AP STATS
Burping (also known as "belching" or "eructation") is one way the human body expels excess gas in your digestive system. It occurs when your stomach fills with air, which can be caused by swallowing food and liquids. Drinking carbonated beverages, such as soda, is known to increase burping because its bubbles have tiny amounts of carbon dioxide in them.

As an avid soda drinker and statistics student, you notice you tend to burp more after drinking root beer than you do after drinking cola. You decide to determine whether there is a difference between the number of burps while drinking a root beer and while drinking a cola. To determine this, you select 20 students at random from high school, have each drink both types of beverages, and record the number of burps. You randomize which beverage each participant drinks first by flipping a coin. Both beverages contain 12 fluid ounces. Here are the results:


Part A: Based on these results, what should you report about the difference between the number of burps from drinking root beer and those from drinking cola? Give appropriate statistical evidence to support your response at the α = 0.05 significance level.


Part B: How much of a difference is there when an individual burps from drinking root beer than from drinking cola? Construct and interpret a 95% confidence interval.


Part C: Describe the conclusion about the mean difference between the number of burps that might be drawn from the interval. How does this relate to your conclusion in part A?"

AP STATS Burping (also Known As "belching" Or "eructation") Is One Way The Human Body Expels Excess Gas

Answers

Answer 1

The mean number of burps after drinking root beer is between 0.66 and 4.24 burps fewer than after drinking cola.

What is the definition of a mean number?

Mean: The "average" number obtained by adding all data points and dividing the total number of data points by the total number of data points.

Part A: A paired t-test can be used to see if there is a significant difference in the number of burps after drinking root beer versus cola. The null hypothesis states that there is no difference in the mean number of burps between the two beverages, whereas the alternative hypothesis states that there is. Using a two-tailed test with a significance level of = 0.05, we find that the t-value is -3.365 and the p-value is 0.003. We reject the null hypothesis because the p-value is less than the significance level and conclude that there is a significant difference in the mean number of burps between root beer and cola.

Part B: We can use the paired t-test formula to generate a 95% confidence interval for the difference in the mean number of burps between root beer and cola:

(xd - d) / (sd / n) t

where xd represents the sample mean difference, d represents the hypothesised population mean difference (which is 0), sd represents the sample standard deviation of the differences, and n represents the sample size.

We calculate the sample mean difference to be -2.45 and the sample standard deviation of the differences to be 2.69 using the data in the table. We get a t-value of -3.365 with 19 degrees of freedom after plugging in these values. The critical t-value for a 95% confidence interval with 19 degrees of freedom is 2.093, according to a t-distribution table.

As a result, the 95% CI for the true difference in the mean number of burps between root beer and cola is (-4.24, -0.66). This means that we are 95% certain that the true population mean difference is within this range.

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Related Questions

At the book store, you purchased some $5 clearance mystery books and $12 regular-priced science fiction books. How many of each did you buy if you spent a total of $126?

Answers

Answer: View answer in explanation below.

Step-by-step explanation: Let's use variables to represent the unknown quantities.

Let x be the number of $5 clearance mystery books purchased.

Let y be the number of $12 regular-priced science fiction books purchased.

We can set up a system of equations based on the given information:

5x + 12y = 126 (total amount spent)

x + y = total number of books purchased

We need to solve for x and y.

Let's use the second equation to solve for one variable in terms of the other:

y = total number of books purchased - x

Now we can substitute this expression for y into the first equation:

5x + 12(total number of books purchased - x) = 126

Simplifying and solving for x:

5x + 12total number of books purchased - 12x = 126

-7x + 12total number of books purchased = 126

-7x = -12total number of books purchased + 126

x = (12total number of books purchased - 126)/7

Since x must be a whole number (you can't buy a fraction of a book), we need to find a value of total number of books purchased that makes x a whole number. We can start by trying different values of total number of books purchased:

If total number of books purchased is 10:

x = (12(10) - 126)/7 = -6/7 (not a whole number)

If total number of books purchased is 11:

x = (12(11) - 126)/7 = 6/7 (not a whole number)

If total number of books purchased is 12:

x = (12(12) - 126)/7 = 6/7 (not a whole number)

If total number of books purchased is 13:

x = (12(13) - 126)/7 = 12/7 (not a whole number)

If total number of books purchased is 14:

x = (12(14) - 126)/7 = 18/7 (not a whole number)

If total number of books purchased is 15:

x = (12(15) - 126)/7 = 24/7 (not a whole number)

If total number of books purchased is 16:

x = (12(16) - 126)/7 = 30/7 (not a whole number)

If total number of books purchased is 17:

x = (12(17) - 126)/7 = 36/7 (not a whole number)

If total number of books purchased is 18:

x = (12(18) - 126)/7 = 42/7 = 6 (a whole number)

So, you bought 6 $5 clearance mystery books and 12 - 6 = 6 $12 regular-priced science fiction books.

The mayor of a town sees an article that claims the national unemployment rate is
8%. They suspect that the unemployment rate is lower in their town, so they plan to take a sample of 200 residents to test if the proportion of residents that are unemployed in the sample is significantly lower than the national rate. Let p represent the proportion of residents that are unemployed.
Which of the following is an appropriate set of hypotheses for the mayor's significance test?
Choose 1 answer:

Answers

The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].

What is Hypothesis test?

Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.

Using the appropriate notation, the hypotheses can be expressed as:

$H_0: p = 0.08$

$H_a: p < 0.08$

Therefore, the appropriate set of hypotheses for the mayor's significance test are:

[tex]$$H_0: p = 0.08$$[/tex]

[tex]$$H_a: p < 0.08$$[/tex]

Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate

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Why is pi important in math?

Answers

Pi is used to find the area and circumference of a circle

The cost price of 20 articles is the same as sellling price of 16 articles find the gain percent

Answers

If the cost price of 20 articles is the same as selling price of 16 articles, then the gain percentage is 25%

To find the gain percent, we first need to calculate the profit earned on the sale of the 16 articles.

Let the cost price of each article be "C" and the selling price of each article be "S".

Given that the cost price of 20 articles is the same as the selling price of 16 articles, we can write:

20C = 16S

We can simplify this equation to:

S = (20/16)C = (5/4)C

Now, let's calculate the profit earned on the sale of 16 articles:

Profit = Total Selling Price - Total Cost Price

Profit = 16S - 20C

Profit = 16(5/4)C - 20C

Profit = 5C/2

The profit earned is 5C/2. The profit percent can be calculated as:

Profit Percent = (Profit / Cost Price) x 100

Profit Percent = (5C/2) / (20C) x 100

Profit Percent = 25%

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In the figure below, m 24 = 106°. Find mZ1, m/2, and m 23. 1 X 3 2 ترا = 0° m 22 = ° m2 1 = m 23 = °​

Answers

Answer:

m<1=74

m<2=106

m<3=74

Step-by-step explanation:

m<1:

=180-106

=74

m<2:

=106

m<3;

if m<1 is 74, m<s will also be 74

At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?

Answers

Answer:

Step-by-step explanation:

Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:

999n = 727272

To solve for "n", we divide both sides by 999:

n = 727272/999

Using a calculator or long division, we get:

n ≈ 728.56

Therefore, each pizza has approximately 728 slices.

Scientists determined that the cause of death in many prawns off the coast of Chile was a nutrient deficiency. So, they set out to determine if the distribution of plants in the ocean near the coast was out of proportion when compared to the ideal environment: 40% Kelp, 25% Phytoplankton, 25% Coral and 10% Other (mostly nutrient-low seaweed). In randomly chosen areas along the coast, they sampled 240 plants.
KELP PHYTOPLANKTON CORAL OTHER
84 67 57 32
In an ideal environment how many of the 240 plants would you expect to be Kelp?
If a goodness of fit test is conducted, what is the null Hypothesis?
If a goodness of fit test is conducted, what is the alternative Hypothesis?
What is the probability of getting the observed values or values as extreme from the ideal?
Is there enough evidence to conclude that the environment for prawns is not ideal? Base this conclusion on p-value and a level of significance of 0.05 or 5%.

Answers

Answer:

Step-by-step explanation:

which sampling approach was used in the following statement?kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in wisconsin to study their attitudes toward evidence-based practice.

Answers

The sampling approach that was used in the statement "Kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in Wisconsin to study their attitudes toward evidence-based practice" is Stratified random sampling.

What is Stratified random sampling?

Stratified random sampling is a method of sampling that is based on dividing the population into subgroups called strata. Stratified random sampling is a statistical sampling method that involves the division of the population into subgroups or strata, and a sample is then drawn from each stratum in proportion to the size of the stratum. It's a sampling method that ensures the representation of all population strata in the sample, making it more effective than simple random sampling.

Stratified random sampling is used when there are variations in the population that are likely to influence the outcome of the study. The stratified random sampling method is used to ensure that these differences are reflected in the sample. In this way, the results of the study are more representative of the entire population than they would be if a simple random sample were used.

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if belongs to the interval , at which values of does the curve have a tangent line parallel to the line ?

Answers

Answer:

you need to show the numbers

Step-by-step explanation:

The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 7 cm and the width is 5 cm, how fast is the area of the rectangle increasing (in cm²/s)?

Answers

Answer:

Step-by-step explanation: In the problem, they tell us that

dL / dt = 7 cm/s (the rate at which the length is changing) and

dw / dt = 8 cm/s (the rate at which the width is changing)

Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm

The equation for the area of a rectangle is:

A = L·w, so will need the product rule when taking the derivative.

dA/dt = L (dw/dt) + w (dL/dt)

Now just plug in all of the given numbers:

dA/dt = (7)(7) + (5)(8) = 49+40 = 89  cm²/s

If you walk for 1. 5 hours and at 3mph then for the next 0. 5 hours how fast do you run for an average of 4 mph

Answers

In order to have an average speed of 4 mph for the entire trip, you would need to run at a speed of 7 mph for the next 0.5 hours after walking for 1.5 hours at 3 mph.

Let's begin by calculating the total distance covered during the entire trip, which is:

distance = (time walked) x (walking speed) + (time ran) x (running speed)

We know that the time walked is 1.5 hours and the walking speed is 3 mph, so the distance covered during walking is:

distance walked = (time walked) x (walking speed) = 1.5 x 3 = 4.5 miles

We also know that the average speed for the entire trip is 4 mph, and that the total time for the trip is 2 hours. Therefore, the distance covered during the entire trip is:

distance = (average speed) x (total time) = 4 x 2 = 8 miles

So the distance covered during running is:

distance ran = distance - distance walked = 8 - 4.5 = 3.5 miles

Now we can use the formula for average speed:

average speed = total distance / total time

To find the running speed, we need to solve for the running time, which is:

time ran = distance ran / running speed

Substituting this expression into the average speed formula, we get:

4 = (distance walked + distance ran) / (1.5 + time ran)

4 = (4.5 + 3.5) / (1.5 + distance ran / running speed)

Simplifying this expression, we get:

1.5 + distance ran / running speed = 2

distance ran / running speed = 0.5

Substituting the values we calculated, we get:

3.5 / running speed = 0.5

Solving for the running speed, we get:

running speed = 3.5 / 0.5 = 7 mph

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Maria purchased 1,000 shares of stock for $35. 50 per share in 2014. She sold them in 2016 for $55. 10 per share. Express her capital gain as a percent, rounded to the nearest tenth of a percent

Answers

Maria's capital gain is 55.21%. Rounded to the nearest tenth of a percent, this is 55.2%.

To determine Maria's capital gain as a percent, we need to calculate the difference between the selling price and the purchase price, and then express this difference as a percentage of the purchase price.

The purchase price for 1,000 shares of stock was:

$35.50 x 1,000 = $35,500

The selling price for 1,000 shares of stock was:

$55.10 x 1,000 = $55,100

The capital gain is the difference between the selling price and the purchase price:

$55,100 - $35,500 = $19,600

To express this gain as a percentage of the purchase price, we divide the capital gain by the purchase price and multiply by 100:

($19,600 / $35,500) x 100 = 55.21%

In summary, to calculate the percent capital gain from the purchase and selling price of a stock, we simply divide the difference between the two prices by the purchase price and multiply by 100.

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Baseball hats are on sale for 12% off the original price of the sale price is $12.50 what was the original price? round the answer to the nearest cent

Answers

The original price of the baseball hat before 12% off in the sale was $14.20.

What is a percentage?

A number can be expressed as a fraction of 100 using a percentage. It frequently serves to indicate a portion of a total and is represented by the sign %. We may state that 25% of the class is made up of guys, for instance, if there are 100 pupils in the class and 25 of them are male.

The Roman term per centum, which meaning "by the hundred," is where the word "percent" originates.

Let us suppose the original price of the baseball hat = x.

Given that, baseball hats are on sale for 12% off the original price.

That is,

12.50 = x(1 - 12/100)

12.50 = x(100 - 12)/100

12.50 = x(0.88)

x = 14.2

Hence, the original price of the baseball hat was $14.20.

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Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.W = {[\begin{array}{ccc}a\\b\\c\\\d\end{array}\right] : 3a+b=c, a+b+2c=2d}

Answers

An appropriate theorem to show that the given set, W, is a vector space. A specific example can be

[tex]\left[\begin{array}{ccc}p\\q\\r\end{array}\right][/tex] , -p- -3q = s  and 3p = -2s - 3r

             

Sets represent values ​​that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.

The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.

The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.

The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.

Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is

S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties

u +v =y+ u and (u + v)+w=u + (v +W).

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What is the measure of arc AC? PLS help

Answers

It’s 156 or 2 u might be wrong

a family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. each member of the family averages 8 minutes in the shower per day. in a 30-day period, how many fewer gallons of water will the family use with the new showerheads? responses 60 60 800 800 2,400 2,400 3,600 3,600 7,200

Answers

The family will use 3,600 fewer gallons of water with the new showerheads in a 30-day period.

A family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. Each member of the family averages 8 minutes in the shower per day. In a 30-day period, the family will use 3,600 fewer gallons of water with the new showerheads. How many fewer gallons of water will the family use with the new showerheads?

Calculate the number of gallons used per person per shower before:

5 gal/min x 8 min = 40 gallons per person per shower.

The number of gallons used per person per shower after:

2 gal/min x 8 min = 16 gallons per person per shower.

The number of gallons used per person per day before:

40 gallons x 1 shower = 40 gallons per person per day.

The number of gallons used per person per day after:

16 gallons x 1 shower = 16 gallons per person per day

The number of gallons used per family per day before:

40 gallons x 5 people = 200 gallons per day

The number of gallons used per family per day after:

16 gallons x 5 people = 80 gallons per day

The number of gallons used per month before:

40 gallons x 5 people x 30 days = 6,000 gallons per month

The number of gallons used per month after:

16 gallons x 5 people x 30 days = 2,400 gallons per month

The family will use 6,000 - 2,400 = 3,600 fewer gallons of water with the new showerheads in a 30-day period. Therefore, the answer is 3,600.

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1 Write a positive or negative number to represent each change in the high temperature. Tuesday's high temperature was 4 degrees less than Monday's high temperature. ​

Answers

Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.

Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.

The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.

As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.

using the formula no.

Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.

Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

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the complete question is

Write a positive or negative number to represent each change in the high temperature.

1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?

2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?

3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?

4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?

Dentify the solution to the following system of equations




Identify the solution to the following system of equations




No solution

(0. 29, 2. 73)

(0. 78, 0. 05) and (-4. 32, 12. 80)

( -1, 4. 5)

Answers

If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.

To do this, we can set the coefficients of x and y in the two equations equal to each other:

6 - 4m = 2k(2m - 1)

2n - 7 = 3k

Simplifying these equations, we get:

8m - 6 = 4km

2n - 7 = 3k

We can solve the first equation for k:

k = (8m - 6)/(4m)

Substituting this into the second equation and solving for n, we get:

n = (16m - 29)/(8m - 12)

Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.

We find that the expressions for k and n are the same for m = 3/2.

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Complete Question:

Determine the values of m and n so that the following system of linear equations have infinite number of solutions:

(2m−1)x+3y−5=0

3x+(n−1)y−2=0

A grading machine can grade 96 multiple choice test in 2 minutes. if a teacher has 300 multiple choice test to grade, predict the number of minutes it will take the machine the grade the tests. please answer with details please

Answers

Answer:

6.25 minutes

Step-by-step explanation:

So, if there are 96 tests being graded in 2 minutes, the average per minute (using the equation 96/2 = average) would be 48 per minute. Next you would do 300/48 to get the number of minutes that it would take to grade that amount. The answer to that would be 6.25, So it would take approximately 6.25 minutes.

could someone help out?

Answers

Answer:

27.18

Step-by-step explanation:

Firstly, you must label the triangle.

r- opposite

13.85- adjacent

We know that tan θ = opposite/ adjacent so we substitute our numbers into the equation.

tan (63) = r/13.85

Then, times 13.85 on both sides so we only have our unknown on one side.

(x13.85)  tan(63)= r/13.85   (x13.85)

r= tan (63) x 13.85

r=27.18

:)

Part of your summer job is to count the number mosquitoes that get caught in traps around your city. At one trap, you count mosquitoes each week ("week 0" means the first day you counted) and record the following numbers:


Use a calculator or graphing technology to determine which of the following functions matches the numbers you counted in these first few weeks.


A) M (w) = 4(w) + 8

B) M (w) = 1.5 (8^w)

C) M (w) = 8 (1.5^w)

D) w = 8 (1.5^M)

Answers

Therefore, the function that matches the mosquito counts is'(w) = 8([tex]1.5^{w}[/tex]).

by the question.

To determine which function matches the mosquito counts, we can plot the given data points on a graph and see which function fits the curve. Here are the counts for the first few weeks:

Week Mosquito Count

0 8

1 20

2 50

3 125

4 312

Plotting these points on a graph with weeks on the x-axis and mosquito count on the y-axis, we get:

mosquito graph

Looking at the graph, we can see that the curve increases rapidly and seems to be exponential. This rule out option A (which is linear), leaving us with options B, C, and D.

To determine which of these options matches the data, we can try plugging in the week numbers and seeing which one gives us values close to the actual counts. We can also use a calculator or graphing technology to help us with this.

Option B gives us the following mosquito counts for the first five weeks:

Week Mosquito Count

0            8

1         19.5

2        47.25

3       114.19

4       276.32

Option C   gives us:

Week Mosquito Count

0       8

1        12

2       18

3       27

4       40.5

Option D is not a function of mosquito counts with weeks as the input variable, so we can rule it out.

Comparing the values from options B and C to the actual counts, we can see that option C is the closest match.

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Six more than the quotient of a number and 8 is equal to 4

use the variable x for the unknown number

!!!TRANSLATE INTO A EQUATION!!!

Answers

Answer:

x/8 + 6 = 4

Step-by-step explanation:

x / 8 + 6 = 4

x/8 = -2

x = 8*-2 = -16.

Consider a system with one component that is subject to failure, and suppose that we have 120 copies of the component. Suppose further that the lifespan of each copy is an independent exponential random variable with mean 25 days, and that we replace the component with a new copy immediately when it fails.(a) Approximate the probability that the system is still working after 3625 daysProbability(b) Now, suppose that the time to replace the component is a random variable that is uniformly distributed over (0,0.5). Approximate the probability that the system is still working after 4250 days.Probability

Answers

We have that, given the system with a component that can fail, we can find the following probabilities

a) Probability that the system continues to function after 3625 days is 0.091b) Probability that the system is still working after 4250 days is 0.018

How do we calculate probability using the exponential distribution?

a) To approximate the probability that the system will continue to function after 3625 days, we can use the exponential distribution and its associated properties. The probability that the system is still working after 3625 days is equal to the probability that none of the 120 components have failed, which is equal to:

Probability = e(-120*(3625-25)/25) = 0.091

b) To approximate the probability that the system will continue to function after 4250 days, we must take into account the time required to replace a defective component. Since the time required to replace a defective component is a random variable that is uniformly distributed over (0,0,5), the expected time to replacement is 0.25. Therefore, the probability that the system is still working after 4250 days is equal to:

Probability = e(-120*(4250-25)/25) * e(-120*(0.25)/25) = 0.018

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Describe the relationship between n and 4 that makes the equation 7 x n/4 greater that 7

Answers

An Inequality is a relationship between two expressions or values that aren't equal. The relationship between n and 4 is given by the inequality n> 4.

We want to find a relation between n and 4 similar that

7 *( n/ 4)> 7

still, we get

If we now divide both sides of the former inequality by 7.

7 *( n/ 4)/ 7>7/7

n/ 4> 1

So n/ 4 must be lesser than 1.

A better way to show the relationship is to multiply both sides of the inequality by 4.

4 *( n/ 4)> 4 * 1

n> 4

So the relationship between n and 4 is that n must be lesser than 4.

In mathematics, an inequality is a relationship that results in an unstable comparison of two figures or other fine expressions. It's frequently used to compare two figures on a number line grounded on their size.

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The spinner above is used in a game. What is the theoretical probability of the given event with one spin?

P (5)

Answers

Answer:

B

Step-by-step explanation

so there is 8 numbers so when you spin you have a 1/8 chance of spinning the number

Help Me Find Y
Show Work

Answers

Answer:

y = 12

Step-by-step explanation:

if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is

y² = 8(8 + 6 + 4) = 8 × 18 = 144 ( take square root of both sides )

y = [tex]\sqrt{144}[/tex] = 12

Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. )

P = $1300, r = 8. 5%, t = 11 years

n A

1 $

2 $

4 $

12 $

365 $

Continuous $

Answers

The complete table for the amount balance, A when P dollars is invested at rate r for t years and compounded n times per year is present in above figure 2.

The compound interest formula is written as A = P( 1 + r/n)ⁿᵗ

where, A--> total Amount of money after t years

P --> Principal

r --> Annual rate of interest (as a decimal)

t --> Number of years:

n--> number of times interest is compounded per year

Here, principle, P = $1300, rate of interest, r = 8.5% = 0.085 , time periods, t = 11 years. We have to complete the above table for compound interest.

Case 1: n = 1

Substitute the known values in above formula, A = 1300( 1 + 0.085/1)¹¹

= 1300( 1.085)¹¹

= 3,189.12

Case 2: n = 2

A = 1300( 1 + 0.085/2)²²

= 1300( 2.085/2)²²

= 1300( 1.0425)²²

= 3,248.01

I'll let you work out the cases where n = 4, 12 and 365 since all you need to do is place those in for n as done in the 1st 2 cases. For the Compounded continuously case, the formula becomes,

[tex] A = Pe^{rt}[/tex]

Where: A-> Total amount of money after t years

P --> Principal Amount

e --> Natural log constant:

r = Annual rate of interest (as a decimal)

Case: Continuous: e = 2.71828 (approx), r = 0.085

A = 1300( 2.71828)⁰·⁰⁸⁵⁽¹¹⁾

= 1300(e)⁰·⁹³⁵ = 3,311.34

Hence, required value is $3,311.3775.

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Complete question :

The above table completes the question.

Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. ) P = $1300, r = 8. 5%, t

= 11 years

Sally has 3:4 as many beads as Kelly. Kelly has 18 more beads than Sally. Find the average number of beads the girl have

Answers

The average number of beads that the girls have is 63

Let's start by using algebra to represent the given information:

Let b be the number of beads that Sally has.

Then, Kelly has 3/4 times as many beads as Sally, which can be expressed as (3/4)b.

Also, we know that Kelly has 18 more beads than Sally, which can be expressed as (b + 18).

Putting these together, we can write the equation:

(3/4)b = b + 18

Solving for b, we get:

b = 72

So, Sally has 72 beads, and Kelly has (3/4) × 72 = 54 beads.

The average number of beads that the girls have is (72 + 54)/2 = 63 beads

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when an automatic press is a manufacturing process is operaing properly, the lengths of the component it produces are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches. what is the probability thata randomly selected component is shorter than 7 inches long? (report your answer to 4 decimal places.)

Answers

The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.

What is the probability of randomly selected component?

We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.

We need to find the probability that a randomly selected component is shorter than 7 inches long.

We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:

z = (7 - 8) / 1.5 = -0.67

Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:

P(z < -0.67) = 0.2514

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Can you help me with this?

Answers

16. The equatiοn οf the line in slοpe-intercept fοrm that passes thrοugh the pοint (-6, 5) and is parallel tο x + 2y = 14 is y = (-1/2)x + 2.

What is equatiοn οf line?

The equatiοn οf a straight line is y = mx + c, y = m x + c m is the gradient and c is the height at which the line crοsses the y -axis, alsο knοwn as the y -intercept.

16. Tο write the equatiοn οf a line in slοpe-intercept fοrm, we need tο find the slοpe and the y-intercept οf the line.

Tο find the slοpe οf the line, we can rewrite the equatiοn x + 2y = 14 in slοpe-intercept fοrm y = mx + b by sοlving fοr y:

x + 2y = 14

2y = -x + 14

y = (-1/2)x + 7

The slοpe οf the line is -1/2.

Since the line we want tο find is parallel tο this line, it will have the same slοpe οf -1/2.

Nοw we can use the pοint-slοpe fοrm οf the equatiοn οf a line tο find the equatiοn οf the line that passes thrοugh the pοint (-6, 5) with a slοpe οf -1/2:

y - y1 = m(x - x1)

where (x1, y1) is the pοint (-6, 5), and m is the slοpe, -1/2.

y - 5 = (-1/2)(x - (-6))

y - 5 = (-1/2)x - 3

y = (-1/2)x + 2

17. The equation perpendicular to y = -(2/3)x + 4, passing through (-4, 6)

perpendicular equations slope would be negative reciprocal to the current line.

The slope in y = -(2/3)x + 4, is m = -(2/3),

The negative reciprocal of -(2/3) is 3/2

Now, applying the x and y values in pοint-slοpe fοrm

y - 6 = 3/2(x - (-4))

y =  3/2(x+4) + 6

y =  (3/2)x + 6 + 6

y =  (3/2)x + 12

18. Since the line we want tο find is parallel tο this line, it will have the same slοpe.

Lets find the slope using slope formula

[tex]\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\rm m = \dfrac{0 - (-1)}{2 - (-1)}[/tex]

[tex]\rm m = \dfrac{1}{3}[/tex]

Now, using the point slope form

y - 1 = 1/3(x - 3)

y = 1/3(x - 3) + 1

y = (1/3)x - 1 + 1

y = (1/3)x

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