Answer: 87
Step-by-step explanation:
Let x^8+3x^4-4=p_1(x)p_2(x)...p_k(x) where each non-constant polynomial p_i(x) is monic with integer coefficients, and cannot be factored further over the integers. Compute p_1(1)+p_2(1)+...+p_k(1).
Answer: We can factor the given polynomial as follows:
x^8 + 3x^4 - 4 = (x^4 - 1)(x^4 + 4)
= (x^2 - 1)(x^2 + 1)(x^2 - 2x + 1)(x^2 + 2x + 1)
The four factors on the right-hand side are all monic polynomials with integer coefficients that cannot be factored further over the integers. Therefore, we have k = 4, and we can compute p_1(1) + p_2(1) + p_3(1) + p_4(1) as follows:
p_1(1) + p_2(1) + p_3(1) + p_4(1) = (1^2 - 1) + (1^2 + 1) + (1^2 - 2(1) + 1) + (1^2 + 2(1) + 1)
= 0 + 2 + 0 + 6
= 8
Therefore, p_1(1) + p_2(1) + p_3(1) + p_4(1) = 8.
Step-by-step explanation:
State if each angle is an inscribed angle. If it is, name the angle and the intercepted arc.
A: Yes; measure QPR, arc PR
B: Yes; measure QPR, arc QPR
C: Yes; measure QPR, arc QR
D: Yes; measure QPR, arc PQ
Answer:
Yes, angle A is an inscribed angle, and it intercepts arc PR. Angle B is also an inscribed angle, and it intercepts arc QPR. Angle C is an inscribed angle that intercepts arc QR, and angle D is an inscribed angle that intercepts arc PQ.
Step-by-step explanation:
Exercise 5.1.3 An object in an environment with ambient temperature A = 80 degrees obeys Newton’s law of cooling (2.14) with cooling constant k = 0.05, with time measured in minutes. The object has temperature 120 degrees at time t = 0. At time t = 50 the object is moved to an environment with ambient temperature A = 90 degrees; the object still obeys Newton’s law of cooling with the same cooling constant k = 0.05. Find the temperature of the object at time t = 70
equation 2.14 = u'(t) = −k(u(t)−A).
The temperature of the object at time t = 70 is approximately 93.26 degrees.
To solve the problem, we can use the solution to the differential equation given by equation 2.15:
u(t) = [tex]Ce^[/tex](-kt) + A,
where C is a constant that we need to determine from the initial condition u(0) = 120. Substituting t = 0 and u(0) = 120 into the equation, we get:
120 = Ce^(-k*0) + A
120 = C + A
Next, we need to determine the value of C using the information that at t = 50, the temperature of the object is 100 degrees:
100 = Ce^(-k*50) + 90
10 = Ce^(-2.5)
Solving for C, we get:
C = 10/e^(-2.5)
C ≈ 14.868
Now we can use the value of C and equation 2.15 to find the temperature of the object at t = 70:
u(70) = 14.868e^(-0.05*70) + 90
u(70) ≈ 93.26 degrees
Therefore, the temperature of the object at time t = 70 is approximately 93.26 degrees.
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Help please!! <3
Anything would be much appreciated!!
Answer:
a) It is not possible to find the mean because these are words, not numbers.
b) If we put these words in alphabetical order, we have:
blue, blue, green, purple, purple, purple, red, red
The median word here is purple.
c) It is possible to find the mode, which in this case is the word that appears the most times in this list. That word is purple, which appears three times.
Find a truth assignment (that is, an assignment of truth values True or False to q, r, and s) to show the pair of statements are not equivalent. Explain in one or two sentences how you assigned your values and why your assigned truth values work. a. sv (sq) and svq b. (s19) ►r and (-84-9) vr Find a compound proposition involving propositional variables a, b, c, and d that is true precisely when at least two of a, b, c, and d are true. Explain in one or two sentences how you got your compound proposition and why your answer works. [Note: By "precisely," it means that the proposition should be false whenever the condition is not met]
For the first question, we need to assign truth values to q, r, and s such that the pair of statements are not equivalent. For (a) sv(sq) and svq, we can assign q = True, r = False, and s = False. This makes sv(sq) True and svq False, thus showing that the two statements are not equivalent. For (b) (s19)►r and (-84-9)vr, we can assign q = False, r = True, and s = False. This makes (s19)►r False and (-84-9)vr True, thus showing that the two statements are not equivalent.
For the second question, we can construct the compound proposition as follows: (a∧b)∨(a∧c)∨(a∧d)∨(b∧c)∨(b∧d)∨(c∧d). This proposition is true precisely when at least two of the variables a, b, c, and d are true. We can see that this is the case because for the proposition to be true, at least two of the terms in the disjunction need to be true, each of which represents the case where at least two variables are true. For example, (a∧b) represents the case where both a and b are true, and (a∧c) represents the case where both a and c are true, and so on. Therefore, the given compound proposition satisfies the condition of being true precisely when at least two of the variables are true.
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Suppose the sample space for a continuous random variable is 0 to 200. If
the area under the density graph for the variable from 0 to 50 is 0.25, then the
area under the density graph from 50 to 200 is 0.75.
OA. True
B. False
What is the principal that will grow to $5100 in two years,
eight months at 4.3% compounded semi-annually? The principal is
$=
The principal that will grow to $5,100 in two years, eight months at 4.3% compounded semi-annually is approximately $4,568.20.
To find the principal that will grow to $5,100 in two years and eight months at 4.3% compounded semi-annually, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount ($5,100)
P = principal amount (what we're trying to find)
r = annual interest rate (4.3% or 0.043)
n = number of times interest is compounded per year (semi-annually, so 2)
t = time in years (2 years and 8 months or 2.67 years)
First, plug in the values:
$5,100 = P(1 + 0.043/2)^(2*2.67)
Next, solve for P:
P = $5,100 / (1 + 0.043/2)^(2*2.67)
P = $5,100 / (1.0215)^(5.34)
P = $5,100 / 1.11726707
P ≈ $4,568.20
The principal that will grow to $5,100 in two years, eight months at 4.3% compounded semi-annually is approximately $4,568.20.
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In the figure there are 5 equal rectangles and each of its sides is marked with a number as indicated in the drawing. Rectangles are placed without rotating or flipping in positions I, II, III, IV, and V in such a way that the sides that stick together in two rectangles have the same number. Which of the rectangles should go in position I?
The rectangle which should go in position I is rectangle A.
We are given that;
The rectangles A,B,C and D with numbers
Now,
To take the same the number of side
If we take A on 1 place
F will be on second place
And B will be on 4th place
Therefore, by algebra the answer will be rectangle A.
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It is estimated that 25% of all california adults are college graduates and that 31% of california adults are regular internet users. It is also estimated that 19% of California adults are both college graduates and regular internet users.
a. Among california adlts, what is the probability that a randomly chosen internet user is a college graduate? roud off to 2 decimal places.
b. What is the probability that a california adult is an internet user, given that he or her is a college graduate? round off to 2 decimal places.
The probability that a randomly chosen internet user is a college graduate is about 0.61, and the probability that a California adult is an internet user, given that he or she is a college graduate, is about 0.76.
Let A be the event that a California adult is a college graduate, and B be the event that a California adult is a regular internet user.
a. We want to find P(A|B), the probability that a randomly chosen internet user is a college graduate. We can use Bayes' theorem:
P(A|B) = P(B|A) * P(A) / P(B)
where P(B|A) is the probability that an college graduate is an internet user, which is given by P(B|A) = P(A and B) / P(A) = 0.19 / 0.25 = 0.76.
P(B) is the probability of being an internet user, which is given by:
P(B) = P(B and A) + P(B and not A) = 0.19 + 0.12 = 0.31
where P(B and not A) is the probability of being an internet user but not a college graduate, which is equal to P(B) - P(A and B) = 0.31 - 0.19 = 0.12.
Therefore, we have:
P(A|B) = 0.76 * 0.25 / 0.31 ≈ 0.61
b. We want to find P(B|A), the probability that a California adult is an internet user, given that he or she is a college graduate. Again, we can use Bayes' theorem:
P(B|A) = P(A|B) * P(B) / P(A)
where P(A) is the probability of being a college graduate, which is given by P(A) = 0.25.
We already know P(A|B) from part (a), and P(B) from the previous calculation.
Therefore, we have:
P(B|A) = 0.61 * 0.31 / 0.25 ≈ 0.76
So the probability that a randomly chosen internet user is a college graduate is about 0.61, and the probability that a California adult is an internet user, given that he or she is a college graduate, is about 0.76.
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you are dealt one card from a standard 52-card deck. find the probability of being dealt an ace or a 8. group of answer choices
There are 4 aces and 4 nights in a standard 52-card deck. So, the total number of cards that can be considered as a successful outcome is 8. Therefore, the probability of being dealt an ace or an 8 is 8/52 or 2/13. To find the probability of being dealt an Ace or an 8, follow these steps:
1. Identify the total number of cards in the deck: There are 52 cards in a standard deck.
2. Determine the number of Aces and 8s in the deck: There are 4 Aces and 4 eights, totaling 8 cards (4 Aces + 4 eights).
3. Calculate the probability: Divide the number of desired outcomes (Aces and 8s) by the total number of cards in the deck.
Probability = (Number of Aces and 8s) / (Total number of cards)
Probability = 8 / 52
4. Simplify the fraction: 8/52 can be simplified to 2/13.
So, the probability of being dealt an Ace or an 8 from a standard 52-card deck is 2/13.
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How many students were in the sample?
Responses
10
10
20
20
15
15
11
11
Answer:
The answer to your problem is, B. 20
Step-by-step explanation:
Well by looking at the graph we can tell that it is not labeled so we will go to our estimate which is on the left side
2 + 3 + 4 + 5 + 6 = 20
Which we can look at our options and see we have a 20.
Thus the answer to your problem is, B. 20
Select Yes or No to state whether each data set is likely to be normally distributed.
the number of eggs collected each day on a farm
the number of yolks in randomly selected eggs
the weights of eggs in the kitchen of a restaurant
the number of eggs in cartons sold at a supermarket
Determine whether each data set is likely to be normally distributed. Here are my evaluations for each data set:
1. The number of eggs collected each day on a farm:
Yes, this data set is likely to be normally distributed. The daily egg collection should follow a bell-shaped curve, with an average number of eggs collected per day and a standard deviation accounting for variability.
2. The number of yolks in randomly selected eggs:
No, this data set is not likely to be normally distributed. The number of yolks in an egg is a discrete variable, with most eggs having only one yolk, and a few having two or more. This distribution would be skewed and not follow a normal distribution.
3. The weights of eggs in the kitchen of a restaurant:
Yes, this data set is likely to be normally distributed. The weights of eggs should follow a bell-shaped curve, with an average weight and a standard deviation accounting for variability.
4. The number of eggs in cartons sold at a supermarket:
No, this data set is not likely to be normally distributed. The number of eggs in a carton is a fixed, discrete variable (e.g., 6, 12, or 18 eggs). The distribution would be discrete and not follow a normal distribution.
Your answer: 1. Yes, 2. No, 3. Yes, 4. No
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The market price of a t-shirt is $15.00. It is discounted at 10% off. What is the selling price of the t-shirt?
(Enter your answer following the model, i.e. $01.01)
Answer: $13.5
Step-by-step explanation:
1. 15 x 10 =150
2. 150/100=1.5
3. 15.00 - 1.50= 13.5
Question 2 wa Given G(s)=w2n/s2+w2n what is the (asymptotically) minimum value of phase in the $2 + when 1 Not yet saved Marked out of Bode Plot? 1.00 Flag question Write your result as an integer number. minimu value of
The answer is -90.
Given G(s) = w2n/s^2+w2n
To find the asymptotically minimum value of phase in the Bode plot, we can use the formula for the phase of a transfer function in the Laplace domain:
Φ(w) = -atan(w/w2n)
where atan is the arctangent function.
To find the minimum value of Φ(w), we need to find the value of w that maximizes the term inside the arctangent function. Taking the derivative of the term inside the arctangent with respect to w, we get:
d/dw (w/w2n) = 1/w2n
Setting this derivative equal to zero, we get:
1/w2n = 0
which has no real solution. Therefore, there is no frequency that maximizes the term inside the arctangent function, and the minimum value of Φ(w) in the Bode plot is -90 degrees, which occurs at high frequencies as w → infinity.
Thus, the answer is -90.
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fill in the price and the total, marginal, and average revenue sendit earns when it rents 0, 1, 2, or 3 trucks during move-in week.
Renting 0 trucks the Marginal Revenue (MR) = Not applicable, and Average Revenue (AR) = Not applicable. Renting 1 truck the Marginal Revenue (MR) = $P (since it's the additional revenue gained from renting 1 truck), Average Revenue (AR) = Total Revenue / Quantity = P / 1 = $P.
Renting 2 trucks Marginal Revenue (MR) = ($2P - $P) = $P (since it's the additional revenue gained from renting the second truck), Average Revenue (AR) = Total Revenue / Quantity = 2P / 2 = $P. Renting 3 trucks Marginal Revenue (MR) = ($3P - $2P) = $P (since it's the additional revenue gained from renting the third truck), Average Revenue (AR) = Total Revenue / Quantity = 3P / 3 = $P.
To help you with your question, we need to know the rental price per truck and the costs associated with renting these trucks. Since this information is not provided, I will assume a rental price of P dollars per truck. Based on this assumption, we can calculate total, marginal, and average revenue for Sendit when renting 0, 1, 2, or 3 trucks during the move-in week.
1. Renting 0 trucks:
Total Revenue (TR) = 0 * P = $0
Marginal Revenue (MR) = Not applicable
Average Revenue (AR) = Not applicable
2. Renting 1 truck:
Total Revenue (TR) = 1 * P = $P
Marginal Revenue (MR) = $P (since it's the additional revenue gained from renting 1 truck)
Average Revenue (AR) = Total Revenue / Quantity = P / 1 = $P
3. Renting 2 trucks:
Total Revenue (TR) = 2 * P = $2P
Marginal Revenue (MR) = ($2P - $P) = $P (since it's the additional revenue gained from renting the second truck)
Average Revenue (AR) = Total Revenue / Quantity = 2P / 2 = $P
4. Renting 3 trucks:
Total Revenue (TR) = 3 * P = $3P
Marginal Revenue (MR) = ($3P - $2P) = $P (since it's the additional revenue gained from renting the third truck)
Average Revenue (AR) = Total Revenue / Quantity = 3P / 3 = $P
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4. What are the median and mode of the
plant height data?
⬇️
Numbers:
13,14,15,17,17,17,19,20,21
Answer: 5
Step-by-step explanation:
Answer:17
Step-by-step explanation:
The median of this data set is 17, since if you cross one # off of both sides, you will eventually get to the middle fo the data set, pointing to 17.
(0.70 * (1 - 0.10) = 0.70 * 0.9)
Answer:
The simplified result of the expression is 0.63.
Step-by-step explanation:
Compound i street at what was an investment made that obtains $136. 85 in interest compounded quarterly on $320 over four years
Wait just ignore this.
Step-by-step explanation:
CI = p(r/100 + 1)^t - p
136.85 = 320(r/100 +1)^4 - 320
320(r/100 + 1)^4 = 456.85
(r/100 + 1)^4 = 456.85/320 = 1.42765625
(r/100+1) = 4th root of 1.42765625 = 1. 093089979
R/100 = 0.93089979
R = 93.0 %
A mountain road drops 5.2 m for every 22.5 m of the road. Calculate the angle at which the road is inclined to the horizontal. ſans: 13 m) 5. A ramp is inclined at 7° to the horizontal. John walks up a distance of 8.5 m on the ramp. How high is he above the ground? [ans: 1.0 m]
The height, which comes out to be approximately 1.0 m.
To calculate the angle at which the mountain road is inclined to the horizontal, we can use the tangent function from trigonometry. The tangent of an angle in a right triangle is the ratio of the opposite side length to the adjacent side length.
1. Set up a right triangle where the vertical drop (5.2 m) represents the opposite side and the horizontal distance (22.5 m) represents the adjacent side.
2. Use the tangent function to find the angle: tan(angle) = opposite / adjacent.
3. Plug in the values: tan(angle) = 5.2 / 22.5.
4. Solve for the angle by taking the inverse tangent (arctan or tan^(-1)): angle = arctan(5.2 / 22.5).
5. Calculate the angle, which comes out to be approximately 13°.
Now, let's address the ramp scenario.
To find the height John is above the ground after walking up the 8.5 m ramp inclined at 7° to the horizontal, we can use the sine function.
1. Set up a right triangle where the unknown height represents the opposite side and the ramp length (8.5 m) represents the hypotenuse.
2. Use the sine function to find the height: sin(angle) = opposite / hypotenuse.
3. Plug in the values: sin(7°) = height / 8.5.
4. Solve for the height: height = 8.5 * sin(7°).
5. Calculate the height, which comes out to be approximately 1.0 m.
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Mrs conley asks her class what kind of party they want to have
There are 3 students who are undecided about the party.
If 20% of the class want an ice cream party, and there are 5 students who want an ice cream party, we can set up the following equation:
5 = 0.2x
Where x is the total number of students in the class. To solve for x, we can divide both sides by 0.2:
5 ÷ 0.2 = x
x = 25
So there are 25 students in the class. To find out how many students are undecided about the party, we can subtract the number of students who want each type of party from the total:
Undecided = 25 - 5 - 7 - 10 = 3
Therefore, there are 3 students who are undecided about the party.
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Full Question ;
Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 5 want an ice cream party, 7 want a movie party, 10 want a costume party, and the rest are undecided.
If 20% want an ice cream party, how many students are in the class?
How to solve for A and Z?
The length of the missing sides of the two quadrilaterals are listed below:
a = 5z = 4.219How to find the missing lengths in quadrilaterals
In this problem we must determine the length of missing sides in two quadrilaterals, this can be done with the help of Pythagorean theorem and properties for special right triangles:
r = √(x² + y²)
45 - 90 - 45 right triangle
r = √2 · x = √2 · y
Where:
x, y - Legsr - HypotenuseNow we proceed to determine the missing sides for each case:
a = √[(6 - 3)² + 4²]
a = √(3² + 4²)
a = √25
a = 5
Case 2
z = √[(22 - 4√2 - 15)² + 4²]
z = √[(7 - 4√2)² + 4²]
z = 4.219
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Show that if x is any real number, there is a sequence of rational numbers converging to x. 46. Show that if x is any real number, there is a sequence of irrational numbers converging to x. 47. Suppose that {an}n=1[infinity] converges to A and that B is an accumulation point of {an:n∈J}. Prove that A=B.
Every neighborhood of A contains a point of B and every neighborhood of B contains a point of A, which implies that A=B.
To show that there exists a sequence of rational numbers converging to any real number x, we can use the fact that the rational numbers are dense in the real numbers. This means that between any two real numbers, there exists a rational number.
So, let x be any real number. We can construct a sequence of rational numbers {q_n} such that q_n is the rational number between x-1/n and x+1/n. In other words,
q_n = a/b, where a and b are integers such that x-1/n < a/b < x+1/n and b > n
Then, it can be shown that as n approaches infinity, q_n converges to x. Therefore, there exists a sequence of rational numbers converging to any real number x.
To prove that A=B, we need to show that every neighborhood of A contains a point of B and every neighborhood of B contains a point of A.
First, let's consider any neighborhood of A. Since {a_n} converges to A, we know that there exists some positive integer N such that for all n > N, |a_n - A| < ε/2, where ε is the radius of the neighborhood.
Now, since B is an accumulation point of {a_n : n ∈ J}, we know that there exists some integer j ∈ J such that |a_j - B| < ε/2.
Thus, we have:
|A - B| ≤ |A - a_j| + |a_j - B| < ε/2 + ε/2 = ε
This shows that B is also in the neighborhood of A.
Next, let's consider any neighborhood of B. Since B is an accumulation point of {a_n : n ∈ J}, we know that there exists some positive integer M such that there are infinitely many n ∈ J satisfying |a_n - B| < ε/2.
Now, let n_1, n_2, n_3, ... be a subsequence of {a_n} such that |a_ni - B| < ε/2 for all i ≥ 1.
Since {a_n} converges to A, we know that there exists some positive integer N such that for all n > N, |a_n - A| < ε/2.
Let N' be the maximum of N and n_1, so that for all n > N', we have:
|a_n - A| < ε/2 and |a_n - B| < ε/2
Then, we have:
|A - B| ≤ |A - a_n| + |a_n - B| < ε/2 + ε/2 = ε
This shows that A is also in the neighborhood of B.
Therefore, we have shown that every neighborhood of A contains a point of B and every neighborhood of B contains a point of A, which implies that A=B.
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Show as much work as possible Simplify. 1. 3(5-7)
To show as much work as possible and simplify the expression 3(5-7), we first need to simplify the expression inside the parentheses. After simplification, we get the answer as -6.
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Provide an overview of the Fentanyl epidemic and layout the
strategy you would utilize to end it.
By employing this comprehensive approach, it is possible to address the Fentanyl epidemic and work towards reducing its devastating impact on individuals and communities
The Fentanyl epidemic refers to the widespread misuse and abuse of Fentanyl, a powerful synthetic opioid painkiller. This opioid is 50 to 100 times more potent than morphine, which makes it highly addictive and prone to overdoses. The epidemic has been exacerbated by the increased availability of illicitly manufactured Fentanyl, leading to a significant increase in overdose deaths and addiction rates.
To end the Fentanyl epidemic, I would suggest the following multi-pronged strategy:
1. Education and awareness: Increase public awareness of the dangers of Fentanyl and its addictive potential through targeted educational campaigns and outreach programs.
2. Monitoring and regulation: Strengthen regulations around prescription and distribution of Fentanyl to reduce over-prescribing and diversion to the illicit market.
3. Access to treatment: Expand access to evidence-based addiction treatment options, including medication-assisted treatment and counseling, to help those struggling with Fentanyl addiction.
4. Law enforcement and interdiction: Improve coordination between law enforcement agencies to better detect and disrupt the supply of illicit Fentanyl and related substances.
5. Harm reduction: Implement harm reduction strategies, such as supervised injection facilities and distribution of naloxone, a medication that can reverse the effects of an opioid overdose, to save lives and reduce the risk of transmission of infectious diseases.
By employing this comprehensive approach, it is possible to address the Fentanyl epidemic and work towards reducing its devastating impact on individuals and communities.
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please help!!
Using the Golfer Data in the Quiz Conf. Intervals Hypoth. Testing Templates compute a 90% confidence interval for the population proportion of females. a. 18 to 29 .19 to 28 20 to 27 9 d. 16 to 31 C
The 90% confidence interval for the population proportion of females is (0.261, 0.375). Answer: d. 16 to 31.
To compute a 90% confidence interval for the population proportion of females using the Golfer Data, you can use the following formula:
CI = p ± z*√(P(1-P)/n)
where P is the sample proportion, z is the z-score associated with the desired confidence level (in this case, 1.645 for 90% confidence), and n is the sample size.
From the Golfer Data, we can see that there are 84 females out of a total of 264 golfers:
n = 264
P = 84/264 = 0.318
Plugging these values into the formula, we get:
CI = 0.318 ± 1.645*√(0.318(1-0.318)/264)
CI = 0.318 ± 0.057
CI = (0.261, 0.375)
Therefore, the 90% confidence interval for the population proportion of females is (0.261, 0.375). Answer: d. 16 to 31.
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kenny is playing on a mall escalator. he can run up the escalator in 30 seconds and it takes im 6 seconds to run up the the up escalator. how many seconds would it take kenny to run up the flight of stairs that is between the escalatos
It would take Kenny 5 seconds to run up the flight of stairs between the escalators without using the escalator.
Let's assume that the escalator has a certain height and Kenny needs to climb the same height by running up the flight of stairs between the escalators.
Let's say that the height of the escalator is h and the speed of Kenny's running is s (measured in units of height per second).
When Kenny runs up the escalator, he covers the same height h in two ways:
by running up the stairs, which takes him t seconds
by using the help of the moving escalator, which takes him 30 seconds
The speed of Kenny's running up the escalator is therefore:
s + h/30
Similarly, when Kenny runs up just the stairs, he covers the same height h in two ways:
by running up the stairs, which takes him t seconds
by running up the up escalator, which takes him 6 seconds
The speed of Kenny's running up the stairs is therefore:
s + h/6
Since the distances covered in both cases are the same, we have:
t(s + h/30) = h
t(s + h/6) = h
Dividing the second equation by the first one, we get:
(s + h/6)/(s + h/30) = 30/t
Simplifying and solving for t, we get:
t = 5 seconds
Therefore, it would take Kenny 5 seconds to run up the flight of stairs between the escalators without using the escalator.
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Question 5(Multiple Choice Worth 2 points)
(Properties of Operations MC)
What is an equivalent form of 15(p+ 4) - 12(2q + 4)?
15p24q+ 12
O15p -24q+8
60p-72q
-9pq
Answer:
15p - 24q +8
Step-by-step explanation:
Type the correct answer in the box. If necessary, use / for the fraction bar.
If a rectangular prism has a length, width, and height of centimeter, centimeter, and centimeter, respectively, then the volume of the prism is
cubic centimeter
For a rectangular prism with a length, width, and height of [tex] \frac{3}{8}[/tex] cm, [tex] \frac{5}{8}[/tex] cm and [tex] \frac{7}{8}[/tex] centimetre respectively. The volume of this rectangular prism is equals to 0.21 cm³.
Volume of a rectangular prism, can be calculated by multiply the length of the prism by the width of the prism by the height of the prism. That is Volume, V = length × width × height
It is expressed in cubic of measurement units like cm³, m³, feet³, etc. We have a rectangular prism with following dimensions, length of rectangular prism, L = [tex]\frac{3}{8}[/tex] cm
Height of rectangular prism, H = [tex] \frac{7}{8}[/tex] cm
width of rectangular prism, W = [tex] \frac{5}{8}[/tex] cm
Using the above volume formula of rectangular prism, Volume, V = L×H×W
Substitute all known values in above formula,
=> V = [tex] \frac{3}{8} \times \frac{5}{8} \times \frac{7}{8}[/tex]
= [tex] \frac{105}{8^{3} }[/tex]
= 0.21 cm³
Hence, required volume value is
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Complete question:
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If a rectangular prism has a length, width, and height of 3/8 centimeter, 5/8 centimeter, and 7/8 centimeter, respectively, then the volume of the prism is ____cubic centimeter.
Andre, Lin, and Noah each designed and built a paper airplane. They launched each plane several times and recorded the distance of each flight in yards. Write the five-number summary for the data for each airplane. Then, calculate the interquartile range for each data set.
Answer:
Andre's: Min = 18, Q1 = 23.5, Median = 28.5, Q3 = 31.5, Max = 35, IQR = 8
Lin's: Min = 15, Q1 = 19, Median = 21.5, Q3 = 24, Max = 33, IQR = 5
Noah's: Min = 10, Q1 = 12.5, Median = 19, Q3 = 22.5, Max = 25, IQR = 10
Step-by-step explanation:
DATAfile: Houston
You may need to use the appropriate appendix table or technology to answer this question.
Data were collected on the amount spent by 64 customers for lunch at a major Houston restaurant. These data are contained in the file named Houston. Based upon past studies the population standard deviation is known with
σ = $6.
20.50 14.63 23.77 29.96 29.49 32.70 9.20 20.89
28.87 15.78 18.16 12.16 11.22 16.43 17.66 9.59
18.89 19.88 23.11 20.11 20.34 20.08 30.36 21.79
21.18 19.22 34.13 27.49 36.55 18.37 32.27 12.63
25.53 27.71 33.81 21.79 19.16 26.35 20.01 26.85
13.63 17.22 13.17 20.12 22.11 22.47 20.36 35.47
11.85 17.88 6.83 30.99 14.62 18.38 26.85 25.10
27.55 25.87 14.37 15.61 26.46 24.24 16.66 20.85
(a)
At 99% confidence, what is the margin of error in dollars? (Round your answer to the nearest cent.)
$
(b)
Develop a 99% confidence interval estimate of the mean amount spent for lunch in dollars. (Round your answers to the nearest cent.)
$ to $
2.
You may need to use the appropriate appendix table or technology to answer this question.
An air transport association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 businesstravelers is selected and each traveler is asked to provide a rating for a certain airport. The ratings obtained from the sample of 50 business travelers follow.
6 4 6 8 7 8 6 3 3 7
10 4 8 7 8 6 5 9 4 8
4 3 8 5 5 4 4 4 8 3
5 5 2 5 9 9 9 4 8 9
9 4 9 7 8 3 10 9 9 6
Develop a 95% confidence interval estimate of the population mean rating for this airport. (Round your answers to two decimal places.)
to
(a) At 99% confidence, the margin of error in dollars is $2.46. (b) The 99% confidence interval lies between $19.11 and $24.03.; 2. The 95% confidence interval lies between 5.98 and 7.26.
(a) Margin of error = z * (σ / sqrt(n))
where z is the z-score = 2.576, σ is the population standard deviation = $6, and n is sample size = 64.
Margin of error = 2.576 * (6 / sqrt(64)) = $2.46
(b) Confidence interval = sample mean ± margin of error
where, Sample mean = (20.50 + 14.63 + 23.77 + ... + 16.66 + 20.85) / 64 = $21.57
Therefore,
Confidence interval = $21.57 ± $2.46 = $19.11 to $24.03
Therefore, 99% Confidence interval is between $19.11 and $24.03.
2. To develop a confidence interval for the population mean rating, we need to use the t-distribution since the population standard deviation is unknown, and the sample size is small (n=50).
Sample mean = (6+4+6+8+7+8+6+3+3+7+10+4+8+7+8+6+5+9+4+8+4+3+8+5+5+4+4+4+8+3+5+5+2+5+9+9+9+4+8+9+9+4+9+7+8+3+10+9+9+6)/50 = 6.62
Sample standard deviation (s) = 2.25
Next, the t-value for a 95% confidence level and 49 degrees of freedom (n-1):
t-value = t(0.025, 49) = 2.0096
ME = t-value x (s / √n) = 2.0096 x (2.25 / √50) = 0.638
Therefore, 95% confidence interval is:
95% CI = sample mean ± ME = 6.62 ± 0.638 = (5.98, 7.26)
Therefore, 95% Confidence interval falls between 5.98 and 7.26.
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