If the pyramids below are similar, what is the
ratio of their surface area?
21 in
14 in
A. 3:2
B. 6:4
C. 9:4
D. 27:8
Answers
The required ratio of the surface area of the given pyramids is (A) 3:2.
What are ratios?A ratio can be used to show a relationship or to compare two numbers of the same type.
To compare things of the same type, ratios are utilized.
We might use a ratio, for example, to compare the proportion of boys to girls in your class.
If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.
A proportion is an equation that equalizes two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)
So, the given surface area is:
- 21 in
- 14 in
Now, calculate the ratio as:
= 21/14
= 3/2
= 3:2
Therefore, the required ratio of the surface area of the given pyramids is (A) 3:2.
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Related Questions
A certain population is strongly skewed to the left. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be closer to normal.
II. The sampling model of the sample means will be closer to normal.
III. The variability of the sample means will be greater.
A. I and II only
B. I only
C. III only
D. II and III only
E. II only
Answers
A. I and II only true if we use a large sample rather than a small one
sampling model
Define sampling modelA sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.
When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.
Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.
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place the publication of three major books on race in chronological order, from earliest to most recent. Start by clicking the first item in the sequence or dragging it here Drag the items below into the box above in the correct order, starting with the first item in the sequence. Tomas Almaguer wrote about historical race relations in California in Racial Fault Lines Michael Omi and Howard Winant wrote about the social construction of race in Racial Formation in the United States. Ta-Nehisi Coates wrote about race and the African American experience in Between the World and Me.
Answers
The publication of three major books on race in chronological order, from earliest to most recent is:
- Micheal Omi and Howard Winant wrote about the social construction of race in Racial Formation in the United States.- Tomas Almaguer wrote about historical race relations in California in Racial Fault Lines.- Ta- Nehisi Coates wrote about race and the African American experience in Between the World and Me.Chronological order is the listing, description, or discussion of when events occurred in relation to time. Essentially, it is similar to looking at a chronology to see what happened initially and what happened after that. For example, if teachers asked their pupils to recount their first day of school, they would expect students to begin by waking up that morning and getting ready. If pupils begin from the time they enter the school, significant information is lost and the listener may become confused due to a lack of knowledge.
Helping pupils grasp what chronological order is and how to use the skill correctly can benefit students ranging from kindergarten to collegiate levels. The concept may appear simple, yet failing to master chronological sequence can cause kids to struggle academically and lack a solid educational foundation.
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I think it’s to do with Pythagoras theorm
Answers
8.6cm is the hypotenuse and 8.6/2 is the length of base.
The Pythagorean theorem: a^2+b^2=c^2
So that means 8.6^2-4.3^2=height
= 73.96 - 18.49 = 55.47
So the square root of 55.47 is the height of the triangle.
The area of a triangle is h * b/2
So the base is 8.6 and the height is the square root of 55.47. 8.6/2=4.3
So 4.3 times the square root of 55.47 is the area.
Mrs Smith walks a half a mile a day after work. She works five days a week. How many yards will she have walked for the week by Friday morning?
Answers
The distance Mrs. Smith covers is 3520 yards during the duration of the week by Friday morning.
One week has seven days in total.
Mrs. Smith walks half a mile each day after work, she walks a total of
0.5 miles/ day × 7 days/ week = 3.5 miles/ week
Now, if we calculate the distance on Friday morning, she must have walked four times till Friday morning since she has to walk after her work.
Therefore,
0.5 miles/ day × 4 days = 2 miles
To convert miles to yards, we can use the fact that there are 1760 yards in one mile:
2 miles/week × 1760 yards/mile = 3520 yards/week
Therefore, by Friday morning, Mrs. Smith will have walked 3520 yards.
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Find an expression that is equivalent to (a - b) ^ 3
Answers
An expression equivalent to (a - b)³ is a³ - 3a²b + 3ab² - b³.
What other expressions are the same as 2 5?The fractions 4/10, 6/15, 8/20, etc. are identical to 2/5. In the reduced form, equivalent fractions have the same value. Explanation: When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number.
One way to expand (a - b)³ is to use the binomial formula:
(a - b)³ = C(3,0) * a³ * (-b)^0 + C(3,1) * a² * (-b) + C(3,2) * a * (-b)² + C(3,3) * a * (-b)³
where C(n,k) denotes the number of ways there are to select k objects from a set of n objects, and "n choose k" is the binomial coefficient.
Simplifying the above expression, we get:
(a-b)³ = a³-3a²b+3ab²-b³.
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the nutty professor sells cashews for $7.70 per pound and brazil nuts for $4.80 per pound. how much of each type should be used to make a 27 pound mixture that sells for $6.41 per pound?
Answers
The amount that each type would be 11.87 lbs of cashews and 15.13 lbs of brazil nuts
1. First, find the total cost of 27 lbs of the mixture: 27 lbs x $6.41/lb = $171.07.
2. Next, find the cost of cashews and brazil nuts in the mixture. Cashews cost $7.70/lb and brazil nuts cost $4.80/lb.
3. Subtract the cost of the brazil nuts from the total cost of the mixture: $171.07 - (27 lbs x $4.80/lb) = $105.27.
4. Divide the cost of the cashews ($105.27) by the cost of one pound of cashews ($7.70): $105.27/$7.70 = 13.66 lbs.
5. Subtract the number of pounds of cashews (13.66) from the total pounds of the mixture (27) to find the number of pounds of brazil nuts: 27 - 13.66 = 15.13 lbs.
6. Therefore, the mixture should contain 11.87 lbs of cashews and 15.13 lbs of brazil nuts.
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Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 9x3, [1, 2] Yes, the Mean Value Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because fis not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = - w f(b) – f(a) 2. (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot Ent b - a be applied, enter NA.) C=
Answers
Answer: Yes, the Mean Value Theorem can be applied to f(x) = 9x^3 on the closed interval [1, 2].
To find all values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a), we first find the derivative of f(x):
f'(x) = 27x^2
Then, we can use the Mean Value Theorem to find a value c in the open interval (1, 2) such that:
f'(c) = (f(2) - f(1))/(2 - 1)
27c^2 = 9(2^3 - 1^3)
27c^2 = 45
c^2 = 5/3
c = +/- sqrt(5/3)
Therefore, the values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a) are:
c = sqrt(5/3), -sqrt(5/3)
Note that these values are not in the closed interval [1, 2], as they are not between 1 and 2, but they are in the open interval (1, 2).
Step-by-step explanation:
The radius of a circle is 8 meters. What is the circle's circumference?
Use 3.14 for л.
Answers
Answer:
circumference=50.24
Step-by-step explanation:
c=2x3.14xr
c=2x3.14x(8)
c=50.24
Elena and Jada were racing on their bikes. Elena started 15 meters ahead of Jada. Elena biked at a rate of 20 meters per second. Jada biked at a rate of 22 meters per second. Let x represent time in seconds and y represent distance in meters. After how many seconds will Jada pass Elena?
Answers
Jada overtakes Elena after 7.5 seconds.
The set of equations that best captures the scenario is =y=15+20x.
Let's establish a coordinate system with Elena's starting point as the origin. Elena's separation from the origin at time x is given by: y=15+20x
y1 = 15 + 20x
Jada's distance from the origin at time x is determined similarly by:
y2 = 22x
Finding the moment x at which Jada overtakes Elena and their distances from the origin are equal is our goal.
y1 = y2
With the formulas for y1 and y2 substituted, we obtain:
15 + 20x = 22x
When we simplify this equation, we obtain:
2x = 15
x = 7.5
Jada therefore overtakes Elena after 7.5 seconds.
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Ryan buys some jumpers to sell on a stall. He spends £190 buying 80 jumpers. He sells 50% of the jumpers for £12 each. He then puts the rest of the jumpers on a Buy one get one half price offer. He manages to sell half the remaining jumpers using this offer. How much profit does Ryan make?
Answers
Ryan makes a profit of £240. the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
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Im a trapezoid measuring 8cm, 10cm, 16 cm and 10cm on its sides. What is my Perimeter? 1-5 po lhat
Answers
Answer:
See Below.
Step-by-step explanation:
To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.
In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.
Perimeter = 8 cm + 10 cm + 16 cm + 10 cm
Perimeter = 44 cm
Therefore, the perimeter of the trapezoid is 44 cm.
two people standing at different locations are looking at a tall building. person a angle of elevation to the building is 35 degrees. person b angle of elevation is 77 degrees. the building is 8 miles away from person b. how far away is person a from the building?
Answers
Therefore, Person A is approximately 95.17 miles away from the building.
To find out how far person A is from the building, we'll need to use trigonometry. The diagram below shows the situation.
Given that Person A's angle of elevation to the building is 35 degrees, we'll let angle BAC be 35 degrees.
Similarly, since Person B's angle of elevation is 77 degrees, we'll let angle ABC be 77 degrees. We'll also let AB be x, the distance from Person A to the building, and BC be 8 miles, the distance from Person B to the building.
First, we'll use the tangent function to find the height of the building. In triangle ABC, tan(77) = height/8. Solving for the height, we get:
height = 8tan(77) ≈ 61.23 miles.
Next, we'll use the tangent function again to find x. In triangle ABC, tan(35) = height/x + 8. Solving for x, we get:
x = (height)/(tan(35)) - 8
≈ 103.17 miles - 8
≈ 95.17 miles.
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What is result of following operation(4623. 56)10+ (110011. 11)2whare (110011. 11(2 mean that 110011. 11as a number express in base 2
Answers
The given numbers are in decimal and binary system and the final result of the given operation is [tex](4675.31)_{10}[/tex].
A binary integer (base-2) is converted to an equivalent decimal number using the binary to decimal conversion formula. (base-10). In mathematics, integers are expressed using a number system. It is a method to display numerical data. The four various numeral systems are as follows:
System of Binary Numbers (Base-2)
system of octal numbers (Base-8)
System of Decimal Numbers (Base-10)
System of Hexadecimal Numbers (Base-16).
We are the two numbers:-
[tex](4623.56)_{10} , (110011.11)_{2}[/tex]
these are in decimal and binary system respectively.
now, we will express them in same system ( here we choose decimal system).
[tex](110011.11)_{2} = (2^{5} + 2^{4} + 0 + 0 + 2^{1} + 2^{0} + 2^{-1} + 2^{-2} )_{10} \\= (2^{5}+2^{4}+0*2^{4}+0*2^{3}+2^{1}+2^{0}+2^{-1}+2^{-2})_{10} \\= (32+16+2+1+0.5+0.25)_{10} \\= (51.75)_{10}[/tex]
Now, addition is done below:-
4623.56+51.75= 4675.31.
hence, the final result of the given operation= [tex](4675.31)_{10}[/tex]
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Jaxon is flying a kite, holding his hands a distance of 3.25 feet above the ground and
letting all the kite's string play out. He measures the angle of elevation from his hand
to the kite to be 24°. If the string from the kite to his hand is 105 feet long, how many
feet is the kite above the ground? Round your answer to the nearest tenth of a foot if
necessary.
Answers
Answer: 46.0 ft
Step-by-step explanation:
[tex]\text{sin} \ 24^o=\dfrac{x}{105}[/tex]
[tex]x=105 \ \text{sin 24}^o[/tex]
So, the distance above the ground is [tex]\text{105 sin} \ 24^o+3.25\thickapprox \boxed{46.0 \ \text{ft}}[/tex]
Prove that sum of measure of three angles of triangle is 180
Answers
Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem
To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.
A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:
Sum of measures of interior angles of triangle = (n-2) × 180 degrees
= (3-2) × 180 degrees [since we are dealing with a triangle]
= 1 × 180 degrees
= 180 degrees
Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.
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The equation y = 8x represents the
relationship between the amount of
time Shanay takes to weave thread
into fabric and the number of rows.
How long will it take Shanay to weave
72 rows of fabric at this constant rate?
Answers
X=9
It will take 9
What is the value of x in the equation 1/4(4 + x) = 4/3
Answers
The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.
Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:
1/4(4 + x) = 4/3
4 * 1/4(4 + x) = 4 * 4/3
Simplifying:
4 + x = 16/3
Subtract 4 from both sides of the equation:
4 + x - 4 = 16/3 - 4
Simplifying:
x = 16/3 - 12/3
x = 4/3
A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.
Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.
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Use the table you created to play the "Two Spinner
Game" below.
For this game, we say the spinners "match" if they
land on the same color (e.g., both red, or both blue).
How do you win? Once again, that's your choice:
(1) If the spinners MATCH, you win.
(2) If the spinners DO NOT MATCH, you win.
Which game would you be more likely to win?
Answers
Therefore, you would be more likely to win the game by choosing option (2) - winning if the spinners do not match.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of mathematics, science, engineering, finance, and other fields to model and analyze uncertain situations. It helps to make predictions, to assess risks and opportunities, and to make informed decisions based on available information. Probability theory provides a foundation for statistical inference, which is used to draw conclusions from data and to test hypotheses about the underlying population.
Here,
In the "Two Spinner Game", there are two possible outcomes for each spin - a match or a non-match. The probability of the spinners matching is the probability of both spinners landing on the same color. Let's say that there are 3 red sections, 3 blue sections, and 2 green sections on each spinner.
The probability of the first spinner landing on red is 3/8, and the probability of the second spinner landing on red is also 3/8. Therefore, the probability of both spinners landing on red (a match) is (3/8) x (3/8) = 9/64.
Similarly, the probability of both spinners landing on blue (another match) is (3/8) x (3/8) = 9/64, and the probability of both spinners landing on green (a match) is (2/8) x (2/8) = 4/64.
The probability of the spinners not matching is the probability of them landing on different colors. There are 3 different pairs of colors that are not a match: red-blue, red-green, and blue-green. The probability of each of these pairs is (3/8) x (3/8) = 9/64.
So, there are 6 possible outcomes, and the probability of winning by a match is 9/64 + 9/64 + 4/64 = 22/64, or about 34.4%. The probability of winning by a non-match is 3 x 9/64 = 27/64, or about 42.2%.
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4. Assume that 4 years from now you will need $1,000. Your bank compounds interest
at an 8% annual rate. A. How much must you deposit 1 year from now to have a balance of $1,000 at
Year 4?
b. If you want to make equal payments at the end of Years 1 through 4 to
accumulate the $1,000, how large must each of the 4 payments be?
c. If your father were to offer either to make the payments calculated in part b
($221. 92) or to give you a lump sum of $750 one year from now, which would
you choose?
d. If you will have only $750 at the end of Year 1, what interest rate, compounded
annually, would you have to earn to have the necessary $1,000 at Year 4?
e. Suppose you can deposit only $186. 29 each at the end of Years 1 through 4, but
you still need $1,000 at the end of Year 4. What interest rate, with annual
Answers
A. deposit $735.03 one year from now. B. $210.48 for each of the four years. C. choose the lump sum of $750 from your father. D. Interest rate of 7.4% compounded annually. E. Interest rate of 12%.
a. To have a balance of $1,000 four years from now, you need to calculate the present value of this amount. Using the compound interest formula, we can calculate that you need to deposit $735.03 one year from now to have a balance of $1,000 four years from now.
b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, you can use the annuity formula to calculate the required payments. The formula gives us a payment of $210.48 for each of the four years.
c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 one year from now, you can compare the present value of both options. The present value of the four payments of $210.48 each, using an 8% annual interest rate, is $682.96. Therefore, you would choose the lump sum of $750 from your father.
d. If you have only $750 one year from now, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 7.4% compounded annually.
e. If you can only deposit $186.29 each at Years 1 through 4, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 12% compounded annually.
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Complete question:
Assume that 4 years from now you will need $1,000. Your bank compounds interest at an 8% annual rate.
a. How much must you deposit 1 year from now to have a balance of $1,000 4 years from now?
b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, how much each of the 4 payments be?
c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 1 year from now, which would you choose?
d. If you have only $750 1 year from now, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 4 years from now? 7.4%
e. Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4. What interest rate, with annual compounding, must you seek out to achieve your goal?
Here is a scale drawing of a garden. Tom wants to plant a tree in the garden according to the following rules: It must be 4 m from A and 2 m from CD. Place a cross where Tom can plant the tree. D 2.5 cm A 4 cm C B 1 cm represents 2m
Answers
Answer:
the cross is the blue color
An urn contains eight green balls and six red balls. Four balls are randomly selected from the urn in succession, with replacement. That is, after each draw the selected ball is returned. What is the probability that all four balls drawn are red. Round your answer to three decimal places
Answers
The probability of drawing four red balls in succession, with replacement, is 0.04 or 4%.
Since we are replacing the ball after each draw, the probability of drawing a red ball remains the same for each draw. The probability of drawing a red ball on any given draw is:
P(Red) = Number of Red Balls / Total Number of Balls
P(Red) = 6 / (8 + 6)
P(Red) = 0.4286
So, the probability of drawing four red balls in a row is the product of the probability of drawing a red ball four times in a row:
P(4 Red Balls) = P(Red) * P(Red) * P(Red) * P(Red)
P(4 Red Balls) = 0.4286 * 0.4286 * 0.4286 * 0.4286
P(4 Red Balls) = 0.04 or 4%
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a
49⁰
Find the measure of a.
127⁰
72⁰
Answers
Answer:
112°
Step-by-step explanation:
Finding the unknown angle in a quadrilateral:
Sum of all angles of a quadrilateral = 360
a + 49 + 72 + 127 = 360
a + 248 = 360
a = 360 - 248
a = 112°
Write the percent as a decimal.
95%
Answers
Answer:
9.5 decimal
espero y te ayude
Martina made $60 for 5 hours of work. At the same rate, how many hours would she have to work to make $204 ?
Answers
Answer:
WELL 17
Step-by-step explanation:
60 DIVED BY 5 IS 12
SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS
There are 30 students in Mr. Hall class. 1/3 of the students are traveling somewhere this summer. Of those traveling, 1/5 are going out of the country. How many students are traveling out of the country?
Answers
The number of students traveling are 2 students out of the 30 who are traveling out of the country this summer. If 1/3 of the students are traveling somewhere this summer, then we can calculate the number of students who are traveling by multiplying the total number of students by 1/3:
Number of students traveling = 30 x 1/3 = 10
Now, we need to find out how many of these 10 students are traveling out of the country. We know that 1/5 of the students who are traveling are going out of the country, so we can find the number of students who are traveling out of the country by multiplying the total number of traveling students by 1/5:
Number of students traveling out of the country = 10 x 1/5 = 2
Therefore, there are 2 students out of the 30 who are traveling out of the country this summer.
It's important to note that fractions can be converted to decimals or percentages to make them easier to work with. For example, 1/3 can be written as 0.33 or 33%, and 1/5 can be written as 0.20 or 20%. This can be particularly useful when dealing with more complex problems or when working with larger numbers.
In summary, by using the information given, we can determine that out of the 30 students in Mr. Hall's class, 10 are traveling somewhere this summer, and out of those 10 students, 2 are going out of the country. This type of problem-solving helps build math skills that are applicable in real-world scenarios, such as budgeting and planning for travel.
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in august 2012, tropical storm isaac formed in the caribbean and was headed for the gulf of mexico. there was an initial probability of .69 that isaac would become a hurricane by the time it reached the gulf of mexico (national hurricane center website, august 21, 2012). a. what was the probability that isaac would not become a hurricane but remain a tropical storm when it reached the gulf of mexico (to 2 decimals)? b. two days later, the national hurricane center projected the path of isaac would pass directly over cuba before reaching the gulf of mexico. hurricanes that reach the gulf of mexico have a .08 probability of having passed over cuba. tropical storms that reach the gulf of mexico have a .20 probability of having passed over cuba. how did passing over cuba alter the probability that isaac would become a hurricane by the time it reached the gulf of mexico? use the above probabilities to answer this question. p(c|h) (to 2 decimals) p(c|t) (to 2 decimals) p(h|c) (to 4 decimals) c. what happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as cuba? select (to 2 decimals) to (to 4 decimals).\
Answers
By using Bayes' theorem in probability.
a) The probability that isaac would not become a hurricane but remain a tropical storm when it reached the gulf of mexico is 0.31.
b) P(H|c) = 0.4493
c) It can be observed that the likelihood of a tropical storm developing into a hurricane decreases slightly when it passes over Cuba. This can be inferred from the fact that the conditional probability of a hurricane forming given that the storm has passed over Cuba (P(H|c) = 0.4493) is lower than the initial probability of 0.69.
a) The probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is:
P(not hurricane) = 1 - P(hurricane) = 1 - 0.69 = 0.31
So the probability is 0.31 (to 2 decimals).
b) We need to use Bayes' theorem to calculate the probabilities:
P(c|H) = P(H|c) * P(c) / P(H)
P(c|T) = P(T|c) * P(c) / P(T)
where c denotes passing over Cuba, H denotes becoming a hurricane, and T denotes remaining a tropical storm.
From the problem, we have:
P(H) = 0.69
P(T) = 1 - P(H) = 0.31
P(c|H) = 0.08
P(c|T) = 0.20
To calculate P(c), we need to use the law of total probability:
P(c) = P(c|H) * P(H) + P(c|T) * P(T)
= 0.08 * 0.69 + 0.20 * 0.31
= 0.1228
Now we can calculate P(c|H) and P(c|T):
P(c|H) = 0.08 * 0.69 / 0.1228
= 0.4493 (to 2 decimals)
P(c|T) = 0.20 * 0.31 / 0.1228
= 0.5065 (to 2 decimals)
To calculate P(H|c), we use Bayes' theorem again:
P(H|c) = P(c|H) * P(H) / P(c)
= 0.08 * 0.69 / 0.1228
= 0.4493 (to 4 decimals)
c) Passing over a landmass such as Cuba can alter the probability of becoming a hurricane because it can either enhance or weaken the storm. In this case, we can see that the probability of becoming a hurricane is actually slightly lower when a tropical storm passes over Cuba, as P(H|c) = 0.4493 is lower than the initial probability of 0.69. However, it is important to note that this is just one example and the effect of passing over a landmass can vary depending on many factors.
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Blaine works for a battery manufacturing company. he wants to develop a method to test the batteries made each day to determine if they work. which method would provide the most valid results?
Answers
Random sampling 50 batteries throughout the day and testing to see if they would provide most valid results.
A sample is described as a smaller, more manageable representation of a larger group. A smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.
The sample may be biased if it is taken from the first 25 batteries made each day or the last 25 batteries made each day.
The first and last battery made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent thought the day.
Although the battery quality can change during the day, sampling the first 50 batteries produced each day may also add bias into the sample.
The ideal course of action is to randomly select 50 batteries throughout the day, since this helps to ensure that the sample is reflective of the general calibre of batteries manufactured that day.
A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.
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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
Answers
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
Triangle lmn will be dilated with respect to the origin by a scale factor of 1/2
what are the new coordinates of L’M’N’
Answers
The triangle LMN, with vertices L(6, −8), M(4, −4), and N(−12, 2), dilated with respect to the origin by a scale factor of 1/2, results in triangle L'M'N', with vertices L'(3, -4), M'(2, -2), and N'(-6, 1)
To dilate a triangle with respect to the origin, we need to multiply the coordinates of each vertex by the scale factor. In this case, the scale factor is 1/2, so we multiply each coordinate by 1/2.
The coordinates of L' are obtained by multiplying the coordinates of L by 1/2:
L'((1/2)6, (1/2)(-8)) = (3, -4)
The coordinates of M' are obtained by multiplying the coordinates of M by 1/2:
M'((1/2)4, (1/2)(-4)) = (2, -2)
The coordinates of N' are obtained by multiplying the coordinates of N by scale factor 1/2:
N'((1/2)×(-12), (1/2)×2) = (-6, 1)
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The given question is incomplete, the complete question is:
Triangle LMN with vertices L(6, −8), M(4, −4), and N(−12, 2) is dilated with respect to origin by a scale factor of 2 to obtain triangle L′M′N′. What are the new coordinates of L′M′N′ ?
Write each equation in slope-intercept form. Identify the slope and y-intercept.
x - 3y = 12
*Work must be shown.*
Answers
Answer:
slope is 1/3
y-intercept is -4
Step-by-step explanation:
x - 3y = 12
3y = x - 12
y = 1/3x - 4
according to y = mx + b, m is slope and b is y-intercept
slope is 1/3
y-intercept is -4
