I need a little bit of help on this one..

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Answer:

option 3

Step-by-step explanation:

\(Formula : a^{-x} = \frac{1}{a^x}\)

\(3^7 \times 3^{-4} = 3^7 \times \frac{1}{3^4}\)

Step-by-step explanation:

\((a.y^{3} +3y^{2} -3 ) = (ay^{2} +(4a+3)y +4(4a+3))(y-4) +64a+45\)

so A = 64a +45

(\(2y^{3} -5y+a =(2y^{2} +8y +27)(y-4) +108 +a\)

so B = 108 +a

2A-B=0--> 2(64a+45)-108-a=0--> a =18/127

The dimensions of the model bed Kyra built are 0.8 ft × 1 ft.

To scale down the dimensions of her bed by a factor of 1/5, Kyra needs to multiply each dimension of the original bed by the scaling factor.

The original bed's dimensions are 4 ft × 5 ft. Multiplying each dimension by 1/5, we get (4 ft) * (1/5) = 0.8 ft for the length and (5 ft) * (1/5) = 1 ft for the width.

Therefore, the dimensions of the model bed Kyra built are 0.8 ft × 1 ft.

This scaling down process reduces the size of the original bed proportionally, maintaining the same ratio between the length and width. The resulting model bed is 1/5 the size of the original bed in both dimensions.

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Nick invested $47250 and Matt also contributed $78750, and Matt owns 62.5% of the company when invested in the ratio 3: 5 .

a)Each initial stage involves calculating the overall amount invested.

Ratio of investment =3 :5

components total = 3x + 5x

Eight sections total.

The cost per part is determined in the subsequent step (x)

Parts cost (x) = 126,000/8

Parts cost (x) = 15750

The third stage is to determine how much Nick and Matt invested.

Nick's investment yield is 3x

Nick's investment: 3 x 15750 = 47250

Nick invested $47250 in total.

Matt invested 5 times as much.

Matt invested 5 x 15750=78750.

$78750 was invested by Matt.

b. Owned wholly by Matt

Using this equation

Percentage that Matt owns equals "part owned by Matt/total part"

Let's enter the formula.

percentage held by Matt is equal to 5x/(3x+5x).

Matt owns 5x/8x of the shares.

Owned by Matt to the tune of 62.5%

Therefore Nick and Matt each invested $47250; Matt also contributed $78750, and Matt owns 62.5% of the company.

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Answer:

d

Step-by-step explanation:

Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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Answer:

U' (5, 1 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

U (5, - 1 ) → U' (5, - (- 1) ) → U' (5, 1 )

Shawn receive $82 money for each week.

And, Number of weeks must Ethan save in order to buy it is, 1.4 weeks.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Shawn received $5 more pocket money than Ethan each week.

Both of them spent $15 per week on food and saved the rest.

And, After a few weeks, Shawn had saved $72 and Ethan had only saved $32.

Now,

Let Ethan pocket money for each week = x

Hence, Shawn pocket money for each week = x + 5

Since, Both of them spent $15 per week on food and saved the rest.

Hence, The save money for Ethan is,

⇒ x - 15

And, Save money for Shawn is,

⇒ x + 5 - 15

⇒ x - 10

Here, Shawn had saved $72 and Ethan had only saved $32

Hence, We get;

⇒ x - 15 = 32

⇒ x = 32 + 15

⇒ x = 47

And,

⇒ x - 10 = 72

⇒ x = 72 + 10

⇒ x = $82

Now, Number of weeks must Ethan save in order to buy it is,

⇒ 32y = 44

⇒ y = 1.4 weeks

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Answer:

C)

Step-by-step explanation:

The correct answer is C: Tony did not use the property correctly because he did not multiply every term on both sides of the equals sign by 1/4.

To solve the equation 4x = 12x + 20, Tony used the multiplicative property of equality but made an error in the application. The correct approach would be to multiply every term on both sides of the equals sign by the reciprocal of the coefficient of x, which is 1/4 in this case.

However, Tony only multiplied one term on each side by 1/4, resulting in equation x = 3x + 20. This action is incorrect because it does not apply the property to every term containing x. To solve the equation correctly, Tony should have multiplied both sides by 1/4, resulting in x/4 = (3x + 20)/4.

Answer: b. y=50x

Step-by-step explanation:

Answer:

  D.  The parabola is translated down 2 units.

Step-by-step explanation:

Comparing the two functions f(x), we see that the second one has a constant of 1 where the first one has a constant of 3. That means every value produced by the second function will be 2 units less than the value produced by the first function.

  D.  The parabola is translated down 2 units.

Answer:

D

Step-by-step explanation:

In 2 hours they wash 8 cars total so...

8

16

24

The extra time is 15 mins for 2 cars

Answer:

50 new fish in total

so lets say 25 per month

Rate: 25 fish per month

Step-by-step explanation:

The rate is the population increasing is  0.135 or 13.5% .

Growth rates refer to the percentage change of a specific variable within a specific time period.

Growth rate= \(\frac{Present value - Past value}{Past value}\)

According to the question

The population of fish increased from 370 to 420

i.e

Present value = 420

Past value = 370

over the months of March and April

By using Growth rate formula :

Growth rate= \(\frac{Present value - Past value}{Past value}\)

Now,

Substituting values in formula

Growth rate= \(\frac{420 - 370}{370}\)  

                    = \(\frac{50}{370}\)

                    = 0.135 or 13.5%

Hence, the rate is the population increasing is  0.135 or 13.5% .

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The length of the rectangular countertop is 6x - 4.

To find the length of the rectangular countertop, we have to substitute the given values in the formula for the area of the rectangle, which is A = l × w
12x² + 10x - 12 = (2x + 3) × l
6x² + 5x - 6 = 3x × l + 3 × l
6x² + 5x - 6 = 3lx + 3l
6x² + 5x - 6 = 3l(x + 1)
3l = (6x² + 5x - 6) / (x + 1)
3l = (6x² + 9x - 4x - 6) / (x + 1)
3l = 3(2x² + 3x - 2) / (x + 1)
l = (2x² + 3x - 2) / (x + 1)
l = [(2x - 1) (x + 2)] / (x + 1)
Therefore, the length of the rectangular countertop is 6x - 4.

Summary:
The formula for the area of the rectangle is A = l × w. We substitute the given values in the formula to find the length of the rectangular countertop. After simplifying the expression, the length of the rectangular countertop is found to be 6x - 4.

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As per the concept of margin of error, the standard deviation increases as the margin of error increases.

The term margin of error is referred as the estimate of a small sample drawn from a relatively large population data.

Here the margin of error is usually governed by parameters such as standard deviation of population, sample size and desired confidence level.

Here we have given that for fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.

And we need to find the missing term in the statement.

Here let us consider that the following values are represented the given situation,

=> σ = Standard deviation for population

=> m = Margin of error

=> Z = Empirical value of Z-score at a given confidence level

Then the minimum sample size for a given confidence level is written as

=> (Z x σ)²/m²

Here from the above given formula it can be inferred that the minimum sample size is directly related to the population standard deviation. Therefore, the minimum sample size required would increase with the increase in population standard deviation.

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Answer:

8.3miles

Step-by-step explanation:

Here Jeff's sister drives 14 miles

his brother only drives 57/10 miles then the question is only asking the difference between their distance of driving to school knowing fully well that Jeff's sister drive farther than his brother, then we find the difference between their drives which is done bow

14miles -57/10 miles

= 83/10

= 8.3miles

Therefore, Jeff's sister drive 8.3miles farther than his brother

Emails, memos, and letters are written forms of communication, but they differ in terms of content and form. Emails are electronic messages typically used for quick, informal communication. Memos are internal documents used for formal communication within an organization. Letters are formal written communications sent externally, often to individuals or organizations outside of the sender's immediate environment.

Emails are commonly used for informal communication, whether within an organization or between individuals. They are typically concise and direct, often lacking the formalities and structure associated with memos and letters. Emails are often used for quick exchanges, sharing information, requesting or providing updates, and informal discussions.

Memos, on the other hand, are formal internal documents used within an organization. They usually follow a specific format, including headings, subject lines, recipient information, and a clear purpose. Memos are used to communicate important information, policy changes, directives, or reports within a business or department. They often have a more professional tone compared to emails and are typically archived for future reference.

Letters are formal written communications sent externally. They follow a traditional format with specific components such as salutations, addresses, dates, and signatures. Letters are used for official or business correspondence and can include inquiries, requests, formal complaints, or invitations. They require a more formal and respectful tone compared to emails and memos and are often used for official documentation or when a more personal touch is required.

In summary, while all three forms of communication serve the purpose of conveying information, emails are informal and quick, memos are formal internal documents within organizations, and letters are formal written communications sent externally. The content and format of each vary based on their intended purpose and target audience.

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Answer:

a = 5 and b = 3

Step-by-step explanation:

2(x + a) + b(x + 7) can be simplified so that it is in the same configuration as the right side of the equation (an x term and then a constant).

2(x + a) + b(x + 7)

2x + 2a + bx + 7b

2x + bx + 2a + 7b

(2+b)x + 2a + 7b

At this point we can see that the x term on the left side of the equation is

(2+b)x and on the right side of the equation the x term is 5x. So b must be 3.

Here's an equation to show that logic.

(2+b)x = 5x

2x + bx = 5x

2x - 2x + bx = 5x -2x

bx = 3x

b = 3 if x isnot= 0

2a +7b was our constant. That was equal to 31, now we know b=3.

2a + 7b = 31

2a + 7(3) = 31

2a + 21 = 31

2a + 21 - 21 = 31 - 21

2a = 10

a = 5

There are several potential problems that might arise if a tutor is asked to record personal information such as student names, dates of birth, home addresses, and phone numbers for a large number of students and then email the spreadsheet to the unit convenor.

One major concern is the security and privacy of the students' personal information.

There are logistical challenges involved in managing and organizing the large amount of data.

One major concern is the security and privacy of the students' personal information. Emailing a spreadsheet containing sensitive data poses a risk of unauthorized access, interception, or data breaches. If the spreadsheet falls into the wrong hands, it could lead to identity theft, privacy violations, or misuse of personal information. Additionally, there is the issue of compliance with data protection regulations, such as the General Data Protection Regulation (GDPR), which requires the protection of personal data and imposes strict guidelines on its handling.

Moreover, there are logistical challenges involved in managing and organizing the large amount of data. Ensuring accuracy and maintaining data integrity becomes increasingly difficult with a higher number of students and multiple tutors. There may be instances of data entry errors, missing information, or duplication, which can lead to confusion and inaccuracies in student records.

To address these problems, it is important to establish secure data management protocols, such as using encrypted file transfer methods or secure file sharing platforms. Implementing strict access controls and limiting the number of individuals handling and transmitting the data can help mitigate the risks. It is also essential to comply with relevant privacy laws and regulations and provide clear guidelines to tutors on data protection and confidentiality. Regular data audits and reviews can help identify and rectify any potential issues in the data management process.

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Answer:

102165

Step-by-step explanation:

92929+8282= 101211

101211 + 828 = 102039

102039 + 81 = 102120

102120 + (9+9+9+9+9) = 102120 + 45 = 102165

Answer:

102165 is your asnwer

Step-by-step explanation:

9+9+9+9+9+81+828+8282+92929=102165

Answer:

it's the third one. x=47/3

Step-by-step explanation:

if needed in decimal form: 15.666

mixed number form: 15 2/3

The p-value is 0.789.To determine if np₀(1 - p₀) ≥ 10, we need to calculate the value.

Given:

n = 500

p₀ = 0.73

Calculating np₀(1 - p₀):

np₀(1 - p₀) = 500 * 0.73 * (1 - 0.73) = 98.55

Since np₀ ( 1 - p₀) is greater than 10, the requirement is satisfied.

Next, we need to calculate (p-hat) = x / n = 360 / 500 = 0.72

The test statistic (z₀) can be calculated using the formula:

  = (0.72 - 0.73) / sqrt(0.73(1 - 0.73) / 500)

  ≈ -0.267

To find the p-value, we look up the absolute value of the test statistic (z₀) in the standard normal distribution table. From the table, we find the corresponding p-value to be approximately 0.789.

Therefore, the p-value is 0.789.

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To find f'(-1), we need to take the derivative of f(x) and then evaluate it at x = -1. Using the chain rule, we get: f'(x) = 8x + 8 / (4x^2 + 8x + 5), f'(-1) = 8(-1) + 8 / (4(-1)^2 + 8(-1) + 5), f'(-1) = -8 + 8 / 1, f'(-1) = 0. So, f'(-1) = 0. We don't need to round to 3 decimal places in this case since the answer is an integer.

To find f'(-1) for f(x) = ln(4x^2 + 8x + 5), we first need to find the derivative of the function with respect to x, and then evaluate it at x = -1. Here's the step-by-step process:

1. Identify the function: f(x) = ln(4x^2 + 8x + 5)
2. Differentiate using the chain rule: f'(x) = (1 / (4x^2 + 8x + 5)) * (d(4x^2 + 8x + 5) / dx)
3. Find the derivative of the inner function: d(4x^2 + 8x + 5) / dx = 8x + 8
4. Substitute the derivative of the inner function back into f'(x): f'(x) = (1 / (4x^2 + 8x + 5)) * (8x + 8)
5. Evaluate f'(-1): f'(-1) = (1 / (4(-1)^2 + 8(-1) + 5)) * (8(-1) + 8)
6. Simplify the expression: f'(-1) = (1 / (4 - 8 + 5)) * (-8 + 8)
7. Continue simplifying: f'(-1) = (1 / 1) * 0
8. Final answer: f'(-1) = 0

Since f'(-1) is an integer, there is no need to round to any decimal places f'(-1) = 0.

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(a) The probability distribution table is provided in the attachment.

(b) The probability distribution of X is discrete.

Let X = number of hours a service calls take.

(a)The probability of an event E is:

P(E)=n(E)/N

Here,

n (E) = number of favorable outcomes

N = total number of outcomes.

The probability distribution table is provided in the attachment.

(b)For a discrete probability distribution:

f(x) >= 0

summation f(x)= 1

Check that the probability distribution of X is discrete as follows:

The value of f (x) for all values of x is greater than 0.

The sum of all f (x) is 1.

Thus, the probability distribution of X is discrete.

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