore, ϕ is a homomorphism.

3. Injective:

Let gK, hK ∈ G/K.

If ϕ(gK) = ϕ(hK), then λ(g) = λ(h).

This implies g\(h^{(-1)\) ∈ ker(λ) = K.

Therefore, gK = hK, and ϕ is injective.

4. Surjective: For any λ(g) ∈ Sym(G/H), ϕ(gK) = λ(g).

Therefore, ϕ is surjective.

Since ϕ is a well-defined homomorphism that is injective and surjective, it is an isomorphism from G/K to a subgroup of Sym(G/H).

Now, let's consider the order of G/K. By Lagrange's theorem, the order of G/K divides the order of G, denoted as |G|.

Since |G/H| = m and each coset G/H contains |H| elements,

|G| = m |H|.

Therefore, |G/K| divides m!.

Moreover, since H is a subgroup of G and |G/H| = m, the order of H divides the order of G, i.e., |G| = n |H|.

Therefore, |H/K| divides (m - 1)!. Since |H/K| is the index of H/K in G/K, denoted as [H/K], we have [H/K] divides (m - 1)!.

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The question attached here seems to be incomplete, the complete question is:

Let G be group with subgroup H <= G and let K = ker(lambda) as in the previous problem. Suppose H has finite index in G, and write m = [G / H] Show that G/K is isomorphic to a subgroup of Sym(G/H). Use this to show that [G / K] divides m !, and then use this to show that [H / K] divides (m - 1)

We are given that the length of a rectangle is 3 inches greater than the width.

Let us draw a rectangle and label the width and length.

Part A:

Let the width of the rectangle is x inches.

Then the length of the rectangle is (x + 3) inches.

Now recall that the area of a rectangle is given by

Where L is the length and W is the width of the rectangle.

Therefore, the above polynomial represents the area of the rectangle.

Part B:

We are given that the width is 4 inches.

Substitute the width (x = 4) into the equation of the area that we found in part A.

Therefore, the area of the rectangle is 28 square inches.

Answer:

The perimeter of the rectangle = 38.4cm

Step-by-step explanation:

Explanation:-

Given that the length of the rectangle(l) = 8.5cm

The width of the rectangle(w) = 10.7cm

The perimeter of the rectangle

                 P = 2(l+w)

                P = 2( 8.5 + 10.7)

                P = 2 ×19.2 = 38.4 cm

The perimeter of the rectangle = 38.4cm

If the angles are ∠1 = 2x + 4 and ∠2 = 3x - 3, then m∠TRS =  36°.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The measure of ∠1 = 2x + 4

The measure of ∠2 = 3x - 3

The measure of ∠TRS is -

∠TRS = ∠1 + ∠2

Since, PR is a bisector then ∠1 = ∠2.

The equation is -

2x + 4 = 3x - 3

2x - 3x = - 3 - 4

-x = -7

x = 7

Substitute the value of x in the angles -

∠1 = 2(7) + 4

∠1 = 14 + 4

∠1 = 18°

∠2 = 3(7) - 3

∠2 = 21 - 3

∠2 = 18°

So, the value of ∠TRS is -

∠1 + ∠2

18° + 18°

36°

Therefore, the measure of ∠TRS is 36°.

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Answer:

the answer is the D(-1,-3)

Answer:

Number of students

5

8

Step-by-step explanation:

Edg 2020

Answer:

number of students,5,8

Step-by-step explanation:

The recursive formula of the arithmetic sequence is:

xₙ = n*4 + 13

With that we can see that x₁₁ = 57

Here we know that the first elements of the sequence are:

17, 21, 25, 29, ...

To find the common difference, d, we take the difference between any two consecutive elements, so we have:

c = 21 - 17 = 4

Then the recursive formula for the n-th term is:

xₙ = n*4 + d

The first element x₁ is 17, so we will have:

17 = 1*4 + d

17 - 4 = d = 13

The recursive formula is:

xₙ = n*4 + 13

b) the eleventh term of the sequence is given by replacing n in the above formula by 11.

x₁₁ = 4*11 + 13 = 44 + 13 = 57

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Dilation does not preserve congruence, as it changes the size of the figure while keeping the same overall shape.

A transformation that does not preserve congruence is a dilation. A dilation is a transformation that changes the size of a figure while keeping the same overall shape. The formula for dilation is:

D(x,y)=(kx,ky)

Where k is the scale factor. A scale factor of less than 1 will decrease the size, whereas a scale factor greater than 1 will increase the size.

For example, if we have a triangle ABC with vertices A(1,1), B(3,3) and C(4,1), after dilation with a scale factor of 0.5, the vertices of the new triangle A'B'C' will be A'(0.5,0.5), B'(1.5,1.5) and C'(2,0.5).

As can be seen from the example, dilation does not preserve congruence. The triangle A'B'C' is not congruent to triangle ABC, since the length of the sides and the angles have changed.

Dilation does not preserve congruence, as it changes the size of the figure while keeping the same overall shape.

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Answer:

f = 19

Step-by-step explanation:

8 = f - (13 - 2)

f - (13 - 2) = 8

f - 11 = 8

f - 11 + 11 = 8 + 11

f = 19

Answer:

i think the answer is f=19

9514 1404 393

Answer:

Step-by-step explanation:

The ratio of distances is ...

  Neptune distance / Mercury distance = (4.503×10^9)/(5.791×10^7)

  = 450.3/5.791 = 77.76 . . . . cancelling factors of 10^7

Neptune is about 77.76 times as far from the Sun as Mercury is.

This sample would be considered A. Cluster sample. In a cluster sample, the researcher divides the population into groups or clusters, and then randomly selects some of these clusters to include in the sample.

In this case, the researcher is selecting nine counties as the clusters, and surveying all shoulder surgery patients within those counties. This is different from a stratified sample, in which the population is divided into subgroups or strata based on certain characteristics, and a representative sample is selected from each stratum. It is also different from a convenience sample, in which the researcher simply selects the individuals who are easiest to reach or who happen to be available at the time of the study. And it is different from a simple random sample, in which every member of the population has an equal chance of being selected for the sample.

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If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.

The energy an item has as a result of motion is known as kinetic energy in mechanics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its propulsion until its speed changes.

The kinetic energy is given as,

KE = (mv²)/2

Where m is the mass and v is the velocity.

Shawn and his bike have a total mass of 48.1 kg. Shawn rides his bike 1.5 km in 12.5 min at a constant velocity.

The velocity is given as,

v = 1.5/12.5

v = 0.12 km/min

v = 0.12 x 1000 / 60

v = 2 m/s

Then the kinetic energy of Shawn will be given as,

KE = (48.1 x 2²) / 2

KE = 48.1 x 2

KE = 96.2 J

If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.

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the probability that Meena will win  = 8/9

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value between 0 and 1 represents the likelihood of an event, with 0 basically denoting impossibility and 1 generally indicating certainty.

Meena must triumph in the subsequent turn or the one after it in order to win; else, she loses. The likelihood of that is determined by deducting the likelihood of the complimentary event, Bob winning in the following two turns, from one. The likelihood of Bob winning the following two turns may be calculated by taking the square of the probability of him winning on one turn because each turn is independent of the others; hence, it is

= (1/3)^2

= 1/9

the probability that Meena will win = 1- 1/9

                                                           = 8/9

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The three-month moving average is calculated by adding up the demand for the past three months and dividing the sum by three.

To calculate the forecast for month four, we need to find the average of the demand over the past three months: 700, 750, and 900.

Step 1: Add up the demand for the past three months:
700 + 750 + 900 = 2350

Step 2: Divide the sum by three:
2350 / 3 = 783.33 (rounded to two decimal places)

Therefore, the forecast for month four, based on the three-month moving average, is approximately 783.33.

Keep in mind that the three-month moving average is a method used to smooth out fluctuations in data and provide a trend. It is important to note that this forecast may not accurately capture sudden changes or seasonal variations in demand.