The quality control department at Food Town Inc., a grocery chain in upstate New York, conducts a monthly check on the comparison of scanned prices to posted prices. The chart below summarizes the results of a sample of 500 items last month. Company management would like to know whether there is any relationship between error rates on regularly priced items and specially priced items.


Regular Price Advertised Special Price

Undercharge 20 10

Overcharge 15 30

Correct Price 200 225

Answer:

Stratified sampling

Step-by-step explanation:

Members of the population are divided into two or more subgroups called strata, that share similar characteristics like age, gender, or ethnicity. A random sample from each stratum is then drawn. For instance, if we divide the population of college students into strata based on the number of years in school, then our strata would be freshmen, sophomores, juniors, and seniors. We would then select our sample by choosing a random sample of freshmen, a random sample of sophomores, and so on.

This technique is used when it is necessary to ensure that particular subsets of a population are represented in the sample. Since a random sample cannot guarantee that sophomores would be chosen, we would used a stratified sample if it were important that sophomores be included in our sample. Furthermore, my using stratified sampling you can preserve certain characteristics of the population. For example, if freshmen make up 40% of our population, then we can choose 40% of our sample from the freshmen stratum. Stratified sampling is one of the best ways to enforce "representativeness" on a sample.

Answer:

Probably the engine from their helicopter

Step-by-step explanation:

With u = <-7, 6> and v = <-4, 17>, we have

u + 3v = <-7, 6> + 3 <-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>

We want to find a vector w such that

u + 3v + w = <1, 0>

Subtract u + 3v from both sides to get

w = <1, 0> - (u + 3v) = <1, 0> - <-19, 57>

w = <20, -57>

To get the required vector, subtract u + 3v from the unit vector <1, 0>. The required vector is <20, -57>.

To find the vector that can be added to u + 3v to get the unit vector <1, 0>, we need to subtract u + 3v from the unit vector. This will give us the required vector. Let's calculate:

Unit vector: <1, 0>

u + 3v: <-7, 6> + 3<-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>

Required vector = Unit vector - (u + 3v) = <1, 0> - <-19, 57> = <1 + 19, 0 - 57> = <20, -57>

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Answer:800 miles

Step-by-step explanation:

Given

Round trip for Penthaven to Jackson takes 6 hr and 24 minutes in absence of wind

[tex]t_1=6+\frac{24}{60}=6.4\ hr[/tex]

When Wind blows from Penthaven to Jackson it takes 6 hr and 40 min i.e.

[tex]t_2=6+\frac{40}{60}=\frac{20}{3}\ hr[/tex]

Speed of wind [tex]v=50\ mph[/tex]

Suppose x be the distance between Penthaven and Jackson and u be the speed of plane

So initially

[tex]6.4=\frac{x}{u}+\frac{x}{u}[/tex]

[tex]6.4=\frac{2x}{u}[/tex]

[tex]x=3.2u \quad \ldots(i)[/tex]

When wind is blowing then,

[tex]\Rightarrow \frac{20}{3}=\frac{x}{u+v}+\frac{x}{u-v}[/tex]

[tex]\Rightarrow \frac{20}{3}=x[\frac{1}{u+50}+\frac{1}{u-50}][/tex]

[tex]\Rightarrow \frac{20}{3}=x[\frac{2u}{u^2-50^2}]\quad \ldots(ii)[/tex]

Substitute the value of x in [tex](ii)[/tex]

[tex]\Rightarrow \frac{20}{3}=\frac{2u[3.2u]}{u^2-50^2}[/tex]

[tex]\Rightarrow 10[u^2-50^2]=9.6u^2[/tex]

[tex]\Rightarrow 0.4u^2=50^2\times 10[/tex]

[tex]\Rightarrow u^2=\frac{50^2\times 10^2}{4}[/tex]

[tex]\Rightarrow u=250\ mph[/tex]

Thus [tex]x=3.2\times 250=800\ miles[/tex]

Answer:

357 bears

Step-by-step explanation:

Given;

Population density of bears in the Kenai Peninsula of Alaska = 42 bears per 1000km^2

Area of habitable region of this peninsula = 8500 km^2

how many bears would you expect to find in a habitable region of this peninsula N;

N = population density × area

N = 42/1000 × 8500

N = 357 bears

Answer:

10%

Step-by-step explanation:

There are many different ways but I did 18 divided by 20 and got 0.9. I did 1 - 0.9 to get 0.1, which is 10%

Answer:

This is a circle with centre (6,-7)  and radius 4.

Step-by-step explanation:

The equation of a circle has the following format:

[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]

In which r is the radius(half the diameter) and the centre is the point [tex](x_{0}, y_{0})[/tex]

In this question:

[tex](x-6)^{2} + (y+7)^{2} = 16[/tex]

So

[tex]x_{0} = 6, y_{0} = -7[/tex]

[tex]r^{2} = 16[/tex]

[tex]r = \pm \sqrt{16}[/tex]

The radius is the positive value.

[tex]r = 4[/tex]

So this is a circle with centre (6,-7)  and radius 4.

Answer:

Given equation

(x-6)^2+(y+7)^2=16

centre (6,-7)  and radius 4.

Step-by-step explanation:

The equation of a circle is (x - a)² + (y - b)² = r²

the radius is r

the centre is (a, b)

Given equation

(x-6)^2+(y+7)^2=16

so ,

a = 6

b = - 7

r² = 16

[tex]r = \pm \sqrt{16}[/tex]

r = 4

Therefore,  the circle with centre (6,-7)  and radius 4.

Answer:

it will hold 25.13 cubic inches of melted ice cream

Step-by-step explanation:

first we get the cone formula because a melted ice cream cone will have a flat top, making it a cone

the cone formula is π*r^2 * h /3

so we input radius and height

π*2^2 * 6 /3

then we simplfy

π * 4 * 6 /3

12.56 *6/3

75.398/3

25.13

Answer:

First by expansion,

mxm +mx4 + mxm + mx(-2)

=m^2 +4m + m^2 - 2m

= 2m^2 + 2m

Note: ^2 means square

Step-by-step explanation:

Answer:

Deepwater Horizon

good movie too btw

-Hops

Answer:

48 000 gallons / 2 days = 24 000 gallons per day

24 000 gallons / 24 hours = 1 000 gallons per hour

1 000 gallons / 60 minutes = 16.(6) gallons per minute

I had the same question on a quizz, the question was:In two days, 48,000 gallons of oil gushed out of a well. At what rate did the oil flow from the well?

Hope that was helpful.Thank you!!!

Answer:

[tex] (9-8) -2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 0.0743[/tex]

[tex] (9-8) +2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 1.926[/tex]

And we are 9% confidence that the true mean for the difference of the population means is given by:

[tex] 0.0743 \leq \mu_1 -\mu_2 \leq 1.926[/tex]

Step-by-step explanation:

For this problem we have the following data given:

[tex]\bar X_1 = 9[/tex] represent the sample mean for one of the departments

[tex]\bar X_2 = 8[/tex] represent the sample mean for the other department

[tex]n_1 = 25[/tex] represent the sample size for the first group

[tex]n_2 = 20[/tex] represent the sample size for the second group

[tex]s_1 = 2[/tex] represent the deviation for the first group

[tex]s_2 =1[/tex] represent the deviation for the second group

Confidence interval

The confidence interval for the difference in the true means is given by:

[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex]

The confidence given is 95% or 9.5, then the significance level is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. The degrees of freedom are given by:

[tex] df=n_1 +n_2 -2= 20+25-2= 43[/tex]

And the critical value for this case is [tex] t_{\alpha/2}=2.02[/tex]

And replacing we got:

[tex] (9-8) -2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 0.0743[/tex]

[tex] (9-8) +2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 1.926[/tex]

And we are 9% confidence that the true mean for the difference of the population means is given by:

[tex] 0.0743 \leq \mu_1 -\mu_2 \leq 1.926[/tex]

Answer:18.0625m^2

Step-by-step explanation:

Length =4 1/4 m

Area= length x length

Area=4 1/4 x 4 1/4

Area=(4x4+1)/4 x (4x4+1)/4

Area=17/4 x 17/4

Area=(17x17)/(4x4)

Area=289/16

Area=18.0625m^2

Answer:

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

30 / 2 = 15

60 / 3 = 20

if we try both numbers to see if the limit is ever crossed, that is the case only with 20

15 is the maximum amount of costumes

Answer:

Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Who caught the longer fish, relative to fish of the same species?

Whosoever fish's had the higher z-score.

Stewart caught a bluefish that was 283mm

The mean length of a bluefish is 264 millimeters with a standard deviation of 57mm.

So we have to find Z when [tex]X = 283, \mu = 264, \sigma = 57[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{283 - 264}{57}[/tex]

[tex]Z = 0.33[/tex]

Gina caught a pompano that was 152mm long.

For pompano, the mean is 157mm with a standard deviation of 28mm.

So we have to find Z when [tex]X = 152, \mu = 157, \sigma = 28[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{152 - 157}{28}[/tex]

[tex]Z = -0.18[/tex]

Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species

The correct answer is Stewart caught the longer fish relative to fish of the same species.

To determine who caught the longer fish relative to the average length of their respective species, we need to calculate the z-scores for both Stewart's bluefish and Gina's pompano. The z-score is a measure of how many standard deviations an observation is above or below the mean.

For Stewart's bluefish:

The mean length of a bluefish is 264 mm, and the standard deviation is 57 mm. Stewart's bluefish is 283 mm long. To find the z-score for Stewart's bluefish, we use the formula:

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

where X is the observed value, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation. Plugging in the values for Stewart's bluefish:

[tex]\[ z_{Stewart} = \frac{283 - 264}{57} \] \[ z_{Stewart} = \frac{19}{57} \] \[ z_{Stewart} \approx 0.333 \][/tex]

For Gina's pompano:

The mean length of a pompano is 157 mm, and the standard deviation is 28 mm. Gina's pompano is 152 mm long. To find the z-score for Gina's pompano:

[tex]\[ z = \frac{X - \mu}{\sigma} \] \[ z_{Gina} = \frac{152 - 157}{28} \] \[ z_{Gina} = \frac{-5}{28} \] \[ z_{Gina} \approx -0.179 \][/tex]

Comparing the z-scores:

Stewart's z-score is approximately 0.333, which means his bluefish is 0.333 standard deviations longer than the average bluefish. Gina's z-score is approximately -0.179, which means her pompano is 0.179 standard deviations shorter than the average pompano.

Since Stewart's z-score is positive and larger in magnitude than Gina's negative z-score, Stewart's bluefish is longer relative to its species than Gina's pompano is relative to its species. Therefore, Stewart caught the longer fish relative to fish of the same species.

Answer:

24

Step-by-step explanation:

y=24 when x=3 because you * 3*3=9 so you do 8*3=24 which you your answer

The value of y when x = 9 such that the y varies directly with respect to x is 24 therefore, option (D) will be correct.

Proportion is the relation of a variable with another. It could be direct or inverse.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

As per the given question,

y varies directly as x

y ∝ x

Removing proportion y = kx

Given that,y=8 when x=3

So, k = 8/3

Therefore, relation converts as, y = (8/3)x

At x = 9 → y = (8/3)9 = 24

Hence "The value of y when x = 9 such that the y varies directly with respect to x is 24".

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Final answer:

The equation representing the total monthly cost of the A Fee and Fee plan based on the number of minutes used is y = 0.20x + 29, where y is the total monthly cost and x is the number of minutes.

Explanation:

To find an equation in the form y = mx + b, where x is the number of monthly minutes used and y is the total monthly cost of the A Fee and Fee plan, we first need to determine the slope (m) and the y-intercept (b).

We have two points based on the information given: (290, 87) and (980, 225). The slope (m) is calculated by the difference in cost divided by the difference in minutes:

m = (225 - 87) / (980 - 290)

m = 138 / 690

m = 0.20

Now that we have the slope, we can use one of the points to find b, the y-intercept.

Using the point (290, 87) and the slope 0.20:

87 = 0.20(290) + b

b = 87 - 58

b = 29

The equation representing the total monthly cost (y) based on the number of minutes used (x) is therefore:

y = 0.20x + 29

Answer:

  C.  F(x) = x²

Step-by-step explanation:

"Quadratic" means "second degree". The only function with an exponent of 2 is choice C.

Answer:

D

Step-by-step explanation:

The absolute value parent function is [tex]\mid x \mid[/tex], or answer choice D. Hope this helps!

Answer:

79

Step-by-step explanation:

[tex]\frac{60}{100}[/tex] of a dollar

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.

Kim spent [tex]\frac{40}{100}[/tex] of a dollar on a snack.

So, she has been left with [tex]1-\frac{40}{100}=\frac{60}{100}[/tex] of a dollar on a snack.

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Final answer:

Kim spent 40/100 of a dollar (40 cents) on a snack, so she has 60 cents left.

Explanation:

The question requires converting a fraction of a dollar into a money amount. Kim spent 40/100 of a dollar on a snack. A dollar is equivalent to 100 cents, so Kim spent 40 cents on her snack. To find out how much she has left, we subtract her spending from the total amount of one dollar.

To perform the calculation: 100 cents - 40 cents = 60 cents.

Therefore, Kim has 60 cents left after purchasing the snack.

Answer:

     [tex]\dfrac{3}{1}=\dfrac{12}{4}[/tex]

Step-by-step explanation:

If you write the proportion as ratios of feet to yards, you have ...

  [tex]\dfrac{3\,\text{ft}}{1\,\text{yd}}=\dfrac{12\,\text{ft}}{4\,\text{yd}}\\\\\boxed{\dfrac{3}{1}=\dfrac{12}{4}}\qquad\text{without the units}[/tex]

__

Please note that a proportion is a true statement. Here, you need only pick the true statement from those offered. For example, here's the first choice written in more readable form:

  [tex]\dfrac{12}{1}=\dfrac{4}{12}\qquad\text{FALSE statement}[/tex]

Answer:

d: 3/1   12/4

Step-by-step explanation:

Answer:

  a) 6 angelfish, 2 clownfish

  b) 4 angelfish, 8 clownfish

Step-by-step explanation:

There are at least a couple of different algorithms for finding integer solutions to problems like this. However, it is easiest to describe a trial-and-error solution.

Here, we have defined a function that tells us the number of clownfish we will get if we purchase some number of angelfish. When the function value is an integer, we have found a solution. We compute the value of the function for all reasonable numbers of angelfish.

a) The problem statement tells us the total purchase amount for "c" clownfish and "a" angelfish will be ...

   3.60c +5.80a = 42.00

We are told that we must buy at least 1 of each kind of fish, so the most clownfish we can buy will be ...

  3.60c +5.80×1 = 42.00

  c = (42.00 -5.80)/3.60 = 10 1/18

And the most angelfish we can buy will be ...

  3.60×1 +5.80a = 42.00

  a = (42.00 -3.60)/5.80 = 6 18/29

Since we can buy fewer angelfish, a trial-and-error solution will look a the number of clownfish we can buy for each different purchase of angelfish.

We can write a function, similar to the equation for "c" above, that tells us the number of clownfish for x angelfish:

  f(x) = (42 -5.80x)/3.60

We want to find the value of x that results in an integer number of clownfish. The attached table shows us that purchase of 6 angelfish will allow purchase of 2 clownfish for $42.

__

b) Using the same idea, we can repeat the process for a total purchase of $52. The attached table tells us the solution is a purchase of 4 angelfish and 8 clownfish for $52.

Answer:

D.) [tex]y+1=-3(x-10)[/tex]

Step-by-step explanation:

The original point slope form equation is as follows:

[tex]y - y_1 = m(x-x_1)[/tex]

When you input a negative or positive value into the equation, the sign may or may not change. In this case, we input a negative y value -- this caused the sign to change to '+1' rather than stay at '-1'

Answer:

3.22% probability that the sample average is greater than $228,500

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 227000, \sigma = 8500, n = 110, s = \frac{8500}{\sqrt{110}} = 810.44[/tex]

What is the probability that the sample average is greater than $228,500?

This is 1 subtracted by the pvalue of Z when X = 228500. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{228500 - 227000}{810.44}[/tex]

[tex]Z = 1.85[/tex]

[tex]Z = 1.85[/tex] has a pvalue of 0.9678

1 - 0.9678 = 0.0322

3.22% probability that the sample average is greater than $228,500

Answer:

[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]    

[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]    

And the best option would be:

c. 1450 +/- 12

Step-by-step explanation:

Information provided

[tex]\bar X=1450[/tex] represent the sample mean for the SAT scores

[tex]\mu[/tex] population mean (variable of interest)

[tex]s^2 = 900[/tex] represent the sample variance given

n=25 represent the sample size  

Solution

The confidence interval for the true mean is given by :

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The sample deviation would be [tex]s=\sqrt{900}= 30[/tex]

The degrees of freedom are given by:

[tex]df=n-1=2-25=24[/tex]

The Confidence is 0.954 or 95.4%, the value of [tex]\alpha=0.046[/tex] and [tex]\alpha/2 =0.023[/tex], assuming that we can use the normal distribution in order to find the quantile the critical value would be [tex]z_{\alpha/2} \approx 2.0[/tex]

The confidence interval would be

[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]    

[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]    

And the best option would be:

c. 1450 +/- 12

Answer:

39 children and 13 adults

Step-by-step explanation:

3children = 1 adult

52 = x * (3children + 1adult)

52= x * 4

13 = x

x = 13

total children = 3x

3x = 39

The problem poses a system of linear equations where the number of attendees 'a + c = 52' and 'c = 3a'. Resolving these equations gives 'a = 13' adults and 'c = 39' children.

This is a problem about creating and solving a system of linear equations. Let's denote the number of adults who attended the ball game as 'a' and the children who attended the game as 'c'. According to the problem, we have two parts of information that can be written as equations:

You can substitute the equation for 'c' in the first equation: a + (3a) = 52. Solving this, you find that 'a' equates to 13. Substitute 'a = 13' into the second equation, you will find that 'c = 39'. This indicates that there were 13 adults and 39 children who attended the game.

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Answer:

b = 7.9

Step-by-step explanation:

A = 37       a =

B = 53       b =

C = 90       c = 10

B = 180 - 90 -37 = 53

[tex]\frac{sinB}{b} = \frac{sinC}{c}\\ \frac{sin(53)}{b} = \frac{sin(90)}{10}\\ b = \frac{10 sin(53)}{sin(90)} \\b = 7.9[/tex]

To find the length of side AC in a right-angled triangle ABC with angle A of 37 degrees and hypotenuse 10, we use the cosine function. AC equals the hypotenuse multiplied by the cosine of angle A, resulting in AC being approximately 7.9 units long.

The student wants to know the length of side AC in a right-angled triangle ABC, where angle C is a right angle, angle A is 37 degrees, and the hypotenuse (side BC) is 10. To find the length of side AC, we will use trigonometric functions. Specifically, we will use the cosine function, which relates the adjacent side to the hypotenuse in a right-angled triangle. The cosine of angle A (cos 37°) is equal to the adjacent side (AC) divided by the hypotenuse (BC).

The formula is: Cosine of angle A = AC / BC

This can be rewritten as: AC = BC * Cosine of angle A

By substituting the given values (BC = 10 and angle A = 37°), we get:

AC = 10 * cos(37°)

To find cos(37°), we can use a calculator set to degree mode. The calculation gives us:

AC = 10 * 0.7986 (approximately)

Therefore, AC ≈ 10 * 0.7986 = 7.986

AC is approximately 7.9 units long.

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Answer:

Probability that the sample average time taken is less than 11 minutes for Day 1 is 0.86864.

Probability that the sample average time taken is less than 11 minutes for Day 2 is 0.88877.

Step-by-step explanation:

We are given that the time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal probability distribution with average time 10 minutes and a standard deviation of 2 minutes.

Also, five individuals fill out the form on Day 1 and six individuals fill out the form on Day 2.

(a) Let [tex]\bar X[/tex] = sample average time taken

The z score probability distribution for sample mean is given by;

                                Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 10 minutes

            [tex]\sigma[/tex] = standard deviation = 2 minutes

            n = sample of individuals fill out form on Day 1 = 5

Now, the probability that the sample average time taken is less than 11 minutes for Day 1 is given by = P([tex]\bar X[/tex] < 11 minutes)

         P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{5} } }[/tex] ) = P(Z < 1.12) = 0.86864

The above probability is calculated by looking at the value of x = 1.12 in the z table which has an area of 0.86864.

(b) Let [tex]\bar X[/tex] = sample average time taken

The z score probability distribution for sample mean is given by;

                                Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 10 minutes

            [tex]\sigma[/tex] = standard deviation = 2 minutes

            n = sample of individuals fill out form on Day 2 = 6

Now, the probability that the sample average time taken is less than 11 minutes for Day 2 is given by = P([tex]\bar X[/tex] < 11 minutes)

         P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{6} } }[/tex] ) = P(Z < 1.22) = 0.88877

The above probability is calculated by looking at the value of x = 1.22 in the z table which has an area of 0.88877.

Answer:

Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water

Step-by-step explanation:

Brian makes a cleaning solution using a ratio of 4 cups of water to 1 cup of vinegar.

Let c be the number of cups of vinegar that Brian should use with 12 cups of water.

1 cup of vinegar uses cup of water = 4

c cups of vinegar uses cup of water = 4c

We are c, the number of cups ofvinegar that Brian should use with 12 cups of water

So, 4c=12

[tex]4=\frac{12}{c}[/tex]

So, equation =[tex]\frac{4}{1}=\frac{12}{c}[/tex]

So, Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water

Answer:

D. g(x)=4x^2

Step-by-step explanation:

Answer: g(x)=4x^2

check picture below