Mr. James is teaching his students about the volume of rectangular prisms. He has various rectangular prisms with a height of 6 inches. The table shows the relationship between the base of the prism and its volume. Which equation can be used to find B, the area of the base with a volume of V?

The sum of the geometric series is 306. We can start by finding the first term and the common ratio of the geometric series.

The first term is 54, and to find the common ratio we divide any term by its previous term:

36 / 54 = 2/3

(2/3) * 54 = 36

128/27 / 36 = 4/3

So the common ratio is 2/3.

S = a * (1 - r^n) / (1 - r)

where S the sum of a geometric series with first term a,  common ratio r, and n terms is no. of terms.

We are given that there are seven terms in the sum, so n = 7.

Using the values we have:

S = 54 * (1 - (2/3)^7) / (1 - 2/3)

S = 54 * (1 - 128/2187) / (1/3)

S = 54 * (2059/2187) * 3

S = 306

Therefore, the sum of the geometric series is 306

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Answer:2/3 or approximately 0.667.

Step-by-step explanation:

total number of outcomes =6

We can obtain a sum of 6: rolling a 1 and a 5, or rolling a 2 and a 4.

Therefore, the number of outcomes that do not result in a sum of 6 is:

6 - 2 = 4

So the probability of getting a sum that is not 6 is:

P(sum is not 6) = number of outcomes that do not result in a sum of 6 / total number of possible outcomes

P(sum is not 6) = 4 / 6

P(sum is not 6) = 2 / 3

The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

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In a case whreby the electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r the simpification of the expression is 1/r(1-r).

Looking at the expression we can see that it is adion of two expression which implies that we will need to perform an addition operation then later simplified the result, this is been done below

We can find the LCM as r(1-r)

(1-r +r)/ r(1-r)

=1/r(1-r)

Therfore, after performing the addition operation as well as the simplification, then the the simpification of the expression is 1/r(1-r).

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complete question;

The electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r simplify the expression.

The most reasonable unit of measurement for 3) is option (C): [tex]m^2[/tex], 4) is option (B): [tex]km^2[/tex], 5) is [tex]in^2[/tex].

3) The most reasonable unit for the measurement of the baseball field is [tex]m^2[/tex] because the baseball field covers a large distance which is not accurately measured by small units  [tex]cm^2[/tex] or [tex]mm^2[/tex]  where it is not that big to be measured in large units like [tex]km^2[/tex]. So option C is the correct option.

4) The most reasonable unit for the measurement of a lake is [tex]km^2[/tex] because lakes are generally very large water bodies that cover a large distance and are not accurately measured by small units like [tex]cm^2[/tex] , [tex]mm^2[/tex] , and [tex]m^2[/tex]. So option B is the correct option.

5) The most reasonable unit for the measurement of the area of a door is [tex]in^2[/tex] because doors are relatively small compared to the other options and are often measured in square inches or square feet. So option B is the correct option.

Therefore the correct answers question-wise are:

3) [tex]m^2[/tex]

4) [tex]km^2[/tex]

5) [tex]in^2[/tex]

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The number of hours when the two stocks would be the same is 1.68 hours.

The first step is to determine the price of stock A at noon.

Price of stock A at noon = price at 9am + (rate of increase per hour x time difference)

Time difference = 12 - 9am = 3 hours

= $13.92 + (0.11 x 3)

= $13.92 + 0.33

= $14.25

Value of stock A t hours after noon = $14.25 + (0.11 x t)

= $14.25 + 0.11t

The equation that can be used to determine the price of stock B at time t is:

Price of stock B at time t = beginning price - (rate of decline x time)

= $14.67 - (0.14 x t)

= $14.67 - 0.14t

When the two stocks are the same, the two equations would be equal to each other:

$14.25 + 0.11t = $14.67 - 0.14t

solve for t:

0.11t + 0.14t = $14.67 - $14.25

0.25t = 0.42

t = 0.42 / 0.25

t = 1.68 hours

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The Galois group of f over R is isomorphic to the symmetric group S4. The given statement "Each intermediate field of F/Q is a Galois extension of Q." is true because f is separable.

The roots of f are given by

x = ±(√(5) + √(2)), ±(√(5) - √(2))

Let φ be the automorphism defined by

φ(√(5) + √(2)) = √(5) + i√(2)

φ(√(5) - √(2)) = √(5) - i√(2)

φ(-√(5) + √(2)) = -√(5) - i√(2)

φ(-√(5) - √(2)) = -√(5) + i√(2)

where i is the imaginary unit. Then φ has order four since φ⁴ is the identity automorphism. Let σ be the automorphism defined by

σ(√(5) + √(2)) = -√(5) + √(2)

σ(√(5) - √(2)) = √(5) - √(2)

σ(-√(5) + √(2)) = -√(5) - √(2)

σ(-√(5) - √(2)) = √(5) + √(2)

Then σ has order two since σ² is the identity automorphism. It can be shown that the Galois group of f over Q is generated by φ and σ. Since φ has order four and σ has order two, the Galois group is a non-abelian group of order eight.

To prove or disprove that each intermediate field of F/Q is a Galois extension of Q, we need to show that each intermediate field is a splitting field of a separable polynomial over Q. Since F is the splitting field of f over Q, any intermediate field of F/Q is also a splitting field of f over Q. Since f is separable (its roots are distinct), every intermediate field of F/Q is a Galois extension of Q, and hence a splitting field of a separable polynomial over Q. Therefore, the statement is true.

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Answer:

The points selected on the graph are:

(0, 0), (2, 4), (3, 6), (4, 8), (6, 12), (4, 8), (8, 16), (5, 10)

Here is a table showing the coordinates of the selected points:

x      y

0      0

2      4

3      6

4      8

6      12

4      8

8      16

5      10

The exponential function for the given data is  y = 1.806(1.107)ˣ ,

Interpretation about parameters are,

a represents  initial population and b increase in growth by 10.7%.

Population size during 35th year is 63.

The exponential function that best represents the population growth of the species of crocodiles.

Values for parameters a and b in equation y = abˣ that best fit given data.

Using the data in the table, set up a system of equations as follows,

2 = ab¹

5 = ab¹⁰

12 = ab²⁰

22 = ab³⁰

25 = ab⁴⁰

To solve for a and b, we can divide the equations to eliminate a.

5/2 = (ab¹⁰)/(ab¹)

⇒5/2 = b⁹

12/5 = (ab²⁰)/(ab¹⁰)

⇒ 12/5= b¹⁰

22/12 = (ab³⁰)/(ab²⁰)

⇒ 22/12= b³/²

25/22 = (ab⁴⁰)/(ab³⁰)

⇒25/22 = b⁴/³

Taking the ninth root of the first equation,

The tenth root of the second

b = 1.107

a = 1.806

Exponential function that best represents the population growth of species of crocodiles is y = 1.806(1.107)ˣ

Interpreting the parameters of the model in the context of the problem.

a represents the initial population when x = 0 which is not given in the table.

And b represents the growth factor or rate of increase.

The growth factor is approximately 1.107, meaning that the population is increasing by about 10.7% each year.

To predict the population size during their 35th year, we simply plug x = 35 into the equation.

y = 1.806(1.107)³⁵

  = 63.4

  = 63(whole number)

Predict that population size of species of crocodiles during their 35th year will be approximately 63 individuals.

Therefore, the exponential function is  y = 1.806(1.107)ˣ ,

Interpretation of parameters are a is the initial population and b represents the growth increased by 10.7%.

During 35th year population is 63.

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Answer:

The circumference of a circle is given by the formula "C = pi x d" where "d" is the diameter and "pi" is the mathematical constant with an approximate value of 3.14.

In this problem, the diameter of the bicycle wheel is 60 centimeters, so its circumference is:

C = pi x d = 3.14 x 60 = 188.4 centimeters

When the wheel makes one revolution, it travels one circumference distance. Therefore, when the wheel makes 35 revolutions, it will travel:

distance = 35 x circumference = 35 x 188.4 = 6584 centimeters

We can convert centimeters to meters by dividing the distance by 100:

distance = 6584 ÷ 100 = 65.84 meters

Therefore, the wheel travels 65.84 meters when it makes 35 revolutions.

The experimental probability that an arrangement will contain at least one red balloon and at least one blue balloon is 0.53. Therefore, option B is the correct answer.

The given sample space is {ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr}

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favorable outcomes =16

Probability of an event 16/30

= 0.53

Therefore, option B is the correct answer.

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The horizontal distance the ball travelled is 2.73 m.

A projectile is any object that is moving in space under the influence of gravity and its momentum. The horizontal distance covered by a projectile from its point of projection is called range. It can be determined by;

R = U[tex]\sqrt{\frac{2H}{g} }[/tex]

where u is the initial speed of the object, H is the height of projection and g is the gravitational constant.

So that in the information given, we can determine the range as;

R = U[tex]\sqrt{\frac{2H}{g} }[/tex]

  = 35[tex]\sqrt{\frac{2*0.39}{10} }[/tex]

  = 35*0.078

  = 2.73

R = 2.73 m

The horizontal distance the ball has travelled is 2.73 m.

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I don't really know but try to read

The given expression ((−3⁴)⁻⁷)⁻³ using only positive exponents is equal to  (-3)⁻⁸⁴.

To write the expression ((−3⁴)⁻⁷)⁻³ using only positive exponents, we can apply the rule of exponentiation that states that a negative exponent can be converted to a positive exponent by moving the base to the denominator and changing the sign of the exponent.

In this case, we have a negative exponent raised to another negative exponent, so we need to apply this rule twice.

First, we can rewrite the expression as:

((-3⁴)⁻⁷)⁻³ = (-3⁴)⁷³

Next, we can apply the rule of negative exponent to obtain:

(-3⁴)⁷³ = (1/(-3⁴))⁻²¹

Finally, we can simplify the expression by moving the negative exponent to the numerator, changing the sign of the exponent and using the power rule of exponents to get:

(1/(-3⁴))⁻²¹ = (-3⁻⁴)²¹ = (-3)⁻⁸⁴

In conclusion, we can convert a negative exponent to a positive exponent by moving the base to the denominator and changing the sign of the exponent. We can use this rule multiple times to simplify expressions with negative exponents.

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Answer: We can use basic trigonometry to solve both of these problems:

Angle of depression from the top of the tree to the lake:

Let's draw a diagram of the situation:

       A (top of tree)

       |\

       | \

    30 |  \ 15 ft

       |   \

       |    \

       |     \

       |      \

       |       \

       |        \

       |         \

       |          \

       |__________\

              B (lake)

In this diagram, A represents the top of the tree, B represents the lake, and the lines connecting them form a right triangle. We want to find the angle of depression, which is the angle between the horizontal line (from the top of the tree to the lake) and the line of sight from the top of the tree to the lake. This is angle θ in the diagram.

We know that the opposite side of this right triangle is 30 feet (the horizontal distance from the top of the tree to the lake) and the adjacent side is 15 feet (the height of the tree). Therefore:

Taking the arctangent of both sides gives us:

Therefore, the angle of depression from the top of the tree to the lake is approximately 63.4 degrees.

Angle of elevation from the boat to the top of the tree:

Let's draw a diagram of the situation:

   C (person on boat)

    |\

    | \

35  |  \

    |   \

    |    \

    |     \

    |      \

    |       \

    |        \

    |         \

    |          \

    |__________\

          A (top of tree)

In this diagram, C represents the person on the boat, A represents the top of the tree, and the lines connecting them form a right triangle. We want to find the angle of elevation, which is the angle between the horizontal line (from the person on the boat to the shore) and the line of sight from the person on the boat to the top of the tree. This is also angle θ in the diagram.

We know that the opposite side of this right triangle is 15 feet (the height of the tree) and the adjacent side is 35 feet (the horizontal distance from the person on the boat to the tree). Therefore:

Taking the arctangent of both sides gives us:

Therefore, the angle of elevation from the boat to the top of the tree is approximately 23.1 degrees.

Answer:

225 is the answer

15 times 15

Step-by-step explanation:

To find the domain of a function, we need to determine all values of the independent variable (usually denoted as x) for which the function is defined and has a real output.

For example, if we have the function:

f(x) = 1/(x-3)

We need to exclude any values of x that would make the denominator zero, since division by zero is undefined. Therefore, the domain of this function would be all real numbers except x = 3. We could write this as:

Domain: x ∈ ℝ, x ≠ 3

If we have a more complex function, we need to consider any other restrictions on the independent variable that may be imposed by the function.

For instance, if we have the function:

g(x) = sqrt(x-2)/(x+3)

Here, the square root function is defined only for nonnegative values of its argument. Therefore, we need to ensure that x-2 ≥ 0, or equivalently, x ≥ 2. Additionally, the denominator of the fraction cannot be zero, so we need to exclude x = -3. Combining these two conditions, we get:

Domain: x ∈ [2, ∞), x ≠ -3

This means that the function g(x) is defined and has a real output for all values of x greater than or equal to 2, except x = -3.

In general, to find the domain of a function, we need to consider any restrictions on the independent variable imposed by the function itself (such as division by zero, taking the square root of a negative number, etc.), as well as any restrictions that may be imposed by the context in which the function is used (such as physical or mathematical constraints). We then express the domain as a set of values of x that satisfy all the relevant conditions.

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Answer:

There are a total of 900 three-digit positive integers, from 100 to 999.

Answer:

Here's how to graph the piecewise function:

First, we graph the function for the first interval, which is f(x) = 3x - 5 when x ≤ -1. This is a straight line with a slope of 3 and a y-intercept of -5. Since this interval includes -1, we draw a closed circle at x = -1 to indicate that it is included in the interval. The line is decreasing as x increases.

Next, we graph the function for the second interval, which is f(x) = -2x + 3 when -1 < x < 4. This is also a straight line, but with a slope of -2 and a y-intercept of 3. Since this interval does not include -1, we draw an open circle at x = -1 to indicate that it is not included in the interval. We also draw an open circle at x = 4 to indicate that it is not included in the interval. The line is increasing as x increases.

Finally, we graph the function for the third interval, which is f(x) = 2 when x ≥ 4. This is a horizontal line at y = 2. Since this interval includes 4, we draw a closed circle at x = 4 to indicate that it is included in the interval.

When we put all three intervals together, we get a graph that looks like this:

```

         |         /

  2      |        /

         |       /

         |      /

         |     /

         |    /

         |   /

         |  /

         | /

         |/

  _______|_____________

         -1   4

```

The graph consists of a downward-sloping line from (-∞, -1], an upward-sloping line from (-1, 4), and a horizontal line from [4, ∞).

The width of each poster cannot be greater than 11/4 feet or 2.75 feet.

For given expression w represents the width, 4w represents the total width of four posters, 5 represents space between posters and edges of wall, and 16 represents width of the wall.

The boundary value satisfies the inequality.

In the given problem, Marie-Renee wants to hang 4 identical posters on her wall, and she needs to leave at least 5 feet of space total between the posters and between the edges of the wall. Let's assume that the width of each poster is w feet.

The inequality 4w + 5 ≤ 16 represents the maximum space the posters can take on the wall. In this inequality,

w represents the width of each poster,

4w represents the total width of four identical posters,

5 represents the total space between the posters and between the edges of the wall, and

16 represents the total width of the wall.

To find the acceptable width of each poster, we need to solve 4w + 5 = 16.

4w + 5 = 16

4w = 16 - 5

4w = 11

w = 11/4

So, the width of each poster cannot be greater than 11/4 feet or 2.75 feet.

Now, we need to check if the boundary value of w satisfies the original inequality or not.

4w + 5 ≤ 16

4(11/4) + 5 ≤ 16

11 + 5 ≤ 16

16 ≤ 16

Since the boundary value satisfies the inequality, the solution to Marie-Renee's inequality is w ≤ 11/4 or w ≤ 2.75 feet.

Therefore, the width of each poster cannot exceed 2.75 feet, and all four posters can be hung on the 16 feet wide wall with at least 5 feet of space total between them and the edges of the wall.

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2 3/4 cups is equivalent to 1 3/8 pints as a mixed number.

There are 2 cups in a pint. To convert 2 3/4 cups into pints, we can follow these steps:

Convert the whole number part of the mixed number to pints by dividing by 2.

Convert the fractional part of the mixed number to cups, then divide by 2 to get the corresponding pints.

Add the two results together to get the total in pints as a mixed number.

So, let's apply these steps to 2 3/4 cups:

The whole number part is 2, so 2 cups = 1 pint.

The fractional part is 3/4 cups, which is equivalent to 3/4 ÷ 2 = 3/8 pints.

Adding the two results, we get:

1 pint (from the whole number part) + 3/8 pint (from the fractional part) = 1 3/8 pints.

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Answer:

  $9.34 per square foot

Step-by-step explanation:

You want the cost per square foot of a 36 foot square building that costs $12,099.

The cost per square foot is found by dividing the cost by the number of square feet. That area is found as the square of the side length:

  A = s²

  A = (36 ft)² = 1296 ft²

Then the cost is ...

  cost per square foot = ($12099)/(1296 ft²) ≈ $9.34/ft²

The cost of the building is about $9.34 per square foot.

<95141404393>

Answer:

B

Step-by-step explanation:

N(0) = 5

m = 2 individuals per unit time

t = 20 unit time

N(20) = 2*20+5 = 45 individuals

The linear growth equation, M(t) = M(0) + m*t, can be used to calculate population growth at a constant rate. By substituting in the given starting population of 5 and growth rate of 2, it is determined that the population at 20 units of time is 45.

In the context of this question, we're dealing with a simple linear growth equation, which can be expressed algebraically as M(t) = m*t + M(0), where M(t) is the population at time t, m is the rate of growth, and M(0) is the starting population.

In this case, the starting population, M(0), is 5 and the growth rate, m, is 2 individuals per unit of time. So if we want to calculate the population at 20 units of time, we would substitute these values into the equation.

According to the equation, M(20) = M(0) + m*20 = 5 + 2*20 = 5 + 40 = 45. Therefore, the population at 20 units of time would be 45 individuals.

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Answer:

True

Explanation:

Bridget Riley was one of the most prominent artists associated with the 1960s 'Op Art' movement, which was an art movement that explored optical illusions and effects to create abstract art that played with the viewer's perception. However, there were many other artists associated with this movement, including Victor Vasarely, Richard Anuszkiewicz, and Yaacov Agam, among others.

Answer:

[tex]100000( {.70}^{3} ) = 34300[/tex]

Answer: The Correct answer is E (2,pie/6)

Step-by-step explanation:

To find the polar coordinates of a point given its Cartesian coordinates (x, y), we can use the following formulas:

r = √(x^2 + y^2)

θ = atan2(y, x)

where r is the radial distance from the origin to the point, and θ is the angle measured counterclockwise from the positive x-axis to the line connecting the origin and the point.

Given the Cartesian coordinates (x, y) = (√3, 1), we can plug these values into the formulas to find the polar coordinates:

r = √(√3^2 + 1^2) = √(3 + 1) = 2

θ = atan2(1, √3)

Using a calculator, we can find that θ is approximately 0.5236 radians.

So, the polar coordinates of the point (√3, 1) are (r, θ) = (2, 0.5236 radians).

Answer:

The length is 35 meters (m).

Step-by-step explanation:

182/2

91 = area of 1/5 of the field.

91 * 3

273 = area of cabbages.

182 + 273

455 = area of whole field.

a/w = l, because l * w = a

455/13

35

Answer:131290

Step-by-step explanation:13129*100/10=131290

The value of 'x' is 1 and value of y is '0'.

An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

We have the equations are:

-3x + 5y = -3 ___eq.1

and, y = -7 + 7 ___eq.2

We have to find the value of 'x' and 'y'

Now, Firstly find the value of y

We know that :

Opposite sign with same digit is cancel to each other it is always zero.

y = -7 + 7

So, y = 0

Now, We have to put the value of y in eq. 1

-3x + 5(0) = -3

-3x + 0 = -3

x = -3/-3

x = 1

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Answer: The answer is 171.2 Miles

Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.

Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.