Consider a physical pendulum with length of 94.7 cm and mass of 166 g. if the pendulum was released from an angle less than 10o, then calculate the angular speed of the pendulum. (g = 9.80 m/s2)

By using the method subtraction, Jackson's height is 1.25m.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

Grace's height is 1.45 m.

Jackson is 0.2 m shorter than Grace.

Jackson's height is 1.45 -0.2 = 1.25

Therefore, Jackson's height is 1.25m.

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Based on the given information, the estimate for the number of cells in a T75 flask can be calculated by comparing the number of cells in the picture to the field of view area and then scaling it up to the size of the T75 flask.

Given that there are 55 cells in the picture, we can use this information to estimate the density of cells in the field of view. The field of view has dimensions of 1.85 mm x 1.23 mm, which gives an area of 2.7095 square millimeters (\(mm^2\)). To calculate the cell density, we divide the number of cells (55) by the area (2.7095 \(mm^2\)), resulting in an approximate cell density of 20.3 cells per \(mm^2\).

Now, to estimate the number of cells in a T75 flask, we need to know the size of the flask's growth area. A T75 flask typically has a growth area of about 75 \(cm^2\). To convert this to \(mm^2\), we multiply by 100 to get 7500 \(mm^2\).

To estimate the number of cells in the T75 flask, we multiply the cell density (20.3 cells/\(mm^2\)) by the growth area of the flask (7500 \(mm^2\)). This calculation gives us an approximate estimate of 152,250 cells in the T75 flask. It's important to note that this is just an estimate, and actual cell counts may vary depending on various factors such as cell size, confluency, and experimental conditions.

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The integrating factor for the given differential equation is y. The general solution to the second differential equation is x² + 4xy - x + y³ = C.

To find the integrating factor for the differential equation (2y^2 + 3x)dx + 2xydy = 18, we check if the equation is exact. If the equation is exact, then the integrating factor is 1. Taking the partial derivative of (2y^2 + 3x) with respect to y gives 4y, and the partial derivative of 2xy with respect to x gives 2y. Since these partial derivatives are not equal, the equation is not exact.

To find the integrating factor, we divide the coefficient of dy by the coefficient of dx and set it equal to a function of x and y:

(2xy)/(2y^2 + 3x) = F(x,y)

To simplify, we have:

y/(y^2 + (3/2)x) = F(x,y)

Comparing this with the standard form of an integrating factor, F(x,y) = 1/g(y), we find that the integrating factor is y. Therefore, the answer is B. y.To find the general solution to the differential equation (2x + 4y + 1)dx + (4x - 3y^2)dy = 0, we check if the equation is exact. If the equation is exact, the general solution can be obtained by integrating.

Taking the partial derivative of (2x + 4y + 1) with respect to y gives 4, and the partial derivative of (4x - 3y^2) with respect to x gives 4. Since these partial derivatives are equal, the equation is exact. To find the general solution, we integrate the coefficient of dx with respect to x and the coefficient of dy with respect to y. The result should be equal to a constant, denoted as C.

∫(2x + 4y + 1)dx = x^2 + 4xy + x + C₁(y)

∫(4x - 3y^2)dy = 4xy - y^3 + C₂(x)

Setting the sum of these two expressions equal to a constant, denoted as C, we have:

x^2 + 4xy + x + C₁(y) - y^3 + C₂(x) = C

Simplifying and combining like terms, we obtain the general solution:

x² + 4xy - x - y³ = C

Therefore, the answer is B. x² + 4xy - x - y³ = C.

Note: The solution C could be different in each explanation, as it represents an arbitrary constant.

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We apply the formula : a^m : a^n = a^(m-n)

-> 3^4 : 3^9 = 3^(4-9) = 3^-5

Since we need the final answer with a positive exponent, 3^5.

There are 3 mangoes left behind after making 39 trays of 9 mangoes each

To find out how many trays can be made from 354 mangoes, we divide the total number of mangoes by the number of mangoes per tray.

Number of mangoes per tray = 9

Number of trays = 354 mangoes / 9 mangoes per tray

Number of trays = 39 trays

So, 39 trays can be made from 354 mangoes.

To determine how many mangoes are left behind, we subtract the number of mangoes used for the trays from the total number of mangoes.

Number of mangoes left behind = Total number of mangoes - Number of mangoes used for trays

Number of mangoes left behind = 354 mangoes - (39 trays * 9 mangoes per tray)

Number of mangoes left behind = 354 mangoes - 351 mangoes

Number of mangoes left behind = 3 mangoes

Therefore, there are 3 mangoes left behind after making 39 trays of 9 mangoes each

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Answer:

An easy way to understand math easily is to study math more and do it more.

Answer:

More practice & write down every step.

Step-by-step explanation:

Answer: You will need 250 boxes of popcorn to meet your $300 goal.

Step-by-step explanation:

Answer:

5 boxes of popcorn makes 300 usd

Step-by-step explanation:

To find the formula for the nth partial sum and determine if the series converges or diverges, we are given a series of the form Σ(α^n)/(6^(n+1)) and need to evaluate it.

The answer involves finding the formula for the nth partial sum, applying the convergence test, and determining the sum of the series if it converges.

The given series is Σ(α^n)/(6^(n+1)), where α is a constant. To find the formula for the nth partial sum, we need to compute the sum of the first n terms of the series.

By using the formula for the sum of a geometric series, we can express the nth partial sum as Sn = (a(1 - r^n))/(1 - r), where a is the first term and r is the common ratio.

In this case, the first term is α/6^2 and the common ratio is α/6. Therefore, the nth partial sum formula becomes Sn = (α/6^2)(1 - (α/6)^n)/(1 - α/6).

To determine if the series converges or diverges, we need to examine the value of the common ratio α/6. If |α/6| < 1, then the series converges; otherwise, it diverges.

Finally, if the series converges, we can find its sum by taking the limit of the nth partial sum as n approaches infinity. The sum of the series will be the limit of Sn as n approaches infinity, which can be evaluated using the formula obtained earlier.

By applying these steps, we can determine the formula for the nth partial sum, assess whether the series converges or diverges, and find the sum of the series if it converges.

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C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

Answer:

p = 3

Step-by-step explanation:

Given

4(2 + px) = 12x

If the coefficient of the x- term is the same on both sides of the equation, it will have no solution.

Distributing gives

8 + 4px = 12x ( equate the coefficients of the x- term )

4p = 12 ( divide both sides by 4 )

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

4(2 + px) = 12x

8 + 4px = 12x

If the coefficient of the x-term is the same on both sides of the equation, it will have no solution.

4p = 12

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

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The inequality that represents all the solutions of -2(3x + 6) ≥ 4(x + 7) is x ≤ -4

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

-2(3x + 6) ≥ 4(x + 7)

Divide both sides of the inequality by -2

So, we have the following representation

3x + 6 ≤ -2(x + 7)

Open the brackets

This gives

3x + 6 ≤ -2x - 14

Add 2x to both sides of the inequality

So, we have the following representations

5x + 6 ≤ -14

Subtract 6 from both sides of the inequality

So, we have the following representations

5x ≤ -20

Divide both side of the inequality

x ≤ -4

Hence, the solution is x ≤ -4

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Step-by-step explanation:

Paxton multiplied 2/3 times the 5 in the numerator. Then he multiplied the 3 and 8 in the denominator.

The correct way to solve this problem would be to multiply the numerators and then multiply the denominators. This would give you 10/24. You can then divide the numerator and deonminator by 2 and get 5/12.

Answer:

10 2 28

9 3 30

8 4 32

7 5 34

6 6 36

Step-by-step explanation:

1. volume = πr²h

= π×(5²)×9

= π×225

= 225π

= 707.1 cubic inches

2. volume = lwh

= 5.2 × 1.8 × 2

= 18.72 square feets

Answer:

$133.50

Step-by-step explanation:

100%-11%=89%

89%=0.89

0.89*$150=$133.50

Answer:

∠2 = 125°

Step-by-step explanation:

∠1 and ∠2 form a straight angle of 180° (∠3 and ∠4 aswell)

∠1 = ∠3, because they are cross angles (∠3 and ∠4 aswell)

We can write an equation according to this and find y:

(8y - 9)° = (6y + 7)°

8y - 6y = 7 + 9

2y = 16 / : 2

y = 8

∠1 = 8 × 8 - 9 = 55°

∠2 = 180° - 55° = 125°

∠3 =∠1 = 6 × 8 + 7 = 55°

∠4 = 180° - 55° = 125°

The probability all cards are black cards is 23/100.

The correct answer is option A.

The probability is determined using the formula below:

The total number of cards in a standard deck is 52.

In a standard deck of 52 cards, there are 26 black cards (clubs and spades).

The first black card can be chosen from 26 black cards out of 52 total cards.

The second black card can be chosen from the remaining 25 black cards out of 51 total cards.

The third black card can be chosen from the remaining 24 black cards out of 50 total cards.

The fourth black card can be chosen from the remaining 23 black cards out of 49 total cards.

The number of favorable outcomes is 26 * 25 * 24 * 23 = 358,800.

The first card can be chosen from 52 total cards.

The second card can be chosen from the remaining 51 cards.

The third card can be chosen from the remaining 50 cards.

The fourth card can be chosen from the remaining 49 cards.

The total number of possible outcomes is 52 * 51 * 50 * 49 = 6497400.

Probability = 358,800 / 6,497,400

Probability = 23/100.

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Answer:

\(f(1)=-7\)

Step-by-step explanation:

We are given the derivative:

\(f^\prime (x) = 3 x^2 + 2x\)

And the initial condition that f(2)=3.

And we want to find f(1).

So, to find our original function f(x), we will find the antiderivative of f'(x). Hence:

\(\displaystyle f(x)=\int f^\prime(x)\, dx=\int3x^2+2x\, dx\)

By integrating, we acquire:

\(f(x)=x^3+x^2+C\)

Since we know that f(2)=3:

\(3=(2)^3+(2)^2+C\)

It follows that:

\(C=-9\)

Therefore, our function is given by:

\(f(x)=x^3+x^2-9\)

Therefore:

\(f(1)=(1)^3+(1)^2-9 = -7\)

Here we want to solve a differential equation, we will find that our function is f(x) = x^3 + x^2 -9

So we want to find f(x) such that we know f'(x).

We know that:

f'(x) = 3x^2 + 2x

To get f(x) we just need to integrate, we will get:

\(f(x) = \int\limits {3x^2 + 2x} \, dx = x^3 + x^2 + c\)

Where c is a constant of integration.

Now, we know that f(2) = 3, with that we can find the value of c.

f(2) = 2^3 + 2^2 + c = 3

          8 +  4 + c = 3

          c = 3 - 12 = -9

So the function is:

f(x) = x^3 + x^2 -9

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The output of the code var x = [4, 7, 11]; x. for each (stepup); function stepup(value, i, arr) { arr[i] = value 1; }  is [5, 8, 12].

Here's an explanation of this code:
1. The code initializes an array called "x" with the values [4, 7, 11].
2. The "foreach" method is called on the array "x". This method is used to iterate over each element in the array.
3. The "stepup" function is passed as an argument to the "foreach" method. This function takes three parameters: "value", "i", and "arr".
4. Inside the "stepup" function, each element in the array is incremented by 1. This is done by assigning "value + 1" to the element at index "i" in the array.
5. The "for each" method iterates over each element in the array and applies the "stepup" function to it.
6. After the "for each" method finishes executing, the modified array is returned as the output.
7. Therefore, the output of the code is [5, 8, 12].

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You  must deposit $13.59 each day for the next 35 years if you want $1 million saved.

Assuming the interest is compounded daily, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)ⁿᵃ - 1] / (r/n)

where:

FV = Future Value (in this case, $1,000,000)

PMT = Deposit amount (what we're trying to find)

r = Annual interest rate (5.5% or 0.055)

n = Number of compounding periods per year (365, since interest is compounded daily)

a = Number of years (35)

Substituting the values:

1,000,000 = PMT x [(1 + 0.055/365)³⁶⁵ˣ³⁵ - 1] / (0.055/365)

Solving for PMT, we get:

PMT = 1,000,000 / {[(1 + 0.055/365)³⁶⁵ˣ³⁵ - 1] / (0.055/365)}

PMT ≈ $13.59

So, you would need to deposit approximately $13.59 every day for the next 35 years to have $1 million saved, assuming the interest is compounded daily at a rate of 5.5%.

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Main Answer: The total area is 26.5 square units.

Supporting Question and Answer:

How can the integral of the absolute value of a function be split into multiple intervals?

When dealing with the integral of the absolute value of a function over an interval, if the function changes its behavior or slope within that interval (such as crossing the x-axis or changing sign), the integral needs to be split into multiple intervals based on those points of change. Each interval is then integrated separately, considering the appropriate sign of the function within each sub-interval, to obtain the total area.

Body of the Solution:To find the total area between the graph of the function f(x)=−x−1 and the x-axis over the interval [−3,6],we need to integrate the absolute value of the function over that interval.

Since the function is negative in the given interval, we can rewrite it as f(x)=∣x+1∣ to simplify the calculations.

To find the total area, we need to evaluate the integral of ∣f(x)∣ over the interval [−3,6]:

Total Area=    \(\int\limits^6_{-3} {|f(x)|} \,dx\)

Since the function f(x)=∣x+1∣ changes its slope at x=−1, we need to split the integral into two parts:

Total Area=   \(\int\limits^{-1}_{-3} {-(x+1)} \, dx +\int\limits^6_{-1} {(x+1)} \, dx\)

Simplifying and evaluating each integral:

Total Area=\([-\frac{1}{2}(-1)^{2} -(-1)]-[-\frac{1}{2}(-3)^{2} -(-3)]+[\frac{1}{2} (6^{2})+6]-[\frac{1}{2} (-1)^{2}+(-1)]\)

Total Area=\([\frac{1}{2}]-[-\frac{3}{2}]+[\frac{1}{2} (48)]-[-\frac{1}{2}]\)

Total Area=24+\(\frac{5}{2}\)

Total Area=26.5

Therefore, the total area between the graph of the function f(x)=−x−1 and the x-axis over the interval [−3,6] is 26.5 square units.

Final Answer:Thus, the total area between the graph of the function f(x)=−x−1 and the x-axis over the interval [−3,6] is 26.5 square units.

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The total area between the graph of the function f(x) = -x - 1 and the x-axis over the interval [-3, 6] is 10 square units.

To find the total area between the graph of the function f(x) = -x - 1 and the x-axis over the interval [-3, 6], we need to calculate the definite integral of the absolute value of the function within that interval.

The graph of f(x) = -x - 1 is a linear function with a negative slope. It intersects the x-axis at x = -1.

Since the function is negative for all x-values within the interval [-3, -1) and positive for all x-values within the interval (-1, 6], we can split the integral into two parts and take the absolute value of the function within each interval.

First, we calculate the integral from -3 to -1:

∫[-3,-1] |-x - 1| dx

Integrating the absolute value of -x - 1 within the interval [-3, -1], we get:

∫[-3,-1] |-x - 1| dx = ∫[-3,-1] (x + 1) dx

\(= [(1/2)x^2 + x] |-3,-1\)

= [(-1/2) - (-7/2)]

= 6/2

= 3

Next, we calculate the integral from -1 to 6:

∫[-1,6] | -x - 1| dx

Integrating the absolute value of -x - 1 within the interval [-1, 6], we get:

∫[-1,6] |-x - 1| dx = ∫[-1,6] -(x + 1) dx

\(= [-(1/2)x^2 - x] |-1,6\)

= [(-17/2) - (-3/2)]

= -7

To find the total area, we sum the absolute values of the two integrals:

Total Area = |3| + |-7| = 3 + 7 = 10

Therefore, the total area between the graph of the function f(x) = -x - 1 and the x-axis over the interval [-3, 6] is 10 square units.

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Answer:

\( \frac{3}{4} \)

Step-by-step explanation:

\( \frac{1}{4} + \frac{1}{2} \: \: lcm \: of \: 4 \: an d \: 2 \: is \: 4 \ \\ = \frac{1 + 2}{4} = \frac{3}{4} \)

ANSWER

• A = 55.5°

• B = 45.5°

• C = 79.1°

EXPLANATION

The lengths of the three sides of a triangle are given. We have to use the Law of Cosines to find the measures of the interior angles,

Solving each of the equations above for the angles, A, B, and C, we can find their measures,

Replace the known values and solve,

Repeat for angle B,

And for angle C,

Hence, the three interior angles of this triangle, rounded to the nearest tenth of a degree, are:

• A = 55.5°

• B = 45.5°

• C = 79.1°

The value of the expression is :

\([1 - \frac{1}{3} ] [1 - 14] [1 - 1/n] is (-\frac{26}{3} ) [(n-1)/n].\)

The given expression is:

\([1 - \frac{1}{3} ] [1 - 14] [1 - 1/n]\)

We are able to simplify each of the terms within the expression:

\([1 - \frac{1}{3} ] = \frac{2}{3}\)

[1 - 14] = -13

\([1 - \frac{1}{n} ] = (n-1)/n\)

Adding those values in to the original equation, we get:

\([1 - \frac{1}{3} ] [1 - 14] [1 - 1/n] = (\frac{2}{3} ) (-13) [(n-1)/n]\)

Simplifying similarly, we get:

\((\frac{2}{3} ) (-13) [(n-1)/n] = (-\frac{26}{3} ) [(n-1)/n]\)

Consequently, the value of the expression:

\([1 - \frac{1}{3} ] [1 - 14] [1 - 1/n] is (-\frac{26}{3} ) [(n-1)/n].\)

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Answer:

9 times 8x9=72

Step-by-step explanation:

hope this helps

if you have anymore questions ask me

Answer:  9 laps

Step-by-step explanation:

1. Divide: 72/8 = ?

2. Solve: 72/8=9

Answer:

It is A on edge 2020

Step-by-step explanation:

The equation of the number of students needed to make $1,500 in profit will be 1,500 = 5n – 300. Then the correct option is A.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Mustafa's soccer team is planning a school dance as a fundraiser.

The DJ charges $200 and decorations cost $100.

The team decides to charge each student $5.00 to attend the dance.

If n represents the number of students attending the dance.

The total amount of expenses will be

Total Expense = $200 + $100

Total Expense = $300

The total amount of charges will be

Total Charge = 5n

Then the amount of the profit will be

Profit = Total charge – Total expense

1,500 = 5n – 300

Then the equation can be used to find the number of students needed to make $1,500 in profit will be 1,500 = 5n – 300.

Then the correct option is A.

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The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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Answer:

-1

Step-by-step explanation:

I assume it's the moon?

Answer:

garbage and rocks and all sorts of stuff

Step-by-step explanation: