Kelly purchased 6 equally-priced CDs for a total of $75.30 what is the cost per CD?

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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The number of subjects that Paige would study D. 2 subjects.

It should be noted that Paige would study for one hour. She spends 1/2 an hour, or 30 minutes, on a subject.

An hour is 60 minutes. If Paige studied 2 subjects, then she would of studied for 60 minutes.

30 + 30 = 60

So, if Paige spends 1/2 hour on Spanish, she would study 2 subjects to reach an hour.

Therefore, the correct option is D.

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Complete question

Paige spends 1 hour on her homework. She spends equal amounts of time on all subjects. If Paige spends 1/2 hour on Spanish, how many subjects does she study?

3 subjects

1 subject

4 subjects

2 subjects

Answer:

6,666

Step-by-step explanation:

A four-digit number: 1,234

All digits are the same: 1111, 2222, 3333...

Value in the hundreds place: 0,600

Answer: 6,666

Answer: Yes Sofia will have enough money

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

Explanation:

Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.

The area of the rectangle is 16*7 = 112 square meters.

The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be

sum of the exterior sides = perimeter

6+7+16+7+6+x = 54

42+x = 54

x = 54-42

x = 12

The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.

area of the trapezoid = 0.5*height*(base1+base2)

area = 0.5*5.66*(16+12)

area = 79.24 square meters

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

Recap so far

The total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.

Let's convert that to square decimeters.

Recall that 1 decimeter = 10 centimeters

Multiply both sides by 10

1 decimeter = 10 centimeters

10*(1 decimeter) = 10*(10 centimeters)

10 decimeters = 100 centimeters

10 decimeters = 1 meter

Then,

\(191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\\)

The entire lawn is 19124 square decimeters.

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

We have one final block of calculations to determine the total price.

x = number of rolls

1 roll covers 90 square decimeters

x rolls cover 90x square decimeters

90x = 19124

x = 19124/90

x = 212.489 approximately

Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).

In short, Sofia needs 213 rolls.

1 roll costs $4.50

213 rolls will cost 213*4.50 = 958.50 dollars.

This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).

Sofia will have enough money to pay for all of the grass.

Answer:

6237

Step-by-step explanation:

43659/7

Answer:

115.15 cm²

Step-by-step explanation:

The area of a trapezoid = 1/2 (b1 + b2)h

Where:

b1 = first base = 8.2 cm

b2 = Second base = 15.3 cm

h = height = 9.8 cm

Hence, Area of the trapezoid =

1/2 (8.2 + 15.3) × 9.8

= 1/2 × (23.5) × 9.8

= 115.15 cm²

Therefore, the area, in square centimeters, of the trapezoid below is 115.15 cm²

Answer:

196

Step-by-step explanation:

2 times 14 times 7=196

Hope this helps!

The graph of the derivative of a function provides information about the rate of change and the slope of the original function at different points.

To graph the derivative of a function given the graph of the function, you can follow these steps:

Start with the graph of the original function. Make sure you have a clear understanding of its shape and behavior.

Identify critical points on the graph of the function, which are the points where the function has maximum or minimum values or where its slope changes abruptly.

Use the information from the critical points to determine the intervals where the derivative is positive or negative. In the intervals where the function is increasing, the derivative will be positive, and in the intervals where the function is decreasing, the derivative will be negative.

Find any vertical asymptotes or discontinuities in the original function. These points will also affect the behavior of the derivative.

Plot the derivative on a separate graph, using the information from steps 3 and 4. On the derivative graph, mark positive values above the x-axis and negative values below the x-axis.

Indicate the critical points and any vertical asymptotes or discontinuities on the derivative graph.

Connect the points on the derivative graph smoothly, considering the behavior of the original function and the values of the derivative at different points.

By following these steps, you can create a graph of the derivative that provides information about the rate of change and the slope of the original function at different points. The derivative graph helps in understanding the increasing and decreasing behavior of the function and provides insights into its concavity and local extrema.

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Answer:

The air the sound travels through cools down.

Step-by-step explanation:

I guessed a different answer on a test but the test said this was the right answer.

C. The air the sound travels through cools down will  cause a sound wave to slow down

A wave of compression and rarefaction, by which sound is propagated in an elastic medium such as air is called a sound wave

Liquid and solid will be more denser than air . So, the sound wave travel faster in them as compared to air

hence , option A. The sound passes from air into a liquid and  D. The sound passes from air into a solid. are wrong options for slowing down the speed of sound wave

Heat is a from of kinetic energy , molecules at higher temperature have more energy and can vibrate faster and allow sound wave to travel more quickly , hence  B. The air the sound travels through warms up.  is wrong answer

correct answer is C. The air the sound travels through cools down will  cause a sound wave to slow down as speed of sound as for each 1 degree Celsius that temperature decreases, the speed of sound decreases by 0.6 m/s .

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The required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line is called a parabola.

Given that, a parabola has the directrix x=6 and the focus (3,-5), we need to find the equation of the parabola,

The standard form of a left-right parabola is given as:

4p(x-h) = (y-k)²

Focus = (p+h, k)

Therefore,

h+p = 3....(i)

Directrix =

x = h-p

h-p = 6...(ii)

Solving the equations we get,

h = 9/2

p = -3/2

Substitute into the standard form:

4p(x-h) = (y-k)²

4(-3/2)(x-9/2) = (y+5)²

-6(x-9/2) = (y+5)²

\(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

Hence, the required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

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The question is incomplete so, i solved for the attached question

Answer:

The answer is "Option A".

Step-by-step explanation:

In this question except for choice "A", all the value is not nearest about the hundred or thousand, that why the correct answer is "1,049".

Answer:

1st:Arthmetic Sequence ,2nd:Geometric Sequence

Step-by-step explanation:

-9,-15,-21,-27

+6

48,24,12,6

half of 2 or divided by 2

The exponent expression that is used to express 75 as sum of the powers of 8 is \(8^0+8^1+8^2+8^\frac{1}{3}\).

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The integer 75 is written as -

\(2^0+2^1+2^2+2^6\)

75 is expressed as sum of the powers of 2, with whole number exponents.

To find 75 expressed as sum of the powers of 8, divide the integer by 8 -

\(8^0=1\)

\(8^1=8\)

\(8^2=64\)

Only one integer 2 is left to complete the sum as 75.

To find what the power value is use the equation -

\(8^x=2\\x=\frac{2}{8} \\x=\frac{1}{3}\)

So, the last exponent is \(8^{\frac{1}3} }\).

So the expression is \(8^0+8^1+8^2+8^\frac{1}{3} =75\).

Therefore, the exponent expression is \(8^0+8^1+8^2+8^\frac{1}{3}\).

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50 dozen donuts should be produced before your average cost per dozen drops to $2.45

Let x be the number of dozen donuts produced.

The total cost to produce x dozen donuts is:

Total cost = cost of raw materials + overhead costs

Total cost = 0.65x + 0.55x

Total cost = 1.20x

The average cost per dozen can be expressed as:

Average cost per dozen = Total cost / number of dozens

2.45 = 1.20x / x

To solve for x, we can cross-multiply and simplify:

2.45x = 1.20x

x = 50

Therefore, you must produce 50 dozen donuts before your average cost per dozen drops to $2.45.

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Answer: Multiply 102 by 8.82 = 899.64x

Step-by-step explanation:

The point (12, 5)

x = 12, y = 5

=> r =√12²+5² =√144+25= √169=13

so, cos θ = x/r = 12/13 and

cot θ = x/y = 12/5

Answer:

\(-\frac{2}{3} x\)

Step-by-step explanation:

Hey there!

To find slope, you take \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

In this case

y2: 6

y1: 4

x2: -3

x1: 0

Now we plug in this information

\(\frac{6-4}{-3-0} \\\\\frac{2}{-3} \\\\-\frac{2}{3}\)

Since this is the slope, you have to add a "x"

So, the slope is \(-\frac{2}{3} x\)

P(X < 4) = 0.8059

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

In which

P(X < 4) = 0.8059

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The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

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Answer:

B union C

Step-by-step explanation:

Hope it will help you

Answer:

b i guess

Step-by-step explanation:

Answer:

Definition of Midpoint

Step-by-step explanation:

C----------A---------T

it says that CA and AT are congruent so they are the exact same on both sides. And a midpoint has to be equal on both sides. And also they two points share the letter A which means it is in the middle. Get it midpoint.

Hope this helps!!

May I have brainliest!!

Answer:

x =6

Explanation:

To solve the system for x, substitute the value of y from the second equation into the first to get

adding 7 to both sides gives

Subtracting 2x from both sides gives

dividing both sides by 2 gives

which is our answer!

There are 24 different possible orders in which the four groups can present their projects. This is the entire sample space for this event.

To describe the entire sample space of this event, we need to list all the possible orders in which the four groups (A, B, C, and D) can present their projects. The sample space consists of all the possible outcomes for this event.

In probability theory, the sample space is the collection of all potential results of a random experiment. It forms the basis for the evaluation and computation of probability. It is frequently represented using a set or list of unique elements and might be finite or infinite. It makes it possible to investigate uncertainty and unpredictability mathematically.

Here is the sample space:
1. ABCD
2. ABDC
3. ACBD
4. ACDB
5. ADBC
6. ADCB
7. BACD
8. BADC
9. BCAD
10. BCDA
11. BDAC
12. BDCA
13. CABD
14. CADB
15. CBAD
16. CBDA
17. CDAB
18. CDBA
19. DABC
20. DACB
21. DBAC
22. DBCA
23. DCAB
24. DCBA

So, there are 24 different possible orders in which the four groups can present their projects. This is the entire sample space for this event.

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Answer:

Here is another case where we have two unknowns (the number of hours each mechanic worked) so we'll need two equations to solve.

Let A = number of hours first mechanic worked (the one who charged $45/hour)

Let B = number of hours second mechanic worked (the one who charged $105/hour)

From the problem statement, we know that the two mechanics worked a combined 35 hours so the first equation is:

Equation 1: A hours + B hours = 35 hours

We also know that in total, the charge was $2475.  So the second equation is:

Equation 2: (A hours x 45 dollars/hour) + (B hours x 105 dollars/hour) = 2475 dollars

So our two equations are:

1: A + B = 35

2: 45A + 105B = 2475

Multiply both sides of the first equation by -45 to get the following:

-45A - 45B = -1575

Now the two equations are:

1: -45A - 45B = -1575

2: 45A + 105B = 2475

Add them together and the "A" term drops out:

-45B + 105B = -1575 + 2475

or

60B = 900

Now divide both sides by 60:

B = 15

Now plug B = 15 into the first equation:

A + 15 = 35 thus A = 20

So Mechanic A (at $45/hour) worked 20 hours and Mechanic B (at $105/hour) worked 15 hours

Check: 20x45 + 15x105 = 900 + 1575 = 2475

Step-by-step explanation:

hope it helps you (:

\(\huge \bf༆ Answer ༄\)

For the given triangles to be congruent by SSS criterion, the sides HJ and LN should be equal ~

therefore correct choice is ~ C

\( \large \boxed{ \sf \: HJ \cong LN}\)

The additional information needed to prove that both triangles are congruent by the SSS Congruence Theorem would be: C. HJ ≅ LN

Recall:

Thus, in the two triangles given, the two triangles has:

Therefore, an additional information needed to prove that both triangles are congruent by the SSS Congruence Theorem would be: C. HJ ≅ LN

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P^12-2t^7-7r^2-1

p^10r

you just substracting

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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Answer:

..y d tu ideograma idiosincrasias

The probability that a defective component can be detected by only one inspector is 0.2112. the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

(a) To calculate the probability that a defective component will be detected by only one inspector, we can use the formula for conditional probability: P(detected by first inspector | not detected by second inspector) = P(detected by first inspector and not detected by second inspector) / P(not detected by second inspector).

The probability that a defective component will be detected by the first inspector and not detected by the second inspector can be calculated as follows: P(detected by first inspector and not detected by second inspector) = P(detected by first inspector) * P(not detected by second inspector | detected by first inspector) = 0.88 * (1 - 0.88) = 0.1056.

The probability that a defective component will not be detected by the second inspector is: P(not detected by second inspector) = 1 - P(detected by second inspector) = 1 - 0.88 = 0.12.

The probability that a defective component will be detected by exactly one of the two inspectors can be calculated as follows: P(detected by exactly one inspector) = P(detected by first inspector and not detected by second inspector) + P(detected by second inspector and not detected by first inspector) = 0.1056 + 0.1056 = 0.2112.

(b) To calculate the probability that all three defective components in a batch escape detection by both inspectors, we can use the formula for independent events: P(all three defective components escape detection) = P(first defective component escapes detection) * P(second defective component escapes detection) * P(third defective component escapes detection) = (1 - 0.88)^3 = 0.00178.

So the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

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Complete question : components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 88% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 24% of all defective components. what is the probability that the following occur? (a) A defective component will be detected only by the first inspector? A defective component will be detected by exactly one of the two inspectors? (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?