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Line CD passes through points C(3, 5) and D(6, 0). What is the equation of line CD in standard form?
5x + 3y = 18
O 5x - 3y = 30
O 5x2y = 30
O 5x + y = 18
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Given:

The expression is:

\(18\dfrac{2}{5}-4\dfrac{1}{10}\)

To find:

The difference.

Solution:

We have,

\(18\dfrac{2}{5}-4\dfrac{1}{10}\)

It can be rewritten as:

\(=\dfrac{90+2}{5}-\dfrac{40+1}{10}\)

\(=\dfrac{92}{5}-\dfrac{41}{10}\)

Taking LCM, we get

\(=\dfrac{184-41}{10}\)

\(=\dfrac{143}{10}\)

\(=\dfrac{140+3}{10}\)

\(=14\dfrac{3}{10}\)

Therefore, the value of the difference is \(14\dfrac{3}{10}\).

Two unit vectors that make an angle of 60 degrees with v = (3, 4) are approximately (2.5000, 4.3301) and (-2.5000, -4.3301).

To find two unit vectors that make an angle of 60 degrees with vector v = (3, 4), we can use trigonometry and vector operations.

Step 1: Calculate the magnitude of vector v:

|v| = sqrt(3^2 + 4^2) = 5

Step 2: Convert the given angle of 60 degrees to radians:

θ = 60 degrees * (π/180) = π/3 radians

Step 3: Calculate the components of the unit vector in the same direction as v:

u1 = cos(θ) = cos(π/3) ≈ 0.5000

u2 = sin(θ) = sin(π/3) ≈ 0.8660

Step 4: Multiply the components by the magnitude of v to obtain the unit vectors:

u1 = u1 * |v| ≈ 0.5000 * 5 ≈ 2.5000

u2 = u2 * |v| ≈ 0.8660 * 5 ≈ 4.3301

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Statistical significance is a measure of the likelihood that the observed results in a study are not due to random chance.  The correct answer is (c) Never.

Statistical significance is a measure of the likelihood that the observed results in a study are not due to random chance. In most statistical tests, a p-value is used to determine statistical significance. A p-value is the probability of obtaining results as extreme as the observed results, assuming that the null hypothesis is true (i.e., there is no true effect). A common threshold for statistical significance is a p-value of 0.05 or lower, which indicates that there is a 5% or lower chance that the results are due to random chance.

In this case, if FDATA = 5 and there are no other details provided about the statistical test or hypothesis being tested, it is not possible to determine statistical significance. The p-value would need to be calculated based on the specific statistical test being used and the sample size, among other factors. A p-value of 5 or any other single value does not provide enough information to determine statistical significance.

Therefore, the correct answer is (c) Never, as statistical significance cannot be determined based solely on the value of FDATA = 5.

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Answer: true

Step-by-step explanation:

The good Samaritan law allows you to help people and not be liable for trying to do so.

The length of the longer base to be 10. Finally, substituting these values into the original formula gives us Total area is = 16 ft².

Using the given formula, we can find the total area to be:

Total area = area of parallelogram + area of trapezoid

= 11 + 1/2(enter your response here + 7)

= enter your response here + 66

= enter your response here ft²

To find the missing values, we need to solve for the unknown side lengths of the parallelogram and trapezoid. From the given information, we know that the area of the parallelogram is 11 and the height of the trapezoid is 1. We can use the area formula for each shape to set up equations in terms of the unknown side lengths.

For the parallelogram, area = base x height = 11. We don't know the base or height, but we know that the opposite sides of a parallelogram are equal in length. Let's call the length of one side x. Then, the length of the other side is also x, and the height is h. Substituting these values into the area formula gives us:

11 = x * h

For the trapezoid, area = (base1 + base2) / 2 * height = 1/2 (enter your response here + 7) * 1. We don't know the lengths of the bases, but we know that they are parallel and that the length of one base is enter your response here greater than the length of the other base. Let's call the length of the shorter base x. Then, the length of the longer base is x + enter your response here, and the height is 1. Substituting these values into the area formula gives us:

1 = (x + enter your response here + x) / 2 * 1

1 = (2x + enter your response here) / 2

2 = 2x + enter your response here

Now we have two equations with two unknowns, which we can solve simultaneously using substitution or elimination. Solving for h in the first equation gives us h = 11 / x, which we can substitute into the second equation:

2 = 2x + enter your response here

2 = 2x + 2h

= 2x + 2(11 / x)

2x^2 = 4x + 22

2x^2 - 4x - 22 = 0

Solving for x using the quadratic formula gives us:

x = (-(-4) ± sqrt((-4)^2 - 4(2)(-22))) / (2(2))

x = (4 ± sqrt(144)) / 4

x = (4 ± 12) / 4

x = -2 or 3

Since the length of a side cannot be negative, the length of the shorter base of the trapezoid is 3. Using this value, we can find the length of the longer base to be 10. Finally, substituting these values into the original formula gives us:

Total area = 11 + 1/2(3 + 7)

= 11 + 5

= 16 ft²

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The probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs is 1/7.

In the given question a parking row has 8 spaces.and four cars are pulled in randomly to park in the parking row.

We have to find the probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs.

Number of ways to arrange 4 cars in 8 places = P(8,4)

Number of ways to arrange 4 cars in 8 places = 1680

Number of ways to arrange 4 cars in 2 pairs = N

(Choose 2 pairs of consecutive place from 8 and arrange 4 cars) = 15*4!

= 360

Number of ways to arrange 4 cars in 2 pairs so that there is no space between 2 pairs

= 5*4!

= 120

therefore,

Number of ways no two pairs are consecutive = 360-120

Number of ways no two pairs are consecutive = 240

probability=240/1680

Probability = 1/7

Therefore, the probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs is 1/7.

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Answer:

Step-by-step explanation:

1. B

2. True

Answer: the awnser is D

Step-by-step explanation:

the awnser would be d becuase the others dont make sense at all enegry cannot be destroyed at all but it can change form hope this helps

Answer:

Smallest 7-digit number= 1 + Greatest 6-digit number = 1 + 9,99,999 = 10,00,000. Hence, the smallest 7-digit number is 10,00,000

Step-by-step explanation:

Answer:

m = -1/4

Step-by-step explanation:

The slope is rise/run or (y2 - y1) / (x2 - x1)

We see the y decrease by 2 and the x increase by 8, so the slope is

-2/8 = -1/4

Answer:

Slope = -1/4

Step-by-step explanation:

Now we have to,

→ find the needed slope.

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Then the slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (1 - 3)/(-1 -(-9))

→ m = -2/(-1 + 9)

→ m = -2/8

→ [ m = -1/4 ]

Hence, the slope is -1/4.

Answer:

=81x^28

Step-by-step explanation:

a) Using mathematical operations, the total amount that the charity will receive is £28,275.

b) If the average donation from the people who fill in a tax form is more than £8.70, the answer to part a) A. It will be higher.

The total donations from 3,000 are determined as £26,100, multiplying the factor by £8.70.

Donations made by tax fillers amounted to £8,700 and 25% of this sum is £2,175.

The overall total receipt from the appeal is the addition of £26,100 and £2,175.

The number of appeal letters sent out = 6,000

The number of those who made a donation = 3,000 (6,000 1/2)

The average donation = £8.70

The total donations received from the donors = £26,100 (3,000 x £8.70)

The number of donors who filled out a tax form = 1,000 (3,000 x 1/3)

The percentage of donations added by the government = 25%

The value of donations by 1,000 donors = £8,700 (1,000 x £8.70)

The value of donations added by the government = £2,175 (£8,700 x 25%)

The total amount the charity will receive = £28,275 (£26,100 + £2,175).

Thus, with the government's 25% matching of the donations, the charity will receive £28,275.

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Answer:

2 L bottle for 1.69

the unit price for the two liters is cheaper than one for 12 pack

Answer:

its true or 0

Step-by-step explanation:

Answer:

y = \(\frac{1}{2}\) x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = \(\frac{3-0}{0-(-6)}\) = \(\frac{3}{0+6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = \(\frac{1}{2}\) x + 3 ← equation of line

Answer:

nice...but theres nothing shown

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

x + y + z  = 0   →-  -(x + y)  = z  →   z^3 =  - (x^3 + 3x^2y + 3xy^2 + y^3)

xyz  = 17

xy [ -(x + y) ]  = 17

xy (x + y)  = -17  →  x^2y + xy^2  = -17  →  3x^2y + 3xy^2  = -51

So......

x^3  + y^3  +  [ z^3 ]

x^3  + y^3  +  [ -  ( x^3 + 3x^2y + 3xy^2 + y^3) ]  =

-3x^2y - 3xy^2  =

-[ 3x^2y + 3xy^2]  =

- [-51]  =

51

please rate 5 stars

Using shell method, the volume of the solid generated by revolving the shaded region about the line y is 200π cubic units.

A solid of revolution is divided into cylindrical shells and its volume is calculated using the shell method. We cut the solid perpendicular to the axis of revolution that produces the shells. The volume of the cylindrical shell is calculated by multiplying the cylinder's surface area by the thickness of the cylindrical wall.

The Shell Method Formula: What Is It?

Let R be the area enclosed by the lines x = a and x = b.

Consider the case when we rotate a solid about a vertical axis to create a solid. Let h(x) be the height of the shell and r(x) be the separation between the rotational axis and x.

V=2bar(x)h(x)dx is a formula for calculating the solid's volume.

How to solve?

The area is enclosed by a horizontal parabola with the equation y = (5x)12, which has its vertex at x=0 and its extremum at x=5. Make a narrow vertical slice with thickness dx and location x.

This thin slice may be rotated about the y-axis to create a cylindrical shell with the dimensions x, dx, and 2y. The shell's volume is as follows:

dV = 2π (x) (2y) (dx)

dV = 4π xy dx

dV = 4π x (5x)^½ dx

dV = 4π√5 (x^³/₂) dx

The total volume is the sum of all the shell volumes from x=0 to x=5.

V = ∫₀⁵ dV

V = ∫₀⁵ 4π√5 (x^³/₂) dx

Evaluating the integral:

V = 4π√5 ∫₀⁵ (x^³/₂) dx

V = 4π√5 (⅖ x^⁵/₂) |₀⁵

V = 4π√5 [(⅖ 5^⁵/₂) − (⅖ 0^⁵/₂)]

V = 200π

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Dilation and rotation transformation produces shapes that are not congruent.

Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

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The term that refers to the arithmetic average of a series of numbers is c. mean. It is calculated by summing up all the values in a data set and dividing the sum by the total number of values.

In statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by summing up all the values in the data set and dividing the sum by the total number of values. The mean provides a representation of the typical or average value in the data set.

Option a, mode, refers to the value or values that appear most frequently in a data set.

Option b, median, is the middle value in a sorted list of numbers. It separates the higher half from the lower half of the data set.

Option d, range, represents the difference between the maximum and minimum values in a data set, providing a measure of dispersion.

Therefore, the correct term that corresponds to the arithmetic average of a series of numbers is c. mean.

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Without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

To calculate a 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B, we can use the least squares means estimates provided in the JMP output.

According to the JMP output, the estimate for the mean time required to stabilize emergency condition 4 using display panel B is 10.375000.

To calculate the confidence interval, we need to find the margin of error. The margin of error can be calculated using the formula:

Margin of Error = Critical Value * Standard Error

In this case, we need to find the critical value for a 95 percent confidence interval. Since we have a sample size of 24 (as mentioned in the question), we can use the t-distribution with (24-1) degrees of freedom to find the critical value.

Looking up the critical value in the t-distribution table, with (24-1) degrees of freedom and a confidence level of 95 percent, we find that the critical value is approximately 2.064.

The standard error can be calculated using the formula:

Standard Error = Standard Deviation / √(sample size)

The standard deviation is not provided in the given information. Therefore, we cannot calculate the standard error or the confidence interval without this information.

In summary, without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

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The two pairs of parallel lines form a quadrilateral whose internal angles are right angles so the value of x is 90°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

Given, line a || line b and line c || d.

These four lines form a quadrilateral whose internal angles are all right angles.

Hence the value of x is 90°.

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Answer:

3/4 or 1/4 stays

Step-by-step explanation:

Function which is used to determine the amount of money J$3,000 deposited by Usain Bolt in Kingston Federal Bank with growth rate 5% for 2 years is given by f(x) = 3000(1.05)².

Amount of money deposited by Usain Bolt 'P' = J$3,000

Growth rate 'r' = 5%

Time period 't' = 2 years

Function 'f (x)' used to determine the amount of money after 2 years :

f (x) = P ( 1  + r% )^t

Substitute the value we get,

⇒ f(x) = 3,000 ( 1 + 5/100 )²

⇒ f(x) = 3,000 ( 1 + 0.05 )²

⇒ f(x) = 3,000 ( 1.05 )²

Therefore, the required function used to represents the growth rate of 5% for 2 years of deposited amount of money is equal to

f(x) = 3000(1.05)².

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Answer:

1.09

Step-by-step explanation:

Answer:

it is b

Step-by-step explanation:

f(4)= 2(4)-5

f(4)=8-5

f(4)=3

Using implicit differentiation, we found that dy/dx = \((18x) / (5y^4)\). When solving the equation explicitly for y, we obtained y =\((9x^2)^(1/5) - 2^(1/5)\), and differentiating this expression gave dy/dx = \((18/5) * x^(-2/5) * (9x^2)^(1/5)\).

A) To find y' by implicit differentiation, we differentiate both sides of the equation with respect to x using the chain rule and product rule:

d/dx (9x^2) - d/dx (y^5) = d/dx (2)

Simplifying, we get:

18x - 5y^4 * (dy/dx) = 0

Rearranging the equation and solving for dy/dx, we have:

dy/dx = (18x) / (5y^4)

B) To solve the equation explicitly for y, we isolate y:

9x^2 - y^5 = 2

9x^2 = y^5 + 2

Taking the fifth root of both sides, we get:

\((9x^2)^(^1^/^5^) = (y^5 + 2)^(1^/^5^)y = (9x^2)^(^1^/^5^) - 2^(^1^/^5^)\)

Now, we differentiate y with respect to x using the power rule:

dy/dx = \((1/5) * (9x^2)^(-4/5) * (18x)\)

Simplifying further:

dy/dx =\((18/5) * x^(-2/5) * (9x^2)^(1/5)\)

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By differentiating the given equation implicitly and then solving for y', we get y' = (18x) / (5y^4). Alternatively, if we first solve for y and then differentiate, we get the same expression for y'.

The given equation is \(9x^2 - y^5 = 2\). We will differentiate it implicitly and solve for y' for part A, and solve for y first and then differentiate to find y' for part B.

Differentiating with respect to x gives 18x - 5y'^4y = 0. Solving this equation for y', we get, \(y' = (18x) / (5y^4).\)

First, solve the equation for y to give y = [(9x^2 −2 )]^(1/5). Differentiating this with respect to x, we find \(y' = 2/5*9x * [(9x^2 -2 )]^(-4/5)\) which simplifies to \(y' = (18x) / (5y^4).\)

Therefore, whether we use implicit differentiation (Part A) or solve for y and differentiate (Part B), we get the same expression for y' in terms of x.

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Answer:

8.726%

Step-by-step explanation:

Purchase price = $45.23

Current selling price of stock = $52.00

Intended increase before sale = 25%

25% of purchase price :

100% + 25% = 125%

125% of $45.23

1.25 × 45.23 = $56.5375

$56.5375 is the price at which Mason intends to sell the stock after purchase.

If current price = $52.00;

What percentage increase above the current price is $56.5375.

Let the percentage increase = p

Therefore,

p% of $52 = $56.5375

(p/100) * 52 = 56.5375

52p/100 = 56.5375

52p = 5653.75

p = 5653.75 / 52

P = 108.72596

Therefore p = 108.72596% - 100%

The percentage increase above the current price is thus :

8.72596%

= 8.726%

Answer:

got u

Step-by-step explanation: