Answer:
(a)His monthly Interest Rate=0.8%
(b)Annual Interest Rate = 9.6%
(c)[tex]500(1.008)^m[/tex]
Step-by-step explanation:
For a Principal P invested at a yearly rate r, compounded m times in t years
Amount at Compound Interest= [tex]P(1+\frac{r}{m})^{mt}[/tex]
Comparing with Jerry's equation y=388 (1.008)
(a)His monthly Interest Rate= 0.008=0.8%
(b)Annual Interest Rate= Monthly Interest Rate X 12 =0.8 X 12 = 9.6%
(c)If I invest $500 at the same rate of return,
Total Money after m months
= [tex]P(1+\frac{r}{m})^{mt}[/tex][tex]=500(1+0.008)^{m}[/tex][tex]=500(1.008)^m[/tex]
Final answer:
Jerry's monthly interest rate is 0.8%, and his annual interest rate is approximately 9.96%. An investment of $500 in the same account would grow according to the equation [tex]y = 500(1.008)^{m}[/tex], where m represents the months invested.
Explanation:
Jerry says he's got his money in a great account that compounds interest monthly. The equation [tex]y=388(1.008)^{m}[/tex] represents how much money he has at the end of the month. The monthly interest rate is found in the equation inside the parentheses, 1.008, which means the monthly interest rate is 0.8% (since 1.008 is equal to 1 plus 0.008 or 1 + 0.8/100). To find the annual interest rate, we need to use the compounding formula, which for monthly compounding can be simplified to [tex](1 + monthly interest rate)^{12} - 1[/tex]. so, [tex](1.008)^{12}- 1[/tex] gives an annual rate of approximately 9.96%.
To write an equation representing your total money if you invest $500 in an account with the same rate of return, we use the formula [tex]y = P(1 + r)^{m}[/tex], where P is the principal amount ($500), r is the monthly interest rate (0.008), and m represents the number of months the money has been invested. Therefore, the equation is [tex]y = 500(1.008)^{m}[/tex].
Which of the following are ordered pairs for the equation y = 2x - 3?
(0,-3) (1,-1) (2,1)
(-3,0) (-2,2) (-1,4)
(0,-3) (2,-2) (4,-1)
(-3,0) (-1,1) (1,2)
Answer:
A.
Step-by-step explanation:
The problem states that -3 is our y-intercept, so (0,-3) must be one of the answer choices. Next, just graph the equation to find the other two coordinate pairs are (1,-1) and (2,1).
A differentiable function f(x,y)f(x,y) has the property that f(2,5)=5f(2,5)=5 and fx(2,5)=−7fx(2,5)=−7 and fy(2,5)=7fy(2,5)=7. Find the equation of the tangent plane at the point on the surface z=f(x,y)z=f(x,y) where x=2x=2, y=5y=5.
Answer:
-7x +7y -z = 16
Step-by-step explanation:
We can define the function ...
F(x, y, z) = f(x, y) -z
and differentiate at the point (x, y, z) = (2, 5, 5) to get ...
fx(2, 5, 5) = -7 . . . . given
fy(2, 5, 5) = 7 . . . . given
fz(2, 5, 5) = -1 . . . . partial derivative of the above equation
Then the equation of the plane can be written as ...
fx(x -2) +fy(y -5) +fz(z -5) = 0
-7(x -2) +7(y -5) -1(z -5) = 0 . . . . . substitute for fx, fy, fz
-7x +14 +7y -35 -z +5 = 0 . . . . . eliminate parentheses
-7x +7y -z = 16 . . . . equation of the tangent plane
In the year 2000, the population of
Adams County was 60,000 residents.
Each year since, its population has
decreased 0.1%. Predict what the
population of Adams County will be
in the year 2015.
12,353 51,604 or 59,106
Answer: 59106
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^ t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 60000
r = 0.1% = 0.1/100 = 0.001
t = 2015 - 2000 = 15 years
Therefore
A = 60000(1 - 0.001)^15
A = 60000(0.999)^15
A = 59106
The predicted population of Adams County in the year 2015 is calculated using the initial population and applying a yearly decrease of 0.1% over 15 years, resulting in approximately 59,106 residents.
The question involves calculating the predicted population of Adams County in the year 2015 based on a yearly decrease of 0.1% from the year 2000.
To find the population in 2015, we need to apply the percentage decrease for each year from 2000 to 2015, which is a total of 15 years. The formula to calculate the population after a certain number of years with a consistent percentage change is: [tex]P = P_0 (1 - r)^t[/tex] where P is the final population, P₀ is the initial population, r is the rate of decrease, and t is the number of years.
Using the given data, P0 = 60,000, r = 0.001 (0.1% expressed as a decimal), and t = 15 years.
So, the calculation will be: P = 60,000 (1 - 0.001)¹⁵ = 60,000 (0.999)¹⁵ = 60,000 (0.985075) ≈ 59,106
Therefore, the predicted population of Adams County in the year 2015 is approximately 59,106 residents.
The scale on the town map is 1inches = 3miles the distance from dinas home to her school is 0.75 on the map when dina rides her bike from her home to school how many miles does ride?
Answer:
2.25 miles.
Step-by-step explanation:
Given,
In map, the scale is, 1 inch = 3 miles,
That is, the number of miles in 1 inch = 3,
The number of miles in 0.75 inch = 0.75 × number of miles in 1 inch,
= 0.75 × 3
= 2.25
Thus, 0.75 inch = 2.25 miles.
According to the question,
Distance from home to school in scale = 0.75 inch
Hence, the actual distance from home to school is 2.25 miles.
Answer:
2.25
Step-by-step explanation:
A friend tells you to apply for a sales job at a certain company because the mean income of salespeople last year was $47,500. Last year, 6 salespeople earned $33,000, 3 earned $46,000, 2 earned $42,000 and 1 earned $150,000. Would you apply for the job based on what your friend says? Explain in reference to the 3 measures of center.
Answer:
it depends on if i think i could succeed in tha job
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
Mean is not a good measure of the centre because 150,000 is an outlier
Mode is $33,000
Median is $39,500
[(33000+46000)/2 = 39500]
Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of 1,000 passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the 1,000 passengers, 345 had more than one bag.
The domestic version of Boeing's 747 has a capacity for 568 passengers. Determine an interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane. Assume the plane is at its passenger capacity.
a) (171.651, 216.214)
b) (181.514, 208.313)
c) (174.412, 217.218)
d) (179.20, 212.716)
Answer:
The correct option is
d) (179.20, 212.716)
Step-by-step explanation:
We have out of a random sample of 1000, 345 carried more than a bag
Therefore in the question our X = 345 passengers carry more than a piece of luggage
n = 1000
Therefore the probability of a passenger carrying more than one luggage = 345/1000 = 0.345
The confidence interval estimator of p is given by
[tex]p'+/-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }[/tex] where p' = 0.345 = probability of desired outcome
n = 1000 = Population size
z at 95 % = Confidence interval estimate, the value is sought from the distribution table as z value is 1.96 at 95 % confidence level
We have [tex]0.345+/-1.96\sqrt{\frac{0.345*(0.655)}{1000} }[/tex] which gives
0.3745 or 0.3155
Which gives the range of confidential interval estimate as
212.695 to 179.224 which is equivalent to
d) (179.20, 212.716).
To determine the interval estimate of the number of passengers carrying more than one piece of luggage on the plane, we use the formula for the confidence interval for a proportion. The interval estimate is (0.3132, 0.3768), so we can expect the number to be between 313 and 377 passengers.
Explanation:To determine the interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane, we can use the formula for the confidence interval for a proportion. First, we calculate the sample proportion of passengers carrying more than one bag, which is 345/1000 = 0.345. Then, we find the standard error using SE = sqrt(p(1-p)/n), where p is the sample proportion and n is the sample size. Substituting the values, we get SE = sqrt(0.345(1-0.345)/1000) = 0.0162.
Next, we find the margin of error by multiplying the standard error by the critical value for the desired level of confidence. Since the problem does not specify a level of confidence, we will use a 95% confidence level, which corresponds to a critical value of 1.96. The margin of error is therefore 1.96 * 0.0162 = 0.0318.
Finally, we construct the confidence interval by subtracting and adding the margin of error from the sample proportion. The interval estimate is given by (0.345 - 0.0318, 0.345 + 0.0318), which simplifies to (0.3132, 0.3768). Therefore, we can expect the number of passengers carrying more than one piece of luggage on the plane to be between 313 and 377.
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piecewise function f(x) is below. What is the value of f(3)?
Option B:
f(3) = 5
Solution:
Given function:
[tex]f(x)=\left\{\begin{aligned}-x^{2}, \ \ & x<-2 \\3, \ \ &-2 \leq x<0 \\x+2, \ \ & x \geq 0\end{aligned}\right.[/tex]
If x value is less than –2, that is –3, –4, –5, –6, ... then f(x) = –x².If x value is greater than or equal to –2 and less than 0, that is –2 and –1 then f(x) = 3.If x value is greater than or equal to 0, that is 0, 1, 2, 3,... then f(x) = x +2.To find the value of f(3):
Here x value is 3 which is greater than 0 (3 > 0).
Therefore, f(x) = x + 2.
Substitute x = 3 in the above function.
f(3) = 3 + 2
f(3) = 5
Hence option B is the correct answer.
The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a lot contains 1000 chips. Approximate the following probabilities: _________.a. More than 25 chips are defective. b. Between 20 and 30 chips are defective.
Answer:
a) The approximate probability that more than 25 chips are defective is 0.1075.
b) The approximate probability of having between 20 and 30 defecitve chips is 0.44.
Step-by-step explanation:
Lets call X the total amount of defective chips. X has Binomial distribution with parameters n=1000, p =0.02. Using the Central Limit Theorem, we can compute approximate probabilities for X using a normal variable with equal mean and standard deviation.
The mean of X is np = 1000*0.2 = 20, and the standard deviation is √np(1-p) = √(20*0.98) = 4.427
We will work with a random variable Y with parameters μ=20, σ=4.427. We will take the standarization of Y, W, given by
[tex] W = \frac{Y-\mu}{\sigma} = \frac{Y-20}{4.427} [/tex]
The values of the cummmulative distribution function of the standard normal random variable W, which we will denote [tex] \phi [/tex] , can be found in the attached file. Now we can compute both probabilities. In order to avoid trouble with integer values, we will correct Y from continuity.
a)
[tex]P(X > 25) = P(X > 25.5) \approx P(Y>25.5) = P(\frac{Y-20}{4.427} > \frac{25.5-20}{4.427}) =\\P(W > 1.2423) = 1-\phi(1.2423) = 1-0.8925 = 0.1075[/tex]
Hence the approximate probability that more than 25 chips are defective is 0.1075.
b)
[tex]P(20<X<30) = P(20.5 < X < 29.5) \approx P(20.5<Y>29.5) = \\P(\frac{20.5-20}{4.427} < \frac{Y-20}{4.427} < \frac{29.5-20}{4.427}) = P(0.1129 < W < 2.14) = \phi(2.14)-\phi(0.1129) = \\0.9838-0.5438 = 0.44[/tex]
As a result, the approximate probability of having between 20 and 30 defecitve chips is 0.44.
Final answer:
To approximate the probabilities of defective chips where 2% are defective from a lot of 1000, the binomial distribution is used, with more complex probability calculations often requiring statistical software. Both (a) more than 25 defective and (b) between 20 and 30 defective scenarios can be estimated using normal approximation due to the large sample size and small defect probability.
Explanation:
To approximate the probability of defective chips in the scenario where 2% of the semiconductor chips produced are defective, we can use the binomial distribution as an approximation because the sample size is large (n=1000) and the probability of a defect (p=0.02) is small.
For part (a), more than 25 chips are defective, we are looking for P(X>25). The calculation for this is more complex and typically done using statistical software or a calculator with binomial capabilities.
For part (b), between 20 and 30 chips are defective, we need to find the probability that X is between 20 and 30 inclusively, or P(20 ≤ X ≤ 30). This requires calculating the cumulative probability for 20 through 30 and then subtracting the lower end from the higher end.
In real-world applications, as the number of trials is large and the probability of success is small, the binomial distribution can be approximated by a normal distribution. The mean (μ) of the distribution is np and the variance (σ2) is np(1-p), which would give us μ = 20 and σ2 = 19.6 for this example. We can then use the standard normal table or a calculator to find the probabilities for parts (a) and (b).
Solve -1 4/5 x = 9.
5
-5
-
Answer:
C) -5
Step-by-step explanation:
-1 4/5 x= 9.
Change the left side to an improper fraction
(5*1+4)/5 = 9/5
-9/5 x =9
Multiply each side by -5/9 to isolate x
-5/9 * 9/5x = 9 * (-5/9)
x = -5
Answer:
x=-5
Step-by-step explanation:
-1 4/5x=9
-9/5x=9
-9x=9*5
-9x=45
x=45/(-9)
x=-5
There were 90 days in the first semester of Margaret’s school year. If she brought her lunch to school 30% of the time, how many days did she bring her lunch during the first semester?There were 90 days in the first semester of Margaret’s school year. If she brought her lunch to school 30% of the time, how many days did she bring her lunch during the first semester?
Answer:
27 days
Step-by-step explanation:
There is a total of 90 days in the semester, and she bought lunch 30% of the total days, then the total number of days she brought the lunch is 27 days.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the information provided in the question,
Total days in the semester = 90
Margaret comes with lunch, 30% of the total days.
So, in total days, Margaret comes with lunch,
D = 90 × 30/100
D = 2700/100
D = 27 days.
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Before polling the students in Scion School of Business, a researcher divides all the current students into groups based on their class standing, such as freshman, sophomores, and so on. Then, she randomly draws a sample of 50 students from each of these groups to create a representative sample of the entire student body in the school. Which of the following sampling methods is the researcher practicing? 1. stratified random sampling 2. simple random sampling 3. cluster sampling 4. systematic random sampling 5. snowball sampling
Answer:
Correct option: 3. Cluster Sampling.
Step-by-step explanation:
Cluster sampling method is the type of sampling where first the entire population is divided into groups and then a random sample of fixed size is selected from each group.
In this case also, the researcher first divides the population of students in Scion School of Business into groups according to their class standing.
Then he selects 50 students from each of these groups to create a representative sample of the entire student body.
Thus, the sampling method used is Cluster Sampling.
Which set of ordered pairs represents a function? A {(22, 5), (23, 10), (22, 7), (23, 5)} B {(22, 5), (26, 10), (23, 7), (23, 5)} C {(22, 10), (23, 10), (24, 7), (25, 5)} D {(24, 10), (23, 6), (22, 7), (24, 5)}
Answer:
C
Step-by-step explanation:
A function is a special kind of relation in which each valid input gives exactly one output.
C {(22, 10), (23, 10), (24, 7), (25, 5)}
So C is the correct option.
Write a quadratic function in vertex form whose graph has the vertex (5,−2) and passes through the point (7,0).
The quadratic function in vertex form is [tex]y=\frac{1}{2} (x-5)^{2}-2[/tex].
Solution:
The equation of a quadratic in vertex form is [tex]y=a(x-h)^{2}+k[/tex].
where (h, k) are the coordinates of the vertex and "a" is a multiplier.
Here (h, k) = (5, –2)
Substitute this in the vertex form.
[tex]y=a(x-5)^{2}+(-2)[/tex]
[tex]y=a(x-5)^{2}-2[/tex] – – – – (1)
Passes through the point (7, 0).
Here x = 7 and y = 0.
Substitute this in equation (1), we get
[tex]0=a(7-5)^{2}-2[/tex]
[tex]0=4a-2[/tex]
Add 2 on both sides.
2 = 4a
Divide 2 on both sides, we get
[tex]$a=\frac{1}{2}[/tex]
Substitute the value of a in equation (1),
[tex]$y=\frac{1}{2} (x-5)^{2}-2[/tex]
The quadratic function in vertex form is [tex]y=\frac{1}{2} (x-5)^{2}-2[/tex].
If the median of a negatively skewed distribution is 31, which value could be the mean of the distribution?
A. 33
B. 36
C. 31
D. 28
Answer:
D. 28
Step-by-step explanation:
If a distribution is negatively skewed, the mean of the distribution is always less than the median.
If the median of a negatively skewed distribution is 31, then from the given options, the only value that is less than 31 is 28.
Therefore the mean could be 28.
The correct answer is D
To win the carnival game Ring Ding, you must toss a wooden ring onto a grid of rectangles so that it lands without touching any of the grid lines. The ring has a 3-inch diameter, the rectangles are twice as long as they are wide, and the game has been designed so that you have a 28% chance of winning. What are the dimensions of each rectangle
Answer:
5in x 10in
Step-by-step explanation:
Solution:
1. You have to assume that the ring will land on the board and as a result, just focus on one rectangle of the board since they are all the same size.
2. For the ring to land entirely inside the rectangle, the center of the ring needs to be 1.5 inches inside the border (radius is 1.5 inches), so the "winning rectangle" will have dimensions:
L = (x - 2(1.5)) = x - 3
w = (2x - 2(1.5)) = 2x-3.
3. Now, we will set up and solve our geometric probability equation. The winning rectangle's area of (x-3)*(2x-3) divided by the total rectangle's area of x*(2x) = 28%
(2x-3)*(x-3)/(2x^2) = .28
2x^2 - 9x + 9 = .56x^2
1.44x^2 - 9x + 9 = 0
4 . Now you can plug that in the quadratic formula and get the solutions x = 1.25 or 5. However, it cannot by 1.25 because that is too small of a dimension for the the circle with diameter of 3 to fit in, the answers has to be 5.
5. As a result, the dimensions of the rectangles are 5in x 10in.
The game Ring Ding involves throwing a wooden ring onto a rectangular grid; the exact dimensions of the rectangles cannot be determined only with the provided information including the 28% win probability.
Explanation:This is a question of probability concerning how a carnival game has been designed. Specifically, the game Ring Ding involves throwing a wooden ring onto a grid of rectangles without the ring touching any lines. Unfortunately, the question doesn't provide sufficient information to determine the exact dimensions of each rectangle. While it mentions the diameter of the ring and the relative dimensions of the rectangles (being twice as long as they are wide), the 28% chance of winning does not give a direct way to calculate the rectangle's dimensions as it depends upon other factors as well like player's skill, distance, angle of throw, etc.
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Rachel is collecting donations for the local animal shelter. So far she has collected $245 which is 70% of what she hopes to collect. How much money does Rachel plan to collect for the shelter?
Answer:
Step-by-step explanation:
Answer
She plans to collect 350 dollars
Step-by-step explanation:
Knowing that 245 dollars is equal to only 70% of what Rachel hopes to collect, the equation:
70% * x = 245
where x = money she plans to collect in total, is applicable,
Solving:
70/100 * x = 245,
7/10 * x =245,
7x/10 = 245,
7x = 2450,
x = 350 dollars
Spinning a roulette wheel 6 times, keeping track of the occurrences of a winning number of "16".
a. Not binomial: there are more than two outcomes for each trial.
b. Procedure results in a binomial distribution.
c. Not binomial: the trials are not independent.
d. Not binomial: there are too many trials.
Answer:
Correct option is b. Procedure results in a binomial distribution.
Step-by-step explanation:
Consider that X is Binomial random variable. The properties that are satisfied by X are:
There are n independent trials.Each trial has only two outcomes: Success & Failure.Each trial has the same probability of success.Suppose a roulette wheel is spun and the number of times the ball lands on '16' is observed.
If the random variable X is defined as the number of times the ball lands on '16', then the random variable X follows a Binomial distribution.
Because,
Each spin is independent of each otherSuccess: The ball lands on '16'Failure: The ball does not lands on '16'The probability of the ball landing on '16' is [tex]\frac{1}{37}[/tex] for each trial.Thus, the correct option is b. Procedure results in a binomial distribution.
What is the rate of change in the y-values with respect to the x-values?
Answer:
The answer to your question is the last option
Step-by-step explanation:
Process
1.- To calculate the rate of change, calculate slope
Formula
m = (y2 - y1) / (x2 - x1)
x1 = 1 y1 = 1200
x2 = 2 y2 = 2400
2.- Substitution
m = (2400 - 1200) / (2 - 1)
3.- Simplification
m = 1200 / 1
4.- Result
m = 1200 meters / minute
Answer:
(d) 1200 Meters per minute
Step-by-step explanation:
Alice and Bob race two toy trains around a circular track. The trains move in the same direction and they meet every 120 seconds. If Alice's and Bob's toy trains move in opposite directions, at constant rates, they meet every 30 seconds. If the track is 1800 m long, what is the speed of each toy train?
Answer:
Step-by-step explanation:
Given that Alice and Bob race two toy trains around a circular track. The trains move in the same direction and they meet every 120 seconds. If Alice's and Bob's toy trains move in opposite directions, at constant rates, they meet every 30 seconds
Circular track is 1800 m.
Let speed be x and y respectively
When in same direction relative speed = x-y and when in opposite directions =x+y
30(x+y) = 1800
x+y= 60
120(x-y) = 1800
x-y = 15
Solving x = 37.5 m/hr and y = 12.5 per hour.
When Alice and Bob's toy trains move in the same direction, their relative speed is the sum of their individual speeds. When they move in opposite directions, their relative speed is the difference between their individual speeds. By solving simultaneous equations, we find that Alice's toy train has a speed of 75 m/s and Bob's toy train has a speed of 60 m/s.
Explanation:Let's assume the speed of Alice's toy train is x m/s and the speed of Bob's toy train is y m/s.
When the trains move in the same direction, they meet every 120 seconds. Since they meet once every 30 seconds when moving in opposite directions, their relative speed is the sum of their individual speeds. So, when they move in the same direction, their relative speed will be x + y and when they move in opposite directions, their relative speed will be x - y.
When they move in the same direction, the distance covered by Alice's toy train in 120 seconds will be equal to the distance covered by Bob's toy train in 120 seconds, which is equal to the length of the circular track (1800 m). So, the equation can be written as:
x × 120 = y × 120 = 1800Simplifying the equation, we get:
x + y = 1800/120 = 15Similarly, when they move in opposite directions, the distance covered by Alice's toy train in 30 seconds will be equal to the distance covered by Bob's toy train in 30 seconds:
x × 30 = y × 30 = 1800Simplifying the equation, we get:
x - y = 1800/30 = 60Solving the equations simultaneously, we find that x = 75 m/s and y = -60 m/s. Since speed is always positive, we consider the magnitude of the velocity. Therefore, the speed of Alice's toy train is 75 m/s and the speed of Bob's toy train is 60 m/s.
The value of John's baseball card collection decreases exponentially over time, and the value of his silver collection increases exponentially over time. If the value of John's two collections combined t years from now is given by the function V = 500(1.05)2t + 600(0.95)t, which statement must be true?
The value of John's silver collection changes at a faster rate than the value of John's baseball card collection.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The exponential function is given in the question
V = 500(1.05)^2t + 600(0.95)^t
Every 6 months, t = 2t
The value of John's silver collection changes = 500(1.05)²ˣ⁶ = 897.928
The value of baseball card collection = 600(0.95)⁶ = 441.055
Thus, the value of John's silver collection changes at a faster rate than the value of John's baseball card collection.
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The question seems to be incomplete the correct question would be
The value of John's baseball card collection decreases exponentially over time, and the value of his silver collection increases exponentially over time. If the value of John's two collections combined t years from now is given by the function V = 500(1.05)^2t + 600(0.95)^t, which statement must be true?
A) John's silver collection is more valuable currency than his baseball collection.
B) The value of John's silver collection changes at a faster rate than the value of John's baseball card collection.
C) John's baseball card collection decreases in value by 10% every six months.
D) The total value of the two collections remains constant over time.
Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of 1,000 passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the 1,000 passengers, 345 had more than one bag.
The domestic version of Boeing's 747 has a capacity for 568 passengers. Determine an interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane. Assume the plane is at its passenger capacity.
a) (171.651, 216.214)
b) (181.514, 208.313)
c) (174.412, 217.218)
d) (179.20, 212.716)
Answer:
d) (179.20, 212.716)
Step-by-step explanation:
1000 : 345
569 : 195.96
Midpoint of (179.20, 212.716) is 195.958 which is the closest to 195.96
Final answer:
The interval estimate for passengers expected to carry more than one piece of luggage on a full Boeing 747 is (179.20, 212.716), calculated using the sample proportion and the standard error for a 95% confidence interval.
Explanation:
To determine an interval estimate of the number of passengers that would be expected to carry more than one piece of luggage on a domestic Boeing 747 with a capacity of 568 passengers, we use the sample proportion of passengers with more than one bag from the given sample, which is 345 out of 1000 passengers. This sample proportion, denoted as p-hat, is 0.345. We will use this proportion to estimate the population proportion in the domestic Boeing 747, assuming the plane is at full capacity.
We can calculate the estimated number of passengers by multiplying the proportion (p-hat) by the capacity of the plane. For a Boeing 747 with 568 passengers, this would be 0.345 * 568. To build an interval estimate, we also need to calculate the standard error (SE) of the proportion which is given by the formula SE = sqrt(p-hat*(1-p-hat)/n), where 'n' is the sample size. With a sample size of 1000, the SE can be calculated and then used to construct the 95% confidence interval using the Z-score for 95% confidence (approximately 1.96).
After calculating the interval estimate, we find that the confidence interval falls within one of the options provided. The correct interval estimate of the number of passengers expected to carry more than one piece of luggage on the plane, assuming it's full, would be (179.20, 212.716), which corresponds to option d.
What is the center of the circle described by the equation
x^2+4x+y^2-6y=12
(4, -6)
(-4, 6)
(-2, 3)
(2, -3)
Answer:
The center of the circle is (-2 , 3) ⇒ 3rd answer
Step-by-step explanation:
The equation of a circle is (x - h)² + (y - k)² = r², where
(h , k) are the coordinates of its centerr is the radius of it∵ The equation of the circle is x² + 4x + y² - 6y = 12
- Lets make a completing square for x² + 4x
∵ x² = (x)(x)
∵ 4x ÷ 2 = 2x
- That means the second term of the bracket (x + ...)² is 2
∴ The bracket is (x + 2)
∵ (x + 2)² = x² + 4x + 4
∴ We must add 4 and subtract 4 in the equation of the circle
∴ (x² + 4x + 4) - 4 + y² - 6y = 12
Lets make a completing square for y² - 6y
∵ y² = (y)(y)
∵ -6y ÷ 2 = -3y
- That means the second term of the bracket (y + ....) is -3
∴ The bracket is (y - 3)
∵ (y - 3)² = y² - 6y + 9
∴ We must add 9 and subtract 9 in the equation of the circle
∴ (x² + 4x + 4) - 4 + (y² - 6y + 9) - 9= 12
Now lets simplify the equation
∵ (x + 2)² + (y - 3)² - 13 = 12
- Add 13 to both sides
∴ (x + 2)² + (y - 3)² = 25
- Compare it with the form of the equation of the circle to
find h and k
∵ (x - h)² + (y - k)² = r²
∴ h = -2 and k = 3
The center of the circle is (-2 , 3)
John Worker had $31,000 in taxable income. What was his tax?
Final answer:
To calculate John Worker's tax, we need to use the tax rate schedule. Assuming the taxable income is $31,000, we can refer to the tax rate schedule to determine the tax. If the tax rate for the income range $30,001 to $40,000 is 20%, then John Worker's tax would be 20% of his taxable income of $31,000, which equals $6,200.
Explanation:
To calculate John Worker's tax, we need to use the tax rate schedule. Assuming the taxable income is $31,000, we can refer to the tax rate schedule to determine the tax.
From the given information, we don't have the specific tax rate for $31,000. However, we can use the tax rates provided in the table to calculate the tax.
For example, if the tax rate for the income range $30,001 to $40,000 is 20%, then John Worker's tax would be 20% of his taxable income of $31,000, which equals $6,200.
Employees at Driscoll's Electronics as a base salary plus a 20% Commission on their total sales for the year. Suppose. The base salary is $40,000.
a. Write an equation to represent the total earnings of an employee. Remember to define your variable(s).
b. Stewart wants to make $65,000 this year. How much?must he make in sales?to achieve this salary? Write and solve an equation to answer this question.
c. Describe the equation 52,000 + 0.3s = 82,000 in terms of the problem situation.
Answer:
Step-by-step explanation:
Let x represent the total sales made in a year.
Employees at Driscoll's Electronics as a base salary plus a 20% Commission on their total sales for the year. If the base salary is $40,000, it means that if the employee makes a total sales of $x in a year, the total equation to represent earnings would be
0.2x + 40000
b) if Stewart wants to make $65,000 this year, it means that
0.2x + 40000 = 65000
0.2x = 65000 - 40000
0.2x = 25000
x = 25000/0.2
x = 125000
c) 52,000 + 0.3s = 82,000
The base salary is $52000
The percentage of commission from sales is 30%
Show that the curve y = 4 x 3 + 7 x − 5 y=4x3+7x-5 has no tangent line with slope 2 2. y = 4 x 3 + 7 x − 5 ⇒ m = y ' = y=4x3+7x-5⇒m=y′= Preview , but x 2 x2 0 0 for all x x, so m ≥ m≥ for all x x.
Answer:
There is no such point where the given curve has a tangent line with slope 2.
Step-by-step explanation:
We have been given a curve [tex]y=4x^3+7x-5[/tex]. We are asked to show that the given curve has no tangent line with slope 2.
First of all, we will find the derivative of given curve as shown below:
[tex]y'=\frac{d}{dx}(4x^3)+\frac{d}{dx}(7x)-\frac{d}{dx}(5)[/tex]
[tex]y'=4\cdot 3x^{3-1}+7x^{1-1}-0[/tex]
[tex]y'=12x^{2}+7x^{0}[/tex]
[tex]y'=12x^{2}+7(1)[/tex]
[tex]y'=12x^{2}+7[/tex]
We know that derivative represents slope of tangent line, so we will equate derivative of the given curve with 2 and solve for the point (x), where the slope of tangent line will be equal to 2 as:
[tex]12x^2+7=2[/tex]
[tex]12x^2+7-7=2-7[/tex]
[tex]12x^2=-5[/tex]
[tex]x^2=-\frac{5}{12}[/tex]
We know that square of any real number could never be negative, therefore, there is no such point where the given curve has a tangent line with slope 2.
Final answer:
The proof involves finding the derivative of the given curve y = 4x³ + 7x - 5, setting it equal to the desired slope (2), and showing that the resulting equation has no real solutions, proving that no tangent line with slope 2 exists for this curve.
Explanation:
The question is about proving that the curve y = 4x³ + 7x - 5 does not have any tangent line with slope 2. To do this, we first need to find the derivative of the curve, which gives us the slope of the tangent at any point (x). The derivative of y with respect to x is given by y' = 12x² + 7. To determine if a tangent with slope 2 exists, we set the derivative equal to 2 and solve for x: 12x² + 7 = 2.
Solving this equation gives us 12x² = -5, which has no real solution since the left side of the equation (a squared term) cannot be negative. This means there is no value of x for which the slope of the tangent (derivative) is equal to 2, proving that no such tangent line exists for the given curve.
How many times will the string literal "Hi" appear in the lblMsg control? Dim intCount As Integer Do While intCount > 4 lblMsg.Text = lblMsg.Text & "Hi" & ControlChars.NewLine intCount += 1
Answer:
0
Step-by-step explanation:
In my opinion, the string won't display because, the intCount was not initialized before you started outputting the "Hi" string. So in order fro you to get the string to appear, the control point or value has to be initialized to maybe 0. then you can start looping from there. And if you are looping from the top or using greater than (>), The loop works best buy subtracting the control value else, you can end up with infinity loop.
A firm offers routine physical examinations as part of a health service program for its employees. The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work, and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work
Answer: 0.206
Step-by-step explanation: the probability of employees that needs corrective shoes are =8%= 8/100 = 0.08
Probability of employees that needs major dental work = 15% = 15/100 = 0.15
Probability of employees that needs both corrective shoes and dental work = 3% = 3/100 = 0.03
The probability that an employee will need either corrective shoes or major dental work = (Probability an employee will need correct shoes and not need dental work) or (probability that an employee will need dental work or not corrective shoes)
Probability of employee not needing corrective shoes = 1 - 0.08 = 0.92
Probability of employee not needing dental work = 1 - 0.15 = 0.85
The probability that an employee will need either corrective shoes or major dental work = (0.08×0.85) + (0.15×0.92) = 0.068 + 0.138 = 0.206 = 20.6%
The probability that an employee will need either corrective shoes or dental work = 0.206.
Please note that the word "either" implies that we must choose one of the two options (corrective shoes or dental work) and not both.
The probability that an employee selected at random will need either corrective shoes or major dental work is 0.206.
Calculation of the probability:Since
The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work, and 3% needed both corrective shoes and major dental work.
So,
Probability of employee not needing corrective shoes should be
= 1 - 0.08
= 0.92
And,
Probability of employee not needing dental work should be
= 1 - 0.15
= 0.85
So final probability should be
= (0.08×0.85) + (0.15×0.92)
= 0.068 + 0.138 = 0.206
= 20.6%
hence, The probability that an employee selected at random will need either corrective shoes or major dental work is 0.206.
Learn more about probability here; https://brainly.com/question/24442276
What is the answer for number 10? please explain step by step
hope it helps you!!!!!
Ms.Lopez has created a floor plan of a dollhouse. The area of the entire dollhouse is 576 square inches
Answer:
(a)Area of the bedroom=96 square inches
(b)Area of the living room =144 square inches
(c)Area of the dollhouse that is not of the bedroom or living room =336 square inches.
Step-by-step explanation:
The area of the bedroom is 1/6 the area of the entire dollhouse
The area of the living room is 3/2 times the area of the bedroom.
The area of the entire dollhouse is 576 square inches
Let the area of bedroom=b
Let the area of living room=l
(a) The area of the bedroom is 1/6 the area of the entire dollhouse
[tex]b=\frac{1}{6}X576=96[/tex] square inches
(b)The area, in square inches, of the living room
The area of the living room is 3/2 times the area of the bedroom
l= [tex]\frac{3}{2}X96=144[/tex] square inches
(c)The total area of the house =576 square inches
Area of the bedroom=96 square inches
Area of the living room =144 square inches
Area of the dollhouse that is not of the bedroom or living room
=576-(96+144)=576-240=336 square inches.
The area of the living room is 3/2 times the area of the bedroom
This is gotten by subtracting the area of the bedroom and living room from the total area of the house.
A school is putting on a play. On the first night of the play, twice as many adults attended the lay as students. Students tickets cost $3 and adults tickets cost $5. The total amount of money earned from tickets sales was $1,131. Write a system of equations that represent this situation.
Answer:
x+2x+$3+$5=$1131
Step-by-step explanation:
Take students to be x then the adults be 2x and the dollars being played and the total money.Then you will take the $3+$8 and subtract from $1131 dollars then you'll get x
Answer: The system of equations that represent this situation is
x = 2y
5x + 3y = 1131
Step-by-step explanation:
Let x represent the number of adult tickets sold on the first night of the play.
Let y represent the number of student tickets sold on the first night of the play.
On the first night of the play, twice as many adults attended the play as students. This means that
x = 2y
Students tickets cost $3 and adults tickets cost $5. The total amount of money earned from tickets sales was $1,131. This means that
5x + 3y = 1131- - - - - - - - - 1