Shown in the picture below are three concentric (having the same
center) circles. Let's name them small, larger and largest. You are
blindfolded and throwing a dart at the target. What is the probability
that the dart will hit the white area inside the circles? The white area
is formed by the small circle and by the area between the larger and
largest circles that looks like a ring. Assume that the dart you throw,
will hit somewhere inside the largest circle,
Enter your answer as a decimal.

Shown In The Picture Below Are Three Concentric (having The Samecenter) Circles. Let's Name Them Small,

Answers

Answer 1

Answer:

The probability that the dart will hit the white area is 16/25

Step-by-step explanation:

The given circle is composed of three concentric circles as follows;

Small circle with radius, r₁ = 1

Larger circle with radius, r₂ = 3

Largest circle with radius, r₃ = 5

The area of the small circle = π × r₁² = π

The area of the larger circle = π × r₂² = π × 3² = 9·π

The area of the largest circle = π × r₃² = π × 5² = 25·π = The total target area

The total white area = The total target area - The area of the larger circle

The total white area = 25·π - 9·π = 16·π

The probability of hitting the white area = 16·π/25·π = 16/25

Therefore, the probability that the dart will hit the white area = 16/25.


Related Questions

the number which best completes the sequence below is: 3 9 4 5 25 20 21 441 ?

Answers

The number that best completes the sequence is 194,481

How to determine the number which best completes the sequence

To find the number that best completes the sequence, let's analyze the pattern:

Looking at the sequence, it appears that every alternate number is the result of squaring the previous number.

3^2 = 9

4^2 = 16

5^2 = 25

20^2 = 400

21^2 = 441

So, based on this pattern, the next number in the sequence would be:

441^2 = 194,481.

Therefore, the number that best completes the sequence is 194,481.

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What is the value of x in the equation 3x – 1/9 = 18, when y = 27?

Answers

Answer:

Here you go mate!

Step-by-step explanation:

What is the value of x in the equation 3x 1/9 = 18, when y = 27?

Answer:

x = 7

Step-by-step explanation:

3x - 1/9y = 18

Put y as 27 and evaluate.

3x - 27/9 = 18

3x - 3 = 18

Add 3 on both sides.

3x = 21

Divide 3 on both sides.

x = 7

Plzs help I give u BRAINLIST

Plzs help I give u BRAINLIST

Answers

Answer:

$30,170.36

Step-by-step explanation:

I'm good at math, and I double checked with someone... I am perfectly sure that $30,170.36 is the answer.

If the scale factor of a dilation is 8: 7, what kind of image does it create?

If the scale factor of a dilation is 8: 7, what kind of image does it create?

Answers

A dilation with a scale factor of 8:7 creates an image that is eight times larger than the original.

What is scale factor?

A scale factor is a numerical value which is used to multiply or divide a given measurement. It is used to compare the sizes of two different objects, or to enlarge or reduce the size of an object. The scale factor can be used to calculate the area, perimeter, and volume of an object. For example, if an object is enlarged by a scale factor of 2, its area will increase by a factor of 4. Similarly, if an object is reduced by a scale factor of 0.5, its area will be reduced by a factor of 0.25.

This means that all of the points in the original image are moved away from the center of the dilation by a factor of eight. This creates an image that is eight times wider and seven times taller than the original. This type of dilation is also known as an enlargement. By enlarging the image, it is possible to see more detail and make the image easier to see. Additionally, it may also be possible to see features that were previously too small to be seen.

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is it possible for two processors that share the same bus to repeatedly invalidate each other’s data even though they do not share any variable?

Answers

Yes, it is possible for two processors that share the same bus to repeatedly invalidate each other’s data even though they do not share any variable.

This can happen due to the inherent characteristics of cache coherence protocols used in modern multiprocessor systems. Cache coherence is a mechanism used to ensure that data stored in the caches of different processors is consistent with the data stored in memory.

To achieve cache coherence, processors must communicate with each other through a shared bus or other interconnect and follow a set of rules that govern how data is updated and invalidated.

One of the most commonly used cache coherence protocols is the MESI protocol, which stands for Modified, Exclusive, Shared, and Invalid. In the MESI protocol, each cache line can be in one of four states:

1. Modified: The cache line is dirty (i.e., has been modified), and no other processor has a copy of the same data.
2. Exclusive: The cache line is clean (i.e., has not been modified), and no other processor has a copy of the same data.
3. Shared: The cache line is clean, and one or more other processors have a copy of the same data.
4. Invalid: The cache line is not valid, and cannot be accessed until it is fetched from memory or updated by another processor.

When a processor wants to access a cache line, it first checks the MESI state of the line to determine if it needs to be fetched from memory, updated, or invalidated. If the cache line is in the Modified or Exclusive state, the processor can read or write to it without any interference from other processors.

However, if the cache line is in the Shared state, the processor must first gain ownership of the line by requesting it from the other processors.

During this process, the other processors may invalidate their copies of the cache line, even if they do not share any variables with the requesting processor.

This is because the MESI protocol is designed to ensure that the data stored in the caches of all processors is consistent with the data stored in memory. If one processor modifies a cache line, all other processors that have a copy of the same line must invalidate their copies to prevent the modified data from being used.

In summary, two processors that share the same bus can repeatedly invalidate each other’s data even though they do not share any variable because of the inherent characteristics of cache coherence protocols used in modern multiprocessor systems.

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Solve each system of equations.
1. 3x + y = 7; 5x +3y = -25
2. 2x + y = 5; 3x - 3y = 3
3. 2x + 3y = -3; x + 2y = 2
4. 2x - y = 7; 6x - 3y = 14
5. 4x - y = 6; 2x -y/2 = 4

Answers

The solution to the system of equations is x = 11.5 and y = -27.5.

The solution to the system of equations is x = 2 and y = 1

The solution to the system of equations is x = -12 and y = 7.

The solution to the system of equations is x = 0.5 and y = -6.

What is Equation?

A system of linear equations can be solved graphically, by substitution, by elimination, and by the use of matrices.

To solve the system of equations:

3x + y = 7

5x + 3y = -25

We can use the method of substitution or elimination to find the values of x and y.

Let's solve it using the method of substitution:

From the first equation, we can express y in terms of x:

y = 7 - 3x

Substitute this expression for y into the second equation:

5x + 3(7 - 3x) = -25

Simplify and solve for x:

5x + 21 - 9x = -25

-4x + 21 = -25

-4x = -25 - 21

-4x = -46

x = -46 / -4

x = 11.5

Substitute the value of x back into the first equation to find y:

3(11.5) + y = 7

34.5 + y = 7

y = 7 - 34.5

y = -27.5

Therefore, the solution to the system of equations is x = 11.5 and y = -27.5.

To solve the system of equations:

2x + y = 5

3x - 3y = 3

Again, we can use the method of substitution or elimination.

Let's solve it using the method of elimination:

Multiply the first equation by 3 and the second equation by 2 to eliminate the y term:

6x + 3y = 15

6x - 6y = 6

Subtract the second equation from the first equation:

(6x + 3y) - (6x - 6y) = 15 - 6

6x + 3y - 6x + 6y = 9

9y = 9

y = 1

Substitute the value of y back into the first equation to find x:

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 2

Therefore, the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations:

2x + 3y = -3

x + 2y = 2

We can again use the method of substitution or elimination.

Let's solve it using the method of substitution:

From the second equation, we can express x in terms of y:

x = 2 - 2y

Substitute this expression for x into the first equation:

2(2 - 2y) + 3y = -3

Simplify and solve for y:

4 - 4y + 3y = -3

-y = -3 - 4

-y = -7

y = 7

Substitute the value of y back into the second equation to find x:

x + 2(7) = 2

x + 14 = 2

x = 2 - 14

x = -12

Therefore, the solution to the system of equations is x = -12 and y = 7.

To solve the system of equations:

2x - y = 7

6x - 3y = 14

Again, we can use the method of substitution or elimination.

Let's solve it using the method of elimination:

Multiply the first equation by 3 to eliminate the y term:

6x - 3y = 21

Subtract the second equation from the first equation:

(6x - 3y) - (6x - 3y) = 21 - 14

0 = 7

The resulting equation is 0 = 7, which is not possible.

Therefore, there is no solution to the system of equations. The two equations are inconsistent and do not intersect.

To solve the system of equations:

4x - y = 6

2x - y/2 = 4

We can use the method of substitution or elimination.

Let's solve it using the method of substitution:

From the second equation, we can express y in terms of x:

y = 8x - 8

Substitute this expression for y into the first equation:

4x - (8x - 8) = 6

Simplify and solve for x:

4x - 8x + 8 = 6

-4x + 8 = 6

-4x = 6 - 8

-4x = -2

x = -2 / -4

x = 0.5

Substitute the value of x back into the second equation to find y:

2(0.5) - y/2 = 4

1 - y/2 = 4

-y/2 = 4 - 1

-y/2 = 3

-y = 6

y = -6

Therefore, the solution to the system of equations is x = 0.5 and y = -6.

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Samantha watched 5 seasons of her favorite show over the winter break.


Each season contained 18 episodes.


1. How many total episodes did Samantha watch of her favorite show?


2. If Samantha's favorite show has 9 seasons, what is the percentage of the entire series


(show) she has already watched? (rounded to the nearest whole percent)

Answers

Samantha watched a total of 90 episodes of her favorite show during the winter break. Each season had 18 episodes, and she watched 5 seasons in total.

To calculate the total number of episodes, we multiply the number of episodes per season (18) by the number of seasons Samantha watched (5). Therefore, 18 episodes/season * 5 seasons = 90 episodes.

If Samantha's favorite show has 9 seasons in total, she has already watched 55.6% of the entire series. To find the percentage, we divide the number of seasons she has watched (5) by the total number of seasons (9) and multiply by 100. So, 5 seasons/9 seasons * 100 = 55.6%. Rounded to the nearest whole percent, Samantha has watched approximately 56% of the entire series.

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what are all the possible factors of the quadratic term for x2 10x − 24?

Answers

Answer:

The factors are,

x + 12 and x - 2

Step-by-step explanation:

x^2 + 10x - 24,

Here, we note that,

12 - 2 = 10,

and (12)(-2) = 24,

so, we  can re-write 10x as 10x = 12x - 2x

so,

\(x^2 + 12x - 2x - 24 = 0\)

Taking x common from the 1st two terms (x^2 and 12x),

and taking -2 common from the last two tems (-2x and -24), we get,

\(x^2 + 12x - 2x - 24 \\x(x+12)-2(x+12)\\taking \ (x+12) \ common,we \ get,\\(x+12)(x-2)\)

So, The factors are,

x + 12 and x - 2

there is a high school with 400 students, of which 120 are male and 280 are female. of the males, 60% are currently enrolled in a mathematics course. of the females, 80% are currently enrolled in a mathematics course. what is the probability that a randomly selected student is a female who is enrolled in a mathematics course?

Answers


The probability that a randomly selected student is a female who is enrolled in a mathematics course is 0.64.


The number of males who are currently enrolled in a mathematics course is: 120 x 60/100 = 72 students.

The number of females who are currently enrolled in a mathematics course is: 280 x 80/100 = 224 students.

Therefore, the total number of students currently enrolled in a mathematics course is: 72 + 224 = 296 students.

Thus, the probability that a randomly selected student is a female who is enrolled in a mathematics course is: Probability= Number of female students enrolled in mathematics/Total number of students= 224/400= 0.64.

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Which is the lower temperature? (Assume temperatures to be exact numbers.) (a) 273

C or 273

F ? 273

C 273∘F They are the same temperature. (b) 200

C or 353

F ? 200

C 353

F They are the same temperature.

Answers

The lower temperature is 200∘C for (a) and 353∘F for (b). In order to determine the lower temperature between two measurements given in different temperature scales, we need to convert them to a common scale.

The common scale we can use is the Kelvin scale, as it is an absolute temperature scale.

(a) To compare 273∘C and 273∘F, we need to convert them to Kelvin. The conversion formula for Celsius to Kelvin is K = C + 273.15, and for Fahrenheit to Kelvin, K = (F - 32) × 5/9 + 273.15.

- For 273∘C, we have K = 273 + 273.15 = 546.15K.

- For 273∘F, we have K = (273 - 32) × 5/9 + 273.15 ≈ 523.15K.

Since 523.15K is lower than 546.15K, the lower temperature is 273∘F.

(b) To compare 200∘C and 353∘F:

- For 200∘C, we have K = 200 + 273.15 = 473.15K.

- For 353∘F, we have K = (353 - 32) × 5/9 + 273.15 ≈ 423.15K.

Since 423.15K is lower than 473.15K, the lower temperature is 353∘F.

In summary, the lower temperature is 200∘C for (a) and 353∘F for (b).

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Assigned Media
Skill Builder
X 2.4.75
The telephone company offers two billing plans for local calls. Plan 1 charges $36 per month for unlimited calls and Plan 2 charges $17 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2
b. Explain the meaning of the answer to part a.

Answers

Answer: a. 36-17 <0.04x ⇒ 475 < x

b. When the number of calls is higher than 475 , Plan 1 is more economical than Plan 2.

Step-by-step explanation:

Hi, to answer this question we have to write an inequality:

The cost of plan 1 (36) must be less (<) than the cost of plan 2 (fixed charge [17] plus the product of the charge per call [0.04] and the number of calls [x] )

a.36 < 17+ 0.04x

Solving for x

36-17 <0.04x

19 < 0.04x

19 /0.04 <x

475 < x

b. When the number of calls is higher than 475 , Plan 1 is more economical than Plan 2.

which division problem does the model below show?

4 fraction bars. The fraction bars are labeled 1 and each have 6 boxes underneath labeled one-sixth.

4 divided by one-sixth = 24
4 divided by one-sixth = 12
24 divided by one-sixth = 4
12 divided by one-sixth = 4


I searched and none was right. :/ Please help im timed.

Answers

The model "4 fraction bars. The fraction bars are labeled 1 and each have 6 boxes underneath labeled one-sixth" shows 4 divided by one-sixth = 24

The correct answer option is option A

How to use division problem to represent a model?

Given:

4 fraction bars

If each fraction bars has 6 boxes, then, the total boxes for 4 fraction bars can be solved using ratio

1 fraction bars : 6 boxes

4 fraction bars : x

Equate the ratios

1 : 6 = 4 : x

1/6 = 4/x

cross product

1 × x = 4 × 6

x = 4 × 6/1

Divide by the reciprocal of 6/1

x = 4 ÷ 1/6

Hence the division problem that modelled the expression is 4 ÷ 1/6

4÷1/6 = 4×6/1

4÷1/6 = 24

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please help!!!!!!!!!!!!!!!!!!!!

please help!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

d

Step-by-step explanation: it is that answer because (r+s)t=rt+st is you r answer i did it and i got it correct please mark me as brainlist

No Cap I can't see the picture at all ! i'm so sorryI'll edit this if you tell me what this says!God Bless!Stay In school!

Alan, Bobby and Chris are comparing their ages. The ratio of Alan's age to
Bobby's is 7: 8 and the ratio of Bobby's to Chris' is 5: 4. If Alan is 70, how
old is Chris?​

Answers

Answer:

1638392772127273930337733930282823829393

Please help with solution needed!!

Please help with solution needed!!

Answers

Step-by-step explanation:

you know how to multiply two expressions ?

every term of every expression is multiplied with every term of the other expression and the results are added (while considering any specific signs, if course).

(2x² + 3)(2x² - 3) = 2x²×2x² + -3×2x² + 3×2x² + 3×-3 =

4x² - 6x² + 6x² - 9 = 4x² - 9

and that is exactly the right side of the original equation.

so, it is correct.

45% of $80=$___

Pls help

Answers

Answer:

$36

Step-by-step explanation:

.45 × 80 = 36

or

45/100 × 80 = 36

Answer:

$ 36

Step-by-step explanation:

hope it helps !

......

A hypothesis test is to be performed for a population mean. Which of the following does the probability of a type II error not depend on?
options:
The significance level
The sample mean
The sample size
The true (population) mean

Answers

When a thesis test is being performed for a population mean, the probability of a type II error isn't dependent on the sample mean. Option B is the right answer.

A type II error occurs when a null thesis isn't rejected despite it being incorrect. It's worth noting that the threat of making a type II error is affected by several factors, including the sample size, the true population mean, the position of significance, and the variability of the data.

As a result, the larger the sample size, the lower the threat of making a type IIerror.The true population mean also has an impact on the liability of a type II error. As the difference between the true mean and the hypothecated mean grows, the threat of a type II error decreases.

The position of significance is also pivotal in determining the threat of a type II error. As the significance position increases, the threat of a type II error decreases.

So, the correct answer is B

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see photo above to anwser

see photo above to anwser

Answers

Answer:

i can see

Step-by-step explanation:

UKDIAMOND is a great place for the people of sentence to get it 4out in a sense that you are a very

Answer:

b = 99°

Step-by-step explanation:

XY is a line segment and so it is a straight line which means that it is a straight angle - 180°

a = 28°

c = 53°

b = ?

=> a + b + c = 180°

=> 28° + b + 53° = 180°

=> b = 180° - (53 + 28)°

=> b = 180° - 81°

=> b = 99°

Therefore b = 99°

Hope it helps :)

Pretest: Unit 3
Question 15 of 70
Which object is a point?
A.
B..
C.
D.

Pretest: Unit 3Question 15 of 70Which object is a point?A.B..C.D.

Answers

Answer:

B

Step-by-step explanation:

B is a point, the other choices have two points.

What score would a student need to have a 30th percentile score on the SAT? Recall that the mean score was 1509, and the standard deviation of the scores is 312. Group of answer choices A. 1244 B. 1345 C. 1456 D. 1673

Answers

The score a student would need to have a 30th percentile score on the SAT is approximately 1345. Option B is correct.

To find the score that corresponds to the 30th percentile, we need to use a z-table to determine the z-score that corresponds to a cumulative probability of 0.30.

Using the formula for converting a raw score to a z-score:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and the σ is the standard deviation.

Rearranging this formula to solve for x:

x = z × σ + μ

To find the z-score for a 30th percentile, we can look up the corresponding value in a z-table or use a calculator with a built-in normal distribution function. The z-score corresponding to a cumulative probability of 0.30 is approximately -0.52.

Substituting the known values into the formula above:

x = -0.52 × 312 + 1509

Simplifying:

x ≈ 1345

Hence, B. 1345 is the correct answer.

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Help me please! can someone summarize it please?





i
need a short summarize about it
Delaunay says that the knowledge of how head and neck cancer metastasize could help in devising the means to confine cancerous cells to primary tumors and thus make them more treatable. "Understanding

Answers

Delaunay suggests that gaining knowledge about the metastasis of head and neck cancer could aid in devising strategies to confine cancerous cells to primary tumors, thereby enhancing their treatability and providing potential avenues for targeted therapeutic interventions.

Delaunay says that the knowledge of how head and neck cancer metastasize could help in devising the means to confine cancerous cells to primary tumors and thus make them more treatable. "Understanding the mechanisms of metastasis in head and neck cancer could provide valuable insights for developing strategies to restrict the spread of cancer cells to primary tumors, ultimately enhancing their treatability," Delaunay states.

This understanding would allow researchers and clinicians to target specific steps or pathways involved in metastasis, potentially leading to the development of novel therapeutic approaches to halt or limit the spread of cancer cells beyond the primary site. By confining the cancerous cells to the initial tumor, treatment options could become more effective and focused, improving patient outcomes in head and neck cancer cases.

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Can sum1 help me plot the point 1/4, -2 1/4, 1 1/2?

Answers

Answer:

I do not have a graph rn but I hope I helped

Step-by-step explanation:

well, yo just have to find 0.25 on the graph, mark it then do the same for -5.25 and 5.5

what is the midpoint between (-4,4) and (-2,2)​

Answers

Answer:

(-3,3)

hoped this helped let me know if it did

what is the midpoint between (-4,4) and (-2,2)

The ratio of the amount of money Karen had to the amount of money Peter had was 2 : 5. After Peter received $75 from his mother, the ratio of the amount of money Karen had to the amount of money Peter had became 4 : 15. How much money did each person have at first?

Answers

Answer:

$60 and $150

Step-by-step explanation:

Initially

Karen : Peter = 2 : 5

After Peter receiving $75 the ratio is

4 : 15

We can suppose that initally the amount of monye Karen has is 2x and Peter is 5x.

The new ratio is

2x :  (5x +75)  = 4 :15

2x (15)= 4 (5x +75)

30 x = 20 x + 300

10 x = 300

x = 30

So at first Karen has 2x =60 dollars while Peter has 5x = 5(3) = 150 dollars.

Find the Unit Price for each bottle of conditioner. Which bottle of hair conditioner is the best buy?
8 oz for $1.49

12 oz for $2.29

15 oz for $2.75

20 oz for $3.89

Answers

Answer:

D.

Step-by-step explanation:

We know that to find unit price, we divide the unit in the numerator by the quantity in the denominator.

For the first option, we must put $1.49 as the numerator and 8 as the denominator. It will then look like this:

\(\frac{1.49 / 8 }{8 / 8\\}\) Then we must divide 1.49 by 8. This will get us $0.18625.

For our second option, we must put $2.29 as the numerator, and 12 as the denominator. It will look like this:

\(\frac{2.29 / 12 }{12 / 12\\}\) Then we must divide 2.29 by 12. This will get us $0.19083 (rounded)

For our third option, we must put $2.75 as the numerator, and 15 as the denominator. It will look like this:

\(\frac{2.75 / 15 }{15 / 15}\)Then we must divide 2.75 by 15. This will get us $\(0.18333\) (rounded)

For our final option, we must put $3.89 as the numerator, and 20 as the denominator. It will look like this:

\(\frac{3.89 / 20 }{3.89 / 20}\)Then we must divide 3.89 by 20. This will get us $0.1945 (rounded)

Therefore, the last option is the best buy because $0.18625 > $0.18333.

27.90 rounded to the nearest hundreth

Answers

Answer:27.9

Step-by-step explanation:

If the digit after hundredth is greater than or equal to 5, add 1 to hundredth. Else remove the digit. Example

124.586

The third digit of right of decimal point is 6

The second digit after decimal point is 8 which is greater than 5

So add 1 to 8

Result = 124.59

hey i need help solving a Krypto
numbers: 13, 16, 23, 1, 3 equals: 20
thanks in advanced :)

Answers

Theres four solutions which you wont find with most Krypto solvers since it uses .333 repeating.

The solutions are:

16 / 3 = 5.3333333333333

5.3333333333333 - 1 = 4.3333333333333

13 / 4.3333333333333 = 3

23 - 3 = 20

13 / 3 = 4.3333333333333

4.3333333333333 + 1 = 5.3333333333333

16 / 5.3333333333333 = 3

23 - 3 = 20

23 / 3 = 7.6666666666667

7.6666666666667 - 1 = 6.6666666666667

16 - 13 = 3

6.6666666666667 x 3 = 20

16 - 13 = 3

23 / 3 = 7.6666666666667

7.6666666666667 - 1 = 6.6666666666667

6.6666666666667 x 3 = 20

what is the constant of posprtainality in the equation y=0.41

Answers

Answer:

The constant of proportionality in the equation y=0.41 is 0.41

Step-by-step explanation:

Find one solution for the equation. Assume that all angles involved are acute angles. tan(2B−29

)=cot(4B+5

) B= (Simplify your answer.) Find one solution for the equation. Assume that all angles involved are acute angles. sin(θ−40

)=cos(3θ+10

) θ= (Simplify your answer.)

Answers

The angles involved are acute angles, which means that 3θ+10° < 90°. Using the identity that sin x = cos (90°-x), we can write: sin(θ-40°) = cos(80°-3θ)θ-40° = 80°-3θ4θ = 120°θ = 30°.Therefore, θ = 30°.

tan(2B-29°) = cot(4B+5°)B = 42°We need to find the value of B.

We can do this by using the identity that says tan x = cot (90°-x).

Let's start by substituting the angles into the equation.

tan(2B-29°) = cot(4B+5°)tan(2B-29°) = tan(90°- (4B+5°))

The angles involved are acute angles, which means that 4B+5° < 90°. Using the identity that tan x = cot (90°-x), we can write:

tan(2B-29°)

= tan(85°-4B)2B - 29°

= 85° - 4B6B = 114°B

= 19°.

Therefore, B = 19°.2. sin(θ-40°) = cos(3θ+10°)We need to find the value of θ.

We can use the identity sin x = cos (90°-x) to solve this equation.

Let's begin by substituting the angles into the equation.

sin(θ-40°) = cos(3θ+10°)sin(θ-40°) = sin(90°- (3θ+10°))

The angles involved are acute angles, which means that 3θ+10° < 90°.

Using the identity that sin x = cos (90°-x), we can write: sin(θ-40°) = cos(80°-3θ)θ-40° = 80°-3θ4θ = 120°θ = 30°.Therefore, θ = 30°.

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1. how do you know when solving a problem that involves decimals requires addition? subtraction? multiplication? division? give examples. 2. describe a strategy that you use when estimating with decimals. explain why it is helpful to you. give examples.

Answers

To determine which operation to use when solving problems involving decimals, we must consider the means context of the problem.

Let us examine each operation and when it can be used:Addition: Used when we are asked to combine two or more numbers.Subtraction: Used when we need to find the difference between two or more numbers.

If we are asked to calculate the total cost of two items priced at $1.99

$3.50,

we would use addition to find the total cost of both items. 2. Strategy used when estimating with decimals:When estimating with decimals, rounding is a common strategy used. In this method, we find a number close to the decimal and round the number to make computation easier

.Example: If we are asked to estimate the total cost of

3.75 + 4.25

, we can round up 3.75 to 4

and 4.25 to 4.5.

By doing so, we get a total of 8.5.

Although this is not the exact answer, it is close enough to help us check our work.

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1. When solving a problem that involves decimals, the operations of addition, subtraction, multiplication, or division may be required based on the specific situation. 2. When estimating with decimals, rounding can be a helpful strategy to simplify calculations and get a rough estimate.

1. When solving a problem that involves decimals, the operations of addition, subtraction, multiplication, or division may be required based on the specific situation. Here are some guidelines to help you determine which operation to use:

- Addition: Addition is used when you need to combine two or more decimal numbers to find a total. For example, if you want to find the sum of 3.5 and 1.2, you would add them together: 3.5 + 1.2 = 4.7.

- Subtraction: Subtraction is used when you need to find the difference between two decimal numbers. For instance, if you have 5.7 and you subtract 2.3, you would calculate: 5.7 - 2.3 = 3.4.

- Multiplication: Multiplication is used when you need to find the product of two decimal numbers. For example, if you want to find the area of a rectangle with a length of 2.5 and a width of 3.2, you would multiply them: 2.5 x 3.2 = 8.0.

- Division: Division is used when you need to divide a decimal number by another decimal number. For instance, if you have 6.4 and you divide it by 2, you would calculate: 6.4 ÷ 2 = 3.2.

2. When estimating with decimals, a helpful strategy is to round the decimal numbers to a certain place value that makes sense in the context of the problem. This allows you to work with simpler numbers while still getting a reasonably accurate estimate. Here's an example:

Let's say you need to estimate the total cost of buying 3.75 pounds of bananas at $1.25 per pound. To estimate, you could round 3.75 to 4 and $1.25 to $1. Then, you can easily calculate the estimate by multiplying: 4 x $1 = $4. This estimate helps you quickly get an idea of the total cost without dealing with the exact decimals.

This strategy is helpful because it simplifies calculations and gives you a rough idea of the answer. It can be especially useful when working with complex decimals or when you need to make quick estimates. However, it's important to remember that the estimate may not be precise, so it's always a good idea to double-check with the actual calculations if accuracy is required.

In summary, when solving problems with decimals, determine which operation to use based on the situation, and when estimating with decimals, rounding can be a helpful strategy to simplify calculations and get a rough estimate.

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