Te surface area of the smaller figure based on the ratio is 1600m²
Calculating the surface area of the smaller figure.The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding sides.
Let x be the scale factor between the smaller and larger figures.
Then we have:
(x³)/(4000) = 6912
x³ = 6912/4000
x³ = 1.728
Taking the cube root of both sides, we get:
x = 1.2
So the scale factor from the larger figure to the smaller figure is 1:1.2.
The surface area of a similar figure is proportional to the square of the scale factor.
So we can use the scale factor to find the ratio of the surface areas:
SA(smaller) / SA(larger) = 1/(1.2)²
We know that the surface area of the larger figure is 2304m^2, so we can solve for the surface area of the smaller figure:
SA(smaller) = 2304 * 1/(1.2)²
SA(smaller) = 1600m²
Therefore, the surface area of the smaller figure is 1600m²
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In a class of students, the following data table summarizes how many students passed
a test and complete the homework due the day of the test. What is the probability that
a student completed the homework given that they failed the test?
Completed the homework
Did not complete the homework
Passed the test Failed the test
8
2
3
сл
The probability that a student completed the homework given that they failed the test is 3/8.
Describe Probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It involves the measurement and analysis of the likelihood or chance of an event occurring. Probability is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.
The concept of probability is used in many fields, such as statistics, physics, finance, and engineering, to make predictions and decisions based on incomplete information. It provides a framework for analyzing situations in which multiple outcomes are possible and assigns a quantitative value to the likelihood of each outcome.
To find the probability that a student completed the homework given that they failed the test, we need to use conditional probability.
Let A be the event that a student completed the homework and B be the event that a student failed the test.
We want to find P(A | B), the probability that a student completed the homework given that they failed the test.
Using the data from the table, we can see that the total number of students who failed the test is 8 (3 who completed the homework and 5 who did not).
Therefore, P(B) = 8/18 = 4/9 (the probability that a student failed the test)
Out of the 8 students who passed the test, 3 also completed the homework, so P(A and not B) = 3/18 = 1/6.
So, P(A | B) = P(A and B) / P(B) = (1/6) / (4/9) = 3/8.
Therefore, the probability that a student completed the homework given that they failed the test is 3/8.
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can anyone help me please???
thank you xxxx
Using the property of a kite: the angles formed by two unequal sides of a kite are equal. The value of ∠BCD∠BCD is
∠BCD = ∠BAD ⇒ ∠BCD = 106°
three cards are drawn with replacement from a standard deck of 52 cards. find the the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability of drawing a diamond, then a black card, and then a face card from a standard deck of 52 cards with replacement is 3/104 or 0.028846 .
What is the probability?The probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card is given by the expression, `(13/52) × (26/52) × (12/52)`.
In a standard deck of 52 cards, there are 13 diamonds, 26 black cards (13 clubs and 13 spades), and 12 face cards (4 Jacks, 4 Queens, and 4 Kings).
To calculate the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card, we use the formula of probability:
`P(E) = n(E) / n(S)`
where, P(E) = Probability of an event
n(E) = Number of favorable outcomes
n(S) = Total number of outcomes
Total number of outcomes = 52
First card will be a diamond
Number of diamonds in a deck of 52 cards = 13
Total number of outcomes after drawing the first card = 52
Probability of drawing a diamond in the first attempt = P(diamond)`= 13/52
Probability of drawing a black card in the second attempt, given that the first card is a diamond= `P(black/diamond)`= (26/52) = `(1/2)`
Probability of drawing a face card in the third attempt, given that the first card is a diamond and second card is a black card= `P(face/diamond and black)`= `(12/52)` = `(3/13)`
Therefore, probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card`= P(diamond) × P(black/diamond) × P(face/diamond and black) = (13/52) × (1/2) × (3/13)= 3/104`
Therefore, the required probability is 3/104 or 0.028846 rounded to the nearest millionth.
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Nonresponse bias occurs when ________.
A) the population has been divided into strata
B) portions of the population are excluded from the sample
C) cluster sampling is used instead of stratified random sampling
D) those responding to a survey or poll differ systematically from the nonrespondents
Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.
Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.
Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.
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give the position of C on this number line
The position of C on the number line is 1/8th position.
Define the term number line?A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.
From the given number line, there are total 8 points between 0 to 1
That means, it's fractions of 8.
Location of point C is on the 1st point,
So, position of C on this number line = (1/8) ÷ (1-0) = 1/8
Therefore, In the number line, C is located in the 1/8th place.
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A square field has a side length of 6x10³ meters. Which of the following is its area in square meter
(1) 6x106
(3) 36x106
(2) 36×10⁹
(4) 6x10⁹
Answer:
36 × 10^6 m²
Step-by-step explanation:
Given the side length of a square = 6 × 10³m,
To solve for the area of a square, use the following formula:
A = S² where:
S = side of the square
Substitute the given value for the side into the formula:
A = S²
A = (6 × 10³)²
A = 36000000 or 36 × 10^6 m²
NOTE:
6 × 10³ is also the same as 6 × 1000 = 6000,
(6 × 10³)² is essentially 6,000² = 36,000,000
Therefore, its area in square meters is 36 × 10^6
You purchased 40 shares for $3.95/sh. If you sold the shares for a total of $200. Did you net a profit or a loss?
Answer: profit
Step-by-step explanation:
3.95 (price of one share) multiplied by 40 (the amount of shares bought) would have cost $158. so selling all for $200 would be a $42 profit
Jen’s assignment is to read at least 85 pages of a novel. Jen has read 31 pages. How many pages p does Jen have left to read? Write an inequality that represents this situation. Then solve the inequality
Jen has 54 pages left to read to meet her assignment requirement.
The inequality that represents this situation is p ≥ 85 - 31
To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.
The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:
p = 85 - 31
p = 54
Therefore, Jen has 54 pages left to read.
To represent this situation with an inequality, we can use:
p ≥ 85 - 31
This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).
Solving for p:
p ≥ 85 - 31
p ≥ 54
This means that Jen must read at least 54 more pages to meet her assignment requirement.
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(x+2)^2=-16 This equation had no solution, why not?
Answer:
It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).
Step-by-step explanation:
The normalized form of the equation
(x+2)^2= - 16
x^2 + 4x + 4 = - 16
x^2 + 4x + 20 = 0
We have in the form ax^2 + abx + c = 0
a = 1
b = 4
c = 20
Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64
Discriminant is negative, therefore, no Real solutions.
Find the surface area of the rectangular prism.
6 km
4 km
4 km
Answer: 88km is your answer
Step-by-step explanation: We just had this on a test
A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Ybe the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by 3. f(x) = { 3/2(x^2 +y^2) 0
Answer:
Step-by-step explanation:
please help!!
4.
Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.
a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given.
b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other?
c. What is the measure of the angle between the bikers?
d. What is the relationship between the measure of the angles and the paths the bikers took?
e. Classify the triangle the paths created.
f. How many miles did they travel together?
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
How to solve:The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
They cover almost equal distances from their starting points:
24 miles ≈ √12²+21² miles
b) They encounter each other.
c) The angle at one vertex measures 30 degrees.
d) e) As shown in the attached picture, it is an almost right triangle.
f) Together, they cover a total distance of 57 miles (12+21+24).
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Please help with these Formal Logic questions;
8.1 Some cashmere sweaters are fashionable garments, so some cashmere sweaters are not suede jackets, for some suede jackets are not fashionable garments.
Which of the following correctly expresses the form of this argument?
a. Some C are F.
Some C are not S.
Some S are not F.
b. Some S are not F.
Some C are F.
Some C are not S.
c. Some C are not F.
Some C are not S.
Some C are F.
d. Some F are not S.
Some F are C.
Some S are not C.
e. Some C are F.
Some F are not S.
Some S are not S.
8.2 Some cashmere sweaters are fashionable garments, so some cashmere sweaters are not suede jackets, for some suede jackets are not fashionable garments.
Which of the following substitutions proves the argument invalid?
a. C = animals, F = cats, S = mammals.
b. C = dogs, F = animals, S = mammals.
c. C = dogs, F = mammals, S = fish.
d. C = mammals, F = animals, S = dogs.
e. C = cats, F = mammals, S = animals.
8.3 If cell phone companies screen text messages, then freedom of speech is threatened. Thus, freedom of speech is not threatened, because cell phone companies do not screen text messages.
Which of the following substitutions proves the argument invalid?
a. C = Abraham Lincoln was assassinated, F = George Washington was assassinated.
b. C = Joe Smith was beheaded, F = Joe Smith is dead.
c. C = Abraham Lincoln was beheaded, F = Abraham Lincoln is dead.
d. C = Abraham Lincoln was assassinated, F = Abraham Lincoln is dead.
e. C = Abraham Lincoln was beheaded, F = Abraham Lincoln is not dead.
8.4 If cell phone companies screen text messages, then freedom of speech is threatened. Thus, freedom of speech is not threatened, because cell phone companies do not screen text messages.
Which of the following correctly expresses the form of this argument?
a) If C then F.
C.
F.
b) Not F.
Not C.
If C then F.
c) All C are F.
C.
F.
d) If C then F.
Not C.
Not F.
e) If C then F.
Not F.
Not C.
8.5 All container ships that are ocean-going are air polluters. Hence, all container ships are air polluters.
Which of the following correctly expresses the form of this argument?
a) All C are A.
All C are O.
b) All C are A.
All C that are O are A.
c) All CS are O.
All CS are A.
d) All C are O.
All C are A.
8.6 All container ships that are ocean-going are air polluters. Hence, all container ships are air polluters.
Which of the following substitutions proves the argument invalid?
a. C = husbands, O = married, A = men.
b. C = men, O = humans, A = mammals.
c. C = men, O = married, A = husbands.
d. C = wives, O = divorced, A = women.
e. C = cats, O = animals, A = dogs.
8.17 All A are B. (T) Contrary
a. No A are B. (Und.)
b. All B are A. (Und.)
c. Some A are B. (T)
d. No A are B. (F)
e. No A are non-B. (T)
8.18 Some A are not non-B. (F) Contradiction
a. Some A are non-B. (T)
b. All A are non-B. (T)
c. Some B are not non-A. (F)
d. Some A are non-B. (T)
e. Some A are B. (T)
8.19 Some non-A are not B. (T) Subcontrary
a. Some non-A are B. (Und.)
b. No non-A are B. (Und.)
c. All non-A are B. (F)
d. Some A are B. (T)
e. Some non-B are not A. (T)
The answers for the questions given are mentioned below respectively.
Define the term expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations that are arranged in a specific way.
It can be a single number or variable, or a combination of them, along with mathematical operations like addition, subtraction, multiplication, division, exponents, and parentheses.
8.1 - The correct expression of the form of this argument is: a. Some C are F. Some C are not S. Some S are not F.
8.2 - The substitution that proves the argument invalid is: b. C = dogs, F = animals, and S = mammals.
8.3 - The substitution that proves the argument invalid is: e. C = Abrahamm Lincoln was beheaded, F = Abraham Lincon is not dead .
8.4 - The correct expression of the form of this argument is: d. If C then F. Not C. Not F.
8.5 - The correct expression of the form of this argument is: b. All C's are A. All C that are O are the A.
8.6 - The substitution that proves the argument invalid is: c. C=men, O=married, A=husbands.
8.17 - The correct truth value of the statement is: c. Some A are B. (T)
8.18 - The correct truth value of the statement is: e. Some A are B. (T)
8.19 - The correct truth value of the statement is: a. Some non-A are B. (Und.)
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What is the slope of the line passing through the points (4, -6) and (2, 3)?
Answer:
m = -9/2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (4, -6) (2, 3)
We see the y increase by 9, and the x decrease by 2, so the slope is
m = -9/2
1,500 decagrams = 150 kilograms.
True?
False?
Answer: FALSE
Step-by-step explanation:
1500 decagram = 15 kg
1 decagram = 0.01 kg
1500 decagram = 1500/0.01 kg
= 1500/100 kg
1500 decagram = 15kg
*9. The consultancy Imagination Inc. Is working with its manufacturing client Parts-R-Us to improve their on-time
performance. The firm can earn a bonus of up to $1,000,000 based on how much the on-time performance actually
improves. It's current (baseline) on-time performance is 90%.
The company typically completes approximately 1,000 orders per month, with approximately 100 orders delayed. The
bonus payment is prorated according to the following criteria:
• The on-time performance improvement is calculated based on a reduction in late events or an improvement in on-
time performance.
• No bonus is earned for the first 25% reduction in late events, say from 100 to 75. Maximum bonus is earned once
Parts-R-Us achieves 95% on-time performance.
Please answer the following:
Write down a formula to
determine the total bonus
amount to be received
Using your formula, show
how much bonus would be
paid if Parts-R-Us achieves
94% on-time performance
Parts-R-Us could be eligible for a $0 bonus if it achieves an on-time performance rate of 94% or more.
The company would have to maintain an order delivery rate of 95% in order to qualify for the bonus. If achieved, the bonus would be as follows: Bonus = 94% * (1 - 100).
The following is the calculation for the bonus:
Bonus = P * (1 - D)
Where:
P represents the proportion of orders that are delivered on time.
D represents the total number of orders placed late.
In the event that Parts-R-Us achieves an on-time performance rate of 94%, the bonus would be as follows:
Bonus = 94% * (1 - 100)
Bonus = $0
If the company only managed to complete its tasks 94% of the time, it will not be eligible for a bonus.
In order to qualify for the maximum bonus, Parts-R-Us would have to maintain an on-time delivery rate of 95%.
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60 identical machines in a factory pack 150 crates of limes per day
between them.
a) Write the ratio of the number of machines to the number of crates
packed per day in the form 1: n.
b) How many crates of limes would 70 of these machines pack per day?
Give any decimals in your answers to 1 d.p.
a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:
Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day
Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.
b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:
1 machine : 2.5 crates/day = 70 machines : x crates/day
Solving for x, we get:
x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day
Therefore, 70 of these machines would pack 175 crates of limes per day.
Step-by-step explanation:
a) The ratio of the number of machines to the number of crates packed per day can be written as:
60 : 150
To simplify this ratio, we can divide both sides by 10:
6 : 15
Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:
1 : 2.5
Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.
b) If 60 machines can pack 150 crates per day, then one machine can pack:
150/60 = 2.5 crates per day
So, 70 machines can pack:
70 × 2.5 = 175 crates per day
Therefore, 70 machines can pack 175 crates of limes per day.
The alpha level is set _____ the analysis of the data. Use the following Distributions tool to identify the boundaries that separate the extreme samples from the samples that are more obviously consistent with the null hypothesis. Assume the null hypothesis is nondirectional, meaning that the critical region is split across both tails of the distribution. The z-score boundaries at an alpha level alpha = .05 are: z = 1.96 and z = -1.96 z = 3.29 and z = -3.29 z = 2.58 and z = -2.58 To use the tool to identify the z-score boundaries, click on the icon with two orange lines, and slide the orange lines until the area in the critical region equals the alpha level. Remember that the probability will need to be split between the two tails. To use the tool to help you evaluate the hypothesis, click on the icon with the purple line, place the two orange lines on the critical values, and then place the purple line on the z statistic. The critical region is _____. The z-score boundaries for an alpha level a = .001 are: z = 2.58 and z = -2.58 z = 1.96 and z = -1.96 z = 3.29 and z = -3. 29 Suppose that the calculated z statistic for a particular hypothesis test is 2.64 and the alpha is .001. This z statistic is _____ the critical region. Therefore, the researcher _____ reject the null hypothesis, and he ______ conclude the alternative hypothesis is probably correct.
The researcher should reject the null hypothesis, and he can conclude the alternative hypothesis is probably correct.
The alpha level is set prior to the analysis of the data. To use the tool to identify the z-score boundaries, the user must slide the orange lines until the area in the critical region equals the alpha level. The critical region is between the two z-score boundaries. The z-score boundaries for an alpha level a = .001 are: z = 2.58 and z = -2.58, z = 1.96 and z = -1.96, z = 3.29 and z = -3.29. With an alpha of .001, the calculated z statistic of 2.64 is within the critical region. Therefore, the researcher should reject the null hypothesis, and he can conclude the alternative hypothesis is probably correct.
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Write this value in order , starting with the smallest 0. 2 1/2 2℅
0, 2%, 2 1/2 The values are ordered from smallest to largest, with 0 being the smallest, followed by 2%, and then 2 1/2.
0 is the smallest value because it represents nothing. It is the absence of a quantity, and therefore, it is always the smallest value.
2% is larger than 0 because it represents a percentage of a whole. Percentages are fractions out of 100, so 2% means 2 out of 100. It is larger than 0, but smaller than 2 1/2.
2 1/2 is the largest value because it represents a whole number and a fraction. It is larger than 2%, because 2 1/2 is equal to 250 out of 10,000 or 25 out of 1,000, which is a larger quantity than 2 out of 100.
Understanding the relative size of different values is an important skill in many areas, including mathematics, science, and finance. Being able to order values from smallest to largest helps us make sense of data and information, and it allows us to make informed decisions based on the relative size of different quantities. It is important to learn how to do this accurately and efficiently in order to be successful in these fields.
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please help asap thanks!
Express the ratio of A's to N's in the word BANANA, in simplest form.
CHOICES!
2:3
1:2
3:2
2:1
Answer:
[tex]3:2[/tex]
Step-by-step explanation:
It is [tex]3:2[/tex] because there are 3 a's in banana, and 2 n's in banana. The question asks the ratio of a's to n's so the number of a's should come first and then the number of n's should come next.
Edith's van can safely carry a maximum land of 920 kilograms.
She wants to use her van to carry
30 sacks of potatoes, each of mass 25 kilograms to the nearest kilogram
and
20 sacks of carots, each of mass 7. 5 kilograms to 1 decimal place
Can she definitely use her van safety in one journey?
You must show your working
(4 marks)
Yes, she can definitely use her van safety in one journey. The total weight is the weight of potatoes plus the weight of carots.
Given,
Number of sacks of potatoes = 30
Mass of each potato = 25
Total weight of Potatoes = 30 * 25
= 750
Number of sacks of carrots = 20
Mass of each Carot = 7.5
Total weight of Carrot = 20 * 7.5
= 150
(The total weight is the weight of potatoes plus the weight of carrots.)
So, total weight = 750 + 150
= 900
The maximum land which Edith can carry safely in the van is 920 kilograms.
∵ 900 < 920
∴ She can use her van safely.
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Please help me as I’m struggling
Therefore , the solution of the given problem of pie chart comes out to be number of adults who selected math (15) outnumbered the number of minors. (10).
Explain pie charts.
A pie chart, also referred to as a circle diagram, is a graphical representation of each of the values of a particular variable or a method to condense a collection of nominal data. (e.g. percentage distribution). A circle with many parts makes up this kind of chart. Each segment represents a particular group.
Here,
for a two-way table: Party A, Party B, and Party C
Men make up 12 8 % of the population while women make up 16 %.
Total 28 15 19
32 ladies make up the group, to start with.
b) 16 female voters plan to support Party A.
Math, English, and science are studied by adults aged 15 to twenty-one and by children aged ten to ten.
Total 25 24 31
15 people selected math.
b) Reeshma is mistaken. The number of adults who selected math (15) outnumbered the number of minors. (10).
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Find the greatest common factor and the least common multiple of the following terms. Submit all
solution steps and your final answers to earn full credit.
8a³b5
16a²b7
Answer:
To find the greatest common factor, we need to find the largest factor that divides both terms evenly. We can factor each term as follows:
8a³b5 = 2³ * a³ * b5
16a²b7 = 2⁴ * a² * b7
The greatest common factor is the product of the lowest exponent of each prime factor that appears in both terms. Therefore, the greatest common factor is:
GCF = 2³ * a² * b5 = 8a²b5
To find the least common multiple, we need to find the smallest multiple that both terms share. We can start by writing out the prime factorization of each term:
8a³b5 = 2³ * a³ * b5
16a²b7 = 2⁴ * a² * b7
The least common multiple is the product of the highest exponent of each prime factor that appears in either term. Therefore, the least common multiple is:
LCM = 2⁴ * a³ * b7 = 16a³b7
So, the greatest common factor is 8a²b5 and the least common multiple is 16a³b7.
The owner of a sports complex wants to carpet a hallway connecting two buildings. The carpet costs $2.50 per square foot. How much does it cost to carpet the hallway?
Therefore, it will cost $510 to carpet the hallway.
What is area?Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width. The concept of area is used in many fields, including mathematics, geometry, engineering, and architecture. It is an important measure for determining the amount of material needed to cover a surface, such as carpet or paint, and is used in a wide variety of real-world applications.
Here,
To find the cost of carpeting the hallway, we need to know the total area of both trapezoids in square feet. Let's assume that the trapezoids have parallel sides of length 16 and 18 feet, and a height of 6 feet.
The area of each trapezoid is given by the formula:
Area = (1/2) x (sum of parallel sides) x height
For the first trapezoid, the sum of parallel sides is 16 + 18 = 34 feet. Therefore, the area of the first trapezoid is:
Area1 = (1/2) x (16 + 18) x 6
Area1 = 102 square feet
For the second trapezoid, the sum of parallel sides is also 16 + 18 = 34 feet. Therefore, the area of the second trapezoid is:
Area2 = (1/2) x (16 + 18) x 6
Area2 = 102 square feet
The total area of both trapezoids is:
Total Area = Area1 + Area2
Total Area = 102 square feet + 102 square feet
Total Area = 204 square feet
Now that we know the area of the hallway, we can calculate the cost of carpeting it. We're told that the carpet costs $2.50 per square foot, so we can multiply the area of the hallway by the cost per square foot to find the total cost:
Total Cost = Area x Cost per square foot
Total Cost = 204 square feet x $2.50 per square foot
Total Cost = $510
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Help me with this please!!!
Answer:
7
Step-by-step explanation:
x + 3 = 10
x + 3 - 3 = 10 - 3
x = 7
Solve each inequality (show work)
Answer:
5 less than or equal to x
Step-by-step explanation:
make x subject
the weights of bunches of bananas in the grocery store are normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. a random sample of four bunches is taken and the mean weight is recorded. which of the following is the mean of the sampling distribution for the mean of all possible samples of size four? a.0.89 b.1.27 c.3.54 d.5.53
The mean of the sampling distribution will be 3.54. Thus, the correct option is C.
The population means is equal to the mean of the sampling distribution for all feasible samples of size 4. In this instance, 3.54 pounds is shown as the population means.
This suggests that the mean weight of the population of banana bunches will be 3.54 pounds if we pick several random samples of size four, compute the mean weight for each sample, and then average those sample means.
The Central Limit Theorem, which asserts that the sampling distribution of the sample means approaches a normal distribution centered on the population mean as the sample size grows, is a fundamental idea in statistics.
Thus, the correct option is C.
More about the Central Limit Theorem link is given below.
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3. Find the distance from A to B. A(-2,2) B (4,-2)
The distance from points A(-2, 2) to B (4, -2) is equal to √52 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given points into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-2))² + (-2 - 2)²]
Distance = √[(6)² + (-4)²]
Distance = √(36 + 16)
Distance = √52 units.
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Can someone please help me with these, I wasn’t able to attend school cause I have Covid and I don’t know what’s going on. Please please help me
Answer: The answer for the first question goes as follows: Which one(s) have both pairs of opposite sides that are parallel? Rectangle, Rhombus, and square. Which one(s) have both pairs of opposite sides that are congruent? Rectangle, square, and rhombus. Which one(s) have all four sides congruent? Square and rhombus.
The answers to the second question are:
Circumference = pi * diameter. So, the distance around it is 100pi.Area of a circle = pi * r^2. So the area of the theater is 7854.0 ft^2.Step-by-step explanation:
Essentially, all of these parallelograms have different properties and properties that they share. For example, a property they share by the definition of a parallelogram is that all of them have two pairs of opposing sides that are parallel. Another property they share from the definition of a parallelogram is that opposite sides are congruent.
As such, rectangles, squares, and rhombuses have the properties that all parallelograms have because they are all parallelograms. However, they also have their own properties.
Rectangles: A rectangle has the properties of a parallelogram, as well as the property of having all of its angles be right angles. This also makes all of its angles congruent.Rhombuses: Rhombuses have the properties of a parallelogram, and they also have all four of their sides congruent. Squares: Squares are like rhombuses and rectangles put together. They have all of their angles as right angles and they have all four of their sides congruent.Second Question Explanation:
1. The question is describing a theater that has a circular base. Therefore, you can use the formula for the circumference of a circle, pi * diameter, to find the circumference (or distance around) the theater. The diameter is given to you: 100 ft. So just multiply that by pi.
2. The question is asking for the area of the theater. This means that you can use the formula for the area of a circle, A = pi * r^2. Note that it is asking you for the area, not the volume, so you would find the area of the circle, not the volume of the hemisphere. r represents the radius of the circle/theater. The diameter is given as 100 ft, and the radius is half of the diameter, so it is 50 ft. Now just plug the radius into the equation and you get the answer I showed.
4.1.60-(15)+(-13 4.2.-2(3)+27 ÷(-3)
Answer:
-15
Step-by-step explanation:
4.1.60 - (15) + (-13) = 32
4.2. -2(3) + 27 ÷ (-3) = -2(3) - 9 = -15
