Answer:
3:20 pm.
Step-by-step explanation:
Time Yasmin got home: 4:25
Time it took to walk home: 15 minutes
Practice started: 20 minutes after bell.
Practice lasted for 30 minutes.
For us to find this out, you have to calculate all the activities.
An hour is 60 minutes.
A half hour is 30 minutes.
15 + 20 + 30 = 65 minutes.
65 minutes = an hour and five minutes.
4:25 - 1:05 = 3:20.
Feel free to let me know if you need more help! :)
Answer:
3:20 p.m
Step-by-step explanation:
A box contains 5 red marbles and 7 green marbles. Find the probability of drawing 2 red marbles:
Answer:
5/33
Step-by-step explanation:
5/12 * 4/11 = 20 /132 = 10 / 66 = 5 / 33
The probability of drawing a red marble on the first try is 5/12 because there are 5 red marbles and 12 marbles in total. The second time you only have 4 red marbles left and 11 marbles left in total. Multiply them to find the probability of drawing 2 red marbles in a row.
Probability of drawing 2 red marble is [tex]\frac{5}{33}[/tex]
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Here,
Number of red marbles = 5 marble
Number of green marbles = 7 marble
Probability = Number of favorable outcome / Number of total outcome
Probability of drawing 1 red marble = [tex]\frac{5}{12}[/tex]
Probability of drawing second marble is red = [tex]\frac{4}{11}[/tex]
Probability of drawing 2 red marbles = [tex](\frac{5}{12})(\frac{4}{11} )=\frac{5}{33}[/tex]
Hence, the probability of drawing 2 red marble is [tex]\frac{5}{33}[/tex]
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Apply the distributive property to the expression to write an equivalent expression. Complete the statements. 4x + 16 Find the GCF of . Now factor out the GCF by dividing each term in the expression by . 4x divided by the GCF is , and 16 divided by the GCF is . The equivalent expression is .
Answer:
[tex]4(x+4)=4x+16[/tex]
Step-by-step explanation:
a) The Greatest Common Factor, of both terms 4x and 16 is 16.
4,16|2
2,8|2
1,4|2
1,2|2
1,1| = 2*2*2*2=16
b) Let's divide each term by 4 their
4x+16
[tex]\frac{4x}{4}=x\\\\\frac{16}{4}=4[/tex]
Placing their common divisor outside the parentheses, and inside the sum of this result:
[tex]4(x+4)=4x+16[/tex]
The equivalent expression after factoring out the GCF is [tex]\(4(x + 4)\)[/tex].
To apply the distributive property to the expression \(4x + 16\), we can factor out the greatest common factor (GCF) of the two terms. In this case, the GCF of 4 and 16 is 4. By dividing each term in the expression by 4, we can factor out the GCF.
\(4x\) divided by the GCF (4) is \(x\), and \(16\) divided by the GCF (4) is \(4\). Therefore, the expression \(4x + 16\) can be factored as \(4(x + 4)\) using the distributive property.
To summarize:
- GCF of 4 and 16 is 4.
- \(4x\) divided by the GCF (4) is \(x\).
- \(16\) divided by the GCF (4) is \(4\).
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What is the slope of the line that passes through the points (-9, 10)(−9,10) and (21, 15) ?(21,15)?
Answer:
1/6 or 1.666667
Step-by-step explanation:
(y2-y1)/(x2-x1)
(15-10)/(21- -9) = 1/6
Answer:
1/6
Step-by-step explanation:
How many flowers, spaced every 4 inches, are needed to surround a circular garden with a 200 inch radius?
Find the distance around the circle ( circumference)
Circumference = 2 x PI x r
Circumference = 2 x 3.14 x 200
Circumference = 1256 inches.
Divide circumference by spacing:
1256 / 4 = 314
You can plant 314 flowers.
Katie has to drive 15 miles east and 36 miles north to get to her aunt's house. What is the direct distance to her aunt's house?
Answer:
39 miles
Step-by-step explanation:
The given distances are at right angles to each other, so form the legs of a right triangle whose hypotenuse is the straight-line distance of interest. The Pythagorean theorem can be used to find the length of the hypotenuse.
__
Your familiarity with Pythagorean triples lets you recognize the ratio of the distances, 15/36 = 5/12, means the triangle of interest is a multiple of the (5, 12, 13) Pythagorean triple. The multiplier is 3, so ...
the direct distance to her aunt's house is 39 miles.
__
Additional comment
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides:
c² = a² +b²
c = √(15² +36²) = √1521 = 39 . . . . hypotenuse for legs 15 and 36
__
Some Pythagorean triples you will run across in algebra, geometry, and trig problems are ...
(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41)
As here, you will also see multiples of these.
The seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7. What is the common difference of the arithmetic sequence?
The common difference is ______
Use the explicit formula to find a1.
a1 = _______
What is the explicit formula for the arithmetic sequence?
A: an = 1.2 + (n - 1)1.5
B: an = 1.5 + (n – 1)1.2
C: an = 1.5 + (n – 1)3.9
D: an = 3.9 + (n – 1)1.5
ANSWERS: 1.5, 1.2, A: an = 1.2 + (n – 1)1.5
Answer:
The common difference is 1.5
Use the explicit formula to find a1.
a1 = 1.2
What is the explicit formula for the arithmetic sequence?
= 1.2 + (n - 1)1.5
Step-by-step explanation:
Final answer:
The common difference of the arithmetic sequence is 1.5, and the first term is 1.2. The explicit formula for the arithmetic sequence is A: an = 1.2 + (n - 1)1.5.
Explanation:
To find the common difference of an arithmetic sequence, we can use the information that the seventh term (a7) is 10.2 and the twelfth term (a12) is 17.7. The formula for the nth term of an arithmetic sequence is an = a1 + (n - 1)d, where a1 is the first term and d is the common difference. By creating a system of equations using the given terms, we can solve for d.
For the seventh term: 10.2 = a1 + 6d
For the twelfth term: 17.7 = a1 + 11d
Subtracting the first equation from the second gives: 17.7 - 10.2 = 5d, which simplifies to 7.5 = 5d or d = 1.5.
We can then plug the value of d back into one of the equations to find a1:
10.2 = a1 + 6(1.5)
10.2 = a1 + 9
a1 = 1.2
Therefore, the explicit formula for this arithmetic sequence is A: an = 1.2 + (n - 1)1.5.
cuanto es 7x8-(31-61)
Answer:
la respuesta es 86
Step-by-step explanation:
What is the seventh term of the geometric sequence with a first term of 729 and a common ratio of ?
Given:
Given that the first term of the geometric sequence is 729.
The common ratio is [tex]\frac{1}{3}[/tex]
We need to determine the seventh term of the sequence.
Seventh term:
The seventh term of the sequence can be determined using the formula,
[tex]a_n=a_1(r)^{n-1}[/tex]
To find the seventh term, let us substitute n = 7 in the above formula, we get;
[tex]a_7=a_1(r)^{6}[/tex]
Now, substituting [tex]a_1= 729[/tex] and [tex]r=\frac{1}{3}[/tex], we get;
[tex]a_7=729(\frac{1}{3})^{6}[/tex]
[tex]a_7=729(\frac{1}{729})[/tex]
[tex]a_7=1[/tex]
Thus, the seventh term of the geometric sequence is 1.
what is the solution to the inequality -3x-42>3
Answer:
X<-15
Step-by-step explanation:
-3x-42>3 collect like terms
-3x>3+42
-3x>45 divide both side by -3
X<-15
Hint ; when you divide both side by a negative sign, the sign changes.
Answer:
Just here for the points also it -135
Step-by-step explanation:
What is 0.21 written as a percentage
Answer:
21 percent
Step-by-step explanation:
Because 0.21 times 100 gives 21 percent
Answer:
21%
Step-by-step explanation:
to change a decimal to a percentage you multiply it by 100 which 0.21 x 100 which will give 21%
Type the expression that results from the following series of steps: Start with x , add 3 , then times by 6
Answer:
6(x + 3), or expanded: 6x + 18
Step-by-step explanation:
We start with x.
"Add 3" means + 3, so we have: x + 3
"Then times by 6" means multiply by 6, or * 6, so we have 6 * (x + 3)
Thus the expression is 6(x + 3), or expanded: 6x + 18
Hope this helps!
Answer:
6(x + 3)
Step-by-step explanation:
Add 3:
x + 3
Times 6:
6(x + 3)
Holly has $462 in her bank account and takes out $15 each week but does not put any back in. Write an equation/expression to represent the amount of money she has in her bank account.
Answer:
Therefore required expression is
y =462 - t×15
where y represents the amount of money in her bank account in dollar after t week.
Step-by-step explanation:
Given that,
Holly has $462 in her bank account and takes out $15 each week but does not put any back in.
She takes out $15 on first week.
The remaining amount of her bank account is =$(462-15)
=$(462 - 1×15)
If she withdraws $15 on second week.
The remaining amount of her bank account is =$(462-15-15)
=$(462 - 2×15)
Similarly after third the amount in her account is =$(462 - 3×15)
From the above it is cleared that
The amount in her account after t week is
=$(462 - t×15)
Therefore required expression is
y =462 - t×15
where y represents the amount of money in her bank account in dollar after t week.
Ashton and Kamir are arguing about how a number trick they heard goes. Ashton tells Andrew to think of a number, multiply it by five and subtract three from the result. Kamir tells Andrew to think of a number, add five and multiply the result by three. Andrew says that whichever way he does the trick he gets the same answer. What was the number?key
Answer: The number was 9.
Step-by-step explanation:
Let the number be 'x;.
think of a number, multiply it by five and subtract three from the result :
According to Ashton, the expression would be :
[tex]5x-3[/tex]
Kamir tells Andrew to think of a number, add five and multiply the result by three:
According to Kamir, the expression would be :
[tex]3(x+5)[/tex]
At last, they get the same number :
[tex]5x-3=3(x+5)\\\\5x-3=3x+15\\\\5x-3x=15+3\\\\2x=18\\\\x=\dfrac{18}{2}\\\\x=9[/tex]
Hence, the number was 9.
By comparing Ashton's algebraic expression '5x-3' with Kamir's expression '3(x+5)', one can find that if these expressions are equal, the number x that Andrew was thinking of is 15.
Explanation:The subject of this question is Mathematics and it is suitable for a Middle School grade level. The trick that Ashton and Kamir are trying to figure out is based on one of the basic properties of numbers. Andrew says that regardless of the trick, he gets the same answer. This implies that the operations used in both tricks must have equivalent results. Let's use algebraic expressions to represent the steps in each trick. If the original number Andrew thinks of is x:
According to Andrew, these expressions are equal. So, we have the equation:
5x - 3 = 3(x + 5)
By solving this equation, you can find the original number that Andrew was thinking about, which is 15.
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3(2x - 1) =
1
2
(4x - 2) + 2
Answer:
x=1
Step-by-step explanation:
HOPE I HELPEDPLZZ MARK AS BRAINLIEST !!!A school is trying to schedule Prayers of chemistry and algebra two. They find that a total of 386,000 are taking either one or both of the two courses. 209 students signed up for algebra two and 300 need to have signed up for chemistry , what would be the probability that a student chosen at random from the 386 will be signed up for both of the courses? Ronja answer to the nearest whole number percent
Answer: 32%
Step-by-step explanation:
The total number of students that signed up for chemistry and algebra
two is 386.
Let x represent the number of students that signed up for both chemistry and algebra two
If 209 students signed up for algebra two, then the number of students that signed up for algebra two only is
209 - x
If 300 need to have signed up for chemistry, then the number of students that need to have signed up for chemistry only is 300 - x
Therefore,
x + 209 - x + 300 - x = 386
- x + 509 = 386
x = 509 - 386
x = 123
If 123 students would be signed up for both courses, then the probability that a student chosen at random from the 386 will be signed up for both of the courses is
123/386 × 100 = 32%
Use The Interactive tool to determine if the two triangles are congruent. Then, select the true statement.
Answer:
it would be the first answer I think. not very sure
What is the distance, to the nearest hundredth, from (6, 5) to (−3, −8)?
Answer:
15.81
Step-by-step explanation:
Use the distance formula:
So the distance formula for two given points is
Distance= sqrt((x2-x1)^2 +(y2-y1)^2 ) =sqrt((-3-6)^2 +(-8-5)^2 )
=sqrt((-9)^2 +(-13)^2 )
=sqrt(81+169)
=sqrt(250)
=15.81
Hope this helped
:)
A plane flies from NY to Chicago, which is about 700 miles, at a speed of 330 mph. How long does the flight take? On a return trip, a tailwind (x) helps the plane move faster. (The plane still operates to produce a basic speed of 330 mph. The total flying time for the round trip is 3.7 hours so how fast is the tailwind?
The flight from NY to Chicago took roughly 2.12 hours, while the return flight took about 1.58 hours due to a tailwind. By using these times to calculate the speeds of the flights, we find that the tailwind was 113.04 mph.
Explanation:The flight time from NY to Chicago can be calculated by dividing the distance (700 miles) by the speed of the plane (330 mph). The result is about 2.12 hours. The total flight time for the round trip is given as 3.7 hours, so the return trip took about 1.58 hours. Divide 700 miles by 1.58 hours and we get a total speed of about 443.04 mph for the return trip. This speed includes both the speed of the plane (330 mph) and the speed of the tailwind (x). Therefore, to find the speed of the tailwind, subtract the speed of the plane from the total speed: 443.04 mph - 330 mph = 113.04 mph. So, the tailwind is 113.04 mph.
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The tailwind speed is found to be approximately 113.04 mph.
Let's find out the time it takes for the initial flight from NY to Chicago.
Distance from NY to Chicago: 700 milesSpeed of the plane: 330 mphTime = Distance / Speed = 700 miles / 330 mph ≈ 2.12 hoursNow, for the return trip, let the tailwind speed be denoted as x.
Speed of the plane with tailwind = 330 + x mphTotal flying time for the round trip: 3.7 hoursLet time for the return trip be t hours. Then, we have:
Time for round trip: 2.12 hours (to Chicago) + t hours (returning)So, t = 3.7 - 2.12 = 1.58 hoursTherefore, the equation for the return trip will be:
700 miles / (330 + x) = 1.58 hoursSolving for x:
330 + x = 700 miles / 1.58 hours ≈ 443.04 mphx ≈ 443.04 - 330 = 113.04 mph
The speed of the tailwind is approximately 113.04 mph.
Consider the matrix show below:
(See picture)
Which matrix below represents Nt?
Answer:
The Answer is B
Step-by-step explanation:
Put the equation into desmos.com/matrix
it is a 2 row, 2 column matrix, hit Enter
Next line, press the letter A, then press the A^t button and it will give you the answer.
The transpose of matrix N is represented by b. [7 0 3 -2 ] , which correctly reflects the switching of rows and columns in the original matrix.
The correct answer is option B.
To find the transpose ([tex]N^t[/tex]) of a matrix N, we need to switch its rows and columns. Let's calculate the transpose of the given matrix N:
Matrix N:
```
N = [ 7 3 ]
[ 0 -2 ]
```
Transpose of N ([tex]N^t[/tex]):
```
[tex]N^t[/tex]= [ 7 0 ]
[ 3 -2 ]
```
So, the transpose of matrix N is:
```
[tex]N^t[/tex] = [ 7 0 ]
[ 3 -2 ]
```
Now, let's compare the transpose we calculated with the options provided:
a. [ 0 -2 7 3 ] - This is not the transpose of N.
b. [7 0 3 -2 ] - This is the transpose of N.
c. [3 7 -2 0 ] - This is not the transpose of N.
d. [-2 3 0 7] - This is not the transpose of N.
So, the correct answer is option b:
```
[tex]N^t[/tex] = [7 0 3 -2 ]
```
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The number of carbon atoms in a fossil is given by the function y= 5100(0.95)^x where x represents the number of years since being discovered what is the percent change each year? Explain your answer.
The function y = 5100(0.95)^x represents an exponential decay of the number of carbon atoms in a fossil, with a base of 0.95. Therefore, the percent change each year is -5%, reflecting a decrease, consistent with the decay of carbon-14.
Explanation:The function y = 5100(0.95)^x represents an exponential decay, with 0.95 being the base of the exponent. This base number, when subtracted from 1 and multiplied by 100, gives the percent change each year for the number of carbon atoms in the fossil.
Using this method, we find: (1-0.95)*100 = 5. So the percent change is -5% each year, with the negative sign indicating a decrease. This is consistent with the decay of carbon-14 (C-14) in fossils, a process used in carbon dating to estimate the age of the fossil.
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A multiple choice test is composed of 10 questions. Each question has four possible answers, only one of the four possible answers is correct. A student randomly selects the answer for each question. Assume that all selections are independent. Let X count the student’s number of correct answers on the test. a) What is the expected number of correct answers? Round your answer to the nearest tenth.
Answer:
Let X the random variable of interest "Number of correct anwers on the tet", on this case we now that:
[tex]X \sim Binom(n=10, p=0.25)[/tex]
And the expected value is given by:
[tex] E(X) = np =10*0.25 = 2.5[/tex]
Step-by-step explanation:
Previous concepts
A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Solution to the problem
Let X the random variable of interest "Number of correct anwers on the tet", on this case we now that:
[tex]X \sim Binom(n=10, p=0.25)[/tex]
And the expected value is given by:
[tex] E(X) = np =10*0.25 = 2.5[/tex]
the difference of two numbers is 15. five times the smaller number is the same as 9 less than twice the larger number. find the numbers
Answer:
your 2 numbers are going to be 7 and 22
11 + (3)(9) Step 1: 11 + (9)(3) Step 2: (11 + 9)(3) Step 3: 20(3) Step 4: 60 Analyze the work to find the error.
Answer:
Step 2 is where this person went wrong
Step-by-step explanation:
Should be
11 + (9)(3)= x
11 + 27= x
x = 38
Answer:
Step 2 is where the error started. You can see the person did the order of operations wrong. The person was supposed to multiple (9)(3) first because of PEMDAS; (9)(3)=27 and then you add the 27 to 11 and get 38
Step-by-step explanation:
Kareem sent a chain email to 10 of his friends the number of people who got the email increases by a factor of 1.4 every week
Answer: 10×1.4^6
Step-by-step explanation:
This question is about exponential growth in mathematics.
Explanation:This question is about exponential growth in mathematics. The number of people who received the email increases by a factor of 1.4 every week.
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---------- is a measure of amount of work that can be done in a given amount of time or in other way rate or doing work
Answer:
Power
Step-by-step explanation:
Term Definition
power: Measure of the amount of work that can be done in a given amount of time.
Answer:
Power
Step-by-step explanation:
power, measure of the amount of work that can be done in a given amount of time.
I hope this helps :)
P = 9r +3q
Work out the value of P when r = 6 and q = -4
P =
Answer:
p= 9(6)+3(-4)
p= 42
hope this help
Answer:
42
Step-by-step explanation:
P=9r+3q
When q equals to a negative 4 and when r is aswell the number 6.It means to substitute
P=9(6)+3(-4)
p=54-12
p=42
Find the quotient of 24 and 0
Answer:
it is either zero or infinity
Step-by-step explanation:
The 2003 Statistical Abstract of the United States reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and non smokers uses a preliminary estimate of the proportion who smoke of .30.a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of.02? use 95% confidence.b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population?c. What is the 95% confidence interval for the proportion of smokers in the population?
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
a) From the information given,
Margin of error = 0.02
p = 0.3
q = 1 - 0.3 = 0.7
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.5 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Therefore,
0.02 = 1.96 × √(0.3 × 0.7)/n
0.02/1.96 = √0.21/n
0.0102 = √0.21/n
Taking square of both sides, it becomes
0.00010404 = 0.21/n
n = 0.21/0.00010404
n = 2018
Sample size = 2018
b) if n = 2018
x = 520
Then
p = 520/2018 = 0.26
Point estimate of the proportion of smokers in the population is 0.26
c) q = 1 - 0.26 = 0.74
the 95% confidence interval for the proportion of smokers in the population is
0.26 ± 1.96 × √(0.26)(0.74)/2018
= 0.26 ± 0.019
Answer:
a) n = 2017
b) Point estimate is 0.2578
c) 95% Confidence Interval is Minimum = 0.2387, Maximum 0.2769
Step-by-step explanation:
Here we have
At 95%, we have
[tex]z_{\alpha /2}[/tex] = 1.96
To determine sample size, we have
[tex]n = \frac{(z_{\alpha /2})^2 \hat p \hat q}{E^2}[/tex]
Where:
[tex]\hat p[/tex] = 0.3
[tex]\hat q[/tex] = [tex]1-\hat p[/tex] = 0.7
E = 0.02
Therefore, n = 2016.84 ≈2017
b) The point estimate is given by
[tex]\hat p =\frac{x}{n} = \frac{520}{2017}[/tex] = 0.2578
c) The confidence interval is given by;
[tex]CI=\hat{p}\pm z\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Which gives
[tex]CI=0.2578\pm 1.96\times \sqrt{\frac{0.2578(1-0.2578)}{2017}}[/tex]
Hence CI = Min = 0.2387 to Max = 0.2769
The circumference of a circle is 16 ft.
what is the radius?
.
Answer:
The answer is 8. And for the love of God people if you don't know the answer don't waste an answer space just for the points. It makes everyone mad. Stop. Just cut it out.
Step-by-step explanation:
Home CoworkHelper
A
A cylinder has a volume of 10 m' What might its dimensions be (height, area of base, radius, and
diameter)? Give 4 possible cylinders.
Volume 10 m
Height
Area of Base
Radius
Diameter
Cylinder A
Cylinder B
Cylinder
Cylinder D
How do you know your answers are reasonable?
How many possibilities are there? Why do you think so?
B. A cylinder has a diameter of 10 cm. What might its volume be? Give the radius, area of base and
height for 4 possible volumes
Diameter 10 cm
Radius
Area of Base
Height
Volume
Cylinder A
Cylinder B
Cylinder
Cylinder D
How do you know your answers are reasonable?
Answer:
See below.
Step-by-step explanation:
PROBLEM A
The formula for the volume of a cylinder is
V = πr²h, where πr² is the area of the base.
V = area of base x height
Choose any four numbers that are less than 10 for the height.Then, substitute into the formula and isolate "r". 10 = πr²hDouble "r" to find the diameter.The area of the base is found (bolded) while you solve πr².*I will use the calculator button for pi (π)
Cylinder A: h = 1
10 = πr²h
10 = πr²(1)
10 = πr² Area of the base is 10m².
r = √ (10/π)
r = 1.78 Radius is 1.78m.
d = 2r = 1.78*2 = 3.56 Diameter is 3.56m.
Cylinder B: h = 2
10 = πr²h
10 = πr²(2)
5 = πr² Area of the base is 5m².
r = √ (5/π)
r = 1.26 Radius is 1.26m.
d = 2r = 1.26*2 = 2.52 Diameter is 2.52m.
Cylinder C: h = 4
10 = πr²h
10 = πr²(4)
2.5 = πr² Area of the base is 2.5m².
r = √ (2.5/π)
r = 0.89 Radius is 0.89m.
d = 2r = 0.89*2 = 1.78 Diameter is 1.78m.
Cylinder D: h = 5
10 = πr²h
10 = πr²(5)
2 = πr² Area of the base is 2m².
r = √ (2/π)
r = 0.80 Radius is 0.8m.
d = 2r = 0.80*2 = 1.6 Diameter is 1.6m.
The answers are reasonable if the answer is close to 10 when you substitute the rounded numbers back into the formula and solve.
There are infinite possibilities because any numbers when used in the formula equates to 10 are possible. The height/radius can be any decimal number, which would make the other dimensions change.
PROBLEM B
Follow similar steps if you know the diameter of a cylinder. Use the same formula V = πr²h.
We need the radius, which is half the diameter. r = d/2 = 10/2 = 5
Choose a random number for volume that divides easily by 25.Substitute "V" and "r²" (r² = 25).Isolate "h".The area of the base is 78.54 cm² every time (A = πr²).Cylinder A: V = 100
100 = π25h
4 = πh
h = 1.27 The height is 1.27m.
Cylinder B: V = 200
200 = π25h
8 = πh
h = 2.55 The height is 2.55m.
Cylinder C: V = 75
75 = π25h
3 = πh
h = 0.95 The height is 0.95m.
Cylinder D: V = 125
125 = π25h
5 = πh
h = 1.59 The height is 1.59m.
The answers are reasonable if I can substitute two rounded values into the formula and get a number close to the third. The height is also a decimal number which occurs because of pi.