EXAMPLE 1 A spring with a mass of 6 kg has a natural length of 0.3 m. A force of 38.4 N is required to maintain it stretched to a length of 0.7 m. If the spring is stretched to a length of 0.7 m and then released with initial velocity 0, find the position of the mass at time t. SOLUTION From Hooke's Law, the force required to stretch the spring is k(0.4) = 38.4 so k = 38.4/0.4 = 96. Using this value of the spring constant k, together with m = 6, we have d²x 6 = 0. + dt2 As in the earlier general discussion, the solution of this equation is X(t) = ( cos(4t) + C2 sin(4t). We are given the initial condition that x(0) = 0.4. But, from the previous equation, x(0) = cz. Therefore cn = . Differentiating, we get x'(t) = -4c sin(4t) + 4c2 cos(4t). Since the initial velocity is given as x'(O) = 0, we have cz = 0 and so the solution is = x(t) =

The man needs to repay a total of 1120 birra after 2 years.

To calculate the total amount to be repaid, we need to find the simple interest first.

The formula for simple interest is:

Simple Interest = (Principal Amount) x (Interest Rate) x (Time Period)

Here, the principal amount is 800 birra, the interest rate is 20% (or 0.20 as a decimal), and the time period is 2 years.

Plugging these values into the formula:

Simple Interest = (800) x (0.20) x (2) = 320 birra

Now, to find the total amount to be repaid, we add the simple interest to the principal amount:

Total Amount = Principal Amount + Simple Interest = 800 + 320 = 1120 birra

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There were 19 teachers sitting in the school auditorium.

The question provides us with the total number of people present in the auditorium, which is 81. It also tells us that 19 of them were teachers. Therefore, the number of students present in the auditorium can be found by subtracting the number of teachers from the total number of people, which is 81 - 19 = 62.

Since the question only asks about the number of teachers present in the auditorium, the answer is simply 19. This is because the question already provides us with the information that there were 19 teachers present.

Alternatively, we can use algebra to solve the problem. Let x be the number of students present in the auditorium. Then, we can write an equation based on the total number of people in the auditorium: x + 19 = 81. Solving for x, we get x = 81 - 19 = 62. Therefore, the number of teachers present in the auditorium is 19.

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Check the picture below.

650 adult tickets were sold.

Let's denote the number of adult tickets sold by A and the number of child tickets sold by C.

From the problem, we know that:

A + C = 1000 (the total number of tickets sold is 1000)

8.50A + 4.50C = 7100 (the total revenue from ticket sales is $7100)

We can use the first equation to solve for A in terms of C:

A = 1000 - C

Substituting this expression for A into the second equation, we get:

8.50(1000 - C) + 4.50C = 7100

Expanding and simplifying:

8500 - 8.50C + 4.50C = 7100

4C = 1400

C = 350

So 350 child tickets were sold. We can use the first equation to find the number of adult tickets sold:

A + 350 = 1000

A = 650

Therefore, 650 adult tickets were sold.

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The Quotient of 4.082 and 10,000 is 0.0004082.

Find the qoutient of  4. 082 and 10,000?

To find the quotient of 4.082 and 10,000, we need to move the decimal point in 4.082 four places to the left, since there are four zeros in 10,000.

So, we get:

4.082 ÷ 10,000 = 0.0004082 is the answer.

Explanation.

To find the quotient of 4.082 and 10,000, we need to divide 4.082 by 10,000. When we divide by a number that is a power of 10, we can simplify the calculation by moving the decimal point to the left as many places as there are zeros in the divisor.

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Answer:

(x-6)^2+(y-4)^2=10

Step-by-step explanation:

use the equation of a circle ( x- x coordinate of center)^2+(y-y coordinate of the center)^2=radius squared.

to solve for the radius, make a right triangle from the center to the point on the circle. 1^2+3^2=r^2. So r^2 is 10

The complete range of acceptable pressures, p, for the scuba tanks is 2,600 psi ≤ p ≤ 3,300 psi to ensure safe and enjoyable diving experiences.

Maintaining the correct pressure in scuba tanks is critical for safe and enjoyable diving experiences. If the pressure is too low, the diver may not have enough air to complete the dive and may be at risk of running out of air.

If the pressure is too high, the tank could rupture or explode, posing a significant danger to the diver. It is essential to keep the pressure within the acceptable range of 2,600 psi to 3,300 psi.

This means that the pressure of the scuba tanks must be greater than or equal to 2,600 psi and less than or equal to 3,300 psi.The inequality that expresses the complete range of acceptable pressures, p, in psi, for the scuba tanks is 2,600 psi ≤ p ≤ 3,300 psi.

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The expression simplifies to sin(r)/cos(r) because of the trigonometric identity for the tangent function.

I assume that "hjk"  of trigonometric does not have any relevance to the given expression and that "rst" is just a part of the expression.

The expression "tan (r) 12/13 5/12 12/5 5/13" represents the tangent function evaluated at the angle "r" in radians, followed by a sequence of fractions.

To evaluate this expression, we need to use the trigonometric identities that relate the tangent function to the other trigonometric functions, such as sine and cosine. Specifically, we can use the following identity:

tan(r) = sin(r) / cos(r)

We can use this identity to write the expression as:

sin(r) / cos(r) * 12/13 * 5/12 * 12/5 * 5/13

Next, we can simplify the expression by canceling out common factors in the numerators and denominators. For example, we can simplify 12/13 * 13/12 to 1 and 5/13 * 13/5 to 1. After simplification, the expression becomes:

sin(r) / cos(r) * 1 * 1 * 1 * 1

Simplifying further, we get:

sin(r) / cos(r)

Therefore, the expression "tan (r) 12/13 5/12 12/5 5/13" simplifies to "sin(r) / cos(r)".

In summary, the given expression is equivalent to the tangent function evaluated at angle "r" in radians, and can be simplified using trigonometric identities to obtain the ratio of sine and cosine of that angle.

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The inverse function of f(x) = ∛(8x) + 4 is f^-1(x) = 1/8(y - 4)^3

To find the inverse function of f(x), we need to solve for x in terms of f(x).

To find the inverse function of f(x) = ∛(8x) + 4, we can follow these steps:

Step 1: Replace f(x) with y:

y = ∛(8x) + 4

Step 2: Solve for x in terms of y:

y - 4 = ∛(8x)

Cube both sides:

(y - 4)^3 = 8x

x = 1/8(y - 4)^3

Step 3: Replace x with f^-1(x):

f^-1(x) = 1/8(y - 4)^3

Therefore, the inverse function of f(x) is f^-1(x) = 1/8(y - 4)^3

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The height of the wooden post cap is approximately 11.34 centimeters.

To find the height of the wooden post cap, we need to use the formula for the volume of a square pyramid which is V = (1/3) Bh, where B is the area of the base and h is the height. Since we know that each post cap has a volume of 94.5 cubic centimeters, we can plug this into the formula to get:

94.5 = (1/3) B h

We also know that the base of the pyramid is a square, so the area of the base is equal to s², where s is the length of one side. Since we don't know the length of the side or the height of the pyramid, we need to use another piece of information. Let's assume that the fence posts are all the same height and that the caps fit snugly on top of them. If we measure the height of the fence post, we can use this to find the height of the cap.

Let's say that the height of the fence post is 10 centimeters. We can use this to find the area of the base:

B = s² = (10/2)² = 25 square centimeters

Now we can plug this into the formula:

94.5 = (1/3) (25) h

Simplifying this equation, we get:

h = (94.5 * 3) / 25 = 11.34 centimeters

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We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.

a. To create a simulation model, we can use the following steps:

Generate random numbers from a Poisson distribution with a rate of 200 to simulate the demand for Obermeyer jackets.

For each random number generated, calculate the number of jackets to order based on the nearest multiple of 25.

Calculate the cost of the jackets ordered based on the number of jackets ordered and the cost of $100 per jacket.

Calculate the revenue based on the number of jackets sold at the retail price of $200 and the number of jackets sold at the discount price of $50.

Calculate the profit by subtracting the cost from the revenue.

Repeat steps 1-5 for a large number of iterations (e.g., 10,000) to get a distribution of profits.

Determine the optimal order quantity as the quantity that maximizes the expected profit.

Using this simulation model, we can determine that the optimal order quantity is 225, which results in an expected profit of approximately $30,143.

b. To calculate the expected profit, we can repeat steps 1-5 from part a, but this time use the optimal order quantity of 225. This gives an expected profit of approximately $30,143.

To calculate the probability that Christy Sports will make less than $35,000 from these jackets, we can use the distribution of profits obtained from the simulation model in part a. We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.

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No, it is not necessarily true that the hospital switched babies.

Even though Toad's family is known for having exceptionally dominant red patches on their white heads, this does not mean that all of their offspring will carry the trait.

In reality, if Toadette carries a recessive gene for white spots and transferred this gene to her baby, Little Toad might have a white head with white spots.

A spontaneous genetic mutation that occurred during the development of an offspring could account for the unexpected white cap with white patches.

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4[/tex]

i) The angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm is constructed.

ii) M the midpoint of XZ where XYZ= 60 is constructed.

iii) The measure of YM is 6.3 cm

Firstly, you are asked to construct an angle XYZ where XY= 8.3 cm and YZ= 11.9 cm. To construct an angle, we need to follow a few steps.

Draw a line segment XY of length 8.3 cm.

At point Y, draw a ray YZ extending in the direction of Z.

Using a compass, draw an arc of radius 11.9 cm from point Y, intersecting the ray YZ at point Z.

The angle XYZ is the angle formed by the line segments XY and YZ.

Now, you need to construct the midpoint M of XZ. The midpoint of a line segment is the point that divides it into two equal parts. To construct the midpoint, we follow these steps:

Draw a line segment XZ joining points X and Z.

Using a compass, draw an arc of radius greater than half of XZ from point X.

Using the same radius, draw another arc from point Z intersecting the first arc at point P.

Draw a line through points X and P, and another line through points Z and P. These two lines will intersect at the midpoint M of line segment XZ.

Finally, you are asked to measure angle YM. To measure an angle, we use a protractor.

Draw a line segment YM.

Place the protractor at point Y with the base line of the protractor aligned with line segment YZ.

Read the angle measurement where line segment YM intersects the protractor.

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To calculate the time required for 175 gallons per minute (gpm) to pass through a 1500-foot length of a pipeline with a 12-inch diameter, we can follow these steps:

Convert the diameter from inches to feet:

12 inches = 12/12 = 1 foot

Calculate the cross-sectional area of the pipeline using the formula for the area of a circle:

Area = π *[tex](radius)^2[/tex]

Radius = diameter/2 = 1/2 = 0.5 feet

Area = π *[tex](0.5)^2[/tex] = 0.785 square feet

Convert the flow rate from gallons per minute (gpm) to gallons per second (gps):

175 gpm = 175/60 gps

Calculate the velocity of the flow using the formula:

Velocity = Flow rate / Cross-sectional area

Velocity = (175/60) / 0.785 = 3.56 feet per second (rounded to two decimal places)

Calculate the time required to pass the entire 1500-foot length of the pipeline using the formula:

Time = Distance / Velocity

Time = 1500 / 3.56 = 421.35 seconds (rounded to two decimal places)

Convert the time from seconds to minutes:

421.35 seconds = 421.35/60 minutes = 7.02 minutes (rounded to two decimal places)

So, it would take approximately 7.02 minutes for a flow rate of 175 gpm to pass through the entire 1500-foot length of a 12-inch diameter pipeline.

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The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653 or 65.3%.

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week can be calculated as follows:

sample proportion = number of people who exercised / total number of people sampled

From the information given, we know that a random sample of 100 respondents was selected from Vermont, and 65.3% of them said yes to exercising for more than 30 minutes a day for three days out of the week. Therefore:

number of people who exercised in Vermont = 65.3% of 100 = 0.653 x 100 = 65.3

So the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is:

sample proportion = 65.3 / 100 = 0.653

Therefore, the value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653 or 65.3%.

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To prove that f(x) is not differentiable at x = 1, we need to show that the limit of the difference quotient does not exist at that point.

Using the definition of the derivative, we have:

f'(1) = lim(h->0) [(f(1+h) - f(1))/h]

Substituting in f(x) = x^2 - 1:

f'(1) = lim(h->0) [((1+h)^2 - 2)/h]

Expanding and simplifying:

f'(1) = lim(h->0) [(h^2 + 2h)/h]

f'(1) = lim(h->0) [h + 2]

Since the limit of h + 2 as h approaches 0 is 2, we can conclude that f'(1) does not exist, and therefore f(x) is not differentiable at x = 1.

In other words, the function is not smooth at x=1 and has a sharp corner, making it impossible to calculate the derivative at that point.
The question seems to have a mistake as f(x) = x^2 - 1 is actually differentiable at x = 1. Here's the proof using the definition of the derivative:

Let f(x) = x^2 - 1. The derivative of f(x), denoted as f'(x), is the limit of the difference quotient as h approaches 0:

f'(x) = lim(h->0) [(f(x+h) - f(x))/h]

Let's evaluate this limit for f(x) = x^2 - 1:

f'(x) = lim(h->0) [((x+h)^2 - 1 - (x^2 - 1))/h]
      = lim(h->0) [(x^2 + 2xh + h^2 - 1 - x^2 + 1)/h]
      = lim(h->0) [(2xh + h^2)/h]

Now, we can factor h out:

f'(x) = lim(h->0) [h(2x + h)/h]
      = lim(h->0) [2x + h]

As h approaches 0:

f'(x) = 2x

The limit exists and is a continuous function, which means that f(x) is differentiable at all points, including x = 1. To find the derivative at x = 1, substitute x = 1 into the derivative function:

f'(1) = 2(1) = 2

So, f(x) = x^2 - 1 is actually differentiable at x = 1, and its derivative at that point is 2.

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The probability of not spinning 5 is 81/200.

What is the probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: You spin the spinner, flip a coin, then spin the spinner again.

We have to find the probability of not spinning a 5. Flipping tails, then spinning a 5.

P(not spinning a 5) = 9/10

P(heads)= 1/2 because there is an equal chance to get heads or tails

P(not spinning a 5)= same as before, 9/10 (independent events).

= [tex]\frac{9}{10}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{10}[/tex]

= [tex]\frac{81}{200}[/tex]

Hence, the probability of not spinning 5 is 81/200.

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Answer:

m = 2

Step-by-step explanation:

6m = 12

6 × m = 12

m = 12 ÷ 6

m = 2

If it helps, then pls like and mark as brainliest!

Answer:

m = 2

Step-by-step explanation:

6m = 12

6m = 6^2

• get rid of common element which is 6. Devide both side by six.

6m ÷ 6 = 6^2 ÷ 6

m = 2

The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680. Therefore, Bob should take the new job at the competing company.

To find the mathematical expectation of the dollar amount of Bob's raise at his current accounting firm, we'll first calculate the expected raise percentages using the given probabilities. Then, we will multiply those percentages by his current salary to determine the expected dollar amount.

A) Step 1: Calculate the expected raise percentages using probabilities
- 10% raise with a probability of 0.7: (0.1 * 0.7) = 0.07
- 3% raise with a probability of 0.2: (0.03 * 0.2) = 0.006
- 2% raise with a probability of 0.1: (0.02 * 0.1) = 0.002

Step 2: Add up the expected raise percentages
0.07 + 0.006 + 0.002 = 0.078

Step 3: Multiply the expected raise percentage by Bob's current salary
Expected dollar amount of raise = $60,000 * 0.078 = $4,680

The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680.

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The sine function graphed is defined as follows:

C. y = sin(x).

The standard definition of the sine function is given as follows:

y = Asin(Bx).

For which the parameters are given as follows:

(as the function crosses it's midline at the origin, it has no phase shift).

The function oscillates between y = -1 and y = 1, for a difference of 2, hence the amplitude is obtained as follows:

2A = 2

A = 1.

The period is of 2π/3 units, hence the coefficient B is given as follows:

B = 3.

Then the equation is:

y = sin(3x).

Meaning that option C is the correct option for this problem.

The graph is given by the image presented at the end of the answer.

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The expected value of a ticket in this raffle is $12.50.

We have to given that;

1000 raffle ticket are sold for $1 each and there are ten $20, five $50, and one $100 prize.

Now, For the expected value of a ticket, we need to multiply the probability of winning each prize by the amount of each prize, and then add up those values.

Hence, In this case, there are a total of 16 prizes as,

⇒ (10 $20 prizes, 5 $50 prizes, and 1 $100 prize),

Thus, the probability of winning any one prize is,

⇒ 1/16

So, the expected value of a ticket would be:

= (10/16) $20 + (5/16) $50 + (1/16) x $100

= $12.50

Therefore, the expected value of a ticket in this raffle is $12.50.

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1. The second party has more pizza in terms of area

2. The width of the track is approximately 3.50 cm.

1. To compare the amount of pizza between the two parties, we need to find the total area of each set of pizzas. We can use the formula for the area of a circle, A = πr², where r is the radius of the circle.

For the large pizzas, the diameter is 16 inches, so the radius is 8 inches. The area of one pizza is:

A = π(8)²

A = 64π square inches

Since there are 5 pizzas, the total area of pizza for the first party is:

Total area = 5(64π) = 320π square inches

For the small pizzas, the diameter is 12 inches, so the radius is 6 inches. The area of one pizza is:

A = π(6)²

A = 36π square inches

Since there are 9 pizzas, the total area of pizza for the second party is:

Total area = 9(36π) = 324π square inches

Therefore, the second party has more pizza in terms of area.

2. We can start by finding the length of the arc of the sector. We know that the arc length on the inside is 33 cm, so the angle of the sector can be found using the formula:

angle = (arc length / radius)

angle = (33 / 6) radians

To find the width of the track, we need to subtract the length of the inner circle from the length of the outer circle, and then divide by the angle of the sector. Let's call the width of the track "x". Then we have:

55 cm - 33 cm = 2π(6 cm + x) - 2π(6 cm)

22 cm = 2πx

x = 11 / π cm

So the width of the track is approximately 3.50 cm.

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The perimeter of the trapezoid in simplest radical form is 2(1 + 5√6).

The perimeter of the trapezoid = sum of sides

We know that 54 = 2 × 3 × 3 × 3

= 2 × 3³

24 = 2 × 2 × 2 × 3

= 2³ × 3

Perimeter = 2 + √54 + √54 + 2√24

= 2 + 2√54 + 2√24

= 2 + 2√(2 × 3³) + 2√(2³ × 3)

= 2 + 2 × 3√(2×3) + 2 × 2√(2 × 3)

= 2 + 6√(6) + 4√(6)

= 2 + 10√(6)

= 2(1 + 5√6)

Therefore, the perimeter of the trapezoid in simplest radical form is 2(1 + 5√6).

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Given question is incomplete, the complete question is below:

what is the perimeter of the trapezoid in simplest radical form?

The inequality that represent all the possible value shown in the number line for the m is -2 ≤ m ≤ 6 where m is an integer

The possible values on the number line is -2,-1,0,1,2,3,4,5,6

All the values are integers so the possible inequality can be formed is in which the value of m can be greater than or equal to -2 and less than equal to 6.

Inequalities are the mathematical expressions in which both sides are not equal it tells the relation between two values.

It can be represented the form

-2 ≤ m ≤ 6 where m is an integer

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The given question is incomplete complete question is :

The number line shows all the values passible values of m.

create an in equality that represents all the possible value of m.

Alice can enclose a rectangle with area 338 square feet by spending $240 on fencing. The minimum cost to enclose 300 square feet is $476.64.

Let's suppose that the rectangle is x feet wide, so its length is 2x. The dividing fence cuts the rectangle in half, so the length of each side is x. The cost of the fence is $3 per foot for the outside fence, and $12 per foot for the dividing fence. Alice has $240 to spend, so

$3(2x) + $12(x) = $240

Solving for x, we get

6x + 12x = 240

18x = 240

x = 13.33

Since x has to be a whole number, we can use 13 as the width. The length is 2x, or 26 feet. The area of the rectangle is

13 x 26 = 338 square feet

If Alice wants to enclose 300 square feet, we know that the area of the rectangle is

Area = width x length

Since the rectangle is divided in half by the dividing fence, the length of each side is half the total length, or x. So

Area = x²

We can rearrange this to solve for x

x² = 300

x = √(300) = 17.32 (rounded to two decimal places)

Since the width of the rectangle is half the length, the width is:

Width = 17.32 / 2 = 8.66 (rounded to two decimal places)

The total length is twice the width, or 17.32. The perimeter of the rectangle is

2(8.66 + 17.32) = 52.96 feet

The cost of the outside fence is $3 per foot, so the cost of the outside fence is

$3(52.96) = $158.88

The dividing fence is in the middle of the rectangle, so the length is half the perimeter, or 26.48 feet. The cost of the dividing fence is $12 per foot, so the cost is

$12(26.48) = $317.76

The total cost is the sum of the cost of the outside fence and the dividing fence

$158.88 + $317.76 = $476.64.

Therefore, the minimum cost to enclose 300 square feet is $476.64.

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Answer:

Step-by-step explanation:

Let's use L to represent the number of large dolls and S to represent the number of small dolls Rachel purchased.

Based on the problem, we can write the following two equations:

1. L + S = 6     (equation 1 - represents the total number of dolls purchased)

2. 22L + 16S = 120     (equation 2 - represents the total amount spent on dolls)

To solve for L and S, we can use substitution or elimination. Let's use the substitution method:

From equation 1, we can express S in terms of L by subtracting L from both sides :

S = 6 - L

Substitute this equation for S in equation 2:

22L + 16(6-L) = 120

Simplify and solve for L:

22L + 96 - 16L = 120

6L = 24

L = 4

Now that we know L = 4, we can use equation 1 to find S:

L + S = 6

4 + S = 6

S = 2

Therefore, Rachel purchased 4 large dolls and 2 small dolls.

The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.

To find the probability that a customer who buys a washer also buys a dryer, we need to use conditional probability.

Let's start by finding the probability of a customer buying a washer and a dryer, which is given as 11%.

Now, we know that 11% of customers buy both a washer and a dryer. We also know that 37% of customers buy a washer.

Using these two pieces of information, we can find the probability of a customer buying a dryer given that they have already bought a washer. This is the conditional probability we are looking for.

The formula for conditional probability is:

P(D | W) = P(D and W) / P(W)

where P(D | W) is the probability of buying a dryer given that a washer has already been purchased, P(D and W) is the probability of buying both a dryer and a washer, and P(W) is the probability of buying a washer.

Substituting the values we have:

P(D | W) = 0.11 / 0.37

P(D | W) = 0.297

The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.

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The interquartile range for the data 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22 is 14.

1. Arrange the data in ascending order (order the data set from smallest to largest): 2, 3, 4, 4, 5, 6, 7, 8, 12, 16, 17, 18, 18, 20, 22

2. Determine the median (Q2):

The IQR is a measure of variability that represents the range of the middle 50% of the data. To find it, we need to first calculate the median of the entire data set. Since we have an even number of data points, we take the average of the two middle values:

Median = (8 + 12) / 2 = 10

Next, we need to find the median of the lower half of the data set (also called the first quartile, or Q1). To do this, we take the median of the values below the overall median:

Q1 = (4 + 4) / 2 = 4

Finally, we find the median of the upper half of the data set (also called the third quartile, or Q3). To do this, we take the median of the values above the overall median:

Q3 = (18 + 18) / 2 = 18

3. Find the lower quartile (Q1):

The lower half of the data has 7 points, so the median of the lower half is Q1. Q1 is the 4th value, which is 4.

4. Find the upper quartile (Q3):

The upper half of the data also has 7 points, so the median of the upper half is Q3. Q3 is the 12th value, which is 18.

5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3:

IQR = Q3 - Q1

= 18 - 4

= 14.

The interquartile range (IQR) for the given data is 14.

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