The commuting time (the average number of hours spent commuting each week) for students at a particular university is normally distributed with a mean of 63 mins and standard deviation of 9.61.

The probability that a randomly student at the university has a commuting time between ​​​​ 55 and 70 mins is about:

The mean of the distribution used in this problem is 3.5.The answer is B. 3.5.

To find the mean of the distribution used in this problem, we need to calculate the expected number of troubles that can be repaired on the same day out of the first five reported. The likelihood of a trouble being repaired on the same day is given as 0.70.

The expected number of troubles repaired on the same day can be calculated by multiplying the probability of each event by the number of trials. In this case, we have five trials (the first five troubles reported) and a probability of 0.70 for each trial.

Expected number of troubles repaired on the same day = Probability of repair on the same day * Number of trials

= 0.70 * 5

= 3.5

This means that, on average, out of the first five troubles reported, we can expect 3.5 of them to be repaired on the same day based on the past data and the given likelihood. So, the correct answer is B. 3.5.

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Answer:

the approximate population of the city after 14 years will be 7.96 thousand residents.

Step-by-step explanation:

to calculate the approximate population of the city after 14 years, we need to take into account the annual growth rate.

Given that the city's population grows by around 420 persons each year, we can calculate the total growth over 14 years by multiplying the annual growth rate by the number of years:

14 years × 420 persons/year = 5,880 persons

To find the approximate population after 14 years, we add the total growth to the current population:

2.08 thousand + 5.88 thousand = 7.96 thousand

Answer:

A = [tex]\frac{4}{3}[/tex] π

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{120}{360}[/tex] ( r is the radius of the circle )

here r = FG = 2 with central angle = 120° , then

A = π × 2² × [tex]\frac{1}{3}[/tex]

  = [tex]\frac{4}{3}[/tex] π

Answer:

To find the cardinality of the set R₁ \ (R₁ ∩ R₂), we need the specific values of sets R₁ and R₂. Please provide the values of these sets for a more accurate answer.

Regarding the polynomial 2x² + y² + 22 - 8x + 2y - 2xy + 2xz - 16z + 35, we can set it equal to zero and solve for x, y, and z.

2x² + y² + 22 - 8x + 2y - 2xy + 2xz - 16z + 35 = 0

To solve this equation, we need more information or specific values assigned to the variables x, y, and z. Please provide the values or any additional conditions for finding the values of x, y, and z.

Answer: the answer is use ur ai in Brainly, it helped me a lot

Step-by-step explanation:

By conducting a statistical test with the provided data and using a significance level of 0.05 and a critical value of 0.811, the educator can determine whether the number of absences significantly affects the final grade of the students.

To analyze the relationship between the number of absences and the final grade of students, an educator collected data from a sample. The obtained data reveals that for 10 absences, the corresponding final grade was 70. In order to determine whether the number of absences significantly impacts the final grade, a statistical test is needed.

The information provided, "Test at α = 0.05, XCV = 0.811," suggests that the educator is referring to a significance level (α) of 0.05 and the critical value (XCV) associated with this level is 0.811.

To conduct a hypothesis test, the educator needs to set up the null (H0) and alternative (Ha) hypotheses. In this case, the null hypothesis would assume that the number of absences does not have a significant effect on the final grade. The alternative hypothesis would assume that the number of absences does have a significant effect on the final grade.

Using the obtained data, the educator would perform the statistical test, such as a correlation analysis or a regression analysis, to determine the strength and significance of the relationship between absences and final grade.

If the test statistic (such as the correlation coefficient or regression coefficient) exceeds the critical value, the null hypothesis would be rejected, suggesting that the number of absences does have a significant impact on the final grade.

The educator can then interpret the results, considering factors such as the direction and strength of the relationship. Additionally, they may explore other variables or factors that could be influencing the final grade and further refine their analysis.

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The total amount to pay would be 8800 Ethiopian Birr.

To find the amount to pay including VAT, we need to know the applicable VAT rate. VAT, or Value Added Tax, is a consumption tax added to the value of goods and services. The VAT rate can vary from country to country or even within different regions.

Assuming a VAT rate of 10%, we can calculate the VAT amount by multiplying the net value of the shoes by the VAT rate. In this case, the net value of the shoes is 8000 Ethiopian Birr. Therefore, the VAT amount would be 8000 * 0.10 = 800 Ethiopian Birr.

To find the total amount to pay including VAT, we add the VAT amount to the net value of the shoes. Thus, the total amount to pay would be 8000 + 800 = 8800 Ethiopian Birr.

It's important to note that the VAT rate and regulations can vary, so it's always advisable to check the specific VAT rate applicable in a given country or region. Additionally, different goods and services may have different VAT rates or exemptions, so it's crucial to consider the specific rules governing the shoe industry in the relevant jurisdiction.

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Answer:

1080yd³

Step-by-step explanation:

1/2x12x9=54

54x20=1080

The answer is:

↬ f(x + 2) = 2x + 11

Work/explanation:

To evaluate the function, plug in x + 2 for x:

[tex]\boxed{\large\begin{gathered}\sf{f(x)=2x+7}\\\\\bf{distribute}\\sf{f(x+2)=2(x+2)+7}\\\\\bf{simplify}\\\sf{f(x+2)=2x+4+7}\\\\\sf{f(x+2)=2x+11}\end{gathered}}[/tex]

Answer:x=-28

Step-by-step explanation:

Distribute the 4 on the left side of the equation:

32 - 8x = 256

Move the constant term to the right side of the equation:

-8x = 256 - 32

-8x = 224

Divide both sides of the equation by -8 to isolate x:

x = 224 / -8

x = -28

Answer:

Hope this helps and have a nice day

Step-by-step explanation:

To find the value of x, we can use the formula:

Time = Distance / Speed

Let's calculate the time taken to travel from Q to P and back to Q.

From Q to P:

Distance = 12 km

Speed = 6 km/h

Time taken from Q to P = Distance / Speed = 12 km / 6 km/h = 2 hours

From P to Q:

Distance = 12 km

Speed = (6 + x) km/h

Time taken from P to Q = Distance / Speed = 12 km / (6 + x) km/h

Given that the total time taken for the round trip is 3 hours 20 minutes, we can convert it to hours:

Total time = 3 hours + (20 minutes / 60) hours = 3 + (1/3) hours = 10/3 hours

According to the problem, the total time is the sum of the time from Q to P and from P to Q:

Total time = Time taken from Q to P + Time taken from P to Q

Substituting the values:

10/3 hours = 2 hours + 12 km / (6 + x) km/h

Simplifying the equation:

10/3 = 2 + 12 / (6 + x)

Multiply both sides by (6 + x) to eliminate the denominator:

10(6 + x) = 2(6 + x) + 12

60 + 10x = 12 + 2x + 12

Collecting like terms:

8x = 24

Dividing both sides by 8:

x = 3

Therefore, the value of x is 3.

Answer:

x = 3

Step-by-step explanation:

speed  = distance / time

time = distance / speed

Total time from P to Q to P:

T = 3h 20min

P to Q :

s = 6 km/h

d = 12 km

t = d/s

= 12/6

t = 2 h

time remaining t₁ = T - t

= 3h 20min - 2h

=  1 hr 20 min

= 60 + 20 min

= 80 min

t₁ = 80/60 hr

Q to P:

d₁ = 12km

t₁ = 80/60 hr

s₁ = d/t₁

[tex]= \frac{12}{\frac{80}{60} }\\ \\= \frac{12*60}{80}[/tex]

= 9

s₁ = 9 km/h

From question, s₁ = (6 + x)km/h

⇒ 6 + x = 9

⇒ x = 3

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

The decay constant for the plutonium is - [ln (0.5 ) / 6300].

option C.

The decay constant for the plutonium is calculated by applying the following formula.

The given function for the radioactive decay;

[tex]Q(t) = Q_0e^{-kt}[/tex]

where;

The decay constant for the plutonium is calculated as;

k = ln(2) / T½

k = ln(2) / 6300

k = ln(0.5⁻¹) / 6300

k = - [ln (0.5 ) / 6300]

Thus, the decay constant for the plutonium is - [ln (0.5 ) / 6300].

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The function f(x) = -x³ - x is an odd function.

Given the function in the question:

f(x) = -x³ - x

To determine if a function is odd, we need to check if it satisfies the given property:

f(-x) = -f(x)

For all x in the domain of the function.

Given that:

f(x) = -x³ - x

Evaluate f(-x) for the given function f(x) = -x³ - x:

f(x) = -x³ - x

Replace x with -x

f(-x) = -(-x)³ - (-x)

f(-x) = -(-x³) + x

f(-x) = x³ + x

Now, check if -f(x) is equal to x³ + x:

-f(x) = -(-x³ - x)

-f(x) = x³ + x

Since -f(x) = x³ + x, f(x) = -x³ - x is an odd function.

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Answer:

Step-by-step explanation:

12

Reason:

The order of ABCD and EFGH is important. This is because the letters pair up based on their position.

D and H pair up because they're the last letters of ABCD and EFGH respectively. Similar polygons have congruent corresponding angles.

Take note of how the angles are marked to indicate which angles pair up.

D = H

4x = 100

x = 100/4

x = 25

Answer:

25 is the answer by matching the equial sides

Step-by-step explanation:

100°/4=X

25=X

The value of y in the figure is

35.134 degrees

The value of y is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The figure shows a right angle triangle of

opposite = 19

adjacent = 27

The angle is calculated using tan, TOA let the angle be y

tan y= Opposite / Adjacent

tan y = 19 / 27

y = arc tan (19/27)

y = 35.134 degrees

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Answer:

Step-by-step explanation:

Given:

<RPS = 35

<PAQ = 130

Solution:  

If <PAQ = 130 then <QAR =50  

because they are a linear pair that add to 180

<QAR = mQR = 50

mRS = 2(<RPS)                    >inscribed angle

mRS = 2(35)

mRS = 70

<PAQ = 130

<PAQ = mPQ

<PSQ = 1/2 (mPQ)                     >inscribed angle

<PSQ = 1/2 (130)

<PSQ = 65

<PBS = 180 - <RPQ - PSQ             >triangle

<PBS = 180 - 35-65

<PBS = 80

<PBS = <QBR                               >vertical angles

<QBR = 80

<ABQ = 180- <QBR                      >linear pair

<ABQ = 180 - 80

<ABQ= 100

<AQB = 180 - <ABQ - <QAR             >triangle

<AQB = 180 -100 - 50

<AQB = 30

<AQB = <AQS

<AQS =30

mRS = 70

mPS = 180-mRS                         180 for semicircle

mPS = 180 - 70

mPS = 110

Answer:  the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

Step-by-step explanation:

a) Let's represent the number of jugs of milk as 'm', the number of loaves of bread as 'b', and the number of pieces of cheese as 'c'. According to the given information:

The total number of items sold today is 224. Therefore, we can write the equation:

m + b + c = 224

The store sold three times as many loaves of bread as jugs of milk. We can write this as:

b = 3m

The store sold four times as many pieces of cheese as loaves of bread. We can write this as:

c = 4b

b) Now, let's solve the equation:

Substituting the value of 'b' from equation (2) into equation (3):

c = 4(3m)

c = 12m

Substituting the values of 'b' and 'c' from equations (2) and (3) into equation (1):

m + 3m + 12m = 224

16m = 224

m = 224 / 16

m = 14

Using the value of 'm' in equation (2):

b = 3m

b = 3(14)

b = 42

Using the value of 'b' in equation (3):

c = 4b

c = 4(42)

c = 168

Answer:

Step-by-step explanation:

a) Let's denote the number of jugs of milk as 'x', the number of loaves of bread as 'y', and the number of pieces of cheese as 'z'.

Based on the given information, we can form two equations:

1) The total number of items sold today is 224:

x + y + z = 224

2) The store sold three times as many loaves of bread as jugs of milk:

y = 3x

3) The store sold four times as many pieces of cheese as loaves of bread:

z = 4y

b) To solve the equations and find the number of jugs of milk, loaves of bread, and pieces of cheese the store sold today, we will substitute equation (2) and equation (3) into equation (1):

x + y + z = 224

x + 3x + 4y = 224

4x + 4y = 224

Now, substitute y = 3x into the equation:

4x + 4(3x) = 224

4x + 12x = 224

16x = 224

Divide both sides by 16:

x = 224 / 16

x = 14

Now substitute the value of x back into equation (2) to find y:

y = 3x

y = 3(14)

y = 42

Finally, substitute the value of y into equation (3) to find z:

z = 4y

z = 4(42)

z = 168

Therefore, the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

The probability that a flight has 100 or more passengers and arrives on time is approximately 0.12 or 12%.

Let A be the event that a flight has 100 or more passengers, and B be the event that the flight arrives on time. We want to find the probability of the intersection of these two events, P(A ∩ B).

We are given:

- P(B) = 0.80, the probability that any given flight arrives on time

- P(A) = 0.30, the probability that any given flight has 100 or more passengers

- P(B | A) = 0.40, the conditional probability that a flight arrives on time given that it has 100 or more passengers (since 60% of such flights are late)

We can use the formula for conditional probability to find P(A ∩ B):

P(A ∩ B) = P(B | A) * P(A)

         = 0.40 * 0.30

         = 0.12

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The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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The transformation that moves the shape is (a) translation

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have:

This means that the only transformation is translation

So, the transformation is (a) translation

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The speed of the boat in still water is 3 times the speed of the river current.

To find the speed of the boat in still water, we can use the concept of relative motion and the given information about the boat's speed while traveling upstream and downstream.

Let's assume the speed of the boat in still water is "v" km/h, and the speed of the river current is "c" km/h.

When the boat is traveling upstream, it moves against the current, so its effective speed is reduced.

The boat's speed relative to the ground is given by (v - c) km/h.

Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is increased.

The boat's speed relative to the ground is given by (v + c) km/h.

According to the problem, the boat can travel 40 km upstream in the same time it would take to travel 80 km downstream.

Since time is constant in both cases, we can set up the following equation:

40/(v - c) = 80/(v + c)

To solve this equation, we can cross-multiply and simplify:

40(v + c) = 80(v - c)

40v + 40c = 80v - 80c

40c + 80c = 80v - 40v

120c = 40v

Dividing both sides by 40, we get:

3c = v.

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The degree of f(x) is 5, and the leading coefficient is negative. There are 3 distinct real zeros and 2 relative maximum values.

From the graph of a function, the zeros of the function are the x-intercepts, that is, the values of x for which the graph crosses or touches the x-axis.

The function in this problem has three distinct zeros, given as follows:

Hence the degree of the function is given as follows:

2 x 2 + 1 = 5.

The leading coefficient is negative, as the function has an odd degree, but increases to left and decreases to right.

The relative maximums of the functions are the points where the function makes a downward turn, changing from increasing to decreasing, hence there are two points.

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The total volume of the dill spears is approximately 160 cm³.

To find the total volume of the dill spears, we'll need to determine the volume of the pickling liquid and subtract it from the total volume of the jar.

Given information:

Base area of the jar = 45 cm²

Height of the jar = 13 cm

Pickle juice drained = 160 cm³

First, let's calculate the volume of the jar:

The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.

The base area of the jar is given as 45 cm², which means πr² = 45.

So, we can find the radius (r) of the base using the formula r = √(45/π).

Let's calculate the value of r:

r = √(45/π) ≈ 3.79 cm

Now we can find the volume of the jar:

V_jar = πr²h

= π(3.79)²(13)

≈ 1818.73 cm³

Next, let's calculate the volume of the pickling liquid:

Given that 160 cm³ of pickle juice was drained, the volume of the pickling liquid is equal to the volume of the jar minus the volume of the drained pickle juice.

V_pickling_liquid = V_jar - 160

≈ 1818.73 cm³ - 160 cm³

≈ 1658.73 cm³

Finally, to find the total volume of the dill spears, we need to subtract the volume of the pickling liquid from the volume of the jar:

Total volume of dill spears = V_jar - V_pickling_liquid

≈ 1818.73 cm³ - 1658.73 cm³

≈ 160 cm³

Therefore, the total volume of the dill spears is approximately 160 cm³.

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The measure of angle of arc UB is 46°

An arc is a part of the circumference.

If two arcs in circles with equal radii have the same length, then their central angles (and measures) will be equal.

To find the measure of angle of arc UB, we use the theorem that says;

angle I = 1/2( angle ZC - angle UB)

angle I = 48°

angle ZC = 142°

Therefore ;

represent angle UB by x

48 = 1/2( 142-x)

142 - x = 96

x = 142 -96

x = 46°

Therefore the measure of angle of arc UB is 46°

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The period of the trigonometric function is -2π/3.

To determine the period of the trigonometric function based on the given information, we need to consider the pattern of the graph and identify the interval over which it repeats.

Given that the maximum point is at (-π, 7.7) and the minimum point is at (-1/3π, -6.7), we can observe that the graph completes one full oscillation between these two points.

The distance between the maximum and minimum points corresponds to half of the period. Therefore, the full period of the function can be found by doubling this distance.

The distance between (-π, 7.7) and (-1/3π, -6.7) can be calculated as follows:

Δx = -1/3π - (-π) = π/3π - π = -π/3

Since the full period is twice this distance, we multiply by 2:

2 * (-π/3) = -2π/3

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Answer:

Step-by-step explanation:

To find the time it takes for the turtle to reach the pond, we can use the formula:

Time = Distance / Speed

Given that the turtle travels at a speed of 1/12 mile per hour and the distance to the pond is 5/6 mile, we can substitute these values into the formula:

Time = (5/6) / (1/12)

To simplify this, we can multiply the numerator by the reciprocal of the denominator:

Time = (5/6) * (12/1) = (5 * 12) / 6 = 60 / 6 = 10

Therefore, it will take the turtle 10 hours to reach the pond.

Answer:

reflex angle

Step-by-step explanation:

the angle of 192 degrees is called a reflex angle