The first step in finding the distance between vertex P and vertex V is find the length of diagonal between vertex P and vertex R.
option A.
What is the distance between vertex P and vertex V?To find the distance between vertex P and vertex V, we need to draw a diagonal line from vertex P to vertex V.
After drawing the diagonal line, we will notice that we have a new right angle triangle.
with a height of 17 inches a base of diagonal length PR or TVa hypotenuse of diagonal PVSo since we know the height of the right triangle, we need to find the base of the right triangle first, which is equal to length of diagonal length PR or TV
So the correct answer will be "find the length of diagonal PR first.".
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9.12 movie lovers, part ii. suppose an online media streaming company is interested in building a movie recommendation system. the website maintains data on the movies in their database (genre, length, cast, director, budget, etc.) and additionally collects data from their subscribers ( demographic information, previously watched movies, how they rated previously watched movies, etc.). the recommendation sys- tem will be deemed successful if subscribers actually watch, and rate highly, the movies recommended to them. should the company use the adjusted r2 or the p-value approach in selecting variables for their recommendation system?
The company should use the adjusted R² approach to select variables for their recommendation system, as it will better account for the influence of multiple variables and help create a more accurate model for predicting subscriber's movie ratings.
To build a successful movie recommendation system for the online media streaming company, it's important to consider the appropriate statistical approach for selecting variables.
In this case, the company should use the adjusted R² approach instead of the p-value approach.
The adjusted R² approach is more suitable for this scenario because it measures the proportion of variance in the dependent variable (subscriber's ratings) that is predictable from the independent variables (movie and subscriber data).
Adjusted R² takes into account the number of variables and adjusts for overfitting, which is important when dealing with a large dataset, like the one the streaming company has.
It helps in identifying the most influential factors and creating a model that better predicts movie ratings.
On the other hand, the p-value approach focuses on the statistical significance of individual variables, which might lead to including variables that are significant but not necessarily the best predictors for movie ratings.
This could result in a less accurate recommendation system.
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a trapezoid has an area of 96 ft. if the base is 11 feet and the height is 8 feet, what is the length of the other base
Answer:
The formula for the area of a trapezoid is:
Area = (b1 + b2) / 2 x h
where b1 and b2 are the lengths of the two parallel bases, and h is the height.
We are given that the area of the trapezoid is 96 ft, the height is 8 ft, and one of the bases (b1) is 11 ft. We can use this information to find the length of the other base (b2).
Substituting the given values into the formula for the area of a trapezoid, we get:
96 = (11 + b2) / 2 x 8
Multiplying both sides by 2 and dividing by 8, we get:
24 = 11 + b2
Subtracting 11 from both sides, we get:
b2 = 13
Therefore, the length of the other base is 13 ft.
Pete Moss is planning to take the Certified Public Accountant Exam (CPA
exam). Records kept by the College of Business from which he graduated
indicate that 71% of the students who have graduated pass the CPA exam.
Assume that the exam is changed every time it is given. Eight of Pete's
friends are going to take the exam. What is the probability that 5 of the
friends will pass?
The probability that exactly 5 of Pete's friends will pass the CPA exam is approximately 0.275
This problem can be solved using the binomial distribution. We know that the probability of passing the CPA exam for a graduate of Pete's College of Business is p = 0.71.
We also know that there are eight friends taking the exam, so the number of trials (n) is 8. We want to find the probability that exactly 5 of them will pass.
The formula for the probability mass function of the binomial distribution is
P(X = k) = (n choose k) × p^k × (1-p)^(n-k)
where X is the random variable representing the number of successes (i.e., the number of Pete's friends who pass), k is the number of successes we want to find (i.e., 5), (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials, and p is the probability of success (i.e., 0.71).
Plugging in the numbers, we get
P(X = 5) = (8 choose 5) × 0.71⁵ × (1-0.71)³
= 56 × 0.71 × 0.29³
≈ 0.275
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An initial investment of $5000 doubles in value in 6. 3 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent
The interest rate is approximately 10.95%, rounded to the nearest tenth of a percent.
Continuous compounding is given by the formula:
[tex]$A = Pe^{rt}$[/tex]
where:
A = final amount
P = initial amount
r = interest rate
t = time in years
We know that the initial investment P is $5000, and the final amount A is $10,000 (since the investment doubles in value). The time t is 6.3 years. We can solve for r as follows:
[tex]$A = Pe^{rt}$[/tex]
[tex]$10,000 = 5000e^{r(6.3)}$[/tex]
Divide both sides by 5000:
[tex]$2 = e^{r(6.3)}$[/tex]
Take the natural logarithm of both sides:
[tex]$\ln(2) = r(6.3)$[/tex]
Divide both sides by 6.3:
[tex]$r = \frac{\ln(2)}{6.3}$[/tex]
Using a calculator, we get:
[tex]$r \approx 0.1095$[/tex]
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I need help with this question can you help?
Answer:
The Correct answer is sinA/3.2=sin110°/4.6
Question:
The current (in amps) in a simple
electrical circuit varies inversely to
the resistance measured in ohms.
The current is 24 amps when the
resistance is 20 ohms. Find the
current (in amps) when the
resistance is 12 ohms.
The current in the circuit when the resistance is 12 ohms is 40 amps.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
We can use the inverse proportionality formula to solve this problem, which states that:
current (in amps) x resistance (in ohms) = constant
Let's call this constant "k". We can use the information given in the problem to find k:
24 amps x 20 ohms = k
k = 480
Now we can use this constant to find the current when the resistance is 12 ohms:
current x 12 ohms = 480
current = 480 / 12
current = 40 amps
Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.
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A rectangular garden has a walkway around it. The area of the garden is 4(4.5x+3.5). The combined area of the garden and the walkway is 5.5(6x+5). Find the area of the walkway around the garden as the sum of two terms.
The product of two terms gives the walkway's area around the garden: 15x+13.5.
Define rectangleA rectangle is a four-sided polygon with two pairs of parallel and congruent sides, and four right angles. The opposite sides of a rectangle are equal in length and parallel to each other, while the adjacent sides are perpendicular to each other.
Area of garden = 4(4.5x + 3.5) = 18x+14
The combined area of the garden and the walkway = 5.5(6x+5) =33x+27.5
The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:
Aw=combined area -Area of garden
=33x+27.5-18x-14
=15x+13.5
Thus, we can say that the area of the walkway around the garden is the sum of two terms: 15x+13.5.
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Select whether the situation could yield variable data, and if so, select the option with the best statistical question. The town council members want to know how much recyclable trash a typical household in town generates each week.
A. Variable data. How many members are on the council?
B. Variable data. When are the recyclables collected?
C. Not variable.
D. Variable data. How many pounds of recyclables trash does each household generate?
The situation could yield variable data, and Variable data. How many pounds of recyclables trash does each household generate? this option is with the best statistical question. The town council members want to know how much recyclable trash a typical household in town generates each week.
Hence, the correct option is D.
Because
Option A, "How many members are on the council?" is not relevant to the situation, as it does not relate to the amount of recyclable trash generated by households in the town. Therefore, the data generated by this question would not be variable in relation to the amount of recyclable trash generated by households.Option B, "When are the recyclables collected?" could potentially yield variable data, as different households may put their recyclables out for collection at different times. However, this question would not provide a direct measure of the amount of recyclable trash generated by each household, which is what the town council is interested in. Therefore, while the data generated by this question may be variable, it would not be the most relevant or useful data for the town council.Option C, "Not variable," means that the situation does not yield variable data. In this case, it would mean that the amount of recyclable trash generated by households in the town does not vary from one household to another.Option D, "How many pounds of recyclables trash does each household generate?" is the best statistical question for this situation because it directly addresses the town council's interest in understanding the amount of recyclable trash generated by households in the town. This question would yield variable data, as different households would generate different amounts of recyclable trash, and this data would be the most useful for the town council in developing strategies for promoting recycling and reducing waste.Hence, the correct option is D.
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I need this answer asap can someone help??
The shortest driving distance between the stadium and the animal shelter is given as follows:
10 blocks.
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The coordinates are given as follows:
Animal shelter: (-3,3).Stadium: (6,2).Since the spaces are filled by houses, we cannot apply the formula, hence the shortest distance is:
6 - (-3) + 3 - 2 = 9 + 1 = 10 blocks.
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Multiply (3 + 4i) (6 + 2i) ?
Answer: 10 + 30i
Step-by-step explanation:
(3 + 4i) (6 + 2i)
= 3(6) + 3(2i) + 4i(6) + 4i(2i) // FOIL method
= 18 + 6i + 24i + 8i^2 // simplify
= 18 + 30i - 8 // i^2 = -1
= 10 + 30i
your school wants to maximize their profit, P, from the sales of tickets, T, to the homecoming football game. They determine the function, P(t)=60t^2+420t-440 models the profit they can earn in hundreds of dollars in terms of price per ticket, in dollars.
The maximum profit occurs at the endpoint t = 100, where the profit is $5551.20.
Maximum profit calculationTo maximize the profit function P(t) = 60t^2 + 420t - 440, we need to find the value of t that will give us the maximum profit.
One way to do this is to use calculus. We can take the derivative of P(t) with respect to t and set it equal to zero to find the critical points:
P'(t) = 120t + 420
Set P'(t) = 0 and solve for t:
120t + 420 = 0
t = -3.5
This gives us one critical point at t = -3.5. However, this value of t doesn't make sense in the context of the problem - we can't sell tickets at a negative price!
So we need to check the endpoints of the domain of the function, which is given by the constraint that t is greater than or equal to zero (we can't charge a negative price for tickets either).
When t = 0, P(0) = -440.
When t is very large, say t = 100, P(100) = 600000 - 44000 - 440 = 555120.
Therefore, the maximum profit occurs at the endpoint t = 100, where the profit is $5551.20.
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If the area is halfway between two entries, use the z-score halfway between the corresponding z-score s. If convenient, use technology to find the z-score. 37. 0. 4364. 38. 0. 1 39. 993. 40. P2. 41. P67. 42. P46. The z-score that has 20. 9% of the distribution’s area to its right
The z- score that has 20.9 of the distribution's area to its right is roughly 0.84.
To find the z- score that has 20.9 of the distribution's area to its right, we can use a standard normal distribution table or a calculator with a normal distribution function.
Using a standard normal distribution table, we can look for the area to the left of the z- score with an area of 1-0.209 = 0.791. The closest value we can find in the table is 0.7901, which corresponds to a z- score of 0.84.
Alternatively, we can use a calculator with a normal distribution function.However, 0, 1) = 0, If we use the formula" normalcdf(z. 209" to find the z- score, we get z = 0.84.
therefore, the z- score that has 20.9 of the distribution's area to its right is roughly 0.84.
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Can someone help me asap? It’s due today. I will give brainliest if it’s correct.
The simulation that represents the context is given as follows:
2,5, 8 of diamonds: gold plastic ring.3, 6, 9 of diamonds: silver plastic ring.4, 7, 10 of diamonds: black plastic ring.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
In the context of this problem, we have an equal number of gold rings, silver rings and black rins, thus each outcome should have the same probability, which is represented by the last option.
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angles of triangles- does anyone know how to do this?
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°
(4) m∠1=88°m∠2=42° m∠3=113°
What is an angle?An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees or radians, and it describes the amount of rotation needed to bring one of the rays into coincidence with the other.
Define triangle?A triangle is a closed two-dimensional shape with three straight sides and three angles.
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°(sum of two interior angles on the same side is equal to the exterior angle)
(4) m∠1=88°(sum of 3 angles of a triangle is always 180°),m∠2=42°(vertically opposite angle theorem), m∠3=113°(sum of 3 angles of a triangle is always 180°)
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Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does
the line with equation y = 2z+ 3 intersect the circle with radius 3 and center (0, 3)?
The point of intersection in the first quadrant is (3, 4) from the equation of circle.
Equation of circle.
We can start by substituting the equation of the line into the equation of the circle and solving for z and y.
The equation for the circle is:
(x - h)^2 + (y - k)^2 = r^2
Substituting h = 0, k = 3, and r = 3, we get:
x^2 + (y - 3)^2 = 9
Now, we substitute y = 2z + 3 into the equation:
x^2 + (2z + 3 - 3)^2 = 9
Simplifying, we get:
x^2 + 4z^2 = 9
Since we are looking for a point in the first quadrant, both x and z must be positive. We can solve for z in terms of x:
4z^2 = 9 - x^2
z^2 = (9 - x^2)/4
z = sqrt[(9 - x^2)/4]
Substituting this into the equation y = 2z + 3, we get:
y = 2sqrt[(9 - x^2)/4] + 3
To find the point of intersection in the first quadrant, we need to find a value of x that satisfies both this equation and the equation of the circle. We can substitute the equation for y into the equation for the circle:
x^2 + [2sqrt((9 - x^2)/4)]^2 = 9
Simplifying, we get:
x^2 + (9 - x^2)/2 = 9
Multiplying both sides by 2:
2x^2 + 9 - x^2 = 18
Solving for x:
x^2 = 9
x = 3
Substituting x = 3 into the equation for y, we get:
y = 2sqrt[(9 - 3^2)/4] + 3 = 4
Therefore, the point of intersection in the first quadrant is (3, 4).
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what is trigonometry
trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc)
a fair coin is flipped 5 times. what is the probability that the first three flips come up heads or the last three flips come up tails (or both)?
The probability that the first three flips come up heads or the last three flips come up tails is 1/4. Hence the answer is 1/4.
The probability of obtaining heads or tails on each single fair coin flip is 1/2. Because the coin flips are independent, the chance of obtaining a certain sequence of heads and tails is the product of the probabilities of each flip.
We want to know what the probability is that the first three flips will be heads, the last three flips will be tails, or both. This can occur in two ways:
Heads for the first three flips: (1/2) x (1/2) x (1/2)
P(H) = 1/8
The final three flips are all tails: (1/2) x (1/2) x (1/2)
P(T) = 1/8
Because these two occurrences are mutually exclusive, we may combine their probabilities to get the total:
P(H) + P(T) = 1/8 + 1/8 = 1/4
So the probability that the first three flips come up heads or the last three flips come up tails (or both) is 1/4.
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write a equation of the line that passes through (2,7) and (0,-5)
Answer:
To write the equation of the line that passes through the points (2, 7) and (0, -5), we can use the slope-intercept form of a linear equation, which is:
y = mx + b
Where m is the slope of the line, and b is the y-intercept.
First, we can find the slope of the line by using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) = (2, 7) and (x2, y2) = (0, -5)
m = (-5 - 7) / (0 - 2)
m = -12 / -2
m = 6
So the slope of the line is 6.
Next, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Where (x1, y1) = (2, 7)
y - 7 = 6(x - 2)
Simplifying this equation, we get:
y - 7 = 6x - 12
y = 6x - 5
So the equation of the line that passes through the points (2, 7) and (0, -5) is y = 6x - 5.
Match the probability of falling BETWEEN the following z-scores.
1) Between -0.34 and 0.34
2) Between 2.6 and 3.14
3) Between -3.04 and -0.56
4) Between -1.17 and 2.23
A) 0.2662
B) 0.0039
C) 0.8661
D) 0.2865
Matching the probability of falling BETWEEN the following z-scores will give: 10 Between -0.34 and 0.34 is A) 0.2662. 2)Between 2.6 and 3.14 is B) 0.0039. 3) Between -3.04 and -0.56 is C) 0.8661.
How to Match the probability of falling BETWEEN the following z-scores.To match the probability of falling between the given z-scores, we need to use a standard normal distribution table or a calculator with a built-in normal distribution function.
Between -0.34 and 0.34
Using the standard normal distribution table, the area between -0.34 and 0.34 is 0.2662. Therefore, the answer is A) 0.2662.
Between 2.6 and 3.14
Using the standard normal distribution table, the area between 2.6 and 3.14 is 0.0039. Therefore, the answer is B) 0.0039.
Between -3.04 and -0.56
Using the standard normal distribution table, the area between -3.04 and -0.56 is 0.8661. Therefore, the answer is C) 0.8661.
Between -1.17 and 2.23
Using the standard normal distribution table, the area between -1.17 and 2.23 is 0.2865. Therefore, the answer is D) 0.2865.
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Fifteen children split $9 among themselves so that each child receives the same amount. How much did each child receive?
The total amount of money received by each child after splitting $9 among 15 children is equal to $0.60.
Total number of children is equal to 15
Total amount of money distributed among 15 children = $9
To find out how much each child receives,
We can divide the total amount of money by the number of children.
In this case, there are 15 children and $9 to split.
So, the amount of money each child receives is equal to,
(Total amount of money )/ ( total number of children )
= $9 ÷ 15
= $0.60
Therefore, amount of money received by each child in the group of 15 children is equal to $0.60.
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the graph of polygon fghi is shown. graph the image of fghi after a refelction across the line y=-1. include the line of reflection. then write the coordinates of the image
The coordinates of the reflected polygon F'G'H'I' are as follows:
F'(-2, -1), G'(5, -4), H'(8, -5), and I'(6, -2).
What is the reflection?
In mathematics, reflection is defined as the mirror image of a figure crossing a line (drawn or imagined), known as the line of reflection.
The vertices of the polygon FGHI are as follows:
F(2, -1)
G(5, 2)
H(8, 3)
I(6, 0)
To reflect the polygon FGHI across the line y = -1, we need to flip the points over the line.
Now we can reflect each of the points of the polygon across the line y = -1 to get the image:
F(2, -1) stays in the same place because it lies on the line of reflection.
G(5, 2) is reflected to G'(5, -4) by flipping it vertically across the line y = -1.
H(8, 3) is reflected to H'(8, -5), and
I(6, 0) is reflected to I'(6, -2).
Hence, The coordinates of the reflected polygon F'G'H'I' are as:
F'(-2, -1), G'(5, -4), H'(8, -5), and I'(6, -2).
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Complete question:
The complete question is attached in the image.
A person has 50,000 in taxable income for a year and pays a 10 percent income tax rate equal to 5,000 which action would reduce the amount the person paid in taxes to 1,000
The action that would reduce the amount the person paid in taxes to 1,000 is option (D) Receiving a $49,000 tax credit
In this scenario, the person has $50,000 in taxable income and pays a 10% income tax rate, which amounts to $5,000 in taxes. To reduce the tax liability to $1,000, the person needs to receive a tax credit of $49,000. Tax credits directly reduce the amount of tax owed, whereas tax deductions reduce taxable income.
A tax deduction of $4,000 would lower the taxable income to $46,000, resulting in a lower tax liability of $4,600, which is not low enough to reach $1,000. Therefore, a tax credit of $49,000 is needed to reduce the tax liability to $1,000.
Therefore, the correct option is (D) Receiving a $49,000 tax credit
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The given question is incomplete, the complete question is:
A person has $50,000 in taxable income for a year and pays a 10 percent income tax rate, equal to $5,000. Which action would reduce the amount the person paid in taxes to $1,000?
A.Receiving a $4,000 tax deduction
B.Receiving a $4,000 tax credit
C. Receiving a $49,000 tax deduction
D. Receiving a $49,000 tax credit
which pair of dotplots provides the strongest statistical evidence that the training group ran faster (small times), on average, than the no training group?
Similarly, if the spread of the training group's distribution is smaller than the spread of the no training group's distribution.
The training group ran faster on average, than the no training group.
To determine which pair of dot plots provides the strongest statistical evidence that the training group ran faster.
Compare the center and spread of the two groups.
The center of the training group's distribution is consistently to the left (i.e., lower times) of the center of the no training group's distribution.
Overlap between the two distributions, then we can conclude that the training group ran faster on average, than the no training group.
100 by adding data.
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We need to examine the dotplots and summary statistics of the two groups to determine which pair of dotplots provides the strongest statistical evidence that the training group ran faster, on average, than the no training group.
To determine which pair of dotplots provides the strongest statistical evidence that the training group ran faster, we need to compare the centers and spreads of the two groups. If the center of the training group is shifted to the left (smaller times) compared to the center of the no training group, and if the spread of the training group is smaller than the spread of the no training group, then we have stronger evidence that the training group ran faster, on average, than the no training group.
Without seeing the actual dotplots, we cannot make a definitive determination. However, we can describe what to look for in the dotplots. Specifically, we want to see a clear separation between the centers of the two groups, and we want to see less overlap between the dots in the training group than in the no training group.
In addition, we can calculate summary statistics for the two groups, such as the mean and standard deviation, to help us compare the centers and spreads of the two groups. If the mean of the training group is significantly smaller than the mean of the no training group, and if the standard deviation of the training group is significantly smaller than the standard deviation of the no training group, then we have stronger evidence that the training group ran faster, on average, than the no training group.
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A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these is true?
The correct statement about scale factor is the radius of the larger can will be 8 inches. (option c).
Let's first consider the dimensions of the small can of tomato paste. We are given that it has a radius of 2 inches and a height of 4 inches. Therefore, its volume can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get:
V_small = π(2²)(4) = 16π cubic inches
Using these dimensions, we can calculate the volume of the larger can using the same formula:
V_large = π(6²)(12) = 432π cubic inches
Now, let's compare the volumes of the small and large cans. We have:
V_large = 432π cubic inches > 16π cubic inches = V_small
Therefore, we can conclude that the volume of the larger can is greater than the volume of the smaller can. But is it three times greater? Let's compare:
V_large = 432π cubic inches 3
V_small = 3(16π) cubic inches = 48π cubic inches
We see that 432π cubic inches is not equal to 48π cubic inches, so option b) is not correct.
Finally, let's consider the radius of the larger can. We found earlier that it is 6 inches, which is greater than the radius of the smaller can, but it is not 8 inches. Therefore, option c) is correct.
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Complete Question:
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these true?
a) The radius of the larger can will be 5 inches.
b) The volume of the larger can will be 3 times the volume of the smaller can
c) The radius of the larger can will be 8 inches.
d) The volume of the larger can is 3 times the volume of smaller can
help me please please
Ned collected rocks at the beach. He placed 12 ounces of rocks in each of 4 different bags. How many ounces of rocks Ned collect?
Answer:
48 ounces
Step-by-step explanation:
12*4= 48
A tram moved downward 12 meters in 4 seconds at a constant rate. What was the change in the tram's elevation each second?
Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.
What is an unitary method?To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.
Here,
By dividing the overall elevation change (12 metres) by the total time required (4 seconds),
it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.
=> Elevation change equals 12 metres
=> Total duration: 4 seconds
=> 12 meters / 4 seconds
=> 3 meters/second
As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.
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how do i solve and what’s the answer
Using the volume of the cylinder we know that 77% of the container B is full when the pumping is complete.
What is a cylinder?A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions.
In elementary geometry, it is regarded as a prism with a circle as its basis.
A cylinder can instead be described as an infinitely curved surface in a number of modern domains of geometry and topology.
The following is a list of the cylinder's attributes: It has two flat circular faces, two curved edges, and one curved surface.
Its uniform cross-section throughout makes it resemble a prism.
They feature two bases that are circular, flat, and arranged in a straight line.
So, the volume of cylinders A and B:
Formula: V=πr²h
Cylinder A:
V=πr²h
V=π10²20
V = 6283.18531
Rounding off: 6283 ft³
Cylinder B:
V=πr²h
V=π12²18
V=8143.00816
Rounding off: 8143 ft³
Then, contain A is what % of container B:
= 6283/8143 * 100
= 77.15
Rounding off: 77%
Therefore, using the volume of the cylinder we know that 77% of container B is full when the pumping is complete.
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a cylinder has a radius of 3 cm and a height of 8 cm. what is the longest segment, in centimeters, that would fit inside the cylinder?
The longest segment that would fit inside the cylinder is approximately 9.06 centimeters.
The longest segment that would fit inside the cylinder would be the diagonal of the cylinder's base, which is equal to the diameter of the base. The diameter of the base is equal to twice the radius, so it is 6 cm. Using the Pythagorean theorem, we can find the length of the diagonal:
[tex]diagonal^2 = radius^2 + height^2 \\diagonal^2 = 3^2 + 8^2 \\diagonal^2 = 9 + 64 \\diagonal^2 = 73 \\diagonal = sqrt(73)[/tex]
Therefore, the longest segment that would fit inside the cylinder is approximately 8.54 cm (rounded to the nearest hundredth).
To find the longest segment that would fit inside the cylinder, we need to calculate the length of the space diagonal of the cylinder. This is the distance between two opposite corners of the cylinder, passing through the center. We can use the Pythagorean theorem in 3D for this calculation.
The terms we'll use are:
- Radius (r): 3 cm
- Height (h): 8 cm
To find the space diagonal (d), we can use the following formula:
[tex]d = \sqrt{r^2 + r^2 + h^2}[/tex]
Plug in the values:
[tex]d = \sqrt{((3 cm)^2 + (3 cm)^2 + (8 cm)^2)} d = \sqrt{(9 cm^2 + 9 cm^2 + 64 cm^2)} d = \sqrt{(82 cm^2)}[/tex]
d ≈ 9.06 cm
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The longest segment that can fit inside the cylinder is. [tex]$\sqrt{73}$ cm[/tex].
The longest segment that can fit inside a cylinder is a diagonal that connects two opposite vertices of the cylinder.
The length of this diagonal by using the Pythagorean theorem.
Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:[1]
[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]
The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.
The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.
The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.
Consider a right triangle with legs equal to the radius.
[tex]$r$[/tex] and the height [tex]$h$[/tex] of the cylinder, and with the diagonal as the hypotenuse.
Then, by the Pythagorean theorem, the length of the diagonal is:
[tex]$\sqrt{r^2 + h^2} = \sqrt{3^2 + 8^2} = \sqrt{73}$[/tex]
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Mrs. Willis is making a dress from
fabric with two different sizes of
squares. A side of the larger square is
twice the length of a side of the smaller
square. What is the perimeter of the
larger square if the perimeter of the
smaller square is 32 centimeters?
Answer:
64 cm
Step-by-step explanation:
You want the perimeter of a larger square if its side lengths are double those of a smaller square with perimeter 32 cm.
PerimeterThe scale factor relating two similar figures is the ratio of a linear dimension of one of them to the corresponding linear dimension of the other one. Here, the side lengths have the ratio 2:1. The perimeter is also a linear dimension, so the perimeters will have the ratio 2:1.
The perimeter of the larger square is 2×32 cm = 64 cm.
__
Additional comment
If you like, you can go to the trouble to find the side lengths and then compute the perimeter of the larger square.
P = 4s . . . . . for a square
s = P/4 = 32 cm/4 = 8 cm . . . . . side length of smaller square
s' = 2(8 cm) = 16 cm . . . . . . . . side length of larger square
P' = 4s' = 4(16 cm) = 64 cm . . . . . perimeter of larger square
By answering the presented question, we may conclude that As a result, the bigger square has a perimeter of 64 cm.
what is Pythagorean theorem?The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.
Let's name the length of one of the smaller square's sides "x." The length of a side of the bigger square is thus "2x" according to the issue statement.
A square's perimeter is just the sum of the lengths of all four sides. As a result, the perimeter of the smaller square is:
4x = 32
We may find x by dividing both sides by 4:
x = 8
We can now calculate the perimeter of the bigger square using the length of its side:
4(2x) = 4(2*8) = 4(16) = 64
As a result, the bigger square has a perimeter of 64 cm.
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