show 3 different ways to measure ¾ cup sugar.

The function f(x - 5/3) is translated 5/3 units right and the function f(x) - 5/3 is translated 5/3 units down.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, A function f(x) is transformed to f(x - 5/3) this results in f(x) is translated 5/3 units to the right along the x-axis.

And, The transformation f(x) - 5/3 is translated 5/3 units down along the y-axis.

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The conditions are: a large enough sample size, probability of success between 0.1 and 0.9, and number of successes and failures both ≥ 10.

The binomial probability must be satisfied to make the probabilities from a binomial probability distribution approximated well by using a normal distribution are:

The sample size, n, must be large enough. A general rule of thumb is that n should be greater than or equal to 20. This ensures that there are enough data points to create a normal distribution.

The probability of success, p, must be between 0.1 and 0.9. If p is too close to 0 or 1, the distribution becomes too skewed and the normal approximation is not accurate.

The number of successes, np, and the number of failures, nq, must both be greater than or equal to 10. This ensures that the normal approximation is accurate enough to be useful.

If these conditions are met, then the probabilities from a binomial probability distribution can be approximated well by using a normal distribution with a mean μ = np, and a standard deviation σ = √(npq). This approximation can be useful in calculating probabilities and making statistical inferences.

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The answer is 486 cm². Thus option c is the right answer.

According to the given question:

The surface area of the cube = 6s²

Surface Area is the area occupied by the six faces of the cube.

where, s ⇒  length of each edge.

Given,

length of each edge = 9cm.

Substituting values in the given formula,

6 × 9²

= 6 × 81

= 486 cm².

Therefore the surface area of the cube is 486cm².

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The evil dragon can choose four maidens to eat in 182 different ways that do not include both Dorothy and Virginia.

There are 120 different ways that the evil dragon can choose four maidens out of the ten without including both Dorothy and Virginia.

To arrive at this answer, we first need to calculate the total number of ways that the dragon can choose any four maidens out of the ten. This can be done using the formula for combinations, which is:

nCr = n! / (r! * (n-r)!)

In this case, n = 10 (the total number of maidens) and r = 4 (the number of maidens the dragon wants to choose). So the total number of ways the dragon can choose four maidens out of ten is:

10C4 = 10! / (4! * (10-4)!) = 210

Next, we need to subtract the number of ways that include both Dorothy and Virginia. The dragon cannot choose both of these maidens, so we need to calculate the number of ways that it can choose the other two maidens. This can be done using the formula for combinations again, but this time with n = 8 (the number of maidens remaining after excluding Dorothy and Virginia) and r = 2 (the number of maidens the dragon still needs to choose).

8C2 = 8! / (2! * (8-2)!) = 28

Finally, we can subtract the number of ways that include both Dorothy and Virginia from the total number of ways to get the answer:

210 - 28 = 182

So the evil dragon has 182 ways to choose four maidens to eat that do not include both Dorothy and Virginia.



The evil dragon can choose four maidens out of ten in 210 different ways. However, it cannot choose both Dorothy and Virginia, so we need to subtract the number of ways that include them both. The dragon can choose two more maidens out of the remaining eight, which can be done in 28 different ways. By subtracting this from the total number of ways, we get that the dragon has 182 ways to choose four maidens to eat that do not include both Dorothy and Virginia.



In conclusion, the evil dragon can choose four maidens to eat in 182 different ways that do not include both Dorothy and Virginia. This calculation was done using the formula for combinations, which involves finding the total number of ways to choose the maidens and then subtracting the number of ways that include both Dorothy and Virginia.

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The value of y when x is 1 is -2

Linear also interpretes as straight and a graph is a diagram which shows a connection or relation between two or more quantity.

We can also define straight graph which is drawn on a plane connecting the points on x and y coordinates. It is a graph of a linear equation.

To calculate any value of x or y we can use the graph to determine the value of x if y is given and the value of y if x is given

Therefore from the graph;

when x is 1 , the reading of y to the straight line is -2. Therefore the value of y is -2.

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Total length of wire = 8.33 + 6.67 + 5.33 + ...20 terms= 100[2 - 0.8^20] / [1.2]≈ 80.99 feet Since the total length of wire required is less than the available wire, Sonja will have enough wire.

Given, Sonja cuts 100 inches for the first piece, 80 inches for the second piece, and 64 inches for the third piece. We need to find the explicit formula for the nth piece.We can see that Sonja is cutting wire in decreasing order of 20%.So, the explicit formula for the nth piece can be given by an = a1 * r^(n-1)where a1 = 100 and r = 0.8 Thus, the explicit formula for the nth piece can be given byan = 100 * (0.8)^(n-1)Now, we need to find if Sonja has enough wire for the mobile as she only has 40 feet of wire to use for the project and wants to cut 20 pieces total for the mobile using her pattern.We know that 1 inch = 0.0833 feet 100 inches = 100 * 0.0833 feet = 8.33 feet80 inches = 80 * 0.0833 feet = 6.67 feet64 inches = 64 * 0.0833 feet = 5.33 feet Now, we can find the total length of wire Sonja needs to cut 20 pieces. Therefore, she can complete the mobile using the given pattern.

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We have proved that AB = CD in the given trapezoid ABCD using the properties of the trapezoid and the circle.

To prove that AB = CD, we will use several properties of the given trapezoid and the circle. Let's start by analyzing the information provided step by step.

AC is the bisector of angle BAD:

This implies that angles BAC and CAD are congruent, denoting them as α.

M is the midpoint of CD:

This means that MC = MD.

The circumcircle of triangle OMD intersects AC again at point K:

Let's denote the center of the circumcircle as P. Since P lies on the perpendicular bisector of segment OM (as it is the center of the circumcircle), we have PM = PO.

BK ⊥ AC:

This states that BK is perpendicular to AC, meaning that angle BKC is a right angle.

Now, let's proceed with the proof:

ΔABK ≅ ΔCDK (By ASA congruence)

We need to prove that ΔABK and ΔCDK are congruent. By construction, we know that BK = DK (as K lies on the perpendicular bisector of CD). Additionally, we have angle ABK = angle CDK (both are right angles due to BK ⊥ AC). Therefore, we can conclude that side AB is congruent to side CD.

Proving that ΔABC and ΔCDA are congruent (By SAS congruence)

We need to prove that ΔABC and ΔCDA are congruent. By construction, we know that AC is common to both triangles. Also, we have AB = CD (from Step 1). Now, we need to prove that angle BAC = angle CDA.

Since AC is the bisector of angle BAD, we have angle BAC = angle CAD (as denoted by α in Step 1). Similarly, we can infer that angle CDA = angle CAD. Therefore, angle BAC = angle CDA.

Finally, we have ΔABC ≅ ΔCDA, which implies that AB = CD.

Proving that AB || CD

Since ΔABC and ΔCDA are congruent (from Step 2), we can conclude that AB || CD (as corresponding sides of congruent triangles are parallel).

Thus, we have proved that AB = CD in the given trapezoid ABCD using the properties of the trapezoid and the circle.

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Therefore, the volume of the paper cone to the nearest tenth is 418.7 inches cubed.

The volume of the paper cone that Gretchen made to hold a gift for a friend is given by;V= (1/3)πr²hWhere;r = radius of the paper coneh = height of the paper coneπ = 3.14

Given that;Height of the paper cone (h) = 16 inches Radius of the paper cone (r) = 5 inchesWe are to find the volume (V) of the paper cone to the nearest tenth of an inch.

To obtain the volume of the paper cone, we can substitute the values of r and h in the formula above to obtain;

\(V= (1/3)\pir^2hV\)= \((\frac{1}{3} ) \times 3.14\times5^2 \times16V = (\frac{1}{3} ) \times 3.14\times25\times16V = (\frac{1}{3}) \times 1256V=418.7\)

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assume the point (10,20) belongs to the graph of f of x what point belongs to the graph of y equals f (x )minus 5 ​

In this problem we have a transformation with the dollowing rule

(x,y) ------> (x,y-5)

so

(10,20) --------> (10, 20-5)

(10,20) --------> (10, 15)

therefore

The answer is

(10, 15)

Answer:

77

Step-by-step explanation:

Answer:

Step-by-step explanation: i don't know sorry

On the survey of 25 randomly selected students from the entire student Population, estimate that approximately 186 students drive to school at Lincoln High.

(a) The best represents the entire student population, we want to ensure that the sample is as representative as possible. This means that the sample should have similar characteristics and proportions as the entire student population. the survey that would likely best represent the entire student population is the one where 25 students are randomly selected from the school itself (Option 1). This survey provides a random sample from the entire student population and is not limited to a specific group or grade level like the other options.

(b) If there are 1550 students at Lincoln High and we want to estimate the number of students who drive to school based on the survey in part (a), we can use proportional reasoning.

From the selected sample of 25 students, we know that 3 of them drive to school. To estimate the number of students who drive to school out of the entire student population, we can set up a proportion:

3/25 = x/1550.

Solving for x (the estimated number of students who drive to school), we can cross-multiply and solve for x

3 * 1550 = 25 * x.

4650 = 25x.

Dividing both sides by 25:

x = 186.

Therefore, based on the survey of 25 randomly selected students from the entire student population, we estimate that approximately 186 students drive to school at Lincoln High.

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Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

Answer:

54

Step-by-step explanation:

\(\dfrac{(14+42-6)}{10}+7^2\)

Parentheses (14 + 42 - 6) = 50:

⇒ 50/10 + 7²

Exponents 7² = 49:

⇒ 50/10 + 49

Multiplication/division  50/10 = 5:

⇒ 5 + 49

Addition/subtraction:  5 + 49 = 54

⇒ 54

Since the line is linear, the sum of the angles should be 180 degrees

x + 28 + 73 = 180

x = 180 - 28 - 73

x = 79 degrees

Hope this helped :)

Answer:

(2x-3)(2x+1)

Step-by-step explanation:

4x^2 - 4x - 3

we need two numbers that give 12 when multiplied and 4 when subtracted

the numbers are 6 and 2 because 6*2=12 and 6-4=4.

4x^2 - (6-2)x -3

4x^2 -6x +2x -3

take common

2x(2x -3)+1(2x-3)

take (2x-3) as common

(2x-3)(2x*1 + 1*1)

(2x-3)(2x+1)

Answer:

Step-by-step explanation:

it’s ca

The magnitude of the average velocity vector is approximately 3.651 m/s.

To find the magnitude of the average velocity vector, we need to calculate the displacement and divide it by the time taken.

Representation:

Initial position: D1 = (50 m North, 10 m East)

Final position: D2 = (5 m North, 35 m East)

Time taken: t = 15 seconds

Equations:

Displacement vector (ΔD) = D2 - D1

Average velocity vector (\(V_{avg}\)) = ΔD / t

Algebra work:

ΔD = D2 - D1

   = (5 m North, 35 m East) - (50 m North, 10 m East)

   = (-45 m North, 25 m East)

|ΔD| = √((-45)^2 + 25^2)  [Magnitude of the displacement vector]

\(V_{avg}\) = ΔD / t

       = (-45 m North, 25 m East) / 15 s

       = (-3 m/s North, 5/3 m/s East)

|\(V_{avg}\)| = √((-3)^2 + (5/3)^2)  [Magnitude of the average velocity vector]

Symbolic answer:

The magnitude of the average velocity vector is approximately 3.651 m/s.

Units check:

The units for displacement are in meters (m) and time in seconds (s). The average velocity is therefore in meters per second (m/s), which confirms the units are consistent with the calculation.

Therefore, the magnitude of the average velocity vector is approximately 3.651 m/s.

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Answer:

=================================

The box is the right rectangular prism.

Its volume is the product of its three dimensions:

We need to find each dimension and multiply them to get the desired function.

The height is same as size of the cut, so it is x units.

The length was 14 units but it is now cut from bot ends so it is now:

The width was 6 units but it is too cut from the both ends by x units:

We have all three dimensions, find the volume:

V = (14 - 2x) (6 - 2x) x cubic units.

The polynomial function formed by given dats is V=(14 - 2x) (6 - 2x) x

Here given,

A rectangle has 14 units of length and 6 units of width.

From each corner of the rectangle, four squares with dimensions of x by x units are cut out.

The box's length is equal to (14 - 2x) units.

The box's width is =(6 - 2x) units.

The box's height is = x unit.

The volume of the box is equal to the sum of its length, width, and height.

Cubic units =(14 - 2x) (6 - 2x) x

∴V=(14 - 2x) (6 - 2x) x

where V is the box's volume in cubic units

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\({\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}\)

❍ Arrange the given data in order either in ascending order or descending order.

2, 3, 4, 7, 9, 11

❍ Number of terms in data [n] = 6 which is even.

As we know,

\(\star \: \sf Median_{(when \: n \: is \: even)} = {\underline{\boxed{\sf{\purple{ \dfrac{ { \bigg (\dfrac{n}{2} \bigg)}^{th}term +{ \bigg( \dfrac{n}{2} + 1 \bigg)}^{th} term } {2} }}}}}\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ { \bigg (\dfrac{6}{2} \bigg)}^{th}term +{ \bigg( \dfrac{6}{2} + 1 \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \dfrac{6 + 2}{2} \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \cancel{ \dfrac{8}{2}} \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ 4}^{th} term } {2} }\)

• Putting,

3rd term as 4 and the 4th term as 7.

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 4 + 7 } {2} }\)

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 11} {2} }\)

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} = \purple{5.5}\)

\(\\\)

\({\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\red{Solution:}}}}}\)

❍ Arrange the given data in order either in ascending order or descending order.

1, 2, 3, 4, 5, 6, 7

❍ Number of terms in data [n] = 7 which is odd.

As we know,

\(\star \: \sf Median_{(when \: n \: is \: odd)} = {\underline{\boxed{\sf{\red{ { \bigg( \frac{n + 1}{2} \bigg)}^{th} term}}}}}\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} = {{ \bigg(\dfrac{ 7 + 1 } {2} \bigg) }}^{th} term\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} = { \bigg(\cancel{\dfrac{8}{2}} \bigg)}^{th} term\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} ={ 4}^{th} term\)

• Putting,

4th term as 4.

\(\longrightarrow \: \sf Median_{(when \: n \: is \: odd)} = \red{ 4}\)

\(\\\)

\({\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\green{Solution:}}}}}\)

The frequency distribution table for calculations of mean :

\(\begin{gathered}\begin{array}{|c|c|c|c|c|c|c|} \hline \rm x_{i} &\rm 3&\rm 1&\rm 7&\rm 4&\rm 6&\rm 2 \rm \\ \hline\rm f_{i} &\rm 4&\rm 6&\rm 2&\rm 2 & \rm 1&\rm 1 \\ \hline \rm f_{i}x_{i} &\rm 12&\rm 6&\rm 14&\rm 8&\rm 6&\rm \rm 2 \\ \hline \end{array} \\ \end{gathered} \)

☆ Calculating the \(\sum f_{i}\)

\( \implies 4 + 6 + 2 + 2 + 1 + 1\)

\( \implies 16\)

☆ Calculating the \(\sum f_{i}x_{i}\)

\( \implies 12 + 6 + 14 + 8 + 6 + 2\)

\(\implies 48\)

As we know,

Mean by direct method :

\( \: \: \boxed{\green{{ { \overline{x} \: = \sf \dfrac{ \sum \: f_{i}x_{i}}{ \sum \: f_{i}}}}}}\)

here,

• \(\sum f_{i}\) = 16

• \(\sum f_{i}x_{i}\) = 48

By putting the values we get,

\(\sf \longrightarrow \overline{x} \: = \: \dfrac{48}{16}\)

\(\sf \longrightarrow \overline{x} \: = \green{3}\)

\({\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}\)

• Swipe to see the full answer.

\(\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}\)

The statement  "If gcd(a,b) ≠ 1 and gcd(b,c) ≠ 1, then gcd(a,c) ≠ 1." is false, and a counterexample is gcd(a) = 2, gcd(b) = 2, gcd(c) = 4. In this case, gcd(a,b) = gcd(b,c) = 2, but gcd(a,c) = 4, which contradicts the statement.

To prove that the given statement  "If gcd(a,b) ≠ 1 and gcd(b,c) ≠ 1, then gcd(a,c) ≠ 1." is false we can look at a counterexample:

Let a = 6, b = 4, and c = 9.

gcd(a,b) = gcd(6,4) = 2 (which is not 1)
gcd(b,c) = gcd(4,9) = 1 (which is 1)

Although gcd(a,b) ≠ 1 and gcd(b,c) ≠ 1, gcd(a,c) = gcd(6,9) = 3, which is not equal to 1. This counterexample shows that the statement is false.

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The area of a rhombus can be found by multiplying the length of one of its sides by the height of a perpendicular line from the center to a side.

The height of the rhombus is the distance from the center of the rhombus to one of its sides, perpendicular to that side.

The formula for the area of a rhombus can be written as A = s*h, where A is the area, s is the length of one of the sides of the rhombus, and h is the height of the rhombus.

It's important to note that this method of finding the area of a rhombus without diagonals can only be used when the rhombus is a regular polygon, a polygon with all sides and angles congruent. When the rhombus is not a regular polygon, then you can find the area by using the diagonals.

Additionally, it's important to mention that a rhombus can be defined as a parallelogram with all sides congruent or a square with its angles not 90 degrees.

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The matrix structure is an organizational design that combines functional and divisional reporting lines within the same company. The three conditions which usually exist when the matrix structure is found are multiple projects, interdependency, and a skilled workforce.

This structure facilitates better coordination and communication, allowing organizations to more effectively manage complex and diverse projects.
There are three conditions that usually exist when the matrix structure is found:
1. Multiple Projects: Matrix structures are often used in organizations that manage multiple projects or products simultaneously. These organizations need to allocate resources and personnel efficiently, and the matrix structure enables them to do so by allowing employees to work on various projects while still maintaining their functional roles.
2. Interdependency: In a matrix structure, there is a high level of interdependency among different departments and project teams. This interdependency promotes collaboration and communication, enabling the organization to respond more quickly to changing market conditions and customer needs.
3. Skilled Workforce: Organizations employing a matrix structure usually require a skilled and diverse workforce. These employees must be able to adapt to new challenges, work in cross-functional teams, and possess strong problem-solving skills. The matrix structure allows organizations to leverage the expertise of their workforce by assigning employees to projects based on their unique skill sets.
In conclusion, the matrix structure is an organizational design that combines functional and divisional reporting lines, enabling organizations to manage complex projects more effectively. This structure is typically found in organizations with multiple projects, a high level of interdependency, and a skilled workforce.

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Answer: 5x + (x + 54) = 6x + 54

So now 6x + 54 = 90 because u are solving a right angle.

90 - 54 is 36. So 6x = 36 and 36 divided by 6 is 6. Your answer for X = 6 Hope this helps you please mark brainliest

Step-by-step explanation:

Minimum Increment operations to make Array unique

The UNIQUE function will return an array, which will spill if it's the final result of a formula. This means that Excel will dynamically create the appropriate sized array range when you press ENTER .

ArrayList is like an array behind the scenes as it’s backed by an array of type java.lang.Object in java.

Normally arrays are fixed in size which means the number of elements that can be added are fixed and cannot be increased once created. ArrayList can dynamically increase in size once the array that backs is full so, these way we won’t encounter runtime exceptions.

When we say list.get(0), it’s equivalent to array[0]. It can be said the ArrayList is a kind of more convenient way to use dynamic arrays.

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Answer:

=10

Step-by-step explanation:

1: Add the numbers

2: Factor the numbers

3: Apply radical rule

Answer: =10

Hope this helps.

Answer:

10

Step-by-step explanation:

ok