Ryan has a semicircular garden as shown.
What is the distance around his garden in feet? Use 3.14 for 7.
Enter the correct answer in the box.
ft

Fig. 2.6 alone does not provide sufficient information to calculate the percent elongation of materials. Percent elongation is a measure of the increase in length of a material after it has been subjected to a tensile load, and is calculated by dividing the increase in length by the original length and multiplying by 100.

Fig. 2.6 shows stress-strain curves for different materials, which provide information about the relationship between stress and strain for those materials. While the curve shape can provide some insight into the behavior of the material under load, it does not provide information about the original length or the change in length of the material, which are necessary to calculate percent elongation.

In order to calculate percent elongation, additional information about the material's original length and the change in length after a tensile load is required. This information can be obtained through laboratory testing or from material specifications provided by the manufacturer.

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After considering the given data we conclude that the probability that both bulbs selected are rated 75 W, given that at least one of them is rated 75 W, is 1/7 or approximately 0.143.

To evaluate the probability that both bulbs selected from a box containing four 40 W bulbs, five 60 W bulbs, and six 75 W bulbs are rated 75 W, given that at least one of them is rated 75 W, we can apply conditional probability.
Let A be the event that the first bulb selected is rated 75 W, and B be the event that the second bulb selected is rated 75 W. We want to find P(B|A'), where A' is the complement of A, i.e., the event that the first bulb selected is not rated 75 W.
We can apply the formula for conditional probability:
\(P(B|A') = P(A' \cap B) / P(A')\)
We can evaluate the probabilities as follows:
\(P(A') = (4+5) / (4+5+6) = 9/15\)
(since there are 4+5 bulbs that are not rated 75 W out of a total of 4+5+6 bulbs)
\(P(A \cap B) = (6/15) * (5/14) = 3/35\)
(since there are 6 bulbs that are rated 75 W out of a total of 15 bulbs on the first draw, and 5 bulbs that are rated 75 W out of a total of 14 bulbs on the second draw, assuming that the first bulb selected is not rated 75 W)
\(P(B|A') = P(A' \cap B) / P(A') = (3/35) / (9/15) = 1/7\)
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The surface areas of the prisms are listed below:

Case 1: 94 in²

Case 2: 72 cm²

Case 3: 40.5 m²

Case 4: 39.1 mm²

Case 5: 130 ft²

Case 6: 136 m²

In this problem we find six cases of prisms, whose surface areas have to be found. Surface area is the sum of the areas of all faces in the prism. Face have either a rectangular or a triangular form, whose area formulas are:

Rectangle

A = b · h

Triangle

A = 0.5 · b ·h

Where:

Now we proceed to determine the surface areas:

Case 1

A = 2 · (4 in) · (5 in) + 2 · (3 in) · (4 in) + 2 · (5 in) · (3 in)

A = 40 in² + 24 in² + 30 in²

A = 94 in²

Case 2

A = 2 · 0.5 · (3 cm) · (4 cm) + (5 cm) · (4 cm) + (5 cm) · (3 cm) + (5 cm)²

A = 12 cm² + 20 cm² + 15 cm² + 25 cm²

A = 72 cm²

Case 3

A = 2 · (3 m) · (7 m) + 2 · (6 m) · (7 m) + 2 · (6 m) · (3 m)

A = 10.5 m² + 21 m² + 9 m²

A = 40.5 m²

Case 4

A = 2 · 0.5 · (4 mm)² + 2 · (4 mm) · (3 mm) + (5.7 mm) · (3 mm)

A = 16 mm² + 6 mm² + 17.1 mm²

A = 39.1 mm²

Case 5

A = 2 · (10 ft) · (5 ft) + 2 · (5 ft) · (1 ft) + 2 · (10 ft) · (1 ft)

A = 100 ft² + 10 ft² + 20 ft²

A = 130 ft²

Case 6

A = 2 · 0.5 · (6 m) · (4 m) + 2 · (7 m) · (5 m) + (7 m) · (6 m)

A = 24 m² + 70 m² + 42 m²

A = 136 m²

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We can eliminate 0.6, since that would result in a smaller shape, not a larger.

If the scale factor was 2, then each coordinate for every point on the original shape would be multiplied by 2.

For example, (3,3) would become (6,6), but it didn't.  So that rules out the scale factor of 2.

If the scale factor was 1.5, then each coordinate for every point on the original shape would be multiplied by 1.5.

For example, (3,3) would become (4.5,4,5), and that checks out.  

Then (4,4) would become (6,6), and that also checks.

And (5,3) would become (7.5, 4.5), and that looks right.

Finally, (2,5) would become (3, 7.5) and that also look good.

I'd say the scale factor is 1.5.

Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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Answer:

X=-9

Step-by-step explanation:

Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

Answer:

14

Step-by-step explanation:

If he has a total of 24

and he just purchased 10

24-10= 14

The number that represents Six times a number is at least four less than eight times the number is the expression 6x ≥ 8x - 4.

What is system of equations?

A system of equations, also referred to as a set of simultaneous equations or an equation system, is a finite set of equations for which we searched for the common solutions. Similar to single equations, a system of equations can also be categorised. In everyday life, systems of equations are used to model situations where the unknown values can be represented by variables.

A system of equations is made up of two or more equations with the same variables. A solution to an equation system is the point at which the lines intersect.

According to given question, x represents the number

So, The number would be 6x ≥ 8x - 4

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Answer:

B. 2

Step-by-step explanation:

(4, 3) (7, 9)     M = Slope

M = \(\frac{y^2-y^1}{x^2-x^1}\)      Slope formula

\(M=\frac{9-3}{7-4}\)       Using the slope formula, plot both x and y intercepts

\(M=\frac{6}{3}\)           Slope needs to be simplified into a whole number

\(M=2\)          

The general equation of a circle is

Here, (h,k) is the center of the circle and r is the radius of the circle.

change the given equation into the general form as follows:

So, the center is (0,0) and the radius is r = 5.

Answer:

x + 5y = 30

x + 5(0) = 30

x1 = 30    y1 = 0

x + 5y = 30

1(0) + 5y = 30

y2 = 6    x2 = 0

(x1,y1) and (x2,y2)

(30,0) and (0,6)

Step-by-step explanation:

Answer:

$48.

Step-by-step explanation:

Annual means yearly.

The question is asking how much will Emma earn after 10% interest for 2 years.

To solve:

Find 120% of $40. This represents 100% (40) and 20% interest for the 2 years.

Round to the nearest cent if it's necessary.

Let's solve:

Let's find 20% of $40 first.

Divide 40 by 5:

$8 is 20% of 40.

Add 8 to 40:

8 + 40

= 48.

48 is your answer.

*48 represents 10% interest for 2 years.

The domain of the function can be written in the form of interval as  (-∞, ∞).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The function is given as y = aˣ.

Its domain can be found as follows,

For x = 0, y is a⁰ = 1.

For x = n, where n > 0, y is given as,

y = aⁿ, which is greater than zero.

For x = n, where n < 0, y is given as,

y = a⁻ⁿ

⇒ y = 1/aⁿ

Thus, the given function is valid for all real numbers.

Which implies its domain is (-∞, ∞).

Hence, the domain of the given function is obtained as (-∞, ∞).

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Answer:

Hey There!

Let's solve...

\( \frac{ {x}^{2} - 2 }{x(x - 1) ^{2} } + \frac{2 - x}{ x{( x - 1)}^{2} } \\ \\ = \frac{ {x}^{2} - 2 + 2 - x }{x {(x - 1)}^{2} } \\ \\ = \frac{ {{x}^{ \cancel{2}}} - \cancel{x} }{ \cancel{x} {(x - 1)}^ {{ \cancel2}} } \\ \\ = \frac{1}{x - 1} \)

In quadrant IV, \(\cos(A)\) is positive. So

\(\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258\)

Then by the definition of tangent,

\(\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}\)

Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

No, the combination lock is not appropriate. This is so as the repetition is  allowed, neither permutation nor the combination rule holds true or valid.

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1)  y = Cetx is the solution of the given differential equation, 2) y = \(e^-2x\) is the solution, 3)y = 2r³ is not the solution, 4)y = 4x² - 3/5 is not the solution, 5) y = Cx² - 3x is the solution,  6)y = giữ + 2x + xy + y is the solution

1. y = Cetx y

= 4y

Differential Equation

y = \(Ce^(rx)\) y'

=r\(Ce^(rx)\)4y

=4\(Ce^(rx)\) (LHS = RHS)

Hence, y = Cetx is the solution of the given differential equation.

2. y = \(e^-2x\) y' + 2y

= 0

Differential Equation

y = \(e^-2x\)y'

= -2\(e^-2x\)2y

=\(2e^(-2x)\)(LHS = RHS)

Thus, y = \(e^-2x\) is the solution of the given differential equation.

3. y = 2r³ y²-²y

= 0

Differential Equation

y = 2r³ y'

=6r² y²

=4r⁶ (LHS ≠ RHS)

Therefore, y = 2r³ is not the solution of the given differential equation.

4. y = 4x² --3/5

=y

=0

Differential Equation

y = 4x² y'

= 8x3/5

y=0 (LHS ≠ RHS)

So, y = 4x² - 3/5 is not the solution of the given differential equation.

5. y = Cx² - 3x xy-3x - 2y

= 0

Differential Equation

y = Cx² - 3x y'

= 2Cx - 3xy - 3x

= 2Cx - 3x( Cx² - 3x)2y

= 2Cx³ - 6x² - 6Cx + 9x (LHS = RHS)

Thus, y = Cx² - 3x is the solution of the given differential equation.

6. y = giữ + 2x + xy + y

= x(3x + 4)CL₃ + C x

Differential Equation

y = giữ + 2x + xy + y y'

= y' + (x + 1)y' + 2y

= 3x + 4(2y = 2g + 4x + 2xy)

LHS = RHS,
so y = giữ + 2x + xy + y is the solution to the given differential equation.

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Answer:

Direct

Step-by-step explanation:

\(\dfrac{x}{y} \ is \ constant.\)

\(\dfrac{20}{120}=\dfrac{1}{6}\\\\\\\dfrac{25}{150}=\dfrac{1}{6}\\\\\\\dfrac{40}{240}=\dfrac{1}{6}\)

So, this is direct variation

Answer:

F, T, T, F

Step-by-step explanation:

I used desmos (graphing calculator) to put in the points and compared the 2. Hope this helps!

Answer:

x = 1

Step-by-step explanation:

Note that triangle ABC is congruent to triangle DEF by SAS congruency

Thus, using CPCTC, BC - FE

or

: 13x-12 = 7x-6

: 6x = 6

: x = 1

:]

An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.

Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.

In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.

To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.

In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.

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Answer:

175=57r

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf \frac{x+3}{x-3}}\)

Step-by-step explanation:

\(\displaystyle = \frac{x+7}{x^2+4x-21} \div \frac{x+5}{x^2+8x+15} \\\\Apply \ mid-term \ break\\\\= \frac{x+7}{x^2 +7x-3x-21} \div \frac{x+5}{x^2 +3x+5x+15} \\\\= \frac{x+7}{x(x+7)-3(x+7)} \div \frac{x+5}{x(x+3)+5(x+3)} \\\\Taking \ (x+3) \ and \ (x+7) \ common\\\\= \frac{x+7}{(x-3)(x+7)} \div \frac{x+5}{(x+3)(x+5)} \\\\= \frac{1}{x-3} \div \frac{1}{x+3} \\\\= \frac{1}{x-3} * (x+3)\\\\= \frac{x+3}{x-3} \\\\\rule[225]{225}{2}\)

Hope this helped!

5x+6y is the answer i jope this helps you