What is the value of 9 cubed?

The smallest angle would be 19 degrees. So option D is correct.

The sum of exterior angles of the regular octagon is 360 degrees.

Given;

The angles

x + 13 + 2x - 1 + 2x + 6 + 2x + 12 + 2x - 17 + 3x - 4 + 3x - 10 + 4x = 360

19x - 1 = 360

19x = 359

x = 18.89

The smallest angle would be

2x - 17 = 2(18.89) - 17 = 19

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Answer:

A and C

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero

The graph that shows a reflection over the line k is the first one.

If we have a figure and we reflect it over a line, the perspective of the image with respect to that line shouldn't change.

For example, in this case we can see that the blue triangle has a "white corner" pointing towards the line k.

Then the image after the reflection also should have the white corner pointing to the line.

And the parallel to the line (the top vertex) shouldn't change, with these two things we can conclude that the correct option is the first one.

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Answer:

  (a)  Step 1

Step-by-step explanation:

The first step to solving the equation is to eliminate parentheses. That involves use of the distributive property.

Devon's solution shows two common mistakes in the first step.

The distributive property tells you ...

  a(b +c) = ab +ac

  -2(x -5) = (-2)(x) +(-2)(-5) = -2x +10

Devon missed the product with the second term, and also got its sign wrong.

The first mistake occurred in Step 1.

__

Additional comment

The solution should look like ...

Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

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If A, B and C be events relative to the sample space S, then the Venn diagram of the representing event has been plotted

Let A, B and C be events relative to the sample space S.

The sample space is the set of all possible outcomes of the experiment.

The Venn diagram is the pictorial representation of the sample space of the experiment by using the circles and the overlapping of the circles.

Here we have to plot the each representing events using the Venn diagram representation

Part a

The event is (A ∩ B)'

Plot the Venn diagram

Part b

The event is (A ∪ B)'

Plot Venn diagram

Part c

The event is (A ∩ C) ∪ B

Plot the Venn diagram

Therefore, the Venn diagram of the each event has been plotted

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Answer: 24 people earnt As

Step-by-step explanation:

1. We know that 18 people are the other 3/7 of the class

2. We first find out 1/7, which is calculated by dividing 3/7 by 3, which is 18 / 3 so 6

3. We can then find 4/7 by multiplying the amount of 1/7 by 4, so 6 x 4 = 24

The equation that represents the total cost of the membership will be y = 5x + 265.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.

Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,

y = 5x + 265

The equation that represents the total cost of the membership will be y = 5x + 265.

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Answer:

5 to the fourth power is 625

625 / 25 is 25

so now you have 25 = 5 to the second power

and five to the second power is 25

Step-by-step explanation:

So the answer should be the third one.

We have 98 % confidence that the true mean time a student sleeps per night is between 6.2928 hours and  7.1832 hours.

Mean = (8.6 + 8.3 + 7.6 + 6 + 7.1 + 5.6 + 5.1 + 6)/ 8 =  6.7875

Standard deviation = √Σ(x - mean)²/n

Σ(x - mean)² = (8.6 - 6.7875)^2 + (8.3 - 6.7875)^2 + (7.6 - 6.7875)^2 + (6 - 6.7875)^2 + (7.1 - 6.7875)^2 + (5.6 - 6.7875)^2 + (5.1 - 6.7875)^2 + (6 - 6.7875)^2

Standard deviation  : \(\sqrt{11.82875}/8\)

s = 0.42991

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

sample standard deviation

number of samples

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 8 - 1 = 7

Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99

Looking at the t distribution table,

z = 2.998

Margin of error = 2.998 × 0.42/√8

                        = 0.4452

The lower limit of this confidence interval is

6.738 - 0.4452 = 6.2928

The upper limit of this confidence interval is

6.738 + 0.4452 = 7.1832

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The trigonometric identities can be proved as follows;

32. Using the substitution, tan(x) = sin(x)/cos(x), and cot(x) = cos(x)/sin(x), we get;

cot(x) - tan(x) = (1 - 2·sin²(x))/(sin(x)·cos(x)) = sec(x)·(csc(x) - 2·sin(x))

36. tan(θ)/(1 + sec(θ)) = sin(θ)/(1 + cos(θ)) = (1 - cos(θ))/(sin(θ)) = -cot(θ) + csc(θ)

Trigonometric identities are equations involving trigonometric functions which are valid for the values of the input variable.

as follows;

cot(x) - tan(x) = sec(x)·(csc(x) - 2·sin(x))

The left hand side of the equation can be expressed using sin(x) and cos(x) as follows;

cot(x) = cos(x)/sin(x)

tan(x) = sin(x)/cos(x)

Therefore;

cot(x) - tan(x) = cos(x)/sin(x) - sin(x)/cos(x) = (cos²(x) - sin²(x))/(sin(x)·cos(x))

cos²(x) = 1 - sin²(x), therefore

(cos²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - sin²(x) - sin²(x))/(sin(x)·cos(x))

(1 - sin²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - 2·sin²(x))/(sin(x)·cos(x))

(1 - 2·sin²(x))/(sin(x)·cos(x)) = csc(x)·sec(x)·(1 - 2·sin²(x))

csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))

Therefore;

cot(x) - tan(x) = csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))

36. tan(θ)/(1 + sec(θ)) = -cot(θ) + csc(θ)

The left hand side can be manipulated as follows;

tan(θ) = sin(θ)/cos(θ)

sec(θ) = 1/cos(θ)

Therefore; tan(θ)/(1 + sec(θ)) = (sin(θ)/cos(θ))/(1 + (1/cos(θ)))

(sin(θ)/cos(θ))/(1 + (1/cos(θ))) = (sin(θ)/cos(θ))/((cos(θ) + 1)/(cos(θ)))

((sin(θ)/cos(θ))×cos(θ))/((cos(θ) + 1)/(cos(θ)) × cos(θ))) = sin(θ)/(cos(θ) + 1)

tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1)

sin(θ)/(cos(θ) + 1) = sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ)))

sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ))) = ((sin(θ)·(1 - cos(θ))/(1 - cos²(θ)))

((sin(θ)·(1 - cos(θ))/(1 - cos²(θ))) = ((sin(θ)·(1 - cos(θ))/(sin²(θ)) = (1 - cos(θ))/(sin(θ))

sin(θ)/(cos(θ) + 1) =  (1 - cos(θ))/(sin(θ)) = csc(θ) - cot(θ) = -cot(θ) + csc(θ)

tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1) = -cot(θ) + csc(θ)

Therefore;

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Answer:

The set M of all square numbers less than 80 is:

M = {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set N of all non-negative even numbers that are under 30 is:

N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

Answer:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Step-by-step explanation:

A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.

The square numbers less than 80 are:

An even number is an integer that is divisible by 2 without leaving a remainder.

The non-negative even numbers that are under 30 are:

Therefore:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Answer:

1. factor

2. prime number

3. composite number

4. GCF

5. LCM

Answer: x=3

Step-by-step explanation:

3x= 11-2

3x=9

then divide each side by 3

3 divide 3 =1 9 divide 3 = 3 so...

x=3

The ratio of the students who own a pet to the total number of students in the pet school is 5:6 ; Therefore, using this ratio, the number of students who own a pet out of the total students of 900 will be 750

Therefore,a total of 750 students own a pet.

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Answer:

13 days

Step-by-step explanation:

She starts with 3

She gets 2 for each year with the company

She has been their 5 years

5*2 = 10

10+3 = 13

The total number of paid vacation days after working for 5 years is 13 days.

The equation having the highest power of its variable as 1 is called a linear equation.

Let the total number of paid vacations be y.

And the number of years Lisa worked for the company be x.

The fixed paid vacation is for 3 days.

The number of additional paid vacation days for each additional year is 2 days.

So, the linear equation formed is,

y = 2x + 3 ... (i)

Put the value of x = 5 in the equation (i),

y = 2(5) + 3

y = 10 + 3

y = 13

Hence, the number of paid vacation days earned by Lisa after 5 years of working is 13 days.

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Answer:

Step-by-step explanation:

B, C, and D

Step-by-step explanation:

The bisection method is a root-finding algorithm that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. To apply the bisection method to the equation x^3 - x - 9 = 0, you need to find two initial values a and b such that f(a) and f(b) have opposite signs. This means that there is at least one root of the equation in the interval [a, b].

Let’s take a = 2 and b = 3 as our initial interval. We can see that f(2) = 2^3 - 2 - 9 = -1 and f(3) = 3^3 - 3 - 9 = 18, so f(a) and f(b) have opposite signs.

Now we can apply the bisection method as follows:

Calculate the midpoint c = (a + b)/2 = (2 + 3)/2 = 2.5.

Evaluate f© = 2.5^3 - 2.5 - 9 ≈ 5.625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

Calculate the new midpoint c = (a + b)/2 = (2 + 2.5)/2 = 2.25.

Evaluate f© ≈ 1.765625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

We can continue this process until we reach the desired level of accuracy.

Answer:

Never seen this before sorry can't help

Step-by-step explination:

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer: A

because slope are

Answer:

write a line above the numbers that repeat.

Step-by-step explanation:

the first one is 0.7 but a line on 35

Answer:

the second one is 42 over 99

42/99

Step-by-step explanation:

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

To establish trust with Martina, the nurse should show respect, use non-verbal communication, incorporate play, involve the parent, and individualize the approach.

To establish a trusting relationship with Martina, the nurse can employ several approaches:

Respect and empathy: The nurse should approach Martina with genuine respect and empathy, recognizing her unique needs and individuality. This can be conveyed through a calm and patient demeanor.

Non-verbal communication: Since Martina may not be responsive to verbal cues, the nurse can utilize non-verbal communication to establish connection and trust. This can include maintaining eye contact, using gentle touch, and respecting Martina's personal space.

Play and familiar objects: Given Martina's engagement with the blue stuffed dog, the nurse can incorporate play into their interactions. Bringing familiar objects or toys that Martina finds comforting can help create a sense of familiarity and security.

Parental involvement: Involving Martina's mother in the care process can be beneficial. The nurse can communicate with the mother, seek her input, and involve her in the administration of medications. This helps build trust not only with Martina but also with her caregiver.

Individualized approach: Recognizing Martina's autistic disorder, the nurse should tailor their approach to her specific needs. Understanding her sensory sensitivities and preferences can help create a safe and comfortable environment.

By implementing these strategies, the nurse can foster trust and a positive therapeutic relationship with Martina, promoting her overall well-being and care.

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Complete Question:

What approach would help the nurse establish a trusting relationship with Martina, a 3-year-old with bronchitis and autistic disorder, who is intensely occupied with a blue stuffed dog and does not seem responsive to the nurse's presence in the room, while the mother is also present?

Answer:

0.683 = 68.3% probability that a randomly chosen doctor is in favor of the vaccine

Step-by-step explanation:

(a) What is the probability that a randomly chosen doctor is in favor of the vaccine

75% of 115/250 = 0.46(German).

60% of 65/250 = 0.26(French).

65% of 70/250 = 0.28(Englishmen). So

\(p = 0.75*0.46 + 0.6*0.26 + 0.65*0.28 = 0.683\)

0.683 = 68.3% probability that a randomly chosen doctor is in favor of the vaccine

The number of hours it will take Santa to visit the whole children is = 10,000hours

The total number of children in UK is = 12million

That is = 12,000,000.

It took Santa 3 seconds to visit each child. That is,

1 child = 3 seconds

Therefore 12,000,000 children = x seconds

x = 12,000,000 × 3 seconds

x = 36,000,000 seconds.

But 3,600 seconds = 1 hour

36,000,000 seconds = x

x = 36,000,000/3,600

x = 10,000 hours.

Therefore, the number of hours it will take Santa to visit the whole children is = 10,000 hours.

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Answer:

f(g(x)) = 9x² - 6x + 1

Step-by-step explanation:

We are told that:

• \(f(x) = x^2\)

• \(g(x) = 3x -1\).

In order to find \(f(g(x))\), we have to replace \(x\) in the definition of \(f(x)\) with the definition of \(g(x)\). In other words, \(3x -1\) has to be the input for \(f(x)\):

\(f(g(x))\) = \(f(3x -1)\)

          ⇒ \((3x - 1)^2\)

          ⇒ \(9x^2 - 6x + 1\)

Therefore, f(g(x)) = 9x² - 6x + 1.

Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.

We can use the following formula to calculate ROI:

ROI = (gain from investment - cost of investment) / cost of investment

where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.

Using the values given in the question, we can calculate the ROI as:

ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000

ROI = 0.16 or 16%

Therefore, the return on the investment is 16%.

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