The Central Limit Theorem (CLT) states that as the sample size n increases, the sample mean approaches a normal distribution with a mean of μ and a standard deviation of σ/√n.
Therefore, when the number of houses in a population is unknown and a random sample of 48 houses is drawn from it, the mean for the sample sum distribution can be calculated using the CLT as follows:Mean for the sample sum distribution = nμ = 48 * 1670 = 80,160. The standard deviation for the sample sum distribution is given by:σ/√n = 140/√48 ≈ 20.20. Therefore, the sample sum distribution has a mean of 80,160 and a standard deviation of 20.20.To verify this, a histogram can be plotted in Excel using the following steps:Enter the data for the square footage of the 48 houses in column A of the Excel worksheet.Highlight column B and enter the formula =SUM(A1:A48) to sum the data in column A and store the result in column B.Highlight column C and enter the formula =B1/48 to calculate the mean for the sample sum distribution and store it in column C.Highlight column D and enter the formula =140/SQRT(48) to calculate the standard deviation for the sample sum distribution and store it in column D.Highlight columns B, C, and D, and select the Insert tab.Click on the Histogram icon under the Charts group.Select the Histogram chart type, and click OK to generate the histogram.The histogram should show a bell-shaped curve with a mean of 80,160 and a standard deviation of 20.20, indicating that the sample sum distribution is approximately normal.
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What are the key features of the graphs of the trigonometric functions?
Select all correct trigonometric functions.The function's period is 2π.
f(x)=sinx
f(x)=cosx
The function's asymptotes are πunits apart.
f(x)=tanx
The function has a maximum value of 1.
f(x)=sinx
f(x)=cosx
The function's period is 2π: f(x)=sinx , f(x)=cosx.
The function has a maximum value of 1: f(x)=sinx
The function's asymptotes are π units apart: f(x)=tanx.
The function's period is 2π:
The period of a trigonometric function is the distance between two consecutive repetitions of its pattern.
For the functions f(x) = sin(x) and f(x) = cos(x), the period is indeed 2π. This means that the graph of these functions repeats its pattern every 2π units along the x-axis.
The function has a maximum value of 1:
The function f(x) = sin(x) has a maximum value of 1.
As you go through the sine wave, it reaches its highest point at 1 and then starts decreasing.
The function's asymptotes are π units apart:
An asymptote is a line that a graph approaches but never quite reaches. The function f(x) = tan(x) has vertical asymptotes that are π units apart.
These asymptotes occur at regular intervals along the x-axis, specifically at x = π/2, x = 3π/2, x = 5π/2, and so on.
The tangent function has a repeating pattern of asymptotes separated by π units.
Hence, The function's period is 2π: f(x)=sinx , f(x)=cosx.
The function has a maximum value of 1: f(x)=sinx
The function's asymptotes are π units apart: f(x)=tanx.
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Complete question:
What are the key features of the graphs of the trigonometric functions?
Select all correct trigonometric functions.
The function's period is 2π.
f(x)=sinx
f(x)=cosx
f(x)=tanx
The function's asymptotes are π units apart.
f(x)=sinx
f(x)=cosx
f(x)=tanx
The function has a maximum value of 1.
f(x)=sinx
f(x)=cosx
f(x)=tanx
b) If Keira has burned 640 calories cycling, how many miles has she cycled? Give any decimal answers to 2 d.p. x distance cycled Number of calories burned against distance cycled calories burned Calories burned 400 350 300 250 200 150 100 50 0 2 6 8 10 12 14 16 4 Distance cycled (miles)
Using the slope we know that the distance Keira traveled is 32 miles.
What is the slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise).
Find the difference between these two points' x-coordinates (run).
Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
So, in the given situation:
c is calories burned and d is the distance.
Then,
x = kd
k is the slope = 200/10 = 20
Calories burned = 20 * distance cycled
When, c = 640:
640 = 20*distance
distance = 640/20
distance = 32 miles
Therefore, using the slope we know that the distance Keira traveled is 32 miles.
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i need help with this aleks assignment
The correct answer to this question is OU=13.7. This answer can be determined by using the Pythagorean Theorem.
What is Pythagorean Theorem?This states that the sum of the squares of the lengths of the two shorter sides of a right triangle will always equal the square of the length of the longest side, or the hypotenuse.
In this problem, the triangle created by points O, U, and V is a right triangle as OV and UW are tangent to the circle at point O. Therefore, the Pythagorean Theorem can be used to solve for OU.
OV is 6.5 and UW is 7.2. This is done by taking the square of the two legs and adding them together. (6.5)2 + (7.2)2 = OU2. Simplifying this equation, OU2 = 73.04. Taking the square root of both sides of this equation yields OU = 13.7
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The answer can be determined by using the Pythagorean Theorem which is OU=9.7.
What is Pythagorean Theorem?This states that the sum of the squares of the lengths of the two shorter sides of a right triangle will always equal the square of the length of the longest side, or the hypotenuse.
In this problem, the triangle created by points O, U, and V is a right triangle as OV and UW are tangent to the circle at point O.
Therefore, the Pythagorean Theorem can be used to solve for OU.
OV= 6.5
UW= 7.2.
(6.5)² + (7.2)² = OU²
Simplifying this equation,
OU² = 94.09.
Taking the square root of both sides of this equation yields
OU = 9.7
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What are the zeros of g(x) = x3 + 6x2 − 9x − 54?
Answer:
Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.
The probability that Mary will win a game is 0.03, so the probability that she will not win is 0.97. If Mary wins, she will be given $60; if she loses, she must pay $3. If X = amount of money Mary wins (or loses), what is the expected value of X? (Round your answer to the nearest cent.)
The expected value of X is -$1.11. This means that on average, Mary can expect to lose $1.11 per game.
The probability that Mary will not win is 0.97; hence, the probability that she will win is 0.03.
Probability:Probability is the likelihood of an event happening. It is a way of measuring the chance or the likelihood of an event occurring. Probability is measured on a scale from 0 to 1, where 0 is impossible and 1 is certain.
Probability = (number of favorable outcomes) / (total number of outcomes)
Expected value:The expected value is the sum of the products of each outcome and its probability. It represents the average value that one can expect to win from a game by placing a bet on that game.
In a game where the probability of winning is 0.03 and the probability of losing is 0.97,
Mary will win $60 if she wins and lose $3 if she loses.
Then, the expected value of X (the amount of money Mary wins or loses) can be calculated as:
E(X) = (0.03)($60) + (0.97)($-3)
E(X) = $1.80 - $2.91E(X) ⇒ $-1.11
The expected value of X is -$1.11 (a negative value).
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Answer: give proper question
Step-by-step explanation:
Al's car travels 40 miles on a gallon of gas the car's gas tank has a capacity of 10 gallons the distance out control was shown on the graph before his trips Al stops at the gas station where 10 gallons of gas cost $27 his tank already 2/5 full and he spends $13.50 on gas what is the maximum distance I'll can travel with the gas he has now in his tank
The maximum distance that can be traveled is given as follows:
360 miles.
How to obtain the maximum distance?The maximum distance that can be traveled is obtained applying the proportions in the context of the problem.
The amount of gas on the tank of Al's car is given as follows:
2/5 full = 2/5 x 10 = 4 gallons.10 gallons of gas cost $27, he spends $13.50, hence he put 5 gallons on the tank.Then he has 9 gallons of gas in the tank, and the car has a rate of 40 miles per gallon, hence the maximum distance that can be traveled is given as follows:
9 x 40 = 360 miles.
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10) When Perry Person got a paycheck, Perry went shopping. He spent $26 on a shirt and twice as much on jeans. Then he spent half of what he had left on a snack. On his way home, he found $10 and ended up with $ 24. How much was Perry's paycheck ?
Perry's paycheck was $100. To find Perry's paycheck, we can work backward from the final amount he had after finding $10 and ending up with $24.
Let's denote Perry's paycheck as "x". After buying the shirt and jeans, he spent a total of $26 + $52 = $78. So he had "x" - $78 left. He then spent half of what he had left on a snack, leaving him with 1/2 * ("x" - $78) = 1/2*x - $39.
When he found $10, he ended up with $24, so we can set up the equation:
1/2*x - $39 + $10 = $24
Simplifying this equation gives us:
1/2*x = $53
Multiplying both sides by 2, we get:
x = $106
Therefore, Perry's paycheck was $100.
In summary, we used a series of calculations to work backward from the final amount Perry had to determine his original paycheck. We accounted for the amount he spent on a shirt, jeans, and a snack, as well as the amount he found on his way home.
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Mr Hall's salary increases from £25,000 to £28,000 a year. Find the percentage increase in his salary.
Answer:
Step-by-step explanation:
To find the percentage increase in Mr Hall's salary, we can use the following formula:
percentage increase = (new value - old value) / old value x 100%
Substituting the given values, we get:
percentage increase = (28000 - 25000) / 25000 x 100%
Simplifying the expression, we get:
percentage increase = 0.12 x 100%
percentage increase = 12%
Therefore, Mr Hall's salary increased by 12%.
The equation and graph show the distance traveled by a covertible and a limousine in miles, y, as a function of time in hours, x.
The rate of change of the distance for limousine is less than the rate of change of the convertible.
What is rate of change?How much a quantity changes over a specific time period or interval is the subject of the mathematical notion of rate of change. Several real-world occurrences are described using this basic calculus notion.
In mathematics, the ratio of a quantity change to a time change or other independent variable is used to indicate the rate of change. For instance, the rate at which a location changes in relation to time is called velocity, and the rate at which a velocity changes in relation to time is called acceleration.
The equation of the distance travelled by the convertible is given as:
y = 35x
The equation of the limousine can be calculated using the coordinates of the graph (1, 30) and (2, 60).
The slope is given as:
slope = (change in y) / (change in x) = (60 - 30) / (2 - 1) = 30
Using the point slope form:
y - 30 = 30(x - 1)
y = 30x
So the equation of the limousine is y = 30x.
Comparing the rates, that is the slope we observe that, the rate of change of the limousine is lower than the rate of change of the convertible.
Hence, the rate of change of the limousine is less than the rate of change of the convertible.
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A company has 6000 arrivals of Internet traffic over a period of 13,710 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)= μx•e−μ x! to find the probability of exactly 3 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?
The parameters to the Poisson distribution, to find the probability of exactly 3 arrivals in one thousandth of a minute, are given as follows:
μ = 6000/13719.x = 3.e = 2.71828.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are listed and explained as follows:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.A company has 6000 arrivals of Internet traffic over a period of 13,710 thousandths of a minute, hence the mean of the distribution is given as follows:
μ = 6000/13719.
The parameter x represents the number of arrivals in each thousandth of a minute, hence it is given as follows:
x = 3.
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3. A double coconut can grow for 10 years and have a mass of 20. 0 kg. If a 20. 0 kg double coconut oscillates on a spring 42. 7 times each minutewhat is the spring constant of the spring?
If a 20. 0 kg double coconut oscillates on a spring 42. 7 times each minute, then the spring constant of the spring is 689 N/m.
The spring constant, also known as the force constant or stiffness, is a measure of the elasticity of a spring or any other elastic object. It is defined as the force required to stretch or compress a spring by a unit distance.
The period of oscillation of the coconut can be calculated as:
[tex]T = \frac{60}{42.7} = 1.405[/tex] seconds
The mass of the coconut is 20.0 kg, so we can use the formula for the period of oscillation of a mass on a spring:
[tex]T=2\pi \sqrt{\frac{m}{k}}[/tex]
where m is the mass of the coconut and k is the spring constant.
Rearranging this formula gives:
[tex]k = (2\pi)^2 *(\frac{m}{T})^2[/tex]
Substituting the values we have:
[tex]k = (2\pi)^2 *(\frac{20.0}{1.405})^2[/tex]
k = 689 N/m (to three significant figures)
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A pharmaceutical company produces caffeine pills that are each supposed to contain 200mg of caffeine. A plant that produces thousands of these pills per batch took an SRS of 15 pills from their latest batch to see if they contained the proper amount of caffeine. The sample data had a mean of 200.4mg of caffeine per pill with a standard deviation of 0.8mg. The amounts were roughly symmetric with no outliers. Based on this sample, which of the following is a 95% confidence interval for the mean amount of caffeine (in mg) per pill in this batch?
options
200.4±1.96(0.8)
200±1.96(0.8/sqrt(15))
200.4±1.96(0.8/sqrt(15))
200.4±2.145(0.8/sqrt(15))
200±2.145(0.8/sqrt(15))
The correct answer is 200.4 + 2.145(0.8/sqrt(15)).
We may use the following calculation to determine the confidence interval for the average caffeine content per tablet in this batch:
Confidence interval = sample mean + (critical value) x (standard error)
The crucial number in this situation is 1.96 since we want a 95% confidence interval. Since the sample size is 15, and the standard deviation is 0.8, the standard error is 0.8/sqrt(15). Here is what we get after entering these values:
Confidence interval = 200.4 + 1.96(0.8/sqrt(15))
The result of computing this expression is:
Confidence interval = 200.4 + 0.347
We achieve by simplifying:
Confidence interval = 200.4 + 2.145(0.8/sqrt(15))
As a result, the right response is 200.4 + 2.145(0.8/sqrt(15)).
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Answer:
Step-by-step explanation:
the length of the diagonal of a square is 12 cm what is the length of which side
The owner of a sports complex wants to carpet a hallway connecting two buildings. The carpet costs $2.50 per square foot. How much does it cost to carpet the hallway?
Therefore, it will cost $510 to carpet the hallway.
What is area?Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width. The concept of area is used in many fields, including mathematics, geometry, engineering, and architecture. It is an important measure for determining the amount of material needed to cover a surface, such as carpet or paint, and is used in a wide variety of real-world applications.
Here,
To find the cost of carpeting the hallway, we need to know the total area of both trapezoids in square feet. Let's assume that the trapezoids have parallel sides of length 16 and 18 feet, and a height of 6 feet.
The area of each trapezoid is given by the formula:
Area = (1/2) x (sum of parallel sides) x height
For the first trapezoid, the sum of parallel sides is 16 + 18 = 34 feet. Therefore, the area of the first trapezoid is:
Area1 = (1/2) x (16 + 18) x 6
Area1 = 102 square feet
For the second trapezoid, the sum of parallel sides is also 16 + 18 = 34 feet. Therefore, the area of the second trapezoid is:
Area2 = (1/2) x (16 + 18) x 6
Area2 = 102 square feet
The total area of both trapezoids is:
Total Area = Area1 + Area2
Total Area = 102 square feet + 102 square feet
Total Area = 204 square feet
Now that we know the area of the hallway, we can calculate the cost of carpeting it. We're told that the carpet costs $2.50 per square foot, so we can multiply the area of the hallway by the cost per square foot to find the total cost:
Total Cost = Area x Cost per square foot
Total Cost = 204 square feet x $2.50 per square foot
Total Cost = $510
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A greengrocer buys fruit and vegetables from the market and sells them at a 25% mark up. On one particular moring her fruit and vegetables cost her €500. If she sells all of her produce, find:
A) her profit
B) her total income
Answer: Below :)
Step-by-step explanation:
A) To find the profit, we first need to calculate the cost of the produce plus the 25% markup.
The markup is 25% of the cost, which is 0.25 * 500 = €125.
So the total cost of the produce plus markup is €500 + €125 = €625.
Now, if the greengrocer sells all the produce, the total revenue will be 100% plus the 25% markup, which is 125% of the original cost.
125% of €500 is 1.25 * 500 = €625, which is the same as the cost plus markup.
Therefore, the profit is the markup, which is €125.
B) To find the total income, we add the profit to the total cost:
Total income = €500 + €125 = €625
Answer:
A) €125
B) €625
PLS HELP GEOMETRY 15 POINTS
polygon ABCD is similar to polygon ZYXW list the relationship between angles and sides
Answer:
Step-by-step explanation:
sorry I don't know
HELP PLEASE !!
Use the information given in the figure to find the length RV.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
5
13
R
T
11
15
0
The length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
so by Pythagoras rule we can evaluate for the length RV by considering the following right triangles:
For ∆TVU:
13² = 5² + TV²
TV = √(13² - 5²) {make TV the subject}
TV = √(169 - 25)
TV = √144
TV = 12
For ∆TVS:
15² = 12² + SV²
SV = √(15² - 12²) {make SV the subject}
SV = √(225 - 44)
SV = √81
SV = 9
For ∆RVS:
11² = 9² + RV²
RV = √(11² - 9²) {make RV the subject}
RV = √(121 - 81)
RV = √49
RV = 6.3246
Therefore, the length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.
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What is the value of x? X = X-38° O X X-33°
Answer:
Step-by-step explanation:
I need some help with this
the solid is really just a right-cylinder missing a chunk.
so a full circle is 360°, now from the one in the picture above we're missing 90°, that means the cylinder is only using 270°, 360-90=270.
Well, 270° is just 3/4 of a full circle, and since the circle extends all the way down the solid cylinder, we can also say that's 3/4 of the volume of the cylinder, so hmmm let's just get the full volume of the cylinder with a radius of 6 and a height of 12 and then only grab 3/4 of it.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2(12)\implies V=432\pi \\\\\\ \stackrel{\textit{now let's just grab }\frac{3}{4}}{432\pi \cdot \cfrac{3}{4}}\implies 324\pi ~~ \approx ~~ \text{\LARGE 1017.88}[/tex]
refer to exercise 7.11. suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample. if a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p (g1 ≤ ( y - u ) ≤ g2 ) = 90
A sample of n = 9 basal areas, the two statistics, g1 and g2, such that the probability of the difference between the sample mean and population mean being between them is 90% are g1 = y - u - (1.64 * (s/sqrt(n))) and g2 = y - u + (1.64 * (s/sqrt(n))).
The goal of this exercise is to find two statistics, g1 and g2, such that the probability of the difference between the sample mean, y, and population mean, u, being between them is 90%. To do this, we will use the z-score equation to calculate the standard deviations, which we will then use to calculate the two statistics.
Given that we are using a sample of n = 9 basal areas, we can calculate the sample standard deviation s using the following equation: s = sqrt[ (1/8) * Σ (x - y)^2], where x is the individual sample value and y is the sample mean.
Once we have the sample standard deviation, we can calculate the two statistics using the following equations:
g1 = y - u - (1.64 * (s/sqrt(n)))
g2 = y - u + (1.64 * (s/sqrt(n)))
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An inequality is shown.
2x - 5 < 33
Select all the values that are solutions to this inequality.
A.28
B.26
C.19
D.18
E.12
Answer:
To solve the inequality 2x - 5 < 33, we can add 5 to both sides to isolate the variable:
2x - 5 + 5 < 33 + 5
2x < 38
Next, we divide both sides by 2 to obtain the value of x:
2x/2 < 38/2
x < 19
Therefore, any value of x that is less than 19 is a solution to this inequality. Among the given values, only 12 and 18 are less than 19. So, the solutions to the inequality are:
E. 12
D. 18
A veterinarian has an annual income of $128,610. The income tax the veterinarian has to pay is 8%. What is the amount of income tax in dollar and cents the veterinarian has to pay?
the veterinarian has to pay $10,288.80 in income tax. To calculate the amount of income tax that the veterinarian has to pay, we can multiply their annual income by the tax rate. In this case, the tax rate is 8%, so we can calculate the income tax as follows:
Income tax = Annual income x Tax rate
Income tax = $128,610 x 0.08
Income tax = $10,288.80
Therefore, the veterinarian has to pay $10,288.80 in income tax.
Income tax is a tax imposed on income earned by individuals or businesses. The tax rate may vary depending on the income level, the type of income, and the tax laws of the country. In this case, the tax rate is 8%, which means that the veterinarian has to pay 8% of their annual income as income tax.
It's important to note that income tax is usually paid on a regular basis, such as monthly or quarterly, throughout the year. The amount of income tax paid is based on the estimated income for the year, and at the end of the year, the actual income and tax liability are calculated, and any overpayments or underpayments are reconciled.
In conclusion, the veterinarian has to pay $10,288.80 in income tax based on their annual income of $128,610 and a tax rate of 8%.
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hich of the these are steps for a proof by mathematical induction that P(n) is true for all positive integers n? a. Verify that P(1) is true. b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k. c. Verify that P(1), P(2), P(3), ..., P(k) are all true, where k is a specific large, positive integer. d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k. e. Demonstrate that P(k+1) implies plk) is true for all integers k.
The steps for proof by mathematical induction that P(n) is true for all positive integers n, All options are true.
The steps for a proof by mathematical induction that P(n) is true for all positive integers n are as follows:
a. Verify that P(1) is true.
b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k.
c. Verify that P(1), P(2), P(3), ..., P(k) is all true, where k is a specific large, positive integer.
d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k.
e. Demonstrate that P(k+1) implies Plk) is true for all integers k.
Therefore, option (a), option (b), option (c), option (d), and option (e) are the steps for proof by mathematical induction that P(n) is true for all positive integers n.
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Each side of a sandbox is 4 feet long. It will cost $2.00 per square foot to replace the sand in the sandbox. What would be the total cost to replace the sand?
Answer:
It would cost $32.00
Step-by-step explanation:
Total square feet:
length * width
4 * 4 = 16 sq ft.
Cost per square foot: $2.00
And so...
16 sq ft. * $2.00 = $32.00
Pablo's is a popular Mexican restaurant, known especially for its homemade salsa. During dinner last night at Pablo's, 7 tables of people ordered chips and salsa for every 2 tables that did not.
Answer: =84
Step-by-step explanation:
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?"
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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Caris has a carton of 12 eggs, two of which have brown shells while the rest have white shells. Caris randomly chooses a brown egg from the carton. Which of the following statements is true? If she rejects this egg, returns it to the carton, and randomly picks again, these will be dependent events. If she uses this egg in a recipe and picks another one from the carton, these will be dependent events. Whether or not these are dependent or independent events depends on what color egg Caris chooses next. If she uses this egg in a recipe and picks another one from the carton, these will be independent events.
Answer:
Step-by-step explanation:
i think you have to times it
Environment An accident at an oil drilling platform is causing a circular oil slick. The slick is 0.08 foot thick, and when the radius of the slick is 150 feet, the radius is increasing at the rate of 0.5 foot per minute. At what rate (in cubic feet per minute) is oil flowing from the site of the accident?
The rate of oil flowing from the site of the accident is 47123.74 cubic feet per minute.
To find the rate at which oil is flowing from the site of the accident, we need to determine the rate of change of the volume of oil in the slick with respect to time.
We know that the slick is circular with a thickness of 0.08 feet and a radius that is increasing at a rate of 0.5 feet per minute. Let's call the radius of the slick at time t "r" and the volume of oil in the slick at time t "V".
The volume of a cylinder (which the slick approximates) is given by the formula V = πr^2h, where π is the constant pi and h is the height or thickness of the cylinder.
Differentiating both sides with respect to time, we get:
dV/dt = 2πrh(dr/dt) + πr^2(dh/dt)
We know that the thickness of the slick is constant at 0.08 feet, so dh/dt = 0. We also know that the radius is increasing at a rate of 0.5 feet per minute, so dr/dt = 0.5. Finally, we know that the radius of the slick is currently 150 feet, so r = 150.
Substituting these values into the formula, we get:
dV/dt = 2π(150)(0.5) + π(150)^2(0)
dV/dt = 47123.74 cubic feet per minute
Therefore, the rate at which oil is flowing from the site of the accident is approximately 47123.74 cubic feet per minute.
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A chemist has 20% and 50% solutions of acid available. How many liters of each solution should be mixed to obtain 600 liters of 21% acid solution?
[tex]x=\textit{Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~x\implies \cfrac{20}{100}(x)\implies 0.2 (x) \\\\\\ y=\textit{Liters of solution at 50\%}\\\\ ~~~~~~ 50\%~of~y\implies \cfrac{50}{100}(y)\implies 0.5 (y) \\\\\\ \textit{600 Liters of solution at 21\%}\\\\ ~~~~~~ 21\%~of~600\implies \cfrac{21}{100}(600)\implies 126 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{acid only}}&\stackrel{\textit{Liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.2&0.2x\\ \textit{2nd Sol'n}&y&0.5&0.5y\\ \cline{2-4}&\\ mixture&600&0.21&126 \end{array}~\hfill \begin{cases} x + y = 600\\\\ 0.2x+0.5y=126 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=600}\implies x=600-y \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.2(600-y)+0.5y=126}\implies 120-0.2y+0.5y=126 \\\\\\ 120+0.3y=126\implies 0.3y=6\implies y=\cfrac{6}{0.3}\implies \boxed{y=20} \\\\\\ \stackrel{\textit{since we know that}}{x=600-y}\implies \boxed{x=580}[/tex]