Find the rectangular components of a vector with a magnitude of 30, acting at a point making a 60° with x-axis to the nearest integer.​

The diameter that separates the bottom 5% of bolt diameters produced in the machine shop is approximately 5.62985 millimeters.

We can use the Z-score formula to find the diameters that separate the top 5% and bottom 5% of the bolt diameters produced in the machine shop.

For the top 5%, we want to find the diameter such that 5% of the bolts have a larger diameter. Using a standard normal distribution table or calculator, we find that the Z-score corresponding to the top 5% is 1.645.

So, the Z-score formula gives us:

1.645 = (x - 5.74) / 0.07

Solving for x, we get:

x = 5.74 + 1.645 * 0.07

x = 5.85015

Therefore, the diameter that separates the top 5% of bolt diameters produced in the machine shop is approximately 5.85015 millimeters.

For the bottom 5%, we want to find the diameter such that 5% of the bolts have a smaller diameter. Using the same Z-score of 1.645, but with a negative sign, we get:

-1.645 = (x - 5.74) / 0.07

Solving for x, we get:

x = 5.74 - 1.645 * 0.07

x = 5.62985

Therefore, the diameter that separates the bottom 5% of bolt diameters produced in the machine shop is approximately 5.62985 millimeters.

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There are 44,352 possible ways to select the top six finalists, and thus six singers finish first through sixth.

There are two methods for counting the number of potential outcomes in a situation: permutations and combinations. Nevertheless, they differ in how they take into account the sequence in which the items were selected.

On the other hand, a combination is a collection of items chosen randomly. The number of possibilities of the three letters A, B, and C taken two at a time would be AB, AC, and BC using the same example.

The total number of singes are 12.

Using the multiplication rule we have:

12 x 11 x 10 x 9 x 8 x 7 = 44,352

Hence, there are 44,352 possible ways to select the top six finalists, and thus six singers finish first through sixth.

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Answer:

r≈3.39

Step-by-step explanation:

I'm not quite sure but it's the best I can do.

Answer:

radius of base = 6 cm

Step-by-step explanation:

In order to calculate the radius of the base of a cone given its volume and height, we have to use the formula for the volume of a cone:

[tex]\boxed{\mathrm{V = \frac{1}{3} \pi r^2h}}[/tex],

where:

• V ⇒ volume of the cone

• r ⇒ radius of the base of the cone

• h ⇒ height of the cone

The question gives us the value of the volume of the cone (72π cm³) as well as its height (6 cm). By substituting these values into the equation above, we can solve for r to get the radius of the base of the cone:

[tex]\mathrm{V = \frac{1}{3} \pi r^2h}[/tex]

⇒ [tex]72 \pi = \frac{1}{3} \times \pi \times r^2 \times 6[/tex]

⇒ [tex]r^2 = \frac{72 \pi}{2 \pi}[/tex]

⇒ [tex]r = \sqrt{\frac{72 \pi}{2 \pi}}[/tex]

⇒ [tex]r = \sqrt{36}[/tex]

⇒ r = 6 cm

Therefore, the radius of the base of the cone is 6 cm.

Answer: 234 are sophomores

Step-by-step explanation:

You would take 26% of 900 to get 234

It's simple, don't overthink it :)

Have a nice day.

Step-by-step explanation:

Sophomores are 26 % of 900 students

26 %  * 900 = the number of sophomores

26% * 900 =  .26 * 900 = 234 sophomores

The GPA corresponding to the 70th percentile at the college is approximately 3.246 based on standard deviation.

We can use the conventional normal distribution table or a calculator with a normal distribution function to determine the 70th percentile of GPAs at a college, which are normally distributed with a mean of 2.9 and a standard deviation of 0.6.

The inverse normal distribution function with a mean of 2.9, a standard deviation of 0.6, and a percentile of 70 can be used on a calculator. This results in:

[tex]3.246 for invNorm(0.7, 2.9, 0.6).[/tex]

As a result, the GPA that represents the 70th percentile is roughly 3.246.

We can determine the z-score corresponding to the 70th percentile, which is 0.5244, by using a common normal distribution table. Thus, we may apply the equation z = (x - ) /, where x is the GPA that corresponds to the 70%ile, is the mean, and is the standard deviation, and all three variables have values of 2.9. After finding x, we obtain:

0.5244 = (x - 2.9) / 0.6

x = 3.246

Once more, doing so yields the same outcome as using a calculator.

In conclusion, the GPA at the college that represents the 70th percentile is roughly 3.246.

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The angles with a common reference angle of 319° in each quadrant are:

First quadrant: 319°, Second quadrant: -139°, Third quadrant: 139°, Fourth quadrant: 41°.

To find an angle in each quadrant with a common reference angle of 319°, we can start by subtracting 360° from 319° repeatedly until we get a result between 0° and 360°. This is because angles that differ by a multiple of 360° are coterminal, which means they have the same reference angle.

319° - 360° = -41° (not in the range 0° to 360°)

319° - 2(360°) = -401° (not in the range 0° to 360°)

319° - 3(360°) = -721° (not in the range 0° to 360°)

319° - 4(360°) = -1041° (not in the range 0° to 360°)

319° - 5(360°) = -1361° (not in the range 0° to 360°)

319° - 6(360°) = -1681° (not in the range 0° to 360°)

319° - 7(360°) = -2001° (not in the range 0° to 360°)

Since none of these results are in the range of 0° to 360°, we need to add multiples of 360° instead.

319° - 1(360°) = -41° (not in the range 0° to 360°)

319° - 0(360°) = 319°

319° + 1(360°) = 679° (not in the range 0° to 360°)

319° + 2(360°) = 1039° (not in the range 0° to 360°)

319° + 3(360°) = 1399° (not in the range 0° to 360°)

So, the angle with a common reference angle of 319° in the first quadrant (0° to 90°) is:

θ = 319° - 1(360°) = -41° + 360° = 319°

The angle with a common reference angle of 319° in the second quadrant (90° to 180°) is:

θ = 180° - 319° = -139°

The angle with a common reference angle of 319° in the third quadrant (180° to 270°) is:

θ = 319° - 180° = 139°

The angle with a common reference angle of 319° in the fourth quadrant (270° to 360°) is:

θ = 360° - 319° = 41°

Therefore, the angles with a common reference angle of 319° in each quadrant are:

First quadrant: 319°

Second quadrant: -139°

Third quadrant: 139°

Fourth quadrant: 41°

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Answer:

Step-by-step explanation:

$499.99 - 15% will give your answers

Answer:

424.99

Step-by-step explanation:

Using simple interest, we can find the value of interest here to be $162 per month.

Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. The principal amount in the case of simple interest does not change, in contrast to compound-interest, where the interest is added to the principal to calculate the principal for the new principal for the following year.

Given in the question,

Principle, P = $18000

Rate of interest, R = 0.45%

= 0.45/100

Time in years, T = 24 months

= 2 years.

I = P R T

= 18000 × 0.45/100 × 2

= $162

Therefore, interest here is $162 per month.

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"Rolling a die until a 3 shows" can be modeled by a geometric distribution due to independent trials with a constant probability of success, with an expected value of 6 rolls.

What is the geometric distribution and how does it model the rolling of a die until a 3 shows?

Rolling a die until a 3 shows can be modeled by a geometric distribution because:

The geometric distribution models the number of trials needed to achieve the first success in a sequence of independent trials with a constant probability of success. In this case, the number of trials needed to roll a 3 for the first time can be modeled by a geometric distribution with a probability of success of 1/6.

The expected value of the geometric distribution is calculated as 1/p, where p is the probability of success. Therefore, the expected number of rolls needed to roll a 3 for the first time is 1/(1/6) = 6.

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The solutions are explained below.

Given that, Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. The figure is attached.

Height of Jeremy's drone = 30 m

Height of Leslie's drone = x m

h / 70 = sin 53°

h = 70 × sin 53°

h = 57.34

Therefore, Leslie's drone is higher than Jeremy's drone.

Difference of height = 57.34 - 30 = 27.34 m

27.34 / x = tan25°

x = 58.63 m

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If a family chose to opt out of paying the $210 monthly premium for health insurance, they would not have coverage under the health insurance plan. This means that they would be responsible for paying for any medical expenses out of pocket.

Without health insurance, the cost of medical care can be quite high, and a family could potentially face financial ruin if they experienced a serious illness or injury. They may also be unable to afford routine check-ups or preventative care, which could lead to undiagnosed health issues.

It's important for individuals and families to carefully consider the costs and benefits of health insurance coverage, and to choose a plan that best fits their needs and budget. While the monthly premium may seem like a significant expense, the cost of not having coverage can be much higher in the long run.

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So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3))

An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "

To find (f o h)(-3), we need to first evaluate h(-3), and then plug that result into the function f(x).

Given:

f(x) = -2x - 1

h(x) = -x - 5

First, we evaluate h(-3):

h(-3) = -(-3) - 5

h(-3) = 3 - 5

h(-3) = -2

Now, we plug the result of h(-3) into the function f(x):

f(h(-3)) = f(-2)

f(h(-3)) = -2(-2) - 1

f(h(-3)) = 4 - 1

f(h(-3)) = 3

So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3)), which means we first evaluate h(-3) and then plug that result into f(x). I hope this helps! Let me know if you have any further questions. :)

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The final equation of the exponential function is [tex]y = 27/3^x[/tex], which passes through the points (2,3) and (5,1/9).

When mοdelling a cοnnectiοn, expοnential functiοns simulate hοw a cοnstant change in the independent variable results in the same prοpοrtiοnal change. The expοnentiaI functiοn is a mathematicaI functiοn denοted by f(x)=[tex]\exp[/tex] or [tex]e^{x}.[/tex]

Let's start by plugging in the values οf the first pοint (2,3) intο the equatiοn:

3 = ab²

Similarly, we can plug in the values οf the secοnd pοint (5,1/9):

1/9 = ab^5

Sοlving fοr a in the first equatiοn:

a = 3/b²

Substituting a in the secοnd equatiοn:

1/9 = (3/b²) * b^5

Simplifying:

1/9 = 3b³

b^3 = 1/27

b = 1/3

Substituting b intο the first equatiοn tο sοlve fοr a:

3 = a(1/3)²

3 = a/9

a = 27

Therefοre, the equatiοn οf the expοnential functiοn is y = 27(1/3)^x οr y = 27/3^x.

So the final equation of the exponential function is [tex]y = 27/3^x[/tex], which passes through the points (2,3) and (5,1/9).

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Step-by-step explanation:

what "normal" trigonometric function did this remind us of ?

it starts at "high" for x = 0.

"high" signs mean "1" for the standard functions.

the trigonometric function that starts with 1 at x = 0 is cosine.

so, this is a cosine function that we need to scale properly.

original value : 1

graph : 15

original value : -1

graph : 12

original value : 0

graph : (15+12)/2 = 27/2 = 13.5

so, we need to add this to the cosine function result.

the distance from the 0 level (13.5) to high or low is 1.5 (instead of originally 1).

Du, we need to stretch the cosine function result to go from -1.5 to +1.5 (12 to 15).

and for the x-axis :

12 hours = 180° or pi (the interval for cosine to go from +1 to -1).

1 hour = 180/12 = 15° or pi/12.

so, for cosine to react to the hour value as for the curdling degrees we need to multiply x by 180/12 or by pi/12.

so, our temperature function temp(x) is then

temp(x) = 1.5×cos(x×180/12) + 13.5

or

temp(x) = 1.5×cos(x×pi/12) + 13.5

The ninth term of the geometric sequence with a1=8 and [tex]r = \frac{1}{2}[/tex] is [tex]\frac{3}{2}[/tex]. The term equal to 36 is the fourth term, the term equal to 32 is the third term, and the common ratio is 1/4.

What are the common ratio of the geometric sequence with a1=8 and r=1/2?

The general formula for the nth term of a geometric sequence is given by:

[tex]a_n &= a_1 \times r^{n-1}[/tex]

a) To find the ninth term of the sequence with a1=8, r=1/2, and n=9, we can plug in these values into the formula:

[tex]a_9 &= a_1 \times r^{9-1} \\&= 8 \times \left(\frac{1}{2}\right)^{9-1} \\&= 8 \times \left(\frac{1}{2}\right)^8 \\&= 8 \times \frac{1}{256} \\&= \frac{1}{32}[/tex]

So the ninth term is 1/32.

b) To find the term that is equal to 36, we can set the formula equal to 36 and solve for n:

[tex]a_n &= a_1 \times r^{n-1} = 36 \\a_1 \times \left(\frac{1}{2}\right)^{n-1} &= 36 \\8 \times \left(\frac{1}{2}\right)^{n-1} &= 36 \\\left(\frac{1}{2}\right)^{n-1} &= \frac{36}{8} \\\left(\frac{1}{2}\right)^{n-1} &= 4.5 \\n-1 &= \log_{1/2}(4.5) \\[/tex]

n-1 = 3.17 (rounded to two decimal places)

n = 4.17 (rounded to two decimal places)

Therefore, the term that is equal to 36 is the fourth term.

c) To find the term that is equal to 32, we can set the formula equal to 32 and solve for n:

[tex]a_n &= a_1 \times r^{n-1} = 32 \\a_1 \times \left(\frac{1}{2}\right)^{n-1} &= 32 \\8 \times \left(\frac{1}{2}\right)^{n-1} &= 32 \\\left(\frac{1}{2}\right)^{n-1} &= 4 \\n-1 &= \log_{1/2}(4) \\[/tex]

n-1 = 2

n = 3

Therefore, the term that is equal to 32 is the third term.

d) To find the common ratio, we can use the formula:

[tex]r &= \frac{a_n}{a_{n-1}}[/tex]

where an is the nth term and a(n-1) is the term before it. For this problem, we are given a1=8 and n=9, so we can use the formula to find a9 and a8, and then calculate the ratio:

[tex]a_9 &= a_1 \times r^{n-1} = 8 \times (1/2)^8 = \frac{1}{256} \\[/tex]

[tex]a_8 &= a_1 \times r^{n-2} = 8 \times (1/2)^7 = \frac{1}{64} \\[/tex]

[tex]r &= \frac{a_9}{a_8} = \frac{\frac{1}{256}}{\frac{1}{64}} = \frac{1}{4}[/tex]

Therefore, the common ratio is 1/4.

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The shaded figure consists of a square with side length x and four identical quarter circles with radius x/2.

The area of the square is given by (side length)^2, so the area of the square is x^2.

The area of one quarter circle is given by (1/4)π(radius)^2, so the area of all four quarter circles is π(x/2)^2 = (1/4)πx^2.

Therefore, the total area of the shaded figure is the area of the square plus the area of the quarter circles, which is:

x^2 + (1/4)πx^2 = (4/4)x^2 + (1/4)πx^2 = (4+π)/4 x^2

So, the expression that represents the total area of the shaded figure is ((4+π)/4)x^2, where x is measured in meters and the area is measured in square meters.

Answer:

[tex] - 2(x - 5)(x + 1)[/tex]

Step-by-step explanation:

[tex]1. \: - 2(x {}^{2} - 4x - 5) \\ 2. \: - 2(x - 5)(x + 1)[/tex]

Answer:       command economic systems:

  China: China's economy has been under the control of the Communist Party since 1949. Although the country has gradually introduced market-oriented reforms in recent decades, the government still exercises significant control over the economy.

   Cuba: Since the Cuban Revolution in 1959, Cuba has been a one-party socialist state with a command economy. The government controls almost all economic activity, including the allocation of resources and setting of prices.

   North Korea: North Korea is a communist state with a command economy. The government controls all economic activity and owns all major industries, including agriculture, manufacturing, and transportation.

   Vietnam: Vietnam is a one-party socialist state with a command economy. The government controls the allocation of resources, sets prices, and owns much of the economy's key industries.

   Venezuela: Venezuela is a socialist state with a command economy that has been in crisis in recent years. The government controls much of the economy, including the country's vast oil reserves, but the country has been plagued by hyperinflation and shortages of basic goods.

5 countries that follow mixed economic system in and out of Africa:

   United States: The United States has a mixed economy, which means that it has both private and public ownership of the means of production. The government regulates some industries and provides social services, while others are left to the free market.

  United Kingdom: The United Kingdom is another example of a mixed economy. It has a strong tradition of free-market capitalism, but the government also provides social services and regulates some industries.

  South Africa: South Africa is a country in Africa that has a mixed economy. It has a well-developed private sector, but the government also provides social services and regulates certain industries.

   Brazil: Brazil is a country in South America that has a mixed economy. It has a large and growing private sector, but the government also plays a significant role in the economy, particularly in areas such as energy, telecommunications, and transportation.

   India: India is a country in South Asia that has a mixed economy. It has a large and diverse private sector, but the government also plays an active role in the economy through regulation, public ownership of some industries, and social services.

The students answered 150 questions correctly in total based on proportions concept if points are given.

If the first paper scored 30 points and the second scored 50 points, then the total score is 30 + 50 = 80 points. Since each question answered correctly is worth 2 points, we can divide the total score by 2 to find the number of questions answered correctly altogether.

80 / 2 = 40

Therefore, the students answered 40 questions correctly in total.

Another way to approach this problem is to use proportions. Let's say that the number of questions answered correctly on the first paper is x, and the number of questions answered correctly on the second paper is y. Then we can set up a proportion:

x/15 + y/25 = 1

where 15 and 25 are the total number of questions on each paper, and 1 represents the total proportion of questions answered correctly.

Multiplying LHS and RHS by least common multiple of 15 and 25, which is 75:

5x + 3y = 75

If we know that x = 30 and y = 50, we substitute these values into equation and check that if its true:

5(30) + 3(50) = 150 + 150 = 300

Dividing sides by 2 to get:

300 / 2 = 150

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Answer:

Step-by-step explanation:

To find the direction of minimum rate of change for the function f(x, y) = x² + xy + y² at the point (5, 2), we need to find the gradient vector (also known as the gradient or the vector of partial derivatives) and then find the direction orthogonal to the gradient vector, as this direction will have the minimum rate of change.

First, let's find the gradient vector by computing the partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x + y

∂f/∂y = x + 2y

Now, evaluate the gradient vector at the point (5, 2):

∇f(5, 2) = (2(5) + 2, 5 + 2(2)) = (12, 9)

The gradient vector is (12, 9). To find the direction orthogonal to the gradient vector, we can swap the x and y components and negate one of them. Since the question asks for a vector with an x-component of 1, 0, or -1, we'll negate the x-component:

Orthogonal vector = (-1, 12)

So, the direction of minimum rate of change at point (5, 2) is given by the vector [-1, 12].

The probability of drawing a prime is 40%.

To calculate the probability of drawing a prime number, use the formula

P(E) = Number of favorable outcomes / Total number of outcomes

Where P(E) is the probability of event E, and we determine the number of favorable outcomes and total possible outcomes based on the given conditions.

Here we have

Ten cards numbered 1 to 10 are placed in a box.  

The total number of outcomes will get in a random experiment = 10

Here set of prime numbers from 1 to 10 = {2, 3, 5, 7}

Number of favorable outcomes that are getting prime number = 4

Hence, the probability of getting a prime number

= 4/10 = 2/5 = 0.4 = 40%    [ Multiplied by 100 ]

Therefore,

The probability of drawing a prime is 40%.

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Answer:

[tex]x ^{2} - 4x + 1[/tex]

Answer:

27/1000 is your answer

Step-by-step explanation:

Answer:

2 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

1 1/9 x 2 2/5 = ?

1 1/9 = 10/9

2 2/5 = 12/5

[tex]\frac{10}{9}[/tex] x [tex]\frac{12}{5}[/tex] = [tex]\frac{120}{45}[/tex] = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex]

So, the answer is 2 [tex]\frac{2}{3}[/tex]

If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:

1.10x

This is because 110% can be written as 1.10 (since 110% means 110 out of 100).

So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.

However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.

Answer:If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:

1.10x

This is because 110% can be written as 1.10 (since 110% means 110 out of 100).

So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.

However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.

Step-by-step explanation:

It would take 64 small cubes to fill the large cube. This is because the volume of a cube is equal to the length of its edges.

The amount of space occupied by an object or the amount of space an object can fill. It is usually expressed in cubic units, such as cubic centimeters or cubic meters.

This is because the volume of a cube is equal to the length of its edges cubed, or V = s³, where s is the length of the edge.

We can calculate the volume of the large cube by replacing the length of its edges with 5 inches, or V = 53 = 125 in³.

To find the number of small cubes, we must first figure out the volume of a single small cube.

We can do this by replacing the length of the small cube's edges with 2.5 inches, or V = 2.53 = 15.625 in³

We can then divide the volume of the large cube (125 in³) by the volume of the small cube (15.625 in³) to get the number of small cubes needed to fill the large cube, which is equal to

125 / 15.625 = 8 * 8 = 64.

Therefore, it would take 64 small cubes to fill the large cube.

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Answer(-2,0) and (3,5)

Step-by-step explanation:

trust me bro

Answer:

B

Step-by-step explanation:

given a parabola in standard form

f(x) = ax² + bx + c (a ≠ 0 ) , then

the x-coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

f(x) = - 4x² - 16x - 13 ← is in standard form

with a = - 4 , b = - 16 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{-16}{2(-4)}[/tex] = - [tex]\frac{-16}{-8}[/tex] = - 2

substitute x = - 2 into f(x) for corresponding y- coordinate

f(- 2) = - 4(- 2)² - 16(- 2) - 13

        = - 4(4) + 32 - 13

        = - 16 + 19

        = 3

vertex = (- 2, 3 )