PLEASE HELP DUE SOON

3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.

4. The cake takes up approximately 7317 cubic inches of space.

5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.

1. The units for Volume are always cubed.

2. Volume is the amount of space an object takes up. True.

3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:

V = 3.14 * (4.5)^2 * 32

V = 3.14 * 20.25 * 32

V ≈ 2034.72 cubic inches

4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.

Tier 1:

V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches

Tier 2:

V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches

Tier 3:

V3 = 3.14 * (5)^2 * 10 = 785 cubic inches

Total volume:

Total V = V1 + V2 + V3

Total V = 4521.6 + 2010.4 + 785

Total V ≈ 7317 cubic inches

5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:

V = (1/3) * 3.14 * (24)^2 * 12

V = (1/3) * 3.14 * 576 * 12

V ≈ 7234.08 cubic centimeters

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Answer:

25 + 9^3

Step-by-step explanation:

Answer: 86950

Step-by-step explanation:

Answer:

6x2+15x

Step-by-step explanation:

The length of the rope swing is approximately 98.9 feet (rounded to the nearest tenth of a foot).

Algebraic expressions are used to represent mathematical relationships and formulas, and can be used to solve equations and manipulate equations in order to isolate variables or solve for unknown quantities. They are used extensively in algebra, calculus, and other branches of mathematics.

We are given that the time for one swing is given by the formula:

t = 2√(L/32.2)

where L is the length of the rope swing in feet, and 32.2 is the acceleration due to gravity in feet per second squared.

We are also given that one swing takes 3.5 seconds, so we can write:

3.5 = 2√(L/32.2)

Squaring both sides, we get:

12.25 = 4(L/32.2)

Multiplying both sides by 32.2/4, we get:

L = 32.2 × 12.25/4

L ≈ 98.9 feet

Therefore, the length of the rope swing is approximately 98.9 feet (rounded to the nearest tenth of a foot).

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Answer:

D.

Step-by-step explanation:

$230 + $360 = $590

$590 - $253* = $337

$337

*( total sum of all the bills )

When solving a linear system of equations, you are looking for the points of intersection between the equations

From the question, we have the following parameters that can be used in our computation:

Solving a system of linear equations

Also, we have the following from the options

The general rile is that

Slope = rate of change

x and y intercepts = when y and x equals 0

points of intersection = solution to the system

Hence, you are looking for the points of intersection between the equations

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Question

When solving a linear system of equations, you are looking for which of the following?

Slope

y-intercept

x-intercept

Points of intersection

Answer:

10 times greater

Step-by-step explanation:

40,000 compared to 4,000. You just add 1 zero to 4,000 to get 40,000, therefore is is 10x greater.

Answer:

Step-by-step explanation:

Answer:

(4;-1)

Step-by-step explanation:

A(-4;2)

B(-2;-1)

C(1;1)

D(-4;-1)

Answer:

-1;4

Step-by-step explanation:

Answer:

\(6x^{2} -9x+3\)

Step-by-step explanation:

\((3x-3) (2x-1)\)

\(3x (2x-1)-3(2x-1)\)

\(6x^{2} -3x-6x+3\)

\(6x^{2} -9x+3\)

Answer:132,090.30

Step-by-step explanation:

r = R/100

r = 4.6%/100

r = 0.046 per year,

A = P(1 + r/n)nt

A = 77,000.00(1 + 0.046/1)(1)(12)

A = $ 132,090.30

Answer:133727.67

Step-by-step explanation:

133727.67

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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9514 1404 393

Answer:

  $1200

Step-by-step explanation:

60 attendees is 12 times 5 attendees, so we expect the amount raised to be 12 times $100.

$1200 will be raised for 60 attendees.

Answer:

Since the ratio is 12 : 5, the statement which is true is there are more than twice as many cows as there are sheep.

The ratio between the number of cows to number of sheep in a field is given as:

12 : 5

Now,

let the number of sheep be 5 x.

So, the number of cows will be 12 x.

So, we get that:

12 x > 2 ( 5 x)

12 x > 10 x

So, the statement which is true will be:

there are more than twice as many cows as there are sheep

Therefore, since the ratio is 12 : 5, the statement which is true is there are more than twice as many cows as there are sheep.

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Step-by-step explanation:

In being able to find out whether it is possible to know the number of students on each team, there simply isn't enough information to do so.

In order to find out the number of students on each team, the following formula is necessary:

= Number of students in general / Number of teams

The number of teams is 4 so the denominator is present.

We however, do not have the number of students in general so we are unable to find out the number of students in each team.

In conclusion, we do not have enough information to find out the number of students in each team.

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Answer:

c

Step-by-step explanation:

it has a repeating domain so it can not be a function

0,−1,2,1,0 has two values corresponding to a range of functions so it will not form a function so option (C) will be correct.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of functin at x = 1 its that f(1) = 1 called range variable.

To be a relation a function for every single unique input there must be single unique output.

Since the interval 0,−1,2,1,0 has 2 inputs for single output so it will not form an function.

Hence "0,−1,2,1,0 has two values corresponding to a range of functions so it will not form a function".

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Answer:

9 days  

To solve the equation your would round 63,500 to 63000. Then divide 63000 by 7000 which gives you 9. We round 63500 to 63000 to use compatible numbers

Answer:

Below.

Step-by-step explanation:

1/20 is a small distance needed to be traveled right?

20/20 is the whole length.

If 1/20 gets traveled in 3/4 of a second,

3/4x2- or 2(1/20) which equals one right?

20(3/4) = 15 seconds

The value of the number is x = 34.

Let's break down the problem and solve it step by step.

1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.

2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).

According to the problem statement, the two expressions are equal. We can set up the equation as follows:

2x - 5 = 3 * (x/2 + 4)

Now, let's solve the equation:

2x - 5 = 3 * (x/2 + 4)

Distribute the 3 to both terms inside the parentheses:

2x - 5 = (3/2)x + 12

Multiply through by 2 to eliminate the fraction:

2(2x - 5) = 2((3/2)x + 12)

4x - 10 = 3x + 24

Next, let's isolate the x term by moving the constant terms to the other side of the equation:

4x - 3x = 24 + 10

Simplify:

x = 34

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Step-by-step explanation:

Simple, she found the sum of the interior angles not exterior angles.

The exterior angles of any polygon add up to 360 degrees.

What Cindy did was found the total interior angle measure of a hexagon which is 720

Segment CD is longer and 0.3 units longer if the points A, B, C, and D have the coordinates: A: (-3, 7) B: (1, 2) C: (-3, 1) D: (3,-2).

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

\(\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

It is given that:

Points A, B, C, and D have the following coordinates: A: (-3, 7) B: (1, 2) C: (-3, 1) D: (3,-2)

Using the distance formula to calculate the distance between the points:

\(\rm AB=\sqrt{(1+3)^2+(2-7)^2}\)

AB = √41 = 6.4 units

Similarly,

CD = √45 = 3√5 = 6.7 units

CD is longer

6.7 - 6.4 = 0.3 units longer

Thus, segment CD is longer and 0.3 units longer if the points A, B, C, and D have the coordinates: A: (-3, 7) B: (1, 2) C: (-3, 1) D: (3,-2).

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Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

Answer: normal formula define the cup full of is Q -2+ you and me 32,000 you’re welcome

Step-by-step explanation:

Answer:

The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Step-by-step explanation:

Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.

The random variable is approximated by the Poisson Distribution with parameter λ = 5.

The probability mass function of X is as follows:

\(P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...\)

Compute the probability that on a randomly selected day she will have five messages as follows:

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}\)

               \(=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755\)

Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Using the concept of proportions and ratios on the similar triangles, the value of x is 48 units

Similar triangles are triangles that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are proportional. In other words, the ratios of the corresponding sides of similar triangles are equal.

The concept of similar triangles is based on the fundamental property that corresponding angles in similar shapes are equal, and the corresponding sides are proportional.

To determine the value of x, we can apply the concept of proportions and ratio on the similar triangle;

x / 36 = 64 / x

Cross multiplying both sides

x * x = 36 * 64

x² = 2304

x  = √2304

x = 48 units

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After calculating a percentile using the z score, you should c. Always check that your answer makes sense.

After calculating a percentile using the z-score, it is important to check that your answer makes sense. This step helps ensure the accuracy and validity of your calculations. Let's go through the process step by step:

Calculate the z-score: The z-score is a measure of how many standard deviations an observation or data point is from the mean. It is calculated using the formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Use the z-score to find the percentile: Once you have the z-score, you can refer to a standard normal distribution table or use statistical software to find the percentile associated with that z-score. The percentile represents the percentage of data points that fall below the given value.

Check the percentile: After obtaining the percentile, it is crucial to examine whether it makes sense in the context of the problem. Percentiles range from 0 to 100, representing the percentage of values below the given data point. Therefore, the percentile should always be between 0 and 100.

a. If the calculated percentile is greater than 100 or less than 0, it suggests an error in the calculation. Review the calculations and ensure accuracy.

b. If the percentile falls within the expected range of 0 to 100, it is a valid result. However, it is still recommended to assess whether the calculated percentile aligns with the problem's context and expectations.

Finalize your answer: Once you have verified that the calculated percentile is within the appropriate range and makes sense in the given context, you can confidently use it as your answer.

Hence, the correct step to take after calculating a percentile using the z-score is c. Always check that your answer makes sense.

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Answer:

155.56m

0.242 hectares

Step-by-step explanation:

\(L=\frac{220}{\sqrt{2} } =155.56m\)

\(A=\frac{155.56^{2}}{10^{5} } =0.242\)