What are the two methods of division?

Answer:

Step-by-step explanation:

there is an obscure rule that looks like this

DB/AB = AB/CB

AB=40 for this problem

DB = x

CB = 20

then

X/40 = 40/20

X = 40(40/20)

X = 40(2)

X=80

I find that hard to believe too,   :D

but the rule says that's right

(a) the equation of the least squares line is y = (3/5)x - 1/5. b) Hence, the least-squares error for the given data points is 26/5.

To find the slope, we use the formula:

m = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)

Using the given data points:

Σx = -1 + 2 + 1 = 2

Σy = -1 + 2 + 0 = 1

Σxy = (-1)(-1) + (2)(2) + (1)(0) = 5

Σx^2 = (-1)^2 + 2^2 + 1^2 = 6

n = 3

Substituting these values into the formula, we get:

m = (3(5) - (2)(1)) / (3(6) - (2)^2) = 3/5

To find the y-intercept, we use the formula:

b = (Σy - mΣx) / n

Substituting the values, we get:

b = (1 - (3/5)(2)) / 3 = -1/5

Therefore, the equation of the least squares line is y = (3/5)x - 1/5.

(b) To compute the least-squares error, we need to calculate the sum of the squared differences between the observed y-values and the predicted y-values using the least squares line.

Using the given data points and the equation of the least squares line, we calculate the squared differences and sum them up:

(-1 - (-1/5))^2 + (2 - (6/5))^2 + (0 - (2/5))^2 = 26/5

Hence, the least-squares error for the given data points is 26/5.

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Answer:

Ф = 22.6

B = 67.3

BC = 5

Step-by-step explanation:

Ф = 22.6

B = 67.3

BC = 5

Answer:

1/24

Step-by-step explanation:

Each time you take one marble out, the total decreases by 1

You take 1 marble out, it decreases from 10 to 9 and there are now 9 marbles left in the bag.

When you will take the next marble, it will be on a total of 9 and after you take it out the total decreases again by 1. You'd have 8 and so on.

Green = 3

Red = 5

Blue = 2

Probability of getting it in the order RGB =

\( \frac{3}{10} \times \frac{5}{9} \times \frac{2}{8} \: = \frac{30}{720} = \frac{1}{24} \)

The equation \((sin(x)cos(x))^2 = sin(2x)\) is verified to be an identity.

Simplify LHS and RHS?

To verify whether the equation \((sin(x)cos(x))^2 = sin(2x)\) is an identity, we can simplify both sides of the equation and see if they are equivalent.

Starting with the left side of the equation:

\((sin(x)cos(x))^2 = (sin(x))^2(cos(x))^2\)

Now, we can use the trigonometric identity \(sin(2x) = 2sin(x)cos(x)\) to rewrite the right side of the equation:

\(sin(2x) = 2sin(x)cos(x)\)

Substituting this into the equation, we have:

\((sin(x))^2(cos(x))^2 = (2sin(x)cos(x))\)

Next, we can simplify the left side of the equation:

\((sin(x))^2(cos(x))^2 = (sin(x))^2(cos(x))^2\)

Since both sides of the equation are identical, we can conclude that the given equation is indeed an identity:

\((sin(x)cos(x))^2 = sin(2x)\)

Hence, the equation \((sin(x)cos(x))^2 = sin(2x)\) is verified to be an identity.

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The multiplication of the algebraic expressions gives x⁴ + 1.5x³ - 2x²

An algebraic expression is an expression that consists of variables, constants, and a finite number of algebraic operations (such as addition, subtraction, multiplication, and division) e.g. 2x + 25

In order to perform the multiplication, you use expression outside the parenthesis to multiply the expressions inside the parenthesis one after the other. That is:

-0.5x²(-2x² - 3x + 4) = -2x²(-0.5x²) - 3x(-0.5x²) + 4(-0.5x²)

= 1x⁴ + 1.5x³ - 2x²

= x⁴ + 1.5x³ - 2x²

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Answer:

If he follows the rate, then at 45 minutes, he will have ran 9 miles.

Step-by-step explanation:

Hope it helps!

The profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).

So, (x-2)³:

Do, the product as follows:

Perfect cube root formula: (a - b)³ = a³ - 3a²b + 3ab² -b³

Simplify:

Therefore, the profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).

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Answer:

is 30 because 3 multiply by 10 is 30

Answer:

x= -2; y= -2

Step-by-step explanation:

The opposite sides of a parallelogram are congruent, and therefore we can make two observations:

9=-9x-9
19=-10y-1

Then we can just solve each of the equations to get x and y:

9 = -9x - 9
+ 9       +9

18=-9x

----------
-9

-2=x

19=-10y-1
+1        +1

20=-10y
------------

-10

-2=y

Answer:

800 CAD = 508 EUR

Step-by-step explanation:

From the above question:

1 CAD = 0.635 EUR

800 CAD = x

Crososs Multiply

x = 800 CAD × 0.635 EUR

x = 508 EUR

Therefore,

800 CAD = 508 EUR

The limit of xy/(√\(x^2+y^2\)) as (x, y) approaches (0, 0) does not exist.

On the x-axis, all points have y = 0. Therefore, the expression xy/(√\(x^2+y^2\)) reduces to 0/|x|, which is equal to 0 for x ≠ 0 and undefined at x = 0.

Next, let's approach (0, 0) along the y-axis. On this path, all points have x = 0. Therefore, the expression xy/(√\(x^2+y^2\)) reduces to 0/|y|, which is equal to 0 for y ≠ 0 and undefined at y = 0.

Since the limit of the expression along the x-axis and y-axis are different, the limit at (0, 0) does not exist.

To prove this, we can also use polar coordinates.

Let x = r cosθ and y = r sinθ, then the expression becomes:

lim (r, θ) -> (0, 0) \(r^2\) cosθ sinθ / r

which simplifies to:

lim (r, θ) -> (0, 0) r cosθ sinθ

This limit does not exist, as the value of r cosθ sinθ depends on the angle θ. For example, when θ = 0, r cosθ sinθ = 0, but when θ = π/4, r cosθ sinθ = \(r^2\)/2.

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To find the limit, if it exists, of Lim (x, y) → (0, 0) xy/(√x^2+y^2), we first examine the limit as we approach (0, 0) along the x-axis. When we follow this path,it helps to analyse the limit.

On the x-axis, y=0 for all points. Therefore, the limit can be examined as lim (x, 0) → (0, 0) x(0)/(√x^2+0^2). Simplifying, we get lim (x, 0) → (0, 0) 0/|x|. As we approach 0 from both positive and negative sides of the x-axis, the denominator |x| approaches 0. However, the numerator remains 0. Thus, the limit is 0. Therefore, all points on the x-axis approach 0 as we approach (0, 0).

that is,  Lim (x, y) → (0, 0) x(0)/(√x^2+0^2) = Lim (x, y) → (0, 0) 0/(√x^2)

As x approaches 0, the numerator is always 0, while the denominator is |x|. Thus, the limit along the x-axis is:

Lim (x, y) → (0, 0) 0/|x| = 0

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An expression that shows what jasper spent and had left: 4.5 - x = 2.21

Let us assume that x represents the amount of money Jasper s[ent on the rock.

t represents the bill amount,

and m represents the amount of money he  spent  with tax on plants for his fish tank.

Jasper had a $10 bill.

⇒ t = 10

He spent $5. 50 with tax on plants for his fish tank.

m = $5.50

So, the remaining amount is:

t - m = 10 - 5.5

       = 4.5 dollars

After he spent x dollars on the rock, he had $2. 21 in change.

So, we get an expression 4.5 - x = 2.21

Therefore, the required expression is: 4.5 - x = 2.21

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The distance between the walkers will increase at the rate of 5mph.

According to the question,

Two people start walking in different direction from same point.

Speed on the person walking west = 3mph

Speed of the person walking south = 4mph

The angle formed by the point connecting two persons will be = 90 degree

Applying Pythagoreans  theorem,

\(p^{2} + b^{2} = h^{2}\)

\(4^{2} + 3^{2} = h^{2}\)

\(16 + 9 = h^{2}\)

\(h^{2} = 25\)

\(h = \sqrt{25}\)

h = 5mph.

Thus after two hours, the distance between same two persons will be 10m.

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Answer:

(a) To find the mean value, we sum up all the values and divide by the number of values:

Mean = (17 + 22 + 25 + 27 + 32 + 40 + 45 + 51 + 59 + 62) / 10 = 36.0

So, the mean value is 36.0.

To find the median value, we first need to put the data set in order from smallest to largest:

17, 22, 25, 27, 32, 40, 45, 51, 59, 62

The median is the middle value of the data set, which is 36 in this case.

So, the median value is 36.0.

(b) To find the mean absolute deviation (MAD), we first need to find the deviation of each value from the mean:

|17 - 36.0| = 19.0

|22 - 36.0| = 14.0

|25 - 36.0| = 11.0

|27 - 36.0| = 9.0

|32 - 36.0| = 4.0

|40 - 36.0| = 4.0

|45 - 36.0| = 9.0

|51 - 36.0| = 15.0

|59 - 36.0| = 23.0

|62 - 36.0| = 26.0

Next, we find the mean of these deviations:

MAD = (19.0 + 14.0 + 11.0 + 9.0 + 4.0 + 4.0 + 9.0 + 15.0 + 23.0 + 26.0) / 10

MAD = 13.0

So, the mean absolute deviation for this data set is 13.0.

(c) To find the percentage of the data set that lies closer than the MAD to the mean, we count how many values are within one MAD of the mean. We have:

17, 22, 25, 27, 32, 40, 45, 51, 59, 62

The values within one MAD of the mean (36.0 +/- 13.0) are:

17, 22, 25, 27, 32, 40, 45, 51

So, 8 out of 10 values are within one MAD of the mean.

The percentage of the data set that lies closer than the MAD to the mean is:

8 / 10 * 100% = 80%

(a) To find the mean value, we sum up all the values and divide by the number of values:

Mean = (7 + 7 + 7 + 8 + 8 + 9 + 10 + 32) / 8 = 9.5

So, the mean value is 9.5.

To find the mean absolute deviation (MAD), we first need to find the deviation of each value from the mean:

|7 - 9.5| = 2.5

|7 - 9.5| = 2.5

|7 - 9.5| = 2.5

|8 - 9.5| = 1.5

|8 - 9.5| = 1.5

|9 - 9.5| = 0.5

|10 - 9.5| = 0.5

|32 - 9.5| = 22.

Answer:

22 units^2

Step-by-step explanation:

Answer:

45 units²

Step-by-step explanation:

The formula I learned for finding the area of a triangle is:

½ x b(base) x h(height)

The base for this triangle is 5. The height is 18. You multiply these two numbers and get 90. Then, you multiply 90 by ½. 90 x 1 is 90. 90 divided by two is 45. Your final answer is 45.

Hope it helps!

Answer:

cp=(SP * 100 ) / ( 100 – percentage loss)

6786*100/100-13

7800

Answer:

11.2

Step-by-step explanation:

The probability that all three of the cards are tens is 0.018.

The probability that the first card drawn is a ten is 4/52 since there are 4 tens in a deck of 52 cards.

The probability that the second card drawn is a ten, given that the first card was a ten and was not put back in the deck, is 3/51 since there are now only 3 tens left in a deck of 51 cards.

The probability that the third card drawn is a ten, given that the first two cards were tens and were not put back in the deck, is 2/50 since there are now only 2 tens left in a deck of 50 cards.

Therefore, the probability that all three cards are tens is:

(4/52) * (3/51) * (2/50) = 1/5525 ≈ 0.00018 or about 0.018%.

So, the probability of drawing three tens in a row without replacement is very low.

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Answer:

12 gallons per hour

Step-by-step explanation:

Given the following :

Start time of flight = 9:30 a.m

Arrival time of flight = 1:45p.m

Gallons of gas used during duration of flight = 51 gallons

Number of hours spent during flight:

Arrival time - start time

1:45 pm - 9:30 am = 4hours and 15minutes

4hours 15minutes = 4.25hours

If 4.25hours requires 51 gallons of gas;

Then 1 hour will require ( 51 / 4.25)gallons

= 51 / 4.25

= 12 gallons

The answer is D. (-160)÷8

The answer can t be a decimal therefore a and c are out. The answer has to be negative bc it was a lost. Therefore since -160 was a loss it has to be negative

Answer:

D

Step-by-step explanation:

Loss = -160

Shared between 8 owners.

So, (-160) ÷ 8

Answer:

In numerals, that number is 811,395,577.

Answer:690

Step-by-step explanation:

690

Answer:  $3,261.

Step-by-step explanation:

The answer is $3,261. Jayden would have more money in his account than Camden because his account pays a higher interest rate and is compounded continuously, which allows more frequent compounding of interest. This means that Jayden's account accumulates more interest than Camden's account over time.

Therefore, the probability of drawing a green card is 0.0769 or 7.69%.

a. To determine the number of elements in the sample space, we need to know the number of cards in the deck and the possible outcomes for each card. Let's assume that the deck contains 52 cards with four different suits (clubs, diamonds, hearts, spades) and 13 cards in each suit (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king).

The possible outcomes for each card are the suit and the rank. Therefore, there are 4 possible outcomes for the suit and 13 possible outcomes for the rank. Using the multiplication principle, we can determine the number of elements in the sample space by multiplying the number of possible outcomes for the suit by the number of possible outcomes for the rank:

Number of elements in the sample space = 4 x 13 = 52

Therefore, there are 52 elements in the sample space.

b. To find the probability of drawing a green card, we need to know how many green cards there are in the deck and how many cards there are in total. Let's assume that there are 4 different colors of cards in the deck: red, blue, yellow, and green. We also assume that there are 13 cards of each color in the deck.

Therefore, there are 4 green cards in the deck. The probability of drawing a green card can be calculated by dividing the number of green cards by the total number of cards in the deck:

Probability of drawing a green card = number of green cards / total number of cards

Probability of drawing a green card = 4 / 52

Probability of drawing a green card = 0.0769 or 7.69%

Therefore, the probability of drawing a green card is 0.0769 or 7.69%.

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The test used to determine whether or not first-order autocorrelation is present is the Durbin-Watson test.

1. Fit a regression model to the data.

2. Obtain the residuals, which represent the differences between the observed values and the predicted values from the regression model.

3. Calculate the Durbin-Watson statistic, which is a ratio of the sum of squared differences between adjacent residuals to the sum of squared residuals.

4. Compare the calculated Durbin-Watson statistic to critical values from a Durbin-Watson table or use statistical software to determine if there is significant autocorrelation.

5. The Durbin-Watson statistic ranges from 0 to 4, where a value around 2 suggests no autocorrelation, a value below 2 indicates positive autocorrelation, and a value above 2 indicates negative autocorrelation.

6. By analyzing the Durbin-Watson statistic, researchers can make conclusions about the presence or absence of first-order autocorrelation in the regression model.

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The amount of 20% and 50% solution that Samantha needs to mix is 70 milliliters and 30 milliliters respectively.

Let the amount of 20% solution that Samantha needs to mix be x millileters.

Therefore, the amount of 50% solution Samantha needs to mix will be (100 - x) millileters.

According to the question, Samantha needs to create 100 millileters of a 29% solution.

The expression below can be used to calculate the volume of the mixture obtained after mixing x milliliters of the 20% solution and (100 - x) milliliters of the 50% solution:

0.20x + 0.50(100 - x) = 0.29(100)

Simplifying and solving for x:

0.20x + 50 - 0.50x = 29

x = (29 - 50) / (-0.30)

x = 70 milliliters

Therefore, the amount of 20% solution that Samantha needs to mix is 70 milliliters.

And, the amount of 50% solution that Samantha needs to mix is 30 milliliters.

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The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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Answer: B common ancestry

Step-by-step explanation: .

Answer: B.

Step-by-step explanation: