if r=3 cm,s=4cm find the area of the shaded area?​

Solution to given logarithmic equations and inequalities are;

x = 1

x = 9

x = 261

x = 10/3

x = 4

3x² - 2x - 1 = 0

x = 1 or x = -1/3

x = 13

x = 0

x = 0 or x = 5

1. 3x = log6 216

Using the definition of logarithm, we have:

\(6^{3x} = 216\)

\(6^{3x} = 6^3\)

3x = 3

x = 1

2. x - 4 = log3 243

Using the definition of logarithm, we have:

\(3^{x - 4} = 243\)

\(3^{x - 4} = 3^5\)

x - 4 = 5

x = 9

3. log4 (4x - 20) = 5

Using the definition of logarithm, we have:

4⁵ = 4x - 20

1024 = 4x - 20

4x = 1044

x = 261

4. log9 (3 - x) = log9(5x – 15)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3 - x = 5x - 15

20 = 6x

x = 10/3

5. log81 (x + 20) = log81 (6x)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x + 20 = 6x

20 = 5x

x = 4

6. log9 (3x²) = log9 (2x + 1)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3x² = 2x + 1

3x² - 2x - 1 = 0

7. Using the quadratic formula, we have:

x = (-(-2) ± √((-2)² - 4(3)(-1))) / (2(3))

x = (2 ± √(16)) / 6

x = (2 ± 4) / 6

x = 1 or x = -1/3

8. log4(x - 1) = log4(12)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x - 1 = 12

x = 13

9. log7(5 - x) = log7 (5)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

5 - x = 5

x = 0

10. logx (5x) = 2

Using the definition of logarithm, we have:

x² = 5x

x² - 5x = 0

x(x - 5) = 0

x = 0 or x = 5

Note that x = 0 is not a valid solution, since log 0 is undefined. Therefore, the only solution is x = 5.

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The Perimeter of wall in inches is 4.724412 inches.

We have the Perimeter = 120 m

We know 1 m = 39.3701 inch

Then, the perimeter inches

= 39.3701 x 120

= 472.4412 inches  

and, 1 cm= 0.393701 inch

Then, perimeter

= 12 x 0.393701

= 4.724412 inches

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a. The resultant magnetic field at point P due to currents in the two wires can be determined by vector addition of the individual magnetic fields.

b. Reversing the direction of currents in both wires would result in a reversed direction of the resultant magnetic field at point P.

a. To construct the vector diagram showing the direction of the resultant magnetic field at point P due to currents in the two wires, we can use the right-hand rule for determining the magnetic field direction around a wire carrying current.

For Wire 1, which has the current coming towards us (out of the plane of the paper), the magnetic field direction can be determined by wrapping the right-hand fingers around the wire in the direction of the current, and the thumb will point in the direction of the magnetic field. Let's say the direction of the magnetic field for Wire 1 is from left to right.

For Wire 2, which has the current going into the plane of the paper, we apply the right-hand rule again. Wrapping the right-hand fingers around the wire in the direction opposite to the current, the thumb will point in the direction of the magnetic field. Let's say the direction of the magnetic field for Wire 2 is from right to left.

At point P, which is equidistant from the two wires, the magnetic fields due to the currents in the wires will combine. The resultant magnetic field direction at point P can be found by vector addition. Drawing the vectors representing the magnetic fields for Wire 1 and Wire 2, with opposite directions, we can add them head-to-tail. The resultant vector will show the direction of the resultant magnetic field at point P.

b. If the currents in both wires were instead directed into the plane of the page (such that the current moved away from us), the directions of the magnetic fields due to the currents in the wires would be reversed compared to the previous case.

For Wire 1, the magnetic field direction would be from right to left, and for Wire 2, it would be from left to right. Following the same process as in part a, we would draw the vectors representing the magnetic fields for Wire 1 and Wire 2 in their respective reversed directions. Adding them head-to-tail would give us the resultant vector indicating the direction of the resultant magnetic field at point P in this scenario.

Complete Question:

Two wires lie perpendicular to the plane of the paper, and equal electric currents pass through the paper in the directions shown. Point P is equidistant from the two wires.

a. Construct a vector diagram showing the direction of the resultant magnetic field at point P due to currents in these two wires. Explain your reasoning.

b. If the currents in both wires were instead directed into the plane of the page (such that the current moved away from us), show the resultant magnetic field at point P.

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a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

b) The probability of scoring no hits is the probability of X being 0.

c) The probability of scoring more hits than misses is the probability of X being greater than 5

d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).

e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3

The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)

f) The expectation of Z: E(Z) = E(X²)

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

(a) To calculate the Probability Mass Function (PMF) of X, we can use the binomial distribution formula. Since the marksman takes 10 shots independently with a probability of 0.2 of hitting the target, the PMF of X follows a binomial distribution with parameters n = 10 (number of trials) and p = 0.2 (probability of success):

PMF of \(X(x) = C(n, x) * p^x * (1 - p)^{(n - x)}\)

Where C(n, x) represents the number of combinations or "n choose x."

Let's calculate the PMF for each value of X from 0 to 10:

PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰

PMF of X(1) = C(10, 1) * (0.2)¹ * (0.8)⁹

PMF of X(2) = C(10, 2) * (0.2)² * (0.8)⁸

...

PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

(b) The probability of scoring no hits is the probability of X being 0. So we calculate PMF of X(0):

PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰

(c) The probability of scoring more hits than misses is the probability of X being greater than 5. We need to calculate the sum of PMF of X from X = 6 to X = 10:

PMF of X(6) + PMF of X(7) + PMF of X(8) + PMF of X(9) + PMF of X(10)

(d) The expectation (mean) of X can be found using the formula:

E(X) = n * p

where n is the number of trials and p is the probability of success. In this case, E(X) = 10 * 0.2.

The variance of X can be calculated using the formula:

Var(X) = n * p * (1 - p)

In this case, Var(X) = 10 * 0.2 * (1 - 0.2).

(e) To calculate the expectation and variance of Y, we need to consider the profit from each hit. Each hit earns $2, and since X represents the number of hits, Y can be calculated as:

Y = 2X - 3

The expectation of Y can be calculated as:

E(Y) = E(2X - 3) = 2E(X) - 3

To calculate the variance of Y, we can use the property Var(aX + b) = a²Var(X) when a and b are constants:

Var(Y) = Var(2X - 3) = 4Var(X)

(f) Similarly, for Z, each hit earns a dollar amount equal to the square of the number of hits:

Z = X²

The expectation of Z can be calculated as:

E(Z) = E(X²)

Hence, a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

b) The probability of scoring no hits is the probability of X being 0.

c) The probability of scoring more hits than misses is the probability of X being greater than 5

d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).

e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3

The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)

f) The expectation of Z: E(Z) = E(X²)

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a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

b) The probability of scoring no hits is the probability of X being 0.

c) The probability of scoring more hits than misses is the probability of X being greater than 5

d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).

e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3

The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)

f) The expectation of Z: E(Z) = E(X²)

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

(a) To calculate the Probability Mass Function (PMF) of X, we can use the binomial distribution formula. Since the marksman takes 10 shots independently with a probability of 0.2 of hitting the target, the PMF of X follows a binomial distribution with parameters n = 10 (number of trials) and p = 0.2 (probability of success):

PMF of

Where C(n, x) represents the number of combinations or "n choose x."

Let's calculate the PMF for each value of X from 0 to 10:

PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰

PMF of X(1) = C(10, 1) * (0.2)¹ * (0.8)⁹

PMF of X(2) = C(10, 2) * (0.2)² * (0.8)⁸

......

PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

(b) The probability of scoring no hits is the probability of X being 0. So we calculate PMF of X(0):

PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰

(c) The probability of scoring more hits than misses is the probability of X being greater than 5. We need to calculate the sum of PMF of X from X = 6 to X = 10:

PMF of X(6) + PMF of X(7) + PMF of X(8) + PMF of X(9) + PMF of X(10)

(d) The expectation (mean) of X can be found using the formula:

E(X) = n * p

where n is the number of trials and p is the probability of success. In this case, E(X) = 10 * 0.2.

The variance of X can be calculated using the formula:

Var(X) = n * p * (1 - p)

In this case, Var(X) = 10 * 0.2 * (1 - 0.2).

(e) To calculate the expectation and variance of Y, we need to consider the profit from each hit. Each hit earns $2, and since X represents the number of hits, Y can be calculated as:

Y = 2X - 3

The expectation of Y can be calculated as:

E(Y) = E(2X - 3) = 2E(X) - 3

To calculate the variance of Y, we can use the property Var(aX + b) = a²Var(X) when a and b are constants:

Var(Y) = Var(2X - 3) = 4Var(X)

(f) Similarly, for Z, each hit earns a dollar amount equal to the square of the number of hits:

Z = X²

The expectation of Z can be calculated as:

E(Z) = E(X²)

Hence, a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰

b) The probability of scoring no hits is the probability of X being 0.

c) The probability of scoring more hits than misses is the probability of X being greater than 5

d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).

e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3

The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)

f) The expectation of Z: E(Z) = E(X²)

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Answer:  \(\frac{28}{27}\) or \(1\frac{1}{27}\)

Step-by-step explanation:

\(\frac{7}{9} /\frac{6}{8} = \frac{7}{9}(\frac{8}{6})\)

\(\frac{7}{9} (\frac{8}{6} ) = \frac{28}{27}\)

\(\frac{28}{27} = 1 \frac{1}{27}\)

A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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Answer:

yep

Step-by-step explanation:

when you divide a fraction u can use the KCF method which is basically:

(keep) the first fraction the same

(change) the division sign in the middle to a multiplication sign

(flip) the second fraction

basically because you have to flip the 1/4 when you divide it, it'll be the same as a 4/1 anyways

To find the simple interest payable, we can use the formula:

Simple Interest = Principal × Rate × Time

where:

Principal = $28,800

Rate = 3.75% per annum (expressed as a decimal, so 3.75% = 0.0375)

Time = 4 years

(a) The simple interest payable is $4,320.

Simple Interest payable:

Simple Interest = $28,800 × 0.0375 × 4

Simple Interest = $4,320

Therefore, the simple interest payable is $4,320.

(b) The monthly repayment amount is approximately $690.

To find the monthly repayment, we need to calculate the total amount to be repaid and then divide it by the number of months in the loan term.

Total amount to be repaid = Principal + Simple Interest

Total amount to be repaid = $28,800 + $4,320

Total amount to be repaid = $33,120

The loan term is 4 years, which is equivalent to 4 × 12 = 48 months.

Monthly repayment = Total amount to be repaid / Number of months

Monthly repayment = $33,120 / 48

Monthly repayment ≈ $690

Therefore, the monthly repayment amount is approximately $690.

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The correct probability notation to represent 40% is P(A1), where A1 represents the event of drivers using entrance 1.

In probability theory, events are represented by capital letters or symbols. The notation P(A) is commonly used to denote the probability of event A occurring. In this case, we are interested in representing the probability of drivers using entrance 1, which accounts for 40% of the total drivers. Therefore, we can use the notation P(A1) to denote the probability of event A1, where A1 represents the event of drivers using entrance 1.

Probability notation allows us to quantify the likelihood of events occurring. In this scenario, the probability notation P(A1) specifically represents the probability of drivers using entrance 1, which is given as 40%. This notation helps us distinguish between different events in the parking lot scenario, where there are three entrances (A1, A2, A3) and associated probabilities for each entrance. By using probability notation, we can express and calculate the likelihood of various events and analyze the overall probabilities in the parking lot system.

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The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.

In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:

Each term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.

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The full question is:

How many terms are in the following expression 6 + 2 x - 4 y + 5 z

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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The night the family can stay at the hotel are-

Equations in mathematics are not always balancing on both sides using a 'equal to' symbol. Sometimes it's a 'not equal to' relationship, as though something is more than or less than the other. In mathematics, an inequality is a relationship that results from a non-equal comparison of two numbers or any other mathematical expressions.

Inequalities are mathematical expressions that fall within the category of algebra.

Now according to the question-

Total cost spent on hotel stay = cost per night + taxes + parking charges + tips.

As, the paid tax is 10% of the original amount.

The original amount is $90

10% of 90 is = 0.1 × 90

10% tax = $9

Let 'x' be the days spent in hotel.

Then,

The cost spent on stay only is $90x.

The cost spend  on tax is $9x.

As, parking is done once only its id added once only.

The total amount spent on tips is $30

Adding all the amount;

90x + 9x + 12 + 30 ≤ 600

On solving,

99x ≤  558

x ≤ 5.6

As, number can not be in decimals, it could be either 5 day sir 6 days.

Then, total amount spend on days will be-

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The complete question is-

One particular hotel in the downtown area costs $90 a night. An additional 10% tax is added to the original cost of the hotel room. There is also a one-time $12 for parking charge, and a family can expect to spend $30 on tips during their stay. How many nights can a family spend at the hotel without exceeding their budget of $600.

Answer:

C

Step-by-step explanation:

if you divide both sides by ax+b you get 1=1 which is not a solution for x.

Answer:

18

Step-by-step explanation:

Without knowing the specific data of the town, it is impossible to provide an exact probability but we can use the following formula to calculate the probability of an individual being employed full-time, given that they are between 18 and 49 years old:

P(full-time employment | age between 18 and 49) = P(full-time employment and age between 18 and 49) / P(age between 18 and 49)

To calculate this probability, we need to know the number of individuals in the town who are both employed full-time and between the ages of 18 and 49, and divide it by the total population of the town.

P(full-time employment and age between 18 and 49) = Number of individuals employed full-time and between the ages of 18 and 49 / Total population of the town

To calculate this probability, we need to know the number of individuals in the town who are between the ages of 18 and 49, and divide it by the total population of the town.

P(age between 18 and 49) = Number of individuals between the ages of 18 and 49 / Total population of the town

We can use the probabilities calculated in steps 1 and 2 to calculate the probability of an individual being employed full-time, given that they are between the ages of 18 and 49, using the formula:

P(full-time employment | age between 18 and 49) = P(full-time employment and age between 18 and 49) / P(age between 18 and 49)

For example, if there are 10,000 people in the town, and 6,000 of them are between the ages of 18 and 49, and out of those 6,000, 4,000 are employed full-time, then:

P(full-time employment and age between 18 and 49) = 4,000 / 10,000 = 0.4

P(age between 18 and 49) = 6,000 / 10,000 = 0.6

P(full-time employment | age between 18 and 49) = 0.4 / 0.6 = 0.67

Therefore, the probability that an individual is employed full-time, given that they are between the ages of 18 and 49, is 0.67 or 67%.

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Answer:

Median is 4

Step-by-step explanation:

The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

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The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

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Answer:

2x⁴-45x-8

Step-by-step explanation:

Using it's concept, it is found that the probability that a person chosen at random from this group has brown or green eyes is of \(\frac{13}{25}\).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, it is found that the group has 20 + 6 + 17 + 7 = 50 people, of which 20 + 6 = 26 have brown or green eyes, hence the probability is given by:

p = 26/50 = 13/25.

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Answer:

The height of this cylinder = 9.55 ins

Step-by-step explanation:

Volume cylinder = pi * r² * h = 30 ins

r=1

pi * r² * h = 30

pi * 1² * h = 30 ins

h = 30/pi

h = 9.55 ins

Answer: 19.56z - 9

Step-by-step explanation: Hello!  Here are the steps to solve this problem:

14.33z - 3 - (6 - 5.23z).  

Firstly, you have to use the distributive property and distribute -1 to the parentheses using PEMDAS, Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

14.33z - 3 + -1(6 - 5.23z)
14.33z - 3 + (-6 + 5.23z)
14.33z + (-3) + (-6) + (5.23z)
14.33z + (5.23z) + (-3) + (-6)
(14.33z + 5.23z) + (-3 - 6)
19.56z + (-3 - 6)

19.56z + (-9)
19.56z - 9.

5.152 L volume will it occupy at STP.

What is ideal gas law?

The equation of state for an ideal gas, in theory, is known as the ideal gas law. Even though it has a number of shortcomings, it provides a good approximation of the behavior of several gases under various circumstances. Theoretical point particles that move randomly and only collide in elastic ways make up an ideal gas.

Using the ideal gas equation PV=nRT, where n is the number of moles, it is possible to determine the volume that will be present at STP as follows.

n= PV/RT

p=0.974 atm

V=6.0  L

R = 0.0821  L.atm/k.mol

T=  35 +273= 308k

n=  (0.974 atm  x  6.0 L)/( 0.0821 L.atm/k.mol  x 308 k)=  0.178 moles

STP  1 mole=  22.4 L  what obout  0.23 moles

=22.4  x0.178moles/ 1moles =5.152 L

Hence, 5.152 L volume will it occupy at STP

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Based on the boxplot, approximately 50% percent of the people who entered the amusement park met the height requirement for the attraction.

Box-Plot is a summary of the sample distribution presented graphically which can describe the shape of data distribution (skewness), a measure of central tendency and a measure of dispersion (diversity) of observational data. There are 5 statistical measures that we can read from the boxplot, namely:

In addition, the boxplot can also show whether there are outlier values and extreme values from the observed data.

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We can use the double number line to find the cost of buying a different number of bags of rice or the number of bags of rice we can buy for a given amount of money.

The given double number line shows that it costs $3 to buy 2 bags of rice. This means that the cost of 1 bag of rice is $1.50.

To find the cost of buying a different number of bags of rice, we can use the double number line.

Suppose we want to know the cost of buying 5 bags of rice. We can do this by starting at the number 2 on the top line and following the diagonal line down to the bottom line.

Then, we can read off the number on the bottom line that corresponds to 5 on the top line.

This gives us a cost of $7.50 for 5 bags of rice.

We can also use the double number line to find the number of bags of rice that we can buy for a given amount of money.

For example, if we have $6, we can find the number of bags of rice we can buy by starting at the number $3 on the bottom line and following the diagonal line up to the top line. Then, we can read off the number on the top line that corresponds to $6 on the bottom line.

This gives us a value of 4 for the number of bags of rice.

Therefore, we can use the double number line to find the cost of buying a different number of bags of rice or the number of bags of rice we can buy for a given amount of money.

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Answer:

n = -s/3 + m/3

Step-by-step explanation:

The equation that reflects the graph of f(x) = x^2 - 4x across the y-axis is y = -(x^2 - 4x).

To graph both equations, we can start by plotting the original equation f(x) = x^2 - 4x. This is a quadratic function with a downward-opening parabola.

To reflect the graph across the y-axis, we change the sign of the x terms in the equation. So, the reflected equation becomes y = -(x^2 + 4x).

Now, let's plot the reflected equation on the same coordinate system. The reflected graph will be symmetric to the original graph with respect to the y-axis.

Here is a visual representation of both equations on a graph:

Original equation: f(x) = x^2 - 4x

Reflected equation: y = -(x^2 + 4x)

(Insert graph of f(x) = x^2 - 4x and y = -(x^2 + 4x) on the same coordinate system)

By comparing the graphs, you can observe that the reflected equation is a mirror image of the original equation across the y-axis.

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

Answer:

254.94

Step-by-step explanation:

Answer:

253.94

Step-by-step explanation:

I added the whole numbers then added the decimals separate. After that I ad Dee we the decimals and the whole numbers and got 253.94.