Kings Department Store has 625 rubies, 800 diamonds, and 700 emeralds from which they will make bracelets and necklaces that they have advertised in their Christmas brochure. Each of the rubies is approximately the same size and shape as the diamonds and the emeralds. Kings will sell each bracelet for $400 and it costs them $150 to make it. Each bracelet is made with 2 rubies, 3 diamonds, and 4 emeralds. Kings will sell each necklace for $700 and it costs them $200 to make it. Each neckalce is made with 5 rubies, 7 diamonds, and 3 emeralds. a) Formulate the above problem as a Linear Programming problem with the objective of maximizing profit

Answer:

The 95% confidence (and interpret) the proportion of all American adults of European an- cestry who dislike the taste of cilantro

(  0.2552  , 0.2709)

b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is  0.2552

Step-by-step explanation:

Explanation:-

Given data a survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro.

large sample size 'n' = 12087 American adults

in survey A total of 3181 said that they dislike the taste of cilantro.

so The sample proportion 'p' = [tex]\frac{3181}{12087} = 0.2631[/tex]

a) Estimate with 95% confidence (and interpret) the proportion of all American adults of European ancestry who dislike the taste of cilantro.

[tex](p - 1.96 \sqrt{\frac{pq}{n} } ,p + 1.96\sqrt{\frac{pq}{n} } )[/tex]

[tex](0.2631 - 1.96 \sqrt{\frac{0.2631 X 0.7369}{12087} } ,0.2631 + 1.96\sqrt{\frac{0.2631 X 0.7369 }{12087} } )[/tex]

(0.2631 - 0.00784 , 0.2631 + 0.00784 )

(  0.2552  , 0.2709)

b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is  0.2552

We are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%, and at least 25.5% dislike the taste.

This question is related to confidence intervals in statistics. To compute a confidence interval for a population proportion, we mainly need the sample proportion and the size of the sample. Here, the proportion is the number of respondents that dislike cilantro (3181) divided by the total number of respondents (12087).

Thus, the sample proportion (value of p) is 3181/12087 = 0.263 or 26.3%.

The formula for a confidence interval is:

CI = p +/- Z * sqrt[ (p(1-p)) / n ],

where Z is the Z-score (for 95% confidence, Z = 1.96), p is the sample proportion, and n is the sample size.

Applying the values, we get:

CI = 0.263 +/- 1.96 * sqrt[ (0.263)(1 - 0.263) / 12087 ]

After calculation, the 95% confidence interval is about (0.255, 0.271). This means we are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%.

For the lower bound, we can take the lower limit of our confidence interval, which is 0.255 or 25.5%. This means we are 95% confident that at least 25.5% of all American adults of European ancestry dislike the taste of cilantro.

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Answer:

see explanation

Step-by-step explanation:

(a)

For the graph to display direct proportion it must pass through the origin.

The graph shown does not pass through the origin thus does not represent direct proportion.

(b)

Given that q is directly proportional to r then the equation relating them is

q = kr ← k is the constant of proportion

To find k use the condition q = 76 when r = 20, thus

76 = 20k ( divide both sides by 20 )

3.8 = k

q = 3.8r ← equation of proportion

When r = 45, then

q = 3.8 × 45 = 171

Answer:

3

Step-by-step explanation:

0 indicates no relationship. must be full number.

Step-by-step explanation:

W(x) = (10x⁴ − 8) (30x + 25)^0.5

A) Take log of both sides.

ln(W) = ln[(10x⁴ − 8) (30x + 25)^0.5]

ln(W) = ln(10x⁴ − 8) + ln[(30x + 25)^0.5]

ln(W) = ln(10x⁴ − 8) + 0.5 ln(30x + 25)

Take derivative.

W' / W = 40x³ / (10x⁴ − 8) + 0.5 (30) / (30x + 25)

W' / W = 20x³ / (5x⁴ − 4) + 3 / (6x + 5)

W' = W [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]

W'(x) = (10x⁴ − 8) (30x + 25)^0.5 [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]

B) Evaluate at x = 0.

W'(0) = (0 − 8) (0 + 25)^0.5 [0 / (0 − 4) + 3 / (0 + 5)]

W'(0) = (-8) (5) (0 + 3/5)

W'(0) = -24

Answer:

[tex]\textsf{A)}\quad W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]

[tex]\textsf{B)}\quad W'(0)=-24[/tex]

Step-by-step explanation:

Given function:

[tex]W(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5}[/tex]

Take the natural logarithm of both sides:

[tex]\ln \left(W(x)\right) = \ln \left( (10x^4 - 8) \cdot (30x + 25)^{0.5} \right)[/tex]

Use properties of logarithms to simplify:

[tex]\ln \left(W(x)\right) = \ln (10x^4 - 8) +\ln(30x + 25)^{0.5} \\\\\\ \ln \left(W(x)\right) = \ln (10x^4 - 8) +0.5 \ln(30x + 25)[/tex]

Differentiate both sides with respect to x:

[tex]\dfrac{d}{dx} \ln \left(W(x)\right) = \dfrac{d}{dx} \left( \ln (10x^4 - 8) + 0.5 \ln (30x + 25) \right)[/tex]

Apply the chain rule on the right-hand side:

[tex]\dfrac{W'(x)}{W(x)} = \dfrac{1}{10x^4 - 8} \cdot \dfrac{d}{dx} (10x^4 - 8) + 0.5 \cdot \dfrac{1}{30x + 25} \cdot \dfrac{d}{dx} (30x + 25) \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{1}{10x^4 - 8} \cdot (40x^3) + 0.5 \cdot \dfrac{1}{30x + 25} \cdot (30) \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{40x^3}{10x^4 - 8} + \dfrac{15}{30x + 25} \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{2(20x^3)}{2(5x^4 - 4)} + \dfrac{5(3)}{5(6x + 5)} \\\\\\ \dfrac{W'(x)}{W(x)} = \dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5}[/tex]

Multiply both sides by W(x) to solve for W'(x):

[tex]W'(x) = W(x) \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]

Substitute W(x) back in:

[tex]W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]

Therefore, the derivative W'(x) is:

[tex]W'(x) = (10x^4 - 8) \cdot (30x + 25)^{0.5} \left(\dfrac{20x^3}{5x^4 - 4} + \dfrac{3}{6x + 5} \right)[/tex]

[tex]\dotfill[/tex]

To find W'(0), substitute x = 0 into W'(x):

[tex]W'(0) = (10(0)^4 - 8) \cdot (30(0) + 25)^{0.5} \left(\dfrac{20(0)^3}{5(0)^4 - 4} + \dfrac{3}{6(0) + 5} \right) \\\\\\ W'(0) = (0 - 8) \cdot (0 + 25)^{0.5} \left(\dfrac{0}{0 - 4} + \dfrac{3}{0 + 5} \right) \\\\\\ W'(0) = (- 8) \cdot (25)^{0.5} \cdot \left( \dfrac{3}{5} \right) \\\\\\ W'(0) = (- 8) \cdot 5 \cdot \dfrac{3}{5} \\\\\\ W'(0)=-24[/tex]

Therefore, the value of W'(0) is -24.

There are 54 two-digit numbers greater than 45. This is calculated by finding the range of valid two-digit numbers (46 to 99) or carefully counting possible combinations without including 45.

The two-digit numbers greater than 45 are any numbers from 46 to 99. We can find the amount of these numbers by subtracting 45 from 99. So, there are 54 two-digit numbers greater than 45.

Another way to visualize this is by considering the two-digit possibilities. The first digit can range from 4 to 9 (six possibilities), and the second digit can range from 0 to 9 (ten possibilities). However, since 40-45 are not included, we subtract 5 from the total possibilities, resulting in 60 (=6*10) -5 = 55. Therefore, it seems that we have one number too many, but we must not forget that 45 itself is not included, hence the total numbers exceeding 45 are 54 (55-1).

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Answer:

a, -b

Step-by-step explanation:

When x is a, the function becomes

[tex]f(a)=3(a-a)(a+b)[/tex]

as you see, a-a is 0, and as your whole function is multiplied by this, it makes it 0.

[tex]f(-b)=3(-b-a)(-b+b)[/tex]

As you see -b+b is 0, and once again, this would make the whole function 0.

Answer:

use 6cm twice and that adds up to 12cm .six is the minimal possible number

A ruler designed to measure lengths from one unit to twelve units with the minimum number of marks would only have marks at every unit. This results in only eleven markings (from 1 to 11), as the 0 marks the start and the twelfth unit marks the end.

The subject of the student's question pertains to the design of a ruler with the minimum possible number of marks that can measure lengths from one to twelve units. To achieve this, the ruler should only be marked at every unit. This way, there would be only eleven marks (1-11), as the 0 marks the start of the ruler and the twelfth unit is considered the end of the ruler but does not require a mark. Therefore, only the spaces between these numbers need to be marked to enable measurement all the way up to twelve units.

In practice, such a ruler is less precise than a ruler with more marks as the latter can measure smaller lengths more accurately. However, the task demands the bare minimum for a measure from 1 to 12, thus we have eleven marks.

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Answer:

Experiement lacked blindness concept

Step-by-step explanation:

In good experiments, the results are totally unbiased and unknown to anyone, even to those conducting the experiment.

In the given case, the interviewer had an idea about which group had gone for meditation so it was obvious that they would yield less anxiety.

Here the concept of blinding was missing, which is essential for a good and fair experiment. A good experiemnt is a double blinded experiement or atleast it should be single blinded

The height of the cylinder with a volume of 384π cubic inches and a radius of 8 inches is 6 inches.

To find the height of a cylinder with a known volume and radius, we use the formula for the volume of a cylinder, which is V =  πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height. We are given a volume of 384π cubic inches and a radius of 8 inches. Plugging these values into the formula gives us:

384 π = π (8²) h
384 π = 64π h
h = 384 π ÷ 64π
h = 6 inches

Therefore, the height of the cylinder is 6 inches.

Answer:

9100

Step-by-step explanation:

I=Prt

I=7,000(.06)5

I=420(5)

I=2,100

2,100+7,000=9,100

Answer:

The 98% confidence interval for the average credit card balance is

(564.04, 635.96).

Step-by-step explanation:

We have to calculate the 98% confidence interval on the average credit card balance.

The sample will consist of the n=30 customers that have credit card.

The sample has a mean of $600 and a standard deviation of $80.

As the population standard deviation is estimated from the sample standard deviation, we will use a t statistic.

The degrees of freedom are:

[tex]df=n-1=30-1=29[/tex]

The critical value for a 98% CI and 29 degrees of freedom is t=2.463 (this can be looked up in a t-table).

Then, the margin of error is:

[tex]E=t\cdot s/\sqrt{n}=2.463*80/\sqrt{30}=197.04/5.48=35.96[/tex]

Then, the upper and lower bounds of the confidence interval are:

[tex]LL=\bar X-E=600-35.96=564.04\\\\UL=\bar X+E=600+35.96=635.96[/tex]

Answer:

The risk consequence of both activities is 1.6 months.

Step-by-step explanation:

We can define a randome variable D: total delay time for the project, and calculate its expected value.

This would be the risk consequence of both activities.

The expected delay time for the project is the sum of the expected delay for task A plus the expected delay for task B. It is assumed the likelihood of a problem in any task is independent of the other.

Then, each expected delay for a task is equal to the probability of a problem multiplied by the consequence (delay time).

[tex]E(D)=E(D_a)+E(D_b)=p_aT_a+p_bT_b\\\\E(D)=0.5*2+0.2*3=1+0.6=1.6[/tex]

The risk consequence of both activities is 1.6 months.

Answer:

(0.339, 0.391)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1295, \pi = \frac{473}{1295} = 0.365[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.365 - 1.96\sqrt{\frac{0.365*0.635}{1295}} = 0.339[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.365 + 1.96\sqrt{\frac{0.365*0.635}{1295}} = 0.391[/tex]

So the correct answer is:

(0.339, 0.391)

Answer:

A. Brand A has a higher average price than brand B.

D. Brand A's prices are less spread out than brand B's prices.

Step-by-step explanation:

We are given the means and standard deviations for samples of prices from two  different brands of shoes below;

 Brand A                                                                  Brand B

Mean : $50                                                           Mean : $40

Standard deviation : $5                                  Standard deviation : $8    

Now, from the given statements;

Statement A is correct that Brand A has a higher average price than brand B because as given above Mean of Brand A ($50) > Mean of Brand B ($40).

Also, Statement D is correct that Brand A's prices are less spread out than brand B's prices because the Variance of Brand A is less than the variance of Brand B, i.e.;

    Variance of Brand A = [tex]5^{2}[/tex] = $25

    Variance of Brand B = [tex]8^{2}[/tex] = $64

Clearly, $25 < $64, so statement D is also correct.

Therefore, the two true statements are Statement A and Statement D.

Final answer:

A. Brand A has a higher average price than brand B.

D. Brand A's prices are less spread out than brand B's prices.

Explanation:

The true statements are that Brand A has a higher average price and less variability in prices than Brand B, which is represented by a lower standard deviation for Brand A.

To expand on these points:

Brand A has a mean price of $50 which is higher than Brand B's mean price of $40, confirming that Brand A has a higher average price (Statement A).

Brand A's standard deviation is $5, while Brand B's standard deviation is $8. A standard deviation is a measure of spread or variability in a set of data. The fact that Brand A's standard deviation is lower indicates that its prices are less variable and more closely clustered around the mean, hence less spread out compared to Brand B (Statement D).

Answer:

13%

Step-by-step explanation:

There are 100 squares and 13 are shaded so

13/100=

13%

Answer:

13%

Step-by-step explanation:

Median: 133.5

Lower/First quartile: 128

Upper/Third quartile: 139

Interquartile range: 139 - 128 = 11

so your interquartile range is 11

5 times,I hoped this helped you out,if not sorry

Answer: C represents a function

Step-by-step explanation: It represents a function because there is exactly one range for each domain, and only one. In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power.

Answer:

(a)Mean=9

(b)Median=9.5

(c)Mode=12

(d)Standard Deviation=2.53

Step-by-step explanation:

The sample of the number of vehicles that proceeded through the intersection after the light changed for 6 days during a 1 month period is given below:

6 12 7 12 8 9

(a)Mean

[tex]Mean=\frac{6+12+ 7+ 12+ 8+ 9}{6} \\=\frac{54}{6} \\Mean=9[/tex]

(b)Median

First, arrange in ascending order

6,7,8,9,12,12

Since we have two terms in the middle, we take the average.

[tex]Median=\frac{8+9}{2}\\Median=8.5[/tex]

(c)Mode

The mode is the number with the highest frequency. The mode number of cars is 12.

(d)Standard Deviation

[tex]S.D.=\sqrt{\dfrac{\sum_{i=1}^{n}(x-\bar{x})^2}{n-1}}[/tex]

[tex]S.D.=\sqrt\frac{(6-9)^2+(7-9)^2+(8-9)^2+(9-9)^2+(12-9)^2+(12-9)^2}{6-1}[/tex]

[tex]=\sqrt{6.4} \\S.D.=2.53[/tex]

Answer:

d

Step-by-step explanation:

C is the center of a circle. Find the length of arc AB to two decimal points

Answer:

d

Step-by-step explanation:

s=13.68

Answer:2

4 th root of 1024 is 5

Since 4 x4x4x4x4=1024

So 1+2x=5

-1 PN both sides

2x= 4

Divide by 2

X=2

Step-by-step explanation:

Answer:

1  1/10 gallons

Step-by-step explanation:

Add 4/5 gallon + 3/10 gallon

Get a common denominator of 10

4/5*2/2  + 3/10

8/10 +3/10

11/10

Change from an improper fraction to a mixed number

10/10 + 1/10

1 1/10 gallons

Answer:

1.1

Step-by-step explanation:

If she added the first 4/5 then she added the 3/10 then you have to add them to figure out how much water is in the bucket.

Answer:

[tex](0.08-0.0888) - 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= -0.0175[/tex]  

[tex](0.08-0.0888) + 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= 0.0015[/tex]  

And the 95% confidence interval would be given (-0.0175;0.0015).  

We are confident at 95% that the difference between the two proportions is between [tex]-0.0175 \leq p_A -p_B \leq 0.0015[/tex]

And since the confidence interval contains the 0 we have enough evidence to conclude that the population proportions are not significantly different at 5% of significance.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

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".  

[tex]p_A[/tex] represent the real population proportion for California

[tex]\hat p_A =0.08[/tex] represent the estimated proportion for California

[tex]n_A=11545[/tex] is the sample size required for California

[tex]p_B[/tex] represent the real population proportion for Oregon

[tex]\hat p_B =0.088[/tex] represent the estimated proportion for Brand B

[tex]n_B=4691[/tex] is the sample size required for Oregon

[tex]z[/tex] represent the critical value for the margin of error  

Solution to the problem

The sample proportion have the following distribution  

[tex]\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]  

The confidence interval for the difference of two proportions would be given by this formula  

[tex](\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}[/tex]  

For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.  

[tex]z_{\alpha/2}=1.96[/tex]  

And replacing into the confidence interval formula we got:  

[tex](0.08-0.0888) - 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= -0.0175[/tex]  

[tex](0.08-0.0888) + 1.96 \sqrt{\frac{0.08(1-0.08)}{11545} +\frac{0.088(1-0.088)}{4691}}= 0.0015[/tex]  

And the 95% confidence interval would be given (-0.0175;0.0015).  

We are confident at 95% that the difference between the two proportions is between [tex]-0.0175 \leq p_A -p_B \leq 0.0015[/tex]

And since the confidence interval contains the 0 we have enough evidence to conclude that the population proportions are not significantly different at 5% of significance.

Answer:

The standard error of the sample proportion is closest to 1%

Step-by-step explanation:

Standard error of the sample proportion is given as

σₓ = √[p(1-p)/n]

where

p = sample proportion = estimated to be 23% = 0.23

n = Sample size = 2500

σₓ = √[p(1-p)/n]

σₓ = √[0.23×0.77/2500]

σₓ = 0.0084166502 = 0.00842

σₓ = 0.00842 = 0.842%

Hence, it is easy to see that the standard error of the sample proportion is closest to 1%.

Hope this Helps!!!

Answer:

[tex]n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92[/tex]

So the answer for this case would be n=92 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

[tex]\bar X[/tex] represent the sample mean for the sample  

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

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =1.5 and we are interested in order to find the value of n, if we solve n from equation (b) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 92% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.04;0;1)", and we got [tex]z_{\alpha/2}=1.75[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92[/tex]

So the answer for this case would be n=92 rounded up to the nearest integer

Answer:

[tex]1100 \text{feet}^3[/tex]

Step-by-step explanation:

GIVEN: A swimming pool is circular with a [tex]20\text{ feet}[/tex] diameter. The depth is constant along east-west lines and increases linearly from [tex]1\text{ feet}[/tex] at the south end to [tex]6\text{ feet}[/tex] at the north end.

TO FIND: Find the volume of water in the pool.

SOLUTION:

Consider the image attached.

when two similar figures are attached a new cylinder is formed. volume of swimming pool is half of volume of new cylinder formed.

radius of new cylinder [tex]=\frac{\text{diameter}}{2}=\frac{20}{2}=10\text{ feet}[/tex]

height of new cylinder [tex]=6+1=7\text{ feet}[/tex]

volume of cylinder [tex]=\pi r^2h=\frac{22}{7}\times(10)^27[/tex]

                               [tex]=2200\text{ feet}^3[/tex]

Volume of swimming pool [tex]=\frac{\text{volume of cylinder}}{2}=\frac{2200}{2}[/tex]

                                           [tex]=1100\text{ feet}^3[/tex]

Hence volume of water in the pool is [tex]1100 \text{feet}^3[/tex].

Final answer:

To find the volume of water in a swimming pool with varying depths, calculate the volume by considering different height sections of the pool.The volume of water in the pool is approximately 13,287 ft³.

Explanation:

A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end.

Given the pool's dimensions, you can calculate the volume of water in the pool by breaking it into sections of different heights.

The volume of water in the pool is approximately 13,287 ft³.

Answer:

i believe it is 4 but i'm not so sure

Step-by-step explanation:

:)

The graph of g(x)=(x-2)^2+3 compared to the graph of f(x)=x^2 is translated 2 units to the right and 3 units upwards.

To understand the transformation of graphs in mathematical terms, consider the initial function f(x) = x^2. The transition to the new function g(x)=(x-2)^2+3 is a result of a shift or translation of the graph. This transformation behaves as per the following rule: g(x) = f(x-h)+k where 'h' units is the horizontal displacement and 'k' units is the vertical displacement.

In the function g(x), x shifts two units to the right (as indicated by (x-2)) and three units upward (as indicated by +3).

So, the correct answer is 2 units right and 3 units up.

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Answer:

The probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches is 0.5319.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard-deviation σ and appropriately huge random-samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the distribution of sample mean is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

[tex]\mu=200\\\sigma=22\\n=83[/tex]

Since n = 83 > 30, the Central Limit Theorem can be used to approximate the sampling distribution of sample mean diameter of the shafts.

Then:

Mean: [tex]\mu_{\bar x}=\mu=200[/tex]

Standard deviation: [tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{22}{\sqrt{83}}=2.415[/tex]

Compute the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches as follows:

[tex]P(\bar X-\mu_{\bar x}<0.20)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{0.20}{2.415})[/tex]

                            [tex]=P(Z<0.08)\\=0.53188\\\approx0.5319[/tex]

*Use a z-table.

Thus, the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches is 0.5319.

Answer:

1/3

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

took a test and its correct.

[tex]\[ s = kt^5 \][/tex]

This equation represents the model for the statement "s is directly proportional to the fifth power of t".

When two variables [tex]\( s \)[/tex] and [tex]\( t \)[/tex] are directly proportional to each other, it means that as one variable increases, the other variable also increases by a constant factor. Mathematically, we can express this relationship as:

[tex]\[ s = kt^n \][/tex]

Where:

- [tex]\( s \)[/tex] is the dependent variable.

-[tex]\( t \)[/tex] is the independent variable.

- [tex]\( k \)[/tex] is the constant of proportionality.

- [tex]\( n \)[/tex] is the exponent representing the power to which the independent variable is raised.

In this case, the statement says that  s is directly proportional to the fifth power of t . So, we have:

[tex]\[ s = kt^5 \][/tex]

This equation represents the model for the statement "s is directly proportional to the fifth power of t".

Complete correct question:

Write a model for the statement

s is directly proportional to the fifth power of t.