a candy factory produces 7 candies a day. How many candies will the factory produce in 100 days ​

The statement is true. If we take any two distinct prime numbers, and the number "1", these numbers will always be pairwise relatively prime.

Two numbers are said to be pairwise relatively prime if their greatest common divisor (GCD) is equal to 1. In this case, since we are considering distinct prime numbers, their GCD will always be 1 since prime numbers have no common factors other than 1 and themselves. Therefore, any two distinct prime numbers will be relatively prime.

Similarly, when we consider the number "1", it is relatively prime to any other number because its only divisor is 1. Hence, when "1" is paired with any prime number, the GCD will be 1.

In summary, whether we consider two distinct prime numbers or pair them with the number "1", the resulting numbers will always be pairwise relatively prime.

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We are given two options diagrams A and B and we are required to use choose either A or B for which option properly represents the scenario presented in the sub-questions of Question 3.

Question 3.1:

The amount of rain this year decreased by 10% compared to last year. This implies that if last year's amount of rain was X, then this year's rain has decreased by 10% of X. Mathematically, we have:

This means that last year's rain must be 100% while this year's rain has a 10% decrease in the rainfall.

The option that depicts this properly is OPTION A

Question 3.2:

The amount of sleet this year is 90% of last year's amount. This implies that if last year's amount of sleet is X, then this year's sleet amount must be 90% of X. That is:

This means that Last year's amount is again 100% while this year is 10% less than last year.

The option that depicts this properly is OPTION A

Question 3.3:

The amount of sunshine this year increased by 10% compared with last year's amount. This implies that if last year's sunshine is X and then this year's sunshine must be 10% greater than X. That is:

This means that last year's amount is 100% while this year's amount is 10% greater.

The option that depicts this properly is OPTION B.

Question 3.4:

The number of windy days this year is 110% of last year's number. This implies that this year's number has increased by 10% given that last year's number was 100%.

The option that depicts this property is OPTION B

Question 3.5:

The percentage change in Graph A is:

The answer is -10%

(Note: This is negative because it is a decrease from last year to this year)

Question 3.6:

The percentage change in Graph B is:

The answer is 10%

Final Answer

Question 3.1:

OPTION A

Question 3.2:

OPTION A

Question 3.3:

OPTION B

Question 3.4:

OPTION B

Question 3.5:

The answer is -10%

Question 3.6:

The answer is 10%

Answer:

Step-by-step explanation:

(a) The mean of the distribution is 27.6 and the standard deviation is approximately 8.1.

(b) Based on the mean and standard deviation, we can make an educated guess about the shape of the distribution. Since the standard deviation is not very small compared to the mean, we can guess that the distribution is somewhat spread out and may not be perfectly symmetrical. A reasonable guess for the shape of the distribution might be a skewed normal distribution, or perhaps a Weibull distribution.

(c) Part (c) relies on our understanding of the shape of the distribution in part (b), so it's difficult to give a complete answer without more information. If we assume a normal distribution, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of the data that falls within certain ranges of the mean. For a normal distribution with a mean of 27.6 and a standard deviation of 8.1, we know that approximately:

68% of the data falls within one standard deviation of the mean, which is between 19.5 and 35.7.

95% of the data falls within two standard deviations of the mean, which is between 11.4 and 43.8.

99.7% of the data falls within three standard deviations of the mean, which is between 3.3 and 51.9.

If the distribution is not normal, we may need to use different methods to estimate the percentage of data within certain ranges.

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\(7\frac{1}{2}\implies 7.5\hspace{5em}1\frac{1}{4}\implies 1.25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Monday through Friday} }{\stackrel{ days }{(5)}\stackrel{ rate }{(10.80)}\stackrel{ hours }{(7.5)}}~~ + ~~\stackrel{ Saturday }{\stackrel{ days }{(1)}\stackrel{ rate }{(10.80)(1.25)}\stackrel{ hours }{(7.5)}} \\\\\\ 405~~ + ~~101.25\implies \text{\LARGE 506.25}\)

A representative sample is defined as a group of subjects who are chosen to participate in research studies to assess the characteristics of the population.

In this case, Sample 1, A set of 550 New Zealanders randomly selected from a list of all licensed car owners in New Zealand, is the most likely to be a representative sample because it is obtained by a random sampling method that covers the entire population and is unbiased. Explanation:In general, a representative sample is essential for ensuring that the results of any analysis are valid. Therefore, the accuracy of the sample is critical. A random sampling method, such as Sample 1, is used to obtain representative samples. All samples other than Sample 1 are not representative samples because of the following reasons:Sample 2: This sample is not representative because it has self-selection bias, meaning that only those who are interested in the topic of the survey respond. Those who are not interested in the subject of the study do not respond.Sample 3:

This sample is not representative because it is biased toward the people who visit the particular Auckland grocery store on the day it was sampled. This sample is also subject to the voluntary response bias because only those who wanted to participate in the survey on that day did so.Sample 4: This sample is not representative because it is not randomly selected. Random sampling, as stated earlier, is necessary for obtaining a representative sample.Therefore, Sample 1 is most likely to be a representative sample because it is unbiased and obtained by a random sampling method that covers the entire population.

All other samples are not representative samples because of self-selection bias, voluntary response bias, or non-random selection. The long answer above provides a comprehensive explanation of why this is so.

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Answer:

2341

Step-by-step explanation:

(π²/4) = 2.465

(π²/8) = 1.234

√2 = 1.414

√3 = 1.732

1. Least - Greatest

(π²/8), √2, √3, (π²/4)

2. Write as quantities

2, 3, 4, 1

3. Answer

2341

I hope this helps!

The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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Answer:

  F = 3x +(2.7×10^7)/x

Step-by-step explanation:

The formulas for area and perimeter of a rectangle can be used to find the desired function.

The area of the rectangle will be the product of its dimensions:

  A = LW

Using the given values, we have ...

  13.5×10^6 = xy

Solving for y gives ...

  y = (13.5×10^6)/x

The perimeter of the rectangle is the sum of the side lengths:

  P = 2(L+W) = 2(x+y)

The total amount of fence required is the perimeter plus one more section that is x feet long.

  F = 2(x +y) +x = 3x +2y

Substituting for y, we have a function of x:

  F = 3x +(2.7×10^7)/x

__

Additional comment

The length of fence required is minimized for x=3000. The overall size of that fenced area is x=3000 ft by y=4500 ft. Each half is 3000 ft by 2250 ft. Half of the total 18000 ft of fence is used for each of the perpendicular directions: 3x=2y=9000 ft.

The year-2 CPI is 102, and the rate of inflation from year 1 to year 2 is 2%.

To calculate the rate of inflation and the Consumer Price Index (CPI) change from year 1 to year 2, we need to follow these steps:

Step 1: Calculate the inflation rate:

Inflation Rate = (Year 2 CPI - Year 1 CPI) / Year 1 CPI

Step 2: Calculate the Year 2 CPI:

Year 2 CPI = (Year 2 Basket Price / Year 1 Basket Price) * 100

Let's calculate the values:

Year 1 Basket Price = $25.00

Year 2 Basket Price = $25.50

Step 1: Calculate the inflation rate:

Inflation Rate = ($25.50 - $25.00) / $25.00

Inflation Rate = $0.50 / $25.00

Inflation Rate = 0.02 or 2%

Step 2: Calculate the Year 2 CPI:

Year 2 CPI = ($25.50 / $25.00) * 100

Year 2 CPI = 1.02 * 100

Year 2 CPI = 102

Therefore, the year-2 CPI is 102, and the rate of inflation from year 1 to year 2 is 2%.

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When a plane passes through the vertex of a double-napped cone, the intersection is a degenerate conic section.

A double-napped cone is formed by rotating a straight line around another straight line that is parallel to it.

The intersection of a plane with a double-napped cone is referred to as a conic section. A degenerate conic section is formed when a plane intersects a double-napped cone at the vertex.

Thus, when a plane passes through the vertex of a double-napped cone, the intersection is a degenerate conic section.

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k = 4

adding 4 to f(x) will make the line shift up 4 points on the y-axis, therefore making the equation equal g(x)

Answer:

the radius is 3 m

Step-by-step explanation:

the radius of a circle is always one half of the diameter.

Here the diameter is 6 m, so the radius is 3 m.

Answer:

your answer should be B

Step-by-step explanation:

p.s I'm sorry if its wrong!!

The degree of the monomial 2π is zero as an expression with only one term, variables, and a coefficient is called a monomial.

A monomial expression is one that contains only one non-zero term. It is made up of various components, including the variable, the coefficient, and its degree. The letters that make up a monomial are its variables. The numbers that result from multiplying the monomial's variables by their respective coefficients. The exponents of all the variables are added to determine a monomial's degree.

The degree of the monomial is calculated by adding the exponents of each included variable. The monomial degree of constants is 0.

In this problem we have the monomial 2π.

2π is a constant.

Therefore, the degree of the monomial 2π is zero.

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Answer:

35

Step-by-step explanation:

1.8 * 15 = 27 total earning

27-20 = 7 profit

$ 7 profit  / $20 cost  = 0.35

0.35*100 = 35%

Answer:

7(4)-7

28-7

21

Step-by-step explanation:

x=1.57142857143 thats your answer all you do is add seven to get rid of it then divide by the other seven and you have what x equals

The largest figure that Ash can built with 61 toothpicks is of:

A composition of 12 hexagons.

The number of toothpicks needed is modeled with a linear function, defined as follows:

y = mx + b.

The coefficients of the function are given as follows:

The number of toothpicks in each figure is represented by the following sequence:

(6, 11, 16, ...).

Hence the parameters are given as follows:

m = 5, b = 6.

Thus the definition of the function is of:

T(n) = 5(n - 1) + 6. (as the first figure is with n = 1).

T(n) = 5n + 1.

Then the number of hexagons with 61 toothpicks is obtained as follows:

5n + 1 = 61

5n = 60

n = 60/5

n = 12 hexagons.

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The likelihood that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.

To compute the probability for the a data point, we must first get the value's z-score.

Mean = μ = 15 points

SD = σ = 3 points

When calculating the likelihood that a score will be higher than 24, the z-score for 24 is:

z-score = (x-μ)/σ

z = (24-15)/3

z = 9/3

z = 3

The chance of z3 must now be determined using the z-score table, and it will be deducted from 1 to determine the likelihood of z>3.

P(z < 3) = 0.9987

P(z > 3) = 1 - P(z < 3)

P(z > 3) = 1 - 0.9987

P(z > 3) = 0.0013 = 13%

Thus, the probability that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.

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Theree numbers that follows given conditions are: 26, 19 and 38

Let a, b and c be three numbers.

We have been given the sum of three numbers is 83.

So, we get an equation a + b + c = 83              ............(1)

The third number is two times the second.

So, we get an equation,

c = 2b                              ...............(2)

The second number is seven less than the first.

So, we get an equation ,

b = a - 7                            

i.e., a = b + 7             ...............(3)

Substitute these values of a and c in equation (1)

b + 7 + b + 2b = 83

4b + 7 = 83

4b = 76

b = 19

Substitute this value of equation (2) and (3),

a = b + 7

a = 19 + 7

a = 26

and c = 2b

c = 2 * 19

c = 38

Therefore, the required numbers are: 26, 19 and 38

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The complete question is:

The sum of three numbers is 83. The third number is two times the second. The second number is seven less than the first. What are the numbers

Answer:

C. volume

Step-by-step explanation:

when youre starting your measurements you want to start the volume first.

Answer:

C

Step-by-step explanation:

got it right

The slope-intercept form of the equation of the line through the given point and parallel to the given line is y=x−14.

In the given question we have to write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

The given points are (–2, –16).

The given equation of line is y = x – 5.

Standard equation of line is y=mx+c.

After comparing to the standard equation.

Slope m(1) = 1

The line passes through (−2,−16), so the point will satisfy the equation y=mx+c. So

−16=−2*1+c

Simlifying

−16=−2+c

Add 2 on both side, we get

c = −16+2

c = −14

As we know that if line is parallel then

m(1)=m(2)

So the value of solpe m = 1

Now the equation of line

y=1*x+(−14)

y=x−14

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The right answer is:

How do you write the slope-intercept form of the equation of the line through the given point and parallel to the given line?

Point (−2,−16), y = x – 5

Answer:

4.3

im not sure

correct me if im wrong

Answer

6.7

Step-by-step explanation:

Works on acellus

Answer:

S=2t

or

T=1/2 S

Step-by-step explanation:

according to the table, the rate of change of the water level =

(40-50)/(2-0)

= -10/2

= -5 ft/hr

_________

\(\:\)

Time = 2 - 0 = 2

Water level = 40 - 50 = -10

Soo :

-10/2 = -5ft/hr

Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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Answer:

AC should be 42

Step-by-step explanation:

35 divided by 7 is 5 same goes with 56 divided by 8 so 6x7 is 42

the Scale factor should be 7:1

Answer:

Line AC's length is 42

Step-by-step explanation:

35 divided by 5 is 7

56 divided by 8 is 7

42 divided by 6 is 7

Answer:

B

Step-by-step explanation:

The correct answer is c. Line graphs show the change in one or more variables progressively across time.

Histograms show the distribution of data, pie charts show the proportions of a whole, bar charts compare categories or groups, and diagrams show the relationships between different elements.

The correct answer is c. Line graphs show the change in one or more variables progressively across time

A histogram is a visual depiction of data distribution in statistics. The histogram is shown as a collection of neighbouring rectangles, where each bar represents a certain type of data. Numerous fields use statistics, which is a branch of mathematics. Frequency, which can be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data.

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Line graphs show the change in one or more variables progressively across time. C

A line graph is a type of chart that displays data as a series of data points connected by straight lines.

The horizontal axis of the graph typically represents time, while the vertical axis represents the value of the variable being measured.

By connecting the data points with lines, a line graph can show the trend or pattern of change in the variable over time.

Line graphs are commonly used in fields such as economics, finance, and science to visualize trends in data over time.

They can be used to identify patterns, compare different variables, or forecast future trends.

In contrast, histograms, pie charts, bar charts, and diagrams are different types of charts that are used to display data in different ways.

Histograms are used to show the distribution of data within a single variable, while pie charts and bar charts are used to compare different categories or groups of data.

Diagrams are used to represent complex systems or relationships, often using visual symbols or icons to represent different components.

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Answer:

B

Step-by-step explanation:

So we have the equation:

\(\frac{3x+9}{2}=\frac{x-4}{3}\)

First, let's get rid of the fractions. We can multiply by the LCM of 2 and 3 which is 6. So, multiply both sides by 6:

\(6(\frac{3x+9}{2})=6(\frac{x-4}{3})\)

On the left, the 6 and 2 cancel, leaving a 3.

On the right, the 6 and 3 cancel, leaving a 2.

So:

\(3(3x+9)=2(x-4)\)

Distribute:

\(9x+27=2x-8\)

Subtract 2x from both sides:

\(7x+27=-8\)

Subtract 27 from both sides:

\(7x=-35\)

Divide both sides by 7:

\(x=-5\)

And we're done!

The value of x is -5.

Our answer is B.

\(\large{\bf Step-by-step~explanation:}\)

Since we are solving for x, our goal is to isolate the variable.

\(\bf Step~1:\)

To solve, we have to cross multiply these fractions. We do this by multiplying 2 by (x - 4), and 3 by (3x + 9).

\(\bf 2*x-4=2x-8\\3*3x+9= 9x+27\)

\(\bf Step~2:\)

After that, we replace the fractions with the expressions.

\(\bf 2x-8=9x+27\)

\(\bf Step~3:\)

Since our goal is to isolate the variable x, we cannot have two variables, one on each side. To end up with only one, we either subtract 9x from both sides or 2x from both sides, to cancel one of the values out. I am going to choose 2x because when you subtract 2x from 9x, you will not end up with a negative number.

\(\bf 2x(-2x)-8=9x(-2x)+27\\-8=7x+27\)

\(\bf Step~4:\)

Now, we have to subtract 27 from both sides to get the term with the variable by itself.

\(\bf-8(-27)=7x+27(-27)\\-35=7x\)

*on these demonstrations, the numbers in parenthesis means to add/subtract, not multiply.

\(\bf Step~5 ~(Final~step!):\)

Finally, we divide both sides by 7 to get x's value.

\(\bf \frac{-35}{7} =\frac{7x}{7}\)

\(\bf -5=x\)

\(\large\boxed{\bf Our~final~answer:~x=-5; ~B}\)