3) We are interested to find out the average amount of time a
person
wants to listen to Blake Shelton. Suppose we took a sample of
n = 35
people and found the sample mean to be 32 minutes. If the
popu

Answer: 47 your welcome :)

10 + 8 = 18

18 x 4 = 72

72 + 5 = 77

The answer is 77

Answer:

2 1/3

1 4/3

2.333...

233.3...%

Step-by-step explanation:

There is a 50% chance that Jane will work on the research project if at least one junior and at least one senior are selected.

The total number of ways the professor can choose 3 students from 6 is:

6C3 = 20

There are three cases to consider: (1) 1 junior and 2 seniors are selected, (2) 2 juniors and 1 senior are selected, and (3) 3 juniors are selected.

Case 1: 1 junior and 2 seniors are selected. The number of ways to choose 1 junior and 2 seniors is:

3C1 x 3C2 = 9

From the 3 juniors, Jane is already selected. From the 3 seniors, the professor can choose 2 in 3C2 = 3 ways. So there are 3 ways for Jane to work on the research project in this case.

Case 2: 2 juniors and 1 senior are selected. The number of ways to choose 2 juniors and 1 senior is:

3C2 x 3C1 = 9

From the 2 remaining juniors (excluding Jane), the professor can choose 1 in 2 ways. From the 3 seniors, the professor can choose 1 in 3 ways. So there are 2 x 3 = 6 ways for Jane to work on the research project in this case.

Case 3: 3 juniors are selected. The number of ways to choose 3 juniors is:

3C3 = 1

Since Jane is one of the 3 juniors, there is only one way for her to work on the research project in this case.

Therefore, the total number of ways for Jane to work on the research project is 3 + 6 + 1 = 10. The probability of Jane working on the research project is:

P(Jane works on project) = 10/20 = 0.5

So there is a 50% chance that Jane will work on the research project if at least one junior and at least one senior are selected.

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Answer:

$12.50

Step-by-step explanation:

18 - 12 = 6

Brandon bought 6 less than Lance and payed $75 dollars shoes.

That means that 6 shirts cost $75.

We need to divide 6 from 75

75/6 = 12.5

So each shirt costs $12.50.

Hope this helped

Stay curious!

Answer: 219 I beleive

Step-by-step explanation: 54(4)+(.750)4=219

Answer:

each tank = 54 + (750÷ 1000) liter = 54.75L

so the capacity of the four tanks = 4x 54.75 = 219litre

Step-by-step explanation:

1) change 750 ml int litre which is equal 750÷1000 = 0.75L

2) add 54 +0.75

3) multiply 4 by 54.75 = 219L

Answer:

2y + 16 +2y +30 +4y –13 +3y - 21

11y + 12

I hope I helped you^_^

The dolphin is 90.67 feet far from the base of the pier.

You look straight parallel to ground. But when you have to watch something down, then you take your sight down by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of depression.

Given that the angle of depression from her to the dolphin is 22°

α = 22°

So, Tan α = opp/adj......... 1

Opp = 33 feet

Adj = x

Substitute the values into equation 1

Tan 22° = 33feet/adj

0.36397 = 33/adj

0.36397×adj = 33

Adj = 33/0.36397

Adj = 90.666

Recall, adj = x = 90.666feet

x = 90.67feet

Hence, the dolphin is 90.67 feet far.

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Answer:

5

Step-by-step explanation:

area of a cylinder;

\(2\pi.r ^{2} + 2\pi.rh\)

\( = 2\pi.r (r +h)\)

\( = 2 \times 3.14 \times 4 \times (10 + 4)\)

\( = 351.68\)

Answer: I believe the correct answer is C.

Step-by-step explanation:

Answer:

its C

Step-by-step explanation:

The number of tellers that should be used if the aim is to keep the mean queuing time to less than 5 minutes is 3.

To determine the number of tellers follow these steps:

1. Arrival rate (λ) = 18 customers per hour
2. Mean service time (μ) = 10 minutes per customer = 1/6 customer per minute
3. Lobby capacity = 15 customers
4. Target mean queuing time = 5 minutes

Now, calculate the service rate and find the number of tellers needed to achieve the target mean queueing time.

Step 1: Convert arrival rate to customers per minute: λ = 18/60 = 0.3 customers per minute
Step 2: Calculate the service rate per teller: 1/μ = 1/(1/6) = 6 customers per hour = 0.1 customers per minute
Step 3: Determine the number of tellers (n) needed to achieve the target queuing time:

Using the formula:
n > λ / (μ * (Wq_target + 1/μ))

Here, Wq_target is the target mean queuing time in minutes.
n > 0.3 / (0.1 * (5/60 + 1/(6/60)))

After solving the inequality, we get:
n > 2.4

Since the number of tellers must be a whole number, therefore, at least 3 tellers should be used in the queueing model of the bank to keep the mean queueing time to less than 5 minutes.

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Answer: 15,048

Step-by-step explanation:

Answer: 6.68

To calculate the number of years before Mickey & Minnie can retire if they earn 10.5% per annum on their stash of cash, we can use the formula for compound interest.

A = P (1 + r/n) ^ nt

where

A = amount

P = principal

r = rate of interest

n = number of times interest is compounded per year

t = time in years

Given:

P = $49 million

r = 10.5%

n = 1 (annual compounding)

A = $90 million

We need to find t. Let's plug in the given values in the formula and solve for t.

A = P (1 + r/n) ^ nt

90 = 49(1 + 0.105/1) ^ t

Dividing both sides by 49, we get:

1.8367 = (1 + 0.105) ^ t

Taking the logarithm of both sides, we get:

t log (1.105) = log (1.8367)

Dividing both sides by log (1.105), we get:

t = log (1.8367) / log (1.105)

Using a calculator, we get:

t ≈ 6.68

Therefore, it will take approximately 6.68 years before Mickey & Minnie can retire if they earn 10.5% per annum on their stash of cash.

When traveling at 35 mph for 5 seconds, you would cover a distance of approximately 256.65 feet. When traveling at 55 mph for 3 seconds, you would cover a distance of approximately 242.01 feet. Finally, when traveling at 20 mph for 2 seconds, you would cover a distance of approximately 58.66 feet.

To determine the distance traveled in feet during a given amount of time, we need to use the formula:

Distance = Speed × Time

First, let's calculate the distance traveled in 10 seconds when traveling at 60 mph:

Speed = 60 mph

Time = 10 seconds

Converting mph to feet per second:

1 mile = 5280 feet

1 hour = 3600 seconds

Speed = (60 mph) × (5280 feet / 1 mile) / (3600 seconds / 1 hour)

Speed = 88 feet per second

Distance = (88 feet/second) × (10 seconds)

Distance = 880 feet

Therefore, when traveling at 60 mph for 10 seconds, you would cover a distance of 880 feet.

Now, let's calculate the distances for the other scenarios:

Traveling at 35 mph for 5 seconds:

Speed = 35 mph

Time = 5 seconds

Converting mph to feet per second:

Speed = (35 mph) × (5280 feet / 1 mile) / (3600 seconds / 1 hour)

Speed = 51.33 feet per second

Distance = (51.33 feet/second) × (5 seconds)

Distance = 256.65 feet (approx.)

Traveling at 55 mph for 3 seconds:

Speed = 55 mph

Time = 3 seconds

Converting mph to feet per second:

Speed = (55 mph) × (5280 feet / 1 mile) / (3600 seconds / 1 hour)

Speed = 80.67 feet per second

Distance = (80.67 feet/second) × (3 seconds)

Distance = 242.01 feet (approx.)

Traveling at 20 mph for 2 seconds:

Speed = 20 mph

Time = 2 seconds

Converting mph to feet per second:

Speed = (20 mph) × (5280 feet / 1 mile) / (3600 seconds / 1 hour)

Speed = 29.33 feet per second

Distance = (29.33 feet/second) × (2 seconds)

Distance = 58.66 feet (approx.)

Therefore, when traveling at 35 mph for 5 seconds, you would cover a distance of approximately 256.65 feet. When traveling at 55 mph for 3 seconds, you would cover a distance of approximately 242.01 feet. Finally, when traveling at 20 mph for 2 seconds, you would cover a distance of approximately 58.66 feet.

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The rate of change of the function f(x) = -2x² + 6x + 1 at x = 1 is approximately 0.302.

What is the definition of a function?

In mathematics, a function is a rule that assigns to each element in a set (called the domain) exactly one element in another set (called the range). In other words, a function takes an input value and produces a unique output value. The input value is usually represented by the variable x, while the output value is represented by the variable y or f(x).

Now,

The rate of change of a function is the slope of the line that connects any two points on the graph of the function. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1)/(x2 - x1)

So to find the rate of change of the function f(x) = -2x² + 6x + 1, we need to choose two values of x and find the corresponding values of f(x), and then calculate the slope of the line passing through these two points.

Let's choose two values of x that are close to each other, say x1 = 1 and x2 = 1.01. Then, we have:

f(x1) = -2(1)² + 6(1) + 1 = 5

f(x2) = -2(1.01)² + 6(1.01) + 1 = 5.0302

Now, we can calculate the slope of the line passing through these two points:

slope = (f(x2) - f(x1))/(x2 - x1) = (5.0302 - 5)/(1.01 - 1) = 0.302

So,

     the rate of change of the function f(x) = -2x² + 6x + 1 at x = 1 is approximately 0.302. Note that the rate of change of a function is not constant, but varies with the value of x.

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Answer:

20 =x

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

x+40 = 3x

Subtract x from each side

x+40-x = 3x-x

40 = 2x

Divide by 2

40/2 = 2x/2

20 =x

Answer:

x = 20

Step-by-step explanation:

3x = x + 40

2x = 40

x = 20

The cost of the weaving equipment at 'nth' year would be, \(y_n = 60000^{(-0.1n)}\).

The formula for exponential growth is \(y = y_0.e^{(kt)}.\)

The formula for exponential decay is \(y = y_0e^{(-kt)}.\)

Given, The cost of weaving equipment for $60,000 depreciate at an average rate of 10% per year.

Therefore, The function representing the cost of the weaving equipment

at any number of years, let it be 'n' is,

\(y_n = 60000^{(-0.1n)}\).

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Answer:

-15 - 3 = -18

Rob owes his father 18 dollars.

Step-by-step explanation:

If he borrowed 15 dollars from his dad, then 3 more, he borrowed a total of 15 + 3 dollars. That means he borrowed a total of 18 dollars. When you borrow money, you owe people, and after you spend the borrowed money it's like subtracting money from your 0 dollars. 0 - 18 = -18. He needs to earn 18 more dollars to pay back his father and get a balance of 0 dollars again.

Hope this helps.

Answer:

1 day=10outfits

5days=10outfits×5

=50outfits

Step-by-step explanation:

hope this is helpful

Based on the calculation, you can wear the 10 outfits in 50 different ways throughout the week.

To calculate the number of ways you can wear 10 outfits to school each day in a 5-day week, you need to consider the total number of outfits across all days. Since there are 10 outfits and 5 days, the total number of outfit combinations can be calculated by multiplying the number of outfits per day by the number of days:

10 outfits/day × 5 days = 50 outfit combinations

Therefore, you can wear the 10 outfits in 50 different ways throughout the week.

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31. Invertible: T^(-1)(x, y) = (-1/4x, 1/4y), 32. Not invertible, 33. Invertible: T^(-1)(x, y) = ((x + y)/2, (y - x)/2), 34. Not invertible, 35. Invertible: T^(-1)(x₁, x₂, x₃) = (x₁, x₂ - x₁, x₃ - x₂), 36. Invertible: T^(-1)(X₁, X₂, X₃, X₄) = (X₁ + 2X₂, X₂, X₃ - X₄, X₃)

The answers are as follows:

31. The linear transformation T(x, y) = (-4x, 4y) is invertible, and its inverse is T^(-1)(x, y) = (-1/4x, 1/4y).

32. The linear transformation T(x, y) = (2x, 0) is not invertible. Since the transformation maps all points to a line along the x-axis, the inverse transformation would need to map each point on the x-axis back to multiple points in the plane, which is not possible for a linear transformation.

33. The linear transformation T(x, y) = (x + y, y - x) is invertible, and its inverse is T^(-1)(x, y) = (x - y, x + y).

34. The linear transformation T(x, y) = (x + y, 3x + 3y) is not invertible. This can be seen by observing that the transformation maps every point in the xy-plane to a line in the xy-plane, specifically, the line y = 3x. Since all points on this line are mapped to the same point in the transformation, it is not possible to uniquely recover the original points, and thus the transformation does not have an inverse.

35. The linear transformation T(x₁, x₂, x₃) = (x₁, x₁ + x₂, x₁ + x₂ + x₃) is invertible, and its inverse is T^(-1)(x₁, x₂, x₃) = (x₁, x₂ - x₁, x₃ - x₂).

36. The linear transformation T(x₁, x₂, x₃, x₄) = (x₁ - 2x₂, x₂, x₃ + x₄, x₃) is invertible, and its inverse is T^(-1)(x₁, x₂, x₃, x₄) = (x₁ + 2x₂, x₂, x₃ - x₄, x₃).

To determine whether a linear transformation is invertible, we need to check if it satisfies two conditions: it must be both injective (one-to-one) and surjective (onto).

Injectivity means that each distinct point in the domain is mapped to a distinct point in the range. If two different points in the domain are mapped to the same point in the range, then the transformation is not invertible since it is not possible to uniquely recover the original points.

Surjectivity means that every point in the range has a corresponding point in the domain. If there are points in the range that cannot be reached from the domain, then the transformation is not invertible.

Now let's analyze each transformation:

31. T(x, y) = (-4x, 4y): This transformation is injective and surjective since for every point (x, y), there is a unique point (-4x, 4y) in the range. Therefore, it is invertible, and the inverse transformation is T^(-1)(x, y) = (-1/4x, 1/4y).

32. T(x, y) = (2x, 0): This transformation is not injective since every point in the domain maps to the same point (2x, 0) in the range. Therefore, it is not invertible.

33. T(x, y) = (x + y, y - x): This transformation is injective and surjective. It is invertible, and the inverse transformation is T^(-1)(x, y) = ((x + y)/2, (y - x)/2). We can verify that applying the original transformation and its inverse will result in the original input.

34. T(x, y) = (y₂x - y) / (y, 3x + 3y): This transformation is not invertible. To determine this, we can consider its matrix representation. The matrix of this transformation is [[y₂, -1], [1, 3]]. If the determinant of this matrix is zero, the transformation is not invertible. Calculating the determinant, we have y₂(3) - (-1)(1) = 3y₂ + 1. Since this can equal zero for certain values of y₂, the transformation is not invertible.

35. T(x₁, x₂, x₃) = (x₁, x₁ + x₂, x₁ + x₂ + x₃): This transformation is injective and surjective. It is invertible, and the inverse transformation is T^(-1)(x₁, x₂, x₃) = (x₁, x₂ - x₁, x₃ - x₂).

36. T(X₁, X₂, X₃, X₄) = (X₁ − 2X₂, X₂, X₃ + X₄, X₃): This transformation is injective and surjective. It is invertible, and the inverse transformation is T^(-1)(X₁, X₂, X₃, X₄) = (X₁ + 2X₂, X₂, X₃ - X₄, X₃).

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Answer:

(6, 2)

Step-by-step explanation:

I did this over 10 times it's so easy it is like a breeze

Answer:(-2,5)

Step-by-step explanation:

a) The regular selling price for the refrigerator is approximately $1,471.43.

b) The amount of profit based on the selling price is approximately $441.43.

a) To calculate the regular selling price, we need to consider the expenses and the desired profit.

Let's denote the regular selling price as "P."

Expenses average 8% of the regular selling price, which means expenses amount to 0.08P.

The desired profit based on selling price is 22% of the regular selling price, which means profit amounts to 0.22P.

The total cost of the refrigerator, including expenses and profit, is the purchase price plus expenses plus profit: $1,030 + 0.08P + 0.22P.

To find the regular selling price, we set the total cost equal to the regular selling price:

$1,030 + 0.08P + 0.22P = P.

Combining like terms, we have:

$1,030 + 0.30P = P.

0.30P - P = -$1,030.

-0.70P = -$1,030.

Dividing both sides by -0.70:

P = -$1,030 / -0.70.

P ≈ $1,471.43.

Therefore, the regular selling price is approximately $1,471.43.

b) To calculate the amount of profit, we can subtract the cost from the regular selling price:

Profit = Regular selling price - Cost.

Profit = $1,471.43 - $1,030.

Profit ≈ $441.43.

Therefore, the amount of profit is approximately $441.43.

Please note that the values are rounded to the nearest cent.

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Answer:

80 spotted frogs

Step-by-step explanation:

We can write a ratio

spotted frogs:frogs

12:180

x:1200

To solve we just multiply 12*6.66667 (because this is what we multiplied 180 to get to 1200)

the answer is 80

Answer:

x = 1

Step-by-step explanation:

The vertex of the graph is (1, - 3 )

The axis of symmetry is a vertical line passing through the vertex with equation

x = c

where c is the value of the x- coordinate of the vertex , that is

x = 1 ← equation of axis of symmetry

The equation of the function is y = 3 * sin[(1/2)(x - π/4)] - 2 which is described by characteristics having a sine curve of  4π amplitude 3, the phase shift of π/4, and a vertical translation down 2 units.

To write the equation for the sine curve with a period of 4π, an amplitude of 3, a left phase shift of π/4, and a vertical translation down 2 units, we'll use the general sine function equation:

y = A * sin(B(x - C)) + D

Where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical translation.

1. Amplitude (A) = 3
2. Period = 4π; The formula to find the frequency (B) is B = 2π / Period.

Therefore, B = 2π / 4π = 1/2.
3. Phase shift (C) = π/4 (left shift is positive)
4. Vertical translation (D) = -2 (down 2 units)

Now, plugging these values into the equation:

y = 3 * sin((1/2)(x - π/4)) - 2

So, the equation of the function is y = 3 * sin[(1/2)(x - π/4)] - 2.

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Answer:

The system of equations are:

s + b = 1650.... Equation 1

0.04s + 1.5b = 1818........ Equation 2

The number of

Small trees = 450 trees

The number of Big trees = 1200 trees

Step-by-step explanation:

From the above question

Small trees = s

Large trees = b

An urban forest has 1,650 large and small trees.

Hence,

s + b = 1650.... Equation 1

s = 1650 -b

A large tree, b, removes 1.5 kg of pollution from the air each year. A small tree, s, removes 0.04 kg of pollution each year. Together, these trees remove 1,818 kg of pollution each year.

Hence:

0.04s + 1.5b = 1818........ Equation 2

We substitute 1650 - b for s

0.04(1650 - b) + 1.5b = 1818

66 - 0.04b + 1.5b = 1818

- 0.04b + 1.5b = 1818 - 66

1.46b = 1752

b = 1752 ÷ 1.46

b = 1200 trees

Solving for x

1650 - b = s

s = 1650 - 1200

s = 450 trees

Answer: i think it is C

Step-by-step explanation: brainiest please?

Answer:

Step 1: Identify the given solid figure. Step 2: Identify the faces and side lengths of the given solid figure. Step 3: Using the side lengths and shape of the faces, draw each face of the solid figure on a plane and mark the corresponding side length. You will get the net of the solid figure.

The Sno-Cone has two identifiable 3D figures, which are cone and hemisphere. Our key point here is to solve the volume of the cone and the hemisphere then add their volumes to solve for the total volume of the Sno-Cone.

The volume of the cone can be solved using the equation

The radius of the sno-cone and its height are provided in the problem. Just substitute it on the equation above and compute, we get

The next thing to solve is the volume of the hemisphere. The volume of the hemisphere is half of the volume of a sphere, which is represented in the equation as

The radius of the cone is the same as the radius of the hemisphere. Substitute it on the equation above and compute, we get

The overall volume of the sno-cone is the sum of the volume of the hemisphere and cone computed above.

There

There are 40 pupil in a class and 30 of them are girl then  the ratio of girl to pupil is 3:4

If there are 40 pupil in total in the class, and 30 of them are girls, that means there are 10 boys in the class

so the ratio of  girls to pupil is 30: 40

to get simplest form, divide by the greatest common factor. which in this case, is 10

3:4

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Answer: The Answer is slope is -4 y-axis is 9