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For the region above x + 3y = 9 and below x + 9 = y², we have:
a = 18, b = -9, f(x) = (y² - 9)/3, and g(x) = (9 - x)/3.
For single integration: α = -6, β = 3 and h(y) = [(9 - y²)/3 - (y² - 9)].
What is the area bounded by the curves?To solve this problem, we first need to find the intersection points of the two curves x + 3y = 9 and x + 9 = y². We can do this by solving the system of equations:
x + 3y = 9
x + 9 = y²
Rearranging the first equation, we get:
x = 9 - 3y
Substituting this expression for x into the second equation, we get:
9 - 3y + 9 = y²
Simplifying, we get:
y² - 3y - 18 = 0
Factorizing, we get:
(y - 6)(y + 3) = 0
So the solutions are:
y = 6 or y = -3
Substituting these values of y into the equation x + 3y = 9, we get:
When y = 6, x = -9
When y = -3, x = 18
So the intersection points of the two curves are (-9, 6) and (18, -3).
Now we can find the area between the two curves by splitting it into two regions: the region above the curve x + 3y = 9 and below the curve x + 9 = y², and the region below the curve x + 3y = 9 and above the curve x + 9 = y².
For the region above x + 3y = 9 and below x + 9 = y², we have:
a = 18
b = -9
f(x) = (y² - 9)/3
g(x) = (9 - x)/3
Alternatively, to compute the area between the two curves x + 3y = 9 and x + 9 = y² using a single integral, we need to express the area as a function of y instead of x.
We can rearrange the equations x + 3y = 9 and x + 9 = y² to get:
x = 9 - 3y
x = y² - 9
Setting these two expressions equal to each other, we get:
9 - 3y = y² - 9
Simplifying, we get:
y² + 3y - 18 = 0
Factorizing, we get:
(y + 6)(y - 3) = 0
So the solutions are:
y = -6 or y = 3
Substituting these values of y into the equation x + 3y = 9, we get:
When y = -6, x = 27
When y = 3, x = 0
So the intersection points of the two curves are (27, -6) and (0, 3).
The area between the curves can be expressed as the difference between the integrals of the curves' respective functions with respect to y, since the curves are better expressed in terms of y.
The function representing the curve x + 3y = 9 in terms of y is:
x = 9 - 3y
We can rearrange this equation to get:
y = (9 - x)/3
Substituting x = y² - 9, we get:
y = (9 - y² + 9)/3
Simplifying, we get:
y² + 3y - 18 = 0
This is the same equation we obtained before, so we know that the bounds of integration are -6 and 3.
The function representing the curve x + 9 = y² in terms of y is:
x = y² - 9
Substituting this expression into the formula for the area of a region between two curves, we get:
Area = ∫(y=α)^(y=β) [(9 - y²)/3 - (y² - 9)] dy
Where;
α = -6 and β = 3 are the bounds of integration, and
the integrand [(9 - y²)/3 - (y² - 9)] represents the difference between the y-values of the two curves at a given x-value.
Simplifying the integrand, we get:
Area = ∫(y=-6)^(y=3) (18 - 2y²)/3 dy
Integrating, we get:
Area = [(6y - (2/3)y³)/3] |(y=-6)^(y=3)
Plugging in the limits of integration, we get:
Area = [(18 - 216)/3] - [(-36 + 216)/3]
Simplifying, we get:
Area = 66
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Related Questions
I need to know how to do these and if I got the one right
Answers
23. The value for x in triangle is 11.14
24. The value for x in the triangle is 18.3
25. The value for x = 30.4
27 The value for x = 63.413 degrees
Sine, Cosine and Tangent23
Cos θ= adj/ hyp
cos 42= x/15
x = 15 cos 42
x = 11.14
24
tan θ= opp/ adj
tan 31= 11/ x
x(tan 31)= 11
x = 11/tan 31
x = 18.3
25
cos θ= adj/ hyp
cos 18= 29/x
x(cos 18) = 29
x = 29/ cos 18
x = 30.4
27
sin x = opp/ hyp
sin x = 17/19
sin x = 0.8947
x = 63.413 degrees
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A research survey of 2006 public and private school students in the united states (grades 10-12) between April 12 and June 12,2016 asked students if they agreed with the statements, "if I make a mistake, I try to figure out where I went wrong. " The survey found that 86% students agreed with the statement. The margin of error for the survey is +/- 3. 7%
Answers
The survey found that 86% of 2006 US students in grades 10-12 agreed with the statement "if I make a mistake, I try to figure out where I went wrong." The survey's margin of error is +/- 3.7%, so we can be 95% confident the true proportion falls between 82.3% and 89.7%.
This means that we can be 95% confident that the true proportion of students who agree with the statement lies between 82.3% and 89.7%. This interval is calculated as follows
Subtract the margin of error from the sample proportion to get the lower bound: 86% - 3.7% = 82.3%
Add the margin of error to the sample proportion to get the upper bound: 86% + 3.7% = 89.7%
So, we can say with 95% confidence that the true proportion of students who agree with the statement is somewhere between 82.3% and 89.7%.
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The chemical element einsteinium-
253
253253 naturally loses its mass over time. When a sample of einsteinium-
253
253253 was initially measured, it had a mass of
15
1515 grams. The relationship between the elapsed time
�
tt, in weeks, and the mass,
�
week
(
�
)
M
week
(t)M, start subscript, start text, w, e, e, k, end text, end subscript, left parenthesis, t, right parenthesis, left in the sample is modeled by the following function:
Mweek(t)=15⋅(0. 79)t
Complete the following sentence about the daily rate of change in the mass of the sample. Round your answer to two decimal places. Every day, the mass of the sample decays by a factor of
Answers
The given information pertains to a sample of einsteinium-253, which naturally loses its mass over time. The initial mass of the sample was 15 grams when it was first measured. The relationship between the elapsed time in weeks, denoted by 't', and the mass of the sample in that week, denoted by 'Mweek(t)', is given by the function.
Mweek(t) = 15 * (0.79)^t.
The daily rate of change in the mass of the sample can be found by taking the derivative of the function with respect to time
Mweek'(t) = 15(0.79)^t ln(0.79)
To find the factor by which the mass decays every day, we can divide the mass at time t by the mass at time t+1.
Mweek(t) / Mweek(t+1) = (15(0.79)^t) / (15(0.79)^(t+1)) = 1/0.79
Therefore, every day, the mass of the sample decays by a factor of approximately 1.26 (rounded to two decimal places).
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What is the sum and the product of x^2-9x+8
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The sum of the roots of x² - 9x + 8 is 9. The product of the roots of x² - 9x + 8 is 8.
What is quadratic equation?A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.
According to question:The expression x² - 9x + 8 can be factored as follows:
x² - 9x + 8 = (x - 1)(x - 8)
To check that this factorization is correct, you can expand the expression using the distributive property:
(x - 1)(x - 8) = x² - 8x - x + 8 = x² - 9x + 8
So the factorization is indeed correct.
The sum of the roots of the quadratic equation ax² + bx + c = 0 is given by -b/a, where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -9, and c = 8, so the sum of the roots is:
-sum of roots = -b/a = -(-9)/1 = 9
Therefore, the sum of the roots of x² - 9x + 8 is 9.
The product of the roots of the quadratic equation ax² + bx + c = 0 is given by c/a. In this case, c = 8 and a = 1, so the product of the roots is:
product of roots = c/a = 8/1 = 8
Therefore, the product of the roots of x² - 9x + 8 is 8.
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Simon wants to fill 8 punch bowls for a birthday party. Each punch bowl holds 9 1/5 quarts of punch. How much punch will Simon need?
Write your answer as a fraction or as a whole or mixed number.
PLEASE HELP ME
Answers
Answer:
73.52 OR 74.00
Step-by-step explanation:
1.) 8 x 1/5 (I prefer converting to decimals first)
2.) 8.00 x 9.19 = 73.52 ----> (Rounding the ones place up) 74.00
3) During the last week of April, Ryan Foss produced 900 dolls. Ryan
receives $.96 per doll, less any defective units. What was Ryan's
gross pay for the last week of April?
Answers
Ryan's gross pay for the last week of April was $864, assuming that 96% of the dolls produced were non-defective.
What was Ryan's gross pay for the last week of April?If Ryan produced 900 dolls during the last week of April and receives $.96 per doll, his gross pay before any defective units are taken into account is:
900 dolls x $0.96/doll = $864
If we need to check if a certain percentage of the dolls produced were defective, we can multiply the gross pay by the percentage of non-defective units to find Ryan's actual gross pay.
For example, if 95% of the dolls produced were non-defective, Ryan's gross pay would be:
$864 x 0.95 = $820.80
Therefore, Ryan's gross pay for the last week of April was $820.80, assuming that 95% of the dolls produced were non-defective.
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The price of an item has dropped to $77 today. Yesterday It was $140. Find the percentage decrease.
Answers
The percentage price of the item has decreased by 45%.
What is the definition of percentage?
A percentage is a quantity or ratio that is stated as a fraction of 100.
"%" is the symbol for percentage.
For example, if 25 of 100 students in a class received a "A," we may represent this as a percentage by dividing the number of "A" students by the total number of students and multiplying by 100:
(25/100) x 100% = 25%
This signifies that 25% of the students in the class received a "A".
Now,
To obtain the % drop, subtract the difference between the original and new prices, divide by the original price, then multiply by 100 to get the percentage decrease.
The difference between the original and updated prices is equal to
140 - 77 = 63
So the percentage decrease is:
(63/140) x 100% = 45%
Therefore, the price of the item has decreased by 45%.
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in which one of the four scenarios would you consider a non-parametric test? group of answer choices when we are dealing with time series when we have numeric data and want to plot a regression line when we want to perform multiple regression when we only have ordered data
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Non-parametric tests are statistical tests that do not require specific assumptions about the population distribution, such as normality or equal variances. They are useful in situations where the data does not meet the assumptions of parametric tests, or when the variables are ordinal or categorical.
There are some additional examples of non-parametric tests.
When the data is skewed or has outliers: If the data is not normally distributed, non-parametric tests such as the Wilcoxon rank-sum test or the Kruskal-Wallis test can be used instead of the t-test or ANOVA.When the sample size is small: If the sample size is small, it may be difficult to determine if the data is normally distributed or if variances are equal. In this case, non-parametric tests such as the Mann-Whitney U test or the Wilcoxon signed-rank test may be more appropriate.When the data is categorical or ordinal: If the data is categorical or ordinal, non-parametric tests such as the Chi-square test or Spearman's rank correlation coefficient can be used instead of parametric tests.When the data violates assumptions of independence: If the data is not independent, non-parametric tests such as the Friedman test or the McNemar's test may be used.Hence, non-parametric tests offer a flexible alternative to traditional parametric tests and can be useful in a variety of situations.
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Which of these nets can be folded to form a square prism?
Answers
Corey buys 27 inches of trim for a craft project
Answers
If Corey buys 27 inches of trim for a craft project, Corey bought 3/4 of a yard of trim for the craft project.
To determine what fraction of a yard Regina buys, we need to know how many inches are in a yard. There are 36 inches in a yard.
To convert 27 inches to yards, we need to divide by 36:
27 ÷ 36 = 0.75 yards
So Corey bought 0.75 yards of trim for the craft project.
To find the fraction of a yard, we need to express 0.75 as a fraction with a denominator of 1:
0.75 = 75/100 = 3/4
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Complete question is:
Corey buys 27 inches of trim for a craft project. What fraction of a yard does Regina buy?
1. Calculate the area of the following parallelogram:
28 in²
26 in²
40 in²
30 in²
Answers
Option D is correct, the area of given parallelogram is 30 square inches
Parallelogram is a simple quadrilateral with two pairs of parallel sides.
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Area of parallelogram =bh
=10×3
=30 square inches
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The population of Log Village is 1800 in 2010, and the population increases each year by 9%. What equation is used to determine the population, y, of Log Village x years after 2010?
Answers
The equation that will be used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ
What is equation?
An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.
The population of Log Village is 1800 in 2010, and the population increases each year by 9%.
Initial population(p)= 1800
rate of increase(r)= 9%
Time(t)= x years.
The formula for the population after n years is p(1+r/100)ⁿ.
To determine the equation for the population after x years we have to put the values in the above expression.
So putting all the values we get,
The population, y, of Log Village x years after 2010 is
y= 1800( 1+9/100)ˣ
y= 1800(1.09)ˣ
Hence, The equation that will be used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ
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The histogram below shows the results of a survey on the number of traffic tickets received by a random group of drivers. 3 86 76 51 Number of People A 1 9 2 Traffic Tickets 10 8 6 Number of Traffic Tickets Step 6: How many people received either 4 or 5 traffic tickets? 12
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In reference to the given histogram, an absence of bars signifying either 4 or 5 traffic tickets implies that no one from the selection had accumulated this amount.
How to explain the histogramIt should be noted that to make sure our point is accurate, we can sum the heights of the separate bars for 3, 6 and 8 tickets which demonstrate the total people included within the survey who have acquired the relevant number of traffic citations.
The height of the bar for three violations measures out at 1.
Conversely, a measurement of 2 denotes the bar for six infringements.
An assessment of 1 has been given to the bar with regards to eight offences.
Due to the lack of representation mentioned in the histogram concerning both 4 and 5 transgressions, it confirms our inference: nobody from the selection received four or five traffic tickets.
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BigDecimal gives you control over how values are rounded. By default:
a. all calculations are approximate and no rounding occurs.
b. all calculations are approximate and rounding occurs.
c. all calculations are exact and no rounding occurs.
d. all calculations are exact and rounding occurs.
Answers
BigDecimal gives you control over how values are rounded. By default option(d) all calculations are exact and rounding occurs.
BigDecimal is a Java class that provides a way to perform exact calculations on decimal numbers with a high degree of precision and control over rounding. Unlike primitive data types, such as double and float, which are prone to rounding errors due to their binary representation, BigDecimal stores numbers using a base-10 representation, allowing for more precise calculations.
Additionally, it allows the programmer to specify rounding rules, such as rounding up or down to a certain number of decimal places, ensuring that the results of calculations are accurate and consistent. This makes BigDecimal a useful tool for applications that require precise numerical calculations, such as financial and scientific applications.
Therefore, the correct option is (d) all calculations are exact and rounding occurs
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please help asap this is for geometry its R.4
Answers
The value of k is given as follows:
k = 2.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that the parameters are given as follows:
k is the hypotenuse.The side length adjacent to the angle of 45º is of [tex]\sqrt{2}[/tex].Hence the equation to obtain k is given as follows:
[tex]\sin{45^\circ} = \frac{\sqrt{2}}{k}[/tex]
[tex]\frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{k}[/tex]
k = 2.
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Select the correct answer.
The graph of function f is shown.
Function g is represented by the equation.
g(x) = 4(1/4)^x +2
Which statement correctly compares the two functions?
A. They have different y-intercepts but the same end behavior.
B. They have different y-intercepts and different end behavior.
C. They have the same y-intercept and the same end behavior.
D. They have the same y-intercept but different end behavior.
Answers
Answer:
A. They have different y-intercepts but the same end behavior.
Step-by-step explanation:
From the shape of f we see that its a descending exponential fnction, so the factor taken to the power x will be a fraction, and from the points the eqation is
f(x) = 2(1/4)^x + 2
and the y-intercept is 4
g(x) has y-intercept of 4(1/4)^0 + 2 = 6 so they are different.
As x approaches infinity both f and g approach 2 so the end behavior s the same.
a one-hectare forest community is sampled in early august. the sample yields 12 small trees, 4 types of vines, as well as 17 native shrubs that represent 10 species. what can be estimated from the sample for the shrubs in the forest community?
Answers
Based on the sample of a one-hectare forest community in early August, an estimate can be made for the total number and diversity of shrub species present in the community.
From the sample of the one-hectare forest community, several estimates can be made for the shrubs in the forest community:
Abundance: The abundance of shrubs in the one-hectare forest community can be estimated by multiplying the number of shrubs in the sample by 10 (the number of species represented by the sample). Therefore, an estimate of the total number of shrubs in the one-hectare forest community would be 17 x 10 = 170 shrubs.
Species richness: The sample contained 10 species of shrubs. This can be used as an estimate of the total number of shrub species in the one-hectare forest community.
Diversity: The diversity of the shrub community in the one-hectare forest can be estimated using the data on species richness and abundance. The most commonly used metric for estimating diversity is the Shannon-Wiener diversity index, which takes into account both the number of species and their relative abundance.
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Help on this pls due tmrw
Answers
5. The value of x in the figure is
C. 6√77. Length of arc AD is 125 degrees
8. Angle ROT is 36.87 degrees
How to find the length of chord xThe length of chord x is solved using Pythagoras theorem as follows
5.
let x/2 = y then we have
y² = 12² - 9 ² = 144 - 81 = 63
y = √63 = 3√7
and x/2 = y = 3√7. so x = 6√7
7. BD is the diameter hence arc BAD = 180 degrees
if arc ABC is 110 then arc BA = 110 /2 = 55
Arc AD = arc BAD - arc BA
Arc AD = 180 - 55
Arc AD = 125 degrees
8. Angle ROT = arc sin (3/5)
Angle ROT = 36.87 degrees
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175% of what number is 31
Answers
Step-by-step explanation:
To find the number that is 175% of 31, we can use the following formula:
175% of X = 31
Mathematically, we can represent 175% as 1.75 (since percentage is a ratio out of 100).
So, the equation becomes:
1.75 * X = 31
To solve for X, we divide both sides of the equation by 1.75:
X = 31 / 1.75
Using a calculator, we can evaluate the right-hand side to find the value of X:
X ≈ 17.714
So, 175% of approximately 17.714 is equal to 31.
Answer:
17.714
Step-by-step explanation:
Estefanía has 2,593 euros and Rocío has 3,238 euros. How much money does Rocío have more than Estefanía?
Answers
The amount of money with Rocio has 645 euros more than Estefania.
Total amount of money with Estefania has = 2,593 euros
Total amount of money with Rocio has = 3,238 euros
When we compare the amount of money of both Estefania and Rocio
Rocio has more amount of money than Estefania .
3,238 Euros is greater than 2,593 Euros
To find out how much money Rocio has more than Estefania,
= Subtract Estefania's amount of money from Rocio's amount of money.
= 3,238 euros (Rocio's money) - 2,593 euros (Estefania's money)
= 645 euros
Therefore, Rocio has 645 euros more amount of money than Estefania.
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Sue and 4 friends share half a pizza. Each piece of pizza is the same size. Sue believes each piece of pizza has an angle measure of 30º. Is Sue correct? Explain.
Answers
Sue statement that each piece of pizza has an angle measure of 30º is incorrect
Stating if Sue's statement is correctAssuming the pizza is circular, we know that the total angle measure of a circle is 360 degrees.
If we cut the pizza into halves, we have two equal pieces, each with an angle measure of 180 degrees.
If Sue and her 4 friends share half a pizza, they are sharing one of these equal pieces.
If we divide the 180 degree angle of the piece of pizza by 5 (Sue and her 4 friends plus Sue herself), we get an angle measure of 36 degrees, which is what Sue believes.
Therefore, Sue is incorrect.
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Sarah is turning 27 today. In the mail, she received 14 envelopes, and each envelope included $2. 70. How much money did she receive in the mail?
Answers
If in the mail, she received 14 envelopes, and each envelope included $2. 70,Sarah received a total of $37.80 in the mail.
Sarah received a total of 14 envelopes, and each envelope had $2.70. To find out how much money she received in total, we can multiply the number of envelopes by the amount of money in each envelope:
Total money = 14 × $2.70
We can simplify the expression by first multiplying the whole number, 14, by the tenths value of $2.70, which is $0.70:
Total money = $37.80
This amount of money is the sum of all the money in the 14 envelopes she received. It can be useful to double-check the answer by adding up the amounts in each envelope manually, but in this case, it is not necessary since we have already calculated the total.
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4. One of the players scored 13. 7 points per game with 4. 1 free throw attempts per game. How does this compare to what the model predicts for this player?
Answers
The model predicts that the player should score around 17.47 points per game based on their 4.1 free throw attempts per game. However, the player's observed score of 13.7 points per game suggests that they may be underperforming compared to what would be expected based on this relationship.
Let us assume that the model predicts a linear relationship between points per game and free throw attempts per game, we can calculate the predicted value of points per game for this player using the regression equation
points per game = slope * free throw attempts per game + intercept
From the given data, we know that the slope of the regression line is 2.6 and the intercept is 7.1. Plugging in the values for this player, we get:
points per game = 2.6 * 4.1 + 7.1 = 17.47
So the model predicts that this player should score approximately 17.47 points per game, which is higher than the observed value of 13.7 points per game. This suggests that this player may be underperforming compared to what would be expected based on their free throw attempts per game.
However, just one player and there may be other factors that could affect their performance beyond just free throw attempts per game.
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If the mogav train travels at a consistent speed of 480 km/h for one fourth of an hour how far does the train travel
Answers
The train travels a distance of 120 kilometers.
To calculate the distance traveled by the train, we can use the formula:
Distance = Speed × Time
Given that the train travels at a consistent speed of 480 km/h and the time is one-fourth of an hour, we can substitute these values into the formula:
Distance = 480 km/h × (1/4) hour
To simplify the calculation, we can convert one-fourth of an hour to minutes. Since there are 60 minutes in an hour, one-fourth of an hour is equal to (1/4) × 60 minutes = 15 minutes.
Now, we can calculate the distance:
Distance = 480 km/h × (1/4) hour
= 480 km/h × (1/4) × 60 minutes / 60 (converting hours to minutes)
= 480 km/h × 15 minutes / 60
= 480 km/h × 0.25
= 120 km
Therefore, distance travelled by train is 120 kilometers.
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A chord is 22 cm long. It is 60 cm from the center of the circle.
What is the radius of the circle?
Answers
R = (22^2 + 4(30)^2) / 8(30)
R = (484 + 4(900)) / 240
R = 2384 / 240
R = 9.933... cm
Therefore, the radius of the circle is approximately 9.933 cm.
The wheels on a bike have a diameter of 26 inches. How many full revolutions will the wheels need to make to travel 100 feet?
Answers
Answer:
Step-by-step explanation:
distance traveled by one revolution = circumference of the wheel
= 2πr = 2π(13 inches) = 26π inches
number of revolutions = distance traveled / distance traveled by one revolution
100 feet = 1200 inches
= 1200 inches / 26π inches
≈ 45.91 full revolutions
Question 3
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
Question 4
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 5
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
Answers
The correct answer is: The IQR of 13 is the most accurate to use, since the data is skewed. (Option B).
The correct answer is: Together, Streetcar and Cable Car are the preferred transportation for 168 residents. (Option A).
The correct answer is: The IQR is the best measure of variability, and it equals 6.
How to Solve the Problem?1. Since the data is skewed, it is not appropriate to use the range as a measure of variability. The range is sensitive to extreme values and can be misleading in skewed data. The interquartile range (IQR) is a better measure of variability for skewed data since it is not affected by extreme values. Therefore, the charity should use the IQR of 13 as the measure of variability for this data.
2. From the circle graph, we can draw the following conclusion:
Together, Streetcar and Cable Car are the preferred transportation for 27% + 15% = 42% of the residents. 42% of 400 is 168 residents.
3. The line plot shows that the data is discrete and not continuous. Also, the data is not normally distributed and is skewed. Therefore, the range is not an appropriate measure of variability. The interquartile range (IQR) is a better measure of variability for skewed data. The IQR is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data.
From the plot, we can see that Q1 is 2 and Q3 is 8. Therefore, the IQR is 8 - 2 = 6.
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An electrician is running wire from the electric box on a house to a utility pole 85 feet away. The angle of elevation to the connection on the pole is 17°. How much wire does the electrician need? (Round your answer to two decimal places.)
Answers
The electrician needs approximately 296.26 feet of wire.
What is trigonometry?The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).
According to question:The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.
Using trigonometry, we can write:
sin(17°) = opposite / hypotenuse
where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:
hypotenuse = opposite / sin(17°)
To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:
tan(17°) = opposite / 85
Solving for the opposite side, we get:
opposite = 85 tan(17°)
Substituting this into the formula for the hypotenuse, we get:
hypotenuse = (85 tan(17°)) / sin(17°)
hypotenuse ≈ 296.26 feet
Therefore, the electrician needs approximately 296.26 feet of wire.
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In the EAI sampling problem, the population mean is $51,800 and the population standard deviation is $4,000. When the sample size is n = 30, there is a .5034 probability of obtaining a sample mean within +/- $500 of the population mean. A. What is the probability that the sample mean is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)?
B. What is the probability that the sample mean is within $500 of the population mean if a sample of size 120 is used (to 4 decimals)?
Answers
A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611
B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362
The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.
The formula for calculating the standard error of the mean is
SE = σ/√n
where SE is the standard error, σ is the population standard deviation, and n is the sample size.
For n = 30, SE = 4,000/√30 = 729.16
A. For a sample size of n = 60, SE = 4,000/√60 = 516.40
To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error.
For a range of +/- $500, the z-scores are
z = ($51,300 - $51,800) / 516.40 = -0.969
z = ($52,300 - $51,800) / 516.40 = 0.969
Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.
B. For a sample size of n = 120, SE = 4,000/√120 = 368.93
Following the same steps as above, the z-scores for a range of +/- $500 are
z = ($51,300 - $51,800) / 368.93 = -1.364
z = ($52,300 - $51,800) / 368.93 = 1.364
Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.
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please help would be amazing
Answers
Answer:
(9,8)
Step-by-step explanation:
Solve the first equation
then solve the second equation with the substitute number from the first equation.