Which formula represents the nth term of arithmetic sequence 2, 5, 8, 11, ...?
Formula: An = A1 + (n - 1)d

A)the mass of $700 billion worth of gold is approximately 24,822,695,035.5 grams. B)The actual length will depend on the exact density of gold and the accuracy of the provided values.

A) In order to calculate the mass of $700 billion worth of gold, we need to convert the dollar value into grams.

To do this, we first need to determine the price of gold per gram. Given that gold was worth $800 per ounce ($28.20 per gram), we can use this conversion factor to calculate the mass.

$800 per ounce is equivalent to $28.20 per gram. Therefore, 1 gram of gold is worth $28.20.

Next, we can divide the total dollar value ($700 billion) by the value of 1 gram of gold ($28.20) to find the mass in grams.

$700 billion / $28.20 per gram = 24,822,695,035.5 grams

So, the mass of $700 billion worth of gold is approximately 24,822,695,035.5 grams.

B)Moving on to the second part of the question, if this amount of gold were in the shape of a cube, we need to calculate the length of each side of the cube.

To find the length, we can use the formula for the volume of a cube, which is side length cubed. Since we know the mass of the gold (24,822,695,035.5 grams), we need to calculate the side length.

Let's assume the density of gold is 19.32 grams per cubic centimeter (g/cm³). By dividing the mass of the gold (24,822,695,035.5 grams) by the density (19.32 g/cm³), we can find the volume of the gold in cubic centimeters.

Volume = Mass / Density = 24,822,695,035.5 g / 19.32 g/cm³

By solving this equation, we can find the volume of the gold.

Finally, we can use the volume of the gold to calculate the length of each side of the cube by taking the cube root of the volume.

This will give us the length of each side of the cube formed by the given amount of gold.

The actual length will depend on the exact density of gold and the accuracy of the provided values. The above calculation is an example based on the given information.

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Answer:

  see attached

Step-by-step explanation:

Rotation 270° counterclockwise is equivalent to rotation 90° clockwise. The transformation of coordinates is ...

  (x, y) ⇒ (y, -x) . . . . . . . rotation 270° CCW

This means the points are moved to ...

  A(-2, 1) ⇒ A'(1, 2)

  B( 1, 2) ⇒ B'(2, -1)

  C(-2, 4) ⇒ C'(4, 2)

The rotated triangle is shown in the attachment. You may notice that A' and B are the same point.

Therefore, the basis for the subspace is \({[1, -1, -2, 5]^T}\), and the dimension of the subspace is 1.

To determine the basis for a subspace spanned by a given vector, we need to find a set of linearly independent vectors that can generate all possible vectors within that subspace.

In this case, we are given the vector \([1, -1, -2, 5]^T\). To determine if this vector can be a basis for the subspace, we need to check if it is linearly independent.

Since the vector is non-zero, it is not a scalar multiple of the zero vector, and therefore, it is not trivially dependent. This means that the vector \([1, -1, -2, 5]^T\) can be considered as a potential basis vector for the subspace.

To confirm that it is indeed a basis vector, we need to check if it can generate all possible vectors within the subspace. Since the vector is non-zero, it spans a one-dimensional subspace, which means that any vector in the subspace can be expressed as a scalar multiple of the given vector.

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The environment changed in such a way that, "guppies with small spots had a better chance of survival and reproduction, leading to an increase in their population and a decrease in the population of guppies with large spots".

Over many generations, guppies with small spots had a survival advantage in the river because the rocks on the river bottom became smaller. This made guppies with small spots harder for larger fish to see and catch, increasing their chances of survival and reproduction.

As a result, more guppies with the small spot gene passed it on to their offspring, leading to an increase in the population of guppies with small spots. At the same time, the population of guppies with large spots decreased as they were more visible to predators and had a lower chance of survival. This process of natural selection led to a change in the frequency of different traits within the population of guppies.

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Answer:

9,2,8

Step-by-step explanation:

A whole number is a number with no fractions or Integers.

Answer:

Step-by-step explanation:

We know that the equation of a circle is:

(

x

−

a

)

2

+

(

y

−

b

)

2

=

R

2

where a and b are the coordinates of the center, and R is the radius.

So in this question we have to complete the squares:

x² + y² - x - 2y - 11/4 = 0       ->

x² - x + 1/4 + y² - 2y = 11/4 +1/4     ->

(x - 1/2)² + y² - 2y + 1 = 12/4 + 1     ->

(x - 1/2)² + (y - 1)² = 4

Therefore, the coordinates of the center are C = ( 1/2, 1) and the Radius is R = 2

      x² + y² - x - 2y - 2³/₄ = 0

               x² + y² - x - 2y = 2³/₄

               x² - x + y² - 2y = 2³/₄

(x² - x + 1) + (y² - 2y + 4) = 2³/₄ + 1 + 4

             (x - 1)² + (y - 2)² = 7³/₄

The coordinates for center of the circle is equal to (1, 2). The coordinates of the length of the radius is √(³¹/₄).

The minimum value is 0.5 and the maximum value is 3.5.

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The width and height of the rectangular display is 50 feet and 28 feet, respectively.

Using algebraic expression and equation, we can find the dimensions of the rectangular display.

Let x be the height of the display

If its width is 6 feet less than twice its height, then the width can be represented as the algebraic expression:

2x - 6 = width of the display

If the area of the display is 1400 square feet, then the equation to represent this relationship:

A = height x width

1400 = x(2x - 6)

Expanding the expression on the right-hand side:

1400 = 2x² - 6x

Dividing the whole equation by 2,

x² - 3x - 700 = 0

Factor the equation,

(x - 28)(x + 25) = 0

x = 28 ; -25

Taking the positive dimension,

height = 28 feet

So the height of the display is 28 feet. To find the width, we can use the expression we derived earlier:

width = 2x - 6

width = 2(28) - 6

width = 50 feet

So the width of the display is 50 feet.

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The hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.

The Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two legs.

If the hypotenuse is taken as a, and the two legs are taken as b and c, then by the Pythagoras Theorem, we can write that:

a² = b² + c².

In the question, we are given that the right triangle ABC, has legs of lengths 5 and 12 inches each, and we are asked to find the length of the hypotenuse.

Thus, taking b = 5 and c = 12, in the above equation, we get:

a² = 5² + 12²,

or, a² = 25 + 144,

or, a² = 169,

or, a² = 13²,

or, a = 13.

Thus, the hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.

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If the correlation coefficient r is -1.0, it means that there is a perfect negative linear relationship between X and Y.

a) As X scores increase, Y scores decrease in a perfectly consistent manner. The magnitude is strong.

b) If the correlation coefficient r is +0.32, it means that there is a positive linear relationship between X and Y, but it is a weak relationship. As X scores increase, Y scores tend to increase, but not in a perfectly consistent manner. The magnitude is weak.

c) If the correlation coefficient r is -0.10, it means that there is a weak negative linear relationship between X and Y. As X scores increase, Y scores tend to decrease, but not in a consistent manner. The magnitude is weak.

d) If the correlation coefficient r is -0.71, it means that there is a strong negative linear relationship between X and Y. As X scores increase, Y scores tend to decrease in a consistent manner. The magnitude is strong.

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The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Answer:

5cm

Step-by-step explanation:

i dont know maybe I'm right

have a nice day

1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water

Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.

From the information given, we have that;

Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water

So, we have that there is 1 liter of water in the tub

In order to displace, you need to put something in that is the same amount

Now, let's convert the units

1 liter = 1000 cubic cm

Hence, you need 1000 cubic cm to displace 1 liter

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Given that,

∠C = (6x-21)° and ∠A = (4x+11)°

To find,

Choose the correct option.

Solution,

For a parallelogram, the opposite angles are equal. ATQ,

(6x-21)° = (4x+11)°

Taking like terms together,

6x-4x = 21 + 11

2x = 32

x = 16

∠C = (6x-21)° = 6(16) -21 = 75°

So, ∠A = 75°

So, ∠A = ∠C = 75°. Hence, the correct option is (B).

Answer:

I think it is triagles A and B

Step-by-step explanation:

Answer:

26 feet, Oliver will have to travel 26 feet deep.

Step-by-step explanation:

8 feet added to 18 feet will be your answer.

Answer:26 feet, Oliver will have to travel 26 feet deep.

Step-by-step explanation:Okay so if you draw a line graph going vertical and you number it 1-32 ( this is if you have to show work ) a is a 11 feet deeper and b is 23 feet deeper

Answer:

y ≥ 3x - 1

y < \(-\frac{1}{2}x+2\)

Step-by-step explanation:

Let the equation of the solid line passing through (x', y') given in graph is,

y = mx + b

Here m = slope of the line

b = y-intercept

Slope of the solid line =

                                 m = \(\frac{3}{1}\)

                                 m = 3

y - intercept 'b' = -1

Therefore, equation of the line will be,

y = 3x - 1

Since, shaded (blue) area is above the line, inequality that will represent the solution area will be,

y ≥ 3x - 1

For the dotted line,

Slope of the line (m) = \(\frac{\text{Rise}}{\text{Run}}\)

                                  = \(\frac{-2}{4}\)

                                  = \(-\frac{1}{2}\)

y-intercept (b) = 2

Equation of the dotted line → y = \(-\frac{1}{2}x+2\)

Since, shaded (grey color) area is below the dotted line,

Inequality representing the solution area will be,

y < \(-\frac{1}{2}x+2\)

Answer:

D=-90+22/7

Step-by-step explanation:

D= 22/7×d-90

D= -90+22d/7

Integration by ordinary substitution is a general technique for simplifying integrals by changing variables, while integration by trigonometric substitution is a specific technique for evaluating integrals involving square roots and trigonometric functions.

Integration by ordinary substitution and integration by trigonometric substitution are two different techniques used to evaluate integrals in calculus.

Integration by ordinary substitution, also known as u-substitution, involves making a change of variables to simplify the integral. It is based on the chain rule for differentiation. The general steps for integration by ordinary substitution are as follows:

1. Identify a part of the integrand that can be replaced by a single variable, denoted by u.

2. Compute the derivative du/dx of the new variable u.

3. Substitute the expression for u and du into the integral, replacing the original integrand.

4. Integrate the resulting expression with respect to u.

5. Replace the variable u with the original variable or expression to obtain the final result.

Integration by trigonometric substitution, on the other hand, is a technique specifically used for integrals involving square roots of quadratic expressions or expressions with a combination of squares. It is based on trigonometric identities and is particularly useful when dealing with integrals that can be simplified using trigonometric functions. The general steps for integration by trigonometric substitution are as follows:

1. Identify a part of the integrand that can be expressed in terms of a trigonometric function.

2. Make a substitution using a trigonometric identity to replace the relevant part of the integrand.

3. Express all other terms in the integrand in terms of the same trigonometric function.

4. Simplify the integral using trigonometric identities and algebraic manipulations.

5. Integrate the resulting expression with respect to the new variable (usually denoted by θ).

6. Replace the trigonometric function with the original variable or expression to obtain the final result.

In summary, integration by ordinary substitution is a general technique for simplifying integrals by changing variables, while integration by trigonometric substitution is a specific technique for evaluating integrals involving square roots and trigonometric functions.

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Answer:

15 multiply by quarter is equal yo 60

Answer:

$ 275

Step-by-step explanation:

20/100 = 55/x (20% is 55 of what number) (%/100 = is/of)

(100 * 55) / 20 = 275

Answer:

68.75

Step-by-step explanation:

The mean fill in ounces should be set at 5.068 to ensure that 98% of 6 oz cups will not overflow.

To determine the value of mean that will ensure that 98% of 6 oz cups will not overflow, we can use the following steps:

Calculate the z-score corresponding to the desired percentile (98%):

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to the 98th percentile is approximately 2.33.

Convert the given cup size (6 oz) to a z-score using the formula:

z = (x - μ) / σ

where x is the given cup size, μ is the mean fill in ounces, and σ is the standard deviation in ounces. Solving for μ, we get:

μ = x - z × σ

= 6 - 2.33 × 0.4

= 5.068

Therefore, the mean fill in ounces should be set at 5.068 to ensure that 98% of 6 oz cups will not overflow.

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Answer:

180 + 48 = 228 :D

Step-by-step explanation:

We will first find the volume of the brown figure :)

6 x 6 x 5

36 x 5

180

Now we will find the volume of the blue figure :)

6 x 1 x 8

6 x 8

48

Now we add!!

180 + 48 =228

Have an amazing day!!!

Please rate and mark brainliest!!

Answer:

180 +48=228 cubic centimeters

the volume of the first shape=180 (you multipy length width and height)

the volume of second shape=48

add them=180+48=228

The equation of a line from the given graph is y=2/3 x. Therefore, option A is the correct answer.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

From the given table, the coordinate points are (0, 0) and (6, 4)

Here, slope m=(4-0)/(6-0)

= 2/3

Substitute, m=2/3 and (x, y)=(0, 0) in y=mx+c, we get

0=2/3(0)+c

c=0

Substitute, m=2/3 and c=0 in y=mx+c, we get

y=2/3 x

Therefore, option A is the correct answer.

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Answer:

See below

Step-by-step explanation:

Answer:

the probability is less than 4% because there are TWO more blue pens. there is a 6% chance of getting blue pen and 2% getting yellow.

Step-by-step explanation:

The expression at the upper and lower limits and the difference is

∫[0,1]√(4-3\(x^2\)) dx \(=(2 - (3/2)(1)^2) - (2 - (3/2)(0)^2) = (2 - 3/2) - (2 - 0) = (4/2 - 3/2) = 1/2.\)

To evaluate the integral ∫√(4-3\(x^2\)) dx, where the interval of integration is 0≤x≤1, we can use various techniques such as substitution or integration by parts. Let's proceed with the method of substitution to simplify the integral and find its value.

First, let's identify a suitable substitution for the integral. Since the expression inside the square root contains a quadratic term, it is beneficial to let u be equal to the square root of the quadratic expression. Therefore, we set u = √(4-3\(x^2\)).

Next, we need to find the differential of u with respect to x. Taking the derivative of both sides with respect to x, we have du/dx = (-6x)/(2√(4-3\(x^2\))) = -3x/√(4-3\(x^2\)).

Now, we can rewrite the integral in terms of the new variable u. Substituting u = √(4-3\(x^2\)) and du = (-3x/√(4-3\(x^2\))) dx into the integral, we have:

∫√(4-3\(x^2\)) dx = ∫u du

Our new integral is now much simpler, as it reduces to the integral of u with respect to u. Integrating u, we get:

∫u du = (1/2)\(u^2\) + C,

where C is the constant of integration.

Now, we can substitute back for u in terms of x. Recall that we set u = √(4-3x^2). Therefore, the final result becomes:

∫√(4-3x^2) dx = (1/2)(√\((4-3x^2))^2 + C = (1/2)(4-3x^2) + C = 2 - (3/2)x^2 + C.\)

To find the definite integral over the interval [0, 1], we need to evaluate the expression at the upper and lower limits and find the difference:

∫[0,1]√(4-3\(x^2\)) dx\(= (2 - (3/2)(1)^2) - (2 - (3/2)(0)^2) = (2 - 3/2) - (2 - 0) = (4/2 - 3/2) = 1/2.\)

Therefore, the value of the definite integral ∫√(4-3\(x^2\)) dx over the interval [0, 1] is 1/2.

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