Answer:
Step-by-step explanation:
The question is incomplete. The complete question is
Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without paying for coaching also usually raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics:
Try 1 Try 2 Gain
n x s x s x s
Coached 427 500 92 529 97 29 59
Uncoached 2733 506 101 527 101 21 52
Use Table C to estimate a 90% confidence interval for the mean gain of all students who are coached.
at 90% confidence.
Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let μ1 be the score gain for all coached students. Let μ2 be the score gain for uncoached students.
(a) Give the alternative hypothesis:
μ1 - μ2.
(b) Give the t test statistic:
(c) Give the appropriate critical value for \alpha =5%:
Solution:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean score gain for all coached students
x2 = sample mean score gain for all uncoached students
s1 = sample standard deviation score gain of coached students
s2 = sample standard deviation score gain of uncoached students
For a 90% confidence interval, the z score is 1.645
From the information given,
x1 = 29
s1 = 59
n1 = 427
x2 = 21
s2 = 52
n2 = 2733
x1 - x2 = 29 - 21 = 8
z√(s1²/n1 + s2²/n2) = 1.645√(59²/427 + 52²/2733) = 4.97
90% Confidence interval = 8 ± 4.97
a) The population standard deviations are not known. it is a two-tailed test. The random variable is μ1 - μ2 = difference in the score gain for coached and uncoached students.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 > μ2 H1 : μ1 - μ2 > 0
This is a right tailed test.
b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (29 - 21)/√(59²/427 + 52²/2733)
t = 2.65
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [59²/427 + 52²/2733]²/[(1/427 - 1)(59²/427)² + (1/2733 - 1)(52²/2733)²] = 9.14/0.1564
df = 58
c) from the t distribution table, the critical value is 1.67
In order to reject the null hypothesis, the test statistic must be smaller than - 1.67 or greater than 1.67
Since - 2.65 < - 1.67 and 2.65 < 1.67, we would reject the null hypothesis.
Therefore, at 5% significance level, we can conclude that the score gain for coached students is greater than the score gain for uncoached students.
how does one convert meters to hectares?
Step-by-step explanation:
Meters measures length, hectares measures area.
1 hectare = 10,000 m²
Answer Meters measures length, hectares measures area.
1 hectare = 10,000 m²
Step-by-step explanation:
The marked price of a water cooler is $ 500. The shopkeeper offers an off-season discount of 15% on it. Find the discount.
Answer:
75 dollars
Step-by-step explanation:
You know that 500=100%, so we can set up the following
15%(500/100%) = 75
so the discount 75 dollars
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. -4<x<2
Step-by-step explanation:
The highest x point is -4 and lowest peak is 2
Answer:
B. -4 ≤ x ≤ 2
Step-by-step explanation:
→Basically, the question is asking, "At what point is the line on the graph decreasing?"
→Looking at the graph, you can see that when x = -4, that's when the line on the graph starts to decrease. The line continues to decrease, until it reaches the point where x = 2.
This makes the correct answer "B. -4 ≤ x ≤ 2."
Mrs. DeMarco wants to estimate the length of her porch so she knows how much paint to buy. What is the best benchmark for her to use? *
Answer:
Without any multiple choice options i would have to guess square feet.
Step-by-step explanation:
Construct an equation that has n = 8 as its solution. Use n on both sides of the equation
Answer:
8n-25=15+3n
Step-by-step explanation:
We can do this by working backwards and making suitable substitutions.
If n=8
Multiply both sides of the equation by 5
5n=8*5
5n=40
Now, we can rewrite the two sides of the equation as follows
5n=8n-3n40=25+15Thus:
5n=40 is equivalent to:
8n-3n=25+15
Add 3n to both sides
8n-3n+3n=25+15+3n
8n=25+15+3n
Subtract 25 from both sides
8n-25=25-25+15+3n
We have:
8n-25=15+3n
Solving this equation will have a solution of n=8.
What’s the correct answer for this?
Answer:
B
Step-by-step explanation:
JK = LM (equidistant from centre)
3x+19=6x+7
19-7=6x-3x
12 = 3x
Dividing both sides by 3
x = 4
JK = 3(4)+19
JK = 12+19
JK = 31
Answer:
31
Step-by-step explanation:
JK = LM (since they are equidistant from centre)
3x + 19 = 6x + 7
- 3x = - 12
x = 4
JK = 3 * (4) + 19
= 12 + 19
= 31
Hope this helps!
A researcher is interested in attitudes towards releasing prisoners with Alzheimer's who have a life sentence. 85 randomly selected Americans were asked, "Prisoners with Alzheimer's who have a life sentence should be released: Strongly Agree, Agree, Disagree, Strongly Disagree". Match the vocabulary word with its corresponding example.
Answer and Step-by-step explanation:
The matching of the vocabulary word with its corresponding example is shown below:-
a. Data - The list of answers that the 85 Americans give.
Data refers the information that is to be collected.
b. Variable - The answer "Strongly Agree" or "Agree" or "Disagree" or "Strongly disagree".
Variable refers the changes of the expression according to the context.
c. Parameter - The proportion of all Americans who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
A parameter is a quantity that affects a mathematical object's production or behavior, but is considered constant
d. Statistics - The proportion of 85 Americans surveyed who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
Statistics is a field of mathematics involved in data collection, organisation and analysis.
e. Sample - The 85 Americans who participated in the survey.
A sample is the result of an experiment on randomly.
f. Population - All Americans
Population refers to the number of the public.
Answer:
a. Data - The list of answers that the 85 Americans give.
Data refers the information that is to be collected.
b. Variable - The answer "Strongly Agree" or "Agree" or "Disagree" or "Strongly disagree".
Variable refers the changes of the expression according to the context.
c. Parameter - The proportion of all Americans who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
A parameter is a quantity that affects a mathematical object's production or behavior, but is considered constant
d. Statistics - The proportion of 85 Americans surveyed who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
Statistics is a field of mathematics involved in data collection, organisation and analysis.
e. Sample - The 85 Americans who participated in the survey.
A sample is the result of an experiment on randomly.
f. Population - All Americans
Population refers to the number of the public.
Step-by-step explanation:
Could someone please give me the answer to this?
Answer:
? = 8.77
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opposite/ hypotenuse
sin 20 = 3/?
? = 3 / sin 20
? =8.7714132
To the nearest hundredth
? = 8.77
We can use the trigonometric function [ sin theta = opposite/hypotenuse ] to solve.
sin(20) = 3/hypotenuse
hypotenuse = 3/sin(20)
hypotenuse = 8.7714...
Round to the nearest hundredth.
8.7714... → 8.77
Therefore, the answer is 8.77
Best of Luck!
On average, 28 percent of 18 to 34 year olds check their social media profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a random variable X, which has a standard deviation of five percent. Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32. Round your answer to four decimal places.
Answer:
0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 28, \sigma = 5[/tex]
Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.
This is the pvalue of Z when X = 32. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32 - 28}{5}[/tex]
[tex]Z = 0.8[/tex]
[tex]Z = 0.8[/tex] has a pvalue of 0.7881
0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.
What is 576 times 36?
A bacteria population is initially 320. After 45 minutes, they've grown in number to 700. What is the doubling time for this population? Round to the nearest second. answer choices 39 minutes 41 seconds 39 minutes 31 seconds 39 minutes 21 seconds 39 minutes 51 seconds
Answer: 39 minutes 51 seconds
Step-by-step explanation:
Nt=N0 * 2^n
N0=Initial population
n=number of times bacteria divide
700=320*2^n
log2(700/320)=1.129283017=n
45/1.129283017=39.84829252 minutes
0.84829252*60=50.89755135≈51seconds
so the answer is
39minutes and 51seconds
Hurry please !!!
The graph of g(x) is a translation of y = V.
Which equation represents g(x)?
ly
g(x) = - 4
5
4
g(x) = 3/X+4
3
27
900)
O g(x) = 5x +1.5
1
g(x) = -1.5
-10 -3 -6 -21
2
6
810
X
Answer:
The translation corresponds to : [tex]g(x)=\sqrt[3]{x-4}[/tex]
which is the first option in your list of possible answers
Step-by-step explanation:
Notice that this new function's graph responds to a horizontal translation to the right of the original graph of [tex]f(x)=\sqrt[3]{x}[/tex]. Notice that the crossing of the x-axis, which for f(x) is at the origin (0, 0), has now moved to the point (4,0), which means a translation to the right in exactly 4 units.
Recall that horizontal translations are performed by subtracting from the independent variable (x) , the number of units you move (in this case 4)
Therefore the new function should look like:
[tex]g(x)=\sqrt[3]{x-4}[/tex]
The answer is A.
did the test
Find the volume of a come with the radius of 80 and the height of 21. Please show step by step
Answer:
= 140800 cubic (ft/meters/yards/cm/inches)
Step-by-step explanation:
For Cone
radius (r) = 80
height (h) = 21
Volume Of Cone
= π r² h/3
= 22/7 x 80 x 80 x 21/3
= 22 x 80 x 80
= 22 x 6400
= 11 x 12800
= 140800 cubic (ft/meters/yards/cm/inches)
Find the roots of the quadratic equation 3y² - 4y+1=0 By
i) completing the square method
ii) the formula
Answer:
i) [tex] 3y^2 -4y +1=0[/tex]
We can divide both sides of the equation by 3 and we got:
[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]
Now we can complete the square and we got:
[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]
[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]
We take square root on both sides and we got:
[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]
And the solutions for y are:
[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]
[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]
ii) [tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
And with [tex] a = 3, b=-4 and c =1[/tex] we got:
[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]
And we got:
[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]
Step-by-step explanation:
Part i
For this case we have the following function given:
[tex] 3y^2 -4y +1=0[/tex]
We can divide both sides of the equation by 3 and we got:
[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]
Now we can complete the square and we got:
[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]
[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]
We take square root on both sides and we got:
[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]
And the solutions for y are:
[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]
[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]
Part ii
We can use the quadratic formula:
[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
And with [tex] a = 3, b=-4 and c =1[/tex] we got:
[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]
And we got:
[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]
What is the domain of the function Begin equation . . . y equals . . . the square root of the quantity x minus ten . . . end equation?
Answer:
Domain: [10, ∞)
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
Step 1: Write equation
f(x) = √(x - 10)
We know that if we get negatives under the square root, we would get imaginary numbers.
Our domain to include all x-values would have to be bigger than 10:
f(10) = √(10 - 10) = √0 = 0
If the number is smaller than 10, we get: f(9) = √(9 - 10) = √-1 = i
Therefore, our real numbers domain would be [10, ∞) or x ≥ 10.
1. A random sample of 64 customers at a drive-through bank window is observed, and it is found that the teller spends an average of 2.8 minutes with each customer, with a standard deviation of 1.2 minutes. Is there sufficient evidence to conclude that the teller spends less than 3 minutes with each customer slader
Answer:
[tex]t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33[/tex]
The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{63}<-1.33)=0.0942[/tex]
If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis
Step-by-step explanation:
Information given
[tex]\bar X=2.8[/tex] represent the sample mean
[tex]s=1.2[/tex] represent the standard deviation
[tex]n=64[/tex] sample size
[tex]\mu_o =3[/tex] represent the value to verify
[tex]\alpha[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to check if the true mean for this case is less than 3 minutes, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 3[/tex]
Alternative hypothesis:[tex]\mu < 3[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33[/tex]
The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{63}<-1.33)=0.0942[/tex]
If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis
What is the circumference of the circle diameter 33 cm
Answer:
≈103.67cm
Step-by-step explanation:
Shape: Circle
Solved for circumference
Diameter: 33cm
Formula: C=πd
Answer: ≈103.67cm
Hope this helps.
Answer:
C = 33 pi
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
C = 33 pi
We can approximate pi by 3.14
C = 33*3.14 =103.62
or by using the pi button
C =103.6725576
(8x^3 + x^2 - 5) / (x-6)
Answer:
the answer is 8x^2+49x+294+1759/x-6
Samir is an expert marksman. When he takes aim at a particular target on the shooting range, there is a 0.950.950, point, 95 probability that he will hit it. One day, Samir decides to attempt to hit 101010 such targets in a row.
Assuming that Samir is equally likely to hit each of the 101010 targets, what is the probability that he will miss at least one of them?
Round your answer to the nearest tenth.
Answer:
40.1% probability that he will miss at least one of them
Step-by-step explanation:
For each target, there are only two possible outcomes. Either he hits it, or he does not. The probability of hitting a target is independent of other targets. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
0.95 probaiblity of hitting a target
This means that [tex]p = 0.95[/tex]
10 targets
This means that [tex]n = 10[/tex]
What is the probability that he will miss at least one of them?
Either he hits all the targets, or he misses at least one of them. The sum of the probabilities of these events is decimal 1. So
[tex]P(X = 10) + P(X < 10) = 1[/tex]
We want P(X < 10). So
[tex]P(X < 10) = 1 - P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987[/tex]
[tex]P(X < 10) = 1 - P(X = 10) = 1 - 0.5987 = 0.401[/tex]
40.1% probability that he will miss at least one of them
Is the sequence arithmetic? (Yes or no) If yes, please also give its common difference. 14) -2.8, -2.2, -1.6, -1.0
Answer:
Yes
The common difference is .6
Step-by-step explanation:
Take the second term and subtract the first term
-2.2 - (-2.8)
-2.2+ 2.8 = .6
Take the third term and subtract the second
-1.6 - (-2.2)
1.6 +2.2
The common difference is .6
Answer:
Yes
Step-by-step explanation:
-2.8, -2.2, -1.6, -1.0
-2.2-(-2.8)= -1.6 - (-2.2)= -1 - (-1.6)= 0.6
This is AP with first term -2.8 and common difference 0.6
The triangle shown below has an area of 16 units2.
Find z.
4
2
units
Answer:
8 units
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
16 = 1/2 (4)*x
16 = 2x
Divide each side by 2
16/2 = 2x/2
8 =x
Bramble’s standard quantities for 1 unit of product include 2 pounds of materials and 2.5 labor hours. The standard rates are $6 per pound and $11 per hour. The standard overhead rate is $12 per direct labor hour. The total standard cost of Bramble’s product is
Answer:
The standard cost of Bramble's product is $69.5 per unit.
Step-by-step explanation:
We can calculate the standard cost per unit of Bramble's product as the sum of the material cost, direct labor cost and overhead cost.
Each unit of product uses 2 pounds of materials, that cost $6 per pound. So the material cost is:
[tex]MC=2\,lb/u\cdot6\,\$/lb=12\,\$/u[/tex]
Each unit needs 2.5 direct labor hours, and they have a cost of $11 per hour, so the direct labor cost is:
[tex]LC=2.5\,h/u\cdot11\,\$/h=27.5\,\$/u[/tex]
The overhead costs are calculated in this case as $12 per direct labor hour. As 2.5 labor hours are needed per unit, we have:
[tex]OC=2.5\,h/u\cdot 12\,\$/h=30\,\$/u[/tex]
The standard cost is then:
[tex]C=MC+LC+OC=12+27.5+30=69.5\,\$/u[/tex]
Tammy rents a storage shed. The storage shed is in the shape of a rectangular prism with measurements
as shown
9 feet
9 feet
10 feet
Select the phrase and number from the drop-down menus to correctly complete each sentence
Tammy can find the volume of the storage unit by
Choose
To completely fill the storage shed, Tammy would need
choose
unit boxes that each
measure 1 cubic foot
9514 1404 393
Answer:
B, D
Step-by-step explanation:
The volume is the product of the dimensions. For dimensions 9 ft, 9 ft, 10 ft, the volume is found by multiplying (9 ft) × (9 ft) × (10 ft) = 810 ft³.
To fill the volume with boxes of volume 1 ft³ would require 810 boxes.
Please help me.
Solve for x in the diagram below:
Answer:
x = 40
Step-by-step explanation:
The angles are vertical angles. We know that vertical angles are equal
120 = 3x
Divide each side by 3
120/3 = 3x/3
40 =x
Answer:
40
Step-by-step explanation:
I forgot what you would call this, but basically 3x = 120. both of the angles are the same. So divide both sides of the equation by 3. 3x/3 = 120/3 and your answer is 40.
It's a bad explanation but I hope it helps!
Given the point (4,5) and the slope of 6 find y when x=24
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
What is the value of y?
Answer:
[tex] \boxed{D. \: 40\degree} [/tex]
Step-by-step explanation:
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°
So,
[tex] = > 2y \degree + (y + 10)\degree + 50\degree = 180\degree \\ \\ = > 2y\degree + y\degree + 10\degree + 50\degree = 180\degree \\ \\ = > 3y\degree + 60\degree = 180\degree \\ \\ = > 3y\degree = 180\degree - 60\degree \\ \\ = > 3y\degree = 120\degree \\ \\ = > y = \frac{120\degree}{3\degree} \\ \\ = > y = 40\degree [/tex]
Subtract the fractions and reduce to lowest terms: 89-6 2/3
Answer:
82 1/3
Step-by-step explanation:
89 - 6 2/3
Borrow 1 from the 89 in the form of 3/3
88 + 3/3 - 6 2/3
88 3/3 - 6 2/3
Subtract the whole numbers
88-6 =82
Subtract the fractions
3/3 - 2/3 = 1/3
82 1/3
A pair of dice was rolled many times
and the results appear below. Based
upon these results, what is the
experimental probability of rolling a
multiple of 3?
7
8
9
10 11 12
Outcome 23
35 6
Frequency 3 6 8 11 14
16
15
12
9
5 1
Answer:
6%
Step-by-step explanation:
Out of 100 rolls, there were 6 instances of 3. The experimental probability of rolling a 3 is ...
6/100 = 6%
PLEASE HELP ME!!! f(x) = x2. What is g(x)?
Answer:
g(x)=3x^2
Step-by-step explanation:
A cone with radius 5 and height 12 has its radius doubled. How many times greater is the volume of the larger cone than the smaller cone? Use a pencil and paper. Explain how the volume of the cone would change if the radius were halved.
Answer:
[tex] V = \frac{1}{3} \pi (5)^2 (12)= 314.159[/tex]
Now if we increase the radius by a factor of 2 the new volume would be:
[tex] V_f = \frac{1}{3} \pi (2*5)^2 (12)= 1256.637[/tex]
And we can find the increase factor for the volume like this:
[tex] \frac{V_f}{V}= \frac{1256.637}{314.159}= 4[/tex]
Then if we increase the radius by 2 the volume increase by a factor of 4
If we reduce the radius by a factor of 2 then we will have that the volume would be reduced by a factor of 4.
On the figure attached we have an illustration for the cases analyzed we see that when we increase the radius the volume increase and in the other case decrease.
Step-by-step explanation:
For this case we have the following info given:
[tex]r = 5 , h =12[/tex]
and we can find the initial volume:
[tex] V = \frac{1}{3} \pi r^2 h[/tex]
And replacing we got:
[tex] V = \frac{1}{3} \pi (5)^2 (12)= 314.159[/tex]
Now if we increase the radius by a factor of 2 the new volume would be:
[tex] V_f = \frac{1}{3} \pi (2*5)^2 (12)= 1256.637[/tex]
And we can find the increase factor for the volume like this:
[tex] \frac{V_f}{V}= \frac{1256.637}{314.159}= 4[/tex]
Then if we increase the radius by 2 the volume increase by a factor of 4
If we reduce the radius by a factor of 2 then we will have that the volume would be reduced by a factor of 4.
On the figure attached we have an illustration for the cases analyzed we see that when we increase the radius the volume increase and in the other case decrease.
