María is shopping for party supplies. She finds that paper plates come in packages of 8, napkins come in packages of 10, and paper cups come in packages of 12. What is the least number of packages of plates, napkins, and cups she has to buy so that she has the same number of each item for her party?

To integrate the function ∫(x² - 36) dx, we first need to factor out the expression inside the parentheses:
∫(x² - 36) dx = ∫(x - 6)(x + 6) dx

We can then use the power rule of integration to find the antiderivative:
∫(x - 6)(x + 6) dx = (1/3)x³ - 6x + C, where C is the constant of integration.

Since the original problem states X > 6, we can evaluate the definite integral using these limits:
∫(x² - 36) dx from 6 to X = [(1/3)X³ - 6X] - [(1/3)(6)³ - 6(6)]
= (1/3)X³ - 6X - 68

Therefore, the answer in exact form is (1/3)X³ - 6X - 68.

To integrate the given function, first note the correct notation for the function: ∫(x^2)/(x^2 - 36) dx for x > 6.

To solve this, we can use partial fraction decomposition. The given function can be rewritten as:

∫(A(x - 6) + B(x + 6))/(x^2 - 36) dx

Solving for A and B, we find that A = 1/12 and B = -1/12. Now we rewrite the integral as:

∫[(1/12)(x - 6) - (1/12)(x + 6)]/(x^2 - 36) dx

Next, separate the two terms and integrate them individually:

(1/12)∫[(x - 6)]/(x^2 - 36) dx - (1/12)∫[(x + 6)]/(x^2 - 36) dx

Now, notice that the integrals are of the form ∫u'/u dx. The integral of this form is ln|u|. So we have:

(1/12)[ln|(x - 6)| - ln|(x + 6)|] + C

Using the logarithm property, we can rewrite the answer as:

(1/12)ln|((x - 6)/(x + 6))| + C

That is the exact form of the antiderivative for the given function.

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The windshield sector area is 706.86 cm².

To calculate the sector area of the windshield wiper, we need to use the formula for the area of a sector of a circle. The formula is:

A = (θ/360°) x πr²

where A is the area of the sector, θ is the central angle of the sector in degrees, and r is the radius of the circle.

In this problem, we are given that the windshield wiper has a length of 45 cm, which means that the radius of the circle traced by the wiper is 45 cm/2 = 22.5 cm.

We are also given that the wiper creates a central angle of 120° in one wipe. Substituting these values into the formula, we get:

A = (120°/360°) x π(22.5 cm)²

A = (1/3) x π x (22.5 cm)²

A ≈ 706.86 cm²

Therefore, the sector area of the windshield wiper is approximately 706.86 square centimeters.

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Answer:

Step-by-step explanation:

The correct answer is:

the initial height of the plant

The y-intercept represents the point where the graph intersects the y-axis. In the context of a relationship between plant growth and time, the y-intercept would represent the initial height of the plant, which is the height of the plant at the start of the experiment, before any growth has occurred.

Answer is 27,529.82
To calculate the total purchase price of the car including tax, license, and title, we need to add the down payment, the financed balance, the sales tax, and the license and title charges.

First, we calculate the down payment:
10% of $25,625 = $2,562.50

Next, we calculate the financed balance:
$25,625 - $2,562.50 = $23,062.50

Then, we calculate the sales tax:
7.5% of $23,062.50 = $1,729.69

Finally, we add the license and title charges:
$1,729.69 + $175.13 = $1,904.82

So the total purchase price of the car including tax, license, and title is:
$2,562.50 + $23,062.50 + $1,904.82 = $27,529.82

Rounded to the nearest cent, the answer is option D: $27,735.14.

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Based on the elevations given, Death Valley (-282 feet) < Tallahassee, Florida (203 feet).

To compare the elevations of Death Valley and Tallahassee, we'll use the inequality symbols i.e., "<" or ">" . The symbol "<" indicate less than and ">" indicate greater than.

Death Valley, California has an elevation of -282 feet, while Tallahassee, Florida has an elevation of 203 feet. Since -282 is less than 203, we use the "<" symbol.

So, the comparison is as follows:

Death Valley (-282 feet) < Tallahassee, Florida (203 feet)

This means that the elevation of Death Valley is lower than or less than the elevation of Tallahassee.

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The value of the distance you will run is 5.62500 miles

From the question, we have the following parameters that can be used in our computation:

This means that

Speed = 7.5 miles per hour

Time = 45 minutes

The distance you will run is calculated as

Distance = Speed * Time

Substitute the known values in the above equation, so, we have the following representation

Distance = 7.5 miles per hour * 45 minutes

Evaluate the product

Distance = 5.62500 miles

Hence, the distance is 5.62500 miles

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Orlando should consider using simple interest and the amount he will have to pay is $696, under the condition that he wants to borrow $3,000 for the purchase of a used car. He needs to clear the loan after 4 years.

Orlando should apply the simple interest method.

The amount of interest he will pay using simple interest is evaluated

I = P × r × t

Here

I = interest paid

P = borrowed principal amount

r =  rate of annual interest

t = time

In this case,

P = $3,000

r = 5.8%

t = 4 years

Therefore,

I = $3,000 × 0.058 × 4

= $696

So Orlando will pay $696 in interest using simple interest.

The amount of interest he will pay using compound interest is calculated as follows:

[tex]A = P * (1 + r/n)^{(n*t)}[/tex]

I = A - P

Here,

A = end term amount

n = count of interest that is compounded each year

In this case,

P = $3,000

r = 5.2%

t = 4 years

Interest is compounded annually so n=1

Therefore,

A = $3,000 × (1 + 0.052/1)⁴

= $3,697.47

I = $3,697.47 - $3,000

= $697.47

So Orlando will pay $697.47 in interest using compound interest.

Therefore, Orlando should choose simple interest method and he will owe $1.47 less using that method.

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You should always measure your following distance in seconds. The correct answer for measuring following distance is A.  

It is important to keep a safe distance between vehicles on the road, which is known as following distance. Measuring following distance in seconds is a more reliable method than measuring it in car lengths or feet.

The recommended following distance is typically two to three seconds. This means that when the vehicle in front of you passes a fixed point on the road, you should not reach that same point before two to three seconds have elapsed.

Measuring in seconds is more effective as it takes into account the speed at which both vehicles are traveling. If you measure in car lengths or feet, it may not be accurate as the length of the cars may differ, and it does not account for the speed of the vehicles. By measuring in seconds, you can maintain a safe distance and reduce the risk of accidents or collisions.

The correct answer for measuring following distance is A.  

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Complete question is:

You should always measure your following distance in __________

A. seconds. B. car lengths. C. feet.

The role of the brackets, and how they effects the sum is given as the inside signs get changed after the opening of the bracket.

The associative property of addition is a mathematical statement that asserts that the arrangement of three or more integers does not affect their total. This indicates that no matter how the numbers are organised, the total of three or more integers remains the same.

The associative property of addition is a mathematical principle that asserts that when adding three or more integers, the amount obtained is constant regardless of how the numbers are grouped. Grouping here refers to where the brackets are positioned.

The sum for the 1st term is 10 + 7 – 5 + 3 = 15

The sum of the 2nd term is 10 + 7 – (5 + 3) = 17 - 8 = 9

Here, the bracket used made all the difference so after opening of the bracket the sign inside changed which impacted the summation of the terms above.

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The number of calories in the 3 ounce bar is 480.

To solve this problem, we can use a proportion. If the 2-ounce protein bar has 320 calories, then we can set up the following proportion:

2 oz / 320 cal = 3 oz / x cal

where x is the number of calories in the 3-ounce protein bar.

We can solve for x by cross-multiplying and simplifying:

2 oz * x cal = 3 oz * 320 cal

2x = 960x = 480

Therefore, the 3-ounce protein bar has 480 calories.

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The constant 1.2 in the function represents the rate of change of the quantity per year.

Specifically, it represents the factor by which the quantity grows or decays over a year.

Since 1.2 is greater than 1, the function describes an exponential growth, where the quantity is multiplied by 1.2 each year.

For example, after one year, the quantity is multiplied by 1.2, after two years it is multiplied by 1.2 squared, and so on.

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Note that the expected value of the retailers profit is - $114. This means he made a loss.

To find the expected value we must proceed as follows

Expected Value - E(F) is

Probability of F - P(F)

= 100 x ($100 - $200) + (P(F) = $50) x ($50 - $200) + (P(F) = $ -200) x ( $ - 200 - $200) +  (P(F)   = $- 350) x ($ -350  $ 200)

= (0.9) x (-100) + (0.07 ) x (-150) + (0.01)  x  (-550)  + (0.02) x (-400)

= - 90  - 10.5  - 5.5 -8

E(F) = $ -114

So it is right to state that the expected value of the retailer's profit per protection plan sold is -$114, which  is a loss.

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Full Question:

An electronics retailer sells mobile phones with an optional protection plan for $100. In case of an accident, the customer pays a $50 deductible and the retailer covers the rest of the repair cost, which is typically $200 per repair. The protection plan covers a maximum of 333 repairs.

Let X be the number of repairs a randomly chosen customer uses under the protection plan, and let F be the retailer's profit from one of these protection plans. The probability distributions of X and F are:

X = number of repairs: 0 1 2 3

Probability: 0.90 0.07 0.02 0.01

F = retailer profit: $100-$50-$200-$350

Probability: 0.90 0.07 0.02 0.01

The task is to find the expected value of the retailer's profit per protection plan sold.

If in Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet, then the length of US to the nearest tenth of a foot is approximately 39.4 feet.

In angle STU, we have a right triangle with U=90°, S=31°, and TU=77 feet. To find the length of US, we can use the sine function:

sin(S) = opposite side (US) / hypotenuse (TU)

sin(31°) = US / 77 feet

To find the length of US, multiply both sides by 77 feet:

US = 77 feet * sin(31°)

US ≈ 39.4 feet

Therefore, the length of US to the nearest tenth of a foot is approximately 39.4 feet.

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Answer: hopefully the image helps

Step-by-step explanation:

The solution of the given inequality, x - 3 ≤ -2, is solved as the possible value of x which is determined as: x ≤ 1.

Given the inequality x - 3 ≤ -2, to find the solution, wr would have to solve for x as explained below:

x - 3 ≤ -2 [given]

Add 3 to both sides:

x - 3 + 3 ≤ -2 + 3 [addition property of equality]

x ≤ 1

This means that the values of x are less than or equal to 1, which is from 1 below.

Thus, the solution to the inequality is solved by finding the possible value of x, which is x ≤ 1.

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Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.

Since Daniel read 77 pages in $\frac{2}{5}$ of an hour, we can set up the proportion:

$\frac{77}{\frac{2}{5}} = x$

where $x$ is the number of pages he would read in 1 hour.

To solve for $x$, we can simplify the left side of the equation by multiplying both the numerator and denominator by 5, which gives:

$\frac{77 \times 5}{2} = x$

Simplifying this expression gives:

$192.5 = x$

Therefore, if Daniel continues reading at the same rate, he will read 192.5 pages in one hour. However, since the number of pages must be a whole number, we can round this answer to the nearest whole number to get:

$x \approx 193$

So, Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.

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The mean is equal to the median, so the data is symmetrical.

Given that :

Colin surveyed 12 teachers at his school to determine how much each person budgets for lunch.

The data is :

10   5   8   10   12   6   8   10   15   6   12   18

Mean is the average of these numbers.

Mean = (10 + 5 + 8 + 10 + 12 + 6 + 8 + 10 + 15 + 6 + 12 + 18) / 12

         = 10

Now median is the element in the middle arranged in an order.

Arrange the data in ascending order.

5  6  6  8  8  10  10  10  12  12  15  18

The middle element is the average of the 6th and 7th elements.

Median = (10  10) / 2 = 10

So mean and the median is equal. So the data is symmetrical.

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If 13 matches are played in total then, 7 2-player matches and 6 6-player matches are played.

Here we see that the table has two columns- 6 player Athletes and 2 player athletes. It is given that no athlete participates in both the type of games. Hence we can say that

If one match for 2 player game is held then 2 players are employed there.

Hence we have 48 players left

hence we will have 48/6 = 8 6-player matches.

Similarly, if 1 6-player match is played then 44 players applied for the 2-player match, hence, we have 44/2 = 22 2-player matches

If 4 2-player matches are held then we will have 8 players booked. Hence 42/6 = 7 6-player matches were held.

If 4 6-player matches were held then, we have 26/2 = 13 2-player matches.

Hence the table will be

Number of 6 Player Games                       Number of 2-player games

                     8                                                                 1

                     1                                                                 22

                     7                                                                 4

                     4                                                                 13

b)

Let the total 2-player games played be x and 6-player games be y

we have,

x + y = 13

2x + 6y = 50

or, 2(x + y) + 4y = 50

or, 26 + 4y = 50

or, 4y = 24

or, y = 6

Hence x = 7

Therefore, in total 7 2-player matches and 6 6-player matches are played.

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Answer:

N'(3, 2), M'(0, 1), O'(1, 3)

Step-by-step explanation:

Please sketch the graphs of the two triangles and the line of reflection to confirm my answer.

Since NMO is reflected over the line

x = -1, the y-coordinates of N'M'O' will remain the same. Since the x-coordinate of N is at -5, which is 4 units to the left of the line of reflection, the x-coordinate of N' is at -1 + 4 = 3. Since the x-coordinate of M is at -2, which is 1 unit to the left of from the line of reflection, the x-coordinate of M' is at -1 + 1 = 0. Since the x-coordinate of O is at -3, which is 2 units to the left of the line of reflection, the x-coordinate of O' is at -1 + 2 = 1. So the vertices of N'M'O' are at (3, 2), (0, 1), and (1, 3).

Answer:

The approximated measure of this angle is 90°, so this may be a right angle.

Place a sheet of paper so that the corner corresponds to the angle. You will notice that the lines will closely align with the edges of the paper.

Cos 165 in terms of sine and cosine of acute angle would give cos(165) = -(1 + √3) / (2√2).

To find the cosine of 165 degrees in terms of sine and cosine of an acute angle, we can use the cosine angle addition formula:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

Since 120 degrees is in the second quadrant, the cosine is negative, and the sine is positive:

cos(120) = -cos(60) and sin(120) = sin(60)

cos(165) = -cos(60)cos(45) - sin(60)sin(45)

Now we can plug in the values of the trigonometric functions:

cos(165) = - (1/2) x (1/√2) - (√3/2) x (1/√2)

cos(165) = -(1 + √3) / (2√2)

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The quotient of the division 10x² + 3x - 77 ÷ 2x + 7 is 5x - 16

The quotient expression is given as

10x² + 3x - 77 ÷ 2x + 7

The long division expression is represented as

2x + 7 | 10x² + 3x - 77

So, we have the following division process

            5x - 16

2x + 7 | 10x² + 3x - 77

            10x²  + 35x

          --------------------------------

             -32x - 77

             -32x - 112

          -------------------------------------

                      35

Hence, the quotient of the long division is 5x - 16

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Answer:

The value of 1/4 (-4^3+10^2) is 9

Answer:

Step-by-step explanation:

In this set,

the maximum is 35

the minimum is 6

So, we can cross out options A, B

the median is 14

The only option that works for this set is option D

According to the information, the customer would save $492 in the first year by switching to Intellivision; the customer would save $207 in the second year by using Intellivision; ElectroniSource would be cheaper in the third year.

a. To calculate the annual cost for ElectroniSource: $42/month for phone service x 12 months = $504/year, $35/month for internet service x 12 months = $420/year, and $59/month for cable television x 12 months = $708/year.

So the total annual cost with ElectroniSource would be $504 + $420 + $708 = $1,632.

With Intellivision, the flat monthly fee for all three services is $95, so the total annual cost would be $95 x 12 months = $1,140.

Therefore, the customer would save $1,632 - $1,140 = $492 in the first year by switching to Intellivision.

b. After the first year, Intellivision raises the rates by 25%, so the new monthly fee would be $95 x 1.25 = $118.75.

The total annual cost in the second year would be $118.75 x 12 months = $1,425.

Using the same services, the annual cost with ElectroniSource would still be $1,632.

Therefore, the customer would save $1,632 - $1,425 = $207 in the second year by using Intellivision.

c. If Intellivision raises the rates by 16% in the third year compared to the second year, the new monthly fee would be $118.75 x 1.16 = $137.95.

The total annual cost in the third year would be $137.95 x 12 months = $1,655.4.

The annual cost with ElectroniSource would still be $1,632.

Therefore, ElectroniSource would be cheaper in the third year.

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The 9th girl ate 51 candies.

Let the number of candies eaten by the 9th girl be x.

The average number of candies eaten by 8 girls is given as (210/x+210)/8, which simplifies to 210/8 + x/8.

After the 9th girl eats x candies, the total number of candies eaten becomes 210 + x.

The new average is given as (210 + x)/9 = 29.

Solving for x, we get:

210 + x = 261

x = 51

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The correct answer is option B, a reflection over the y-axis followed by a translation of (1,y) → (1, y-6).

To solve this problem, we need to find the sequence of rigid motions (i.e., transformations that preserve distance and angle) that maps quadrilateral ABCD to quadrilateral EFGH.

First, we need to identify the corresponding vertices of the two quadrilaterals. Let's assume that vertex A maps to vertex E, vertex B maps to vertex F, vertex C maps to vertex G, and vertex D maps to vertex H.

Now, we can apply different transformations to map each vertex of quadrilateral ABCD to the corresponding vertex of quadrilateral EFGH. We can try each option provided and check if it maps all the vertices correctly.

Option A involves a reflection over the x-axis, followed by a translation of (0,y) → (0, y - 4). This transformation does not map vertex A to vertex E correctly.

Option B involves a reflection over the y-axis, followed by a translation of (1,y) → (1, y - 6). This transformation maps vertex A to vertex E, vertex B to vertex F, vertex C to vertex G, and vertex D to vertex H, which is the correct mapping.

Option C involves a translation of (+,y) → (2, y - 3) followed by a reflection over the y-axis. This transformation does not map vertex A to vertex E correctly.

Option D involves a translation of (1-6, y) followed by a reflection over the x-axis. This transformation does not map vertex A to vertex E correctly.

Therefore, the unique sequence of rigid motions that maps quadrilateral ABCD to quadrilateral EFGH is a reflection over the y-axis followed by a translation of (1,y) → (1, y-6), which is option B.

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Pen demand decrease reduces pen price, quantity supplied; increases pencil demand, price, and quantity supplied as a substitute.

If the demand for ink pens falls, this would likely result in a decrease in the demand for pens and an increase in the demand for pencils, since they are substitutes.

As a result, the price of pens would likely fall, as producers try to entice buyers to purchase pens over pencils. This decrease in the price of pens would, in turn, lead to a decrease in the quantity supplied of pens, as producers shift their focus to producing other goods that are more in demand.

However, the quantity demanded of pencils would increase, leading to an increase in the price of pencils and an increase in the quantity supplied of pencils. Ultimately, the market for ink pens and pencils would adjust to reflect the changes in demand, resulting in changes in both price and quantity.

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To calculate the volume of the moon, we can use the formula V = (4/3)πr^3, where r is the radius of the moon.

Given that the radius of the moon is about 1.738 mega meters (or 1,738,000 meters), we can substitute this value into the formula and simplify as follows: V = (4/3) × 3.14 × (1.738 × 10^6)^3 V ≈ 2.196 × 10^19 cubic meters Therefore, approximately, the volume of the moon is 2.196 × 10^19 cubic meters.

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When a number is chosen from set x, there is a 0.2 chance that the chosen number will also be found in sets y and z. The answer is option (B). 0.2.

The ratio of favourable outcomes to all possible outcomes of an event is known as the probability. The symbol x can be used to express the quantity of successful outcomes for a study with 'n' outcomes. The probability formula determines the likelihood that an event will occur.

It is the ratio of effective results to all effective results. The study of probability is a branch of mathematics that examines the likelihood that an event will occur. Probability, which expresses the likelihood that an event will occur, is calculated by dividing the total number of occurrences by the total number of positive events.

The number of elements of Both Y and Z answer is 5 and 25.

The probability of selecting a number from x that is an element of y and z

Intersection of y and z is (5, 25)

No.of elements in x is = 2/10

= 1/5

= 0.2

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