9 N = 480 ´ 109
(a) Write N as a number in standard form.
(1)
(b) Write N as a product of powers of its prime factors.
Show your working clearly.
(3)
(c) Find the largest factor of N that is an odd number.

Answer:

Step-by-step explanation:

[tex]\frac{1}{5}[/tex] ∠ 7x

[tex]\frac{1/5}{7}[/tex] ∠ x

1/35 ∠x

x ≥ [tex]\frac{1}{35}[/tex]

Based on the information in the image, we can infer that the surface area is 863.5cm³.

To find the surface of the figure we must divide the figure in two, into the cone and the cylinder and find the surface of each one separately and then add it.

Cylinder surface area:

To calculate the surface area of a cylinder we must apply the following formula:

[tex]A = 2\pi r h ++ 2 \pi r^{2} \\A = 2 * \pi * 5 * 15 + 2 * \pi * 5^{2} \\A = 471 + 157\\A = 628cm^{3}[/tex]

Cone surface area:

[tex]A = \pi rh + \pi r^{2} \\A = \pi * 5 * 10 + \pi * 5^{2} \\A = 157 + 78.5 \\A = 235.5 cm^{3}[/tex]

Surface area of the entire figure:

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If 30,15,90 and x are in proportion the value of x is 5.

The given terms 30, 15, 90 and x are in proportion, so they follow the proportion formula:

a : b = c : x.

We can use this to solve for the value of x.

First, let's set up the equation:

30 : 15 = 90 : x

To solve for x, we must multiply both sides of the equation by 15:

30 * 15 = 90 * x

Now we have:

450 = 90x

To solve for x, we need to divide both sides by 90:

450 / 90 = 90x / 90

Which simplifies to:

x = 5

Therefore, the value of x is 5.

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The probability that a person rolling a die gets the first 2 on the third roll is 25/216 and the first 2 on the fifth roll is 15625/7776.

The probability that a person rolling a die gets a) the first 2 on the third roll b) the first 2 on the fifth roll are calculated as follows:

(a) The probability of getting a 2 on any roll is 1/6.The probability of not getting a 2 on the first roll is 5/6The probability of not getting a 2 on the second roll is also 5/6The probability of getting a 2 on the third roll is 1/6Therefore, the probability of getting a 2 on the third roll is: 5/6 × 5/6 × 1/6 = 25/216

(b) The probability of getting a 2 on any roll is 1/6.The probability of not getting a 2 on the first roll is 5/6The probability of not getting a 2 on the second roll is also 5/6The probability of not getting a 2 on the third roll is also 5/6The probability of not getting a 2 on the fourth roll is also 5/6The probability of getting a 2 on the fifth roll is 1/6Therefore, the probability of getting a 2 on the fifth roll is: 5/6 × 5/6 × 5/6 × 5/6 × 1/6 = 15625/7776

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The value of the sides are;

h = 2√3

c = 4√2

To determine the value, we need to note that the trigonometric identities are represented with the fraction;

sin θ = opposite /hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have that;

Using the sine identity

sin 60 = 3/h

Now, cross multiply the values, we have;

h = 3/sin 60

find the sine value

h = 3/√3/2

divide the values

h = 6√3/3 = 2√3

For the second triangle.

sin 45 = 4/c

cross multiply

c = 4/1/√2

c = 4√2

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Answer:

[tex]h = \boxed{2\sqrt{3}}\\\\c = \boxed{4\sqrt{2}}[/tex]

Step-by-step explanation:

We can use the law of sines to determine the sides indicated

Law Of Sines

The ratio of the sides of a triangle to the sine of the angle opposite to that side is the same for all sides

In the triangle on the leftwe have side of length 3 opposite 60° and side of length h opposite 90°

So
[tex]\dfrac{h}{\sin 90} = \dfrac{3}{\sin 60}\\[/tex]

sin 90 = 1
[tex]\sin 60 = \dfrac{\sqrt{3}}{2}[/tex]

Therefore we get
[tex]\dfrac{h}{1} = \dfrac{3}{\dfrac{\sqrt{3}}{2}}\\\\h = 3 \times \dfrac{2}{\sqrt{3}}\\\\h = \dfrac{6}{\sqrt{3}}\\\\[/tex]

Rationalizing the denominator by multiplying by √3 we get
[tex]h = \dfrac{6\sqrt{3}}{3} = \boxed{2\sqrt{3}}[/tex]  
(Answer)

-----------------------------------------------------------------------------------------

For the triangle on the right we have
[tex]\dfrac{c}{\sin 90} = \dfrac{4}{\sin 45}\\\\\sin 90 = 1\\\sin 45 = \dfrac{1}{\sqrt{2}}\\\\c = \dfrac{4}{\dfrac{1}{\sqrt{2}}}\\\\c = 4 \times \sqrt{2}\\\\c = \boxed{4\sqrt{2}}[/tex]

(Answer)

-----------------------------------------------------------------------------------------

In the both above computations we are using the fact that dividing by a fraction involves flipping the denominator fraction and multiplying

The intersection of two sets is the set of elements that are common to both sets, while the union of two sets is the set of elements that are in either of the two sets. Intersection and union are two of the most important operations in set theory and are used for a variety of purposes.

The purpose of the intersection operation is to find common elements between two sets, such as the common elements in two groups of people. The intersection operation produces a new set, which contains only the elements that are in both sets.
The purpose of the union operation is to join two sets together. The union operation produces a new set, which contains all the elements that are in either of the two sets. This is useful when you want to combine two different sets of data.

In summary, the intersection operation finds the common elements between two sets, while the union operation combines two sets of data into one. Both operations are important in set theory and are used for a variety of purposes.

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The three classifications of fundamental skull shapes are: +

The number of degrees of angulation (formed by the petrous pyramids and the midsagittal plane) for each classification is 45, 30, and 15 degrees, respectively.

The skull is a bony structure that supports the face and protects the brain. There are several different skull shapes, which can be classified into three main categories based on their length and width: brachycephalic, mesocephalic, and dolichocephalic.

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Answer: I mean technically no. grades don't really matter until high school. You can get held back but that's up to your parents if you do

answer:

probobly not because it can also depend on the fsa or fast test u have to take but a 68 is not bad its a d+ really close to 70 so i dont think u will dont worry.

Answer:

x = 7 square root 84

OR

x = 1.88320258...

Step-by-step explanation:

Answer:

[tex]x=\sqrt[7]{84}[/tex]

Step-by-step explanation:

1) Take the 7th root of both sides.

[tex]x=\sqrt[7]{84}[/tex]

Check the answer:

[tex]x^7=84[/tex]

1) let x = ^7sqrt84

(^7sqrt84)^7 = 84

2) use this rule: ^7sqrtx^7 = x.

84=84

Answer:

x = 4

y = 30

Step-by-step explanation:

I added a photo of my solution

We can conclude that the correct answer is OA. A(1, -3), B(4, -3), C'(4, -4), D'(1,-4).

What are the factors?

what are factorsIn mathematics, a factor is a number that divides another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these numbers divide 12 without leaving a remainder.

The figure given in the question is a quadrilateral with vertices at points A(-4,-1), B(-2,-1), C(-2,-3), and D(-4,-3), as shown in the diagram.

To dilate the figure by a scale factor of 2 with the origin as the center of dilation, we need to multiply the coordinates of each point by 2. When we multiply the x-coordinate of a point by 2, we stretch the figure horizontally by a factor of 2, and when we multiply the y-coordinate of a point by 2, we stretch the figure vertically by a factor of 2.

To find the new coordinates of each point, we apply the transformation:

A' = (2 * x-coordinate of A, 2 * y-coordinate of A) = (2 * (-4), 2 * (-1)) = (-8, -2)

B' = (2 * x-coordinate of B, 2 * y-coordinate of B) = (2 * (-2), 2 * (-1)) = (-4, -2)

C' = (2 * x-coordinate of C, 2 * y-coordinate of C) = (2 * (-2), 2 * (-3)) = (-4, -6)

D' = (2 * x-coordinate of D, 2 * y-coordinate of D) = (2 * (-4), 2 * (-3)) = (-8, -6)

So the new coordinates of the vertices of the dilated figure are A'(-8, -2), B'(-4, -2), C'(-4, -6), and D'(-8, -6), as shown in the diagram below.

To check our answer, we can see that the coordinates of A', B', C', and D' match with those given in option (OA).

Threfore, we can conclude that the correct answer is OA. A(1, -3), B(4, -3), C'(4, -4), D'(1,-4).

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According to the question, "Suppose we randomly select 5 cell-phone owners. What is the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating?"The formula for finding the probability of an event is:P(E) = number of favorable outcomes/number of total possible outcomes.The given data in the question states that 67% of cell-phone owners find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating.

Therefore, the probability of any cell-phone owner checking their phone when it is not ringing or vibrating is:P(E) = 67/100 = 0.67To find the probability of 5 cell-phone owners checking their phones when they are not ringing or vibrating, we have to use the multiplication rule of probability. [tex]P(E₁∩E₂∩E₃∩E₄∩E₅) = P(E₁) × P(E₂) × P(E₃) × P(E₄) × P(E₅)P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.67 × 0.67 × 0.67 × 0.67 × 0.67P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.2197[/tex]

Therefore, the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating is approximately 0.2197 or 22%.

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Answer:

Step-by-step explanation:

don’t worry I’m Going to help

4.b

5.b

6.c

7.a

8.not sure of answer

Hope they’re right

A line perpendicular to the x-axis is a vertical line, which means it has an undefined slope. Therefore, the equation of a line perpendicular to the x-axis is of the form x = a, where "a" is a constant.

The farmer must plant between 2.750 and 3.500 pistacho trees on his or her 5, 3, and 4, 6 ha of land.

The whole area of the land that will be used for cultivation must be known in order to calculate the number of pistacho trees that the farmer must plant.

The aggregate of the two parcels makes up the entire land surface:

5,3 x 4,6 x 9 h = 9,9 h

We converted this surface to square metres:

9,9 ha times 10.000 m2/ha equals 99,000 m2.

We need to know how many square metres of land the farmer can cultivate in order to calculate the number of pistacho trees that they must plant.

We may calculate this by dividing the entire area by the number of square metres per tree:

2.750 árboles from 99.000 m2 divided by 36 m2/árbol.

As a result, the farmer must plant between 2.750 and 3.500 pistacho trees on his or her 5, 3, and 4, 6 ha of land.

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Photosynthesis is maximum in red light because chlorophyll, the primary pigment responsible for capturing light energy in plants, absorbs red light most efficiently.

What is red light in Photosynthesis?

Red light is a part of the electromagnetic spectrum with a longer wavelength and lower energy than blue and green light.

Red light is particularly effective for photosynthesis because it has a longer wavelength and lower energy, which allows chlorophyll to efficiently absorb it and use it for the photosynthetic process.

In photosynthesis, plants use light energy to synthesize glucose from carbon dioxide and water.

As a result, photosynthesis is maximum in red light because plants can absorb and utilize this light energy most efficiently for their growth and energy production.

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The sky Train from the terminal to the Cental car and long-term parking center is supposed to arrive every 6 minutes. The waiting times for the train are known to follow a uniform distribution. The 60th percentile of the waiting times is 3 minutes.

Using the formula, `P(X≤x) = Percentile, where `X` is the random variable whose percentile is required, and `x` is the value at which the percentile is required.

Given that the waiting times for the train follow a uniform distribution, the probability density function of the uniform distribution is given as: `f(x) = 1/(b-a)` , where `a` and `b` are the lower and upper limits of the distribution.

Now, it is given that the sky train is supposed to arrive every 6 minutes. This means that the minimum and maximum times for waiting will be 0 and 6 minutes, respectively. Hence, `a = 0` and `b = 6`.

Using the formula for the uniform distribution, we have `f(x) = 1/(6 - 0) = 1/6`. Therefore, the cumulative distribution function (CDF) is given by: `F(x) = ∫f(x) dx = (1/6) * ∫dx = x/6.

`Using the formula to find the 60th percentile of the waiting times: `P(X≤x) = Percentile`, we have: `0.6 = P(X≤x)`. Therefore, the value of `x` at which the 60th percentile of the waiting times is achieved is: `x = 0.6 * (b - a) + a = 0.6 * (6 - 0) + 0 = 3`. Thus, the 60th percentile of the waiting times is 3 minutes.

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The surface area οf the cylinder is  170π & the lateral area οf the cylinder is apprοximately 376.99 square  centimetres.

In geometry, a cylinder is one of the basic three-dimensional shapes with two distant parallel circular bases.

Tο find the surface area and lateral area οf the given shape, we need tο first identify the shape. Based οn the given image, it appears tο be a right circular cylinder.

The surface area οf a right circular cylinder is given by the fοrmula:

Surface Area = 2πr² + 2πrh

where r is the radius οf the base and h is the height οf the cylinder.

Frοm the image, we can see that the radius οf the cylinder is 5 cm and the height is 12 cm.

Consequently, the cylinder's surface area is as follows:

Surface Area = 2π(5)² + 2π(5)(12)

Surface Area = 2π(25) + 2π(60)

Surface Area = 50π + 120π

Surface Area = 170π

Sο, the surface area οf the cylinder is apprοximately 533.15 square centimetres.

The lateral area οf the cylinder is the area οf the curved surface, which is given by: Lateral Area = 2πrh.

Substituting the values οf r and h, we get:

Lateral Area = 2π(5)(12)

Lateral Area = 120π

Sο, the lateral area οf the cylinder is apprοximately 376.99 square centimetres.

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Thus, the value of y for the given set of parallel lines is found as:  y = (115)⁰.

Co-interior angles are located on the same sides of a transversal and between two lines. The two defined angles in each diagram are referred to as co-interior angles.

Co-interior angles are supplementary if the two lines remain parallel since they add to 180 degrees.

Given data:

AB || CD

EF || GH

(3x - 4) and (5x) are the linear co-interior angles.

Thus,

(3x - 4) + (5x) = 180 (supplementary angles).

8x - 4 = 180

8x = 184

x = 23

Then,

(5x)⁰ = (5*23)⁰ = (115)⁰

Now,

(5x)⁰ = y = (115)⁰ (corresponding angles)

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The inverse function is as follows: f-1(x) = (x - 2) with y > 0 as the domain as limit the range of the inverse function to y > 0 .

A function is a mathematical rule that relates every element in one set, known as the domain, to a single element in another set, known as the range. A function, then, is a relationship between two sets in which each input in the domain has a single output in the range. Equations, tables, graphs, and symbols can all be used to express it. Consider the function f(x) = 2x + 1 as an illustration. This function multiplies an input value x by 2, adds 1, and returns the result.

given

The steps listed below can be used to determine the inverse of the function f(x) = x2 + 2:

Step 1: Substituting y for f(x)

[tex]y = x^2 + 2[/tex]

Switch x and y in step 2:

[tex]x = y^2 + 2[/tex]

Step 3: Calculate y

[tex]x - 2 = y^2[/tex]

y = ± √(x - 2) (x - 2)

Since we want the inverse to be a function as well, we may limit the range of the inverse function to y > 0 because the original function's domain is x > 0.

The inverse function is as follows: f-1(x) = (x - 2) with y > 0 as the domain.

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The two numbers are 6 and 2.

Let's assume the first number is x and the second number is y.

From the first statement, we can write the equation x = y + 4.

From the second statement, we can write the equation 2x = 4y + 2.

Now, we can substitute x in terms of y from the first equation into the second equation:

2(y + 4) = 4y + 2

Simplifying this equation, we get:

2y + 8 = 4y + 2

2y = 6

y = 3

Substituting y = 3 in the first equation, we get:

x = y + 4 = 3 + 4 = 7

Therefore, 6 and 2 are the two numbers,


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The dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).

The perimeter of the bottom of a rectangular swimming pool is 60 meters, and the area is 221 square meters.

To find the dimensions of the pool, we can use the formula P = 2(l + w) where P is the perimeter and l and w are the length and width of the pool respectively. We can rearrange this formula to solve for either l or w, so we'll solve for l.

2(l + w) = 60
2l + 2w = 60
2l = 60 - 2w
l = (60 - 2w)/2

Now, we can use the formula A = l*w to solve for w.

221 = l*w
221 = (60 - 2w)/2 * w
221 = (60w - 2w^2)/2
442 = 60w - 2w^2
2w^2 - 60w + 442 = 0

Using the quadratic formula, we get w = 16.45 or 7.55.

Now that we know the width, we can use the formula l = (60 - 2w)/2 to find the length. For w = 16.45, l = 21.55, and for w = 7.55, l = 28.45.

Therefore, the dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).

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We know that the workers are required to pay 4 and a half of their salaries into an education fund.

If the salary is S = 120.00, the educational fund receive from that worker:

[tex]F=4.5\times S=4.5 \times120=540[/tex]

Answer: he pays GH 540.00 into the education fund.

Answer:

True

Step-by-step explanation:

The given statement "John Graunt is said to be the first to employ quantitative methods to describe population vital statistics" is true as he was interested in how various factors affected mortality rates and population growth.

Quantitative methods are used to quantify and assess data. These techniques are employed by statisticians and scientists in a variety of fields, including psychology, economics, and public health. Quantitative data can be transformed into statistical analyses to make sense of patterns, patterns, and relationships.

John Graunt was a London haberdasher who lived from 1620 to 1674. He is known as the father of vital statistics, and he was the first to employ quantitative methods to describe population vital statistics.

Graunt was interested in how various factors affected mortality rates and population growth, and he used statistical methods to investigate these issues.

In summary, John Graunt is said to be the first to employ quantitative methods to describe population vital statistics.

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The number of seconds that the ball was in the air is approximately 5.11 seconds

To find the time the ball was in the air, we need to find the time when the ball hits the balcony, which is located 218 feet above the ground.

Let's set h = 218 in the equation h = -16t^2 + 48t + 506 and solve for t

218 = -16t^2 + 48t + 506

Simplifying, we get

16t^2 - 48t - 288 = 0

Dividing both sides by 16, we get

t^2 - 3t - 18 = 0

Using the quadratic formula, we can solve for t:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -3, and c = -18

t = (3 ± sqrt(3^2 - 4(1)(-18))) / 2(1)

t = (3 ± sqrt(105)) / 2

We can ignore the negative solution because time cannot be negative. Therefore, we have

t = (3 + sqrt(105)) / 2

t ≈ 5.11 seconds

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The given question is incomplete, the complete question is:

A person throws a ball upward from a 506 foot tall building the balls height h in feet after t seconds is given by the equation h= -16t^2+48t+506 the ball lands on a balcony that is 218 feet above the ground how many seconds was it in the air

Answer:

  301

Step-by-step explanation:

You want a number that has a remainder of 1 when divided by 2, 3, 4, 5, or 6, and has a remainder of 0 when divided by 7.

If 1 is subtracted from the number of eggs, the remaining number will be an even multiple of 2, 3, 4, 5, 6. That is, it will be a multiple of the least common multiple of these numbers. That LCM will be ...

  LCM(LCM(6, 5), 4) . . . . . . 6 is already a multiple of 2 and 3

  = LCM((6·5/GCF(6, 5)), 4) = LCM(30, 4)

  = (30·4)/GCF(30, 4) = 120/2 = 60

The number of eggs will be 1 more than a multiple of 60 that is a multiple of 7.

We only need to try multiples of 60 up to 7×60. The attached calculator display shows that (5·60 +1) = 301 has a remainder of 0 when divided by 7.

The number of eggs in the cart is 301.

__

Additional comment

The answer can be found by solving the Diophantine equation 7m -60n = 1. Using the Extended Euclidean Algorithm, the solutions to that are found to be m=60x-17 and n=7x-2 for integer x. The value x=1 gives (m, n) = (43, 5), or 301 -300 = 1. The next higher value for 7m is 721.

The bball3 dataset appears to take the form of panel data, which is a type of longitudinal data consisting of multiple observations of the same individuals over time

The bball3 dataset appears to take the form of panel data. Panel data is a type of longitudinal data where observations are made on the same individuals over time. This means that the dataset likely consists of multiple observations of a set of individuals, with the observations collected at different points in time. In a panel data set, each individual can be referred to as a ‘panel unit’.

Cross-sectional data, on the other hand, consists of observations that are collected only once, at a single point in time. This means that each observation consists of a snapshot of the population at a given moment, which is different from panel data where each observation may represent different points in time for the same individuals.

Time series data is a type of data that is collected over a period of time. It captures how a certain variable changes over time, and is often used for forecasting purposes. This is different from panel data, which captures information about the same individuals at different points in time.

In conclusion, the bball3 dataset appears to take the form of panel data, which is a type of longitudinal data consisting of multiple observations of the same individuals over time. It is not cross-sectional or time series data.

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Similarly, the conditional pdf of Y given X, fy|x(y|x), is found by dividing the joint pdf, fxy(x,y), by the marginal pdf of X, fx(x). Thus, fy|x(y|x) = fxy(x,y)/fx(x) = 3/11e-ly for 0 < x < y < ∞.

The marginal pdf of X, fx(x), is the probability density function of X. It is found by integrating the joint pdf, fxy(x,y), with respect to Y over all possible values of Y. Thus, fx(x) = ∫-∞∞fxy(x,y)dy = 11e-ly for 0 < x < ∞. The marginal pdf of Y, fy(y), is found in the same way, but by integrating with respect to X over all possible values of X. Thus, fy(y) =[tex]∫0yfxy(x,y)dx = 11e-lyy for 0 < y < ∞.[/tex]

The conditional pdf of X given Y, fx|y(x|y), is the probability density function of X given that Y has a certain value. It is found by dividing the joint pdf, fxy(x,y), by the marginal pdf of Y, fy(y).

Thus, fx|y(x|y) =[tex]fxy(x,y)/fy(y) = 3/11e-lyy for 0 < x < y < ∞.[/tex]

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Answer:

∠ FZG = 38°

Step-by-step explanation:

∠ HZJ and ∠ FZG are vertically opposite angles and are congruent , then

∠ ZFG = ∠ HZJ = 38°