Y=2write the equation of the line in slope intercept form

Answer:

0.15 x A

Step-by-step explanation:

15% is equal to 0.15

of means multiplication

0.15 x A

Answer:

\(\frac{mCD-mGE}{2}\)

Step-by-step explanation:

It's the equation to find an exterior angle.

The company has approximately 67,905 employees in total.

By using proportion to solve this problem.

If 12,700 represents 18.7% of the company's employees, we can set up the proportion:

12,700/x = 18.7/100

where x is the total number of employees.

To solve for x, we can cross-multiply and simplify:

12,700 * 100 = 18.7 * x

1,270,000 = 18.7x

x = 67,904.86 (rounded to the nearest whole number)

Therefore, the company has approximately 67,905 employees in total.

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Answer: (0, -2)

Step-by-step explanation:

The value of p is 2 and 4.

What is a quadratic equation?

Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation. Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Here, we have

Given: p² - 6p + 8

we have to solve the quadratic formula or complete the square.

= p² - 6p + 8

= p² -4p - 2p + 8

= p(p-4) -2(p-4)

= (p-4)(p-2)

(p-4)(p-2) = 0

p-4 = 0,

p-2 = 0

p = 4, 2

Hence, the value of p is 2 and 4,

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Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

Answer:

Here

Step-by-step explanation:

Just pick numbers and substitute it into the equation for x

Answer:

2

Step-by-step explanation:

(a) The equation 5x^2 - 6xy^2z^2 = 7 in cylindrical coordinates can be expressed as:

ρ^2 cos^2(θ) - 6ρ^2 sin^2(θ)z^2 = 7,

where ρ represents the radial distance from the origin, θ denotes the azimuthal angle, and z represents the height coordinate.

(b) The equation z = 2x^2 - 2y^2 in cylindrical coordinates can be written as:

z = 2(ρ cos(θ))^2 - 2(ρ sin(θ))^2,

where ρ represents the radial distance from the origin, θ denotes the azimuthal angle, and z represents the height coordinate.

Cylindrical coordinates provide an alternative way to express points in three-dimensional space. In this system, a point is specified by its radial distance (ρ), azimuthal angle (θ), and height coordinate (z). These coordinates are related to the familiar Cartesian coordinates (x, y, z) through the following equations:

x = ρ cos(θ),

y = ρ sin(θ),

z = z.

The first equation relates the radial distance ρ and the azimuthal angle θ to the x-coordinate. The second equation relates them to the y-coordinate, and the third equation simply states that the z-coordinate remains the same. By substituting these equations into a given Cartesian equation, we can express it in cylindrical coordinates.

The transformation between Cartesian and cylindrical coordinates is widely used in various fields of science and engineering, particularly in problems involving rotational symmetry or cylindrical symmetry. Understanding these coordinate systems allows for more intuitive interpretations and simplifications of equations in different contexts.

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The difference in the dollar value of Assistantship (Stipend) between art and science fields with  standard errors is equal to 1.214.

Mean      24041.62203                 25952.36501

Sample mean difference between Assistantship (stipend) in arts and science is equal to

=  $25952.36501 - $24041.62203

= $1910.74298.

Hypothesized mean difference is 0 (there is no difference in stipend between the two fields).

Variance        621483.0801            615193.5853

Sample size    521                             479

Standard error of the difference is,

=√[(variance in arts / sample size in arts) + (variance in science / sample size in science)]

= √[(615193.5853 / 479) + (621483.0801 / 521)]

= $49.77

t-statistic

= (sample mean difference - hypothesized mean difference) / standard error of the difference

Substitute the values into the t-statistic formula,

⇒ t-statistic = ($1910.74298 - 0) / $49.77

⇒ t-statistic = 38.39

t-critical value for a two-tailed test with 992 degrees of freedom at a significance level of 0.05 is 1.9624.

t-statistic (38.39) > t-critical value (1.9624)

⇒Reject the null hypothesis that there is no difference in stipend between the two fields.

standard errors

= t-statistic / √(sample size)

= 38.39 / √(479 + 521)

= 38.39 /31.62

=1.214

Therefore,  the difference in the dollar value of Assistantship (Stipend) between these two fields is 1.214 standard errors away from the hypothesized difference.

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To find the partial derivative of the function u = sin(x1 2x2 ⋯ nxn) with respect to xi, where i is an integer between 1 and n, we need to use the chain rule. The answer can be expressed as follows: ∂u/∂xi = cos(x1 2x2 ⋯ nxn) * 2ixi * x1 2x2 ⋯ xi-1 2xi-1 xi+1 2xi+1 ⋯ xn.

To explain further, we start by applying the chain rule to u = sin(x1 2x2 ⋯ nxn) with respect to xi. We treat all the variables except xi as constants, so we get:

∂u/∂xi = cos(x1 2x2 ⋯ nxn) * ∂(x1 2x2 ⋯ nxn)/∂xi

Next, we use the product rule to differentiate x1 2x2 ⋯ nxn with respect to xi. We treat all the variables except xi as constants, so we get:

∂(x1 2x2 ⋯ nxn)/∂xi = 2ixi * x1 2x2 ⋯ xi-1 2xi-1 xi+1 2xi+1 ⋯ xn

Substituting this result back into our original equation, we get:

∂u/∂xi = cos(x1 2x2 ⋯ nxn) * 2ixi * x1 2x2 ⋯ xi-1 2xi-1 xi+1 2xi+1 ⋯ xn

Therefore, the partial derivative of the function u = sin(x1 2x2 ⋯ nxn) with respect to xi is cos(x1 2x2 ⋯ nxn) multiplied by 2ixi multiplied by the product of all the variables except xi in the original function.

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Answer:

56°

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

36 + x = 90

x = 90 - 34

x = 56

The dimensions of the parallelogram are: Height = -6 + sqrt(61) cm, Base = 6 + sqrt(61) cm

To solve this problem, we need to use the formula for the area of a parallelogram, which is:
Area = base x height
Let's call the height of the parallelogram "h" and the base "b". We know from the problem that:

b = h + 12

We also know that the area of the parallelogram is 13 cm^2. So we can write:

13 = b x h

Substituting the first equation into the second equation, we get:

13 = (h + 12) x h

Expanding the brackets, we get:

13 = h^2 + 12h

Rearranging, we get:

h^2 + 12h - 13 = 0

This is a quadratic equation that we can solve using the quadratic formula:

h = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 12, and c = -13. Plugging in these values, we get:

h = (-12 ± sqrt(12^2 - 4(1)(-13))) / 2(1)
h = (-12 ± sqrt(244)) / 2
h = (-12 ± 2sqrt(61)) / 2

We can simplify this by dividing both the numerator and denominator by 2:

h = -6 ± sqrt(61)

Since the height of the parallelogram cannot be negative, we take the positive value:

h = -6 + sqrt(61)

Now we can use the equation b = h + 12 to find the base:

b = (-6 + sqrt(61)) + 12
b = 6 + sqrt(61)

So the dimensions of the parallelogram are:

Height = -6 + sqrt(61) cm
Base = 6 + sqrt(61) cm
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Answer: 3234 cubic units

Step-by-step explanation:

Volume of cylinder: πr²h

The diameter of the cylinder is 14 units so the radius is 7 units.

Now we'll substitute.

π = 22/7

h = 21

πr²h

π × 7² × 21

22/7 × 49 × 21 = 3,234

The volume is 3,234 cubic units.

Answer:

Betty is 27. Her son is 9.

Step-by-step explanation:

We will use b to represent Betty's age. We will use s to represent her son's age.

This year:

b = 3s

In 12 years' time:

b + 12 = 2(s + 12) - 3

b + 12 = 2s + 24 - 3

b + 12 = 2s + 21

b = 2s + 9

We know that b = 3s, so we can substitute this value into our equation.

3s = 2s + 9

s = 9

b = 3 x 9

b = 27

Answer:

a) 0.073044

b) 0.75033

c) The normal distribution can be used in part (b), even though the sample size does not exceed 30 because initial population size is been distributed normally , therefore, the mean of the samples will be normally distributed regardless of their size(meaning whether the sample size is less than or equal to or exceeds 30, the sample means the mean of the samples will be normally distributed regardless of their size).

Step-by-step explanation:

The overhead reach distances of adult females are normally distributed with a mean of 205.5 and a standard deviation of 8.6 .

a. Find the probability that an individual distance is greater than 218.00 cm.

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 218

μ is the population mean = 205.5

σ is the population standard deviation = 8.6

For x > 218

z = 218 - 205.5/8.6

z = 1.45349

Probability value from Z-Table:

P(x<218) = 0.92696

P(x>218) = 1 - P(x<218) = 0.073044

b. Find the probability that the mean for 15 randomly selected distances is greater than 204.00

When = random number of samples is given, we solve using this z score formula

z = (x-μ)/σ/√n

where

x is the raw score = 204

μ is the population mean = 205.5

σ is the population standard deviation = 8.6

n = 15

For x > 204

Hence

z = 204 - 205.5/8.6/√15

z = -0.67552

Probability value from Z-Table:

P(x<204) = 0.24967

P(x>204) = 1 - P(x<204) = 0.75033

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The normal distribution can be used in part (b), even though the sample size does not exceed 30 because initial population size is been distributed normally , therefore, the mean of the samples will be normally distributed regardless of their size(meaning whether the sample size is less than or equal to or exceeds 30, the sample means the mean of the samples will be normally distributed regardless of their size).

Answer:

x≥-2

y<3

y≥x+3

Step-by-step explanation:

For x≥-2 the line is passing through -2 on the X axis

For y<3 the dotted line is passing through 3 on the y axis and as it is dotted it is just less than

For y≥x+3 the line is passing through -3 on the x axis and 3 on the y axis so it must be y=x+3. Then you apply the inequality so it becomes y≥x+3

Hope it helps :)

The inequalities to describe the shaded area on the grid​ are

\(\rm \bold {x\geq -2}\\\bold{y<3}\\\\bold{y \geq\ x+3}\)

The shaded area of the grid is surrounded by three lines the equations of all three lines are given as below in form of inequalities.

For a solid line the " equality"  is included but for a dashed line " equality" is not included.

x ≥ -2

y < 3

The equation of third line can be found out by writing standard form of straight line

\(\rm y = mx +c \\m = Slope \;of\; the\; line\\c = y\; axis \; intercept \; value\)

As we can observe from the figure that the line passes through (0,3) and (-3,0) and hence we write the equation of line as

\(\rm y = (3-0) /(0-(-3)) ( x+3) \\y = 1\times x + 3\\y = x+3 \\So \; the\; inequality\; can \; be\; written\; as\\y\geq x+3\)

Since the area above the line y = x+3 is of our concern hence greater than equal to sign is used.

So the inequality for third line is

\(\rm\bold{ {y\geq x+3}}\)

The inequalities to describe the shaded area on the grid​

\(\rm \bold {x\geq -2}\\\bold{y<3}\\\\bold{y \geq\ x+3}\)

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Answer: 162

Step-by-step explanation:

Multiply 54 by 3 to get your answer 162. To continue the sequence keep multiplying the previous number by 3.

Answer:

2,905.4

Step-by-step explanation:

365 times 4 for the number of days in a year times the number of years.the multiply that by $1.99 for the price of the can per day.

Answer:

2 3/5 x 3 1/3 = 26/3 = 8 2/3

The first 3 consecutive odd numbers are 1,3,5. x and x + 2 are consecutive odd numbers if x is an odd number.

Consecutive numbers are those that always appear in the same order, from smallest to largest.

For instance:

The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.

consecutive odd numbers:

Let's call the odd number "x." The subsequent term becomes "x + 4" and the next consecutive odd number becomes "x + 2."

Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.

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Answer:

0 is your y intercept and 5 is the x intercept

Answer: As a fraction it is 1/5 but as a percent 20%

Step-by-step explanation:

this is because 12/60=1/5 or 20%

answer is 20%

heres why

ok so if there is 60 balls all together out of all the color and you want to get a blue ball but the blue has less balls out of all the other colored balls so there is would be a less percent of getting a ball of that color out of 100%

you would need to take the blue color of balls and put in a fraction with the amount of balls together

so that would be 12/60

you half 12/60 and you would need to get the percent which is 20% so you have a 20% of getting a blue colored ball

Answer:

Step-by-step explanation:

Answer:

Bet the answer is

half way

LOL its yes

Answer:

x = 3

Step-by-step explanation:

9x + 8 = 4x + 23

9x - 4x + 8 = 4x - 4x + 23

5x + 8 = 23

5x = 23 - 8

5x = 15

5x/5 = 15/5

x = 3

Upon evaluating the integral we arrive to the solution, ∬R (-4v^2 / 21 - 10uv / 21 + 8uv / 21 + 4u^2 / 21 + 20u / 21 - 20v / 21) dudv

To evaluate the given double integral ∬R (24x − yx − 5y) dA, where R is the parallelogram enclosed by the lines x − 5y = 0, x − 5y = 9, 4x − y = 4, and 4x − y = 9, we can make a change of variables to simplify the problem.

Let's introduce a new set of variables u and v such that:

u = x - 5y, v = 4x - y

To determine the new bounds for the variables u and v, we can solve the system of equations formed by the lines that enclose the region R.

From the equations x − 5y = 0 and x − 5y = 9, we have:

u = x - 5y, u = 0 and u = 9

From the equations 4x − y = 4 and 4x − y = 9, we have:

v = 4x - y, v = 4 and v = 9

The Jacobian determinant for the transformation is given by:

|J| = ∣∣∂(x, y)/∂(u, v)∣∣ = ∣∣∣∂x/∂u  ∂x/∂v∣∣∣

                                ∣∣∣∂y/∂u  ∂y/∂v∣∣∣

To find the Jacobian determinant, we need to express x and y in terms of u and v. Solving the equations u = x - 5y and v = 4x - y simultaneously, we obtain:

x = (v + 5u) / 21

y = (4u - v) / 21

Taking partial derivatives with respect to u and v:

∂x/∂u = 5 / 21, ∂x/∂v = 1 / 21, ∂y/∂u = 4 / 21, ∂y/∂v = -1 / 21

Therefore, the Jacobian determinant |J| = (∂x/∂u)(∂y/∂v) - (∂x/∂v)(∂y/∂u) is given by:

|J| = (5/21)(-1/21) - (1/21)(4/21) = -1/21

Now we can rewrite the given integral in terms of the new variables:

∬R (24x − yx − 5y) dA = ∬R (24((v + 5u) / 21) − ((4u - v) / 21)((v + 5u) / 21) - 5((4u - v) / 21)) |J| dudv

Simplifying this expression, we get:

∬R (24v / 21 + 5u / 21 - (4u - v)((v + 5u) / 21) - 5(4u - v) / 21) (-1/21) dudv

Expanding and rearranging the terms, we have:

∬R (-4v^2 / 21 - 10uv / 21 + 8uv / 21 + 4u^2 / 21 + 20u / 21 - 20v / 21) dudv

Now we can integrate term by term over the region R. We need

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