What are the steps to determine which
solutions will be extraneous in a rational
equation?

Answer:

Yes

Step-by-step explanation:

b is as in 1b so. . .

2 + 1 = 3

We can plug in b or as "b"

2b + b = 3b

So yes in whatever case 2b + b's value  will always equal 3b's value

Answer:

yes

Step-by-step explanation:

because you can use any number to put for B and they will have the same value as an example we will use 3 for b so 2b = 6 + b = 9 and 3b = 9

The function is f(x)= 2x+1/x+3.

A work domain is a set of all possible inputs for a job. For example, the domain f (x) = x² is all real numbers, and the domain g (x) = 1 / x is all real numbers except x = 0. And we can define the special functions of its most limited domains.

The function domain f (x) is a set of all values ​​defined by the function, and the scope of the function is a set of all values ​​taken by f. (In grammar school, you probably call the domain a set of substitutes and a set of solutions.

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Answer:

B

Step-by-step explanation:

i got it right! :)

Answer:

Step 1 of 4

Point estimate for the population mean of the paired differences = -8.2

Step 2 of 4

Sample standard deviation of the paired differences = 16.116244

Step 3 of 4

Margin of Error = ±9.326419

Step 4 of 4

90% Confidence interval = (-17.5, 1.1)

Step-by-step explanation:

The ratings from last year and this year are given in table as

Rating (last year) | x1 | 87 67 68 75 59 60 50 41 75 72

Rating (this year) | x2| 85 52 51 53 50 52 80 44 48 57

Difference | x2 - x1 | -2 -15 -17 -22 -9 -8 30 3 -27 -15

Step 1 of 4

Mean = (Σx)/N = (-82/10) = -8.2 to 1 d.p.

Step 2 of 4

Standard deviation for the sample

= √{[Σ(x - xbar)²]/(N-1)} = 16.116244392951 = 16.116244 to 6 d.p.

Step 3 of 4

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = -8.2

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 10 - 1 = 9.

Significance level for 90% confidence interval

= (100% - 90%)/2 = 5% = 0.05

t (0.05, 9) = 1.83 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 16.116244

n = sample size = 10

σₓ = (16.116244/√10) = 5.0964038367

Margin of Error = (Critical value) × (standard Error of the mean) = 1.83 × 5.0964038367 = 9.3264190212 = 9.326419 to 6 d.p.

Step 4 of 4

90% Confidence Interval = (Sample mean) ± (Margin of Error)

CI = -8.2 ± (9.326419)

90% CI = (-17.5264190212, 1.1264190212)

90% Confidence interval = (-17.5, 1.1)

Hope this Helps!!!

Answer:

D.y-4=f(x+3)

Step-by-step explanation:

The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

The equation of the translation image of the function is  y - 4 = f(x + 3).

which is the correct answer would be an option (D).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

If shift down by 4 units, subtract 4 from the function

To determine the graph of y (x) is translated as 3 units right and 4 units down.

The x-coordinate will increase by 3 if we move it to the right.

If we shift it downward, it will become negative and read as y - 4.

So y - 4 = f(x + 3)

Therefore, the equation of the translation image of the function is  y - 4 = f(x + 3).

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Answer:

option 1 both statements are true

Step-by-step explanation:

Prove by PMI -- Principle of Mathematical  Induction

1) n³ + 2n

n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1   ---->divisible by 3

n = 2 ; 2³ + 2*2 = 8+4 = 12  = 3*4  ----> is divisible by 3

Assume that It is valid for n = k ;  

[tex]k^{3}+2k[/tex] = 3*m -----(I) , for all m ∈ N

We have to prove for n =k +1 , the statement is true.

n = k+1, [tex](k+1)^{3}+2(k +1) =k^{3}+3k^{2}+3k +1 +2k +2[/tex]

                                           = k³ + 3k² + 3k + 3 + 2k

                                           =  k³ +  2k + 3k² + 3k + 3

                                           = 3m + 3 (k² + k + 1)

                                          = 3(3 + [k² + k + 1] ) is divisible by 3

Therefore, this statement is true

2) [tex]5^{2n}-1\\[/tex]

[tex]n=1 ; 5^{2}-1 = 25 -1 = 24 divisible by 24\\\\n = 2 ; 5^{2*2}-1 = 5^{4}-1 = 625 - 1 = 624 divisible by 24[/tex]

This statement is also true

Answer:

The simplified expression is:

[tex]\dfrac{-7}{10}p^2q^2r+\dfrac{1}{2}pq^2r-\dfrac{11}{28}pqr^2+\dfrac{1}{8}p^2qr[/tex]

Step-by-step explanation:

To find:

[tex]-\dfrac{1}{2}p^{2} q^{2} r+\dfrac{1}{3}p q^{2} r-\dfrac{1}{4}p q r^{2}-\dfrac{1}{5}rq^{2} p^{2} +\dfrac{1}{6}rq^{2} p-\dfrac{1}{7}r^{2}pq+\dfrac{1}{8}rp^{2}q[/tex]

Solution:

We can see that pqr having power 1 is common throughout.

Let us take it common to make the expression simpler and then we will add by taking LCM:

[tex]\Rightarrow pqr(-\dfrac{1}{2}p q+\dfrac{1}{3}q-\dfrac{1}{4}r-\dfrac{1}{5}pq+\dfrac{1}{6}q-\dfrac{1}{7}r+\dfrac{1}{8}p)\\\Rightarrow pqr(-\dfrac{1}{2}p q-\dfrac{1}{5}pq+\dfrac{1}{3}q+\dfrac{1}{6}q-\dfrac{1}{4}r-\dfrac{1}{7}r+\dfrac{1}{8}p)\\\Rightarrow pqr(\dfrac{-5pq-2pq}{2\times 5}+\dfrac{2q+q}{2 \times 3}+\dfrac{-7r-4r}{7 \times 4}+\dfrac{1}{8}p)\\\Rightarrow pqr(\dfrac{-7pq}{10}+\dfrac{3q}{6}+\dfrac{-11r}{28}+\dfrac{1}{8}p)\\\Rightarrow pqr(\dfrac{-7}{10}pq+\dfrac{1}{2}q+\dfrac{-11}{28}r+\dfrac{1}{8}p)[/tex]

Now, multiplying pqr again to the expression:

[tex]\Rightarrow \dfrac{-7}{10}p^2q^2r+\dfrac{1}{2}pq^2r-\dfrac{11}{28}pqr^2+\dfrac{1}{8}p^2qr[/tex]

So, the answer is:

[tex]\dfrac{-7}{10}p^2q^2r+\dfrac{1}{2}pq^2r-\dfrac{11}{28}pqr^2+\dfrac{1}{8}p^2qr[/tex]

Answer:

Width is 15, length is 35.We can check our answer by multiplying the length by 2 and the width by two in order for the perimeter to be equal to 200.15 times 2 is 30 and 35 times two equals 70.70+30=100 so our solution satisfies our problem.

Step-by-step explanation:

Let the width be x.Then the length should be x+20.The farmer can’t use more than 100 ft of fencing and by mentioning enclosing a rectangle area for a pigpen, we can tell that 100 is the perimeter.So 2(x+20) + 2(x)=100.2x+ 40 + 2x=100.4x+40=100.4x=60.X is 15 which is the width so then the length is 35.

ANSWER:

EXPLANATION:

A simple random sample of size has mean and standard deviation. Construct a confidence interval for the population mean. The parameter is the population The correct method to find the confidence interval is the method.

The sample size is not given. Mean and Standard Deviation are not given.

To construct a confidence interval for the population mean, first find out the margin of error of the sample mean. This is why you need a confidence interval. If you are 90% confident that the population mean lies somewhere around the sample mean then you construct a 90% confidence interval.

This is equivalent to an alpha level of 0.10

If you are 95% sure that the population mean lies somewhere around the sample mean, your alpha level will be 0.05

In summary, get the values for sample size (n), sample mean, and sample standard deviation.

Make use of a degrees of freedom of (n-1).

Answer:

Step-by-step explanation:

We assume you want the integral ...

  [tex]\displaystyle\int_4^{14}{\sqrt{\ln{x}}}\,dx[/tex]

The width of each interval is 1/6 of the difference between the limits, so is ...

  interval width = (14 -4)/6 = 10/6 = 5/3

Then the point p[n] at the left end of each interval is ...

  p[n] = 4 +(5/3)n

__

Trapezoidal Rule

The area of a trapezoid is the product of its average base length multiplied by the width of the trapezoid. Here, the "bases" are the function values at each end of the interval. The integral according to the trapezoidal rule can be figured as ...

  [tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}\left(\dfrac{f(p[n])+f(p[n+1])}{2}\right)[/tex]

  integral ≈ 14.559027

If you're doing this on a spreadsheet, you can avoid evaluating the function twice at the same point by using a weighted sum. Weights are 1, 2, 2, ..., 2, 1.

__

Midpoint Rule

This rule uses the area of the rectangle whose height is the function value at the midpoint of the interval.

  [tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}{f(p[n+\frac{1}{2}])}[/tex]

  integral ≈ 14.587831

__

Simpson's Rule

This rule gives the result of approximating the function over each double-interval by a parabola. It is like the trapezoidal rule in that the sum is a weighted sum of function values. However, the weights are different. Again, multiple evaluations of the function can be avoided by using a weighted sum in a spreadsheet. Weights for 6 intervals are 1, 4, 2, 4, 2, 4, 1. The sum of areas is ...

  [tex]\dfrac{10}{3}\sum\limits_{n=0}^{2}{\left(\dfrac{f(p[2n])+4f(p[2n+1])+f(p[2n+2])}{6}\right)}[/tex]

  integral ≈ 14.577542

Answer:

For 3x^2+4x+4=0

Discriminant= = -32

The solutions are

(-b+√x)/2a= (-2+2√-2)/3

(-b-√x)/2a= (-2-2√-2)/3

For 3x^2+2x+4=0

Discriminant= -44

The solutions

(-b+√x)/2a= (-1+√-11)/3

(-b-√x)/2a= (-1-√-11)/3

For 9x^2-6x+2=0

Discriminant= -36

The solutions

(-b+√x)/2a= (1+√-1)/3

(-b-√x)/2a= (1-√-1)/3

Step-by-step explanation:

Formula for the discriminant = b²-4ac

let the discriminant be = x for the equations

The solution of the equations

= (-b+√x)/2a and = (-b-√x)/2a

For 3x^2+4x+4=0

Discriminant= 4²-4(3)(4)

Discriminant= 16-48

Discriminant= = -32

The solutions

(-b+√x)/2a =( -4+√-32)/6

(-b+√x)/2a= (-4 +4√-2)/6

(-b+√x)/2a= (-2+2√-2)/3

(-b-√x)/2a =( -4-√-32)/6

(-b-√x)/2a= (-4 -4√-2)/6

(-b-√x)/2a= (-2-2√-2)/3

For 3x^2+2x+4=0

Discriminant= 2²-4(3)(4)

Discriminant= 4-48

Discriminant= -44

The solutions

(-b+√x)/2a =( -2+√-44)/6

(-b+√x)/2a= (-2 +2√-11)/6

(-b+√x)/2a= (-1+√-11)/3

(-b-√x)/2a =( -2-√-44)/6

(-b-√x)/2a= (-2 -2√-11)/6

(-b-√x)/2a= (-1-√-11)/3

For 9x^2-6x+2=0

Discriminant= (-6)²-4(9)(2)

Discriminant= 36 -72

Discriminant= -36

The solutions

(-b+√x)/2a =( 6+√-36)/18

(-b+√x)/2a= (6 +6√-1)/18

(-b+√x)/2a= (1+√-1)/3

(-b-√x)/2a =( 6-√-36)/18

(-b-√x)/2a= (6 -6√-1)/18

(-b-√x)/2a= (1-√-1)/3

Answer:

equation: 3x²+4x+4=0 value: -32   solutions: -2±2i√2 / 3

equation: 3x²+2x+4=0 value: -44   solutions: -1±i√11 / 3

equation: 9x²−6x+2=0 value: -36   solutions: 1±i / 3

Answer:

0.43 x 370= 159.1

Step-by-step explanation:

Answer:

Refraction is what happens when light passes through some medium and changes it's direction because of it. For instance, when light travels through a lens light is bent as it goes from air to glass and back to air again. :)

Answer:

y = Vx - 5

Step-by-step explanation:

shift down is -5

y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The function y = Vx represents the square root function, which is a graph of a half of a parabola opening upwards and passing through the point (0, 0).

To translate this function 5 units downward, we need to subtract 5 from the function. Therefore, the function we need is:

y = Vx - 5

This is the square root function shifted downward by 5 units.

The graph of this function will be the same as the graph of y = Vx, but shifted 5 units downward.

Hence, y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.

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Answer:

solution,

[tex]48 > 2x - 10 \\ 48 + 10 > 2x \\ \frac{58}{2} > \frac{2x}{2} \\ 29 > x \\ x < 29[/tex]

but,

[tex]2x - 10 > 0 \\ \frac{2x}{2} > \frac{10}{2} \\ x > 5 \\ \\ 5 < x < 29 \: is \: the \: answer.[/tex]

Hope this helps...

Good luck on your assignment..

The range of value of x is 5 < x < 29.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

Given:

A quadrilateral ABCD.

From the diagram,

2x - 10 < 48

2x < 58

x < 29.

And 0 < 2x - 10

10 < 2x

5 < x

Therefore, the range is 5 < x < 29.

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Answer:

Step-by-step explanation: 4

Answer:

2/3

Step-by-step explanation:

divide by a fraction = multiply by reciprocal

1/4 * 8/3

2/3

Answer:

⅔

Step-by-step explanation:

= ¼ ÷ ⅜

= ¼ × ⁸/3

= ⅔

Have a great day !

Answer:

1/16

Step-by-step explanation:

Here,

Vertex =(3,5)

x= -1, y=6

Simply,eqn of parabola is given by ax^2+bx+c=y

So, coefficient of squared term (x^2) is 'a'

Therefore, we've to find the value of a

Moving on to solution:

a-b+c=6 ___(i) (by putting the given values of x and y in eqn of parabola )

We know that,

Vetex=(-b/2a, ( 4ac-b^2)/4a)

(3,5) = (-b/2a , (4ac-b^2)/4a)

Equating corresponding sides,we get

3= -b/2a

b=-6a___(ii)

Again,

5=(4ac-b^2)/4a

5=(4ac/4a) - (b^2/4a)

5= c- (36a^2/4a) (by putting value of b from eqn ii )

5= c-9a___(iii)

Now,moving back to the first eqn

a+6a+5+9a=6

16a=1

therefore,a=1/16

Hence ,the required value of coefficient of squared term is 1/16.

I tried my best to give clear explanation as much as I know. It's just we've have to find the value of a . For that, you can use any method you find easier.

Answer:

39°

Step-by-step explanation:

==>Given:

Shadow length = 20ft

Flag height = 16ft

==>Required:

Angle of elevation of sun (θ)

==>Solution:

To calculate the angle of elevation of the sun, recall the trigonometry formula SOHCAHTOA.

We are given adjacent side = 20ft, and opposite side = 16ft

Therefore, we would use TOA, which is:

tan θ = Opposite/Adjacent

tan θ = 16/20

tan θ = 0.8

θ = 38.6598083 ≈ 39°

Angle of elevation of the sun = 39°

The Answer is 2

34.989.I used a physics book

Answer:

y-1 = 3(x +2)

Step-by-step explanation:

Ok, so the point-slope form is:

y-k = m(x-h)  where m is the slope and (h,k) is the given point.

Since you are given  m = 3 ,  and (h,k) = (-2,1)

y-1 = 3(x +2)

Since your question specified using the point-slope form, make sure you use this equation when answering it. Otherwise, you may get it wrong.

Answer:

Step-by-step explanation:

Product of 5 and a number:  5n

Six more than that would be 5n + 6

Finally, "six more than the product of 5 and a number, decreased by one" would be

5n + 6 - 1, or 5n + 5

Answer: A) 6 + 5n - 1

Step-by-step explanation: edge. 2022

Answer:

(C)[tex]6t^2+5[/tex]

Step-by-step explanation:

Given the distance, d(t) of a particle moving in a straight line at any time t is:

[tex]d(t) = 2t^3 + 5t - 2, $ where t is given in seconds and d is measured in meters.[/tex]

To find an expression for the instantaneous velocity v(t) of the particle at any given point in time, we take the derivative of d(t).

[tex]v(t)=\dfrac{d}{dt}\\\\v(t) =\dfrac{d}{dt}(2t^3 + 5t - 2) =3(2)t^{3-1}+5t^{1-1}\\\\v(t)=6t^2+5[/tex]

The correct option is C.

Answer:

6t2+5

Step-by-step explanation:

Answer: 1/3

Step-by-step explanation: Since there are six sides to a number cube, the total number of outcomes will be 6.

Since there are 2 favorable outcomes, rolling a 1 or a 6,

the probability of rolling a 1 or a 6 is 2/6 which reduces to 1/3.

Answer:

1/3

Step-by-step explanation:

A cube by default has 6 sides, and a number cube generally is tallied from 1 - 6 (being the numbers are 1, 2, 3, 4, 5, 6).

You are solving for the probability of the numbers 1 or 6 being rolled, which are 2 numbers of the given amount. Change into a fraction form by placing part over the total amount of numbers:

2/6

Most likely, you will be told to simplify. Divide common factors from both the numerator & denominator:

(2/6)/(2/2) = 1/3

1/3 is the probability that a 1 or a 6 is rolled in a standard number cube.

~

Answer: 30 folders - 15 folders which she keeps = 15 folders; 15 folders / 3 friends = 5 folders per firend.

Step-by-step explanation:

Answer:

x= (30 -15)/3

Step-by-step explanation:

If we call x the number each friend gets, then the equation is:

Solving this we get:

Each friend gets 5 folders

Answer:

0.8413

Step-by-step explanation:

p = 0.10

σ = √(pq/n) = 0.01

z = (x − μ) / σ

z = (0.11 − 0.10) / 0.01

z = 1

P(Z < 1) = 0.8413

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

We have,

We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.

First, we need to calculate the mean and standard deviation of the binomial distribution:

Mean:

np = 899 × 0.1 = 89.9

Standard deviation:

√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427

Next, we need to standardize the sample proportion of 11% using the formula:

z = (x - μ) / σ

where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Substituting the values we have, we get:

z = (0.11 - 0.1) / 0.9427 = 0.1059

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.

Therefore,

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

Rounded to four decimal places, the answer is 0.5425.

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Answer and Step-by-step explanation:

According to the situation the solution is shown below:-

The expected value is

[tex]\mu = 5[/tex]

The standard deviation is

= $3

The sample distribution of the sample standard deviation is

[tex]\sigma_x = \frac{\sigma}{\sqrt{n} } \\\\ = \frac{3}{\sqrt{36} } \\\\ = \frac{3}{6}[/tex]

After solving the above equation  we will get

= 0.5

Basically we applied the applied formula so that each part could be determined

Answer:

a = 10

Step-by-step explanation:

From the solution given, x = a and y = -1

Substitute for x and y in either of the equations

y = -x + 9

-1 = -a + 9

a = 9 + 1 = 10

Answer:

Answer is 10

Step-by-step explanation:

Since the graphe cross only at one point there is only one solution for the equation.

Can I get brianliest plz.

Answer:

  [tex]10e^{i\frac{7\pi}{4}}[/tex]

Step-by-step explanation:

The magnitude of the number is ...

  [tex]|5\sqrt{2}-5i\sqrt{2}|=\sqrt{(5\sqrt{2})^2+(-5\sqrt{2})^2}=\sqrt{50+50}=10[/tex]

The angle of the number is in the 4th quadrant:

  [tex]\arctan{\dfrac{-5\sqrt{2}}{5\sqrt{2}}}=\arctan{(-1)}=\dfrac{7\pi}{4}[/tex]

So, the exponential form of the number is ...

  [tex]\boxed{10e^{i\frac{7\pi}{4}}}[/tex]

Answer:

[tex]\frac{1}{256}[/tex]

Step-by-step explanation:

Geometric sequence means there is a common ratio. All that means is term divided previous term is the same across your sequence.

ONE WAY:

So we are given here that:

[tex]\frac{f(2)}{f(1)}=\frac{1}{2}[/tex] and that the first term which is [tex]f(1)[/tex] is 2.

[tex]\frac{f(2)}{2}=\frac{1}{2}[/tex]

This implies [tex]f(2)=1[/tex] after multiplying both sides by 2 and getting that [tex]f(2)=\frac{1}{2}(2)=\frac{2}{2}=1[/tex].

So you have that

2,1,...

basically you can just multiply by 1/2 to keep generating more terms of the sequence.

Third term would be [tex]f(3)=1(\frac{1}{2})=\frac{1}{2}[/tex].

Fourth term would be [tex]f(4)=\frac{1}{2}(\frac{1}{2})=\frac{1}{4}[/tex].

...keep doing this til you get to the 10th term.

ANOTHER WAY:

Let's make a formula.

[tex]f(n)=ar^{n-1}[/tex]

[tex]a[/tex] is the first term.

[tex]r[/tex] is the common ratio.

And we want to figure out what happens at [tex]n=10[/tex].

Let's plug in our information we have

[tex]a=2[/tex]

[tex]r=\frac{1}{2}[/tex]:

[tex]f(10)=2(\frac{1}{2})^{10-1}[/tex]

Put into calculator or do by hand...

[tex]f(10)=2(\frac{1}{2})^9[/tex]

[tex]f(10)=2(\frac{1^9}{2^9})[/tex]

[tex]f(10)=2(\frac{1}{2^9})[/tex]

[tex]f(10)=\frac{2}{2^9}[/tex]

[tex]f(10)=\frac{2}{2(2^8)}[/tex]

[tex]f(10)=\frac{1}{2^8}[/tex]

Scratch work:

[tex]2^8=2^5 \cdot 2^3=32 \cdot 8=256[/tex].

End scratch work.

The answer is that the tenth term is [tex]\frac{1}{256}[/tex]

Answer:

For an nth term in a geometric sequence

[tex]U(n) = a ({r})^{n - 1} [/tex]

where n is the number of terms

r is the common ratio

a is the first term

From the question

a = 2

r = 1/2

n = 10

So the 10th term of the sequence is

[tex]U(10) = 2 ({ \frac{1}{2} })^{10 - 1} \\ \\ = 2 ({ \frac{1}{2} })^{9} \\ \\ \\ = \frac{1}{256} [/tex]

Hope this helps you

Answer:

No. At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average number of sick days a worker takes per year is significantly less than 5.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=5\\\\H_a:\mu< 5[/tex]

The significance level is 0.01.

The sample has a size n=30.

The sample mean is M=4.8.

The standard deviation of the population is known and has a value of σ=1.2.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1.2}{\sqrt{30}}=0.219[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{4.8-5}{0.219}=\dfrac{-0.2}{0.219}=-0.913[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-0.913)=0.181[/tex]

As the P-value (0.181) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.

Using the z-distribution, it is found that since the test statistic is greater then the critical value for the left-tailed test, this is not enough evidence to support the claim at [tex]\alpja = 0.01[/tex].

At the null hypothesis, it is tested if the number of sick days is of at least 5, that is:

[tex]H_0: \mu \geq 5[/tex]

At the alternative hypothesis, we test if it is less than 5, that is:

[tex]H_1: \mu < 5[/tex]

We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The parameters are:

For this problem, the values of the parameters are: [tex]\overline{x} = 4.8, \mu = 5, \sigma = 1.2, n = 30[/tex]

Hence, the value of the test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{4.8 - 5}{\frac{1.2}{\sqrt{30}}}[/tex]

[tex]z = -0.91[/tex]

The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.01 is of [tex]z^{-\ast} = -2.327[/tex].

Since the test statistic is greater then the critical value for the left-tailed test, this is not enough evidence to support the claim at [tex]\alpja = 0.01[/tex].

A similar problem is given at https://brainly.com/question/16194574