A health and wellbeing committee claims that working an average of 40 hours per week is recommended for maintaining a good work-life balance. A random sample of 48 full-time employees was surveyed about how many hours they worked; the data are recorded in the Excel file WorkingHours.xlsx . You may assume that the data come from a population that is normally distributed. Use Excel and an appropriate hypothesis test to answer the following research question:

Research Question: Are full-time employees working an average of 40 hours per week?

(1 mark) What is the sample mean? Answer hours (2dp)

(1 mark) What is the sample standard deviation? Answer hours (3dp)

(1 mark) The most appropriate hypothesis test for these data is Answera one-sample z-test for a population meana one-sample t-test for a population meana two-sample t-test for comparing meansa paired t-test for comparing means

(1 mark) The null hypothesis is that the average working hours equal Answer40 hours47.54 hours40.54 hours54.54 hours (Hint: this is the value of 0μ0 in the H0H0: =0μ=μ0)

(2 marks) What is the absolute value of the test statistic? Answer(3dp)

(2 marks) Is the p-value for this test statistic greater or less than 0.05? Answerthe p-value is less than 0.05the p-value is greater than 0.05

(1 mark) What is the most appropriate conclusion for this test? AnswerA. The average working hours are significantly different from the 40 hours claimed by the health and wellbeing committee. The average working hours possibly increased.B. The average working hours are significantly different from the 40 hours claimed by the health and wellbeing committee. The average working hours possibly decreased.C. The average working hours have not changed since 2017.

A. The average working hours are significantly different from the 40 hours claimed by the health and wellbeing committee. The average working hours possibly increased.

B. The average working hours are significantly different from the 40 hours claimed by the health and wellbeing committee. The average working hours possibly decreased.

C. The average working hours are consistent with the 40 hours claimed by the health and wellbeing committee.

A health and wellbeing committee member believes that the average working hours per week have shifted due to the COVID-19. S/he wants to estimate the 95% confidence interval for the population mean using a random sample of 33 full-time employees. Their average working hours are 47 hours, and the standard deviation is 6 hours.
(1 mark) The Absolute Value of the Critical Value for a 95% confidence interval is Answer (3dp)

(1 mark) Lower Bound = Answer hours (2dp)

(1 mark) Upper Bound = Answer hours (2dp)

WorkingHours
45
44
44
47
49
46
41
43
52
50
49
50
48
47
49
46
48
51
50
59
45
48
42
49
43
41
48
47
52
42
52
42
55
52
50
50
52
47
43
57
43
47
49
47
44
57
39
41

Answer:

X-coordinate: 2 and 3

Y-coordinate: 2 and 3

Step-by-step explanation:

Your welcome God bless you guys!!!

Answer:

Step-by-step explanation: X-coordinate: 2 and 3

Y-coordinate: 2 and 3.

Answer:

29 runs are needed to break the record.

Step-by-step explanation: He has 32 runs batted in.

Answer: 61 runs

Step-by-step explanation: Tell me if correct

Answer:

Step-by-step explanation:

Answer:

The graph f(x)=\(-2(x+3)^2-4\) is a reflection over the x-axis, vertical stretch by a factor of 2, a horizontal translation left 3 units and a vertical translation 4 units down of the graph y=\(x^2\).

Step-by-step explanation:

The graph f(x) is reflected over the x-axis because the negative is outside of the parenthesis.

it's a vertical stretch by a factor of 2 because 2 is outside of the parenthesis and is greater than 1.

(x+3) is a horizontal translation left 3 units because it is inside the parenthesis.

-4 is vertical translation 4 units down because it is outside of the parenthesis.

Answer: 16x^2+144x+18

Step-by-step explanation:

The sum of two given expressions is 16x²-6x+14.

Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.

The given expressions are 8x²-x+9 and 8x²-5x+5.

Now, sum =8x²-x+9+8x²-5x+5

Group like terms and simplify, we get

(8x²+8x²)+(-x-5x)+(9+5)

= 16x²+(-6x)+14

= 16x²-6x+14

Therefore, the sum of two given expressions is 16x²-6x+14.

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Answer:

y<-15

Step-by-step explanation:

2y+5/y=2y/y-3

2y^2=2y^2-6y+5y-15

y=-15

Answer:

5 nickels

Skills needed: Coins and Money

Step-by-step explanation:

1) We need to understand the different coins in the problem.

There is a nickel in the problem.

The problem states that:

- A nickel is \(\$0.05\) which is \(5 \text{ } cents\)

From above: A nickel is 5 cents.

2) After understanding the coin values, we need to understand what the problem is asking. It asks how many nickels Sam has if he has $0.25 (25 cents) in nickels.

---> In other words: How many nickels make up 25 CENTS?

- We can use division for that:

\(25 \text{ } cents \div 5 \text{ } cents = nickels\)

(The amount of money divided by the money value of a nickel will equal the number of nickels).

---> 25 divided by 5 is 5.

5 would be your answer.

Answer:Joe would have 40$

he will have 7 5 dollar bills and 5 1 dollar bills

Answer:

B

Step-by-step explanation:

Given

\(\left[\begin{array}{ccc}3&2\\-4&6\\7&5\end{array}\right]\) - \(\left[\begin{array}{ccc}-1&0\\5&2\\4&9\end{array}\right]\)

Subtract corresponding elements to obtain difference, that is

\(\left[\begin{array}{ccc}3+1&2-0\\-4+5&6-2\\7-4&5-9\end{array}\right]\)

= \(\left[\begin{array}{ccc}4&2\\1&4\\3&-4\end{array}\right]\)  → B

Answer:

12a+200=644

Step-by-step explanation:

take the equation and cancel out 200 and do it to both sides

12a+200=644

-200. -200

------------------------

12a=444

then we need to get the variable alone so divide by 12.

12a = 444

---- ----

12. 12

a=37

444 divided by 12 will equal 37

question 1, The perimeter of the door will be equal to 24 cm. Hence, option B is correct.

question 2, We are given a triangle with a perimeter of 3 meters from which an another triangle with a perimeter of 36 meters was created. Let the scale factor be 'x' So, 3x=36 x=12 Hence, the scale factor is 12:1

question 3, D

question 4, Given that, A rectangular flag is 80 centimeters by 92 centimeters. we need to find dimensions of a scale drawing of the flag using the scale 1:4,

Therefore,

80 / 92 = 20 / 23

Hence, the dimensions for the scale drawing of the flag is 20 cm by 23 cm.

question 4,      31.5/7 or 4.5

By simply taking the width after it was enlarged and dividing it by the width before it was enlarged we can find the scale factor that was used. In this case it would be 31.5 (width after)/ 7 (width before) which gives us a scale factor of 31.5/7. Simplifying would yield a scale factor of 4.5 times.

question 5,

Part A: 3.5x6 feet

14x3=42   24x3=72

42/12=3.5   72/12=6

Part B: 21 square feet

3.5x6=21

a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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We know that function f(x) is given by

where the slope is the coefficient of the variable x, that is, the slope,m, is

Since g(x) is given by

we have that

where the slope is equal to 6, in other words

Therefore, the slope of the graph of g(x) is 6 times the slope of the graph of f(x).

Since the y-intercept of f(x) is zero, then the y-intercept of g(x) is zero too. Then, the answer is: the y-intercept does not change.

The woodworker should make atmost 4 rocking kitchen chair and 3 simple kitchen chair to maximize the profit under given conditions of 192 woodworking hours and 21 painting hours.

Profit maximization is a process that businesses go through to make sure the best levels of output and prices are realized in order to maximize their returns. The company modifies important variables like sale price, production costs, and output levels in order to achieve its profit objectives.

inequality, A mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to etc.

Given,

Time needed to woodwork a rocking kitchen chair= 30 hours

Time needed to paint a rocking kitchen chair=3 hours

Time needed to woodwork a simple kitchen chair= 24 hours

Time needed to paint a simple kitchen chair=3 hours

Maximum time given by worker= 192 hours for woodwork and 21 hours to paint

Let x and y be the maximum number of chairs created by woodworker of both the types.

so the system of inequality would be,

30x+24y<192      ......(1)

3x+3y<21             ......(2)

To find x and y,

multiply the (2) by 10

30x+30y<210

subtract (1) from (2)

30x+24y-(30x+30y)<192-210

-6y<-18

y<3

3x+3y<21

3x+3*3<21

3x<12

x<4

By this, he can make maximum 4 rocking and 3 simple kitchen chair to earn the maximum profit.

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Answer:

mean:89

median:89

mode:89

range:22

Mean : total sum of numbers/ the amount of numbers

: 98 + 89.../5

: 445/5

Mean = 89

Median : middle number, ordering the numbers from smallest to largest first.

:76, 89, 89, 93, 98

Median = 89

Mode : the number that appears the most

Mode = 89

Range : largest - smallest

: 98 - 76

Range = 22

Hope this helps!

Answer:

G(9, -5)

Step-by-step explanation:

Point G is not shown in the figure, but I assume point G is on the bottom side of the square, directly below point F.

We are told each side of the square is 8 units long.

Starting at point E, to get to point G, go 8 units right and 8 units down.

Start at E(1, 3).

Then go 8 units right to point F(9, 3).

Now go 8 units down to point G(9, -5).

Answer:

x = 15

LM = 18

MN = 18

LN = 18

Step-by-step explanation:

To find x:

x + 3 + 2x - 12 + 33 - x = 54

2x + 24 = 54

2x = 54 - 24

2x = 30

x = 15

LM:

x + 3

15 + 3

18

MN:

33 - x

33 - 15

18

LN:

2x - 12

2(15) - 12

30 - 12

18

The probability that exactly 2 of the 5 customers are vegetarian is approximately 0.2837, or 28.37%.

The binomial distribution, which describes the likelihood of achieving a specific number of successes in a fixed number of independent trials with an identical likelihood of success, can be used to solve this problem.

With a success rate of p = 0.12 (because 12% of customers are vegetarian), let X represent the proportion of vegetarian consumers among the 5 people surveyed. Then, X has a binomial distribution with parameters n = 5 and p = 0.12.

P(X = 2) can be used to determine the probability that exactly 2 of the 5 customers are vegetarians.

The formula for the binomial probability mass function can be used to determine this:

\(P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)\)

where the binomial coefficient (n choose k) = n! / (k! * (n - k)!)! indicates the number of possible ways to select item k from a set of item n.

Substituting n = 5, p = 0.12, and k = 2, we get:

\(P(X = 2) = (5 choose 2) * 0.12^2 * (1 - 0.12)^(5 - 2)\)

= 0.2837 (rounded to four decimal places)

Therefore, the probability that exactly 2 of the 5 customers are vegetarian is approximately 0.2837, or 28.37%.

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Given :

Suppose there are 1200 pencils in 30 jars with an equal number of pencils per jar.

To Find :

Expression to show how to find the number of pencils per jar.

Solution :

Let, number of pencil per jar is x.

We know that when objects are equally distributed we should use divide to get our desired answer.

\(x = \dfrac{1200}{30}\\\\x = 40\)

Therefore, number of pencil per jar is 40.

The expansion of the expression given as y^4 is y^4 = y * y * y * 4

The expression is given as:

y^4

According to the exponent law of indices, we have

x^n = x * x * x * ..... *xn

This means that, the expansion of the expression given as y^4 is

y^4 = y * y * y * 4

Hence, the expansion of the expression given as y^4 is y^4 = y * y * y * 4

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Answer: y * y * y * y

Step-by-step explanation:

y is being multiplied by itself four times

Answer:

4.75 m

Step-by-step explanation:

s=ut+1/2at²

s=10(1/2)+1/2(-2)(1/2)²

s=4.75 m

Answer:

b = 1/3

Step-by-step explanation:

The general structure of equations in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

The given equation is already in slope-intercept form. In other words, you have already been given "m" and "b". Therefore, the value which corresponds with the y-intercept is (1/3).

f(x) = mx + b

f(x) = -(2/9)x + 1/3

About 75% of the students' scores exceeded the score mentioned in the boxplot.

In a boxplot, the box represents the interquartile range (IQR), which contains the middle 50% of the data. The lower whisker extends to the minimum value within 1.5 times the IQR below the first quartile (Q1), and the upper whisker extends to the maximum value within 1.5 times the IQR above the third quartile (Q3).

Since the boxplot does not provide specific numerical values, we can infer that the mentioned score lies within the upper whisker, which represents the top 25% of the data. Therefore, about 75% of the students' scores exceeded this score.

It's important to note that without the actual values or specific percentiles, we can only estimate the percentage based on the visual representation of the boxplot. The exact percentage may vary depending on the scale and distribution of the data. To obtain a more precise estimate, additional information such as the quartiles or a histogram of the scores would be needed.

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Answer:

Exact Form:

7/2

Decimal Form:

3.5

Mixed Number Form:

3 (1/2)

I hope this helps! :)

Answer:

59

Step-by-step explanation:

The equation is

944 - 5x = 1180 - 9x

Notice what is being said. You start with 944 gallons and take off 5 per week

You also start with 1180 gallons and take on 9 per week.

You want to know when the two are equal. The second tank is larger, but it leaks more. That's what's going to bring about equality.

Add 9x to both sides

944 - 5x + 9x = 1180

944 + 4x = 1180                

Subtract 944 from both sides.

4x = 1180 - 944

4x = 236      

Divide by 4

x = 236/4

x = 59 weeks

Answer:

24=10

Step-by-step explanation:

The value of y when  x = 10 is 5/4

If y varies directly as x, this is expressed as:

\(y \alpha x\\y = kx\\\)

where

k is the constant of proportionality

If y = 3 when x = 24, then:

3 = 24k

k = 3/24

k = 1/8

In order to get the value of x when y = 10

Recall that y = kx

y = 1/8 * 10

x = 10/8

y = 5/4

Hence the value of y when  x = 10 is 5/4

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Answer:

10.452+6.3

=10.452+6.3

=16.752

Step-by-step explanation: