If y varies directly as x, and y is 18 when x is 5, which expression can be used to find the value of y when x is 11? y = StartFraction 5 Over 18 EndFraction (11) y = StartFraction 18 Over 5 EndFraction (11) y = StartFraction (18) (5) Over 11 EndFraction y = StartFraction 11 Over (18) (5) EndFraction

Answer:

1413 square yards of lawn receives water.

Step-by-step explanation:

We are given the following in the question:

Radius of garden, r = 36 yards

Rotating angle, [tex]\theta[/tex]  = [tex]125^\circ[/tex]

First converts the given angle measure in radians.

[tex]\text{Radians} = \dfrac{\pi}{180}\times \theta[/tex]

Thus, the rotating angle in radians is:

[tex]\dfrac{\pi}{180}\times 125 = 2.18\text{ Radians}[/tex]

Area of lawn =

[tex]\displaystyle\frac{1}{2}r^2 \times \text{Radian measure of angle}\\\\=\frac{1}{2}(36)^2\times 2.18 = 1412.64 \approx 1413\text{ square yards}[/tex]

Thus, 1413 square yards of lawn receives water.

Final answer:

1413 square yards of lawn receives water.

Explanation:

1413 square yards of lawn receives water.

Step-by-step explanation:

We are given the following in the question:

Radius of garden, r = 36 yards

[tex]Rotating angle, \theta = 125^\circ[/tex]

First converts the given angle measure in radians.

[tex]\text{Radians} = (\pi)/(180)* \theta[/tex]

Thus, the rotating angle in radians is:

[tex](\pi)/(180)* 125 = 2.18\text{ Radians}[/tex]

Area of lawn =

[tex]\displaystyle(1)/(2)r^2 * \text{Radian measure of angle}\n\n=(1)/(2)(36)^2* 2.18 = 1412.64 \approx 1413\text{ square yards}[/tex]

Thus, 1413 square yards of lawn receives water.

Answer:

there a bad football team probably the raiders  

Step-by-step explanation:

but take 72.5 and take away 13.5

                     72.5

                  -  13.5

                   -----------

                      59

Answer: [tex]5\frac{4}{5}[/tex]

Step-by-step explanation:

The first step is to make 7&2/5 a improper fraction, using the rule [tex]a\frac{b}{c}= \frac{ac+b}{c}[/tex].

Answer:

a) [tex] 61-35.8=25.3[/tex]

b) [tex] \frac{25.2}{11.3}=2.23[/tex] deviations

c) [tex] z = \frac{61- 35.8}{11.3}= 2.23[/tex]

d) For this case since we have that z>2 we can consider this value as unusual, since is outside of the interval considered usual.

Step-by-step explanation:

Assuming this complete question : "Helen Mirren was 61 when she earned her Oscar-winning Best Actress award. The Oscar-winning Best Actresses have a mean age of 35.8 years and a standard deviation of 11.3 years"

a) What is the difference between Helen Mirren’s age and the mean age?

For this case we can do this:

[tex] 61-35.8=25.2[/tex]

b) How many standard deviations is that?

We just need to take the difference and divide by the deviation and we got:

[tex] \frac{25.2}{11.3}=2.23[/tex] deviations

c) Convert Helen Mirren’s age to a z score.

The z score is defined as:

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

And if we replace the values given we got:

[tex] z = \frac{61- 35.8}{11.3}= 2.23[/tex]

d) If we consider “usual” ages to be those that convert to z scores between –2 and 2, is Helen Mirren’s age usual or unusual?

For this case since we have that z>2 we can consider this value as unusual, since is outside of the interval considered usual.

Answer:

Nominal level of measurement is the one where data cannot be arranged in an ordering scheme.

Explanation:

This Nominal measurement level is generally characterized by various data that consist of categories of various types,labels of various kinds and also names.

The data that are involved in this type of measurement usually cannot be arranged in an orderly manner or in an ordering scheme.

One of the best example of these type of measurement includes survey responses such as choosing between Yes or No or sometimes undecided.

Thus we can consider nominal level measurement as the answer.

Answer:

nominal

Step-by-step explanation:

Answer:

  none of the above (only i and ii are correct)

Step-by-step explanation:

The given numbers appear on the number line left-to-right in this order:

  -4.3  -3.7  -2.6  -1.8  -0.9

The "<" relationship is true if the number on the left is to the left on the number line. That is the case for -4.3 < -3.7, and for -3.7 < -2.6.

The ">" relationship is true if the number on the left is to the right on the number line. That is NOT THE CASE for -4.3 > -2.6 or -1.8 > -0.9.

Hence, only options i and ii are true. None of the answer choices A, B, C, or D lists only these two options.

When comparing these negative rational numbers remember that on the number line numbers get smaller as you move to the left. This means -4.3 is less than -3.7, -3.7 is less than -2.6, and -4.3 is certainly not greater than -2.6. Similarly, -1.8 is not 'greater' than -0.9. So the correct answer is D. i and iii.

In Mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Here, we are comparing some negative rational numbers. To interpret these, remember that on the number line, numbers become smaller as you move to the left. So, -4.3 is less than -3.7, -3.7 is less than -2.6, -4.3 is not greater than -2.6 because it is more to the left on the number line, and -1.8 is not greater than -0.9 for the same reason. So option A. i,ii,iii,iv is not correct, option B. iii and iv is not correct, option C. ii,iii is not correct but option D. i and iii is correct according to the comparison results of the rational numbers.

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Answer:

a) The population is all the Hispanic residents of Denver.

The sample is 300 adults which very visited by the officer.

b) The results are likely to be biased because the adults may be fearful of the Hispanic officer, may be intimidated by their presence and not want to tell how they really feel about this question.

Step-by-step explanation:

This is a common statistic method.

If you want to estimate something about a big population, you select a random sample of the population, and estimate for the entire population.

For example, if you want to estimate the proportion of residents of Buffalo, New York, that are Buffalo Bills fans, you are going to ask, for example, 1000 Buffalo residents. The population is all the residents of Buffalo, New York. and the sample are the 1000 Buffalo residents.

However, if you send a Bills player to ask this question, people will try to make him happy, which could lead to a biased answer.

So, for this question

a. What are the population and the sample?

The population is all the Hispanic residents of Denver.

The sample is 300 adults which very visited by the officer.

b. Why are the results likely to be biased even though the sample is an SRS?

The results are likely to be biased because the adults may be fearful of the Hispanic officer, may be intimidated by their presence and not want to tell how they really feel about this question.

Final answer:

The wind chill table can be used to determine how cold it feels at different combinations of temperature and wind speed.

Explanation:

Wind chill is a measure of how cold it feels when the temperature is combined with wind speed. To determine how cold it feels when the temperature is 0°F and the wind speed is 10 mph, we can look at the table provided. At 0°F and 10 mph wind speed, the temperature adjusted for wind chill is -10°F.

If the temperature is 35°F and we want to know the wind speed that makes it feel like 25°F, we can look at the table and find that at 35°F, a wind speed of 15 mph makes it feel like 25°F.

If the wind speed is 10 mph and we want to know the approximate temperature that feels like 0°F, we can look at the table and find that at 10 mph wind speed, a temperature of 5°F feels like 0°F.

(a) At 0°F with a wind speed of 10 mph, it feels like -11°F.

(b) To make 35°F feel like 25°F, a wind speed of 15 mph is needed.

(c) With a wind speed of 10 mph, a temperature of 5°F feels like 0°F.

To find the adjusted temperature for wind-chill, we can use the given table which provides adjustments based on both temperature and wind speed.

(a) If the temperature is 0°F and the wind speed is 10 mph, we can find the adjusted temperature from the table:

Temperature: 0°F

Wind speed: 10 mph

From the table:

Adjusted temperature: -11°F

So, it feels like -11°F when the temperature is 0°F with a wind speed of 10 mph.

(b) If the temperature is 35°F, and we want it to feel like 25°F, we need to find the wind speed that corresponds to this adjusted temperature from the table:

Temperature: 35°F

Adjusted temperature desired: 25°F

From the table, look for the entry where the adjusted temperature is 25°F:

Adjusted temperature: 25°F

Wind speed corresponding to this adjusted temperature: 15 mph

So, a wind speed of 15 mph would make a temperature of 35°F feel like 25°F.

(c) If the wind speed is 10 mph and we want to find the temperature that feels like 0°F, we can find this from the table:

Wind speed: 10 mph

Adjusted temperature desired: 0°F

From the table, look for the entry where the adjusted temperature is 0°F:

Adjusted temperature: 0°F

Corresponding temperature: 5°F

So, approximately, a temperature of 5°F would feel like 0°F with a wind speed of 10 mph.

Answer:

The equation to represent g(x) will be [tex]g(x)=log(x)+4[/tex]

Step-by-step explanation:

Considering the logarithmic function

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

As we know that when a constant c gets added to the parent function, the result would be a vertical shift c units in the direction of the sign of c.

So,

[tex]g(x)=log(x)+4[/tex] is basically the shift up by 4 units, and the graph also showing the same situation.

Therefore, the equation to represent g(x) will be [tex]g(x)=log(x)+4[/tex]

Also, the graphs of both [tex]f(x)=log(x)[/tex] and  [tex]g(x)=log(x)+4[/tex] is attached where black mark graph represents  [tex]f(x)=log(x)[/tex] and red mark graph represents [tex]g(x)=log(x)+4[/tex].

Keywords: transformation, vertical shift, graph

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Answer:

Step-by-step explanation:

from the word Bi "meaning two"

Bivariate data are two different variables obtained from the same population element. Bivariate data are used if the sampled data cannot be graphically displayed using a single variable.

To form a bivariate data, there are three combinations of variable

1. Both variables are qualitative i.e attribute in nature

2. Both variables are quantitative i.e numerical

3. One of them is qualitative whilee the other is quantitative

Qualitative data are data that are measure of type which could represent a name, colour,symbol. traits or characteristics

Quantitative data are data that can be counted, measured and expressed using numbers/

Answer:

a) [tex]29.4-1.96\frac{7}{\sqrt{10}}=25.06[/tex]  

[tex]29.4+1.96\frac{7}{\sqrt{10}}=33.74[/tex]  

So on this case the 95% confidence interval would be given by (25.06;33.74)  

b) [tex]z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988[/tex]  

[tex]p_v =P(z>1.988)=0.0234[/tex]    

If we compare the p value and the significance level given [tex]\alpha=

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".  

Part a

Data given: 30 30 42 35 22 33 31 29 19 23

We can calculate the sample mean with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}= 29.4[/tex] the sample mean

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

[tex]\sigma=7[/tex] represent the population standard deviation  

n=10 represent the sample size  

95% confidence interval  

The confidence interval for the mean is given by the following formula:  

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

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]  

Now we have everything in order to replace into formula (1):  

[tex]29.4-1.96\frac{7}{\sqrt{10}}=25.06[/tex]  

[tex]29.4+1.96\frac{7}{\sqrt{10}}=33.74[/tex]  

So on this case the 95% confidence interval would be given by (25.06;33.74)  

Part b

What are H0 and Ha for this study?  

Null hypothesis:  [tex]\mu \leq 25[/tex]  

Alternative hypothesis :[tex]\mu>25[/tex]  

Compute the test statistic

The statistic for this case is given by:  

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

We can replace in formula (1) the info given like this:  

[tex]z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988[/tex]  

Give the appropriate conclusion for the test

Since is a one side right tailed test the p value would be:  

[tex]p_v =P(z>1.988)=0.0234[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis.    

The mean DMS odor threshold among all students is estimated to be between 29.959 μg/l and 34.441 μg/l with 95% confidence. A significance test shows that the mean odor threshold for students is higher than the published threshold of 25 μg/l.

  The mean DMS odor threshold among all students can be estimated using a confidence interval. In this case, since the sample size is large and the population standard deviation is known, we can use a normal distribution to construct the confidence interval. Calculating the 95% confidence interval, we find that the range is (29.959, 34.441) μg/l.

  To determine if the mean odor threshold for students is higher than the published threshold of 25 μg/l, we can conduct a significance test. Using a one-sample t-test with a significance level of 0.05, we compare the sample mean (mean of the untrained students' thresholds) to the hypothesized mean of 25 μg/l. Calculating the test statistic and comparing it to the critical value, we find that the test statistic falls in the rejection region. Therefore, we can conclude that the mean odor threshold for students is indeed higher than the published threshold of 25 μg/l.

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The best point estimate for the number of excess pounds that the overweight men weighed is the mean value given, which is 35 pounds. Furthermore, the standard deviation of 3.5 pounds indicates that majority of these men's excess weight is within 3.5 pounds of this mean value.

In this problem, you have been given a random sample of 90 overweight men with a mean weight being overweight by 35 pounds. This mean (35 pounds) represents the best point estimate of the amount of excessive weight that the men of your study hold. What this means is that our best guess, considering this sample data, of an overweight man's excess weight is 35 pounds. We compute this mean value by adding up all the data values and dividing by the total number, in this case, 90. The standard deviation tells us somewhat about how much variation exists in the population's weights from this mean value. In this scenario, the standard deviation is 3.5 pounds, which means that the majority of the men in this study were within 3.5 pounds of the mean excess weight of 35 pounds.

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The best point estimate of the number of excess pounds that the sample of 90 overweight men weighed is the mean of their weights, which is given as 35 pounds.

In this problem, the best point estimate of the number of excess pounds that the men weighed would be the mean of their weights. Since we are given that the mean number of excess pounds that they were overweight was 35, the best point estimate would also be 35. This is because in statistics, the mean of a sample is used as the best point estimate of the population mean. The fact that they mentioned the standard deviation of 3.5 pounds does not affect the best point estimate, as that is related more to the dispersion or spread of the data around the mean, and not the central point (which is the mean).

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Answer: 332640 anagrams

Step-by-step explanation:

Given the word:

'masslessness'

Total number of letters= 12

Number of S = 6

E =2

The rest are one each.

The number of possible arrangements can be written as;

N = 12!/(6!2!)

N = 332640

The number of anagrams that can be created from the word 'masslessness' is 239500800, calculated using the formula for permutations with repetition.

This question is an application of the concept of permutations from combinatorics in mathematics. In this case, the word 'masslessness' consists of 12 characters including 3 's', 2 's', and 2 'l'. The formula for calculating permutations when there are repeating members within a set is n!/(r1! * r2! * ... * rn!), where n is the total number of members and r is the number of repeating members. Applying this formula, the number of anagrams of 'masslessness' would be 12!/(3! * 2! * 2!) = 239500800.

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Vectors u, v, and w are represented graphically in ℝ². Scalars λ₁ and λ₂ for w = λ₁u + λ₂v are found as λ₁ = 3/2t + 5 and λ₂ = t, where t is any real number.

a) Vector Representation:

To draw vectors u, v, and w in ℝ², we can use their respective components. Vector u = (1, 2) starts at the origin and extends to the point (1, 2). Vector v = (-3, 4) starts at the origin and extends to the point (-3, 4). Vector w = (5, 0) starts at the origin and extends to the point (5, 0).

b) Scalar Representation:

We want to find scalars λ₁ and λ₂ such that w = λ₁u + λ₂v. This can be expressed as a system of equations:

w₁ = λ₁u₁ + λ₂v₁

w₂ = λ₁u₂ + λ₂v₂

Substitute the values:

5 = λ₁(1) + λ₂(-3)

0 = λ₁(2) + λ₂(4)

Solve the system of equations to find λ₁ and λ₂. Multiplying the first equation by 2 and adding it to the second equation:

10 = 2λ₁ - 3λ₂ + 0

10 = 2λ₁ - 3λ₂

Solving for λ₁:

2λ₁ = 3λ₂ + 10

λ₁ = 3/2λ₂ + 5

Now, let λ₂ = t, then λ₁ = 3/2t + 5.

So, the scalars λ₁ and λ₂ are λ₁ = 3/2t + 5 and λ₂ = t, where t is any real number.

Step-by-step explanation:

using trigonometric ratios,

sin theta= opposite ÷ hypoteneus (h)

sin 45°= 3 root 2 ÷ h

1/root 2= 3 root 2 ÷h

h= 3× root 2 × root 2

= 3×2

= 6 unit

Answer:

Step-by-step explanation:

The given triangle is a right angle triangle and also an isosceles triangle.

The hypotenuse is the longest side of the right angle triangle. To determine the hypotenuse, we will apply trigonometric ratio

Sin θ = opposite side/hypotenuse

Looking at the triangle.

θ = 45 degrees = 1/√2

opposite side = 3√2

Therefore,

Sin 45 = 3√2/hypotenuse

1/√2 = 3√2/hypotenuse

hypotenuse × 1 = √2 × 3√2

hypotenuse = 3√2 × √2

hypotenuse = 3 × 2 = 6

Alternatively,

We can apply Pythagoras theorem since both sides are equal

Since the length of one side is 3√2, then the length of the other side is also 3√2

Hypotenuse^2 = opposite side^2 + adjacent side^2

Hypotenuse^2 = (3√2)^2 + (3√2)^2

Hypotenuse^2 = 18 + 18 = 36

Hypotenuse = √36 = 6

Answer:

36

Step-by-step explanation:

We have been given that you have 8 friends, of whom 5 will be invited to your big party in IV on Friday night. We are asked to find the number of choices if 2 of the friends are feuding and will not attend together.

We can choose 5 friends from 8 friends in [tex]^8C_5[/tex] ways.

[tex]^8C_5=\frac{8!}{5!(8-5)!}=\frac{8!}{5!(3)!}=\frac{8*7*6*5!}{5!*3*2*1}=8*7=56[/tex]

Therefore, we can choose 5 friends from 8 friends in 56 ways.

Since two friends are feuding, so we need to choose 3 friends from 6 friends and subtract them from total ways.

We can choose 3 friends from 6 friends in [tex]^6C_3[/tex] ways.

[tex]^6C_3=\frac{6!}{3!(6-3)!}=\frac{6!}{3!(3)!}=\frac{6*5*4*3!}{3!*3*2*1}=5*4=20[/tex]

[tex]56-20=36[/tex]

Therefore, we have 36 choices, if 2 of the friends are feuding and will not attend together.

Final answer:

The number of different choices for inviting friends to the party without the feuding friends attending together is 41 different choices.

Explanation:

The student's question deals with a combinatorial problem where they have 8 friends but can only invite 5 to a party. However, there is a constraint: 2 of the friends are feuding and cannot attend together. To solve this, we calculate the number of ways to choose 5 friends out of 8 without the feuding friends both attending.

Calculating Combinations with Restrictions

First, we find the total number of ways to invite 5 friends out of 8 without any restrictions, which is calculated using the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of friends and k is the number of friends to be invited.

C(8, 5) = 8! / (5!(8 - 5)!) = (8 × 7 × 6) / (3 × 2 × 1) = 56 ways.

Next, we calculate the number of combinations where the feuding friends would attend together. We treat them as a single entity and find combinations of the remaining 6 friends to invite 4 plus the 'unit' of feuding friends.

C(6, 4) = 6! / (4!(6 - 4)!) = (6 × 5) / (2 × 1) = 15 ways.

To get the total number of combinations without the feuding friends attending together, we subtract the 15 'restricted' combinations from the total 56 combinations.

56 - 15 = 41.

Therefore, there are 41 different choices for inviting friends to the party without the feuding friends attending together.

Answer:

The sum of first five term of GP is 19607.

Step-by-step explanation:

We are given the following in the question:

A geometric progression with 7 as the first term and 7 as the common ration.

[tex]a, ar, ar^2,...\\a = 7\\r = 7[/tex]

[tex]7, 7^2, 7^3, 7^4...[/tex]

Sum of n terms in a geometric progression:

[tex]S_n = \displaystyle\frac{a(r^n - 1)}{(r-1)}[/tex]

For sum of five terms, we put n= 5, a = 7, r = 7

[tex]S_5 = \displaystyle\frac{7(7^5 - 1)}{(7-1)}\\\\S_5 = 19607[/tex]

The sum of first five term of GP is 19607.

Verification:

[tex]2801\times 7 = 19607[/tex]

Thus, the sum is equal to product of 2801 and 7.

To find the sum of a geometric progression with a common ratio of 7, we use the formula Sum = (first term) * (1 - (common ratio)^n) / (1 - common ratio). When we substitute the values given in the question, the sum comes out to be the product of 2801 and 7.

A geometric progression is a sequence in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio is 7.

The sum of a geometric progression can be found using the formula:

Sum = (first term) * (1 - (common ratio)^n) / (1 - common ratio)

Plugging in the values for this problem, we have:

Sum = 7 * (1 - 7^5) / (1 - 7) = 7 * (-39304) / (-6) = 2801 * 7

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Answer:

Randomized experiment

Step-by-step explanation:

Such a statement is said to be Randomized experiment as the kids in the school have been selected at random and their performances are observed and recorded. Later it is inquired if they are breast fed or not. This information is later assessed and a conclusion is reached. This type of research or experiment is Randomized experiment.

Considering that the experiment is Randomized, the statement should be "Link found between breast-feeding and school performances". This statement does not restrict the performances of the student specifically on breast-feeding but shows a probable affect of it.

Answer:

$2743.66

Step-by-step explanation:

Data provided in the question:

Interest rate = 5%

Future value = $55,000

Time, t = 4.5 years

Now,

Since the interest is compounded quarterly

therefore,

Number of periods in a year = 4

Interest rate per period = 5% ÷ 4 = 1.25% = 0.0125

Total number of periods in 4.5 years = 4.5 × 4 = 18

also,

PMT = Future value × [ r × (( 1 + r )ⁿ - 1)⁻¹ ]

therefore,

PMT = $55,000 × [ 0.125 × ( ( 1 + 0.0125 )¹⁸ - 1 )⁻¹ ]

or

PMT = $55,000 × 0.0498

or

PMT = $2743.66

Answer:the total discounted price for two dogs to be groomed is 22.75

Step-by-step explanation:

A dog groomer is offering 20% off a full groom for one dog, and 15% off for each additional dog. Normally, a full groom costs $65 for each dog.

If you decide to take your two furry friends to be groomed,

the discount on the first one would be

20/100 × 65 = 0.2 × 65 = 13

the discount on the second one would be

10/100 × 65 = 0.15 × 65 = 9.75

the total discounted price for two dogs to be groomed would be

13 + 9.75 = 22.75

Answer:

First, calculate the discounted price for the first dog,

Discount=(20/100) $65=$13.

The discounted price is $65−$13=$52. Now, we can calculate the discounted price for the second dog,

Discount=(15/100) $65=$9.75.

The discounted price for the second dog is $65−$9.75=$55.25. The total discounted price for both dogs is,

$52+$55.25=$107.25

Step-by-step explanation:

Answer:

B. stratified random sample.

Step-by-step explanation:

The Stratified sampling is a type of sampling method in which the observer divides the whole sample population in the different or the separate groups.

These separated different groups are known as strata.

And from these, probability sample also called as simple random sample is taken out from each group.

The sampling method used in this scenario is defined as stratified random sampling, where the population is divided into groups (or strata) and random samples are taken from each group.

The technique described in your question is an example of a stratified random sample. This sampling method is characterized by dividing a population into smaller groups, known as 'strata', and then selecting a simple random sample from each group. In your example, the population is first divided into men and women, these are your strata. Then, a simple random sample is chosen from each group: 500 men and 700 women. This method ensures representation from all sections of the population and can often lead to more accurate results compared to a simple random sample.

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Answer:

Test scores of 10.2 or lower are significantly low.

Test scores of 31.4 or higher are significantly high.

Step-by-step explanation:

Problems of normally distributed samples can be 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.

In this problem, we have that:

[tex]\mu = 20.8, \sigma = 5.3[/tex]

Identify the test scores that are significantly low or significantly high.

Significantly low

Z = -2 and lower.

So the significantly low scores are thoses values that are lower or equal than X when Z = -2. So

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

[tex]-2 = \frac{X - 20.8}{5.3}[/tex]

[tex]X - 20.8 = -2*5.3[/tex]

[tex]X = 10.2[/tex]

Test scores of 10.2 or lower are significantly low.

Significantly high

Z = 2 and higher.

So the significantly high scores are thoses values that are higherr or equal than X when Z = 2. So

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

[tex]2 = \frac{X - 20.8}{5.3}[/tex]

[tex]X - 20.8 = 2*5.3[/tex]

[tex]X = 31.4[/tex]

Test scores of 31.4 or higher are significantly high.

Final answer:

Using the z-score formula, test scores below 10.2 are significantly low, and scores above 31.4 are significantly high for the college readiness test with a mean of 20.8 and a standard deviation of 5.3.

Explanation:

To identify test scores that are considered significantly high or low based on their z-scores, we use the provided mean score (μ = 20.8) and standard deviation (σ = 5.3) of the college readiness test. According to the criteria, a z-score less than or equal to -2 is significantly low, while a z-score greater than or equal to 2 is significantly high. To find the actual test scores corresponding to these z-scores, we apply the formula:

Z = (x - μ) / σ

For a significantly low score (Z = -2):

-2 = (x - 20.8) / 5.3

x = -2 × 5.3 + 20.8 = -10.6 + 20.8 = 10.2

For a significantly high score (Z = 2):

2 = (x - 20.8) / 5.3

x = 2 × 5.3 + 20.8 = 10.6 + 20.8 = 31.4

Thus, test scores below 10.2 are considered significantly low, and scores above 31.4 are considered significantly high.

Answer:

Each unit cost $800

Step-by-step explanation:

Annual compensation = $48,000

Annual number of units sold = 2000

Commission on each item sold = 3%

Compensation for 2000 units = $48,000

Compensation for 1 unit = $48,000/2000 = $24

Cost of one unit = compensation for one unit ÷ commission on one unit = $24 ÷ 3% = $24 ÷ 0.03 = $800

Answer: cost of one unit = $280

Question:

A salesman has a base salary $2600 per month and makes 3% commission on each unit sold. If his total annual compensation is $48,000 and he sold 2000 units, how much does each unit cost

Step-by-step explanation:

Given;

base salary = $2600 per month

Total annual compensation = $48,000 per annum

Number of units sold = 2000

Commission = 3% per unit

Salesman's Salary per annum = $2600 × 12 = $31,200

Total commission earned = total compensation - total yearly salary

Total commission = $48,000 - $31,200 = $16,800

Commission on each unit = total commission/number of units

Unit commission = $16800/2000 = $8.4

Given that the commission per unit is 3% per unit

That is $8.4 is 3% of the cost of each unit.

Cost of each unit = $8.4/3% = $8.4/0.03 = $280

Answer:

aₙ = 6n - 6

Step-by-step explanation:

a1 = 6 x 1 - 6 = 0

a₂ = 6 x 2 - 6 = 6

Answer:

a) 0.73684

b) 2/3

Step-by-step explanation:

part a)

[tex]P ( A is 1 / exactly two balls are 1) = \frac{P ( A is 1 and that exactly two balls are 1)}{P (Exactly two balls are one)}[/tex]

Using conditional probability as above:

(A,B,C)

Cases for numerator when:

P( A is 1 and exactly two balls are 1) = P( 1, not 1, 1) + P(1, 1, not 1)

= [tex](\frac{1}{6}* \frac{11}{12}*\frac{1}{4}) + (\frac{1}{6}*\frac{1}{12}*\frac{3}{4}) = 0.048611111[/tex]

Cases for denominator when:

P( Exactly two balls are 1) = P( 1, not 1, 1) + P(1, 1, not 1) + P(not 1, 1 , 1)

[tex]= (\frac{1}{6}* \frac{11}{12}*\frac{1}{4}) + (\frac{1}{6}*\frac{1}{12}*\frac{3}{4}) + (\frac{5}{6}*\frac{1}{12}*\frac{1}{4})= 0.0659722222[/tex]

Hence,

[tex]P ( A is 1 / exactly two balls are 1) = \frac{P ( A is 1 and that exactly two balls are 1)}{P (Exactly two balls are one)} = \frac{0.048611111}{0.06597222} \\\\= 0.73684[/tex]

Part b

[tex]P ( B = 12 / A+B+C = 21) = \frac{P ( B = 12 and A+B+C = 21)}{P (A+B+C = 21)}[/tex]

Cases for denominator when:

P ( A + B + C = 21) = P(5,12,4) + P(6,11,4) + P(6,12,3)

[tex]= 3*P(5,12,4 ) =3* \frac{1}{6}*\frac{1}{12}*\frac{1}{4}\\\\= \frac{1}{96}[/tex]

Cases for numerator when:

P (B = 12 & A + B + C = 21) = P(5,12,4) + P(6,12,3)

[tex]= 2*P(5,12,4 ) =2* \frac{1}{6}*\frac{1}{12}*\frac{1}{4}\\\\= \frac{1}{144}[/tex]

Hence,

[tex]P ( B = 12 / A+B+C = 21) = \frac{\frac{1}{144} }{\frac{1}{96} }\\\\= \frac{2}{3}[/tex]

Final answer:

The question involves calculating probabilities of selecting specific numbered balls from different boxes under given conditions. Part (a) addresses the probability of selecting a ball numbered 1 from box A when exactly two balls numbered 1 are chosen in total, which is generically 1/6. Part (b) asks about the probability of choosing a ball numbered 12 from box B when the arithmetic mean of numbers on the selected balls is 7, which needs combinatorial analysis of possible valid combinations.

Explanation:

The student's question involves probability and combinatorics, focusing on selecting balls from different boxes. There are two parts to the question:

(a) Probability that the ball chosen from box A is labeled 1 if exactly two balls numbered 1 were selected

For exactly two balls numbered 1 to be selected across the three boxes, one must come from box A and one must either come from box B or C. The probability of choosing the number 1 ball from box A is 1/6, assuming a uniform random selection. However, since the condition specifies exactly two balls numbered 1 need to be selected, and there's no way to determine how this condition impacts the selection without further context (like an overall occurrence rate), this part can only provide the probability of selecting a number 1 from box A in general, which is 1/6.

(b) Probability that the ball chosen from box B is 12 if the arithmetic mean of the three balls selected is exactly 7

To find the probability that the ball chosen from box B is 12 given that the arithmetic mean of the three balls is exactly 7, we must consider that the total sum of the numbers on the balls must be 21 (since 7*3=21). If the ball from box B is 12, the sum of the numbers from the other two balls must be 9. With these criteria, we can explore the combinations that result in a sum of 9 from boxes A and C. However, without specific combinations provided, detailed calculation is not feasible in this response. Generally, this would involve enumerating all valid combinations from boxes A and C that sum to 9, and then dividing that by the total number of possible draws from all boxes, taking into account the condition specified.

Answer:

28

Step-by-step explanation:

People he interviewed on that day (x)

1.50x + 10 = 52

1.50x = 42

x = 42/1.50

x = 28

The number of people is 28 if the University of Florida student earns $10 per day delivering advertising brochures door-to-door.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A University of Florida student earns $10 per day delivering advertising brochures door-to-door, plus $1.50 for each person he interviews.

Let's suppose the people he interviewed on that day x

The linear equation can be framed as per the question:

1.50x + 10 = 52

After solving:

x = 42/1.50

x = 28

Thus, the number of people is 28 if the University of Florida student earns $10 per day delivering advertising brochures door-to-door, plus $1.50 for each person he interviews.

Learn more about the linear equation here:

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Answer:

a) Permutations

b) combination

Step-by-step explanation:

a)

Since the order of 15 most important artwork pieces matter, with most popular at first and then at N0.2, 3,4, and so on. Whenever we are dealing with "order of placement" the question at hand is of permutations.

b)

Out of 320 pieces, 125 pieces are to be "selected" and displayed, the process of selection incurs Combinations in which the order in which we select does not matter.  

Scenario a) represents a permutation and the 15 popular pieces can be arranged in 15! ways.

Scenario b) represents a combination and the 125 pieces can be selected in 320 choose 125 ways.

a) This scenario is an example of a permutation. In a permutation, the order of the items matters. In this case, the 15 popular pieces can be arranged in 15! (15 factorial) ways.
b) This scenario is an example of a combination. In a combination, the order of the items does not matter. In this case, the 125 pieces can be selected from the total of 320 pieces in a total of 320 choose 125 ways.

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Answer:7

Step-by-step explanation:

Answer:

a. Standard error of mean

Step-by-step explanation:

The standard error of mean is computed by dividing the standard deviation to the square root of sample size. It can be represented as

[tex]Standard error=\frac{standard deviation}{\sqrt{n}}[/tex]

The standard deviation of the sampling distribution is known as the standard error of mean because it measures the accuracy of sample mean as compared to population mean

The standard deviation of the sampling distribution of the mean is referred to as the Standard Error of the Mean, which measures the dispersion of sample means around the true population mean.

The standard deviation of the sampling distribution of the mean is known as the Standard Error of the Mean. When we say sampling distribution of the mean, we're referring to the distribution of means for all possible samples of a given size from the same population. The Standard Error of the Mean measures the dispersion of these sample means around the true population mean.

For example, if you have a population of test scores with a mean of 70 and a standard deviation of 10, and you were to take many samples of 30 scores from this population, the standard error of the mean would be the standard deviation of all those sample means.

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Finding the z-value in a standard normal distribution for certain proportions involves using a standard normal (Z-score) table. For (a) the z-value is -0.36, and for (b), the z-value is 0.36.

To find the value of z that allows for a proportion of observations less or greater than it in a standard normal distribution, you need to use a standard normal (Z-score) table, or use an online calculator that allows you to find the Z-score associated with a specific proportion.

(a) For the proportion of observations that are less than z = 0.36, you would look up this proportion in the body of a standard normal table to find the associated Z-score. Alternatively, using a Z-score calculator, the z value is approximately -0.36.

(b) For the proportion of observations that are greater than Z = 0.36, it would be equivalent to looking for the proportion that is less than Z = 1 - 0.36 = 0.64 in the standard normal table. The z value here is approximately 0.36.

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Final answer:

To solve the given separable differential equation, we separate the variables, integrate both sides, and then apply the initial condition to find the particular solution that fits x(0) = 6.

Explanation:

The question asks to solve the separable differential equation dx/dt = x^2 + (1/9) and find the particular solution that satisfies the initial condition x(0) = 6. To solve this, first, we separate the variables and integrate both sides. The separated form of the equation is dx / (x^2 + (1/9)) = dt. Integrating both sides, we utilize the integral form that applies to the left side, leading us to an arctan function after simplification. This results in the solution to the differential equation. Subsequently, to find the particular solution satisfying the initial condition, we substitute x(0) = 6 into the obtained general solution and solve for the integration constant.

With x(0) = 6, we determine the value of the constant that makes the solution particular to the initial condition provided. By inserting this constant back into the general solution, we acquire the exact expression for x(t) that meets the initial condition specified.