How much is 2000mg in grams?

A system of vectors v1, v2, . . . , vn in a vector space v of dimension n is linearly independent if and only if it spans v.

Let's first assume that the system of vectors v1, v2, . . . , vn in v is linearly independent. This means that none of the vectors can be written as a linear combination of the others. Since there are n vectors and v has dimension n, it follows that the system is a basis for v. Therefore, every vector in v can be written as a unique linear combination of the vectors in the system, which means that the system spans v.

Conversely, let's assume that the system of vectors v1, v2, . . . , vn in v spans v. This means that every vector in v can be written as a linear combination of the vectors in the system. Suppose that the system is linearly dependent. This means that there exists at least one vector in the system that can be written as a linear combination of the others. Without loss of generality, let's assume that vn can be written as a linear combination of v1, v2, . . . , vn-1. Since v1, v2, . . . , vn-1 span v, it follows that vn can also be written as a linear combination of these vectors. This contradicts the assumption that vn cannot be written as a linear combination of the others. Therefore, the system must be linearly independent.

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Answer:-2,6

Step-by-step explanation:

The required answer of given fractional problem is  \(\frac{12\sqrt{8a}-24a\sqrt{6} }{128a^{2} }\)

Rationalization is the mathematical operation, in which denominator get multiply with the numerator and denominator.

⇒  \(\frac{3-3\sqrt{3a} }{4\sqrt{8a} }\)

⇒  \(\frac{3-3\sqrt{3a} }{4\sqrt{8a} }\) × \(\frac{4\sqrt{8a} }{4\sqrt{8a} }\)

⇒  \(\frac{12\sqrt{8a}-24a\sqrt{6} }{128a^{2} }\)

In maths, under root is not allow in denominator, so calculated answer best.

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a. d(x)/dx = 1, the final derivative is: dy/dx = 1/x

b. d(ln10)/dx = 0 (ln10 is a constant), the final derivative is: dy/dx = (1/x) / (ln(10))
So, d/dx(lnx) = 1/x and d/dx(logx) = 1/(ln10 × x).

To justify the derivatives using implicit differentiation, follow these steps:
a. To find the derivative d/dx(lnx) = 1/x:
1. Start with the natural logarithm function: y = lnx
2. Apply the implicit differentiation: d/dx(y) = d/dx(lnx)
3. Use the chain rule: dy/dx = d(lnx)/dx × d(x)/dx
4. Recall the derivative of lnx: d(lnx)/dx = 1/x
5. Since d(x)/dx = 1, the final derivative is: dy/dx = 1/x

b. To find the derivative d/dx(logx) = 1/(ln10 × x):
1. Start with the logarithm function: y = logx
2. Convert it to natural logarithm: y = ln(x)/ln(10)
3. Apply implicit differentiation: d/dx(y) = d/dx(ln(x)/ln(10))
4. Use the quotient rule: dy/dx = [ln(10) × d(lnx)/dx - ln(x) × d(ln10)/dx] / (ln(10))^2
5. Recall the derivative of lnx: d(lnx)/dx = 1/x
6. Since d(ln10)/dx = 0 (ln10 is a constant), the final derivative is: dy/dx = (1/x) / (ln(10))
So, d/dx(lnx) = 1/x and d/dx(logx) = 1/(ln10 × x).

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Variance and Standard deviation can tell us the variation of data within a group of samples.

What is a variance?

Variance is a term used in probability theory and statistics to measure how far a group of numbers are spread out from their mean value.

In the context of hypothesis testing, the variance of two groups of data is compared to see if they are statistically significant.

A smaller variance indicates that the data points are closer together, whereas a larger variance indicates that the data points are farther apart.

What is Standard deviation?

The standard deviation is the square root of the variance, and it is used to express the average distance that data points deviate from the mean in a group of samples.

It is used in statistics to measure how tightly a set of data is clustered around its mean.

What is Mean?

The average value of a group of numbers is referred to as the mean.

It is calculated by adding all of the numbers together and then dividing by the total number of numbers.

What is T-value?

The t-value is used to test the null hypothesis, which states that there is no significant difference between two groups of data.

The t-value is calculated by subtracting the mean of one group from the mean of the other group and then dividing by the standard deviation of the two groups combined.

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Answer:

(x - 8)^2 + (y + 6)^2 = 4.

Step-by-step explanation:

The general equation is:

(x - a)^2 + (y - b)^2 = r^2.

Plugging in the given values:

(x - 8)^2 + (y - (-6))^2 = 2^2

(x - 8)^2 + (y + 6)^2 = 4.

Answer:

1124.

Step-by-step explanation:

The common difference (d)   is -16 - (-28) = 12,  ( also -28 - (-40) = 12).

The nth term of an A.S.  is a1 + d(n - 1)  where a1 = first term, d=common difference.

so the 96th term of the given A.S. is:

-16 + 12(96 - 1)

= -16 + 12*95

= 1124.

-1156Answer:

Step-by-step explanation:

The answer is quite simply x=4

Answer:

84m

Step-by-step explanation:

The perimeter of a triangle is the sum of the length of the external sides.

Therefore, the perimeter of the triangle = 21m + 28m + 35m = 84m.

Hey there!

What is the formula for finding the perimeter of a triangle?
a + b + c = perimeter

What does the labels mean?
a = side 1

b = base

c = side 2

What should the equation look like?
21m + 28m + 35m = perimeter

How do should it be solve?
21m + 28m + 35m = perimeter

49m + 35m = perimeter

84m = perimeter

What is the answer to the question?

84m

Good luck on your assignment and enjoy your day!

~Amphitrite1040

To write the equation for a circle with a diameter whose endpoints are (1, 14) and (7, -12) in standard form, we'll need to follow the following steps:Step 1: Find the center of the circle by finding the midpoint of the diameter.

= [(x1 + x2)/2, (y1 + y2)/2]Midpoint

= [(1 + 7)/2, (14 + (-12))/2]Midpoint

= (4, 1)So, the center of the circle is (4, 1).Step 2: Find the radius of the circle. The radius of the circle is half the length of the diameter, which is the distance between the two endpoints. The distance formula can be used to find this distance. Diameter

= √((x2 - x1)² + (y2 - y1)²)Diameter

= √((7 - 1)² + (-12 - 14)²)Diameter

= √(6² + (-26)²)Diameter

= √(676)Diameter

= 26So, the radius of the circle is half the diameter or 26/2 = 13.Step 3: Write the equation of the circle in standard form, which is (x - h)² + (y - k)²

= r². Replacing the center (h, k) and radius r, we get:(x - 4)² + (y - 1)² = 13²Simplifying this equation, we get:x² - 8x + 16 + y² - 2y + 1 = 169x² + y² - 8x - 2y - 152

= 0

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Answer:

The jelly beans cost $2.25 / pound

The trail mix costs $1.25 / pound

Step-by-step explanation:

Let +a+ = cost/pound of jelly beans

Let +b+ = cost/pound of trail mix

(1) 6a + 2b =16

(2) 3a + 5b =13

Multiply both sides by 2  

and subtract (1) from (2)

(2) 6a -2b = -16

(1) -6a -2b = -16

8b=10

b=1.25

and

(1) 6a+2b=16

(1) +3a+b=8

(1) 3a+1.25=8

(1) +3a=6.75

(1) a=2.25

The P-value in this case is approximately 0.1131.

In the given problem, we are given a test statistic t = 1.212, a sample size n = 6, and an alternative hypothesis H1: μ > μ0.

To calculate the P-value, we need to find the area to the right of the test statistic t in the t-distribution with n - 1 degree of freedom (df), assuming the null hypothesis is true.

Using a t-table or calculator, we can find that the area to the right of t = 1.212 with 5 degrees of freedom is approximately 0.1131. This means that if the null hypothesis were true (i.e., if the population mean were equal to the hypothesized value μ0), we would expect to observe a test statistic as extreme as t = 1.212 or more extreme in about 11.31% of random samples of size 6.

Since the P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming that the null hypothesis is true, we can conclude that the P-value in this case is approximately 0.1131.

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Answer:

b=sqrt7

Step-by-step explanation:

16=9+b^2

To find the equation of a plane passing through two points and perpendicular to another plane, use the cross product.

First calculate the vector between the two given points,

then use the cross product to find a vector that is perpendicular to both the vector between the two points and the equation of the other plane.

Finally, use the two points and the perpendicular vector to find the equation of the plane.

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The cos(m) In the right triangle lmn is  19/20.

Complementary angles are formed when the total of two angles equals 90 degrees. 30 degrees and 60 degrees, for example, are complementary angles.

We have L + M = 90 because the angles L and M are complimentary.

Assuming that,

sin L = sin (90 - L) = sin M

sin (L) = 19/20.

As we know from our rule, the sine of angle L is equal to the cosine of L's complement, which is M.

This implies that the cosine of M is 19/20.

As a result, cos(M) equals 19/20.

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The overall vertical change of the commercial jet is -175 feet.

The overall vertical change of the commercial jet can be determined by subtraction operation.

Subtraction operation is one of the four basic mathematical operations, including addition, multiplication, and division.

Subtraction involves the minuend, subtrahend, and the difference.

The initial drop of the commerical jet = 201 feet

The ascent of the commerical jet = 132 feet

The final drop of the commercial jet = 106 feet

The overall vertical change = -175 feet (132 - 201 - 106)

Thus, overall, using subtraction operation, the comercial jet changed its vertical position by -175 feet.

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Answer:

mean= 12.8

median=13

mode=there is no mode

Step-by-step explanation:

mean/average=14+10+12+15+ 13​=64/5=12.8

median=10,12,13,14,15=13

mode= is the number that repeats more often. = there is no mode

Answer:

type 2 in the first box,

13/4 in the second box, and

-9/8 in the third one

Step-by-step explanation:Notice that you are asked to write the following quadratic expression in vertex form, so you need to find the "x" value of the vertex, and then the "y" value of the vertex:

\(x_{vertex}= -b/2a\)

Which in our case is: -13/4

and the value of the y for the vertex is obtained using the functional expression when x equals -13/4:

\(f(-13/4)= -9/8\)

Then your expression for this quadratic should be:

\(f(x)=2\,(x+\frac{13}{4} )^2+(-\frac{9}{8})\)

Then type 2 in the first box, 13/4 in the second box, and -9/8 in the third one

Answer:

40%

Step-by-step explanation:

20-15 = 5, 2 students passed and did the assignment, 0.4 = 40%

Formular for total surface area of a cylinder

S = 1231.5 sq ft

Answer:

True

Step-by-step explanation:

x - 4y = 11 → (1)

- 3x + 5y = 25 → (2)

Multiply (1) by 5 and (2) by 4 to eliminate the y- term

5x - 20 y = 55 → (3)

- 12x + 20y = 100 → (4)

Add (3) and (4) term by term to eliminate y

- 7x + 0 = 155

- 7x = 155 ← y- term is eliminated

Answer:

Step-by-step explanation:

tanx=27/38

take the inverse...

tan^-1(27/38)

≈35.4 degrees

Answer:

Equation is a quadratic equation (polynomial ax+by+c with highest degree 2), so it has two solutions.

Answer:

B. is correct because it only can go 1 way.

Step-by-step explanation:

Sarah's charges per hour for working during the week will be $9.5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.

Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be

45x + 5y = 902.5           ...1

50x + 10y = 1045

25x + 5y = 522.5          ...2

Subtract equation 2 from equation 1, then we have

45x - 25x = 902.5 - 522.5

20x = 380

x = 19

And the value of y will be

25 (19) + 5y = 522.5

475 + 5y = 522.5

5y = 47.5

y = 9.5

Sarah's charges per hour for working during the week will be $9.5.

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The angle of elevation from a point from  the level of ground

is 39 degrees

The angle of elevation is the angle which is created between the line of sight and the horizontal line . The angle which is created is an angle of elevation if the line of sight is upward from the horizontal line.

As details given from the question

The given height of the building (h) is 250 feet

the distance building is away from the point of view which is on the level of ground is 200 feet

To find the elevation is

\(tan \theta\) is equals to opposite by adjacent

\(tan\theta\) = 200/250

=> \(tan\theta\) = 4/5

=> \(tan \theta\) = 0.8

=> \(tan ^{-1} (0.8) =\) 38.6

=> ~ 39 degrees

The angle of elevation is 39 degrees

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The distance from the top of the flag pole to your standing position is 19.21m

Pythagorean theorem states that, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

Given that: You are standing 12m from the base of a flag pole that is 16m high (check the attached image to see the drawing)

using Pythagorean on the image:

Let d is the distance from the top of the flag pole to where you're standing

d² = 12² + 15²

d² = 144 + 225

d² = 369

d =√369 = 19.21m

Therefore, the distance from the top of the flag pole to where you're standing is 19.21m (check the attached image for the diagram)

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in Dallas, Texas to be classified as extremely wet, the amount of precipitation that must fall is approximately 4.74 inches.

To find the amount of precipitation that must fall in April for it to be classified as extremely wet, we need to find the z-score that corresponds to the upper 5% of the normal distribution.

Using a standard normal distribution table, we can find that the z-score corresponding to the upper 5% is approximately 1.645.

Now we can use the formula z = (x - μ) / σ, where z is the z-score, x is the amount of precipitation, μ is the mean (3.2 inches), and σ is the standard deviation (0.9 inches).

Plugging in the values, we get:

1.645 = (x - 3.2) / 0.9

Solving for x, we get:

x = 3.2 + 1.645 * 0.9

x = 4.7425

Therefore, for April in Dallas, Texas to be classified as extremely wet, the amount of precipitation that must fall is approximately 4.74 inches.
To determine the amount of precipitation required for April to be classified as extremely wet in Dallas, Texas, we need to find the value at the 95th percentile of the normal distribution, since the upper 5% corresponds to extremely wet conditions. The average precipitation is 3.2 inches, and the standard deviation is 0.9 inches.

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a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

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