Here is a box plot that summarizes data for the time, in minutes, that a fire department took to respond to 100 emergency calls.
Select all the statements that are true, according to the box plot.
a) Most of the response times were under 13 minutes.
b) Fewer than 30 of the response times were over 13 minutes.
c) More than half of the response times were 11 minutes or greater.
d) There were more response times that were greater than 13 minutes than those that were less than 9 minutes.
e) About 75% of the response times were 13 minutes or less.
Answers
According to the given box plot:
Most of the response times were under 13 minutes is true
Fewer than 30 of the response times were over 13 minutes is true
More than half of the response times were 11 minutes or greater is true
About 75% of the response times were 13 minutes or less is true
In box plot the difference between a dataset's first and third quartiles is used to determine the interquartile range (IQR), a measure of variability.
The interquartile range (IQR) depicts the range of values centred on the data's median. Because it is more resistant to outliers than other measures of variability like the range or the standard deviation, it is valuable in statistics.
Observations that are more than 1.5 times the IQR from the adjacent quartile are considered probable outliers and can be located using the IQR.
Box plots and the IQR are frequently combined to compare and summarise data from several groups or samples.
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Related Questions
What is the value of −2(7/5÷14)?
Answers
Answer:
-0.2
Step-by-step explanation:
the priority is for the parenthesis
7÷5÷14= 0.1
0.1×-2 = -0.2
Two monomials are shown below. 28x²y 34x y What is the greatest common factor (GCF) of these monomials? A
7xy B
4x²y
C2xy
D2x²y
I need an answer asap
Answers
Answer: 2xy
Step-by-step explanation:
you need the biggest factor that goes into
What number must be added to 101 to produce a number equal to the product of 101 × 21?
Answers
Answer: 2020
Step-by-step explanation:
101 x 21 = 2121
let x be the number to be added:
101 + x = 2121
x = 2121 - 101
x = 2020
thats your answer :)
Answer:2121
Step-by-step explanation:
Select the correct answer.
Amy constructed this figure by using a compass to draw circle C and then a straightedge to draw diameter AB through point C. Then, with the compass still set equal to the radius of the circle, Amy drew two arcs centered at point B and labeled the points of intersection D and E. She used the straightedge to draw chords AD, AE, and DE.
A circle has an arc at its center and is labeled C. Three points A D and E complete a triangle. The diameter is A B through point C. Two broken lines are drawn from C to D and D to B.
Amy notes that arcs ADB and AEB are semicircles and that ΔBDC is equilateral. Because ∠BCD is a central angle, she can say that
= 60°. She uses these facts to determine
=
=
= 120°. Finally, she concludes ΔADE is equilateral because congruent arcs are intercepted by congruent chords.
Why is ΔBDC is equilateral?
A.
Triangle BDC is equilateral because diameter AB is a perpendicular bisector of chord BD.
B.
Triangle BDC is equilateral because arcs BD and BE are two arcs with the same radius and center.
C.
Triangle BDC is equilateral because the sum of the three angle measures in ΔADE is the same as the measure of a semicircle.
D.
Triangle BDC is equilateral because the distance between all three vertices is equal to the radius of the circle.
Answers
The reason why ΔBDC is equilateral include the following: D. Triangle BDC is equilateral because the distance between all three vertices is equal to the radius of the circle.
What is an equilateral triangle?In Mathematics, an equilateral triangle can be defined as a special type of triangle that has equal side lengths and all of its three (3) interior angles are equal.
In order to determine whether the triangle with any given vertices is an equilateral triangle, we would apply the distance formula to calculate the length of each side of this triangle.
In conclusion, we can logically deduce that the triangle with these vertices is an equilateral triangle because C = A = B i.e "the distance between all three vertices is equal to the radius of the circle."
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You are asked to estimate the water flow rate in a pipe of radius 2m at a remote area location with a harsh environment. You already know that velocity v varies along the radial location, but you do not know how it varies. The flow rate Q is given by
Q = ∫(0 to 2) 2 π r v dr
To save money, you are allowed to put only two velocity probes (these probes send the data to the central office in New York by satellite). Radial location r is measured from center of the pipe, i.e., r = 0 is the center of the pipe, and r = 2m is the pipe radius. The radial locations you will suggest for the two velocity probes for the most accurate calculation of the flow rate are
0.42, 1.42
0.00, 1.00
0.42, 1.58
0.58, 1.58
Answers
To estimate the water flow rate in the pipe, we need to measure the velocity at two radial locations and then use the integral formula to calculate the flow rate. The formula tells us that the flow rate is equal to the integral of 2πrv with respect to r, where r is the radial location, v is the velocity, and the limits of integration are 0 to 2 (since the pipe has a radius of 2m).
Since we don't know how the velocity varies along the radial location, we need to choose two locations that will give us the most accurate estimate of the flow rate. The best locations to choose are where the velocity varies the most, which is usually near the center and near the edge of the pipe.
Based on this, the two radial locations that would give us the most accurate calculation of the flow rate are 0.42 and 1.58. These locations are close to the center and the edge of the pipe, respectively, and will give us a good estimate of how the velocity varies along the radial location.
Therefore, the answer is 0.42, 1.58.
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How do I solve this in excel?
Use the data for pre- and post- grades provided.
Apply the Excel Regression tool using the Pre-Test grade as the independent variable and the Post-Test grade as the dependent variable.
Please answer the following questions on the worksheet labeled Problem 1 Questions that is located directly after the worksheet labeled Problem 1.
a. In complete sentences, please write your interpretation of the following:
1. The regression results.
2. The hypothesis tests.
3. The confidence intervals.
b. Based on the residuals, are the assumptions underlying the regression analysis valid?
• See Checking Assumptions on page 247 in the textbook.
• See *Note below.
c. Based on the standard residuals, do any outliers exist?
Answers
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Ashley keeps track of their fuel efficiency when they buy gas. The last time, they got 16.6 gallons and had driven 385 miles. What is the fuel efficiency? Select an answer Select an answer miles/gallo
Answers
Ashley's fuel efficiency is approximately 23.19 miles per gallon. To calculate Ashley's fuel efficiency in miles per gallon, you can follow these steps:
Step:1. Fuel efficiency = Miles driven / Gallons of fuel used Step:2. Fuel efficiency = 385 miles / 16.6 gallons Step:3. Fuel efficiency = 23.193 miles/gallon (rounded to three decimal places)
Therefore, Ashley's fuel efficiency for this particular fill-up was approximately 23.193 miles per gallon. This means that for every gallon of fuel used, Ashley's car was able to travel approximately 23.193 miles. It's important to note that fuel efficiency can vary depending on factors such as driving habits, vehicle condition, and fuel quality.
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An analysis of variance is used to evaluate the mean differences for a research study comparing four treatment conditions with a separate sample of n = 5 in each treatment. The analysis produces SSwithin treatments = 32, SSbetween treatments = 40, and SStotal = 72 For this analysis, what is MSwithin treatments?
Answers
The MSwithin treatments for this analysis is 2.
In analysis of variance (ANOVA), we partition the total variation in a set of data into two types of variation: variation within groups and variation between groups. This partitioning helps us to test whether the means of the groups are significantly different from each other or not.
The formula for calculating the mean square within treatments (MSW) is:
MSW = SSW / dfW
where SSW is the sum of squares within treatments and dfW is the degrees of freedom associated with the SSW.
To calculate MSW, we first need to calculate dfW, which is equal to the total number of observations minus the total number of groups. In this case, there are 4 groups, each with 5 observations, so there are a total of 20 observations:
dfW = 20 - 4 = 16
Next, we can use the given SSwithin treatments value of 32 to calculate SSW:
SSW = 32
Finally, we can plug in the values we have calculated to find MSW:
MSW = SSW / dfW
MSW = 32 / 16
MSW = 2
Therefore, the MSwithin treatments for this analysis is 2.
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Hey can anyone help me
Answers
Answer: 12 units
Step-by-step explanation:
Since in this situation we're going by units it will be easier. First to create the rectangle just fill in 3 boxes horizontally and 4 units vertically. connect the squares together.
Then to find the area, the formula for that is Base x Height so all you have to do is multiply 4*3 and that's 12.
100 PTS solve for x ................
Answers
Answer:
x ≈ 36.2
Step-by-step explanation:
the segment from the vertex of the triangle to the base is a perpendicular bisector, then
consider the right triangle on the right with legs 15 and 33 , hypotenuse x
using Pythagoras' identity in the right triangle
x² = 15² + 33² = 225 + 1089 = 1314 ( take square root of both sides )
x = [tex]\sqrt{1314}[/tex] ≈ 36.2 ( to the nearest tenth )
Answer:
36.2
Step-by-step explanation:
The tick marks on the two sides of the triangle indicate that the sides are of equal length. Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.
In an isosceles triangle, the altitude is the perpendicular bisector of the base. Therefore, the triangle is made up of two congruent right triangles with:
height = 33base = 30/2 = 15hypotenuse = xTo calculate the value of x, we can use Pythagoras Theorem:
[tex]\boxed{a^2+b^2=c^2}[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Substitute the values into the formula and solve for x:
[tex]\implies 15^2+33^2=x^2[/tex]
[tex]\implies 225+1089=x^2[/tex]
[tex]\implies 1314=x^2[/tex]
[tex]\implies x^2=1314[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{1314}[/tex]
[tex]\implies x=36.2491379...[/tex]
[tex]\implies x=36.2\; \rm (nearest\;tenth)[/tex]
Therefore, the value of x is 36.2 units (nearest tenth).
what is the best way to solve ratios
Answers
When looking at a ratio problem, the key pieces of information that you need are what the ratio is, whether you have been given the whole amount or a part of the whole and what you are trying to work out.
If you have been given the whole amount you can follow these steps to answer the question:
Add together the parts of the ratio to find the total number of shares.
Divide the total amount by the total number of shares.
Multiply by the number of shares required.
If you have been been given a part of the whole you can follow these steps:
Identify which part you have been given and how many shares it is worth.
Use equivalent ratios to find the other parts.
Use the values you have to answer your problem.
Use the given confidence interval to find the margin of error
and the sample proportion.
(0.622,0.652)
Question content area bottom
Part 1
E=
Part 2
p=
Answers
Margin of error (E) is 0.015 and proportion (p) is 0.637.
We are given the confidence interval (0.622, 0.652) and we need to find the margin of error (E) and the sample proportion (p).
Part 1: Margin of error (E) 1. Calculate the midpoint of the confidence interval by adding the lower limit (0.622) and the upper limit (0.652), then divide by 2: Midpoint = (0.622 + 0.652) / 2 = 1.274 / 2 = 0.637 2.
Find the margin of error (E) by subtracting the midpoint from the upper limit (or lower limit, it should give the same value): E = 0.652 - 0.637 = 0.015
Part 2: Sample proportion (p) 3. The midpoint we calculated earlier is the sample proportion (p): p = 0.637
Your answer: Part 1 E = 0.015 Part 2 p = 0.637
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Consider the following initial value problem: y" – 7y - 18y = sin(5t) y(0) = -2, 7(0) = 7 = = Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}; find the equation you get by taking the La
Answers
The equation obtained by taking the Laplace transform of the given initial value problem is:
Y = [5 / ([tex]s^2[/tex] + 25) - 2s - 7] / (s^2 - 25)
To solve the given initial value problem using Laplace transform, we first take the Laplace transform of both sides of the differential equation:
L[y"] - 7L[y] - 18L[y] = L[sin(5t)]
Using the properties of Laplace transform, we have:
[tex]s^2[/tex] Y - s y(0) - y'(0) - 7Y - 18Y = 5 / (s^2 + 25)
Substituting the initial conditions y(0) = -2 and y'(0) = 7, we get:
s^2 Y + 2s + 7 - 7Y - 18Y = 5 / (s^2 + 25)
Simplifying this equation, we get:
s^2 Y - 25Y = 5 / (s^2 + 25) - 2s - 7
Now we can solve for Y:
Y = [5 / (s^2 + 25) - 2s - 7] / (s^2 - 25)
We can use partial fraction decomposition to simplify the expression further:
Y = [A s + B] / (s + 5) + [C s + D] / (s - 5) - (2s + 7) / (s^2 + 25)
Multiplying both sides by the denominator (s^2 - 25), we get:
[tex]As^3 + Bs^2 - 5As^2 - 5Bs + Cs^3 - Ds^2 - 5Cs + 5D - (2s + 7)(s^2 - 25) = 5[/tex]
Simplifying and equating the coefficients of the like powers of s on both sides, we get:
A + C = 0
B - 5A - D + 50 = 0
5B - 5C - 2 = 0
Solving these equations, we get:
A = -C
B = 20/9
C = -20/9
D = -7/9
Substituting these values, we get:
Y = [-20s/9 - 20/9] / (s + 5) + [20s/9 + 7/9] / (s - 5) - (2s + 7) / (s^2 + 25)
Taking the inverse Laplace transform, we get the solution y(t):
y(t) = [-20/9 exp(-5t) - 20/9] + [20/9 exp(5t) + 7/9] cos(5t) - (2/5) sin(5t)
Therefore, the equation obtained by taking the Laplace transform of the given initial value problem is:
Y = [5 / (s^2 + 25) - 2s - 7] / ([tex]s^2 - 25[/tex])
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Angle xzw ~ to angle xvy, find the perimeter of angle xzw
Answers
The perimeter of the triangle XZW is 176.4 units
Finding the perimeter of triangle XZWFrom the question, we have the following parameters that can be used in our computation:
The similar triangles
We start by calculating the missing side lengths using proportions
So, we have
YZ/32 = 28/40
So, we have
YZ = 32 * 28/40
YZ = 22.4
Next, we have
30/WZ = 40/(40 + 32)
So, we have
WZ = 30 * (40 + 32)/40
WZ = 54
The perimeter of triangle XZW is
P = 28 + 22.4 + 54 + 32 + 40
Evaluate
P = 176.4
Hence, the perimeter is 176.4 units
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A box with fifteen integrated circuit chips contains five defectives. If a random sample of three chips is drawn, what is the probability that all three are defective?
Answers
The probability that all three chips drawn are defective is 2.2%.
To find the probability that all three chips are defective, we can use the formula for the probability of independent events.
First, we need to find the probability of drawing one defective chip from the box. Since there are five defective chips out of fifteen total chips, the probability of drawing a defective chip on the first try is 5/15.
Next, we need to find the probability of drawing another defective chip on the second try. Since we are drawing without replacement, there are now only 14 chips left in the box, including four defectives. So the probability of drawing a defective chip on the second try is 4/14.
Finally, we need to find the probability of drawing a third defective chip. Again, since we are drawing without replacement, there are now only 13 chips left in the box, including three defectives. So the probability of drawing a defective chip on the third try is 3/13.
To find the probability of all three events occurring, we can multiply the probabilities together:
(5/15) x (4/14) x (3/13) = 0.022
So the probability that all three chips drawn are defective is 0.022, or approximately 2.2%.
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Shannon’s Ice Cream Shop, Shenanigans, sells three types of ice cream: Peanut Butter Cup, Coffee Cream and Oreo. Last week Shenanigans sold a total of 489 ice cream cones that were either Coffee Cream or Oreo. In total, they sold 711 ice cream cones last week. What is the probability Shenanigan’s will sell a Peanut Butter Cup cone next? Express your answer as a percent.
Answers
The probability of Shenanigans selling a Peanut Butter Cup cone next is approximately 31.22%.
To calculate the probability of Shenanigans selling a Peanut Butter Cup cone next, we need to determine the number of cones sold that were not Peanut Butter Cup cones and divide that by the total number of cones sold.
Given that Shenanigans sold a total of 711 ice cream cones last week and 489 of those were either Coffee Cream or Oreo, we can subtract 489 from 711 to find the number of cones that were not Coffee Cream or Oreo;
Number of cones that were not Coffee Cream or Oreo = 711 - 489 = 222
So, out of the total 711 cones sold, 222 were not Coffee Cream or Oreo cones. Therefore, the remaining cones must be Peanut Butter Cup cones.
Now, we can calculate the probability of selling a Peanut Butter Cup cone next by dividing the number of Peanut Butter Cup cones by the total number of cones sold, and then multiplying by 100 to find the result as a percentage;
Probability of selling a Peanut Butter Cup cone next = (Number of Peanut Butter Cup cones / Total number of cones sold) × 100
Probability of selling a Peanut Butter Cup cone next = (222 / 711) × 100
≈ 31.22%
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Make x the subject of y = 3√(x²+2) 15
Answers
The value of the equation in terms of x is x = [tex]\sqrt{\frac{y^2-270}{135}}[/tex].
Given is an equation, y = 3√(x²+2)15, we need to convert it in terms of x,
So,
y = 3√(x²+2) 15
Squaring both sides,
y² = 9 [(x²+2)15]
y² = 9 [15x²+30]
y² = 135x²+270
y²-270 = 135x²
y²-270 / 135 = x²
x = [tex]\sqrt{\frac{y^2-270}{135}}[/tex]
Hence, the value of the equation in terms of x is x = [tex]\sqrt{\frac{y^2-270}{135}}[/tex].
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Write the notations for these compositions of transformations. I will mark brainliest
Answers
The final coordinates after the given transformation is:
A) (-(x + 2), -y)
B) (0, 5)
How to interpret the transformation?A) When the coordinate (x, y) is mapped by a reflection about the line x = 2, we note:
(1) The y-coordinate is unaffected.
(2) For reflections the distance from the line of reflection to the object is equal to the distance to the image point.
∴ a = 2 + 2 = 4 units
Thus, the image point is 4 units from the line of reflection
The new coordinate is:
((x + 2), y)
The rule for a rotation by 180° about the origin is: (x, y) → (−x, −y) .
The final transformation is: (-(x + 2), -y)
2) Sequel to the translation, the coordinate is (0, 5).
Now, if the point (x, y) is reflected across the line y = a, then the relation between coordinates of actual point and image point will be:
(x, y) → (x, 2a − y) .
Thus, a reflection around the line y = 5 gives:
(0, 2(5) - 5) = (0, 5)
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Which figure shows a line segment?
Answers
"In each case suppose R"" has usual norm. Decide whether the statement is true and give a reason for your answer: (a) In R, 2 € B.(-2) (b) In R. -1.5 € B (0) c) In R(1,5,0.5) € B.(-1,0) (d) In R."
Answers
This statement is incomplete and does not make sense. It cannot be evaluated as true or false without more information.
(a) In R, 2 € B.(-2)
False.
Explanation: The statement means that 2 is an element of the closed ball centered at -2 with radius 1. But this is not true since the distance between 2 and -2 is greater than 1 (|2 - (-2)| = 4).
(b) In R, -1.5 € B(0)
True.
Explanation: The statement means that -1.5 is an element of the closed ball centered at 0 with radius 1. Since the distance between -1.5 and 0 is less than 1 (|-1.5 - 0| = 1.5 < 1), the statement is true.
(c) In R(1,5,0.5) € B(-1,0)
False.
Explanation: The statement means that (1,5,0.5) is an element of the closed ball centered at (-1,0) with radius 1. But the distance between these two points is greater than 1, since
d((1,5,0.5), (-1,0)) = √[(1-(-1))^2 + (5-0)^2 + (0.5-0)^2] = √[4+25+0.25] = √29.25 > 1.
(d) In R.
True.
Explanation: This statement is incomplete and does not make sense. It cannot be evaluated as true or false without more information.
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A recent study found that the weight of a certain species of fish living in the Bahamas can be modeled by the function 0. 034213, where w is measured in grams and L, the length of the fish is measured in centimeters. Calculate the approximate length of a fish that weighs 250 grams. Round your answer to the nearest tenth of a centimeter.
L=____ centimeters
Answers
To solve this problem, we need to use the given function to find the length of a fish that weighs 250 grams. We can do this by setting the weight of the fish (w) to 250 grams and solving for the length of the fish (L):
w = 0.034213 L
250 = 0.034213 L
L = 250 / 0.034213
L ≈ 7304.4
Rounding to the nearest tenth of a centimeter, the approximate length of the fish is:
L ≈ 730.4 centimeters
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"Evaluate the following continuous-time convolution integrals
(k) y(t)=e-yt u (t) x (u(t+2)-u(t))
This question is in the Signals and Sysytems 2nd edition."
Answers
The continuous-time convolution integral of y(t) is [tex]$y(t) = k e^{-yt} u(t) * (u(t+2)-u(t))$[/tex].
To evaluate this convolution integral, we first need to express the integrand as a piecewise function. Since u(t) is 1 for t >= 0 and 0 for t < 0, we can rewrite u(t+2)-u(t) as a piecewise function:
u(t+2)-u(t) =
1, 0 <= t < 2
0, t >= 2
0, t < 0
Now we can evaluate the convolution integral using the definition:
y(t) = ∫[tex]_0^t[/tex] x(τ)h(t-τ)dτ
Substituting the given functions for x(t) and h(t) and simplifying using the piecewise function for u(t+2)-u(t), we get:
y(t) = k ∫[tex]_0^t[/tex] [tex]e^}(-yt)}[/tex]dτ = [tex]k[-(1/y)e^{(-yt)}]_0^t = k(1 - e^{(-yt)})/y[/tex], t >= 0
Therefore, the continuous-time convolution integral of y(t) is [tex]$y(t) = k e^{-yt} u(t) * (u(t+2)-u(t))$[/tex] for t >= 0.
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Joe began reading at
9:04. He read for 47
minutes. What time did
he finish reading?
Answers
Answer: 9:51
Step-by-step explanation:
A group of 125 pick up truck owners were asked what brand truck they owned and whether it had four-wheel drive. The results are given in the two-way table.
You randomly select one truck owner. Which one of the following is true about the events "Owner has a Chevy" and "Owner's truck has four-wheel drive"?
These two events are mutually exclusive and independent.
These two events are mutually exclusive, but not independent.
These two events are not mutually exclusive, but they are independent.
These two events are neither mutually exclusive nor independent.
Answers
These two events are not mutually exclusive, but they are not independent.
To determine the relationship between the two events, "Owner has a Chevy" and "Owner's truck has four-wheel drive," it is necessary to analyze the information provided in the two-way table. Unfortunately, the table is not included in your question.
1. Mutually exclusive: Two events are mutually exclusive if the occurrence of one event excludes the occurrence of the other event. In other words, they cannot happen at the same time.
2. Independent: Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.
After analyzing the two-way table, you should be able to determine if these events are mutually exclusive, independent, or neither.
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If you have $50,000 today and deflation is 5% each year. How much would you need in 20 years to have the same buying power?
Use the formula: A=P(1-r)1^
A 103,946,41
B 23,164,56
C 132,664,89
D 17,924,30
Answers
You would need about $17,924.30 in 20 years to have the same buying power as $50,000 today, assuming a 5% annual deflation rate.
Option D is the correct answer.
We have,
To calculate the future value of money adjusted for deflation, we can use the formula:
A = P(1 - r)^n
Where:
A = future value of money
P = present value of money
r = deflation rate
n = number of years
Plugging in the given values, we get:
A = 50,000(1 - 0.05)^20
Simplifying the expression inside the parentheses:
A = 50,000(0.95)^20
A ≈ 17,924.30
Therefore,
You would need about $17,924.30 in 20 years to have the same buying power as $50,000 today, assuming a 5% annual deflation rate.
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Let A = {1,2,3,4}, give an example of a relation on A|| that is • reflexive and symmetric but not transitive. You may give your example in the form R = {(x,y),(y,w), (w,y), ... } or draw a directed graph reflexive and transitive but not symmetric. You may give your example in the form R = {(x,y),(y,w),(w,y),... } or draw a directed graph
Answers
For the first part of the question, let R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (2,3), (3,2)}. This relation is reflexive because every element in A is related to itself, and it is symmetric because if (x,y) is in R, then (y,x) is also in R. However, it is not transitive because (1,2) and (2,3) are in R, but (1,3) is not in R.
For the second part of the question, let R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,3), (3,4), (1,3), (2,4)}. This relation is reflexive because every element in A is related to itself, and it is transitive because if (x,y) and (y,z) are in R, then (x,z) is also in R. However, it is not symmetric because (1,2) is in R, but (2,1) is not in R.
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How does the graph of f(x) = (x − 8)^3 + 4 compare to the parent function g(x) = x^3? SHOW WORK!!!!!
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Answer:
Step-by-step explanation:
g(x) = x^3 is the parent function starting at the origin (0,0)
f(x) is the translation of the g(x).
Your teacher taught you that y = (x - h)^3 + k
(h,k) is your shift.
(8,4) meaning right 8 on the x-axis and 4 up on the y-axis.
A random sample of 258 observations has a mean of 35, a median of 32, and a mode of 35. The population standard deviation is known and is equal to 5.8. The 99% confidence interval for the population mean is: "Answer is: {LowerLimit} to {UpperLimit}"
Group of answer choices
A. 30.5 to 38.1
B. 34.1 to 35.9
C. 24.2 to 25.8
D. 24.3 to 25.7
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The 99% confidence interval for the population mean is (33.49, 36.51), so the answer is A. 30.5 to 38.1.
We can use the formula for the confidence interval for the population mean when the population standard deviation is known:
CI = X ± z*(σ/√n)
where X is the sample mean, σ is the population standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level.
First, let's calculate the z-score for a 99% confidence level. From a standard normal distribution table, we find that the z-score for a 99% confidence level is approximately 2.576.
Next, we can plug in the given values and solve for the confidence interval:
CI = 35 ± 2.576*(5.8/√258)
CI = 35 ± 1.51
CI = (33.49, 36.51)
Therefore, the 99% confidence interval for the population mean is (33.49, 36.51), so the answer is A. 30.5 to 38.1.
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The current of a system is defined as the following function i(t) = Ae-1-1-1 Evaluate the rate of change of the current at time t = 0.01s and A = 20 0 28.79 O 18.79 O 10.79 O None 0 20.79
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The rate of change of the current is -19.79.
You provided the function i(t) = Ae^(-t) and you'd like to evaluate the rate of change of the current at time t = 0.01s with A = 20.
Step 1: Find the derivative of the function i(t) with respect to time (t). This will give us the rate of change.
di/dt = -Ae^(-t)
Step 2: Substitute the given values for A and t into the derivative equation.
di/dt = -20e^(-0.01)
Step 3: Evaluate the expression.
di/dt ≈ -20 * 0.99004983 ≈ -19.79
So, the rate of change of the current at time t = 0.01s and A = 20 is approximately -19.79.
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PLS HELP ASAP THANKS
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The description of the parabola of the quadratic function is:
It opens upwards and is thinner than the parent function
How to describe the quadratic function?The general formula for expressing a quadratic equation in standard form is:
y = ax² + bx + c
Quadratic equation In vertex form is:
y = a(x − h)² + k .
In both forms, y is the y -coordinate, x is the x -coordinate, and a is the constant that tells you whether the parabola is facing up ( + a ) or down ( − a ), (h, k) are coordinates of the vertex
In this case, a is positive and as such it indicates that it opens upwards and is thinner than the parent function
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