Answer:
[tex]y = {1.5}^{x} [/tex]
[tex] ln(y) = ln( {1.5}^{x} ) [/tex]
[tex] ln(y) = x ln(1.5) [/tex]
[tex]x = \frac{ ln(y) }{ ln(3) - ln(2) } [/tex]
[tex]y = \frac{ ln(x) }{ ln(3) - ln(2) } [/tex]
marvin is trying to get to his friend's house. he walks 4 blocks north to the park, then turns right and walks 3 blocks. finally he turns right and walks 4 blocks. how far from his starting point does he wind up?
Answer: Marvin walks a total of 4 + 3 + 4 = 11 blocks.
To find how far he is from his starting point, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the 4 blocks north and 3 blocks east form the legs of a right triangle, and the distance Marvin is from his starting point is the hypotenuse.
So we can calculate it as follows:
distance = sqrt(4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
Therefore, Marvin is 5 blocks from his starting point.
Step-by-step explanation:
3) During the last week of April, Ryan Foss produced 900 dolls. Ryan
receives $.96 per doll, less any defective units. What was Ryan's
gross pay for the last week of April?
Ryan's gross pay for the last week of April was $864, assuming that 96% of the dolls produced were non-defective.
What was Ryan's gross pay for the last week of April?If Ryan produced 900 dolls during the last week of April and receives $.96 per doll, his gross pay before any defective units are taken into account is:
900 dolls x $0.96/doll = $864
If we need to check if a certain percentage of the dolls produced were defective, we can multiply the gross pay by the percentage of non-defective units to find Ryan's actual gross pay.
For example, if 95% of the dolls produced were non-defective, Ryan's gross pay would be:
$864 x 0.95 = $820.80
Therefore, Ryan's gross pay for the last week of April was $820.80, assuming that 95% of the dolls produced were non-defective.
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The graph of line m is shown. What is the
equation of the line that is perpendicular to line
m and passes through the point (3,2)?
WRITE IN POINT SLOPE FORM
Answer:6
Step-by-step explanation:
Roger can finish his math homework in 6 hours. Trish can finish the
same homework in 5 hours.
What part of the homework will Roger and Trish finish if they
work together for 1 hour?
In linear equation, Roger and Trish can finish 11x/30 of the homework if they work together for x hours.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
In one hour, Roger can finish 1/6 of the work, and Trish can finish 1/5 of the work. So, working together for one hour, they can finish:
(1/6) + (1/5)
= (5/30) + (6/30)
= 11/30 of the work.
If they work together for x hours, then they will finish:
x × (11/30) = 11x/30
of the work in x hours.
Therefore, Roger and Trish can finish 11x/30 of the homework if they work together for x hours.
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ΔDEF ∼ ΔABC. What is the sequence of transformations that maps ΔABC to ΔDEF?
The sequence of transformation that maps ΔABC to ΔDEF is a rotation of 90° about the origin and a translation 2-units down.
What is rotation?An thing rotates when it moves about its own axis. This can be used to describe the rotation of natural items like wheels and gears as well as the rotation of celestial bodies like planets and stars. A fundamental idea in physics, rotation is used to describe a variety of motions.
What is translation?The act of shifting an object from one point to another without altering its size, shape, or orientation is referred to as translation. The coordinates of each point in the object are adjusted by a set amount to achieve this. In geometry and computer graphics, translation is a type of transformation that is frequently used to reposition objects on a two-dimensional plane or in three-dimensional space. In physics, the term "translation" can also refer to an object moving straight ahead without rotating or deforming.
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The temperature rose 5 degrees from 6:00am to 12:00pm.
The average rate of change per hour in the temperature is 0.83 degrees.
What is the average rate of change per hourTo find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.
The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.
Therefore, the average rate of change per hour can be calculated as follows:
average rate of change per hour = total change in temperature / number of hours
So, we have
average rate of change per hour = 5 degrees / 6 hours
average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)
So, the average rate of change per hour is 0.83 degrees.
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PLEASE HELP ME WITH THIS QUESTION IF YOU DO I WILL APPRECIATE IT AND ILL GIVE BRAINLYIEST!
Justin wants to buy a frame for his painting. The frame is 22 1/2 inches wide and 26 1/2 inches long around the exterior. The wood all around the frame is exactly 2 1/2 inches wide. How big does Justin's painting need to be to fit in this frame?
The size of Justin's painting that needs to be to fit in this frame is 530 square inches
How to determine the areaIt is important to note that the formula for the area of a rectangle is expressed with the equation;
A = lw
Such that the parameters of the formula are;
A is the area of the rectanglel is the length of the rectanglew is the width of the rectangleFrom the information given, we have that;
Width of the frame = 22 1/2 inches
Length of the frame = 26 1/2 inches
But the width around the frame = 221/2 - 2 1/2 = 45/2 - 5/2 = 20 inches
Substitute the values
Area = 20(53/2)
multiply the values
Area = 530 square inches
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For the sequence below, which of the following functions best defines this sequence? 7, 13, 19, 25, 31, 37, ...
The function which defines the best fit for the sequence 7,13,19,25,31,37,.... is An= [tex]A_{n-1}[/tex]+6
what is a sequence?A sequence is a grouping of any items or a collection of numbers in a specific order that adheres to some norm. If a1, a2, a3, a4,... etc. represent the terms in a series, then 1, 2, 3, 4,... represent the term's position.
A sequence can be classified as either an infinite or a finite sequence depending on the number of terms.
The equivalent series is given by if a1, a2, a3, a4,....... is a sequence.
Sn = a1 + a2 + a3,a4..... + an
Note: Depending on whether the sequence is finite or infinite, the series is either infinite or finite.
here in this problem,
a2=13⇒ [tex]A_{n} =A_{n-1} +6[/tex] ⇔ [tex]A_{2}[/tex]=7+6=13
and so on for 3rd, 4th, 5th and nth term.
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Mitchell reads only mysteries and sports books. Last year, he read 5 mysteries for every 2 sports books. If Mitchell read 12 more mysteries than sports books, how many mysteries did he read?
Let's start by setting up some equations to represent the information given in the problem.
Let's assume that Mitchell read x sports books last year. According to the problem, he read 5 mysteries for every 2 sports books, so he must have read (5/2)x mysteries.
We also know that he read 12 more mysteries than sports books, so:
(5/2)x - x = 12
Simplifying this equation, we get:
(3/2)x = 12
Multiplying both sides by 2/3, we get:
x = 8
So Mitchell read 8 sports books last year. To find out how many mysteries he read, we can use the equation we derived earlier:
(5/2)x = (5/2)(8) = 20
Therefore, Mitchell read 20 mysteries last year.
Suppose a house has a floor area of 2,250 square feet. What is this area in units ofsquare centimeters?A) 2.42 cm2 D) 6.86 × 104 cm2B) 2.09 × 106 cm2 E) 101 cm2C) 5.02 × 104 cm2
The area in units of square meter is 2,090,318.4 sq cm, under the given condition that a house has a floor area of 2,250 square feet. So , the correct option from the following is Option B.
To convert 2,250 square feet to square centimeters, we can use the conversion factor of 1 square foot = 929.0304 square centimeters⁵. Therefore,
2,250 sq ft = 2,250 x 929.0304 sq cm/ sq ft = 2,090,318.4 sq cm.
The area in units of square meter is 2,090,318.4 sq cm, under the given condition that a house has a floor area of 2,250 square feet. So , the correct option from the following is Option B.
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Two similar solids have edges of 4 feet in 24 feet if the smaller saw that has a volume of 16 ft.³ find the volume of the other solid?
Answer: 3,456
Step-by-step explanation:
Please help!! Equation is in image below.
The real values of "a" that make (x - a) a factor of the given polynomial are: a = 3, a = 2, and a = 3/14.
What are all the real values of a?
To find the values of "a" for which (x - a) is a factor of the given polynomial x⁴ + 3x³ - 6x² - 28x - 24, we can use the Remainder Theorem.
So, let's divide the given polynomial by (x - a) and set the remainder to zero to find the values of "a".
Using long division or synthetic division, we get:
x³ + (a - 3)x² + (3a - 6)x + (6 - 28a)
__________________________________________
x - a | x⁴ + 3x³ - 6x² - 28x - 24
Since the remainder is zero, we have;
x³ + (a - 3)x² + (3a - 6)x + (6 - 28a) = 0
Now, for (x - a) to be a factor of the given polynomial, the coefficients of x², x, and the constant term must be zero, because these are the coefficients of (a - 3)x², (3a - 6)x, and (6 - 28a), respectively.
So, we can set them to zero and solve for "a":
a - 3 = 0 (Coefficient of x²)
3a - 6 = 0 (Coefficient of x)
6 - 28a = 0 (Constant term)
Solving these equations, we get:
a - 3 = 0 => a = 3
3a - 6 = 0 => 3a = 6 => a = 2
6 - 28a = 0 => 28a = 6 => a = 6/28 => a = 3/14
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Question 3
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
Question 4
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 5
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
The correct answer is: The IQR of 13 is the most accurate to use, since the data is skewed. (Option B).
The correct answer is: Together, Streetcar and Cable Car are the preferred transportation for 168 residents. (Option A).
The correct answer is: The IQR is the best measure of variability, and it equals 6.
How to Solve the Problem?1. Since the data is skewed, it is not appropriate to use the range as a measure of variability. The range is sensitive to extreme values and can be misleading in skewed data. The interquartile range (IQR) is a better measure of variability for skewed data since it is not affected by extreme values. Therefore, the charity should use the IQR of 13 as the measure of variability for this data.
2. From the circle graph, we can draw the following conclusion:
Together, Streetcar and Cable Car are the preferred transportation for 27% + 15% = 42% of the residents. 42% of 400 is 168 residents.
3. The line plot shows that the data is discrete and not continuous. Also, the data is not normally distributed and is skewed. Therefore, the range is not an appropriate measure of variability. The interquartile range (IQR) is a better measure of variability for skewed data. The IQR is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data.
From the plot, we can see that Q1 is 2 and Q3 is 8. Therefore, the IQR is 8 - 2 = 6.
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1)what is the answer with transformations
A) (x,y) →>(5x, 5y)
B) (x,y) → (1/5x1/5)
C) (x,y) →(x+ 5, y+5)
D) (x,y) →(x-5, y-5)
A) represents a dilation by a scale factor of 5 with respect to the origin.
B) represents a dilation by a scale factor of 1/5 with respect to the origin.
C) represents a translation 5 units to the right and 5 units up.
D) represents a translation 5 units to the left and 5 units down.
A transformation is a process of changing the position, size, or shape of a geometric object or set of points in the coordinate plane.
The given expressions represent different types of transformations in the coordinate plane:
A) (x, y) → (5x, 5y) represents a dilation, where the image is five times larger than the original point with respect to the origin.
B) (x, y) → (1/5x, 1/5y) represents a dilation, where the image is one-fifth the size of the original point with respect to the origin.
C) (x, y) → (x+5, y+5) represents a translation, where the image is shifted 5 units to the right and 5 units up from the original point.
D) (x, y) → (x-5, y-5) represents a translation, where the image is shifted 5 units to the left and 5 units down from the original point.
In summary:
A) represents a dilation by a scale factor of 5 with respect to the origin.
B) represents a dilation by a scale factor of 1/5 with respect to the origin.
C) represents a translation 5 units to the right and 5 units up.
D) represents a translation 5 units to the left and 5 units down.
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find the antiderivative:x/square root of x
The antiderivative of f(x) = x/√x is [tex](2/3)x^{3/2} + C[/tex],
where C is the constant of integration.
To find the antiderivative of the given function.
The function is: f(x) = x/√x
First, let's rewrite the function in a more convenient form for integration:
f(x) = x / √x
[tex]= x / x^{1/2}[/tex]
[tex]= x^{1 - 1/2}[/tex]
[tex]= x^{1/2}[/tex]
Now, let's find the antiderivative using the power rule for integration:
∫[tex]x^{1/2} dx[/tex]
To apply the power rule, we need to add 1 to the exponent and then divide by the new exponent:
Antiderivative = [tex](x^{(1/2) + 1)) / ((1/2) + 1} ) + C[/tex]
Antiderivative =[tex](x^{3/2/ 3/2} + C)[/tex]
Finally, multiply by the reciprocal to simplify the expression:
Antiderivative = [tex](2/3)x^{3/2} + C.[/tex].
An antiderivative, also known as an indefinite integral, is a function that, when differentiated, yields a given function. In other words, an antiderivative of a function f(x) is a function F(x) such that F'(x) = f(x).
For example, if f(x) = 2x, then an antiderivative of f(x) would be F(x) = x^2 + C,
where C is a constant of integration.
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The list shows the numbers of hours 5 employees worked at a store.
14 23 26 40 26
What is the mean of the numbers of hours worked by the employees?
Enter your answer as a decimal in the box provided.
Therefore, 25.8 hours per employee each week is the mean number of hours worked.
What does that mean?The mean in mathematics is the average value among a group of numbers. It is calculated by adding up all of the set's numbers, then dividing the result by the total number of numbers in the set.
You may calculate the mean, for instance, if you have the set of numbers 2, 4, 6, and 8, by adding them all together and dividing by the total number of numbers:
(2 + 4 + 6 + 8) / 4 = 20 / 4 = 5
Consequently, 5 is the mean of these numbers.
In this instance, a store employed 5 workers for varying shifts. The list displays each individual's hours worked.
14 23 26 40 26
We add up all of these numbers and divide by the total number of numbers to determine the mean:
(14 + 23 + 26 + 40 + 26) / 5
= 129 / 5 mean of the numbers of hours worked by the employees = 25.8
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What is the median?
0 7 27 10 0 3
Answer: Median is 5
Step-by-step explanation: To find the median, we first need to arrange the numbers in order from least to greatest:
0 0 3 7 10 27
The median is the middle number, or the average of the two middle numbers if there are an even number of values. In this case, there are 6 values, so the median is the average of the two middle numbers:
median = (3 + 7) / 2
median = 5
Therefore, the median of the given numbers is 5.
A teacher has a prize box that has 6 fidgets,2 rubix cubes,and 2 pop its-as well as a bag of candy that has 4 lollipops and 3 fieces of chocolate. Esther wins the weekly prize in class and can pick one toy from the prize box and one candy from the candy bag. What is the probability she will pick a fidget and a piece of chocolate?
The probability of Esther picking a fidget and a piece of chocolate is 3/14.
How to obtain the probabilityTo obtain the probability, we first need to list the items and then determine the chances of them being picked. Fisrt, there are a total of 12 items in the prize box and 7 items in the candy bag.
The probability of Esther picking a fidget from the prize box is 6/12 or 1/2, and the probability of her picking a piece of chocolate from the candy bag is 3/7. Since these events are independent, we can multiply their probabilities to find the probability of both events occurring:
P(fidget and chocolate) = P(fidget) x P(chocolate)
P(fidget and chocolate) = (1/2) x (3/7)
P(fidget and chocolate) = 3/14
Therefore, the probability of Esther picking a fidget and a piece of chocolate is 3/14.
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What function is represented by the mapping diagram shown?
-2
00
6
2135
A. F(x)= x+3
B. F(x)= 3x
C. F(x) = 2x
D. F(x)=x-3
24600
2
8
Answer:c. F(x)=2x
Step-by-step explanation:
Weights of the Pacific yellowfin tuna follow a normal distribution with mean weight 68 pounds and standard deviation 12 pounds. For a randomly caught Pacific yellowfin tuna, what is the probability that the weight is less than 50 pounds
The probability that the weight of a randomly caught Pacific yellowfin tuna is less than 50 pounds is approximately 0.0668 or 6.68%.
The weights of the Pacific yellow fin tuna follow a normal distribution with a mean weight of 68 pounds and a standard deviation of 12 pounds. To find the probability that a randomly caught Pacific yellow fin tuna weighs less than 50 pounds, we can follow these steps:
1. Calculate the z-score for the weight of 50 pounds using the formula:
z = (X - μ) / σ
where X is the weight, μ is the mean, and σ is the standard deviation.
2. Find the probability associated with the z-score using a z-table or calculator.
Let's calculate the z-score:
z = (50 - 68) / 12
z = -18 / 12
z = -1.5
Now, we can use a z-table or calculator to find the probability associated with the z-score of -1.5. The probability that a randomly caught Pacific yellow fin tuna weighs less than 50 pounds is approximately 0.0668, or 6.68%.
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 write a division expression for each 2. 5/6,3. 9/15,4. 10/25,5. 16/31
The division expressions are given below.
Given are divisions, we need to write their division expressions,
5/6 = 5÷6
9/15 = 9÷15 = 3÷5
10/25 = 10÷25 = 2÷5
16/31 = 16÷31
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7. A bag contains 8 cards numbered from 1 through 8. Jeremiah records the experimental probability of randomly choosing the number 5 after 50, 100, 150, and 200 trials. For which number of trials would you expect the experimental probability to be closest to ? (A) 50 trials B 100 trials C 150 trials (D) 200 trials
Among the given options, the number of trials that comes closest to a large number is 200 trials (option D). Therefore, we would expect the experimental probability to be closest to 1/8 after 200 trials.
What is probability?
The probability of randomly choosing the number 5 from the bag of 8 cards is:
P(choosing 5) = number of 5 cards / total number of cards
Since there is only one card numbered 5 in the bag, the probability of choosing the number 5 is 1/8.
The experimental probability of choosing the number 5 after "n" trials can be calculated by counting the number of times the number 5 is chosen in "n" trials and dividing by "n".
For example, after 50 trials, we expect to choose the number 5 approximately:
P(choosing 5 after 50 trials) = number of times 5 is chosen in 50 trials / 50
We can simplify this expression as:
P(choosing 5 after 50 trials) = (1/8) x number of times 5 is chosen in 50 trials
Similarly, we can calculate the experimental probability for 100, 150, and 200 trials:
P(choosing 5 after 100 trials) = (1/8) x number of times 5 is chosen in 100 trials
P(choosing 5 after 150 trials) = (1/8) x number of times 5 is chosen in 150 trials
P(choosing 5 after 200 trials) = (1/8) x number of times 5 is chosen in 200 trials
To determine which number of trials would give us the experimental probability closest to 1/8, we need to consider the law of large numbers, which states that as the number of trials increases, the experimental probability approaches the theoretical probability.
Therefore, we would expect the experimental probability to be closest to 1/8 after a large number of trials. Among the given options, the number of trials that comes closest to a large number is 200 trials (option D). Therefore, we would expect the experimental probability to be closest to 1/8 after 200 trials.
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Chloe had 74 pennies and then lost 10. Now she wants to buy a treat that costs 5 eighths of the pennies she has left. How many pennies does the treat cost?
The cost of the treat would be 40 pennies.
In mathematics, an expression is a combination of symbols (such as numbers, variables, and operations) that represents a value.
Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple operations and variables. They can also include functions, exponents, and other mathematical concepts.
Chloe started with 74 pennies and lost 10, so she has 74 - 10 = 64 pennies left. The treat costs 5/8 of her remaining pennies,
Calculate the cost by multiplying 5/8 by 64:
(5/8) x 64 = 40
Therefore, the treat costs 40 pennies.
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Frahan travels from Town A to Town B at an average speed of 4 Km/h and from Town B to Town A at an average
speed of 3 Km/h. He takes 25 minutes to complete the entire journey.
(a) Convert 25 minutes into hours.
(b) Find his total distance travelled.
to convert 25min into hours we divide 25 by 60 so the answer would be 0.416 hours
the formula to find the distance is we multiply speed and time so
distance=4km/p X 0.416 hours =1.664
so now we have the first answer
now we do the same thing for the other part of the question
distance= timeXspeed
distance=0.416X3=1.248
then we add to find total distance
1.248+1.644=2.912
2.912 is the total distance
Find the probability
The probability that point X is on segment DE is given as follows:
1/9.
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.
The length of segment AE is given as follows:
28 - (-8) = 36 units.
The length of segment DE is given as follows:
28 - 24 = 4 units.
Hence the probability is given as follows:
p = 4/36
p = 1/9.
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Which of the following is the best example of a defined benefits plan?
O a set amount an employee will receive at retirement
O the wages and benefits an employee receives at a job
O the amount of pay an employee receives each hour
O the money the an employer puts into a retirement fund for each employee
Answer:
The best example of a defined benefits plan is: "a set amount an employee will receive at retirement".
In a defined benefits plan, the employer promises to pay employees a specific, predetermined amount of money upon retirement. This amount is typically based on factors such as the employee's salary and years of service. The employer is responsible for contributing to and managing the retirement fund, and the employee receives a guaranteed amount of money upon retirement, regardless of how the fund performs.
The other options listed are not examples of defined benefits plans. The wages and benefits an employee receives at a job are part of their compensation package and may include retirement benefits, but they do not guarantee a specific amount of money at retirement. The amount of pay an employee receives each hour is their hourly wage and is not related to retirement benefits. The money an employer puts into a retirement fund for each employee may be part of a defined benefits plan, but it is not a complete plan in and of itself.
the mean of a normal probability distribution is 480; the standard deviation is 12. a. about 68% of the observations lie between what two values?
The difference between two observation concerning the values are 68% of observation lie in between 468 and 492 , then 95% of observation lie in 456 and 504.
The normal distribution is considered a continuous probability distribution that has a different bell-shaped probability density function. Therefore, the mean of a normal distribution is the center of its symmetric bell-shaped curve.
Therefore it is given , a normal distribution with mean of 480 and standard deviation 12
Lower limit = Mean - Standard deviation = 480 - 12 = 468
Upper limit = Mean + Standard deviation = 480 + 12 = 492
Following the same procedure then the results to evaluate for 95%
The difference between two observation concerning the values are 68% of observation lie in between 468 and 492 , whereas 95% of observation lie in 456 and 504.
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how do i solve this please help
The percentage of Container B that is full after the pumping is complete is 77.2%.
How to find the percentage ?To find the percentage of Container B that is full after the water from Container A is pumped into it, we first need to find the volume of both containers.
The volume V of a cylinder can be calculated using the formula:
V = πr²h
Volume of Container A (V A) = π x (10^2) x 20 = 2000π cubic feet
Volume of Container B (V B) = π x (12^2) x 18 = 2592π cubic feet
Percentage = (V A / V B) x 100
Percentage = (2000π / 2592π) x 100
Percentage = (2000 / 2592) x 100 = 77.1604938
To the nearest tenth, the percent of Container B that is full after the pumping is complete is approximately 77.2%.
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What transformations take the graph of f(x)=e^x to f(x)=-e^x-2?
Answer:
the transformations that take the graph of those two equations are a reflection about the x-axis followed by a vertical shift downward by 2 units.
Step-by-step explanation:
Reflection: this reflects the original graph f(x)=e^x below the x-axis, resulting in the graph of -e^x.
Vertical shift: this will shift the graph -e^x downwards by 2 units.
Therefore, the transformations are a reflection about the x-axis followed by a vertical shift downward by 2 units.
Using the calculus rule, how could the following derivative be rewritten as 2 partial derivatives?(dx/dz) at constant y
Using the calculus rule, we can rewrite the total derivative (dx/dz) at constant y as the sum of two partial derivatives.
The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y
Apply the chain rule
The chain rule in calculus allows us to find the derivative of a function with respect to another variable, by considering how the intermediate variables change.
In this case, we want to find (dx/dz) at constant y.
The chain rule states:
(dx/dz) = (dx/dy)*(dy/dz) + (dx/dz) at constant y
Identify the partial derivatives:
Since we want to rewrite (dx/dz) as a sum of two partial derivatives, we will keep the terms (dx/dy) and (dy/dz) as partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y
Final answer
The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y.
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