Find the probability choosing 7 numbers that match 7 randomly selected balls numbered 1-34.

Answer:

1) ∭(z−2) dV  negative.

2) ∭e^{−xyz} dV  positive.

3) ∭( z-\sqrt{x²+y²})  positive.

Step-by-step explanation:

From Exercise we have:

z=\sqrt{x²+y²}

z=2

⇒2=\sqrt{x²+y²}

4=x²+y²

Therefore, we get that  the solid bounded by:

\sqrt{x²+y²}≤z≤2

4=x²+y²

1) From initial condition we have that

\sqrt{x²+y²}≤z≤2

⇒ 2-z≤0

Therefore, we get that the triple integral is

∭(z−2) dV  negative.

2) We know that e^{-xyz} is always positive number.

Therefore, we get that the triple integral is

∭e^{−xyz} dV  positive.

3) From initial condition we have that

\sqrt{x²+y²}≤z≤2

⇒ z-\sqrt{x²+y²}>0

Therefore, we get that the triple integral is

∭( z-\sqrt{x²+y²})  positive.

The given triple integrals, when evaluated over the defined region, result in the first integral being zero, while the second and third integrals yield positive values. This determination is made based on the properties of the integrand over the given region, without resorting to complete calculation.

The question involves the evaluation of triple integrals over a given region W bounded by the surfaces z = sqrt(x^2 + y^2) and z = 2.1. Without explicit calculations, we can determine the sign of the integrals by assessing the integrand function over the specified region.

Therefore, the first integral would yield zero, while the second and third integrals would yield positive values.

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Answer:

The best predicted pulse rate of a woman who is 74 inches tall is 80.4 (beats per minute).



Step-by-step explanation:

The best predicted pulse rate of a woman who is 74 inches tall is obtained below:

Let x denotes height (in inches) and y denotes pulse rates (in beats per minute).

From the information, the regression equation is, the total number of women is 60 and the linear correlation coefficient between height and pulse rates is 0.234 and the mean of heights is 63.4 and the mean of pulse rates is 75.6. The estimated regression line is

^y= 17.5 + 0.850x

     The required best predicted pulse rates is,

      =17.5 + (0.850×74)

=17.5 + 62.9

=   80.4  beats per minute

​

The correct answer is: False.

As the sample size increases, the variation of the sample mean from the population mean typically becomes smaller. This is known as the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution with a mean equal to the population mean and a standard deviation that decreases as the sample size increases. Therefore, with larger sample sizes, the sample mean tends to be a more accurate estimate of the population mean, and the variation around the population mean decreases.

The 'Duration (amount of time)' in the study is an example of quantitative data. Quantitative data is numerical data that can be measured or counted.

The 'Duration (amount of time)' in the study is an example of quantitative data.

Quantitative data is numerical data that can be measured or counted. In this case, the duration of resident use of the local park is being measured in terms of time (amount of time).

Examples of other quantitative data include age and number of times per week.

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Answer:

D. 6.3 in^3

Step-by-step explanation:

V= 1/3 (3.14)(r^2)(h)

V= 1/3 (3.14) (1^2)(6)

V=6.3 in^3

Answer:

c

Step-by-step explanation: it was on usa test prep and the answer that was there was wrong.

The sampling technique described is called 'sampling without replacement'. In this case, names are drawn from the bag and not returned, decreasing the pool for subsequent draws. It's a type of 'simple random sampling'.

The sampling technique used when 50 contestants’ names are written on 50 cards, placed in a bag, and three are chosen, is a method called sampling without replacement. In this process, once a name is chosen, it is not returned to the bag, reducing the pool of options for subsequent selections. As each card is drawn, the remaining pool of names shrinks, meaning the probability of drawing any remaining name changes with each draw. This process is often used when the desire is to avoid repetition in the selection.

In contrast, sampling with replacement would mean that after a card is drawn, it is put back into the bag before the next draw, ensuring that the same name could potentially be drawn more than once. Both methods are types of simple random sampling, a fundamental sampling method in statistics.

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Answer:

99

Step-by-step explanation:

Since the caterpillar crawled through the origin, her movement can be described by a straight line equation modeled with the points (-2.5; -5.5) and (0; 0).

The slope of a linear equation is given by:

[tex]m=\frac{y-y_0}{x-x_0}\\m=\frac{-5.5-0}{-2.5-0}\\m=2.2[/tex]

For x = 45, the value of y is:

[tex]y= 2.2x\\y= 2.2*45\\y=99[/tex]

The value of the y-axis is 99.

Answer:

[tex]C(d,m) = 20 + 45d + 0.15m[/tex]

Step-by-step explanation:

In this problem, we have that the cost of renting a car C is a function of the number of days d, and the number of miles driven, m.

There is also a fixed cost F.

So the equation for the cost of renting a car is:

[tex]C(d,m) = F + a*d + b*m[/tex]

In which a is the daily cost and b is the cost per mile.

A car rental company charges a one-time application fee of 20 dollars, 45 dollars per day, and 15 cents per mile for its cars.

This means that [tex]F = 20, a = 45, b = 0.15[/tex]

Write a formula for the cost, C, of renting a car as a function of the number of days, d, and the number of miles driven, m.

[tex]C(d,m) = 20 + 45d + 0.15m[/tex]

Answer:

Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).

Step-by-step explanation:

The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.

The first quartile(Q1) separates the lower 25% from the upper 75% of a set. So 25% of the values in a data set lie at or below the first quartile, and 75% of the values in a data set lie at or above the first quartile.

The third quartile(Q3) separates the lower 75% from the upper 25% of a set. So 75% of the values in a data set lie at or below the third quartile, and 25% of the values in a data set lie at or the third quartile.

The answer is:

Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).

Answer:

a)  sample mean = 2.63 inches

     sample standard deviation = [tex]\frac{standard \hspace{0.15cm} deviation}{\sqrt{n} } = \frac{0.03}{\sqrt{9} } = \frac{0.03}{3} = 0.01[/tex]

b)  P(X < 2.61) = 0.0228

c.) P(2.62 < X < 2.64)  = 0.6827

d.)  Therefore 0.06 = P(2.6292 < X < 2.6307)

Step-by-step explanation:

i) the diameter of a brand of tennis balls is approximately normally distributed.

ii) mean  = 2.63 inches

iii) standard deviation = 0.03 inches

iv) random sample of 9 tennis balls

v) sample mean = 2.63 inches

vi) sample standard deviation = [tex]\frac{standard \hspace{0.15cm} deviation}{\sqrt{n} } = \frac{0.03}{\sqrt{9} } = \frac{0.03}{3} = 0.01[/tex]

vii) the sample mean is less than 2.61 inches = P(X < 2.61) = 0.0228

viii)the probability that the sample mean is between 2.62 and 2.64 inches

     P(2.62 < X < 2.64)  = 0.6827

ix) The probability is 6-% that the sample mean will be between what two values symmetrically distributed around the population measure

  Therefore 0.06 = P(2.6292 < X < 2.6307)

a) The sampling distribution of the mean is 2.63 inches and sample standard deviation = 0.01

b)  P(X < 2.61) = 0.0228

c) P(2.62 < X < 2.64)  = 0.6827

d)  0.06 = P(2.6292 < X < 2.6307)

Let's solve this step by step:

Step 1: The diameter of a brand of tennis balls is approximately normally distributed.

Given:

Mean  = 2.63 inches

Standard deviation = 0.03 inches

For random sample of 9 tennis balls

Step 2: Sample mean = 2.63 inches

Sample standard deviation = [tex]\frac{\text{standard deviation}}{\sqrt{n} } =\frac{0.03}{\sqrt{9} } =\frac{0.03}{3} =0.01[/tex]

Step 3: The sample mean is less than 2.61 inches = P(X < 2.61) = 0.0228

Step 4: The probability that the sample mean is between 2.62 and 2.64 inches = P(2.62 < X < 2.64)  = 0.6827

Step 5: The probability is 6-% that the sample mean will be between what two values symmetrically distributed around the population measure

Therefore 0.06 = P(2.6292 < X < 2.6307)

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The probability  that a sample taken from the site will have water content above 16% or below 12% is 0.3862.

Given that,

Mean = µ

= 14%

= 0.14

Standard deviation = σ

= 2.5%

= 0.025

[Using standard normal table]

16% or 12% = 0.16 or 0.12

P(X < 0.16 or X > 0.12)

Using standard normal table,    

To see the z value -0.9 in the row and 0.06 in the column of the standard normal table the cumulative probability of z = -0.96  is = 0.1685

To see the z value 0.7 in the row and 0.08 in the column of the standard normal table the cumulative probability of z = 0.78  is = 0.7823

[tex]P(X < 0.6\ or \ x > 0.12)=1-[P(0.16 < X < 0.12)][/tex]

[tex]=1-{P[\frac{0.16-0.142}{0.023} < \frac{x-\mu}{\sigma} < \frac{0.12-0.142}{0.023}]}[/tex]

[tex]= 1-[P(0.78 < z < -0.96)][/tex]

[tex]= [P(z < -0.96)-P(z < 0.78)][/tex]

[tex]=1-(0.1685-0.7823)[/tex]

[tex]= 1-0.6138[/tex]

[tex]P(X < 0.16 \ or \ X > 0.12)=0.3862[/tex]

Therefore, the probability  that a sample taken from the site will have water content above 16% or below 12% is 0.3862.

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The probability that a random sample’s water content will be higher than 16% or lower than 12% is calculated by converting the values to Z-scores and then using the standard normal distribution's cumulative probability. The values from a Z-table or calculator are used to determine this probability.

The subject of this question is Probability and Statistics, specifically related to the normal distribution. In this scenario, the water content of soil from a borrow site is normally distributed with a mean (μ) of 14% and a standard deviation (σ) of 2.5%.

To find the probability of the soil having a water content above 16% or below 12%, we first need to calculate the Z-scores for these values. The Z-score represents how many standard deviations an element is from the mean. It is calculated as (X - μ)/σ.

For X = 16%, Z = (16 - 14) / 2.5 = 0.8

For X = 12%, Z = (12 - 14) / 2.5 = -0.8

Using a Z-table or a calculator function that outputs standard normal probabilities, we would find that P(Z > 0.8) or P(Z < -0.8). By convention, Z-tables only give values as P(Z < z), for z > 0, so to find P(Z > 0.8), we can do 1 - P(Z < 0.8). Same for P(Z < -0.8).

As such, the desired probability is the sum of these two probabilities.

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Answer:

Standard error

Step-by-step explanation:

Standard error: In statistics, the term standard error is also denoted as SE, and is reffered to as the estimate of a particular parameter.

It is defined as the standard deviation in statistics related to its sampling distribution or else the the standard deviation's estimate.

Therefore, if a particular parameter or statistic is considered as a mean then it would be denoted as the standard error of that mean.

The standard error of an estimate may also be defined as the square root of the estimated error variance √[tex]\sigma^{2}[/tex] of the quantity,

[tex]S_{e}[/tex] =√[tex]\sigma^{2}[/tex]

In the given question, the appropriate answer would be standard error.

Options A, C, and F are solutions to the differential equation.

The given differential equation is y''+4y'+4y=0.

To check which of the given functions are solutions of the differential equation, we substitute each function into the equation and check if it satisfies the equation.

By substituting each function and simplifying, we find that options A, C, and F are solutions to the differential equation.

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Answer:

Statistical Inference.

Step-by-step explanation:

Statistical Inference:

Thus,

The branch of Statistics concerned with using the sample data to make an inference about a large set of data is called statistical inference.

Answer:The percentage of the plants that are grasses is 83%

Step-by-step explanation:

Seventeen percent of the plants in the greenhouse are broad leaf plants and the rest are grasses

The total number of grasses and broad leaf plants in the greenhouse is 100%. Therefore,

The percentage of the plants that are grasses would be

100% - 17% = 83%

Final answer:

By subtracting the percentage of broad-leaf plants (17%) from the total (100%), we find that 83% of the plants in the greenhouse are grasses.

Explanation:

If seventeen percent of the plants in the greenhouse are broad-leaf plants, then the remaining percentage of plants must be grasses. Since the total percentage must add up to 100%, we can subtract the percentage of broad-leaf plants from the total to find out the percentage of grasses.

To calculate the percentage of grasses, we use the following steps:

Start with the total percentage which is 100%.

Subtract the percentage of broad-leaf plants which is 17%.

The result is the percentage of grasses.

100% - 17% = 83%

Therefore, 83% of the plants in the greenhouse are grasses.

Answer:

The answer to your question is See the picture below

Step-by-step explanation:

Analysis of the graphs

a) In the first graph, we observe that Natasha is running after 1 h and 1/4, the comeback for to her origin, finally she continues running forward. This option is incorrect.

b) In the second graph, Natasha runs for 1 1/4 hours, after this time, she comes back to her origin, takes a rest and continues running forward. This answer is incorrect.

c) In the third graph, Natasha runs for 1 1/4 hour, takes a rest and comes back to the origin. This option is incorrect.

d) In the forth graph, Natasha runs for 1 1/4 hour, takes a rest and continues running upwards. This is the right option.

Answer:

the last one to the far right at the bottom

Step-by-step explanation:

Answer:

With a skewed distribution and data with outliers.

Step-by-step explanation:

There are three measures of central tendency.

The median is not affected by outliers and skewed data as compared to the mean.

Thus, median likely to produce a better measure of central tendency than the mean with a skewed distribution and data with outliers.

The total number of different license plates possible with 2 letters and 5 digits is 67,600,000. If no letter or digit can be repeated, the number reduces to 32,760,000.

This problem involves combinations and permutations, which are fundamental concepts in discrete mathematics. If a license plate has 2 letters followed by 5 digits, each chosen independently, we consider the product of the number of possibilities for each space. There are 26 possible letters (A-Z) for each of the 2 letter spaces and 10 possible digits (0-9) for each of the 5 digit spaces. Therefore, the total number of different license plates is 26 * 26 * 10 * 10 * 10 * 10 * 10 = 67,600,000.

However, if no letter or digit can be repeated, the number of possibilities for the second letter space becomes 25 (since one letter has already been used), and similarly for the digits, it gets reduced by one with each additional digit. Hence, the total number of different license plates without repeated letters and digits would be 26 * 25 * 10 * 9 * 8 * 7 * 6 = 32,760,000.

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There are 67,600,000 total possible license plates with two letters and five digits. When restricting to plates with no repeated letters or digits, there are 165,765,000 possible plates.

The possible license plates can be calculated using the principle of multiplication. This principle states that if there are m ways to do one thing, and n ways to do another, then there are m*n ways to do both. In this case, there are 26 options for the first letter, another 26 for the second letter, and 10 options for each of the 5 digits (0-9). So, we can multiply these options to get our answer.

To calculate the number of possible combinations, we use the formula 26*26*10*10*10*10*10 = 67,600,000. Therefore, there are 67,600,000 possible license plates.

For the plates with no repeated letters or numbers, we still use the principle of multiplication but reduce each subsequent option by one. It will be 26*25 (because one letter has been used already and it can't be reused) *10*9*8*7*6 (same as for digits). Our formula is 26*25*10*9*8*7*6 = 165,765,000 plates.

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Given the exchange rate of $5 = £1 and the conversion rate of 6 pounds per ounce of gold, the equivalent amount for an ounce of gold would be $30.

In this scenario, given that the exchange rate between pounds and U.S. dollars is $5 = £1 and the conversion rate of pound to gold is six pounds per ounce, we want to find the value of an ounce of gold in U.S. dollars. Firstly, we need to establish how many pounds per ounce of gold, which is set at six pounds. With the currency exchange rate, $5 equals one pound. Therefore, to find the value in dollars, simply multiply these two rates together. That comes to 6 (pounds per ounce of gold) * 5 (dollars per pound) = $30. Hence, an ounce of gold would be worth $30.

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Answer:

No. it's not enough

Step-by-step explanation:

1) No. it's not enough

2) To compute the area of a parallelogram it's necessary the height of the parallelogram, i.e. a perpendicular line segment from the base up to its parallel side.

3) Because a parallelogram is made up by two triangles and the area of it is calculated using the height. Then to cover the area of a parallelogram it's mandatory to calculate the height, the perpendicular distance between their horizontal sides.

No, the lengths of the sides of a parallelogram alone are not enough to compute its area. Additional information, such as the length of the perpendicular distance between the sides, is needed to calculate the area.

No, the lengths of the sides of a parallelogram alone are not enough to compute its area. To calculate the area of a parallelogram, you need two pieces of information: the length of one of its sides and the length of the corresponding altitude (or height), which is the perpendicular distance between the side and the opposite side. With just the lengths of a and b, we don't know the height, so we can't calculate the area.

To find the area of a parallelogram, you can use the formula: Area = base x height. The base is one of the side lengths, and the height is the length of the perpendicular from the base to the opposite side.

For example, if side a is the base, the height is the distance between side a and the opposite side, which can be found by drawing a perpendicular line. Once you know the height, you can calculate the area using the formula: Area = a x height.

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Answer:

Exponential function if the form [tex]e^{Kx}[/tex] is the constant multiple K of itself if.

[tex]y'=\frac{dy}{dx}=cKe^{Kx} \\y'=Ky[/tex]

Step-by-step explanation:

The exponential function of the form [tex]e^x[/tex] is the function which is the derivative of itself.

Where:

x is independent variable

Now if we talk about constant then again exponential function if the form [tex]e^{Kx}[/tex] is the constant multiple K of itself if we take the dervative.

Mathmatical Prove:

Consider the general equation

let [tex]y=ce^{Kx}[/tex]

Where:

K is a constant

c is the cofficient(could be any number)

Now:

Taking derivative of above equation w.r.t x:

[tex]y'=\frac{dy}{dx}=cKe^{Kx} \\y'=Ky[/tex]

Hence proved exponential function is a constant multiple K of it self.

The function is [tex]f(x) = Ae^kx[/tex]. This function is a solution of the differential equation y' = ky.

We know that the derivative of the exponential function is the function itself. Consider the function [tex]f(x) = Ae^kx[/tex], where A is a constant. Then, take the derivative of [tex]f(x) = Ae^kx[/tex], we get:

[tex]f'(x) = Ake^{kx} = k (Ae^{kx}) = k f(x)[/tex]

Thus, a function whose first derivative is a constant multiple k of itself is[tex]f(x) = Ae^{kx}[/tex], where A is a constant.

Since [tex]f'(x) = k f(x)[/tex] for the function [tex]f(x) = Ae^{kx}[/tex], this function must be the solution of the differential equation y' = ky.

Complete question:

What function do you know from calculus is such that its first derivative is a constant multiple k of itself? (Do not use the function f(x)=0.)

f(x)=____

The above function is a solution of which of the following differential equations?

[tex]y'=y^k[/tex]

[tex]y'=y+k[/tex]

[tex]y'=ky[/tex]

[tex]y'=e^{ky}[/tex]

[tex]y'=k[/tex]

Answer:

  The sub rose 121 feet.

Step-by-step explanation:

The sub was less deep at 12 pm than at 10 am, so rose in the water. The amount it rose was ...

  410 -289 = 121 . . . . feet

__

If you like, you can think of the sub's elevation relative to the surface as changing from -410 feet to -289 feet. The difference is then an increase in elevation (rise) of ...

  -289 -(-410) = -289 +410 = 121 . . . feet

_____

12 am is midnight, 14 hours after 10 am. The time 2 hours after 10 am is 12 pm, noon.

Answer:

a) [tex]\hat{p} = 0.27[/tex]    

b) All the conditions are met for constructing a confidence interval.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 167

Number of people who had side effects, x = 45

a)  point estimate

[tex]\hat{p} = \dfrac{x}{n} = \dfrac{45}{167} = 0.27[/tex]

The point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported headache as a side effect is 0.27

b) Conditions for constructing a confidence interval

[tex]n\hat{p}>10\\167\times 0.27 = 45.09 > 10\\n(1-\hat{p})>10\\167(1-0.27) = 121.91 > 10[/tex]

Thus, all the conditions are met for constructing a confidence interval.

To reach a $8000 down payment in 4 years with an account that compounds quarterly at an APR of 6%, you would need to make an initial deposit of approximately $6304.05 today.

To calculate the initial deposit needed to save for a $8000 down payment in 4 years with an account that offers quarterly compounding at an APR of 6%, we use the compound interest formula:

[tex]P = A / (1 + r/n)^{(nt)[/tex]

Where:

Given:

Now we can calculate the initial deposit:

[tex]P = $8000 / (1 + 0.06/4)^(4*4)P = $8000 / (1 + 0.015)^(16)P = $8000 / (1.015)^16P \approx $8000 / 1.26824179P \approx $6304.05[/tex]

Therefore, you would need to deposit approximately $6304.05 today to have $8000 in 4 years in the account with the given interest rate and compounding frequency.

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To reach an $8000 goal in 4 years with a 6% APR compounded quarterly, you need to deposit approximately $6307.17 now.

To determine how much to deposit now to reach your $8000 goal in 4 years with quarterly compounding and an APR of 6%, you can use the formula for compound interest:

[tex]P = A / (1 + r/n)^(nt)[/tex]

Where:

Now, substitute the given values into the formula:

P = [tex]$8000 / (1 + 0.06/4)^(4*4)[/tex]

P = $8000 / [tex](1 + 0.015)^(16)[/tex]

P = $8000 / [tex](1.015)^(16)[/tex]

P = $8000 / 1.2682 (approximately)

P = $6307.17 (approximately)

So, you would need to deposit approximately $6307.17 now to reach your $8000 goal in 4 years with quarterly compounding at a 6% APR.

Answer:

Step-by-step explanation:

The simplified formula for payback period (assuming even cashflow) is as follows:

Payback Period (in years) = Cost / cashflow per year

Generally, the choice which gives the shorter payback period is desired

For project A,

Cost = $250,000 and  cashflow per year = $75,000

Payback Period for project A

= 250,000 ÷ 75,000 = 3.333 years

For Project B

Cost = $150,000 and  cashflow per year = $52,000

Payback Period for project B

= 150,000 ÷ 52,000 = 2.88 years

comparing the PP for A & B, it is clear that B has the shorter payback period, and hence choice B is more desirable

The simplified formula for the payback period (assuming even cashflow) is as follows:

Payback Period (in years) = Cost / cashflow per year

Generally, the choice which gives the shorter payback period is desired

For project A,

Cost = $250,000 and  cashflow per year = $75,000

Payback Period for project A

= 250,000 ÷ 75,000 = 3.333 years

For Project B

Cost = $150,000 and  cashflow per year = $52,000

Payback Period for project B

= 150,000 ÷ 52,000 = 2.88 years

comparing the PP for A & B, it is clear that B has the shorter payback period, and hence choice B is more desirable

Word problem usually consists of mathematical modeling questions, where statistics and information about a sure machine are given and a student is required to expand a version. for example, Jane had $five.00, then spent $2.00. How lots does she have now?

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Answer:

a. Quantitative

b. Quantitative

c. Qualitative

d. Qualitative

e. Qualitative

Step-by-step explanation:

a. The temperature readings can be quantify and can be represented numerically so, it is quantitative variable.

b. The scores in English test can be quantify and can be represented numerically so, it is quantitative variable.

c. The blood type can be categorized as O plus, O negative, A plus, A negative, AB plus, Ab negative, B plus, B negative and cannot be represented numerically so, it is qualitative variable.

d. The last four digit of social security number take numerical values, yet they are qualitative because these are used as identifiers and mathematical operations of social security don't have meaningful interpretation.

e. The number on the jerseys of 53 football players also takes numerical values yet they are qualitative because these are used as identifiers for players and mathematical operations of number on the jerseys of football players don't have meaningful interpretation.

The measures in question are classified as either quantitative or qualitative.

a. The 30 high-temperature readings of the last 30 days - Quantitative. These temperatures are numerical values that can be measured and compared.

b. The scores of 40 students on an English test - Quantitative. The scores represent numerical values that can be added, averaged, and compared.

c. The blood types of 120 teachers in a middle school - Qualitative. Blood types are descriptive categories or labels that cannot be measured numerically.

d. The last four digits of social security numbers of all students in a class - Qualitative. The last four digits are specific identifiers that cannot be measured or compared numerically.

e. The numbers on the jerseys of 53 football players on a team - Qualitative. The numbers are labels or identifiers, not measurable quantities.

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Answer:  52, 92 , 132, 172

Step-by-step explanation:

Given : Systematic Sampling Technique is used to select 5 numbers between 1 and 200.

⇒ Population size : N=200

Required Sample size  : n=5

Since , Sampling interval is given by :-

[tex]k=\dfrac{N}{n}[/tex]

⇒ [tex]k=\dfrac{200}{5}[=40/tex]

If the first selected number is 12, then the next four numbers would be :

(12+K) , (12+2k) , (12+3k) , (12+4k)

Put value of k , we get

(12+40) , (12+2(40)) , (12+3(40)) , (12+4(40)) =(52, 92 , 132, 172)

Hence, the  next four numbers are : 52, 92 , 132, 172

Answer:

a) True

Step-by-step explanation:

The given statement is true.

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

The standard deviation express the variation of data from the mean and therefore, have the same unit as the data like lbs, inches, dollars, etc.

Coefficient of variation on the other hand is the ratio of standard deviation and mean. It is also a measure of dispersion but since it is a ratio, the units cancel each other.

[tex]C.V = \dfrac{s}{\bar{x}}[/tex]

Thus, coefficient of variation is dimensionless.

Thus, it is a relative measure.

Answer: x = 5.0, y = 4.0

We multiply the second equation by -2.

-2(0.50 x + 0.20 y)= -2(3.30)

-x - 0.40y = -6.60

Then we add it to x + y = 9.0.

So we get: -x - 0.40y + x + y = -6.60 + 9.0

or, 0.60y = 2.4

or, y = 4.0

From x + y = 9.0 we get:

x + 4.0 = 9.0

x = 5.0

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To solve the system of linear equations, we used the substitution method, resulting in the solution x = 5 and y = 4.

The system of linear equations provided is:

To find the values of x and y, we can use the method of substitution or elimination. In this case, we'll use substitution:

Therefore, the solution to the system of equations is x = 5 and y = 4.

Answer: 248mL

Step-by-step explanation:

Given:

Concentration of buffer solution Cs = 1.24%w/v of boric acid

Concentration of boric acid solution Cb = 5 % w/v boric acid

For 1 liter of buffer solution, the weight of boric acid needed is:

mb = 1 × 1.24 = 1.24 unit weight

mb = Cb × Vb .....1

Cb = concentration of boric acid solution.

Vb = volume of boric acid solution needed.

mb = weight of boric acid needed.

From equation 1.

Vb = mb/Cb

Vb = 1.24/5

Vb = 0.248L

Vb = 248mL

248 milli-liters of a 5% w / v boric acid solution should be used to obtain the boric acid needed.

Since the formula for a buffer solution contains 1.24% w / v of boric acid, to determine how many milli-liters of a 5% w / v boric acid solution should be used to obtain the boric acid needed in preparing 1 liter of the buffer solution, the following calculation must be performed:

Therefore, 248 milli-liters of a 5% w / v boric acid solution should be used to obtain the boric acid needed.

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