send help please, i struggled with these kinds of questions minutes ago!

Step 1

Remove full rotations of 360 degrees until the angle is between 0 and 360 degrees

Step 2

Hence, we find sin 120 using reference angles in the first quadrant

Therefore,

Answer sin 480 =(√3)/2

A. A sample size of 62 should be taken for a 95% level of confidence.

B. The sample size of 107 should be taken for a 99% level of confidence.

a. To estimate the sample size needed to estimate the mean time a staff member spends with each patient, we can use the formula for sample size calculation:

n = (Z^2 * σ^2) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired level of confidence

σ = population standard deviation

E = desired margin of error

For a 95% level of confidence:

Z = 1.96 (corresponding to a 95% confidence level)

E = 2 minutes

σ = 8 minutes (population standard deviation)

Substituting these values into the formula:

n = (1.96^2 * 8^2) / 2^2

n = (3.8416 * 64) / 4

n = 245.9904 / 4

n ≈ 61.4976

Since we can't have a fraction of a sample, we round up the sample size to the nearest whole number. Therefore, a sample size of 62 should be taken for a 95% level of confidence.

b. For a 99% level of confidence:

Z = 2.58 (corresponding to a 99% confidence level)

E = 2 minutes

σ = 8 minutes (population standard deviation)

Substituting these values into the formula:

n = (2.58^2 * 8^2) / 2^2

n = (6.6564 * 64) / 4

n = 426.0096 / 4

n ≈ 106.5024

Rounding up the sample size to the nearest whole number, a sample size of 107 should be taken for a 99% level of confidence.

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Based on the information provided, we can assume that the sample of 700 births is representative of the population of births in the local area. The distribution of these 700 births across the days of the week can be analyzed to determine whether or not newborn babies are uniformly distributed across the days of the week.If the distribution of the 700 births is approximately equal across all seven days of the week, then we can conclude that newborn babies are uniformly distributed. However, if the distribution is significantly different from what would be expected if births were uniformly distributed, then we can conclude that there may be a non-uniform pattern of births.

Without knowing the actual distribution of the 700 births, we cannot definitively answer this question. However, if the distribution is close to equal, then we can tentatively say that newborn babies are uniformly distributed across the days of the week.

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Answer:

Step-by-step explanation:

x - 8y = 16

Write in slope-intercept form: y = mx + b

-8y = -x + 16

Divide the entire equation by (-8)

\(y =\dfrac{-1}{-8}x+\dfrac{16}{-8}\\\\\\y=\dfrac{1}{8}x-2\)

Parallel lines have slope. So, the slope of the required line = 1/8

\(y =\dfrac{1}{8}x+b\\\\\\\)

(-8,2) is on the line. so, plugin the values in the above equation and find the y-intercept b

\(2=\dfrac{1}{8}*(-8)+b\\\\\\2=-1+b\\\\b = 2+1\\\\b = 3\\\\Equation \ of \ the \ required \ line:\\\\y=\dfrac{1}{8}x+3\)

Answer:

\(\displaystyle x - 8y = -24\:or\:y = \frac{1}{8}x + 3\)

Step-by-step explanation:

First off, convert this standard equation to a Slope-Intercept equation:

\(\displaystyle x - 8y = 16 \hookrightarrow \frac{-8y}{-8} = \frac{-x + 16}{-8} \\ \\ \boxed{y = \frac{1}{8}x - 2}\)

Remember, parallel equations have SIMILAR RATE OF CHANGES, so ⅛ remains as is as you move forward with plugging the information into the Slope-Intercept Formula:

\(\displaystyle 2 = \frac{1}{8}[-8] + b \hookrightarrow 2 = -1 + b; 3 = b \\ \\ \boxed{\boxed{y = \frac{1}{8}x + 3}}\)

Now, suppose you need to write this parallel equation in Standard Form. You would follow the procedures below:

y = ⅛x + 3

- ⅛x - ⅛x

__________

−⅛x + y = 3 [We CANNOT leave the equation this way, so multiply by –8 to eradicate the fraction.]

−8[−⅛x + y = 3]

\(\displaystyle x - 8y = -24\)

With that, you have your equation(s).

\(\displaystyle -x + 8y = 24\)

*About this equation, INSTEAD of multiplying by –8, you multiply by its oppocite, 8. Now, you can leave it like this, but UNIVERSALLY, the A-term is positive, so you must multiply the negative out as well.

I am joyous to assist you at any time.

The expected amount of each cube in the complete bag is given as follows:

The expected amounts are obtained applying the proportions in the context of the problem.

15 cubes were selected from a bag of 60, hence the fraction collected is given as follows:

15/60 = 1/4.

Meaning that the expected amounts on the bag are given by the amounts on the sample multiplied by 4.

The problem asks for the expected amount of each cube in the complete bag.

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Three cards are drawn from a standard deck. Thus, the probability to get an ace, followed by a king, and then a queen, is  16/34,425

The formula for conditional probability is:

P(A∩B) = P(B|A) . P(A)

In the given problem:

P(ace) = 4 / 54

After an ace was drawn, the number of cards now is 51.

Hence,

P(king | ace) = 4/51

After the second drawn, the remaining cards is 50. Hence,

P(queen | (king | ace)) = 4/50

Therefore,

P(ace,king,queen) = 4/54 x 4/51 x 4/50 = 64 / 137,700 = 16/34,425

Thus, the probability to get an ace, followed by a king, and then a queen, is  16/34,425

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Answer:

Step-by-step explanation:

According to Pythagorean:

Two sides are 15 cm and 17 cm

If the third side is hypotenuse, its length is:

If the third side is leg, its length is:

#4

Apply Pythagorean theorem

#5

If base

If Hypotenuse

Answer:

22 is x

Step-by-step explanation:

diagonal of rhombus make 90° on intersection

5x-20 = 90

5x = 110

x = 22

Answer:

Graph A

Step-by-step explanation:

Answer:

He can fill 3 crates, there would be 1 orange left over

Step-by-step explanation:

four equal rows of three oranges = 12 total. 12x3= 36, so 1 left over

Answer:

Assuming a normal distribution of data with a mean μ and a standard deviation σ, we can use the empirical rule to find the percentage of values that lie within a certain range.

The empirical rule states that for a normal distribution:

- Approximately 68% of the values lie within one standard deviation of the mean.

- Approximately 95% of the values lie within two standard deviations of the mean.

- Approximately 99.7% of the values lie within three standard deviations of the mean.

Based on this rule, we can determine the percentage of values that lie within different ranges. For example:

- Within one standard deviation: Approximately 68% of the values.

- Within two standard deviations: Approximately 95% of the values.

- Within three standard deviations: Approximately 99.7% of the values.

Please note that the exact percentage may vary depending on the specific values of the mean and standard deviation. It is important to calculate the values based on the actual mean and standard deviation provided.

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Answer:

Below.

Step-by-step explanation:

That is the incenter.

The point where the three angle bisectors of a triangle intersect is called as the incenter of the triangle

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of angles are ∠A , ∠B , ∠C

where the three angle bisectors are drawn

Now , point where the three angle bisectors of a triangle intersect is the incenter of the triangle

And , when all three angles of a triangle's bisectors come together at a location inside a circle, all three triangle vertices are equally far from that point.

Hence , triangle's incenter is also the center of the biggest circle that can be encircled by the triangle.

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A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.

Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.

\( \bar{AB}\)

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Answer:

the four consecutive numbers are   89, 90, 91, 93.

Step-by-step explanation:

let the four consecutive numbers be x, x+2, x+4, x+6

according to the condition in the question

x+x+2+x+4+x+6=368

4x+12=368

4x=356

x= 89

So,  the numbers are   89, 90, 91, 93.

hope this will help :)

Answer:

The equation rewritten in standard from --->

46x = 65.

solution --> x = 65/46

Alternate form --> x = 1 19/46, x = 1.41

Answer:

26.9 - 56.16a

Step-by-step explanation:

-1.7 + 5.2(5.5 - 10.8a)

use the distributive property

-1.7 + 28.6 - 56.16a

combine like terms

-1.7 + 28.6 = 26.9

26.9 - 56.16a

plz mark as brianliest if correct!!!

Answer: #The tank holds 80,000 gallons of water when filled to capacity.

Step-by-step explanation:

4/5 - 3/4 = 1/20

The fraction (1/20) represents the 4000 gallons of water.

     1/20 = 4,000

       1    =?                  

then u cross multiply

1*4,000*20/1

= 80,000 gallons of water

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Answer:

$350

Step-by-step explanation:

8-6 is 10 hours per day

3 days x 10 hours per day gives you 30 hours

30 hours x $10 per hour gives you $300

$300 plus the $50 flat fe gives you $350 in total

Answer:

6x2 + 16x = 672

Reorder the terms:

16x + 16x2 = 672

Solving

16x + 16x2 = 672

Solving for variable 'x'.

Reorder the terms:

-672 + 16x + 16x2 = 672 + -672

Combine like terms: 672 + -672 = 0

-672 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.

16(-42 + x + x2) = 0

Factor a trinomial.

16((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

Solution

x = {-7, 6}

Step-by-step explanation:

The given quadratic function models the projectile of the object as it is

launched off the top of the building.

The interpretation of the function values are;

The appropriate domain is 0 ≤ x ≤ 7

Reasons:

The given function for the height of the object is f(x) = -16·x² + 16·x + 672

The domain is given by the values of x for which the value of y ≥ 0

Therefore, when -16·x² + 16·x + 672 = 0, we get;

-16·x² + 16·x + 672 = 0

16·(-x² + x + 42) = 0

-x² + x + 42 = 0

x² - x - 42 = 0

(x - 7)·(x + 6) = 0

x = 7, or x = -6

The minimum value of time, x is 0, which is the x-value at the top of the

building, and when x = 7, the object is on the ground.

Therefore;

The maximum value of f(x) = a·x² + b·x + c, is given at \(x = -\dfrac{b}{2 \cdot a}\)

Therefore;

We have;

\(x = -\dfrac{16}{2 \times (-16)} = \dfrac{1}{2}\)

Which gives;

\(f \left(\frac{1}{2} \right) = -16 \times \left(\dfrac{1}{2} \right)^2 + 16 \times \left(\dfrac{1}{2} \right)+ 672 = 676\)

The height of the building is given when the time, x = 0, as follows;

Height of building, f(0) = -16 × 0² + 16 × 0 + 672 = 672

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The standard error of mean is option a) 0.475.

To estimate the standard error of the mean, we can use the formula:

Standard Error of the Mean = Population Standard Deviation / Square Root of Sample Size

In this case, the population standard deviation is given as 3.8 hours, and the sample size is 64. Plugging these values into the formula, we get:

Standard Error of the Mean = 3.8 / sqrt(64)

Simplifying this equation, we have:

Standard Error of the Mean = 3.8 / 8

Standard Error of the Mean = 0.475

So the correct answer is a. 0.475.

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Answer:  D) as x → ∞, y → ∞

Step-by-step explanation:

see graph

Notice that as x approaches negative infinity (goes to the left), the y-value decreases (goes toward negative infinity).

And as x approaches positive infinity (goes to the right), the y-value increases (goes toward positive infinity).

Answer:

D

Step-by-step explanation:

on the edge D

The answer in simplest form is x = -3/4

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

The given equation is

3x + 3 +9 =-x-9

Collecting like terms to have

3x + x = -9+9-3

4x = -3

Making x the subject of the relation

Therefore, the value of x is x = -3/4

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Answer:

30 m

Step-by-step explanation:

500 x 6cm = 3000 cm = 30 m

Since the scale is 1:500, you can simply multiply the length you were given by 500.

500 * 6 = 3000

So the wall in reality will be 3000cm or 30m.

The uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

To calculate the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ for the given wave packet, we need to find the expectation values of the observables (x^ - ⟨x⟩)^2 and (p^ - ⟨p⟩)^2, respectively.

The wave packet is represented by the function ψ(x) = [2πa^2]^(1/2) exp[-4a^2(x - ⟨x⟩)^2 + iℏpx]. Here, a is a constant, ⟨x⟩ represents the expectation value of x, and p is the momentum operator.

To find ⟨Δx^2⟩, we calculate the expectation value of (x^ - ⟨x⟩)^2 with respect to ψ(x). By integrating (x - ⟨x⟩)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δx^2⟩ = a^2/2.

Similarly, to find ⟨Δp^2⟩, we calculate the expectation value of (p^ - ⟨p⟩)^2 with respect to ψ(x). Since p is the momentum operator, its expectation value is ⟨p⟩ = 0 for the given wave packet. By integrating (p^ - 0)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

Therefore, the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

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Answer:

i think that the answer is D. I did it wrong

Answer:

i think its D

Step-by-step explanation:

bc the 500 has to stay constant (so 500 cannot change to 501,502 etc)

gl for the rest of the questions

As a result, when the circle's radius is specified as 7 units, its area is 49 units, or 153.86 units2.

A circle is formed when every point in the plane that is a specific distance apart from another point does so (center). Thus, it is a curve made up of points that are separated from one another by a set distance while moving in the plane. It is also rotationally symmetric about the center at all angles. A circle is a closed, two-dimensional object where each pair of points in the plane is equally separated from the "center." A specular symmetry line is made by drawing a line through the circle. It is also rotationally symmetric about the center at all angles.

given

Radius of the circle

Radius,  = d / 2 = 7

Area of the circle = pi * r * r = pi *49 = 49pi

Substituting the value of π = 3.14,

Area of the circle = 49 * 3.14 = 153.86 unit²

As a result, when the circle's radius is specified as 7 units, its area is 49 units, or 153.86 units2.

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Answer:

Many solutions

Step-by-step explanation:

Answer:

They are the same angle.

Step-by-step explanation:

We have a diagonal line and two 180° parallel lines running through it. The x and y values should be identical because of the placement. The diagonal on the right and right above the 180° angle.

Option 2: Corresponding angles.

Hope this helps!

If not, I am sorry.