In a large population of nurses, suppose 20% of the nurses would prefer the night shift. If a random sample of 10 nurses is taken, what is the probability that exactly 2 nurses prefer the night shift?

The "loading" of the die makes P(1)=112, P(6)=312, and the following four outcomes equally likely. A roll with an even number larger than two has a 50% probability of occurring.

The probability of rolling an even number is 1/2 since there are three even numbers (2, 4, 6) and six possible outcomes in total.

The probability of rolling a number greater than two is 5/6 since there are five outcomes (3, 4, 5, 6) greater than two and six possible outcomes in total.

To find the probability that the number rolled is both even and greater than two, we need to find the probability of rolling a 4 or a 6 since these are even numbers that are greater than two.

The probability of rolling a 4 is P(4) = 1/12 + 1/6 = 1/4 since the die is loaded to favour a 6 over the other numbers, but all other outcomes are equally likely.

The probability of rolling a 6 is P(6) = 3/12 = 1/4 since the probability of rolling a 6 is given as 3/12.

Therefore, the probability of rolling an even number that is greater than two is:

P(even and greater than two) = P(4 or 6) = P(4) + P(6) = 1/4 + 1/4 = 1/2.

So the probability of rolling an even number that is greater than two is 1/2.

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The volume integral for f(x,y,z) = 1 over the region E : x² + y² + z² ≤ 4,

1) In spherical coordinates system is

[tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]

2) In cylinderical coordinates system is

[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]

3) In rectangular coordinates syatm is

[tex]V = \int_{0}^{2}\int_{-\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]

We pick a region E : x² + y² + z² ≤ 4 and determine volume over the region E for function, f(x,y,z ) = 1 .

[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]

In spherical coordinates system we plug,

[tex]x = \rho sin \phi cos \theta[/tex]

[tex]y = \rho sin \phi sin \theta[/tex]

[tex]z = \rho cos \phi [/tex]

[tex]dV = dx dy dz = |J| d\rho d\phi d\theta [/tex]

where, [tex]|J| = \rho² sin \phi[/tex]

=> [tex]dx dy dz = \rho² sin \rho d\rho d\phi d\theta[/tex]

So, [tex]V = {\int \int \int}_{x² + y² + z² ≤ 4} 1 \: dxdy dz[/tex]

Now, [tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]

Region , E : x² + y² + z² ≤ 4

=> z² ≤ 4 - x² - y²

=> z ≤ ± √4 - x² - y²

[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]

here, r∈[0, 2], θ∈[0,2π]

[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]

[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]

[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]

Here, y² ≤ 4 - x²

=> y = ± √4 - x² and x∈ [0,2], So,

[tex]V = \int_{0}^{2}\int_{ -\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]

Hence, in above we determined the volume integral for region, E in all three coordinates systems.

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Answer:

undetermined  or most likely Tasmania

Step-by-step explanation:

Based on the choices of experts in the first round of the Australian netball competition, we can conclude that Victoria played against WA. This is because, out of the common tips, WA was tipped by an expert who also tipped Victoria and didn't tip Queensland. Therefore, WA is the likely team that Victoria played against.

To identify which team Victoria played in the Australian netball competition we can reason through our experts' tips. The experts' tips overlap at Queensland and WA as indicated by Expert A and Expert B. However, Expert C tipped Victoria, and they did not tip Queensland which tells us that Victoria did not play against Queensland, leaving us with WA. Hence Victoria must've played against WA.

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Answer:

False.

Step-by-step explanation:

When using multiple adjectives in a sentence, there is a general order that native English speakers tend to follow: opinion, size, age, shape, color, origin, material, purpose. This is known as the "OSASCOMP" order. However, this order is not always strictly followed, and there can be exceptions depending on the specific context or style of writing.

Answer:

It is False

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

by the similarity theorem

the ratios of corresponding sides are in proportion , that is

[tex]\frac{x}{9}[/tex] = [tex]\frac{16}{6}[/tex] ( cross- multiply )

6x = 9 × 16 = 144 ( divide both sides by 6 )

x = 24

Answer:

Delia's hair grew less since her last haircut

Step-by-step explanation:

2.45 centimeters is a higher number then 2.03, making Delia's hair shorter than Carolyn's.

Answer:

Delia's hair grew less.

Step-by-step explanation:

2.45 - 2.03 = 0.42

Deila's hair is 0.42 less than Carolyn's hair.

Drag the following statement, equation or reason to each box to complete this proof accordingly:

2. Multiplication Property of Equality

3. x-2 = 8  

4. Addition Property of Equality

5. x = 10               Simplifying

An equation is a mathematical statement that expresses the equality between two expressions. It contains an equal sign "=" that separates the two expressions.

The proof of the equation with reason can be completed as follow:

(x-2)/4 = 2                                 Given

4(x-2)/4 = 4 * 2                         Multiplication Property of Equality

x-2 = 8                                      Simplifying

x - 2+ 2 = 8 + 2                         Addition Property of Equality

x = 10                                        Simplifying

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Answer: x= 24 and y= 73

Step-by-step explanation:

we know

The opposite interior angles are equal and

The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees.
the sum of the interior angles of a parallelogram is 360 degrees.

So 107 + y = 180

180 - 107 = 73

Y = 73

y is equal to its opposite angle so

X can be found by 73 = 3x + 1

Subtract 1 from both sides

73 - 1 = 3x +1 -1

Simplify

72 = 3x

Divide both sides by 3 to solve for x

72/3 = 3/3x

x=24

Check your work by adding the 4 angles together to equal 360

107 + 107 + 73 + 73 = 360

360 = 360

They equal so your solution is correct

Answer:

12.5

Step-by-step explanation:

9.6² + 2.8² = 10²

10² + 7.5² = 12.5²

Answer:

The sonar station will not detect the submarine.

Step-by-step explanation:

The area that the sonar station can detect can be modelled as a circle with center (0, 0) and radius 5 km.

The equation of a circle formula is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Therefore, the equation of the circle modelling the perimeter of the sonar station detection area is:

[tex]\implies (x-0)^2+(y-0)^2=5^2[/tex]

[tex]\implies x^2+y^2=25[/tex]

To determine whether the sonar station will detect a swiss submarine traveling along a trajectory defined by y = -2/3x + 26/3, substitute the equation of the trajectory into the found equation of the circle.

[tex]\implies x^2+\left(-\dfrac{2}{3}x+\dfrac{26}{3}\right)^2=25[/tex]

Simplify:

[tex]\implies x^2+\dfrac{4}{9}x^2-\dfrac{104}{9}x+\dfrac{676}{9}=25[/tex]

[tex]\implies 9x^2+4x^2-104x+676=225[/tex]

[tex]\implies 13x^2-104x+451=0[/tex]

Solve the equation for x using the quadratic formula:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\implies x=\dfrac{-(-104) \pm \sqrt{(-104)^2-4(13)(451)}}{2(13)}[/tex]

[tex]\implies x=\dfrac{104 \pm \sqrt{-12636}}{26}[/tex]

[tex]\implies x=\dfrac{104 \pm 18\sqrt{39}\:i}{26}[/tex]

[tex]\implies x=4 \pm \dfrac{9\sqrt{39}}{13}\:i[/tex]

As the solutions are complex numbers, this means that the linear trajectory of the submarine will not intersect the detection area of the sonar station. Therefore, the sonar station will not detect the submarine.

By similarity of triangle the height of a children will be 4ft.

Similar triangles are that kind of triangles that have the same shape, but different  sizes. examples of similar objects are All equilateral triangles, squares of any side lengths. In another words, if two triangles having their corresponding angles are congruent and corresponding sides are in equal proportion then two triangles are said to be similar. It is denoted  by ‘~’ symbol.

We can use the property of similar triangles to estimate the height of the child:

The ratio of the height of the adult to the length of their shadow is the same as the ratio of the height of the child to the length of their shadow:

height of adult / length of adult shadow = height of child / length of child shadow

Plugging in the values we know:

6 / 15 = height of child / 10

Solving for the height of the child:

height of child = (6 / 15) * 10 = 4 feet

Therefore, the estimated height of the child is 4 feet.

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Answer: 2(x-6) < -3(x-1) is x < 3.

Step-by-step explanation:
2(x-6) < -3(x-1)

Expanding the brackets, we get:

2x - 12 < -3x + 3

Adding 3x to both sides, we get:

5x - 12 < 3

Adding 12 to both sides, we get:

5x < 15

Dividing both sides by 5, we get:

x < 3

Answer:

x>12

Step-by-step explanation:

1/3(x-6)>2

distribute 1/3

1/3x-2>2

add 2 to both sides

1/3x>4

multiply both sides by 3

x>12

Angle Y measures 125 degrees and angle Z measures 63 degrees.

what is a circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.

Since quadrilateral WXYZ is inscribed in a circle, we know that opposite angles add up to 180 degrees. Therefore:

m∠Y + m∠W = 180 degrees ...(1)

m∠Z + m∠X = 180 degrees ...(2)

We are given that m∠W = 55 degrees and m∠X = 117 degrees, so we can substitute those values into equations (1) and (2):

m∠Y + 55 = 180 ...(1)

m∠Z + 117 = 180 ...(2)

Solving for m∠Y and m∠Z, we get:

m∠Y = 125 degrees

m∠Z = 63 degrees

Therefore, angle Y measures 125 degrees and angle Z measures 63 degrees.

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The probability of flipping heads is 1/2, and the probability of rolling an even number is 1/2 (since there are three even numbers and three odd numbers on the cube). To find the probability of both events happening (flipping heads and rolling an even number), we multiply the probabilities together:

1/2 x 1/2 = 1/4

So the probability that Olive flipped heads and rolled an even number is 1/4 or 25%.

Answer: 1/4

Step-by-step explanation:

Answer:

a) Distance is 40m b)0 c)2.5m/min

Step-by-step explanation:

a)8*5=40 b)He went from A to A c)16 min s=d/t 40/16

The image of the triangle is attached with coordinates

(0, 0)

(0. 3)

(3, 3)

In mathematics, a scale factor is a constant that multiplies every length of an object, changing its size while preserving its shape. In the context of dilation, which is a type of transformation that changes the size of a shape, the scale factor determines the amount by which the shape is enlarged or reduced.

When a shape is dilated with a scale factor greater than 1, the resulting shape is larger than the original. Conversely, when a shape is dilated with a scale factor between 0 and 1, the resulting shape is smaller than the original. If the scale factor is exactly 1, then the shape remains the same size.

In the problem the image is dilated with a scale factor less than one hence the resulting image is lesser

The new coordinates are gotten as follows

(0, 0) * 1/3 =  (0, 0)

(0. 9) * 1/3 =  (0. 3)

(9, 9) * 1/3 =  (3. 3)

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2/3 of 35 is 23. Kofi is 23.

Using equations,

The quotient of 3 times a number and 7: 3n/7

5 less than a number is x:  x = n - 5

The sum of twice a number and 9: 2n + 9

Two times the sum of a number and 9: 2 (n+9)

The product of 3 times a number and 7: (3n) (7)

The difference between 5 and a number is x: 5 - n = x

A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15.

Many types of equations exist, including linear, quadratic, cubic, and others.

The quotient of 3 times a number and 7: 3n/7

5 less than a number is x:  x = n - 5

The sum of twice a number and 9: 2n + 9

Two times the sum of a number and 9: 2 (n+9)

The product of 3 times a number and 7: (3n) (7)

The difference between 5 and a number is x: 5 - n = x

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Answer:

[tex]y=40\sqrt{\frac{6}{x} }[/tex]

[tex]y=-40\sqrt{\frac{6}{x} } ,x > 0[/tex]

Step-by-step explanation:

pls tell me if wrong have a good night/day

Using the circumference formula the number of full revolutions the wheels need to make to travel 220 feet is obtained as 35.

What is circumference?

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.

The distance traveled by the car in one full revolution of the wheel is equal to the circumference of the wheel.

The circumference of a circle is given by the formula -

C = 2πr

where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Since the diameter of the wheel is 2 feet, the radius is half of that, or 1 foot.

Therefore, the circumference of the wheel is -

C = 2π(1 foot) = 2π feet

To find how many full revolutions the wheel needs to make to travel 220 feet, we can divide the distance traveled by the circumference of the wheel -

Number of revolutions = distance traveled / circumference of the wheel

Number of revolutions = 220 feet / (2π feet) ≈ 35.03

Therefore, the wheels need to make 35 full revolutions to travel 220 feet.

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The value of the angle m<C is 27 degrees. Option B

First, we need to know the different trigonometric identities and their ratios.

We have;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given in the diagram, we have;

Opposite side of angle C = 5

Adjacent side of angle C = 7.5

Hypotenuse side of angle C = 11

Using the sine identity

sin C = 5/11

sin C = 0. 4545

Take sine inverse

C = 27 degrees

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The composite figure compromising of a sector, a triangle and a trapezoid have a total area calculated to be 15.9 square units.

We can observe from the figure that it is a combination of a sector, a triangle and a trapezoid, so we shall calculate the area of each shape and add their result to get the area of the composite figure as follows:

area of the sector = 135°/360° × 22/7 × 2 × 2

area of the sector = 33/7

area of the sector = 4.7 square units

area of triangle = 2.6 × 1

area of the triangle = 2.6 square units

area of the trapezoid = 1/2 × (2.6 + 6) × 2

area of the trapezoid = 8.6 square units

area of the composite figure = 4.7 + 2.6 + 8.6

area of the composite figure = 15.9 square units

In conclusion, the composite figure compromising of a sector, a triangle and a trapezoid have a total area calculated to be 15.9 square units.

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Answer: √698 or 26.42 (2 d.p.)

Step-by-step explanation:

Pythagoras' Threorem is a² + b² = c²

Substitute 13 for a and 23 for b

13² + 23² = x²

169 + 529 = x²

698 = x²

x = √698 = 26.42 (2 d.p.)

Answer: To find out how many rides take place in 28 minutes, we need to divide the total ride length by the length of one side, and then round down to the nearest whole number.

The length of one ride can be calculated by dividing the total ride length by the number of rides. Since we don't know the number of rides, let's call it "n":

length of one ride = total ride length / n

314 minutes / n

Now we can set up an equation to solve for "n":

28 minutes = length of one ride * number of rides

28 minutes = (314 minutes / n) * number of rides

We can simplify this equation by multiplying both sides by "n":

28 minutes * n = 314 minutes * number of rides

Dividing both sides by 314 minutes, we get:

n = (28 minutes * number of rides) / 314 minutes

Multiplying both sides by 314 minutes and dividing by 28 minutes, we get:

number of rides = (n * 314 minutes) / 28 minutes

number of rides = 11.21

Rounding down to the nearest whole number, we get:

number of rides = 11

Therefore, in 28 minutes, 11 rides take place.

Step-by-step explanation:

Answer:y=-x+6

Step-by-step explanation:

The rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex] when its length is 10 cm and its width is 6 cm, this is the case.

One quantity's rate of change with regard to another quantity is known as the rate of change function. In order to calculate the rate of change, one simply divides the amount of change in one item by the equivalent amount of change in another.

Let L and W represent the length and breadth of the rectangle, respectively, and A represents the area of the rectangle. Next, we have:

A = L * W

When L = 10 cm and W = 6 cm, we are interested in determining the rate of increase of the rectangle's area with regard to time, or dA/dt.

We can begin by finding the derivative of A = L * W with regard to time t for both sides of the equation:

Derivate the equation by both sides with respective t.

[tex]\frac{d}{dt} (L * W) = \frac{dA}{dt}[/tex]

Using the principle of product rule of derivative, we arrive at:

[tex]L * W + L * \frac{dw}{dt} = \frac{dA}{dt}[/tex]

To determine dA/dt when L = 10 cm and W = 6 cm, we are provided that [tex]\frac{dL}{dt}[/tex] = 8 cm/s and [tex]\frac{dw}{dt}[/tex]= 9 cm/s. Therefore, we replace these numbers in the previous equation to obtain:

[tex]\frac{dA}{dt}[/tex] = (8 [tex]\frac{cm}{s}[/tex]) * (6 cm) + (10 cm * 9 [tex]\frac{cm}{s}[/tex]).

[tex]\frac{dA}{dt} = 48 \frac{cm^{2}}{s} + 90 \frac{cm^{2}}{s} \\[/tex]

[tex]138 \frac{cm^{2} }{s} = \frac{dA}{dt}[/tex]

Since the rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex]when its length is 10 cm and its width is 6 cm, this is the case.

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The confidence level is the probability that a confidence interval will contain the true population parameter in repeated sampling.

Confidence level is a statistical measure used to indicate the level of certainty or reliability in a statistical inference or estimate. In other words, it represents the success rate of the method used to construct a confidence interval. For example, a 95% confidence level indicates that if we were to repeat the same experiment many times and calculate the confidence interval for each trial, then we would expect 95% of these intervals to contain the true value.

The confidence level is typically chosen by the researcher based on the level of certainty they want to achieve. A higher confidence level corresponds to a wider confidence interval, which increases the likelihood of containing the true value, but reduces the precision of the estimate.

It is important to note that the confidence level does not guarantee that a particular confidence interval contains the true value, but rather it indicates the long-run success rate of the method used to construct the interval. Therefore, it is crucial to understand the underlying assumptions and limitations of the statistical method used to construct the confidence interval.

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The confidence level is a percentage between 0% and 100% that measures the success rate of the method used to construct the confidence interval. If we were to draw many samples and use each one to construct a confidence interval, then in the long run, the percentage of confidence intervals that cover the true value would be equal to the ________?

We can use substitution to solve this system of equations. We can solve the first equation for y and get:

y = (2x + 12)/3

We can then substitute this expression for y into the second equation:

(2x + 12)/3 + 3x = -7

Multiplying both sides of this equation by 3 to eliminate the denominator, we get:

2x + 12 + 9x = -21

Simplifying this equation gives:

11x = -33

Dividing both sides by 11, we get:

x = -3

We can then substitute this value of x back into either of the two original equations to find y. Using the first equation, we get:

3y = 2(-3) + 12

3y = 6

y = 2

Therefore, the solution to the system of equations is x = -3 and y = 2.

To check the solution, we substitute these values back into both equations:

3y = 2x + 12 3(2) = 2(-3) + 12 6 = 6

This equation is true, so the solution (x = -3, y = 2) checks out.