Match each circular flower bed on the left to its circumference and its area on the right. Some answer options on the right will not be used.

Answer:

n^3( 4n+1)

Step-by-step explanation:

4n^4 + n^3

2*2*n^3*n + 1*n^3

Factor out the common terms

n^3( 4n+1)

Answer:

The answer is below

Step-by-step explanation:

Let x represent the length of the rectangular pen and y represent the width of the rectangular pen. Since the total area of the pen is 169 ft², hence:

Area = length * width

169 = xy

y = 169/x

Also the perimeter of the rectangular pen is:

Perimeter (P) = 2(length + width)

P = 2(x + y)

P = 2x + 2y

P = 2x + 2(169/x)

P = 2x + 338/x

The least amount of fencing is at dP/dx = 0, hence:

dP/dx = 2 - 338/x² = 0

338/x² = 2

2x² = 338

x² = 169

x = 13 feet

y = 169 / x = 169/13 = 13 feet

The least amount of fencing = P = 2(x + y) =  2(13 + 13) = 52 feet

Answer:

∠ G = 85°

Step-by-step explanation:

∠ G is an inscribed angle whose measure is half the measure of its intercepted arc.

the sum of the arcs in a circle = 360° , then

arc DF = 360° - 120° - 70° = 360° - 190° = 170° , then

∠ G = \(\frac{1}{2}\) DF = \(\frac{1}{2}\) × 170° = 85°

\( \frac{24}{13} = \frac{x}{39} \)

We move 39 to multiply 24/13.

\( \frac{24}{13} (39) = x \\ 24(3) = x \\ 72 = x\)

Substitute x = 72 in the equation.

\( \frac{24}{13} = \frac{72}{39} \\ \frac{24}{13} = \frac{24}{13} \)

The equation is true for x = 72.

\( \large \boxed {x = 72}\)

Answer:

3 loaves of bread

Step-by-step explanation:

2/3*3=6/3= 2 cups of oil

Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

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Answer:

t>=45

Step-by-step explanation:

\(g(x)=x^3-x\\g(-2)=(-2)^3-(-2)\\g(-2)=-8+2\\g(-2)=-6\)

Therefore, g(-2) = -6

Basically substitute x = -2 in the equation.

The particle crosses the origin at a time of 2.346 seconds.

To find the time at which the particle crosses the origin, we need to determine the value of t when x(t) is equal to zero, since the particle will be at the origin when its position is zero.

Using the given position function x(t) = 5.42 m - 2.31 m/s t, we can set x(t) equal to zero and solve for t:

x(t) = 0

5.42 m - 2.31 m/s t = 0

Subtracting 5.42 m from both sides, we get:

-2.31 m/s t = -5.42 m

Dividing both sides by -2.31 m/s, we get:

t = 5.42 m / 2.31 m/s

t = 2.346 s

Therefore, the particle crosses the origin at a time of 2.346 seconds.

In summary, we find the time at which the particle crosses the origin by setting the position function equal to zero and solving for the corresponding value of t. This method works for any one-dimensional motion along a straight line.

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Answer: -4

Step-by-step explanation:

Divide by -4 each time to get the next number in the sequence.

Answer:

2.25$

Step-by-step explanation:

The cost of each cupcake the food court mall sells is $2.28.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Desiree works at a dessert counter in the food court of a mall. The dessert counter sells cupcakes and cookies.

Each cookie costs $1.25 and assuming the cost of the cupcake is x.

∴ (1.25×12) + (8x) = 33.30.

15 + 8x = 33.30.

8x = 18.3

x = 2.28

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The Recurrence Relation T(n) for T(n) = 2n.T(n-1) + 12 2 is:

T(n) = 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0) = 2^n * n! * T(0).

To solve the given recurrence relation T(n) = 2n * T(n-1) + 12, we can use iteration or expansion methods. Let's use the expansion method to find an explicit formula for T(n).

Expanding the recurrence relation, we have:

T(n) = 2n * (2(n-1) * T(n-2) + 12) + 12

= 2n * 2(n-1) * T(n-2) + 2n * 12 + 12

= 2n * 2(n-1) * (2(n-2) * T(n-3) + 12) + 2n * 12 + 12

By continuing this process, we can observe a pattern. Each term in the expansion will be of the form 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0), where T(0) is the initial term.

The number of factors of 2 will depend on the value of n. We can see that for each term, the number of factors of 2 is n! (n factorial). Therefore, the explicit formula for T(n) is:

T(n) = 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0) = 2^n * n! * T(0).

In this case, T(0) represents the initial term of the sequence. Without knowing its value, we cannot provide a specific numerical solution. However, the above formula provides a general expression for T(n) in terms of n and T(0), satisfying the given recurrence relation.

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The numerical value of 1.2 × 1.222 is approximately 1.4664.

To calculate the numerical value of 1.2 × 1.222, we multiply the two numbers together. Let's break it down step by step:

Start with the multiplication operation: 1.2 × 1.222.

Multiply the decimal numbers without considering the decimal point. We have 12 × 1222.

Perform the multiplication of the whole numbers: 12 × 1222 = 14,664.

Count the total number of decimal places in both factors. In this case, we have one decimal place in 1.2 and three decimal places in 1.222.

Add the total number of decimal places from both factors. 1 + 3 = 4.

Place the decimal point in the product by counting four places from the right of the final result obtained in step 3.

The final result is 14,664, with the decimal point placed four places from the right, giving us 1.4664. Therefore, the numerical value of 1.2 × 1.222 is approximately 1.4664.

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The number of children and men at the party will be 30 and 15, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

There are 90 people at the party. Half of the people at the party are women. The number of women at the party is 3 times the number of men at the party. The rest of the people at the party are children.

Let the number of children be 'x', the number of men be 'y', and the number of women be 'z'. Then we have

z = 90 / 2

z = 45

Then the other equation is given as,

z = 3y

45 = 3y

y = 15

Then the number of children is calculated as,

x + y + z = 90

x + 15 + 45 = 90

x = 30

The number of children and men at the party will be 30 and 15, respectively.

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9514 1404 393

Explanation:

In general, a system of equations has a solution that satisfies all of the equations. That is, the solution set is the intersection (and) of the solution sets of the individual equations in the system. Equations involving the absolute value function are no different.

That being said, you need to consider the meaning of an equation involving the absolute value function.

The function itself is piecewise defined:

  \(\displaystyle |x|=\left\{ {x, x\ge0} \atop {-x, x<0}} \right.\)

So, any equation involving the absolute value function automatically resolves to two equations, each with its own condition on the function value.

__

Example 1:

  |x+1| > 3

is equivalent to the two disjoint conditional equations ...

  (x +1) > 3  and  (x +1) ≥ 0 . . . . OR

  -(x +1) > 3  and  (x +1) < 0

the first of these has the solution x > 2; the second of these has the solution x < -4. The solution set of this equation is the OR of the two solution sets:

  x < -4  or  x > 2

__

Example 2:

  |x +1| < 3

is equivalent to the two disjoint conditional equations ...

  (x +1) < 3  and  (x +1) ≥ 0 . . . . OR

  -(x +1) < 3  and  (x +1) < 0

The first of these has the solution -1 ≤ x < 2, and the second of these has the solution -4 < x < -1. Again, the solution set of this equation is the OR of the two solution sets. However, we find we can write that union as a single compound inequality:

  -4 < x < 2

__

When an absolute value equation involves more than one absolute value function, then the equation will probably resolve into multiple equations, each defined on its own domain. Sometimes keeping those domains straight can be tedious.

Above, we have considered inequalities. If you have an equation, you need to consider that it will likely resolve to two equations. The solution set will be the OR of the solutions to those two equations.

Example 3:

  |x +1| = 3

is equivalent to the two conditional equations ...

  (x +1) = 3  and  (x +1) ≥ 0 . . . . OR

  -(x +1) = 3  and  (x +1) < 0

The first of these has the solution x = 2; the second has the solution x = -4. The solution set is the OR of these two solutions:

  x = -4  or  x = 2

__

The "and" condition restricts the domain of each of the individual pieces of the equation. The "or" condition applies to the collection of solutions that may exist in each of those restricted domains.

2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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If a random variable "z" follows a standard normal distribution and the probability of "z" being greater than "k" is 0.39, then the value of "k" such that satisfies the equation [p(z > k) = 0.39] will be 0.28

As per the question statement, a random variable "z" follows a standard normal distribution.

We are required to determine the value of "k" such that the equation   [p(z > k) = 0.39] is satisfied.

To solve this question, first we will have to calculate the probability of "z" being greater than "k" and then from the Z-table, we will determine the z-score corresponding the above calculated probability value. This z-score will be our desired answer, i.e.,

Given, P(Z > k)  = 0.39

Or, P(Z < k) = (1 - 0.39)

Or, P(Z < k) = 0.61

Now, from the Z table, we get the z-score corresponding to probability value of 0.61 is 0.28

Hence, (k = 0.28)

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Answer:

the square root of 2

Step-by-step explanation:

any number itself equals 1

Answer:

THERE IS NO DARN SHAPE MAN

Step-by-step explanation:

Answer:

-17.7

Step-by-step explanation:

-9.1-14.6-(-6)

-9.1-14.6+6

-23.7+6

-17.7

A piecewise function is a function that behaves differently in different intervals of its domain.

The piecewise function is:

Here the given information for the function is:

Then if we define x as the age of the person, the function f(x) that tells the cost of the ticket will be:

So as you can see, depending on the value of x and in which interval it belongs, the function behaves differently.

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Answer:

79

Step-by-step explanation:

80 divided by 8+72-3

10+72-3

82-3

79

Hope this helps!

Option D is correct, the area of given parallelogram is 30 square inches

Parallelogram is a simple quadrilateral with two pairs of parallel sides.

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Area of parallelogram =bh

=10×3

=30 square inches

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The computation of δy and dy for the given values of x and dx = δx. y = x2 − 5x, x = 4, δx = 0.5 is δy = -0.5 and dy = δy/dx = -1/6

Given, y = x2 - 5x, x = 4, δx = 0.5

We have to compute δy and dy for the given values of x and dx = δx.δy is given by: δy = dy/dx * δx

To find dy/dx, we need to differentiate y with respect to x. dy/dx = d/dx (x^2 - 5x) = 2x - 5

Thus, dy/dx = 2x - 5

Now, let's substitute x = 4 and δx = 0.5 in the above equation. dy/dx = 2(4) - 5 = 3

So, δy = (2x - 5) * δx = (2 * 4 - 5) * 0.5= -0.5

Therefore, δy = -0.5 and dy = δy/dx = -0.5/3 = -1/6

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Answer:

can u help me

Step-by-step explanation:

Answer:

first one is: 8

second one is: 2

Step-by-step explanation:

correct on edg 2021!!!

Answer:

164 With the parenthesis

266 without parenthesis

On solving the provided question, we can say that Probability (marble in blue) = 4/14 and Probability (marble in red ) = 10/14

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

total marble = 14

total red = 4

total blue = 10

Probability (marble in blue) = 4/14

Probability (marble in red ) = 10/14

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Answer:

j=12

Step-by-step explanation:

\(-\frac{1}{3}=\frac{j}{4}-\frac{10}{3}\) is what we start with.  first, do the inverse of -10/3. therefore, we add 10/3 to both sides.

\(\frac{9}{3}=\frac{j}{4}\) is what we end up with. then simplify.

\(3=\frac{j}{4}\) is what we have after simplifying. next we do the inverse of dividing by 4, so we multiply by 4.

\(12=j\) is the final answer. or j=12. hope this helps!

83% of pupils passed the test as a group.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)

It is claimed that two ratios are in proportion if they are the same. A/B Equals C/D if the four elements are a, b, c, and d in that order. The terms a and d are referred to as extremes, whereas b and c are referred to as medium terms. The ratio equates the product of extremes to the product of means.

Results in total: 65% of the review was finished.

The desired results were 55% exam pass.

The percentage is as follows:

p = 55/65 x 100%

  = 82.3%.

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