To best collect a sample of books from the 13,000 titles at the bookstore, Miguel should use a cluster sampling method.
What is the best sampling method?The best sampling method Miguel should use is a cluster sample.
A cluster sample involves dividing the population into clusters or groups and randomly selecting entire clusters to include in the sample.
In this situation, Miguel could divide the bookstore's titles into clusters, such as by genre or shelf location, and randomly select clusters to sample books from.
his method would help ensure representation from different areas of the bookstore and provide a diverse sample of books.
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A one-sided significance test gives a P-value of .02. From this we can a) Reject the null hypothesis with 97% confidence. b) Reject the null hypothesis with 98% confidence. c) O Say that the probability that the null hypothesis is false is .02. d) Say that the probability that the null hypothesis is true is .02.
A one-sided significance test gives a P-value of .02. From this we can conclude that we can reject the null hypothesis with 98% confidence.
Here’s why: In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic at least as extreme as the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the significance level (α), the null hypothesis can be rejected. Conversely, if the p-value is greater than the significance level, there is insufficient evidence to reject the null hypothesis. Since a one-sided significance test was performed, we are only interested in the probability that the test statistic will fall in one tail of the distribution.
Thus, the p-value is the probability of obtaining a test statistic as extreme as the observed value in one tail of the distribution. If the p-value is .02, this means that there is a 2% chance of obtaining a test statistic as extreme or more extreme than the observed value if the null hypothesis is true. Since the p-value is less than the standard significance level of .05, we can reject the null hypothesis with 98% confidence. This is because we can be 98% confident that the true population parameter falls in the alternative hypothesis range.
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A swimmer swims 2 kilometers every 15 minutes. If he comes to swim at the same rate which graph best represents his swimming speed in kilometers per minute
Answer:
62
Step-by-step explanation:
divide lang yan.piste kasi bat kailangan 20 letters
Answer:
la respuesta es la D
Step-by-step explanation:
la velocidad es constante
Help me please thanks
Answer:
64 square cm
Step-by-step explanation:
(I pulled this out of the comments in case someone else needs this answer. Easier to see as an answer than as comments in the app)
Area 2 is easier, so we’ll start with that one. Area of a rectangle is length x width.
8 x 6 = 48 square cm
Area 1 is a triangle, so the formula is 1/2(base)(height). The height of the triangle is 8, because it’s the same as the base of the rectangle. The base of the triangle is 4, because we can subtract the 6 from the rectangle from the total side length of 10. Does that make sense?
So 1/2 (4)(8)= 1/2(32) = 16 square cm
Then we add 16 + 48 = 64 square cm
Lin opened a savings account that pays 5.25% interest and deposited $5000. If she makes no deposits and no withdrawals for 3 years, how much money will be in her account?
Answer:
$5829.57
Step-by-step explanation:
Annually compounding interest formula: [tex]PV(1+i)^t[/tex]
5000(1+.0525)^3
5829.567266
which rounds to: 5829.57
A company needs to determine the optimum power and time settings for their new licorice-flavored microwaveable popcorn. They want to find a combination of power and time that delivers high-quality popcorn with less than 11% of the kernels left unpopped, on average-a value that their market research says is demanded by their customers. Their research department experiments with several settings and determines that power 9 at 4 minutes is optimum. Their tests confirm that this setting meets the less than 11% requirement. They change the instructions on the box and promote a new money back guarantee of less than 11% unpopped kernels. Complete parts a) and b) below.
a) If, in fact, the setting results in more than 11% kernels unpopped, what kind of error have they made? What will the consequence be for the company? What are the null and alternative hypotheses in this case?
A. H_o: μ< 11 vs. H_A: μ = 11
B. H_o: μ= 11 vs. H_A: μ> 11
C. H_o: μ= 11 vs. H_A: μ< 11
D. H_o: μ> 11 vs. H_A: μ = 11
b) To be sure that the method was successful, the research department popped 8 more bags of popcorn (selected at random) at this setting. All were of high quality, with the percentages of unpopped kernels being 6.7,12.9, 10.6, 7, 7.1, 3.1, 2.0, and 4.8. Does this provide evidence that they met their goal of an average of fewer than 11% unpopped kernels? Assume α=0.05.
c) Find T
d) Find P
A The null and alternative hypotheses in this case are:
Null hypothesis: H_o: μ ≥ 11
Alternative hypothesis: H_A: μ < 11
B We have statistically significant evidence to conclude that the setting results in less than 11% kernels unpopped.
C The t-statistic is -2.94.
d) The p-value is 0.004.
How to explain the informationa) In this case, the company has made a Type I error. This is when the null hypothesis is rejected, even though it is true. In this case, the company would be rejecting the hypothesis that the setting results in less than 11% kernels unpopped, even though it is actually true. The consequence of this would be that the company would be losing money on refunds for popcorn that is not actually defective.
b) In order to answer this question, we need to calculate the t-statistic and the p-value.
The t-statistic is calculated as follows:
t = (x - μ) / (s / √n)
Substituting these values into the formula for the t-statistic, we get:
t = (6.7 - 11) / (3.5 / √8)
= -2.94
The p-value is the probability of obtaining a t-statistic that is at least as extreme as the one we observed, assuming that the null hypothesis is true. In this case, the p-value is 0.004.
c) The t-statistic is -2.94.
d) The p-value is the probability of obtaining a t-statistic that is at least as extreme as the one we observed, assuming that the null hypothesis is true. In this case, the p-value is 0.004.The p-value is 0.004.
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I have a statistic that is normally distributed with a very large sample size. I add a single subject that is way above the median to the sample. What is likely to happen?
Adding a single subject that is way above the median to a sample with a very large sample size is likely to have a minimal impact on the overall distribution and statistics of the sample.
When the sample size is very large and the distribution of the statistic is approximately normal, the Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution, regardless of the underlying population distribution. This means that the sample mean is less sensitive to individual extreme values.
If a single subject is added to the sample that is way above the median, it will have a relatively small effect on the overall sample mean. This is because the impact of a single extreme value diminishes as the sample size increases.
When adding a single subject that is way above the median to a sample with a very large sample size, the effect on the overall distribution and statistics of the sample is expected to be minimal. The large sample size ensures that the sample mean remains robust and less influenced by individual extreme values. Therefore, the addition of a single subject with a very high value is unlikely to significantly alter the characteristics of the sample distribution or the calculated statistics such as the mean or standard deviation.
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Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(2) dac 4+2 with n = 12 SO T12 = ___ M12 = ___ S12 =___. Report answers accurate to 4 places. Remember not to round too early in your calculations.
Using the Trapezoidal Rule with n = 12, the approximation is T12 = -15.6667. Using the Midpoint Rule with n = 12, the approximation is M12 = -92. Using Simpson's Rule with n = 12, the approximation is S12 = -155.7778. So T12 =-15.6667, M12 =-92, S12 = -155.7778.
To approximate the integral using numerical methods, we'll use the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with n = 12.
Using the Trapezoidal Rule, the approximation is given by:
T12 = h/2 * [f(a) + 2(f(x1) + f(x2) + ... + f(x11)) + f(b)]
where h = (b - a)/n and xi represents the equally spaced points between a and b.
Using the Midpoint Rule, the approximation is given by:
M12 = h * [f(x1/2) + f(x3/2) + ... + f(x23/2)]
where xi/2 represents the midpoints between xi-1 and xi.
Using Simpson's Rule, the approximation is given by:
S12 = h/3 * [f(a) + 4(f(x1) + f(x3) + ... + f(x11)) + 2(f(x2) + f(x4) + ... + f(x10)) + f(b)]
Now, let's calculate the approximations:
For T12:
h = (2 - 4)/12 = -1/3
T12 = (-1/3)/2 * [4 + 2(4 + 2 + ... + 4) + 2]
T12 = -1/6 * [4 + 2(4*11) + 2]
T12 = -1/6 * [4 + 88 + 2]
T12 = -1/6 * 94
T12 = -15.6667
For M12:
h = (2 - 4)/12 = -1/3
M12 = (-1/3) * [4 + 4*3 + 4*5 + ... + 4*23]
M12 = -1/3 * [4 + 12 + 20 + ... + 44]
M12 = -1/3 * [4 + 12 + 20 + ... + 44]
M12 = -1/3 * 276
M12 = -92
For S12:
h = (2 - 4)/12 = -1/3
S12 = (-1/3)/3 * [4 + 4*4 + 2(4 + 4*3 + 4*5 + ... + 4*11) + 2(4 + 4*2 + 4*4 + ... + 4*10) + 2]
S12 = (-1/9) * [4 + 16 + 2(4 + 12 + 20 + ... + 44) + 2(4 + 8 + 16 + ... + 40) + 2]
S12 = (-1/9) * [4 + 16 + 2(276) + 2(220) + 2]
S12 = (-1/9) * 1402
S12 = -155.7778
Therefore, the approximations are:
T12 = -15.6667
M12 = -92
S12 = -155.7778
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Jennifer painted a tabletop that is shaped like a circle. the circumference of the tabletop is 6π. Which measurement is closest to the area of the tabletop in square feet?
28.26 sq. Ft is the area of the table top
The height of a cylindrical vase is 11 inches as shown below. The base of the cylinder has a diameter of 4½ inches. Which measurement is closest to the volume of the cylinder in cubic inches? * 34 points 1,710.6 cubic inches 155.51 cubic inches 699.79 cubic inches 174.95 cubic inches
Answer:
174.95
Step-by-step explanation:
Volume=πr^2h
3.142 * (4.5÷2)^2 *11
=174.95
p is a plane in r3. its equation is: x 4y − 3z = 0. this plane is the nullspace of what matrix a ? find the basis for the nullspace of a. find the basis for the line p⊥ that is perpendicular to p.
The vector [1, 1, 1]ᵀ as it is symmetrical to the ordinary vector. Thus, "[1, 1, 1]T" serves as the foundation for the line p.
We can rewrite the plane's equation as a matrix equation to find the matrix A whose nullspace matches the given plane. The plane's equation is as follows:
x - 4y + 3z = 0
We can revise it in lattice structure as:
Where [A] is a 1x3 matrix and [x, y, z]T is a column vector, [A] = [0]. The rows of the matrix [A] will serve as the equation's coefficients for x, y, and z due to the equation's homogeneity and linearity.
As a result, matrix A is:
[A] = [1, -4, 3] We must solve the equation A * x = 0, where x is a column vector, in order to determine the nullspace's basis. For this situation, we really want to address:
We can represent it as a system of equations: [1, -4, 3,] [x, y, z]T = [0].
x - 4y + 3z = 0
To track down the reason for the nullspace, we settle the arrangement of conditions and express the arrangement concerning boundaries. Let's figure out the system:
x = 4y - 3z
Picking y = t (a boundary), we can revamp the arrangement as:
The nullspace of matrix A is spanned by the vector [4, 1, 1]T, so "[4, 1, 1]T" serves as the foundation for the nullspace of A. Since x = 4t, y = t, and z = t,
Presently, to find the reason for the line p⊥ that is opposite to p, we know that any vector in p⊥ is symmetrical to any vector in p. Hence, the reason for p⊥ can be found by finding a vector that is symmetrical to the ordinary vector of p (which is [1, - 4, 3]ᵀ).
We can pick the vector [1, 1, 1]ᵀ as it is symmetrical to the ordinary vector. Thus, "[1, 1, 1]T" serves as the foundation for the line p.
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A pizza cut into 8 pieces cost $10.00.
What is the cost per piece?
Answer:
$1.25
Step-by-step explanation:
10/8 =1.25
Answer:
$1.25
Step-by-step explanation:
just divided 10 with 8
Rosalind Franklin played an important role in the discovery of DNA's structure. Her data was used to support Watson's and Crick's hypothesis that DNA had the structure of a double helix. Even with this data and support from other scientists, the structure of DNA was not a widely accepted theory. Select all of the reasons why was their discovery was not considered a theory at the time of the paper's publication? 1. A newly released hypothesis must wait a least a year before the scientific community can vote for it to become a theory. 2. Theories are never developed by three people. 3. Theories need to undergo peer-review. 4.The hypothesis wasn't supported by their own data.
Answer:
The correct option is;
3. Theories need to undergo peer-review
Step-by-step explanation:
Within the scientific community, a theory has to be peer-reviewed by subject matter experts before it can be normally considered a valid theory. The peer-review process is one in which another scientific expert on the subject analyze, study, and repeat the experiments in the same conditions as stated in a publication submitted to a journal as a theory. The peer-review process aims to confirm the theory. A discovery which survives the peer review process will be considered a scientific theory and can then be expanded upon.
2
M2|L23
Division Diver Duo
5,626 ÷ 62
How many times can 62 go into 562
The result of 5,626 divided by 62 is approximately 90 with a remainder of 48.
To calculate the division of 5,626 by 62, you can use long division. Here are the steps:
90
______________
62 | 5,626
- 4,96
-----
1,66
1,55
----
110
62
----
48
Therefore, the result of 5,626 divided by 62 is approximately 90 with a remainder of 48.
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You must exert a force of 4.5 N on a book to slide it across a table. If you moved it 5 meters. How much work was done on the book?
Answer:
22.5 JStep-by-step explanation:
The work done by an object can be found by using the formula
workdone = force × distance
From the question we have
workdone = 4.5 × 5
We have the final answer as
22.5 JHope this helps you
To find the x-intercept, we let y = 0 and solve for x and to find y-intercept, we let x=0 and solve for y. Figure out the x-intercept and y-intercept in given equation of the line. 6x + 2y = 12
Answer:
X-intercept: (2, 0) Y-intercept: (0, 6)Step-by-step explanation:
X-intercept means y-coordinate of 0:
6x +2×0 = 12
6x = 12
x = 2 ← x-coordinate
Y-intercept means x-coordinate of 0:
6×0 + 2y = 12
2y = 12
y = 6 ← y-coordinate
determine the type i error if the null hypothesis, h0, is: carmin believes that her chemistry exam will only cover material from chapters four and five.
a. Carmin believes that her chemistry exam will only cover material from chapters four and five when, in fact, it will cover material only from chapters four and five. b. Carmin believes that her chemistry exam will not cover material only from chapters four and five when, in fact, it will only cover material from chapters four and five. c. Carmin believes that her chemistry exam will only cover material from chapters four and five when, in fact, it will not cover material only from chapters four and five. d. Carmin believes that her chemistry exam will not cover material only from chapters four and five when, in fact, it will not cover material only from chapters four and five.
The type I error occurs when the null hypothesis is rejected, but in reality, the null hypothesis is true. In this case, the null hypothesis is "Carmin believes that her chemistry exam will only cover material from chapters four and five." The correct statement that corresponds to the type I error is option C: "Carmin believes that her chemistry exam will only cover material from chapters four and five when, in fact, it will not cover material only from chapters four and five."
A type I error is a false positive result, where the null hypothesis is incorrectly rejected even though it is true. In this scenario, if carmin believes that her chemistry exam will only cover material from chapters four and five, but in reality, the exam includes additional material beyond chapters four and five, it would be a type I error. Option C describes this situation, where Carmin believes the exam will cover only chapters four and five, but it actually includes material from other chapters.
Options A, B, and D do not correspond to a type I error because they either describe the correct belief or a different scenario where the null hypothesis is true.Therefore, option C represents the type I error in this context.
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Use the given conditions to write an equation for the line. Passing through (-8,6) and parallel to the line whose equation is 8x - 3y -4 = 0 The equation of the line is (Simplify your answer. Type an equation using X and y as the variables.
The equation of the line that passes through (-8, 6) and parallel to the line whose equation is 8x - 3y -4 = 0, is 3y - 8x + 46 = 0
How do i determine the equation of the line?First, we shall obtain the slope of the line. Details below:
8x - 3y -4 = 0
Rearrange the equation with y as the subject, we have
8x - 4 = 3y
y = 8x/3 - 4/3
Thus,
Slope (m₁) = 8/3
Recall,
Slope of parallel lines are equal.
Thus,
The slope of line, is given as:
m₂ = m₁ = 8/3
Now, we shall obtain the equation of line. Details below
Coordinate = (-8, 6) x coordinate 1 (x₁) = -8y coordinate 1 (y₁) = 6Slope of line (m₂) = 8/3Equation of line =?y - y₁ = m₂(x - x₁)
y - 6 = 8/3(x - (-8))
y - 6 = 8/3(x + 8)
Multiply through by 3
3(y - 6) = 8(x + 8)
Clear bracket
3y - 18 = 8x - 64
Rearrange
3y - 8x - 18 + 64 = 0
3y - 8x + 46 = 0
Thus, the equation of line is 3y - 8x + 46 = 0
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Brianna is going to the amusement park, where she has to pay a set price of
admission and another price for tickets to go on each of the rides. Brianna made the
linear graph below to indicate the money she might spend in total. What does the
y-intercept in the graph represent?
Im pretty sure the answer is A but if not then it is C
This is bcuz B doesn’t make sense because the graph doesn’t say anything close to 100 rides and D doesn’t make sense either.
Hope this helped.
Use the consumption function C = C₁ + bY and the income function Y=C+ S. to derive expressions for the MPC, APC, MPS. and APS. 7 marks 5. Given the consumption functions C= 50+ 0.5Y, Deduce expressions for the marginal propensity to save and the average propensity to save. Show that the MPS>APS. Confirm this statement by evaluating APS and MPS at Y = 20. 6 marks 6. Find the derivatives of the following functions. AC = + QI(Q) 3 marks Page 2 y=(√2+1)(√2-3) 3 marks 7. Determine the intervals along which each of the following curves is increasing or decreasing (consider the positive half of the plane, z>0) 5 marks (a) AC=Q²-20Q+120 (b) TR=50Q-Q²
In the given problem, we start by deriving expressions for the marginal propensity to consume (MPC), average propensity to consume (APC), marginal propensity to save (MPS), and average propensity to save (APS) using the consumption function and income function.
Deriving expressions for MPC, APC, MPS, and APS:
Using the consumption function C = C₁ + bY and the income function Y = C + S, we can derive the following expressions:
MPC (Marginal Propensity to Consume) = ΔC / ΔY
APC (Average Propensity to Consume) = C / Y
MPS (Marginal Propensity to Save) = ΔS / ΔY
APS (Average Propensity to Save) = S / Y
Deducing expressions for MPS and APS:
Given the consumption function C = 50 + 0.5Y, we can deduce the expressions for MPS and APS as follows:
MPS = ΔS / ΔY = Δ(Y - C) / ΔY = 1 - MPC
APC = C / Y = (50 + 0.5Y) / Y
APS = S / Y = (Y - C) / Y = 1 - APC
Confirming MPS > APS:
To confirm that MPS is greater than APS, we evaluate them at Y = 20:
MPS = 1 - MPC = 1 - 0.5 = 0.5
APC = C / Y = (50 + 0.5 * 20) / 20 = 52.5 / 20 = 2.625
APS = 1 - APC = 1 - 2.625 = -1.625
Since APS is negative and MPS is positive, it is evident that MPS > APS.
Derivatives of the given functions:
a) AC = Q² - 20Q + 120
The derivative of AC with respect to Q is: d(AC)/dQ = 2Q - 20
b) TR = 50Q - Q²
The derivative of TR with respect to Q is: d(TR)/dQ = 50 - 2Q
Determining intervals of increase or decrease:
a) AC = Q² - 20Q + 120
The quadratic function AC has a positive coefficient for the quadratic term (Q²), indicating a U-shaped curve. It opens upward, which means it is increasing for Q values less than the vertex of the parabola (Q = 10) and decreasing for Q values greater than the vertex.
b) TR = 50Q - Q²
The quadratic function TR has a negative coefficient for the quadratic term (Q²), indicating a downward-opening parabola. It is decreasing for all values of Q.
In summary, we derived expressions for MPC, APC, MPS, and APS using the consumption function and income function. We confirmed that MPS > APS by evaluating them at a given income level.
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asfjpasjfaafdad adsafdshfd
4020
you're supposed to multiply the length value by 1760
:P
On average, the number of text messages students send is within 100 messages of the average, which is 500 text messages per day. The mean absolute deviation in this situation is
The mean absolute deviation in the given situation, where the average number of text messages students send is within 100 messages of the mean of 500 messages per day, can be calculated.
Mean absolute deviation (MAD) measures the average distance between each data point and the mean of the data set.
In this case, the average number of text messages sent by students is 500 messages per day.
Since the average is within 100 messages of the mean, we can assume a range of 400 to 600 messages.
To calculate the MAD, we need to determine the deviation of each data point from the mean. In this case, the deviations can range from -100 to 100 messages.
Since the data points are evenly distributed around the mean, the sum of these deviations will be zero.
However, to calculate the absolute deviation, we take the absolute values of the deviations.
Considering the range of -100 to 100 messages, the absolute deviations for each data point would be 100, 99, 98, ..., 2, 1, 0, 1, 2, ..., 98, 99, 100.
The average absolute deviation would be the sum of these absolute deviations divided by the total number of data points, which is 201 (from -100 to 100 inclusive).
Therefore, the mean absolute deviation in this situation is the average of these absolute deviations, which can be calculated as (100 + 99 + 98 + ... + 2 + 1 + 0 + 1 + 2 + ... + 98 + 99 + 100) / 201.
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A triangle has a 90° angle. What type of triangle is it?
Acute triangle
Right triangle
Equilateral triangle
Isosceles triangle
A triangle with a 90° angle is called a right triangle.
Option B is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
Acute triangle:
The angle is less than 90 degrees.
Right triangle:
The angle is 90 degrees.
Equilateral triangle:
All sides of the triangle are equal.
Isosceles triangle:
Two sides of the triangle are equal.
Thus,
A triangle with a 90° angle is called a right triangle.
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qüîz 10-2 Gina wilson answers please
Answer:
I don't know how to do it the subject
Andy and Hershel folded the same- size square papers. Candy shaded 2 4 and Hershel shaded 1 2. Are the fractions equivalent? Explain.
Answer:
Yes, the fraction are equivalent
Step-by-step explanation:
Fraction shaded by candy = 2/4
Fraction shaded by Hershel = 1/2
If candy's fraction of 2/4 is reduced to it's lowest term ;
2 /4 = 1 /2 ; we also obtain the same fraction obtained by Hershel.
Hence, 2/4 is equivalent to 1/2
Let X be a topological space and A ⊂ X. The closure of A, denoted
A¯, is the intersection of all closed sets containing A.
(a) Show that A¯ is the smallest closed subset of X containing A, in
the following sense: if A ⊂ F ⊂ X and F is closed, then A¯ ⊂ F.
The "closure(A⁻)" of "subset-A" in a topological-space X is the intersection of all "closed-sets" containing A. It is smallest closed subset of X that contains A, means that if A⊂F⊂X and F is closed, then A⁻ is a subset of F.
In order to show that the closure(A⁻) is the smallest closed subset of X which contains "A", we need to prove that if A ⊂ F ⊂ X and F is closed, then A⁻ ⊂ F,
We know that, A⁻ is intersection of all "closed-sets" containing A. Since F is "closed-set" which contains "A", it is one of the sets in the intersection defining A⁻. So, A⁻ is contained in F.
To show that A⁻ ⊂ F, we consider an arbitrary point x ∈ A⁻, which means that x is in the intersection of all closed sets containing A. Since, F is one such "closed-set" containing A, x must be in F as well.
Since x was an "arbitrary-point" in A⁻, we have shown that every point in A⁻ is also in F, So, A⁻ ⊂ F.
Therefore, we have proved that if A ⊂ F ⊂ X and F is closed, then A¯ ⊂ F.
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I need to know how much metal is needed to make the can
Answer:
we don't have any wasted metal and everything goes perfectly. In the real world, waste is inevitable.
Question 98 Unleaded gas is $2.80 per gallon. Which equation best represents y, the total cost at x pounds of plum?
Answer:
y = $2.80x
Step-by-step explanation:
Based in the information given :
Cost per gallon = $2.80
Number of gallons = x
The total cost, y which is the total cost of x gallons of gas will be :
Cost per gallon * number of gallons
$2.80 * x
Hence,
y = $2.80x
| 50 Points | Please give explanation | Reporting false answers | Giving correct brainliest
Answer: answer is D
Step-by-step explanation:
because science is more important than life
PLEASE HELP! What is the ratio of the volumes of two spheres, if the ratio of their radii is 13: 9
Answer:
[tex] V_1 : V_2= 2197 : 729[/tex]
Step-by-step explanation:
Let the volumes of both the spheres be [tex] V_1, \:V_2[/tex] and their radii be [tex] r_1, \:r_2[/tex] respectively.
[tex] \huge r_1 : r_2= 13 : 9[/tex] (given)
[tex] \implies\huge \frac{r_1}{r_2}= \frac{13}{9}.....(1)[/tex]
[tex] \huge \frac{V_1}{V_2}=\frac{\cancel {\frac{4}{3} \pi} r_1^3}{\cancel {\frac{4}{3} \pi} r_2^3}[/tex]
[tex] \huge \frac{V_1}{V_2}=\frac{ r_1^3}{r_2^3}[/tex]
[tex]\huge \frac{V_1}{V_2}=\bigg(\frac{ r_1}{r_2}\bigg) ^3..... (2)[/tex]
From equations (1) & (2), we have:
[tex]\huge \frac{V_1}{V_2}=\bigg(\frac{13}{9}\bigg) ^3[/tex]
[tex] \huge \frac{V_1}{V_2}=\frac{2197}{729}[/tex]
[tex] \huge \therefore V_1 : V_2= 2197 : 729[/tex]
Thus, the ratio of the volumes of two spheres would be 2197 : 729.
Answer:
2197:729
hope it helps
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Julio recibió $640.000: gastó las ⅜ partes para pagar sus estudios y la ¼ parte para reparar el auto, ¿cuánto dinero le queda?
Answer:
Resto= $240.000
Step-by-step explanation:
Dada la siguiente información:
Cantidad total de dinero= $640.000
Costo de estudio= 3/8= 0,375
Costo de auto= 1/4= 0,25
Primero debemos calcular la cantidad total gastada, y después la diferencia:
Costo de estudio= 0,375*640.000= 240.000
Costo de auto= 0,25*640.000= 160.000
Gasto total= $400.000
Resto= 640.000 - 400.000
Resto= $240.000