Matthew is working two summer jobs, making $9 per hour babysitting and making $13 per hour landscaping. In a given week, he can work a maximum of 16 total hours and must earn at least $180. If Matthew worked 3 hours babysitting, determine the maximum number of whole hours landscaping that he can work and still meet his requirements. If there are no possible solutions, submit an empty answer.
Answer:
Step-by-step explanation:
3 hours of babysitting = $27
if he needs $180 per week he needs to work at least 12 hours in landscaping.
12 hours of Landscaping = $156
156 + 27 = 183
It cuts down about an hour of work.
If I misunderstood something, please let me know. Have a good day :)
0.0625 What is the equivalent percent? %
Answer:6.25%
Step-by-step explanation:
7: An entrance examination for a job consists of 25% English, 30% Mathematics, 25% computer and 20% accounting, and the passing mark is 45. If an applicant sat for the examination and scored 60% in English, 35% in Mathematics, 80% in computer and 50% in Accounting, do you think she will be accepted?
Answer: The overall score obtained is 55.5, which is higher than the passing mark of 45. Therefore, the applicant will be accepted.
Step-by-step explanation:To determine if the applicant will be accepted, we need to calculate their overall score based on the percentage weights and passing mark given for each subject.
The overall score can be calculated as follows:
Overall score = (0.25 x English score) + (0.3 x Math score) + (0.25 x Computer score) + (0.2 x Accounting score)
Substituting the given scores, we get:
Overall score = (0.25 x 60) + (0.3 x 35) + (0.25 x 80) + (0.2 x 50)
= 15 + 10.5 + 20 + 10
= 55.5
HOW MANY WAYS ARE THERE TO PICK 3 ASTRONAUTS TO GO TO THE MOON OUT OF 10 CANDIDATES
The number of ways to pick 3 astronauts from 10 candidates can be found using the combination formula, which is:
nCk = n! / (k!(n-k)!)
where n is the total number of candidates, k is the number of candidates to be chosen, and "!" denotes the factorial function.
In this case, we want to choose 3 astronauts from a pool of 10 candidates, so we can plug these values into the formula:
10C3 = 10! / (3!(10-3)!)
= (10 x 9 x 8) / (3 x 2 x 1)
= 120
Therefore, there are 120 ways to pick 3 astronauts to go to the moon out of 10 candidates.
Answer:
120 or 220
Step-by-step explanation:
What kind of geometric transformation is shown in the line of music?
•
reflection
translation
glide reflection
Question 2 Mohammed and Mira are getting married. They are looking for a catering service for their wedding day. The cost of hiring a catering service to serve food is depends on the number of persons (pax). It costs RM120/pax for 30 persons or less, RM105/pax for 31 to 60 persons, and RM95/pax for 61 to 100 persons. For more than 100 persons, the cost is at RM80/pax. a) Construct the piecewise function for the problem. b) Graph the piecewise functions. c) If they pay RM9025 for the catering service, how many persons that they invite to their wedding? (8 Marks)
a) The piecewise function is 80p, if p > 100 b) For p > 100, the graph will be a straight line passing through the point (100, 100 × 80) with a slope of 8
How to determine the piecewise function for the problema) We can define a piecewise function f(p) to represent the cost of catering service depending on the number of persons (pax).
f(p) =
120p, if p ≤ 30
105p, if 31 ≤ p ≤ 60
95p, if 61 ≤ p ≤ 100
80p, if p > 100
b) To graph the piecewise function, we can plot the points for each of the four parts of the function, and connect them with line segments. The graph will have four segments, each with a different slope.
For p ≤ 30, the graph will be a straight line passing through the origin with a slope of 120.
For 31 ≤ p ≤ 60, the graph will be a straight line passing through the point (31, 31 × 105) with a slope of 105.
For 61 ≤ p ≤ 100, the graph will be a straight line passing through the point (61, 61 × 95) with a slope of 95.
For p > 100, the graph will be a straight line passing through the point (100, 100 × 80) with a slope of 80.
c) To find how many persons they invite to their wedding, we can use the inverse function of f(p) and plug in the given cost of RM9025.
Let C = RM9025, then
120p, if p ≤ 30
105p, if 31 ≤ p ≤ 60
95p, if 61 ≤ p ≤ 100
80p, if p > 100
Case 1: p ≤ 30
120p = C
p = C/120 = 9025/120 = 75.2083
Since p must be an integer, we round up to the nearest integer. Therefore, if they invite 76 persons, the cost of catering service will be more than RM9025.
Case 2: 31 ≤ p ≤ 60
Let x = p - 30, then
105x + 120 × 30 = C
105x = C - 3600
x = (C - 3600)/105 = (9025 - 3600)/105 = 54.5238
Therefore, if they invite 31 + 54 = 85 persons, the cost of catering service will be RM9025.
Case 3: 61 ≤ p ≤ 100
Let x = p - 60, then
95x + 120 × 30 + 105 × 30 = C
95x = C - 9750
x = (C - 9750)/95 = (9025 - 9750)/95 = 0.7632
Therefore, if they invite 60 + 0.7632 × 100 = 137 persons, the cost of catering service will be RM9025.
Case 4: p > 100
Let x = p - 100, then
80x + 120 × 30 + 105 × 30 + 95 × 40 = C
80x = C - 17700
x = (C - 17700)/80 = (9025 - 17700)/80 = -109.375
Since p must be a positive integer, this case is not possible.
Therefore, Mohammed and Mira should invite 85 persons to their wedding to pay RM9025 for the catering service.
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Help Please The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?
A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.
Answer:
the number is even
Step-by-step explanation:
an even number plus an even number will aalways be even. adding 6 to an odd number will never be even. Therefore the number will be even
12,59,294,1469,7344 what is the pattern rule
Both equations give the correct terms, so we can conclude that the pattern rule is: [tex]an^2 - 131n + 80[/tex] , where [tex]a=63[/tex] .
What is the consecutive terms?To find the pattern rule for the given sequence 12, 59, 294, 1469, 7344, we need to observe the differences between consecutive terms. Let's find the differences between each pair of terms:
[tex]59 - 12 = 47[/tex]
[tex]294 - 59 = 235[/tex]
[tex]1469 - 294 = 1175[/tex]
[tex]7344 - 1469 = 5875[/tex]
The differences are not constant, so we need to find the differences between these differences:
[tex]235 - 47 = 188[/tex]
[tex]1175 - 235 = 940[/tex]
[tex]5875 - 1175 = 4700[/tex]
Now, the second differences are constant (equal to 940), which suggests that the pattern rule is a quadratic equation. Let's assume the pattern rule is of the form:
[tex]an^2 + bn + c[/tex]
where n is the term number (starting with n=1 for the first term).
To find the coefficients a, b, and c, we can use the first three terms of the sequence. Let's substitute n=1,2,3 into the equation and equate it to the corresponding terms:
[tex]a + b + c = 12 (for n=1)[/tex]
[tex]4a + 2b + c = 59 (for n=2)[/tex]
[tex]9a + 3b + c = 294 (for n=3)[/tex]
We can solve these equations simultaneously to get the values of a, b, and c:
[tex]a = 63[/tex]
[tex]b = -131[/tex]
[tex]c = 80[/tex]
Therefore, the pattern rule for the sequence is:
[tex]an^2 - 131n + 80[/tex]
where a=63.
To check if this pattern rule works for the other terms of the sequence, we can substitute n=4 and n=5:
[tex]a(4^2) - 131(4) + 80 = 1469[/tex]
[tex]a(5^2) - 131(5) + 80 = 7344[/tex]
Therefore, Both equations give the correct terms, so we can conclude that the pattern rule is:
[tex]an^2 - 131n + 80, where a=63.[/tex]
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esson Quiz
The ages, in years, of 6 volunteers at the local food pantry are listed below. If a 7th volunteer joins them, what would their age be so that the range of their ages will be 557
(56, 81, 54, 47, 45, 94)
O
S
8
18
10
The age of the 7th volunteer has to be 602 years so that the range of the all volunteer ages will be 557.
Given ages of 6 volunteers = (56, 81, 54, 47, 45, 94)
The range = maximum value - minimum value.
So, range of the given list = 94 - 45 = 49.
To increase, the range to 557, we have to add an age that is greater than 94, To obtain that age we have to solve 557 - 45 = 508. [here 557 is the maximum value]
Now, by adding the obtained range to the 94 we can get the required age of 7th volunteer. So 508 + 94 = 602.
From the above explanation, we can conclude that the age of the 7th volunteer has to be 602 years which is unrealistic so that the range becomes 557.
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Examine the steps below. Between which two lines was a mistake made?
A.
between line 1 and line 2
B.
between line 2 and line 3
C.
between line 3 and line 4
D.
between line 4 and line 5
Answer:
A and D
Step-by-step explanation:
A- when multiplying -5 and -3 it should be positive 15.
D- when dividing 3 they just outta nowhere forgot about the negative, it should've been -5
Can anyone help me on this
.If $10,000 is deposited in an account earning 5 ¾ % interest compounded monthly. How much money will be in the account in 5 years.
The total amount in the acount in 5 years is approximately $13,321.76.
What is the accrued amount in the account in 5 years?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n} )^{n*t}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $10,000Compounded monthly n = 12Time t = 5 yearsInterest rate r = 5 3/4% = 5.75%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 5.75/100
r = 0.0575
Plug the given values into the above formula and solve for A.
[tex]A = P( 1 + \frac{r}{n} )^{n*t}\\\\A = 10000( 1 + \frac{0.0575}{12} )^{(12*5)}\\[/tex]
A = $13,321.76
Therefore, the accrued amount is $13,321.76.
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The first three terms of a geometric sequence are as follows.
810, 270, 90
Find the next two terms of this sequence.
Answer:
30 and 10
Step-by-step explanation:
Main concepts:
Concept 1. Geometric Sequence
Concept 2. Common ratio
Concept 3. Finding the next terms
Concept 1. Geometric Sequence
Geometric sequences are a specific type of sequence with a pattern where a specific number is multiplied to each term to get the next term.
For instance, a completely different geometric sequence 1,2,4,8,16,... is geometric because you multiply any term by 2 to get the next term.
Concept 2. Common ratio
In a geometric sequence, this number that you can multiply by to get the next term (in the "1,2,4,8,16,..." example, the number 2) is called the common ratio because taking the ratio of two sequential terms of the sequence (dividing two terms in a row) always gives the same answer:
2/1 = 24/2 = 28/4 = 216/8 = 2This process of finding ratios will yield a common ratio only if the sequence is a Geometric Sequence.
Concept 3. Finding the next terms
Since we're told that the sequence we're given in the question is a Geometric sequence, it must have a common ratio (otherwise, it wouldn't be a geometric sequence).
Find the common ratio by dividing sequential terms:
270/810 = 1/3
90/270 = 1/3
So, for the sequence in the question, the common ratio is 1/3. Each term is multiplied by 1/3 to get the next term in the sequence. (This is equivalent to dividing each term by 3 to get the next term in the sequence, if you prefer division and/or to avoid fractions)
So, to get the next two terms in the sequence, multiply by the common ratio:
90 * 1/3 = 30
30 * 1/3 = 10
So, the next two terms of the sequence are 30 and 10
Julieta says that it is not possible to draw a quadrilateral that is not a trapezoid and a parallelogram. Is Julieta correct explain why or why not.
Julieta's claim about the quadrilateral is false.
How to prove or disprove Julieta claim?The statement is given as:
It is impossible to draw a quadrilateral that is not a trapezoid and not a parallelogram.
The condition for a shape to be a quadrilateral is that the shape must have four sides.
An irregular shape that has four sides is a quadrilateral, but neither a quadrilateral nor a parallelogram
Therefore, Julieta's claim is false
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3)
Which decimal number is equivalent to
73
100
?
Find the length of the missing side
Answer:
24
Step-by-step explanation:
10^2+x^2=26^2
x^2=26^2-10^2
x^2=576
x=[tex]\sqrt{576}[/tex]=24
A binomial experiment with probability of success p=0.45 and n=7 trials is conducted. What is the probability that the experiment results in exactly 1 success?
The calculated value of the probability that the experiment results in exactly 1 success is 0.08719
Calculating the probability that the experiment results in exactly 1 success?From the question, we have the following parameters that can be used in our computation:
n = 7
x = 1
p = 0.45
The probability is then calculated as
P(x = x) = nCr * p^x * (1 - p)^(n - x)
Substitute the known values in the above equation, so, we have the following representation
P(x = 1) = 7C1 * (0.45)^1 * (1 - 0.45)^(7-1)
Evaluate the expression
So, we have
P(x = 1) = 0.08719
Hence, the probability is 0.08719
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solve the rational equation 2/x-2+3/x-4=1/x^2=6x+8
the solution to the original rational equation is: [tex]x = 4.678[/tex] (rounded to three decimal places)
What is the rational equation?A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, it is a number that can be written in the form of a/b, where a and b are integers and b is not equal to zero
According to InformationThere are two equal signs in the equation, which is incorrect. Assuming you meant to write:
[tex]2/(x-2) + 3/(x-4) = 1/(x^2 + 6x + 8)[/tex]
We can start by finding a common denominator for the left-hand side of the equation:
[tex]2/(x-2) + 3/(x-4) = 1/[(x+2)(x+4)][/tex]
Multiplying both sides of the equation by (x-2)(x-4)(x+2)(x+4), we get:
[tex]2(x-4)(x+2)(x+4) + 3(x-2)(x+2)(x+4) = (x-2)(x-4)[/tex]
Expanding and simplifying, we get:
[tex]5x^3 - 19x^2 - 39x + 56 = 0[/tex]
This polynomial equation does not factor nicely, so we can use the rational root theorem or numerical methods to find approximate solutions. Using a calculator or computer, we find that there is one real solution to the equation:
[tex]x \approx 4.678[/tex]
Therefore, the solution to the original rational equation is:
[tex]x = 4.678[/tex] (rounded to three decimal places)
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Which transformation would move Point A(-5, -2) to Quadrant IV? Mark all that apply.
To move Point A(-5, -2) to Quadrant IV, we need to apply one or more transformations that result in a reflection about the x-axis and/or a rotation of 180 degrees. The following transformations would move Point A to Quadrant IV:
Reflection about the x-axis: This transformation would change the sign of the y-coordinate, making it positive. So, the image of A after this transformation would be (−5, 2).
Rotation of 180 degrees about the origin: This transformation would change the sign of both the x and y-coordinates, making them positive. So, the image of A after this transformation would be (5, 2).
Therefore, either a reflection about the x-axis or a rotation of 180 degrees would move Point A to Quadrant IV.
I need to find both of the solutions to the equation 100+(n-2)^ = 149
The solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5
Finding the solutions to the equation 100+ (n - 2)² = 149From the question, we have the following parameters that can be used in our computation:
The equation 100+ (n - 2)² = 149
Express as
100+ (n - 2)² = 149
Subtract 100 from both sides of the equation
So, we have the following representation
(n - 2)² = 49
Take the square root of both sides
n - 2 = 7 and n - 2 = -7
Add 2 to both sides
n = 9 and n = -5
Hence, the solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5
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What is Mine-craft Incorrect Responses Only
Mine-craft Incorrect Responses is known to be a sort of game or challenge where members are inquired to reply to Mine-craft-related questions or explanations with intentioned inaccurate answers.
What is Mine-craft?
The thought is to utilize humor and creativity to come up with reactions that are totally off-base but still somehow related to Mine-craft.
Mine-craft Incorrect Responses is an amusing way of reacting to questions or statements related to the prevalent sandbox video diversion Mine-craft with intentioned off base answers. The objective is to be as imaginative and amusing as conceivable whereas intentionally giving off-base answers to Mine-craft-related questions or comments.
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The test scores of 40 students are listed below.
30 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
a. Find the standard deviation and the variance for the data
b find the five-number summery for the data
c construct a boxplot for the given data. Include the value of the 5-number summery in the boxplot
a. the standard deviation is approximately 25.01 and the variance is approximately 625.21.
b.the five-number summary for the data is: 30, 57, 71, 81, 98.
what is standard deviation?The standard deviation is a measurement of how widely apart a group of data points are from the mean (average) value. You can see how far each data point deviates from the mean value. When the standard deviation is minimal, the data points are densely packed around the mean; when it is great, the data points are more widely spaced from the mean. The standard deviation is a statistical concept that is frequently used to compare the degree of variability across various data sets as well as to infer and make conclusions about a population from a sample.
a. To find the standard deviation and variance for the given data, we can use the following formulas:
Variance: σ² = ∑(x - μ)² / n
Standard deviation: σ = sqrt(σ²)
where x is the data point, μ is the mean of the data, and n is the sample size.
First, we need to find the mean of the data:
μ = (30 + 35 + 43 + 44 + 47 + 48 + 54 + 55 + 56 + 57 + 59 + 62 + 63 + 65 + 66 + 68 + 69 + 69 + 71 + 72 + 72 + 73 + 74 + 76 + 77 + 77 + 78 + 79 + 80 + 81 + 81 + 82 + 83 + 85 + 89 + 92 + 93 + 94 + 97 + 98) / 40
μ = 69.3
Now, we can use the variance formula:
σ² = ∑(x - μ)² / n
σ² = [(30 - 69.3)² + (35 - 69.3)² + ... + (98 - 69.3)²] / 40
σ² = 625.21
Finally, we can find the standard deviation:
σ = sqrt(σ²)
σ = sqrt(625.21)
σ ≈ 25.01
Therefore, the standard deviation is approximately 25.01 and the variance is approximately 625.21.
b. To find the five-number summary, we need to find the minimum, maximum, median, and quartiles (Q1 and Q3) of the data:
Minimum: 30
Q1: 57
Median: 71
Q3: 81
Maximum: 98
Therefore, the five-number summary for the data is: 30, 57, 71, 81, 98.
c. To construct a boxplot for the given data, we can use the five-number summary:
Draw a number line and mark the minimum, Q1, median, Q3, and maximum.
Draw a box from Q1 to Q3.
Draw a vertical line inside the box at the median.
Draw whiskers from the ends of the box to the minimum and maximum, or to the nearest data point within 1.5 times the interquartile range (IQR).
Mark any outliers outside the whiskers.
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 106, and the sample
standard deviation, s, is found to be 10.
(a) Construct a 95% confidence interval about u if the sample size, n, is 16.
(b) Construct a 95% confidence interval about u if the sample size, n, is 11.
(c) Construct a 90% confidence interval about μ if the sample size, n, is 16.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.
what is standard deviation ?A collection of information's values' standard deviation serves as a gauge for how much variance or dispersion there is. It is a statistical word used to describe the degree to which the individual data points depart as from mean or average value that is contained in the data set. By taking taking square root of the variance—the sum of the squared deviations amongst each point in the data and the mean—we can determine the standard deviation. While a high standard deviation suggests that the data points are widely dispersed, a modest standard deviation suggests that the statistics are close to the mean.
given
(a) When the sample size, n, is 16, we can apply the following formula to create a 95% confidence interval regarding the population mean, :
x ± tα/2 * (s/√n)
where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.
We determine that t0.025,15 = 2.131 using a t-distribution table or calculator.
When we enter the values, we obtain:
106 ± 2.131 * (10/√16)
which is equivalent to:
106 ± 5.33
In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.
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There are 8 blue marbles, 6 red marbles, 2 green marbles and 4 black marbles in a box.
What is the probability that the marble is not green?
the probability that the marble is not green is 0.9 or 90%. This means that if we were to randomly select a marble from the box, there is a 90% chance that it will not be green.
How to solve probability?
To calculate the probability that a marble is not green, we need to first determine the total number of marbles in the box, which is given by:
Total number of marbles = 8 + 6 + 2 + 4 = 20
Next, we need to determine the number of marbles that are not green. Since there are 2 green marbles, the number of marbles that are not green is given by:
Number of marbles that are not green = 20 - 2 = 18
Finally, we can calculate the probability of selecting a marble that is not green by dividing the number of marbles that are not green by the total number of marbles in the box, as follows:
Probability of selecting a marble that is not green = Number of marbles that are not green / Total number of marbles
= 18 / 20
= 0.9 or 90%
Therefore, the probability that the marble is not green is 0.9 or 90%. This means that if we were to randomly select a marble from the box, there is a 90% chance that it will not be green.
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LESSON 26 SESSION 3
There are at least 12 people on a bus.
a. Write and graph an inequality to show the number of people who may be on
the bus.
An inequality to show the number of people is p ≥ 12
Writing and graphing an inequality to show the number of peopleLet p be the number of people on the bus. We know that there are at least 12 people on the bus, so we can write:
p ≥ 12
This inequality means that the number of people on the bus, p, must be greater than or equal to 12.
To graph this inequality, we can draw a horizontal line at y = 12 on the y-axis, and shade the area above the line, since any value of p that is greater than or equal to 12 satisfies the inequality.
Here's a graph of the inequality attached
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I need help with this econ question. Thank you.
Answer:
c + 3.6 + 3.4 + 4.1 + 2.3 = 18.6
c + 13.4 = 18.6
c = 5.2
$5.2 trillion was spent on consumption.
. The students in a furniture-making class make a tabletop shaped like the figure shown. The tabletop has squares cut out of the corners. a. What is the area of the tabletop?
The area of the tabletop made by the students in the furniture - making class would be 26 ft ²
How to find the area ?We can see that this tabletop made by students in the furniture - making class takes the form of a composite shape with two smaller rectangles and one large rectangle.
The area of the large rectangle is:
= 4 ft x ( 1 + 3 + 1 )
= 4 ft x 5 ft
= 20 ft ²
The area of the two smaller rectangles is:
= 2 x ( 3 ft x 1 ft )
= 2 x 3
= 6 ft ²
The total area of the tabletop is:
= 20 + 6
= 26 ft ²
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Which expression is equivalent to 5(6x + 3y)?
A 11x+3y
B 11x+8y
C 30x+3y
D 30x+15y
Answer:
The answer is **D. 30x+15y**.
```
5(6x + 3y) = 5*6x + 5*3y = 30x + 15y
```
Step-by-step explanation:
1. Distribute the 5:
```
5(6x + 3y) = (5 * 6x) + (5 * 3y)
```
2. Simplify:
```
5(6x + 3y) = 30x + 15y
```
Therefore, 5(6x + 3y) is equivalent to 30x + 15y.
Find the consumers' surplus at a price level of $1 for the price-demand equation
p= D(x) = 20-0.1x
where p is the price and x is the demand. Do not include a dollar sign or any commas in your answer.
The consumers' surplus at a price level of $1 for the price-demand equation is -1072.5.
Given that price-demand equation p= D(x) = 20-0.1x, we need to find the consumers' surplus at a price level of $1.
So,
From the equation we have,
20-0.1x = 1
0.1x = 19
x = 190
Therefore, the equilibrium point = (190, 1) = (xe, Pe)
Now,
Cs = [tex]\int\limits^{x_e}_0 {D(x)} \ dx\, -Pexe[/tex]
[tex]\int\limits^{190}_0 {20-0.1x} \ dx\, -(190)[/tex]
= 20-0.1{9025}-190
= -1072.5
Hence the consumers' surplus at a price level of $1 for the price-demand equation is -1072.5
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Please Help Quick ASAP Hurry
Two similar solids have a scale factor of 2 : 5
What is the ratio of their volumes expressed in lowest terms?
A cone with volume 2625 m³ is dilated by a scale factor of 15.
What is the volume of the resulting cone?
a) If two similar solids have a scale factor of 2 : 5, the ratio of their volumes is 8:125, expressed in the lowest terms.
b) If cone with volume 2625 m³ is dilated by a scale factor of 15, the volume of the resulting cone is 10,640,625 m³.
(a) When two solids are similar, their corresponding linear dimensions are in the same ratio, which is known as the scale factor. For example, if two similar solids have a scale factor of 2:5, it means that the corresponding sides of the two solids are in the ratio 2:5.
The volume of a solid is proportional to the cube of its linear dimensions. Therefore, if the linear dimensions of two similar solids are in the ratio 2:5, the ratio of their volumes would be:
(2/5)³ = 8/125
(b) The volume of a cone is given by the formula:
V = (1/3)πr²h
where V is the volume, r is the radius, and h is the height of the cone.
When a cone is dilated by a scale factor of k, its linear dimensions increase by a factor of k, and its volume increases by a factor of k³. Therefore, if the volume of a cone is V and it is dilated by a scale factor of k, the volume of the resulting cone would be:
V' = k³V
In this case, the volume of the original cone is given as 2625 m³, and it is dilated by a scale factor of 15. Substituting these values in the formula, we get:
V' = 15³(2625)
V' = 15³(2625/1)
V' = 10640625
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