The electrician's rate experienced a 25% increase compared to what he charged in the year 2018.
A percentage is a number or ratio expressed as a fraction of 100, used to indicate the portion of something in relation to its whole.
To find the percentage increase in the rate, we need to calculate the difference between the two rates and express it as a percentage of the original rate.
The difference between the two rates is
$12,500 - $10,000 = $2,500
To express this difference as a percentage of the original rate, we need to divide it by the original rate and then multiply by 100:
($2,500 / $10,000) x 100% = 25%
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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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An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist's findings is that 18 months after the workshop, a sample of 81 job seekers who received training on using the Internet to find job listings worked more than 30 hours per week an average of 8. 7 months in the last year, with a standard deviation of 4. 1. The typical job seeker works 7. 4 months. The psychologist finds that the estimated Cohen's d is _____, the t statistic is 2. 83, and r^2 is ______. Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a ______ treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size using r^2, there is a ______ treatment effect. Another one of the psychologist's findings is that a sample of 81 job seekers who received training on interview skills scored an average of 8. 1 as measured on a 9-point job search motivation scale, with a standard deviation of. 8. The typical job seeker scores 7. 4 points. She finds that the estimated Cohen's d is _____, the t statistic is 7. 78, and r^2 is _____ Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size with r^2, there is a ___ treatment effect
The psychologist finds that the estimated Cohen's d is 0.32, the t statistic is 2. 83, and r² is 0.073. Using r² and the extension of Cohen's guidelines for interpreting the effect size using r², there is a small treatment effect. job seeker finds that the estimated Cohen's d is 0.88, the t statistic is 7. 78, and r² is 0.479.Using r² and the extension of Cohen's guidelines for interpreting the effect size with r², there is a large treatment effect
To calculate the estimated Cohen's d, we use the formula
d = (M - M0) / SD
where M is the mean of the treatment group (job seekers who received training on using the Internet to find job listings), M0 is the mean of the control group (typical job seeker), and SD is the pooled standard deviation of the two groups. Using the given values, we have
M = 8.7 months
M0 = 7.4 months
SD = 4.1 months
So, d = (8.7 - 7.4) / 4.1 = 0.32
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.32, there is a small treatment effect.
To calculate r², we use the formula
r² = t² / (t² + df)
where t is the t statistic, df is the degrees of freedom (n-2 for a two-group design), and n is the sample size. Using the given values for the Internet training group, we have
t = 2.83
n = 81
df = 79
So, r² = 2.83² / (2.83² + 79) = 0.073
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.073, there is a small treatment effect.
For the job seekers who received training on interview skills, we can calculate Cohen's d and r² in a similar way
d = (M - M0) / SD = (8.1 - 7.4) / 0.8 = 0.88
t = 7.78
n = 81
df = 79
r² = 7.78² / (7.78² + 79) = 0.479
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.88, there is a large treatment effect.
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.479, there is a medium to large treatment effect.
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Answer:.317
.091
Small to med
Med
.875
.431
Large
Large
Step-by-step explanation:
help me please please
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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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
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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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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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.
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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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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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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Use the equation below to answer the question. 6x + 3 = 3(2x + 3) Which statement correctly explains whether the equation is true or not?
Answer:
It should be the first one
Step-by-step explanation:
3x2=6
3x3=9
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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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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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
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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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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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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(Please help!!!) The heights of 14 plants, in inches, are listed.
12, 14, 15, 15, 16, 16, 16, 17, 18, 18 ,19, 20, 22, 25
If another plant with a height of 13 inches is added to the data, how would the mean be impacted?
The mean would stay the same value of about 17.1 inches.
The mean would decrease in value to about 17.1 inches.
The mean would stay the same value of about 17.4 inches.
The mean would increase in value to about 17.4 inches.
As a result, the mean would be approximately **15.87** inches. The solution is **B**.
The mean would decrease in value to about 17.1 inches.
Defining Mean?The mean in mathematics is a measurement of a set of numbers' central tendency. The average is another name for it. A set of numbers are added together to determine the mean, which is then divided by the total number of values in that set.
The sum of a collection of integers divided by the total number of values in the set yields the mean of the set.
12 + 14 + 15 + 15 + 16 + 16 + 17 + 18 + 18 + 19 + 20 + 22 + 25 = **225** is the total height of the 14 plants.
Rounding to two decimal places, the mean height of these plants is 225/14, or **16.07** inches.
The revised sum of heights would be **238** if an additional plant with a height of 13 inches were to be included in the data.
238/15 = **15.87** inches (rounded to two decimal places) would be the new mean height.
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Impactation in the mean is B)The mean would decrease in value to about 17.1 inches.
Defining Mean?
The mean in mathematics is a measurement of a set of numbers' central tendency. The average is another name for it. A set of numbers are added together to determine the mean, which is then divided by the total number of values in that set.
The sum of a collection of integers divided by the total number of values in the set yields the mean of the set.
=>12 + 14 + 15 + 15 + 16 + 16 + 17 + 18 + 18 + 19 + 20 + 22 + 25 = **225** is the total height of the 14 plants.
Rounding to two decimal places, the mean height of these plants is
=> 225/14, or **16.07** inches.
The revised sum of heights would be **238** if an additional plant with a height of 13 inches were to be included in the data.
=> 238/15 = **15.87** inches (rounded to two decimal places) would be the new mean height.
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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
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
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.
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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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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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)
PLEASE HELP!!!
The picture explains the problem
The inequality represented by the given number line is: -60 ≥ m.
Explain about the inequality on number line:We can see the values that an inequality represents by placing it on a number line.
On a number line, inequalities are represented by drawing a straight line and designating the end points as an open or closed circle.
An empty circle indicates that the value is not included.A closed circle indicates that the value is included.On a number line, inequality is represented as follows:
Choose the value or values that must be displayed on the number line.Determine if an > or < open circle or a ≥ or ≤closed circle is required; the situation either requires an open circle or a closed circle.Draw a straight line either to the number's left or right side or in between the circles to indicate the solution set.For the given number line,
-6 is shown with the closed circle, with lines extending towards +∞
Thus, the inequality represented by the given number line is: -60 ≥ m.
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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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I need help with this question can you help?
Answer:
The Correct answer is sinA/3.2=sin110°/4.6