Area of the plane figure

The value of  x of chord = 5

By definition of circle,

The chord of a circle is defined as the line segment connecting any two locations on the circle's perimeter; nevertheless, the diameter is the longest chord of a circle that goes through the centre of the circle.

The chord is one of the several line segments that may be made in a circle, and its endpoints are on the circumference.

⇒ 6 (6 + x) = 7 (7 + 11)

Solve for x;

⇒ 36 + 6x = 7 × 18

⇒ 36 + 6x = 126

⇒ 6x = 126 - 36

⇒ 6x = 90

⇒ x = 15

Thus, The value of x = 5

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Answer:

Options (1), (3) and (7)

Step-by-step explanation:

Characteristics of the given graph are as followed.

1). For every input value (x-value) there is a different output values (y-values).

   So the points on the graph represent a function.

2). Coordinates of all the points are distinct and separate (not in fractions or decimals).

    Function given is a discrete function.

3). For every increase in the x-values of the points there is a decrease in y-values.

  Therefore, given function is a decreasing function.

Therefore, Options (1), (3) and (7) are the correct options.

Answer:

nonlinear

Step-by-step explanation:

Hey There!

A linear function would have a straight line when graphed meaning that it would have a constant slope

This is a nonlinear function because y is not moving at a constant rate with x

16-8=8

8-2=6

It went down 8 then it went down 6

therefore it is a nonlinear function

Answer:

Knowns:

initial velocity (v₀) = 0

final velocity (v₁) = 100 km/h

acceleration (a) = 9.00 m/s²

Unknowns: how long the acceleration took (Δt) = ?

Step-by-step explanation:

Use one of the kinematics equations to find what you're looking for.

This equation with a little algebra should help

v₁ = v₀ + aΔt

The triangles are similar by SAS (Side-Angle-Side) similarity.

option B is the correct answer.

Similar triangles have the same corresponding angle measures and proportional side lengths.

The triangle similarity criteria are:

From the given diagram, we can see that the bases of the two triangles are not equal to each other but they have equal corresponding angles.

Thus, going by the criteria for similarity of triangles, we can conclude that the two triangles are similar by SAS since the lengths of each side of the triangle are of equal proportion.

9/15 = 3/5

So the answer will be;

Side - Angle - Side ( SAS)

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Answer:

$9600 saving / year

Step-by-step explanation:

1/5 of $21000 = 21000 / 5 = $4200 / month on rent

3/7 of $21000 = (21000 / 7) x 3 = $9000 / month on food (shocking right :) food is expensive)

1/3 of $21000 = 21000 / 3 = $7000 on other expenses / month

total savings/month = salary/month - rent/month - food/month - other expenses/month

total savings/month = 21000 - 4200 - 9000 - 7000

total savings/month = $800

BUT the question asks for savings per year. therefore, we must multiply the savings per month by total months per year (12)

800 x 12 = $9600

the person's total savings per year, with a salary of $21000 per month, is equal to $9600 per year

The distance between the skew lines P(t) = (1, 5, -4) + t(-1, 3, 1) and Q(t) = (4, -3, 2) + t(-2, 1, 2) is approximately 1.784 units.

To find the distance between two skew lines P(t) and Q(t), we can use the formula of the shortest distance between two skew lines. The formula involves finding a vector that is perpendicular to both lines. In this case, we can find this vector by taking the cross product of the slope vectors of P and Q.

The slope vector of line P is (-1, 3, 1) and the slope vector of line Q is (-2, 1, 2). To find a vector perpendicular to both of these vectors, we take their cross product:

n = (-1, 3, 1) × (-2, 1, 2)

Using the determinant expansion method to calculate the cross product, we get:

n = ((3 * 2) - (1 * 1), (-1 * 2) - (1 * (-2)), (-1 * 1) - (3 * (-2)))

= (4, 0, 5)

Now that we have the direction vector of the line that is perpendicular to both P and Q, we can find a point on this line. Let's choose a point on line P, for example, the point (1, 5, -4).

Now we can use the point-to-line distance formula to find the distance between the two skew lines:

distance = |(1, 5, -4) - (4, -3, 2)| / |(4, 0, 5)|

= |(-3, 8, -6)| / √(4² + 0² + 5²)

= √(9 + 64 + 36) / √41

= √109 / √41

= √(109/41)

≈ 1.784

Therefore, the distance between the skew lines P(t) = (1, 5, -4) + t(-1, 3, 1) and Q(t) = (4, -3, 2) + t(-2, 1, 2) is approximately 1.784 units.

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The purchase price of Wynona’s boots is 85.5% of the original price.

It is given that

The marked price of boots = $85.79

The percentage is a relative value indicating the hundredth parts of any quantity.

Price after a discount of 10% = \(85.79 - 85.79*10/100 = 77.211\)

Price after another discount of 5% = \(77.211-77.211*5/100 = 73.35\)

\(\frac{PurchasePrice}{OriginalPrice}*100 =\frac{73.35}{85.79}*100 = 85.5\)

Therefore, The purchase price of Wynona’s boots is 85.5% of the original price.

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Answer:

6×2 = 12

Step-by-step explanation:

for each of the 6 possible outcomes of the die are 2 possible outcomes of the coin.

so, 6×2 = 12 different possible outcomes.

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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As per the concept of numbers, the way of explaining the greater than, less than, and equal to are defined below.

The term number in math is referred to an arithmetic value used for representing the quantity and used in making calculations.

Here we have to know that the greater than sign (>) denotes that the number after the more than sign is smaller than the number before the symbol whereas less than sign (<) denotes that the number after the sign is bigger than the number before the sign.

Similarly, to this definition, the term equal defines the number as being equal to each other or it can be used to assign the value to the variable that has been placed on the left-hand side.

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The expression 1.3 cubed over 1.2 raised to the fourth power all raised to the power of negative six is equivalent to the expression 0.707.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Create an equivalent expression for 1.3 cubed over 1.2 raised to the fourth power all raised to the power of negative six. Then the expression is written in mathematical form. Then we have

\(\rm \rightarrow \left [ \dfrac{(1.3)^3}{(1.2)^4} \right ]^{-6}\)

Simplify the expression, then we have

\(\rm \rightarrow \left [ \dfrac{(1.2)^4}{(1.3)^3} \right ]^{6}\\\\\\\rm \rightarrow \left [ \dfrac{2.0736}{2.197} \right ]^{6}\)

Further, simplify the expression, then the value of the expression will be

⇒ (0.9438)⁶

⇒ 0.707

The expression is equivalent to the expression 0.707.

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Step-by-step explanation:

f(2) = -3 means when x is 2, the f(x) is equal to -3. To solve b, we plugin in 2 into x, and plugin -3 for f(x), we get

f(x) = 3x + b

- 3 = 3(2) + b

- 3 = 6 + b

  b = -9

Answer:

False.

Step-by-step explanation:

The RMS (Root Mean Square) value of a sine wave represents the equivalent DC voltage that would produce the same amount of power in a resistive load. However, the heat produced in a resistor is directly proportional to the square of the current passing through it (according to Joule's Law). In the case of an AC waveform, the current continuously changes direction, resulting in a time-varying power dissipation. Therefore, comparing the RMS value of an AC waveform to a DC voltage is not directly applicable in terms of heat produced in a resistor.

The IQ score that is higher than 90% of the population is 112.8.

We know that the IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 10.

Let X be the random variable representing the IQ scores. We want to find the value x such that 90% of the observations lie above x.

Using the standard normal distribution table or calculator, we can find the z-score corresponding to the 90th percentile as 1.28.

The z-score formula is z = (x - μ) / σ, where μ is the mean, σ is the standard deviation and x is the value we want to find.

Plugging in the values, we get 1.28 = (x - 100) / 10. Solving for x, we get x = 100 + 12.8 = 112.8.

Therefore, the IQ score that is higher than 90% of the population is 112.8.

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Answer:

h=12.5

Step-by-step explanation:

It’s a right triangle, so you can use the Pythagorean Theorem.  

9.2²+8.5²=h²

84.64+72.25=h²

156.89=h²

√156.89=h

h=12.5255

h=12.5

The length of AD is 2 inches.

Let x be the length of AD. By the Pythagorean theorem in triangle ABD, we have:

\(BD^2 + x^2 = AB^2\)

Substituting AB = BC, we get:

\(BD^2 + x^2 = BC^2\)

Using the fact that triangle ABC is isosceles, we can use the Pythagorean theorem in triangle ABC to find BC:

\(BC^2 = AC^2 - AB^2 = 8^2 - AB^2\)

Substituting this expression for\(BC^2\) in the previous equation, we get:

\(BD^2 + x^2 = 8^2 - AB^2\)

Since BD is the perpendicular bisector of AC, we have AD = DC = (AC/2) = 4 inches. Therefore, we can write:

AB = AD + DB = 4 + DB

Substituting this expression for AB in the previous equation, we get:

\(BD^2 + x^2 = 8^2 - (4 + DB)^2\)

Simplifying this equation, we get:

\(BD^2 + x^2 = 16 - 8DB - DB^2 + x^2\)

Solving for DB, we get:

\(DB = (16 - BD^2 - x^2)/(8 + DB)\)

Now, we can use the fact that BD is the perpendicular bisector of AC to write:

\(BD^2 = AD \times DC = 4x\)

Substituting this expression for\(BD^2\) in the previous equation, we get:

\(4x = (16 - 4x - x^2)/(8 + DB)\)

Simplifying this equation, we get:

\(32x + 4x^2 = 16 - 4x - x^2\)

Solving for x, we get:

x = 2 inches

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Answer:

x = 28

Step-by-step explanation:

4 + 2 ( x - 8) = 44

4 + 2x - 16 = 44

2x - 12 = 44

2x - 12 + 12 = 44 + 12

2x = 56

x = 28

Order matters is permutation

Order doesn't matters is combination

So

The correct combinations are

Answer:

A 1/6

Step-by-step explanation:

i got this because if you add all the marbles it is 12 so the real percentage would be 3/12 but they divided it by 2 to get 1/6

Answer:

Oblique rectangular prism

The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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Owning a boat for 3 years will cost her $177,120

Cost is the sum of money needed to produce, market, and sell goods and services or to purchase assets. A cost is added to costs when anything is sold or consumed.

Given Data

The cost of gallon- $3.89

To calculate miles per gallon of gas, we take the 40(12) = $480 miles the boat travels.

Dividing it by the amount of gallons in a full tank of gas, 3.89 gallons.

=\(\frac{480}{3.89}\)

= $123.3, or $123 when rounded to the tenths place

She plans to own boat for 3 years, which will cost her

=$480(123)(3)

-$1770,120

Owning a boat for 3 years will cost her $177,120

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The transformation from function f(x) to g(x) is a vertical shift of 4 units up.

The transformation from f(x) to g(x) is a vertical shift of 4 units up. This can be seen by comparing

f(x) = |x| to g(x) = |x| + 4

. In other words, the graph of g(x) is 4 units higher than that of f(x), and the x-intercepts of the two functions are 4 units apart.

The transformation from f(x) to g(x) is a vertical shift of 4 units up. This can be seen by comparing the equations of the two functions. The parent function, f(x), is defined as f(x) = |x|, and the transformed function, g(x), is defined as g(x) = |x| + 4. By adding 4 to the parent function, the graph of the transformed function is shifted up 4 units, which is the same as saying it is shifted 4 units in the positive y-direction. This can be seen in the graphs of the two functions, where the x-intercepts of the two functions are 4 units apart. The transformation from f(x) to g(x) is a vertical shift of 4 units up, and it is the same as the transformation of

y = f(x) to y = f(x) + 4.

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In this problem, we have a continuous exponential growth model

so

the equation is of the form

where

a is the initial value ------> a=2,100

y is the number of bacteria

x ----> number of hours

so

For x=2.5 hours, y=2,249 bacteria

substitute

solve for k

apply ln both sides

k=0.0274

convert to percentage

Answer:

sina

Step-by-step explanation:

Using the cofunction identity

cos(90 - x) = sinx , then

cos(120 - (30 + a) )

= cos(120 - 30 - a)

= cos(90 - a)

= sina

An expression is defined as a set of numbers, variables, and mathematical operations. Using a cosine function identity cos(120° − (30° + a)) can be written as sin a.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given cosine expression can be rewritten as,

cos(120° − (30° + a))

Opening the bracket, to simplify the angle,

= cos(120° − 30° − a)

= cos(90° − a)

Since the cosine and sine angles are complementary to each other, therefore, cos(90° − x) = sin(x), thus, we can write the expression as,

= sin a

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The approximate value obtained using the number of points and taking their standard deviation is known as uncertainty.

Uncertainty is the approximate value determined by counting the points and subtracting their standard deviations. The range of potential values within which the true value of the measurement sits is referred to as uncertainty in this context. Other names with similar meanings now have different usages.

The value will be close to the value but not exactly the value. The upper bound of the chance of obtaining the next value of the point near 68% is defined by standard deviation.

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Step-by-step explanation:

please mark me as brainlest

Answer:

  10 mm

Step-by-step explanation:

You can find the missing dimension using the triangle area formula with the dimensions you know.

  A = 1/2bh

  40 mm² = 1/2(b)(8 mm)

  b = 40 mm²/(4 mm) = 10 mm . . . . . . . divide by the coefficient of b

The triangle's base is b = 10 mm.

The U.S. Census Bureau is responsible for collecting and analyzing a vast amount of data related to families in the United States.

This data includes information about the number of households, family size, marital status, and living arrangements. The Bureau also collects data on the number of children who live with their parents or other relatives, as well as the number of children who do not live with their parents.

In 2010, the U.S. Census Bureau reported that there were approximately 7.6 million children who did not live with their parents. Of these children, 54% were living with their grandparents or other relatives, while the remaining 46% were living with non-relatives.

The Bureau collects this data in order to better understand the needs of families and to develop policies that can help support them.

The Census Bureau also collects data on a wide range of other statistics related to families, including income, education, employment, and health. This information is used to identify trends and patterns that can help inform decisions about social programs and policies that affect families.

Overall, the U.S. Census Bureau plays a vital role in providing policymakers and researchers with the data they need to better understand and address the needs of families in the United States.

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a) True, b) False, c) False, d) True, e) False, f) False, g) True

a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.

b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.

c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.

d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.

e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.

f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.

g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.

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