The value of (f-g)(2) is 16, provided that Megan has made no mistakes in the calculation.
Find the error in the given problem solved by Megan?The problem asks us to compute the value of (f - g)(2) where f(x) = 3x^2 - 2x + 4 and g(x) = x^2 - 5x + 2.
The notation (f - g)(2) means that we need to subtract g(x) from f(x) and then evaluate the result at x = 2. We can do this as follows:
(f - g)(x) = f(x) - g(x) = (3x^2 - 2x + 4) - (x^2 - 5x + 2) = 2x^2 + 3x + 2
Substituting x = 2, we get:
(f - g)(2) = 2(2)^2 + 3(2) + 2 = 16
Therefore, the value of (f - g)(2) is 16.
It's worth noting that the problem statement mentions "what did she do wrong?" without providing any context or information about what Megan did or didn't do. So, it's not possible to identify any error in Megan's solution based on the given information. However, based on the correct computation above, we can be sure that (f - g)(2) is indeed equal to 16.
In other words, it can be described as,
The error in Megan's solution is not clear from the given statement. However, it seems that she may have made an error while computing (f-g)(2).
To compute (f-g)(2), we need to subtract g(2) from f(2) as follows:
f(2) = 3(2)^2 - 2(2) + 4 = 12
g(2) = (2)^2 - 5(2) + 2 = -4
Therefore, (f-g)(2) = f(2) - g(2) = 12 - (-4) = 16. is the final conclusion.
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Put the numbers in order from least to greatest.
4.27, 2.704, 4.2, 2.74, 4.72
Answer: In order least to greatest, our answer would be-
2.704 , 2.74 , 4.2 , 4.27 , 4.72
.70 is less than .74. In the second set of numbers .2 is less than .27, while they are all less than .72, which gives us the number arrangement above.
I hope this helped & Good Luck!!!
Answer: The answer is 2.704, 2.74, 4.2, 4.27, 4.72
Step-by-step explanation:
The mean shoe size of the students in a math class is 7. 5. Most of the shoe sizes fall within 1 standard deviation, or between a size 6 and a size 9. What is the standard deviation of the shoe size data for the math class?.
The standard deviation of the shoe size data for the math class is 1.5. Standard deviation is a measure of how spread out the data is, and it is calculated by taking the square root of the variance.
Calculate the difference between each shoe size and the mean (7.5)
if the shoe sizes in the class are 6, 7, 8, 9, 10
The differences from the mean are (-1.5), (-0.5), 0.5, 1.5, 2.5
Square each difference
(-1.5)² = 2.25
(-0.5)² = 0.25
0.5² = 0.25
1.5² = 2.25
2.5² = 6.25
Add up all the squared differences
2.25 + 0.25 + 0.25 + 2.25 + 6.25 = 11.25
Divide the sum of squared differences by the number of shoe sizes (n):
11.25 / 5 = 2.25
Take the square root of the result to get the standard deviation
√(2.25) = 1.5
Therefore, the standard deviation of the shoe size data for the math class is 1.5.
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Maria invests $6,154 in a savings account with a fixed annual interest rate of 8% compounded weekly. What will the account balance be after 10 years? There are 52 weeks in a year. (Round our answer to the nearest cent)
Answer:
A = P(1 + r/n)^(n*t) is the formula
Where:
A = the account balance after t years
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time in years
P = $6,154
r = 0.08 (8% expressed as a decimal)
n = 52 (compounded weekly)
t = 10
A = 6154(1 + 0.08/52)^(52*10)
A ≈ $14,239.44
Therefore, the account balance after 10 years will be approximately $14,239.44.
Look at the map and choose the correct option with the country indicated on the map.
Map of Central and South America. The country south to Brazil and with the Atlantic Ocean to its east is highlighted.
El Salvador
Uruguay
Costa Rica
Venezuela
The description concerns Uruguay, option B, since it is the only country among the answer choices that is located in South America to the South of Brazil.
Which countries are in South America?South America is a continent located in the western hemisphere of the Earth. It is situated south of North America, east of the Pacific Ocean, and west of the Atlantic Ocean. The continent is home to 12 independent countries and 3 dependent territories, with a total population of approximately 422 million people.
The largest country in South America is Brazil, followed by Argentina, Peru, and Colombia. The continent is characterized by diverse topography, including the Andes mountain range, the Amazon rainforest, the Atacama Desert, and the Patagonian plains. The region is also known for its rich cultural heritage, including pre-Columbian civilizations such as the Incas and the Mayas, as well as colonial influences from Spain and Portugal. Today, South America is a rapidly developing region with a diverse economy, including agriculture, mining, and manufacturing industries.
Uruguay is also a part of South America. It is located South of Brazil and, as a matter of fact, during colonization, it was a part of Brazil. We can conclude option B is the right answer.
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The volume of a cone is 2560π cm^3 . The diameter of the circular base is 32 cm. What is the height of the cone?
The height of the cone is 30 cm
How to calculate the height of the cone?
The first step is to write out the parameters given in the question
Volume of the cone= 2560π cm³
Diameter of the circular base is 32 cm
radius= diameter/2
= 32/2
= 16
The formula for calculating the height of the cone is
Height= volume ÷ 1/3 πr²
height= 2560 πcm³ ÷ 1/3 πr²
height= 2560 ÷ 0.333(16²)
height= 2560 ÷ 0.333(256)
height= 2560÷ 85.248
height= 30
Hence the height of the cone is 30 cm
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Answer:
height = 9.54cm
Step-by-step explanation:
Volume of a cone = 2560cm³
Radius = diameter/ 2 = 32/2 = 16
height = ?
volume of a cone =
[tex]volume \: of \: a \: cone = \frac{1}{3} \pi {r}^{2} h \\ 2560 = \frac{1}{3} \times \frac{22}{7} \times 16 \times 16 \times h \\ 2560 = \frac{22}{21} \times 256 \times h \\ 2560 = \frac{5,632h}{21} \\ 21 \times 2560 = 21 \times \frac{5632h}{21} \\ 53,760 = 5632h \\ \frac{53760}{5632} = \frac{5632h}{5632} \\ 9.54cm = h[/tex]
height = 9.54cm
Use the formula SA = 2π
rh + 2π
r2
to find is the surface area of the cylindrical food storage container. Use 3. 14 for π. Round your answer to the nearest hundredth of a square inch
The surface area of the cylindrical food storage container given by the formula SA = 2πrh + 2πr² is 954. 56 inch².
The region is the space taken up by a flat, two-dimensional surface. Its unit of measurement is the square. A three-dimensional object's surface area is the area occupied by its outside surface. It is also measured in square units.
Surface area and volume are calculated for each geometric object in three dimensions. The surface area of an object refers to the space that it takes up.
As, we Know the Surface Area of Cylinder
= 2πr² + 2πrh
Radius of the base = 8 inches
Height of the cylinder = 11 inches.
Now, putting the values we get
= 2πr² + 2πrh
= 2 x 3.14 x 8 x 8 + 2 x 3.14 x 8 x 11
= 401.92 + 552.64
= 954. 56 inch²
Therefore, the surface area of the cylinder is 954. 56 inch².
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Complete question
Use the formula SA = 2πrh + 2πr2 to find is the surface area of the cylindrical food storage container. Use 3. 14 for π. Round your answer to the nearest hundredth of a square inch
Please Help!
For Ln=1n∑ni=1i−1n , given Ln as indicated, express their limits as n→[infinity] as definite integrals, identifying the correct intervals
The limit of Ln as n approaches infinity is -1/2, and it can be expressed as the definite integral ∫0¹ (x - 1) dx over the interval [0, 1].
To express the limit of Ln as n approaches infinity as a definite integral, we can use the definition of the definite integral as the limit of a Riemann sum. We can divide the interval [0, 1] into n subintervals of equal width Δx = 1/n, and evaluate Ln as the limit of the Riemann sum:
Ln = 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]
where f(x) = x - 1 is the function being integrated.
Taking the limit as n approaches infinity, we have:
lim(n→∞) Ln = lim(n→∞) 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]
= ∫0¹ (x - 1) dx
where we have used the fact that the limit of the Riemann sum is equal to the definite integral of the function being integrated.
Therefore, the limit of Ln as n approaches infinity is equal to the definite integral of (x - 1) over the interval [0, 1].
So,
lim(n→∞) Ln = ∫0¹ (x - 1) dx = [x¹ - x] from 0 to 1
= [1/2 - 1] - [0 - 0]
= -1/2
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The South African mathematician John Kerrich, while a prisoner of war during World War II, tossed a coin10,000 times and obtained 5067 heads. (2pts)a) Is this significant evidence at the 5% level that the probability that Kerrich’scoin comes up heads is not 0. 5?Remember to specifythe null and alternative hypotheses, the test statistic, and the P-value. B) Give a 95% confidence interval to see what probabilities of heads are roughlyconsistent with Kerrich’s result
a) We can conclude that there is significant evidence that the probability of heads is not 0.5.
b) A 95% confidence interval for the true probability of heads is (0.4872, 0.5262).
a) To test whether the probability of heads is significantly different from 0.5, we can use a two-tailed z-test with a significance level of 0.05. The null hypothesis (H₀) is that the probability of heads is 0.5, while the alternative hypothesis (Hₐ) is that it is not 0.5.
The test statistic is given by:
z = (x - np) / √(np(1-p))
where x is the number of heads observed (5067), n is the total number of coin tosses (10,000), and p is the hypothesized probability of heads under the null hypothesis (0.5).
Plugging in the values, we get:
z = (5067 - 5000) / √(10,000 * 0.5 * 0.5) = 2.20
The P-value for this test is the probability of getting a z-score greater than 2.20 or less than -2.20, which is approximately 0.0287. Since the P-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is significant evidence that the probability of heads is not 0.5.
b) To find a 95% confidence interval for the true probability of heads, we can use the formula:
p ± z*√(p(1-p)/n)
where p is the sample proportion (5067/10000), n is the sample size (10,000), and z is the critical value from the standard normal distribution corresponding to a 95% confidence level (1.96).
Plugging in the values, we get:
p ± 1.96*√(p(1-p)/n) = 0.5067 ± 0.0195
So a 95% confidence interval for the true probability of heads is (0.4872, 0.5262). This means that we can be 95% confident that the true probability of heads falls within this interval based on the observed sample proportion.
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1. Does the graph below represent a function? Explain how you know.
Q1
A. Yes; the graph is linear.
B. No; the graph does not pass the vertical line test.
C. Yes; the graph passes the vertical line test.
D. No; the graph intersects the x and y axis.
p.s i might fail and retake 7th grade
C. Yes; the graph passes the vertical line test.
How does the graph below represent a function?The correct answer is C. Yes; the graph passes the vertical line test.
To determine whether a graph represents a function, we apply the vertical line test. The vertical line test states that for a graph to represent a function, no vertical line should intersect the graph in more than one point.
In this case, the graph passes the vertical line test if each vertical line crosses the graph at most once. If this condition is satisfied, then each x-value corresponds to a unique y-value, indicating that the graph represents a function.
Since the question states that the graph passes the vertical line test, we can conclude that it represents a function.
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Jan and Jackie check out the same number of library books. Jan turns in 4 books after 3 weeks. Jackie returns 2 books that week and 4 books later. Write algebraic expressions to represent the books Jan and Jackie have left
The algebraic expressions representing the books Jan and Jackie have left are J - 4 and J - 2 - 4, respectively, where J is the initial number of books checked out by both.
Let's use "J" to represent the number of books Jan and Jackie checked out from the library. After 3 weeks, Jan turned in 4 books, so she has J - 4 books left.
Jackie returned 2 books after the first week, so she has J - 2 books left. When she returned 4 more books later, she had J - 2 - 4 = J - 6 books left. Therefore, the algebraic expressions for the number of books Jan and Jackie have left are
Jan: J - 4
Jackie: J - 6
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Loudness of sound. The loudness L of a sound of intensity I is defined as 1 L = 10 log 1/1o' where lo is the minimum intensity detectable by the human ear and L is the loudness measured in decibels
Yes, the loudness L of a sound of intensity I is defined as:
L = 10 log(I/Io)
where Lo is the minimum intensity detectable by the human ear (also known as the threshold of hearing) and L is the loudness measured in decibels (dB).
In this equation, the intensity I is typically measured in watts per square meter (W/m^2), and Io is equal to 1 x 10^-12 W/m^2.
The logarithmic scale used in this equation means that each increase of 10 decibels represents a tenfold increase in sound intensity. For example, a sound that is 50 dB louder than another sound has an intensity that is 10 times greater.
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Triangle Z Y X is shown with its exterior angles. Point Z extends to point L, point X extends to point N, and point Y extends to point M.
Analyze the diagram to complete the statements.
The m∠MXN is
the m∠YZX.
The m∠LZX is
the m∠ZYX + m∠YXZ.
The m∠MYL is
180° − m∠ZYX.
The completed statements, obtained from the relationship between the exterior angles of a triangle and supplementary angles are;
The m∠MXN is greater than m∠YZX
The m∠LZX is equal to m∠ZYX + m∠YXZ
The m∠MYL is equal to 180° - m∠ZYX
What are supplementary angles?Supplementary angles are angles that form a linear pair and when added together are equivalent to 180°
The exterior angle of a triangle theorem indicates, that we get;
m∠MXN = m∠YZX + m∠ZYX
Therefore; m∠MXN > m∠YZXm∠LZX = m∠ZYX + m∠YXZ∠MYL is a supplementary angle to the angle ∠ZYX
Therefore; m∠MYL + m∠ZYX = 180°
m∠MYL = 180° - m∠ZYXThe completed statements are therefore;
m∠MXN is greater than m∠YZX
m∠LZX equal to m∠ZYX + m∠YXZ
m∠MYL equal to 180° - m∠ZYX
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The population of pine trees in a 200-acre area has decreased by roughly the same percentage over the past 4 years. The table below shows data values for the population of these trees, p (t) , after t years.
The function that would best represent this is given as p(t) = 1150 (0.8769)^t
What is an exponential function?An exponential function is a mathematical function of the form f(x) = a^x, where "a" is a constant called the base and "x" is the variable. The base is usually a positive number greater than 1, but it can also be a fraction between 0 and 1, or even a negative number.
Exponential functions are characterized by the fact that the variable "x" appears as an exponent. As a result, these functions grow or decay very rapidly as "x" increases or decreases, depending on the value of the base "a".
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An artist is sculpting a spherical statue that has a diameter of 10 inches. if the clay to sculpt the statue weighs approximately 1.1 oz/in3 what is the weight of the statue to the nearest ounce?
The weight of the statue to the nearest ounce is 576 ounces.
The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter is given as 10 inches, the radius is half of that, or 5 inches.
Using the formula, we can find the volume of the sphere:
V = (4/3)πr^3
V = (4/3)π(5^3)
V = (4/3)π(125)
V = 523.6 cubic inches (rounded to one decimal place)
Since we know the weight of the clay per cubic inch, we can find the weight of the statue by multiplying the volume by the weight per cubic inch:
Weight = Volume × Weight per cubic inch
Weight = 523.6 in^3 × 1.1 oz/in^3
Weight = 575.96 oz (rounded to two decimal places)
Therefore, the weight of the statue is approximately 576 ounces or 36 pounds (rounded to the nearest pound).
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which of the following factors help to determine sample size? a. population size b. the desired confidence level c. margin of error d. both b and c
The factors that help to determine sample size are the desired confidence level and the margin of error. Therefore, the correct option is D) both b and c.
The desired confidence level and margin of error are two important factors that help to determine the sample size. The confidence level represents the level of certainty that the sample mean is close to the true population mean, while the margin of error is the range of error that is acceptable in the estimation of the population mean.
Both of these factors are interdependent, and an increase in either of them would require a larger sample size to achieve a certain level of accuracy. Therefore, carefully considering these factors and determining an appropriate sample size is essential for obtaining valid and reliable results.
The population size can also have an impact on the sample size calculation, but it is not a direct factor. So, the correct answer is D).
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One of the flights was 350 miles and its residual was -
105. 0. What was the fare for this flight?
Based on data taken from airline fares and distances
flown, it is determined that the equation of the least-
squares regression line is ý = 102. 50 +0. 65x, where
ý is the predicted fare and x is the distance, in miles.
O $102. 50
O $435. 00
O $225. 00
O $330. 00
The fare for this flight would be: $225.
How we get the fare for the flight?To determine the fare for the flight that was 350 miles with a residual of -105, we need to use the least-squares regression equation:
ý = 102.50 + 0.65x
where ý is the predicted fare and x is the distance in miles.
We know that the distance for this flight is 350 miles, so we can substitute x = 350 into the equation:
ý = 102.50 + 0.65(350)
ý = 102.50 + 227.50
ý = 330
Therefore, the predicted fare for this flight is $330.
The residual of -105 means that the actual fare for this flight was $105 less than the predicted fare based on the regression line. Therefore, the actual fare for this flight would be:
$330 - $105 = $225
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evaluate functions from a graph
PLEASE HELP
The value of the function at x = 7, f(7) on the graph is 2, therefore;
f(7) = 2
What is a function?A function is a rule or defines that maps an input munto an output.
The evaluation of the function using the graph of the function can be performed by drawing a vertical line at the point of the corresponding input or x-value, and reading the point of intersection of the vertical line and the point on the graph, as follows;
f(7) = The value of the function at x = 7
The vertical line at x = 7, intersects the graph at the point f(7) = 2
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What is the exact solution to the system of equations?
Answer:
Step-by-step explanation:
the point at which the lines representing the linear equations intersect
Which inequalities are true when m= -4
The inequailty y < m + 4 would be true when m = -4 and all values of y are less than 0
Which inequalities are true when m= -4From the question, we have the following parameters that can be used in our computation:
The statement that m = -4
The above value implies that we substitute -4 for m in an inequality and solve for the other variable (say y)
Take for instance, we have
y < m + 4
Substitute the known values in the above equation, so, we have the following representation
y < -4 + 4
Evaluate
y < 0
This means that the inequailty y < m + 4 would be true when m = -4 and all values of y are less than 0
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there are at present 40 solar energy construction firms in the state of indiana. an average of 20 solar energy construction firms open each year in the state. the average firm stays in business for 10 years. if present trends continue, what is the expected number of solar energy construction firms that will be found in indiana? if the time between the entries of firms into the industry is exponentially distributed, what is the probability that (in the steady state) there will be more than 300 solar energy firms in business? (hint: for large l, the poisson distribution can be approximated by a normal distribution.)
a) The expected number of solar energy construction firms that will be in indiana
is equal to 200 firms.
b) In case of exponential Probability distribution that there will be more than 300 solar energy firms in business is equals to the 0.305 × 10⁻⁵ .
The Poisson process is used when events are independent of each other and the average rate is constant. Two events cannot occur simultaneously. We have a data of about the number of solar energy construction firms in the state of indiana. Number of solar energy construction firms in the state at present
= 40
Average of solar energy construction firms open each year in the state = 20
For number of year average firm stays in business = 10 years.
We have to determine the expected number of solar energy construction firms that will be found in indiana. Let X be excepted value,then (X∼Poi(λt)X∼ Poi(200),
a) If the present trends continue, then the expected number of energy construction firms that will be found in Indiana will be
Expected Number of firms = 20× 10
= 200 firms
(b) If the time between the entries of firms into the industry is exponentially distributed. Then the probability that there will be more than 300 solar energy firms in business, P ( x> 300) = e⁻ᵐˣ , where m = 1/20 and x
= 300
=> P( x> 300) = 1/exp.( 300/20)
= e⁻¹⁵
= 0.0000003059 = 0.305 × 10⁻⁵
Hence, required probability value is 0.305 × 10⁻⁵.
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Jasmine deposited $400 in a bank that paid her 2. 15% interest every year. Assuming no deposits or withdrawals were made. How much money will she have in 5 years? round to nearest.
Help
Answer:
$444.89
Step-by-step explanation:
PV = $400
i = 2.15%
n = 5
Compound formula:
FV = PV (1 + i)^n
FV = 400 (1 +2.15%)^5
FV = $444.89 (round to nearest cents)
A textbook company will ship a box of textbooks to college students. The weight of the box in pounds can be determined by the function w(x) = 7. 5x + 2, where x is the number of textbooks in the box. The company requires a student to order at least 2 books but not more than 6 books. What is the range of the function for this situation? *
A. 2 ≤ x ≤ 6
B. 17 ≤ y ≤ 47
C. {17, 24. 5, 32, 39. 5, 47}
D. {2, 3, 4, 5, 6}
The range of the function for this situation is {17, 24.5, 32, 39.5, 47}, The correct option is C.
To find the range of the function for this situation, we need to evaluate the function for x = 2, 3, 4, 5, and 6, since these are the only valid inputs based on the problem statement.
w(2) = 7.5(2) + 2 = 17
w(3) = 7.5(3) + 2 = 24.5
w(4) = 7.5(4) + 2 = 32
w(5) = 7.5(5) + 2 = 39.5
w(6) = 7.5(6) + 2 = 47
Therefore, the range of the function for this situation is {17, 24.5, 32, 39.5, 47}, which is option C.
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Sheri wrote the following entries in her checkbook:-$13.52,-$15.88,
+$500,-$451.57. +$275, $244.58. + $2,516. what is the total of her
deposits? what is the average amount of her checks? what overall
change in her balance would occur as a result of these 7
transactions?
Total deposits of Sheri are $3,535.58 and Average check amount $160.32 and Change in balance is $3,055.61.
As the change in balance is positive, we can say that her overall balance increased as a result of these transactions.
To find the total of Sheri's deposits, we add up all the positive values in her checkbook:
Total deposits = $500 + $275 + $244.58 + $2,516 = $3,535.58
To find the average amount of her checks, we first need to find the total value of all her checks:
Total checks = -$13.52 - $15.88 - $451.57 = -$480.97
Then we can divide this total by the number of checks to get the average amount:
Average check amount = -$480.97 ÷ 3 = -$160.32
Note that the negative sign indicates that these are payments she made, rather than deposits.
To find the overall change in her balance, we add up all the entries in her checkbook:
Change in balance = -$13.52 - $15.88 + $500 - $451.57 + $275 + $244.58 + $2,516 = $3,055.61
Since this value is positive, we can say that her overall balance increased as a result of these transactions.
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On the average the time spent by college students every week on computer gaming is 15 hours with a standard deviation 3. a random sample of 350 students were taken. find the best point estimated of the population mean and 95% confidence interval for the population mean
The best point estimate is 15 hours. The 95% confidence interval for the population mean is (14.71, 15.29).
The best point estimate of the population mean is the sample mean, which is 15 hours since it was stated in the problem that the average time spent by college students on computer gaming is 15 hours.
To calculate the 95% confidence interval for the population mean, we use the formula:
CI = [tex]\bar{X}[/tex] ± z*(σ/√n)
where [tex]\bar{X}[/tex] is the sample mean, z is the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96), σ is the population standard deviation (given as 3), and n is the sample size (given as 350).
Plugging in the values, we get:
CI = 15 ± 1.96*(3/√350)
Simplifying, we get:
CI = 15 ± 0.29
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The main span of a suspension bridge is the roadway between the bridges towers. The main span of the Walt Whitman Bridge in Philadelphia is 2000 feet long. This is 600 feet longer than two-fifths of the length of the main span of the George Washington Bridge in New York City. Write an equation to represent the given problem and solve it to find the length of the main span of the George Washington Bridge
The length of the main span of the George Washington Bridge is 3500 feet.
Let x be the length of the main span of the George Washington Bridge.
We know that the main span of the Walt Whitman Bridge is 600 feet longer than two-fifths of the length of the main span of the George Washington Bridge, so we can write the equation:
2000 = (2/5)x + 600
To solve for x, we can start by isolating the term with x on one side of the equation:
(2/5)x = 2000 - 600
(2/5)x = 1400
Then, we can solve for x by multiplying both sides by the reciprocal of (2/5):
x = 1400 / (2/5)
x = 3500
Therefore, the length of the main span of the George Washington Bridge is 3500 feet.
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Help pls..
How many solutions does the system of linear equations represented in the graph have?
Coordinate plane with one line that passes through the points 0 comma negative 2 and 2 comma negative 1.
One solution at (−2, 0)
One solution at (0, −2)
Infinitely many solutions
No solution
The number of solutions which this system of linear equations represented in the graph have is: C. Infinitely many solutions.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-1 + 2)/(2 - 0)
Slope (m) = 1/2
At data point (0, -2) and a slope of 1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 2 = 1/2(x - 0)
y = 1/2(x) - 2
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WEATHER Suppose during springtime it rains about 40% of the time when school is dismissed for the day, Describe a model that could be used to simulate whether it will be raining when school is dismissed on a particular day during springtime.
One way to model this situation is by using a probability distribution, such as the binomial distribution. The binomial distribution models the probability of a certain number of successes (in this case, rain) in a fixed number of trials (in this case, school days during springtime).
Let's say we want to simulate whether it will be raining when school is dismissed on a particular day during springtime. We can define a success as rain and a failure as no rain. Then, the probability of success (rain) is 0.4, and the probability of failure (no rain) is 0.6.
To simulate whether it will be raining on a particular day, we can use a random number generator to generate a value between 0 and 1. If the value is less than or equal to 0.4, we can consider it a success (rain) and if it's greater than 0.4, we can consider it a failure (no rain).
We can repeat this process for a large number of trials (school days during springtime) to simulate the probability of rain over a given period of time. By keeping track of the number of successes (rainy days) and failures (non-rainy days), we can estimate the probability of rain during springtime when school is dismissed.
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Does anyone have answers 3 and 4 for 4. 4. 3 Practice: Modeling: Solids?
Extremely lost and help with be appreciated :)
Answer:
search them up it should give you the answers
Step-by-step explanation:
tan(x)>(3^1/2)+1 Range for x( 0
Answer:
Step-by-step explanation:
1 A square is a rectangle.
always
sometimes
never
2 The diagonals of a rhombus are perpendicular.
always3 The diagonals of a rectangle are equal.
always4 The diagonals of a trapezoid are equal.
alwaysThe statements that are always true for geometric shapes are:
1) Always
2) Always
3) Sometimes
4) Never
Which statements are always true for geometric shapes?1) A square is a type of rectangle in which all four sides are equal. Therefore, all of the properties that apply to rectangles (such as having four right angles and opposite sides that are parallel) also apply to squares, making the statement "A square is a rectangle" always true.
2) The diagonals of a rhombus are always perpendicular to each other. This is because a rhombus has opposite sides that are parallel, and the diagonals bisect each other at a right angle.
3) The diagonals of a rectangle are sometimes equal. This is true only if the rectangle is a square (where all four sides are equal) or if the rectangle is a "golden rectangle" (where the ratio of the longer side to the shorter side is equal to the golden ratio).
4) The diagonals of a trapezoid are never equal unless the trapezoid happens to be an isosceles trapezoid (where the legs are equal in length). In general, the diagonals of a trapezoid will have different lengths, and there is no special relationship between them.
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