write the equation of the line in fully simplified slope-intercept form​

Answer:

1,666,667

Step-by-step explanation:

1000 milligrams is equal to one gram.

First, convert the mass of the grain of salt in milligrams to grams by dividing the mass in milligrams by 1000:

[tex]\implies \dfrac{0.06}{1000}=0.00006\; \rm g[/tex]

To calculate how many grains of salt would be in 100 grams of sand, divide 100 g by 0.00006 g:

[tex]\implies \dfrac{100}{0.00006}=1,666,666.6666...[/tex]

Therefore, there are 1,666,667 grains of salt in 100 grams of sand (to the nearest whole number).

Answer:

Let x be the width of the pool. Then the length of the pool is 2x, since it is twice as long as it is wide.

The area of the pool is (2x)(x)=2x^2

The total area of the pool and the walkway is 2x^2+196 square feet.

We can set up the equation using this information:

2x^2 + 22x = 196

Where 22x is the area of the walkway, 22x = 2x * 2 = 4x

2x^2 + 4x = 196

2x^2 + 4x - 196 = 0

Using the quadratic formula to solve the equation above:

x = (-b ± √(b^2 - 4ac))/2a

x = (-4 ± √(4^2 - 42196))/2*2

x = (-4 ± √(16 - 1568))/4

x = (-4 ± √(-1552))/4

Since x is width of the pool, it cannot be a negative value, the x value that is negative must be rejected. Therefore x = (-4 + √1552)/4 = 8

The width of the pool is 8 feet and the length is 2x = 2*8 = 16 feet

The lateral surface area is 1562.5  If the floor of a cuboidal hall has a perimeter of 225m and height 25m.

What is volume of Cuboid ?

volume of cuboid can be defined as the product of length , breadth and height.

Given,

If the floor of a cuboidal hall has a perimeter of 225m and height 25m

Lateral Surface area = 2h(l+b)

Given perimeter is 225m

so,

perimeter = 4 (l+b+h)

225 = 4 (l+b+25)

Given h = 25

225 = 4(l+b) + 100

4(l+b) = 225-100

4(l+b) = 125

l+b = 125/ 4

So,

Lateral surface area = 2h (l+b)

= 2 * 25 * ( l+b)

= 50*125/4

= 1562.5

Hence , The lateral surface area is 1562.5  If the floor of a cuboidal hall has a perimeter of 225m and height 25m.

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The answer is 486 cm². Thus option c is the right answer.

According to the given question:

The surface area of the cube = 6s²

Surface Area is the area occupied by the six faces of the cube.

where, s ⇒  length of each edge.

Given,

length of each edge = 9cm.

Substituting values in the given formula,

6 × 9²

= 6 × 81

= 486 cm².

Therefore the surface area of the cube is 486cm².

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The equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

What is point slope form of line?

The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.

One of the formulas used to determine a line's equation is the point slope formula. According to the point slope formula, y - y1 = m (x - x1) is the equation for a line with slope "m" and the points (x, y1) on it.

We have to find the equation of line that passes through the points (6, 5) and (0, -7).

First to find the slope of the line,

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{-7-5}{0-6}= \frac{-12}{-6} = 2[/tex]

Now, consider the point slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex]m = 2, (x_1, y_1) = (0, -7)[/tex]

⇒

[tex]y-(-7)=2(x-0)\\y+7=2x\\y=2x-7[/tex]

Hence, the equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

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The velocity of the object is 21.1 m/s.

We have to note that when we drop the ball from the height, the ball is going to obey the equation of motion that is taking place under gravity. We can now look at the question to obtain the model for the problem.

We can see that in the question, the model of the problem have been given as; v = √19h where h is the height form which it fell. In this case h = 23.4 m

Then;

v = √19 * 23.4

v =21.1 m/s

The velocity of the ball as it falls to the ground is 21.1 m/s.

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Answer: 1/11

Step-by-step explanation:

16 is close to 20

217 is close to 220

20/220=2/22=1/11

Answer:

1 is a common factor of all numbers and every number is a factor of itself.

Step-by-step explanation:

so yes it can be a common factor

Answer:

Domain: ℝ or (-∞, ∞)

Range: ℝ or (-∞, ∞)

Step-by-step explanation:

Domain is the set of valid x-values that will result in a real output when plugged into a function. On this graph, we can see that the line continues left past x = 0 and right past x = 14. So, we have to assume that the line continues on forever, and thus its domain is all real numbers (represented by ℝ). In the context of this problem, it means that there are infinite points in time where the falling object will exist at some height.

Range is the set of valid y-values that will result in a real output when plugged into the equation of a line. On this graph, the line continues upwards past y = 7 and downwards past y = 0. So, we have to assume that the line continues on forever, and thus its domain is all real numbers. In the context of this problem, that means that there are infinite heights which the falling object can be at.

8 percentage of the buttons were large. The solution has been obtained using arithmetic operations.

What are arithmetic operations?

There are four fundamental operations that all real numbers in mathematics must comprehend:

1. Adding the numbers together to get their total (with a "+").

2. Using the "-" sign to subtract two numbers yields the difference between the values.

3. Multiplication('×') is used to create the numbers' product.

4. The division('÷') procedure, which determines the numbers' quotient.

We are given that Victoria bought a bag of mixed buttons and she got 12 large buttons and 138 small buttons.

So, the total number of buttons = 138 + 12 = 150

Out of 150, she got 12 large buttons.

So, percentage of large buttons = 12*100/150 = 8%

Hence, 8 percentage of the buttons were large.

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C(m) = 850 + 65m is the formula for the total cumulative cost (C) per month (m).

Linear equations are equations that has a leading degree of 1. An example of a linear equation is y = mx + b

where:

According to the given question, Janine is getting a new phone. She needs to purchase her phone, which is $850.

Amount paid monthly = $65

If she completes the payment in 'm' months, the equation for total cumulative cost (C) per month (m) is C(m) = 850 + 65m

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The inequality relation for the given problem would be p ≥ 1580.

What is inequality?

An inequality is a statement that compares the value of two expressions using one of the mathematical symbols <, >, ≤, ≥, ≠. It shows the relationship between two values, but unlike an equation, it does not set them equal to each other.

The inequality that shows the possible power per year, p, the waste-to-energy facilities in the country are capable of producing is:

p ≥ 1580

This inequality shows that the power per year, p, is greater than or equal to 1580. This is based on the information provided that the 65 facilities in the country have the capacity to produce 1,580 megawatts of power per year by processing more than 16 million tons of waste per year. The inequality is written in this way because we know the minimum amount of power that the facilities can produce, but not the maximum, so we use "greater than or equal to" to show that the power produced could be equal to 1,580 megawatts or greater.

Hence, The inequality relation for the given problem would be p ≥ 1580.

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Answer:

35, 189

Step-by-step explanation:

2 1/2 + 11 = 13 1/2 minutes
After 2 1/2 min after 11 min: 2 1/2 x 14 = 35 gallons are added after 2 1/2 min
A total of: 154 + 35 = 189 gallons will be pumped in after 13 1/2 min

The volume of coal is 42.41 cubic meters when a pile of coal is stored in a barrel-shaped bin whose base has a radius of 3 meters, and the height of the pile measures 1.5 meters.

The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another.

The volume of a cylinder V= b*h

where b is the area of the base

h is the height of the cylinder.

And since the area of a circle is πr², we have this equation for the volume of a cylinder  

V = π×r²×h    

Now substitute, the known values for r and h, then calculate the result:  

V = π×r²×h  

V = 3.14159×3²×1.5  

V = 3.14159×9×1.5  

V = 42.411465  

V = 42.41  

So the volume of the coal pile is 42.41 cubic meters.

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(a) A larger random sample can potentially reduce the bias of the poll result and (b) a larger random sample will generally reduce the variability of the result.

(a) A larger random sample can potentially reduce the bias of the poll result. Bias in a poll refers to systematic errors in the sampling process that result in inaccurate or unfair representation of the population being polled. A larger sample size means that the poll is more likely to include a diverse range of perspectives and opinions, which can make the results more representative of the population as a whole. However, the sample size alone is not enough to guarantee unbiased results, it also depends on how the sample is selected and how the questions are phrased.

(b) A larger random sample will generally reduce the variability of the result. Variability refers to the degree to which the results of a poll can vary depending on the specific sample that is selected. A larger sample size means that there are more data points being included, which makes the results less susceptible to fluctuations caused by chance. However, the variability also depends on how the sample is selected, having a larger sample size does not guarantee less variability.

In summary, increasing the size of a random sample from 1500 to 4000 people can help reduce bias and variability in the poll results, but it is not a guarantee. Other factors such as the sampling method and question design also play an important role in determining the accuracy and fairness of the poll results.

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A value of about 32.9 years. The remaining balance will not reach $3,317 for 33 years, rounded up to the closest year.

Interest is often expressed as an annual percentage of the borrowed amount. This percentage represents the loan's interest rate. For instance, a bank will pay interest if you deposit money in an account savings account.

The initial deposit into the personal savings account is denoted by P, and the yearly interest rate is denoted by r. The following formula determines the account balance after t years:

A = Pe^(rt)

P = $1,000, r equals 5.8%, as Well as a is $3,317 in this scenario. To determine how many years it will be for such balance to reach $3,317, apply the following formula:

3,317 = 1,000e^(5.8% * t)

You must isolate t over one portion of the equation to find the solution:

t = ln(3,317 / 1,000) / (5.8% / 100)

That amounts to:

t = ln(3.317) / 0.058

Calculating this yields a result of around 32.9 years. The remaining balance will not reach $3,317 for 33 years, rounded up to the closest year.

Therefore, 33 years are needed to complete the process.

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If Angel is trying to find the height of a radio antenna on the roof of a local building. The height of the antenna (the distance from point A to point B) is 8m.

Given data:

Horizontal distance = 18 meters

Angle of elevation from his eyes to the roof (point A) = 21°

Angle of elevation from his eyes to the top of the antenna (point B) = 39°

So,

AB= 18 × (Tan 39° - Tan 21°)

AB = 18 × ( 0.8098 - 0.3839)

AB = 18 × 0.4259

AB = 7.67

AB = 8m (Approximately)

Therefore the height of the antenna (the distance from point A to point B) is 8m.

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According to the separable differential equation, the family of implicit solution is  1/2 (x² - y²)

The term separable differential equation is defined as in which the variables can be separated from each other are called separable differential equations.

As per the definition the general form to write separable differential equations is dy/dx = f(x) g(y), where the variables x and y can be separated from each other.

Here we have given that (dy/dx) = (x/y)

When we cross multiply the terms, then we get,

=> y dy = x dx

When we differentiate the terms, then we get the following,

=> ∫y dy = ∫x dx

The solution of this integral can be written as,

=> y²/2 + C = x²/2 + C

When we simplify this one then we get the resulting expression as,

=> x²/2 - y²/2 = 0

=> 1/2 (x² - y²)

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1.False, 2.True, 3.False, and 4.False

This question uses probability theory, which is used to analyze the likelihood of different outcomes occurring. It is based on the idea that there is a certain probability that any given outcome will happen.

The given question steps by step explanations are as follows

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The correct answer for each row - 1.False, 2.True, 3.False, and 4.False

This question uses probability theory, which is used to analyze the likelihood of different outcomes occurring. It is based on the idea that there is a certain probability that any given outcome will happen.

In the given question,

It is less likely that Eleanor will choose a pair of gray socks than a pair of black socks: False - There are 14 pairs of gray socks and 8 pairs of black socks, so it is more likely that Eleanor will choose a pair of gray socks.

It is more likely that Eleanor will choose a pair of white socks than a pair of gray socks: True - There are 6 pairs of white socks and 14 pairs of gray socks, so it is more likely that Eleanor will choose a pair of white socks.

The most likely outcome is that Eleanor will choose a pair of black socks: False - There are 8 pairs of black socks and 14 pairs of gray socks, so it is more likely that Eleanor will choose a pair of gray socks.

The least likely outcome is that Eleanor will choose a pair of white socks: False - There are 6 pairs of white socks and 14 pairs of gray socks, so it is least likely that Eleanor will choose a pair of white socks.

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Answer:

-4

Step-by-step explanation:

-16 divided by 4

4 times 4 = 16

16 divided by 4

negative with positive makes a negative

-4

Using proportions, it is found that Product A sold 345600 units.

In this problem, we have that Product B sold 70% less, that is, 30% of Product C, which sold 39,000 units, hence:

B = 0.3 x 33000 = 9900.

Product A sold 3.5 times more than Product B. So, the number of units sold by Product A is given by:

A = 3.5 x 9900 = 346500.

Therefore, Product A sold 345600 units.

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The algebraic expression that shows the amount Ms. Jackson wants to rent a van for a week is T=320+0.50m

In order to calculate the total amount that Ms. Jackson will need to pay for renting we need to multiply the number of miles that she will drive by the price per mile driven.

Once we have that product we can simply add the weekly fee (w) to it which will give us the total (T) amount that Ms. Jackson will have to pay for her trip. This can all be combined into the following formula.

T = w + 0.50m

As per the mentioned table, a van containing ret for a week is 320, which is equal to the W value, then substitute the value in the equation we get:

T=320+0.50m

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Answer:

There are 6 workers in the team.

Step-by-step explanation:

Let's call the number of workers "n".

We know that the team of workers could have completed the job in 24 hours if they had worked together. We also know that the resulting work time would have been reduced by 6 hours if all but 5 workers had worked together from the start.

So, if n workers worked together from the start, the work time would be 24 - 6 = 18 hours.

We also know that the workers joined one by one, starting with 1 worker and ending with n workers working together.

The total work time can be calculated using the arithmetic series formula:

work time = n/2 * (1 + n)

So, if we set the work time to 18 hours:

18 = n/2 * (1 + n)

We can solve this equation for n:

18 = n/2 * (n+1)

36 = n^2 + n

n^2 + n - 36 = 0

We can solve this quadratic equation by factoring it.

(n-6)(n+6) = 0

So the solutions are n = 6 and n = -6.

But the number of workers can not be negative, so the answer is n=6.

Therefore , the solution of the circle comes out to be the parametric curves cross at position (4, 1, 32).

Each point in the plane that is a certain distance from some other point forms a circle (center). Thus, it is an arc composed of points that also are spaced apart from one another in the plane. Additionally, at every angle, it is radial symmetric about the center. In the closed, two-dimensional plane of a circle, every pair of endpoints is uniformly separated from the "center." By drawing lines through the circle, one can create a line of circular symmetry. Additionally, it rotates equally at all angles about the center.

Here,

This is what we get when we use the parametric values in both r2 and r1 as functions of t:

Curve 1: x1(t), y(t), and z(t) = 48-12

Figure 2: Curve 2:

x2(t)=8-t, y2(t)=t-3, 22(t) = 12

Where they meet, they are equal, so:

x1(t) Equals x2(t),

where t=8-t 2t8 and t=4

(x(t), y(t), z(t)) = using curve 1 (t,5-t,48-12)

Following that,

(x(4), y(4), 2(4)) = (4,5-4, 48-42) = (4,1,32)

They get together at point (4, 1, 32).

Therefore , the solution of the circle comes out to be the parametric curves cross at position (4, 1, 32).

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Answer: 20 inches

Step-by-step explanation:

The midsection is 1/2(base #1 + base #2)

27 = 0.5(34+x)

34+x = 54
x = 20

The transformation is a vertical stretch

From the question, we have

f(x) = -|x| + 1

g(x) = -8|x| + 8

The transformation from the graph of f(x) = -|x| + 1 to the graph of g(x) = -8|x| + 8 is a vertical stretching by a factor of 8.

The transformation results in the graph of g(x) being 8 times taller than the graph of f(x).

Mathmatically, this is

g(x) = 8f(x)

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If the sample standard deviation from the sample distribution is 0.0005 mm, the sample should have 16 axes.

Given,

μ = 40.125 mm, σ = 0.002mm σ(x) = 0.0005mm

The standard deviation of the sampling distribution of the sample mean is the population standard deviation divided by the square root of the sample.

    σ₁ = σ/√n

By multiplying both sides by √n

   √nσ(x) = σ

By dividing both the side by σ₂

    √n = σ / σ₁

By squaring both the sides

  n = σ²/σ²(x)

Now,

Calculate the value of n

n = 0.002² / 0.0005²

  = 16

Therefore,

If the sample's standard deviation of the sampling distribution is 0.0005mm, then the sample should be 16 axles.

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Answer: The maximum height of the arrow is the vertex of the parabola. To find this, we can set the derivative of the function equal to zero and solve for x.

y' = -32x + 100

Setting y' = 0 and solving for x:

0 = -32x + 100

32x = 100

x = 100/32

So the arrow reaches its maximum height of y = -16(100/32)² + 100(100/32) + 4 = 100 feet at x = 100/32 seconds after it is shot into the air.

Step-by-step explanation:

Convergent series:A series is said to be convergent when the limits of the series converge to the finite possible value for the series.

Consider a series

Sn=a1+a2+a3+a4+........+an

this form a new series as ,

Sn(n=1 to infinity)=

=s.

It is important that the partial sum of series, there should be a limit existed and that is finite in nature then only the series converges.

The geometric series gives a proper idea of how the limit decides the convergent and divergent nature.

A series in which the individual term, approaches zero then series is convergent in nature but not for all time.

The series,

A convergent series is a series for which limits exist.

If the sequence of the partial sum is a convergent sequence.

G(r,c)=  r+c

where r≠1 then series converges.

Divergent series:

A series is an infinite series that does not converge at  any point,

had an infinite sequence of partial sums with no finite limit.

A series where the individual sum does not approaches zero diverges.

For e.g.

This series diverges.

Or harmonic series which diverges.

Where is limit tends to infinity, eventually series added up to infinity means no exact answer will be there.

For summing the divergent series  there method is:

FT

extrapolation methods.

Abelian theorems

Regularity, linearity, and stability test for the series.

If this test is checked then we will get to know which series diverges and converges.

It is not possible to determine whether a series converges or diverges based on its sum alone. The sum of a series can be finite, infinite, or undefined, but it does not provide information on whether the series converges or diverges. Other mathematical tests, such as the ratio test or the integral test, are used to determine whether a series converges or diverges.

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