Lie detectors Refer to Exercise 82. Let Y = the number of people who the lie detector says are telling the truth.



(a) Find P(Y ≥ 10). How is this related to P(X ≤ 2)? Explain.


(b) Calculate μX and σY. How do they compare with μX and σY? Explain why this makes sense.

==========================================

Explanation:

As you stated in problem 4, tan(angle) = opposite/adjacent

We'll use this idea to help find angle Z. First lets set up the proper tangent ratio for this problem

tan(Z) = XY/YZ

tan(Z) = 8/10

tan(Z) = 0.8

To isolate Z, we need to undo the tangent function. We will use the inverse tangent or the arctangent function to do this.

tan(Z) = 0.8

arctan( tan(Z) ) = arctan(0.8)

Z = 38.6598 which is approximate

This rounds to 38.66

Answer:

x = 35.98

Step-by-step explanation:

The given triangle is a right angle triangle.

From the given right angle triangle

The unlabelled side represents the hypotenuse of the right angle triangle.

With 17 degrees as the reference angle,

x represents the adjacent side of the right angle triangle.

The length of the opposite side of the right angle triangle is 11

θ = 17 degrees

To determine x, we would apply trigonometric ratio

Tan θ = opposite side/adjacent side. Therefore,

Tan 17= 11/x

0.3057 = 11/x

Crossmultiplying,

0.3057x = 11

x = 11/0.3057 = 35.98

Answer:

a) Unit: College Student

Variables of measurement: Procrastination and illness habits.

b) Unit: SUV cars

Variables: Manufacturing and car damage for two car manufactures.

Step-by-step explanation:

We are given the following in the question:

In a research, a unit is a single individual or object that is measured.

a) A study finds that college students who often procrastinate tend to be sick more often than students who do not procrastinate.

Since college students are asked about procrastination, then the unit in this study is college students.

Unit: College Student

Variables of measurement: Procrastination and illness habits.

b) A study finds that sport utility vehicles (SUVs) made by one car manufacturer tend to be more heavily damaged in a crash test than SUVs made by a second car manufacturer.

Since all SUVs cars are considered, the unit in this research is  SUV cars

Unit: SUV cars

Variables: Manufacturing and car damage for two car manufactures.

The unit of analysis in the first study is individual college students, measuring procrastination and sickness. In the second study, individual SUVs are analyzed, comparing car manufacturer brands with crash test damage.

Understanding Variables and Units of Analysis in Studies

In the first study about college students and procrastination, the individual unit of analysis is each college student participating in the study. The two variables measured are the tendency to procrastinate (independent variable) and the frequency of being sick (dependent variable).

In the second study about SUVs and crash tests, the individual unit of analysis is each SUV manufactured by the car companies. The two variables measured are the brand of car manufacturer (independent variable) and the extent of damage sustained in a crash test (dependent variable).

These studies illustrate the importance of properly identifying units of analysis and measuring variables to avoid errors such as the ecological fallacy and to account for potential lurking variables.

Answer:

0.5

Step-by-step explanation:

Probability is the possibility of an event happening,

probability = number of required outcomes/ number of possible outcomes

number of red marbles = 10

number of blue marbles = 15

The selection of two marbles  is done without replacement.

Pr( of same color) = RR or BB

which means; (the first is red and second is red) or (the first is blue and the second is blue)

OR in probability means adition while AND means multiplication.

Pr( of same color) = [tex](\frac{10}{25}*\frac{15}{24})+(\frac{15}{25}*\frac{10}{24})[/tex]

                    =[tex]\frac{1}{4} +\frac{1}{4}[/tex]

      =0.5

Probabilities are used to illustrate the chances of an event

The probability that marbles of the same color are picked is 0.50

The numbers of marbles are given as:

[tex]\mathbf{Red =10}[/tex]

[tex]\mathbf{Blue =15}[/tex]

[tex]\mathbf{Total =25}[/tex]

The probability that marbles of the same color are picked is:

[tex]\mathbf{Pr = (Red\ and\ Red) + (Blue\ and\ Blue)}[/tex]

So, we have:

[tex]\mathbf{Pr = (10/25 \times 9/24) + (15/25 \times 14/24)}[/tex]

[tex]\mathbf{Pr = (0.15) + (0.35)}[/tex]

Add

[tex]\mathbf{Pr = 0.50}[/tex]

Hence, the probability that marbles of the same color are picked is 0.50

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Answer:The new perimeter of the field is 2800 feet.

Step-by-step explanation:

The formula for determining the area of a square is expressed as

Area = 4L

Where L represents length of each side of the square.

The small farm field is a square measuring 350 ft on a side. This means that the perimeter of the field would be

Perimeter = 350 × 4 = 1400 feet.

If you double the length of each side of the field, the new length would be

350 × 2 = 700 feet.

The new perimeter of the field would be

700 × 4 = 2800 feet

Answer: 6 root 7

Step-by-step explanation:

The biggest whole number you can take out is 36, so the root of 36 on the outside and the 252/36 remains inside the root.

Answer:

6√7.

Step-by-step explanation:

First find the prime factors of 252:

252 =  2*2*3*3*7

Square root of 2*2*3*3 = 2*3 = 6.

Therefore:

√252 = 6√7.

Answer:

(7,-4)

Step-by-step explanation:

Answer:

(7, -4)

Step-by-step explanation:

Answer:

Bottles of soda filled on March 11.

Step-by-step explanation:

Population is usually constitutes of the set that contains the set of all possible observation in the undergoing study.

Here, sample known as the part of population consists of 80 bottles selected from the bottles of soda filled on March to check the calibration of filling machine. So, the population in the given scenario consists of the bottles of soda filled on March 11.

Answer: 3x -12y

Step-by-step explanation:

Hi, to answer this question we have to add both expressions, the times "from" and "to" school.

Total time spent: time to school + time from school

Mathematically speaking:

Adding alike terms:

In conclusion, the expression that represents the total time Henry spends commuting to and from school each day is 3x -12y.

Answer:Robert's minimum age is 11 years.

Step-by-step explanation:

Let x represent George's age.

Let y represent Edward's age.

Let z represent Robert's age.

George is twice as old as Edward. It means that

x = 2y

Edward's age exceeds Robert's age by 4 years. It means that

z = y - 4

If the sum of the three ages is at least 56 years, it means that

x + y + z ≥ 56 - - - - - - - - - - 1

Substituting x = 2y and z = y - 4 into equation 1, it becomes

2y + y + y - 4 ≥ 56

4y - 4 ≥ 56

4y ≥ 56 + 4

y ≥ 60/4

y ≥ 15

z = y - 4 = 15 - 4

z ≥ 11

Final answer:

To find Robert's minimum age, we need to calculate the ages of Edward, George, and Robert based on the given information.

Explanation:

Minimum Age Calculation:

Let's denote the age of Edward as E, George as 2E (twice as old as Edward), and Robert as E - 4 (Edward's age exceeds Robert's by 4 years).

The sum of their ages is at least 56, so E + 2E + (E - 4) ≥ 56.

Solving the inequality, we get E ≥ 20, George's age (2E) is at least 40, and Robert's minimum age (E - 4) is at least 16.

Answer:

Hilang = 10%

(Di sini tanda negatif dihilangkan karena sudah ditetapkan sebagai hilang )

Step-by-step explanation:

Kami memiliki bahwa jika Rp 50.000.000 sama dengan 100%, berapa yang seharusnya mewakili Rp 45.000.000?

[tex]x=\frac{45.000.000Rp*100}{50.000.000Rp}=90[/tex]

90 ini adalah persentase yang mewakili 45.000.000, jadi kerugiannya dinyatakan sebagai:

h=(nilai jual /biaya )*100%-100% = (nilai jual /biaya -1)*100% = -10%

perhatikan: tanda negatif mewakili kerugian, keuntungan positif

Answer: Our required probability is 50%.

Step-by-step explanation:

Since we have given that

Probability of consuming regularly coffee = 65%

Probability of consuming carbonated soda = 60%

Probability of consuming atleast one of these two products =75%

So, we need to find the probability that they consumes both coffee and soda.

So, using "Probability rules", we get that

[tex]P(C\cap S)=P(S)+P(C)-P(C\cup S)\\\\0.75=0.65+0.60-x\\\\0.75=1.25-x\\\\0.75-1.25=-x\\\\-0.5=-x\\\\x=50\%[/tex]

Hence, our required probability is 50%.

Answer:

a) [tex]a=225 +0.674*16.5=236.121[/tex]

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

b) [tex] P(X \geq 3) = 1-P(X<3) = 1-P(X \leq 2) = 1-[P(X=0)+P(X=1) +P(X=2)]= 1-0.5256=0.4744[/tex]

c) [tex]P(\bar X \geq 225)=1- P(\bar X <225) = 1-P(Z<\frac{225-225}{\frac{16.5}{\sqrt{5}}}) = 1-P(Z<0) = 1-0.5 = 0.5[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(225,16.5)[/tex]  

Where [tex]\mu=225[/tex] and [tex]\sigma=16.5[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.25[/tex]   (a)

[tex]P(X<a)=0.75[/tex]   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.75[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.75[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=0.674=\frac{a-225}{16.5}[/tex]

And if we solve for a we got

[tex]a=225 +0.674*16.5=236.121[/tex]

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

[tex] X\sim Bin(n=10, p=0.25)[/tex]

And we want this probability:

[tex] P(X \geq 3) = 1-P(X<3) = 1-P(X \leq 2) = 1-[P(X=0)+P(X=1) +P(X=2)][/tex]

We can find the individual probabilities like this:

[tex]P(X=0)=(10C0)(0.25)^0 (1-0.25)^{10-0}=0.0563[/tex]

[tex]P(X=1)=(10C1)(0.25)^1 (1-0.25)^{10-1}=0.1877[/tex]

[tex]P(X=2)=(10C2)(0.25)^2 (1-0.25)^{10-2}=0.2816[/tex]

[tex] P(X \geq 3) = 1-P(X<3) = 1-P(X \leq 2) = 1-[P(X=0)+P(X=1) +P(X=2)]= 1-0.5256=0.4744[/tex]

Part c

For this case we know that the distribution for the sample mean is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And we want this probability:

[tex]P(\bar X \geq 225)[/tex]

And for this case we can use the complement rule and the z score given by:

[tex] z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we replace we got:

[tex]P(\bar X \geq 225)=1- P(\bar X <225) = 1-P(Z<\frac{225-225}{\frac{16.5}{\sqrt{5}}}) = 1-P(Z<0) = 1-0.5 = 0.5[/tex]

This problem involves using statistics and probability to interpret and make predictions from data involving the distribution of cutting rates of grinding wheels. It involves understanding mean and standard deviation values and the concept of percentiles in the context of normal distribution. To tackle similar problems, you need to understand how to calculate z-scores, use standard normal tables or functions and probabilities involving multiple events, which may involve the use of formulas such as the binomial probability formula.

Please note that the information provided in your question doesn't directly relate to the grinding wheel problems outlined. However, generally, these types of problems involve an understanding of statistics, probability, and the properties of the normal distribution, especially when using mean and standard deviation values to make calculations and predictions. It also involves understanding percentiles of a distribution and how these relate to the standard normal distribution and z-scores.

For example, if we consider that your calculated 75th percentile of the distribution of cutting rates (236.137 SFM) is correct, you can find the probability of a wheel having a cutting rate greater than this value by finding the corresponding z-score and looking this up on a table of standard normal probabilities, or using a computer program or calculator function that will provide this value. To calculate a probability involving multiple randomly selected wheels, we might need to use a binomial probability formula or similar.

Understanding these methods will allow you to generalise to other such problems. Given the complexity of these concepts however, I would recommend finding a tutor or seeking assistance from your teacher or lecturer to guide you through them.

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Answer:

Domain [-5,∞)

Range [0,∞)

Step-by-step explanation:

Part 1) Find the domain

we have

[tex]f(x)=\frac{1}{2}\sqrt{x+5}[/tex]

we know that

The radicand must be greater than or equal to zero

so

[tex]x+5\geq 0[/tex]

solve for x

subtract 5 both sides

[tex]x\geq -5[/tex]

The solution for x is the interval [-5,∞)

All real numbers greater than or equal to -5

Remember that

The domain of a function is the set of all possible values of x

therefore

The domain of the function f(x) is the interval  [-5,∞)

Part 2) Find the range

we have

[tex]f(x)=\frac{1}{2}\sqrt{x+5}[/tex]

Find the value of f(x) for the minimum value of x

For x=-5

[tex]f(x)=\frac{1}{2}\sqrt{-5+5}[/tex]

[tex]f(x)=0[/tex]

The minimum value of f(x) is equal to zero

so

The solution for f(x) is the interval [0,∞)

All real numbers greater than or equal to 0

Remember that

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

therefore

The range of the function is the interval [0,∞)

Option B

[tex]\frac{a^2b^7c^2}{a^2c^2} = b^7[/tex]

Solution:

Given that, we have to simplify the given expression

Given expression is:

[tex]\frac{a^2b^7c^2}{a^2c^2}[/tex]

We can simplify the expression by cancelling the common terms in numerator and denominator

Take the common terms out in given expression

[tex]\frac{a^2b^7c^2}{a^2c^2} = \frac{a^2c^2(b^7)}{a^2c^2}[/tex]

Cancel the common terms in numerator and denominator

[tex]\frac{a^2b^7c^2}{a^2c^2} = \frac{a^2c^2(b^7)}{a^2c^2} = b^7[/tex]

Thus the simplified form of given expression:

[tex]\frac{a^2b^7c^2}{a^2c^2}=b^7[/tex]

Thus option B is correct

Answer: A) 0.99n + 9.9

B) the total cost is $11.88

Step-by-step explanation:

Let n represent the number of songs that Sophia purchases.

A) Sophia pays a $9.99 membership fee for Apple Music. If Sophia purchases n songs for $0.99 each,then an expression for the total cost would be

0.99n + 9.9

B) If she buys two songs from a new album at a price of $0.99 each, it means that the total cost would be

0.99 × 2 + 9.9

= 1.98 + 9.9

= $11.88

Answer:

The given sums 11+17+23+29+35+41  can be written as in sigma notation is  [tex]\sum\limits_{i=1}^{6}5+6i[/tex]

Therefore 11+17+23+29+35+41=[tex]\sum\limits_{i=1}^{6}5+6i[/tex]

Step-by-step explanation:

Given series is 11+17+23+29+35+41

To find the given sum expressed in sigma notation :

11+17+23+29+35+41  can be written as the given sums in sigma notation is  [tex]\sum\limits_{i=1}^{6}5+6i[/tex]

That is

11+17+23+29+35+41=[tex]\sum\limits_{i=1}^{6}5+6i[/tex]

Now expand the sums and to verify that whether the summation is true or not :

[tex]\sum\limits_{i=1}^{6}5+6i=(5+6(1))+(5+6(2))+(5+6(3))+(5+6(4))+(5+6(5))+(5+6(6))[/tex]

[tex]=(5+6)+(5+12)+(5+18)+(5+24)+(5+30)+(5+36)[/tex]

[tex]=11+17+23+29+35+41[/tex]

Therefore 11+17+23+29+35+41=[tex]\sum\limits_{i=1}^{6}5+6i[/tex]

The sum can be expressed as [tex]\sum_{(i=1)}^6 = 5+6i[/tex].

As we can see in the following series,

Every number in the series can be expressed in the form of (5+6i) where i is the position of the series,

The sum can be verified by expanding the sum from i=1 to6.

[tex]\sum_{(i=1)}^6 = 5+6i\\\sum_{(i=1)}^6 = [5 + 6(1)]+[5 + 6(2)]+[5 + 6(3)]+[5 + 6(4)]+[5+ 6(5)]+[5 + 6(6)]\\\sum_{(i=1)}^6 = 11 + 17 + 23 + 29 + 35 + 41\\\sum_{(i=1)}^6 = 156[/tex]

therefore, the sum can be expressed as,

[tex]\sum_{(i=1)}^6 = 5+6i[/tex].

Learn more about sigma notation:

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Answer: The dilation factor is 1.33, this dilation is an enlargement.

Step-by-step explanation:

Given : A dilation is applied to △ABC to create △DEF.

Since , dilation creates similar figures .

⇒ △ABC≈ △DEF

here , AB corresponds to DE.

BC corresponds to EF.

AC corresponds to DF.

The side-length of corresponding side in image= k x (original length) , where k is dilation factor.

⇒ DE = k (AB)

[tex]\Rightarrow\ k=\dfrac{DE}{AB}=\dfrac{8}{6}=\dfrac{4}{3}=1.33[/tex]

Since , the dilation factor 1.33> 1 , therefore it is an enlargement.

Hence, the dilation factor is 1.33, this dilation is an enlargement.

Answer:

The answer is -343.

Step-by-step explanation:

If a term doesn't have an exponent, it's considered that the exponent is 1 (so basically, (-7)² x (-7)^1.

Multiply the terms with the same base (by adding the exponents - (-7)²+1<- (as the exponential value) (couldn't find the sign so sorry.)

Add the numbers: (-7)³

A negative base raised to an odd power equals a negative: -7³

Write the problem out: -(7 x 7 x 7).

Multiply: -343

Answer:

Therefore, ' 19 ' smaller lawn mover and '11' larger lawn mover were sold.

Step-by-step explanation:

Given:

let the smaller lawn mover  be 'x'

let the larger lawn mower be 'y'

According to condition total mover will be

[tex]x+y=30\\x=30-y[/tex]................( 1 )

and total cost will be given as

[tex]249.99x+329.99y=8379.7[/tex]................( 2 )

To Find:

x =? and y =?

Solution:

Substituting equation 1 in equation 2 we get

[tex]249.99(30-y)+329.99y=8379.7\\7499.7-249.99y+329.99y=8379.7\\80y=880\\\\y=\dfrac{880}{80}\\\\y=11[/tex]

Substituting ' y 'in ( 1 ) we get

[tex]x=30-11=19\\x=19[/tex]

Therefore, ' 19 ' smaller lawn mover and '11' larger lawn mover were sold.

Answer:

5/12

Step-by-step explanation:

For a coin

Number of sample space = 2

Probability of flipping a tail = 1/2

P(T) = 1/2

For a die

Number of sample space = 6

Let D be the event of rolling at least 2.

D = {2,3,4,5,6}

P(D) = 5/6

P(T) and P(D) = P(T) * P(D)

= 1/2 * 5/6

= 5/12

Answer:

1/12

Step-by-step explanation:

got it right

Answer:

Explanation:

First, you must find the pattern behind the set of data in the table shown in the question.

It is said that this is a growing exponentially pattern. Thus, the data should be modeled by a function of the form P(x) = A(B)ˣ.

And you must find both A and B.

B is the multiplicative rate of change of the function which is a constant that you can find by dividing consecutive terms:

Thus, B = 1.55

So far, you know P(x) = A (1.55)ˣ

To find A, you can use P(0)=40, which drives to:

Thus, your function is P(x) = 40(1.55)ˣ

The population of moose after 12 years, is given by P(12):

Thus, round to the nearest whole number, those are 7,692 moose.

Answer:

Aubrey tip $25.50 tip to the staff.

Step-by-step explanation:

Aubrey's dinner cost $ 85.

She tips the waitstaff 30%, percent for excellent service.

Now, to find the tip Aubrey pay to the staff.

Cost of dinner = $85.

Percent of tip = 30%.

So, to get the amount of tip:

30% of $85.

[tex]=\frac{30}{100} \times 85[/tex]

[tex]=0.30\times 85[/tex]

[tex]=\$25.50.[/tex]

Therefore, Aubrey tip $25.50 tip to the staff.

Final answer:

Aubrey tips the waitstaff $25.50 for excellent service on an $85 meal by converting the tip percentage to a decimal and multiplying it with the cost of her meal.

Explanation:

To calculate the tip that Aubrey would leave for excellent service, we first convert the tip percentage to a decimal by dividing by 100. A 30% tip becomes 0.30 in decimal form. Then, we multiply the decimal tip rate by the cost of her meal to find the amount of the tip.

For Aubrey's dinner which cost $85, the calculation would be as follows:

The exact calculation: $85 * 0.30 = $25.50.

Hence, Aubrey tips the waitstaff $25.50 for her $85 meal.

Answer:

20% of apples in Georgia's  bushel basket of apples are not ripe yet.

Step-by-step explanation:

Given:

Total number of apples = 5

Number of apples not ripe yet = 1

We need to find the percent of her apples are not  ripe.

Solution:

Now we know that;

To find the percent of her apples are not  ripe we will divide Number of apples not ripe yet by Total number of apples and then multiply by 100.

framing in equation form we get;

percent of her apples are not  ripe = [tex]\frac{1}{5}\times 100 =20\%[/tex]

Hence 20% of apples in Georgia's  bushel basket of apples are not ripe yet.

Answer:

The answer to your question is (-∞, 3)

Step-by-step explanation:

Data

y(x) = -2x² + 3

v(x) = x

Process

1.- Evaluate y(x) in v(x)

   yov(x) = -2(x)² + 3

   yov(x) = -2x² + 3

2.- Graph the function

In the graph we observe that the posible values of "y" are from (-∞, 3) that is the range.

Answer: 1/5

Step-by-step explanation:

P(both are Orange)

P(at least one is orange)

By using conditional probability:

-The P(both are Orange) is (2C2)/4C2)=1/6

-at least one orange is 1 - 1/6=5/6

P(both are Orange / at least one is orange)=(1/6) / (5/6)

=6/30

=1/5

Given one ball has been established to be orange with no replacement, there are three possible outcomes left in the urn (OO, OB, BO). Only one outcome contains both balls as orange, hence, the probability is 1/3 or approximately 0.333.

Here, we already know that one ball selected is orange from an urn containing two orange and two blue balls. There was no replacement after the first draw, reforming the context of the problem and the counts of the balls in the urn for the second draw.

For the two-draw scenario under question, there are a total of six possible outcomes: (Orange, Orange), (Orange, Blue), (Blue, Orange), (Blue, Blue) - but since we know that at least one ball is orange, the (Blue, Blue) outcome is impossible, leaving us with three valid outcomes. Among these, only one outcome has both balls Orange.

Therefore, the probability that the other ball is also orange, given that at least one is Orange, is 1/3 or approximately 0.333, assuming that all outcomes are equally likely.

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Answer:

The equation representing the the scenario is [tex]72+6m=144[/tex].

It will take 12 month for the company to doubled the number of employees.

Step-by-step explanation:

Given:

Number of employees in the company =72

Number of employee increase per month = 6

We need to find the number of months required to double the number of employees.

Solution:

Doubled number of employees = [tex]2\times[/tex] Number of employees = 144

Let the number of months be 'm'

So we can say that;

Doubled number of employees is equal to Current number of employees in the company plus Number of employee increase per month multiplied by number of months.

framing in equation form we get;

[tex]72+6m=144[/tex]

Hence The equation representing the the scenario is [tex]72+6m=144[/tex].

On solving the above equation we get;

we will subtract both side by 72 we get;

[tex]72+6m-72=144-72\\\\6m=72[/tex]

Dividing both side by 6 we get;

[tex]\frac{6m}{6}=\frac{72}{6}\\\\m =12[/tex]

Hence It will take 12 month for the company to doubled the number of employees.

Final answer:

The distribution of the sample means from samples of size n=600 is a normal distribution, according to the Central Limit Theorem, option C.

Explanation:

When samples of size n=600 are taken and the mean age is calculated from each sample, the distribution of sample means is best described by a normal distribution. This is due to the Central Limit Theorem which states that as the sample size becomes large (n ≥ 30 is a commonly used threshold), the sampling distribution of the sample means will tend to be normal regardless of the shape of the population distribution.

This property of the distribution of sample means applies as long as the samples are taken with replacement or if sampling without replacement, the population is at least ten times larger than the sample. In this case, with a sample size of 600, which is well above 30, we can confidently expect the distribution of sample means to follow a normal distribution.

Answer:

her weekly allowance is $16

Step-by-step explanation:

Let x represent Imani's weekly allowance.

Imani spent half of her weekly allowance playing Mini-golf. This means that the total amount that she spent playing Mini-golf is x/2. The amount that she is left with would be

x - x/2 = x/2

In order to earn more money her parents let her wash the car for $4. This means that the total amount left with her is

x/2 + 4

if she ended with $12, it means that

x/2 + 4 = 12

x/2 = 12 - 4 = 8

x = 2 × 8 = $16