A route up a mountain is 20 Km long. john followed this route at an average speed of xkm/h. write down an expression in terms of x,for the number of hours he took to walk up the mountain.​

Answers

Answer 1

Answer:

20/x

Step-by-step explanation:

speed = distance /time

x km/h is speed

20 km is distance

x= 20/t

t= 20/x

Answer 2
Speed = d/t
T = d/ speed
T = 20/ X

Related Questions

The distance between point (3,0) and (7, 2p) is √80. Find the value of p.

Answers

Distance = √[ ( 7 - 3 )^2 + ( 2p - 0 )^2 ]

Distance = √(4)^2 + ( 2p)^2

Distance = √16 + 4p^2

As the question said : Distance = √80

80 = √16 + 4p^2

Thus :

16 + 4p^2 = 80

Subtract both sides 16

16 - 16 + 4p^2 = 80 - 16

4p^2 = 64

Divide both sides by 4

4p^2 ÷ 4 = 64 ÷ 4

p^2 = 16

Thus :

p = 4 or p = - 4

Plz this is due today help me explain the answer

Answers

Answer:

177.3 feet

This is a classic find the vertex of a parabola question.

if this was a calculus class the solution would be to take the derivative and set it equal to zero... -32t+ 105 = 0

BUT i assume that you are not in a calculus class..

so we try plan "B" the  highest (or lowest) point of parabola is it's vertex

the vertex formula is [-b/2a,f(-b/2a)]

in your problem a = -16, b=105, c= 5

so the "X" (TIME) is located at -(105)/(2*-16) = 3.28

plug in 3.28 into -16(3.28)^2 + 105(3.28) + 5 = 177.27

and you will get

Step-by-step explanation:

Please help! Thank you.

Answers

Answer:

B  at -1 minus we go to - ∞

at -1 plus  we to + ∞

Step-by-step explanation:

         x^2 -x

g(x) = ---------

         x+1

Factor out x

         x(x-1)

g(x) = ---------

         x+1

As x is to the left of -1

   x is negative (x-1) is negative

        x+1  will be slightly negative

g(-1 minus) = -*-/ -  = -  and we know that the denominator is very close to zero  we are close to infinity  so we go to - ∞

As x is to the right of -1

   x is negative (x-1) is negative

        x+1  will be slightly positive

g(-1 plus) = -*-/ +  = +  and we know that the denominator is very close to zero  we are close to infinity  so we go to  ∞

½ sejam berapa minit?​

Answers

Answer:

1/2 jam 30 menit mungkin?

1/2 jam adalah 30 minit

1/2 × 60 = 30 mins

English translation

1/2 an hour is 30 minutes

1/2 × 60 = 30 mins

Answered by Gauthmath must click thanks and mark brainliest

Two ice cream stands are deciding where to set up along a 1-mile-long beach. The people are uniformly located along the beach, and each person sitting on the beach buys exactly 1 ice cream cone per day from the nearest stand. Each ice cream seller wants the maximum number of customers. True or False: The two stands will most likely be 1/3 mile away from each other. True

Answers

Answer:

Each ice cream seller wants the maximum number of customers:

True

The two ice cream stands will most likely be 1/3 mile away from each other.

True

Step-by-step explanation:

This distance enables the two ice cream stands to give access to the maximum number of customers at the beach, which will be almost equal at their right-hand and left-hand sides.  Therefore, the two ice cream stands will most likely be 1/3 mile away from each other.  Such positioning exposes the ice cream stands to almost equal number of customers since the people standing along the beach are uniformly located.  Taking the extreme locations along the 1-mile-long beach will shrink location opportunities for both stands.

Factor the following expressions completely. Show and check all work on your own paper.
x^2+169

Factor the following expressions completely. Show and check all work on your own paper.
5x^2-50x+125

Factor the following expressions completely. Show and check all work on your own paper.
100x^2-25y2

Answers

Answer:

See the expressions and the answers below

Step-by-step explanation:

Given data

The first expression is given as

x^2+169 .-> we can not factorize the expression anymore

The second expression

5x^2-50x+125

5(x^2-10x+25)

The third expression

100x^2-25y2

25(4x^2-y^2)

PLEASE HELP ME

An expression is shown below:

6x^2y − 3xy − 24xy^2 + 12y^2

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Answers

9514 1404 393

Answer:

(3y)(2x^2 -1x -8xy +4y)(3y)(x -4y)(2x -1)

Step-by-step explanation:

Part A: All of the coefficients have a common factor of 3. All of the variable products have a common factor of y, so the greatest common factor of all terms is 3y. The expression can be written as ...

  (3y)(2x^2 -1x -8xy +4y)

__

Part B: The remaining factor can be factored pairwise:

  3y(x(2x -1) -4y(2x -1)) = 3y(x -4y)(2x -1)

Andre owns a computer backup service. He charges his customers $2.50 for each backup CD. His expenses include $875 for the CD recording equipment and $0.35 for each blank CD. Which equation could Andre use to calculate his profit p for the recording of n CDs?

Answers

Answer:

[tex]p =2.15n - 875[/tex]

Step-by-step explanation:

Given

[tex]CD_s= n[/tex]

[tex]Charges = 2.50[/tex] per CD

Expenses

[tex]E_1 = 875[/tex]

[tex]E_2 = 0.35[/tex] per CD

Required

The profit (p)

First, calculate the total income on n CDs

[tex]Total = Charges * n[/tex]

[tex]Total = 2.50 * n[/tex]

[tex]Total = 2.50n[/tex]

Next, the expenses on n CDs

[tex]Expenses = E_1 + E_2 * n[/tex]

[tex]Expenses = 875 + 0.35 * n[/tex]

[tex]Expenses = 875 + 0.35n[/tex]

The profit (p) is:

[tex]p = Total - Expenses[/tex]

[tex]p =2.50n - (875 + 0.35n)[/tex]

Open bracket

[tex]p =2.50n - 875 - 0.35n[/tex]

Collect like terms

[tex]p =2.50n - 0.35n - 875[/tex]

[tex]p =2.15n - 875[/tex]

b) An achievement test was administered to a class of 20,000 students. The mean score was 80 and the standard deviation was 11. If Lingard scored 72 in the test, how many students did better than him

Answers

Answer: 15328

Step-by-step explanation:

The following can be deduced from the information given:

N = 20000

μ = 80

σ = 11

P(X>72) = 1 - P (X<72)

= 1 - P(Z < 72-80/11)

= 1 - P(Z < -8/11)

= 1 - P(Z < 0.7272)

= 1 - 0.2336 = 0.7664

Therefore, the number of students that were better than Lingard n(X > 72) will be:

= 20000 × 0.7664

= 15328

OMG!! I’m stuck on 4a) b) c)
Help please

Answers

Answer:

a) 750 cmb) 288 cmc) 2112 cm

Step-by-step explanation:

Formula for getting the surface area of a rectangular prism: SA = 2 (WL + HL + HW)a) SA = 2 (WL + HL + HW) = 2(75) + 2(225) + 2(75) = 150 + 450 + 150 = 750 cm^2b) SA = 2 (WL + HL + HW)= 2(48) + 2(72) + 2(24)= 96 + 144 + 48=288 cm^2c) SA = 2 (WL + HL + HW)= 2(400) + 2(400) + 2(256)= 800 + 800 + 512= 2112 cm^2

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

(a) The surface area  consists of the sum of the area of 3 sets of 2 congruent rectangles. The 2 rectangles are on opposite sides of the solid.

= 2(15*15) + 2(5*15) + 2(5&15)

= 450 + 150 + 150

= 750 unit^2.

(b). Similarly to the above:

Surface area = 2(12*6) + 2(4*12) + 2(4*6)

= 144 + 96 + 48

= 288 unit^2.

(c)  Again:

Surface area =  2(25*16) + 2(25*16) + 2(16*16)

= 400 + 400 + 256

= 1056 unit^2.

A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 50 cells.

Required:
a. Find the relative growth rate.
b. Find an expression for the number of cells after t hours.
c. Find the rate of growth after 6 hours. (Round your answer to the nearest integer.)
d. Find the number of cells after 6 hours.

Answers

Answer:

a. Relative Growth rate = 10% (6/60 * 100)

b. Number of cells after t hours = 50 * 1.1^t

c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)

d. The number of cells after 6 hours is

= 89 cells

Step-by-step explanation:

A cell divides into two cells every 20 minutes

In one hour, the cell will divide into 60/20 * 2 = 6 cells

Each cell growth 6 cells per hour

Initial population of a culture = 50 cells

t = time in hours

a. Relative Growth rate = 10% (6/60 * 100)

b. Number of cells after t hours = 50 * 1.1^t

c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)

d. The number of cells after 6 hours = initial population * growth factor

= 50 * 1.772

= 88.6

= 89 cells

Which shows the image of rectangle ABCD after the rotation () (W)?
13
VA
1
V

Answers

Answer:

Graph (1)

Step-by-step explanation:

Given rule for the rotation of a figure is,

A(x, y) → A'(-y, x)

This rule defines the rotation of point A by 90° counterclockwise about the origin.

Coordinates of point A → (-2, 0)

Coordinates of point C → (-1, 0)

Following the rule of rotation,

A(x, y) → A'(-y, x)

A(-2, 0) → A'(0, -2)

C(-1, 4) → C'(-4, -1)

Now search the image points from the graphs attached,

Graph (1) will be the answer.

h is a trigonometric function of the form h(x)=a sin(bx+c)+d. Below is the graph h(x). The function intersects its midline at (-pi,-8) and has a maximum point at (pi/4, "-1.5)." Find a formula for h(x). Give an exact expression.

Answers

Answer:

6.5sin(.04x+.4pi)-8

The function intersects its midline at (-pi,-8) and has a maximum point at (pi/4, "-1.5). The  final equation is h(x) = 4 sin(2x +  π /2) + 3.

What is a function?

A function is defined as a relation between the set of inputs having exactly one output each.

The function intersects its midline at (3π/4, 3) then the midline is d= 3.

The amplitude is just the positive distance between the maximum/minimum and the midline,

so the amplitude a = 7 - 3 = 4

Also, given that period is 2π/b and the fact that the period is π from our given maximum,

we have the equation 2π/b= π where b = 2

we know that the phase shift, -c/b is - π/4 (or  to the left)

since -π /4. Therefore, c = π /2.

our final equation is

h(x) = 4 sin(2x +  π /2) + 3.

Learn more about function;

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a car completes a journey in 8hours it covers half the distance at 40kms per hours and the rest at 60 km per hour. what is the total distance of the journey?​

Answers

Answer:

384 kmph

Step-by-step explanation:

A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course: 16, 21, 22, 12, 22
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer:

The critical value used is [tex]T_c = 2.132[/tex]

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

[tex]\overline{x} = \frac{16+21+22+12+22}{5} = 18.6[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(16-18.6)^2+(21-18.6)^2+(22-18.6)^2+(12-18.6)^2+(22-18.6)^2}{4}} = 4.45[/tex]

Confidence interval:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 5 - 1 = 4

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.132. The critical value used is [tex]T_c = 2.132[/tex]

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.132\frac{4.45}{\sqrt{5}} = 4.243[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 18.6 - 4.243 = 14.357

The upper end of the interval is the sample mean added to M. So it is 18.6 + 4.243 = 22.843.

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

In a random sample of seven aerospace engineers, the sample mean monthly income is $6824 and the sample standard deviation is $340. Construct a 95% confidence interval for the population mean. Assume that the monthly incomes are normally distributed.

Answers

Answer:

The 95% confidence interval for the population mean is ($6510, $7138).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 7 - 1 = 6

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{340}{\sqrt{7}} = 314[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 6824 - 314 = $6510.

The upper end of the interval is the sample mean added to M. So it is 6824 + 314 = $7138.

The 95% confidence interval for the population mean is ($6510, $7138).

What is the mean of 86, 80, and 95

Answers

87 is the mean.

To find the mean, you must

- add all of the numbers

- divide by the amount of numbers given

In this case, you would want to do (86 + 80 + 95)/3. This would give you an answer of 87.

87 is the answer.
Mean is the same thing as average so you just all the given numbers and divide by the number of terms given (in this case 3 were given)

Kevin's supervisor, Jill, has asked for an update on today's sales, Jill is pretty busy moving back and forth between different store locations. How can Kevin most effectively deliver an update to her ? a) Call with a quick update Ob ) Send a detailed text message c ) Book a one-hour meeting for tomorrow morning d) Send a detailed email

Answers

The answer is A, calling is effective and you can know that the message is heard quickly and easily.

Y<3/2•x-4
Match the equation to a graph.

Answers

Answer:

Last option

Step-by-step explanation:

The slope 3/2 determines the line (although you can plot points to find (0,-4) and (4,2), connecting them, you'll get the equation of the line, and the area it covers will be to the right side, putting x = 0, y<-4, which is below the line, that's how you determine it.

Answered by GAUTHMATH

what is the value of k

Answers

Answer:

(A)

Step-by-step explanation:

M=-2

therefore

x¹=3, y¹=-12, x²=6 y²=k

M=(y²-y¹)/(x²-x¹)

-2=(k+12)/(6-3)

-2×3=k+12

-6=k+12

k=-18

Answer:

A. -18

Step-by-step explanation:

The end points of a line segment AB are A (3, -12) & B (6, k)

What is the value of k if the slope of line segment AB is -2?
•••••••••••••••••••••••••••••••••••••••••••••••••
Answer + explanation:

Basically they’re asking us to find out the y2 of the second point of the line segment.

To find out k, use Slope-Formula

m = slope

m = (y2 - y1)/(x2 - x1)

where the first point describes (x1, y1) & the second point describes (x2, y2)

Points: (3, -12) & (6, k)

m = (k - -12)/(6 - 3)

Place the slope at the end of the formula to solve for k

(k - -12)/(6 - 3) = -2

Subtract 6 - 3

(k - -12)/(3) = -2

K is a negative number since we have a negative slope

Substitute k for the possible value

((-18) - (-12))/3 = -2

Two negative signs make addition

-6/3 = -2

The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 28 ft^2. Find the dimensions of the rectangle.

Answers

Answer:

7 x 4

Step-by-step explanation:

Let the width be x, length will be 3x-5. ATQ, x(3x-5)=28. x=4 and x=-7/3, since length isn't negative, x=4. Width=4 and length=7

Pls help

Q.2 Choose the correct alternative for each question.
1. 400 is successor of ______.
A. 399 B.401 C. 398 D. 402
(1 Marks each)
2. The product of a non-zero whole number and its predecessor is always_________.
A. an odd number B. an even numberC. 0 D. a prime number
KHALSA LITTLE FLOWER SCHOOL | GRADE 6 | Mathematics 1

3. The predecessor of 1 million is ___________.
A. 99999 B. 1000001 C. 2000000 D. 999999
4. Whole numbers are closed under ________.
A. addition and subtraction B. addition and multiplication C. addition and division D. subtraction and division
5. The only whole number which does not have a predecessor is ________. A.2 B.0 C.3 D.1
6. ________ million make 1 crore.
A. 100 B. 10 C. 1000 D. 10,000
7. 3856 is rounded off to the nearest tens as ______.
A. 3850 B. 3860 C. 3800 D. 3000 8. In Roman numerals, the symbol ______ can be repeated.
A. D B. V C. X D. L
9. The Roman numeral for 91 is _______.
A. IXLL B. CXI C. IXC D. XCI
10. The Roman numeral LV stands for _______.
A. 65 B. 45 C. 55 D. 105

Answers

Answer:

Step-by-step explanation:

1-399

2  C

 3-A 99999

4a  

5b

7 b

8 C

9D

10c

A box contains orange balls and green The number of more four the number of orange If there 38 balls how many green balls and how balls are there in the box ?

Answers

let number of green balls= x

let number of orange balls=x+4

x+x+4=38

2x=38-4

2x=34

x=17

number of green balls=17

number of orange balls=21

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data.
A supervisor must give a summary evaluation rating from among the choices given below:
1) Poor   
2) Fair   
3) Good   
4) Very good   
5) Excellent
a. Are these data qualitative or quantitative?
b. Are these data discrete or continuous?
c. What is the highest level of measurement the data possesses?

Answers

Answer:

Qualitative data

Neither discrete or continous

Ordinal

Step-by-step explanation:

Qualitative data simply refers to Non-numeric measure, they make use of data labels which are expressed in words rather than figures or numbers.

For a data to be either discrete or continous, then it has to be numeric, since the data is qualitative and non- numeric, then it is neither continous or discrete.

This is an ordinal scale representation of data as data are ordered or ranked in terms of performance, however, there is no measure of difference between each rank or order. The highest level of performance in the scale is Excellent.

Which matrix equation represents the system of equations?

Answers

Answer:

B. [tex]\left[\begin{array}{ccc}-1&2\\0&1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}0\\-2\\\end{array}\right][/tex]

Step-by-step explanation:

Given the systems of equations

-x + 2y = 0

y = -2

This can also be written as:

-x + 2y = 0

0x + y = -2

We are to write in this form AX = b

A is a 2by2 matrix with coefficients of x nd y

X is a column matrix containing the unknown

b is a column matrix with the values at the right hand sides (0 and -2)

Writing in matrix form;

[tex]\left[\begin{array}{ccc}-1&2\\0&1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}0\\-2\\\end{array}\right][/tex]


Which of the following is equivalent to 5 + 5x > 8(x-1) ?
-3x > -12
3x 13
3x < 6
-4X > -12

Answers

5+5x>8(x-1)

5+5x>8x-8

5x-8x>-8+5

-3x>-3

5 + 5x > 8(x-1) is equivalent to -3x > -13.

How to estimate the equivalent function to 5 + 5x > 8(x-1) ?

Let, the expression be 5 + 5x > 8(x-1)

By applying Multiplicative Distribution Law, we get

5 + 5x > 8x - 8

Rearrange unknown terms to the left side of the equation, then

5x - 8x > -8 - 5

Combine like terms, we get

-3x > -8 - 5

Calculate the sum or difference

-3x > -13

Divide both sides of the inequality by the coefficient of the variable, then we get

[tex]$x < \frac{-13}{-3}$[/tex]

Determine the sign for multiplication or division:

[tex]$x < \frac{13}{3}$[/tex]

Therefore, the correct answer is -3x > -13.

Complete question:

Which of the following is equivalent to 5 + 5x > 8(x - 1)?

-3x > -12

3x < 13

3x < 6

-4x > -12

To learn more about algebraic expression

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It is claimed that the average child has no time to go to school. For the child spends 8 hours per day,or one third of his/her time sleeping. Based on a 365 day year, that’s 121.67days sleeping. Also the child spends three hours per day eating. That’s a total of 45 days in the year spent eating. Also the child spends 90 days taking summer vacation. Also the child spends 21 days on Christmas and Easter holiday. Finally, the child has each Saturday and Sunday off. That’s a total of 104 days. In short, we (rounding to whole days accounted for 122+45+90+21+104=382 days of the year taken up by ordinary child inlike activities. This is already more than the 365 days that are known to comprise a year. We conclude that there is certainly no time for the child to attend school. What is wrong with this reasoning?

Answers

Answer:

See below.

Step-by-step explanation:

Sleeping:

8/24 * 365 = 121.76 days

Eating:

3/24 * 365 = 45.63 days

Total sleeping and eating: 167 days

Summer Vacation & Holidays:

90 + 21 = 111 days

Saturdays and Sundays: 52 + 52 = 104 days

Vacation + Holidays Saturdays + Sundays = 111 + 104 = 215 days

It may be true that all days of vacation, holiday, Saturdays, and Sundays combined are a total of 215 days, but these 215 days cannot be added to the 167 days above because these 215 days include time for sleeping and eating which was already included in the sleeping and eating times for the entire year. The mistake in the reasoning is counting twice the time of sleeping and eating on the 215 days in which there is no school.

guys help me I really need your help​

Answers

Answer:

a x^2/2 is a polynomial because the power of x is 2 which is a positive whole number but 2/x^2 is not a polynomial because the power of x is -2 which is negative whole number.

b.in

[tex] \sqrt{2 x} [/tex]

the power if x will be

[tex]x {}^{ \frac{1}{2} } [/tex]

which is not a whole number so it is not a polynomial.

but in

[tex] \sqrt{2} x[/tex]

the power if x is a positive whole number.so it is a polynomial.

c.the greatest power of variable of the term is called degree of polynomial

Each marble bag sold by Debra's Marble Company contains 8 yellow marbles for every 4 blue marbles. If a bag has 56 yellow marbles, how many blue marbles does it contain?

Answers

Answer:

28 blue marbles

Step-by-step explanation:

yellow: blue

8               4

To get to 56 yellow marbles multiply by 7  

yellow: blue

8*7           4*7

56             28

There will be 28 blue marbles

Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week. A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 35 students studied each week was 21.1 hours. The sample standard deviation of 4.3 hours.
Find the p-value.
The p-value should be rounded to 4-decimal places.

Answers

Answer:

0.0698

Step-by-step explanation:

Given :

Population mean, μ = 20

Sample mean, xbar = 21.1

Sample standard deviation, s = 4.3

Sample size, n = 35

The hypothesis :

H0 : μ = 20

H0 : μ > 20

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (21.1 - 20) ÷ (4.3/√(35))

T = 1.1 ÷ 0.7268326

Test statistic = 1.513

Using the Pvalue calculator :

df = n - 1 = 35 - 1 = 34

Pvalue(1.513, 34) = 0.06976

Pvalue = 0.0698 (4 decimal places)

The p-value is 0.0698 if rounded to 4-decimal places.

It is given that students study an average of more than 20 hours each week and the random sample of 35 students was asked to keep a diary of their activities over a period of several weeks.

The average number of hours that the 35 students was 21.1 hours.

The sample standard deviation is 4.3 hours.

It is required to find the p-value.

What is the standard deviation?

It is defined as the measure of data dispersement, It gives an idea about how much is the data spread out.

We can test the hypothesis using the Z test, the formula for the Z-test is given below:

[tex]\rm Z= \frac{(x-u)}{\frac{S}{\sqrt{n} } }[/tex]

Where x is the sample mean

            u is the population mean

            s is the standard deviation

            n is the sample size.

The hypothesis are: H0 : μ = 20  V/s  H1 : μ > 20

We have x = 21.1

               u = 20

               s = 4.3

               n = 35

Putting these values in the above formula, we get:

[tex]\rm Z= \frac{(21.1-20)}{\frac{4.3}{\sqrt{35} } }\\\\\rm Z= \frac{(1.1)}{\frac{4.3}{\sqrt{35} } }\\\\[/tex]

Z = 1.513

difference or df = n -1 ⇒ 35-1 ⇒ 34

P-value at (1.513, 34) =  0.06976  (From the p-value calculator)

P-value = 0.0698 (Rounded to 4-decimal places)

Thus, the p-value is 0.0698 if rounded to 4-decimal places.

Learn more about the standard deviation here:

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