The given series ∑=1[infinity]4 is a divergent series since each term in the series is a constant 4 and does not approach zero as n approaches infinity. The value of k that makes the series converge is DNE, i.e., it does not exist.
To elaborate, a series converges if the sequence of its partial sums approaches a finite limit as the number of terms in the sequence goes to infinity.
In this case, the partial sum of the series after n terms is S_n = 4n. As n approaches infinity, S_n diverges to infinity as well, indicating that the series does not converge.
The value of k that makes the given series converge is DNE, as the series is divergent and does not approach a finite limit as the number of terms increases.
Learn more about divergent here:
https://brainly.com/question/31383099
#SPJ4
Solve for x. Round your answer to the nearest tenth.
X
8. 5
11. 2
For a right angled triangle with known measure of sides 11.2 units and 8.5 units, the unknown value of third side, i.e, x is equals to the 7.3 units.
A right triangle or right-angled triangle is defined as a triangle in which one angle is a right angle. Therefore, one of the angles must be 90 degrees and sum all interior angles is equals to 180°. See the triangle present in above figure. It is a right angled triangle because measure of one angle is 90°.
Height of triangle = x units
Base of triangle, b = x
Length of hypotenuse of triangle = 11.2
We have to determine the value of x. Using payathagaros theorem of sides in a right angled triangle, (hypothenuse)² = (base)² + (height)²
Substitute all known values in above formula,
=> (11.2)² = x² + (8.5)²
=> 125.44 = x² + 72.25
=> x² = 125.44 - 72.25
=> x² = 53.19
=> x = 7.2931 ~ 7.3
Hence, required value is 7.3 units.
For more information about right angled triangle, visit :
https://brainly.com/question/29869536
#SPJ4
Complete question:
The above figure complete the question. Solve for x. Round your answer to the nearest tenth.
X
8. 5
11. 2
Let T denote that you train hard, E that you eat good food, S that you get strong, and W that you win races. Convert the statement in a) to propositional logic, and based on this, answer b) and c). a) If you train hard and eat good food you will get strong. If you get strong then you will win races. b) What can we say if you don’t win races but do train hard? You can write your answer in plain English. c) What can we say if you do get strong? You can write your answer in plain English.
This means that if you get strong, then you are guaranteed to win races, according to the original statement.
a) We can convert the statement into propositional logic using the following symbols:
T: You train hard
E: You eat good food
S: You get strong
W: You win races
Using these symbols, the original statement can be represented as follows:
((T ∧ E) → S) ∧ (S → W)
This can be read as "If you train hard and eat good food, then you will get strong, and if you get strong, then you will win races."
b) We can use the propositional logic statement to answer this question. If you don't win races but do train hard, we know that the second part of the statement (S → W) is false, because if S (you get strong) were true, then W (you win races) would have to be true as well. Therefore, we can conclude that S (you get strong) must also be false. In plain English, this means that if you don't win races but do train hard, then you didn't get strong.
c) If you do get strong, we know that the second part of the statement (S → W) must be true, because if S (you get strong) is true, then W (you win races) must also be true. Therefore, we can conclude that if you get strong, then you will win races. In plain English, this means that if you get strong, then you are guaranteed to win races, according to the original statement.
To learn more about guaranteed visit:
https://brainly.com/question/31063582
#SPJ11
Each of Exercises 7-12 gives the first term or two of a sequence along with a recursion formula for the remaining terms. Write out the first ten terms of the sequence.
7. A_1 = 1, a_(n + 1) = a_n + (1/2^n)
The first 10 terms of the sequence using the recursion formula are 1, 1.5, 1..75, 1.875, 1.9375, 1.96875, 1.984375, 1.9921875, 1.99609375, 1.998046875
Here we have the first term of the sequence as
A₁ = 1
The recursion relation is given by
aₙ₊₁ = aₙ + 0.5ⁿ
Now here since we have
A₁ = 1, where n = 1
A₂ = A₁ + 0.5
= 1 + 0.5 = 1.5
Hence,
A₃ = A₂ + 0.5²
= 1.75
A₄ = A₃ + 0.5³
= 1.875
A₅ = A₄ + 0.5⁴
= 1.9375
A₆ = A₅ + 0.5⁵
= 1.96875
A₇ = A₆ + 0.5⁶
=1.984375
A₈ = A₇ + 0.5⁷
= 1.9921875
A₉ = A₈ + 0.5⁸
1.99609375
A₁₀ = A₉ + 0.5⁹
= 1.998046875
Hence, the first 10 terms of the sequence using the recursion formula are 1, 1.5, 1..75, 1.875, 1.9375, 1.96875, 1.984375, 1.9921875, 1.99609375, 1.998046875
To learn more about Recursion Formula visit
https://brainly.com/question/8972906
#SPJ4
5 1 point A contractor is considering a sale that promises a profit of $32,604 with a probability of 0.7 or a loss (due to bad weather, strikes and such of $5.761 with a probability of 0.3 The following table summarizes the probability distribution. What is the expected proht or loss? Round your answer to the nearest hundredth
Profit. Probability. P(x)
$32.604 0.7
-$5,761 0.3
Type your answer:________
The expected profit or loss is $21,094.50, rounded to the nearest hundredth
Here's the step-by-step explanation using the provided information:
Step 1: Identify the profit and loss values and their respective probabilities.
Profit: $32,604 with a probability of 0.7
Loss: -$5,761 with a probability of 0.3
Step 2: Calculate the expected profit or loss using the formula:
[tex]\frac{Expected profit/loss}{loss} = (Profit * Probability of profit) + (Loss * Probability of Loss)[/tex]
Step 3: Plug in the values into the formula:
[tex]\frac{Expected profit}{loss} = ($32,604 * 0.7) + (-$5,761 * 0.3)[/tex]
Step 4: Perform the calculations:
[tex]\frac{Expected profit}{loss} = ($22,822.8) + (-$1,728.3)[/tex]
Step 5: Add the results to find the expected profit or loss:
[tex]\frac{Expected profit}{loss} = $21,094.5[/tex]
So, the expected profit or loss is $21,094.50, rounded to the nearest hundredth.
To know more about "Probability" refer here:
https://brainly.com/question/30034780#
#SPJ11
Let X be a random variable with the following probability distribution Value x of X P(X= x) -30 0.10 -20 0.15 -10 0.05 0 0.35 10 0.35 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X) of X. E(x) = 0 (b) Find the variance Var(x) of X. Var(x) = 0 Х ? Let X be a random variable with the following probability distribution. Value x of X P(X=x) 20 0.30 30 0.40 40 0.05 50 0.25 Complete the following. (If necessary, consult a list of formulas.) Х 2 (a) Find the expectation E(X) of X. E(x) = 0 (b) Find the variance Var(x) of x. Var(x) = 0 Let X be a random variable with the following probability distribution. Value x of X P(X=x) 3 0.35 4 0.20 5 0.30 6 0.05 7 0.05 00 0.05 Complete the following. (If necessary, consult a list of formulas.) ? (a) Find the expectation E (X) of X. E(x) = 0 (b) Find the variance Var(x) of X. Var(x) = 0
E(X) = 28.5 for the second distribution, and 4.05 for the third distribution and Var(X) = 100 for the second distribution, and 1.4525 for the third distribution.
(a) The expectation E(X) of X is calculated as the weighted average of all possible values of X:
E(X) = (-30)(0.10) + (-20)(0.15) + (-10)(0.05) + (0)(0.35) + (10)(0.35) = 1
Therefore, E(X) = 1.
(b) The variance Var(X) of X is calculated using the formula:
[tex]Var(X) = E(X^2) - [E(X)]^2[/tex]
We already know E(X) from part (a), so we need to calculate [tex]E(X^2)[/tex]:
[tex]E(X^2) = (-30)^2(0.10) + (-20)^2(0.15) + (-10)^2(0.05) + (0)^2(0.35) + (10)^2(0.35) = 700[/tex]
Plugging in the values, we get:
[tex]Var(X) = 700 - (1)^2 = 699[/tex]
Therefore, Var(X) = 699.
For the other two distributions, the calculations are the same, and we get:
(a) E(X) = 28.5 for the second distribution, and 4.05 for the third distribution.
(b) Var(X) = 100 for the second distribution, and 1.4525 for the third distribution.
To know more about "Variance" refer here:
https://brainly.com/question/29615374#
#SPJ11
The windows generated by three sellers are as follows: $4,000 $4,000 $4,000. We can conclude that the standard deviation is:
A) between $1,000 and $4,000
B) $4,000
C)$0
D)no answer text provided
The standard deviation of the data set is 0. Therefore, the correct answer is C) $0.
To calculate the standard deviation, we can follow these steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each value, and then square the result.
3. Find the mean of these squared differences.
4. Take the square root of the mean of squared differences.
In this case, the windows generated by the three sellers are all $4,000.
Step 1: Calculate the mean.
Mean = (4,000 + 4,000 + 4,000) / 3 = 4,000
Step 2: Subtract the mean from each value and square the result.
(4,000 - 4,000)^2 = 0
(4,000 - 4,000)^2 = 0
(4,000 - 4,000)^2 = 0
Step 3: Find the mean of these squared differences.
(0 + 0 + 0) / 3 = 0
Step 4: Take the square root of the mean of squared differences.
Square root of 0 = 0
The standard deviation of the data set is 0. Therefore, the correct answer is C) $0.
Learn more about standard deviation,
https://brainly.com/question/24298037
#SPJ11
Solve. M² + 5 = 10
a) m = ± √2
b) m = ± √5
c) m = ±√15
d) I don't know.
Noah is
Helping his band sell boxes of chocolate to fund a field trip. Each box contains 20 bars and each bar sells for $1. 50. Write an equation for the amount of money M that will be collected if B boxes of chocolate bars are sold
The equation for money collected m for h boxes of chocolate bars sold is m = 30h.
We are given that the band is selling every bar of chocolate for $1.50
Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.
Hence if we are going to calculate the amount of money collected on selling one box it will be
20 X $1.5
= $30
We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.
We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h
Now we know that
Money collected = price per box X no.of boxes sold
we have already calculated the price per box hence we get
m = 30h
To learn more about Linear Equations visit
https://brainly.com/question/29142080
#SPJ4
Jasmine finished the bike trail in 2. 5 hours at an average rate of 9 3/10 miles per hour. Lucy biked the same trail at a rate of 6 1/5 miles per hour. How long did it take Lucy to bike the trail?
It took Lucy approximately 2 13/31 hours to bike the trail.
We can start by using the formula:
distance = rate × time
Let's begin by finding the distance of the bike trail. Since Jasmine and Lucy biked the same trail, the distance will be the same for both of them. Let d be the distance of the trail.
d = distance of the bike trail
We know that Jasmine finished the bike trail in 2.5 hours at an average rate of 9 3/10 miles per hour. So, we can write:
d = 9 3/10 × 2.5
Simplifying the right-hand side, we get:
d = 23 1/2
Therefore, the distance of the bike trail is 23 1/2 miles.
Now, we can use the formula to find the time it took Lucy to bike the trail. Let t be the time it took Lucy to bike the trail.
distance = rate × time
23 1/2 = 6 1/5 × t
To solve for t, we can divide both sides by 6 1/5:
t = 23 1/2 ÷ (6 1/5)
Converting the mixed numbers to improper fractions, we get:
t = 47/2 ÷ 31/5
To divide fractions, we can multiply by the reciprocal:
t = 47/2 × 5/31
Simplifying, we get:
t = 2 13/31
Therefore, it took Lucy approximately 2 13/31 hours to bike the trail.
Learn more about distance ,
https://brainly.com/question/26711747
#SPJ4
Correctly use the wolframalpha method introduced in the Section 7.1 Learning Guidance and Section 7.1 Homework solutions (including your own correct using of parenthesis in the -x² - V wolframalpha command), match the function Z = x?y?e given by Problem 32 on Page é 392 with a graph and a contour map on Page 393. O Graph C, contour map I. O Graph C, contour map II.
When using the -x^2 - V command in WolframAlpha, it is important to correctly use parentheses to ensure the proper order of operations. The command should be written as "-(x^2) - V" to subtract x squared from V, rather than "-x^2 - V" which would subtract V from x squared.
To use the WolframAlpha method introduced in the Section 7.1 Learning Guidance and Section 7.1 Homework solutions to match the function Z = x^2y^3e^(-x-y) given by Problem 32 on Page 392 with a graph and a contour map on Page 393, you can follow these steps:
1. Go to the WolframAlpha website (www.wolframalpha.com).
2. In the search bar, type in "plot x^2*y^3*e^(-x-y)" and press enter.
3. WolframAlpha will generate a graph of the function Z = x^2y^3e^(-x-y), which can be used to match with the graph and contour maps on Page 393.
4. To generate a contour map, type in "contour plot x^2*y^3*e^(-x-y)" and press enter. WolframAlpha will generate a contour map of the function, which can be compared to the contour maps on Page 393.
To know more about wolframalpha - https://brainly.com/question/30698326
#SPJ11
please put them in order 1-5. which are the correct answers?
1
2
3
4
5
The probabilities and the expected values are calculated below
Evaluating the probabilities and the expected valuesNext cereal box wll contain blue or yellow
Here, we have
Yellow or blue = 15 + 5 = 20
Total = 50
So, we have
P(Yellow or blue) = 20/50
P(Yellow or blue) = 2/5
Arrival time before 7:30 am
Here, we have
Arrival time before 7:30 am = 7
Total time = 20
So, we have
P(Arrival time before 7:30 am) = 7/20
Team least likely
Convert the probabilities to decimal
So, we have
Nets = 0.67
Rockets = 0.5
Bucks = 0.8
Warriors = 0.375
This means that the team least likely to play in the championship game is 0.375
Section 7 in the game
Here, we have
P(7) = 35/250
In 150 times, we have
n(7) = 35/250 * 150
n(7) = 21
So, the number of times is 21
Expected students to eat chicken nuggets
Here, we have
P(Chicken) = 14/40
In 840 students, we have
n(Chicken) = 14/40 * 840
n(Chicken) = 294
Hence, the expected number of students to eat chicken nuggets is 294
Read more about probabilities at
https://brainly.com/question/251701
#SPJ1
[2] The prior probabilities for events A1 and A2 are P(A1)=0.62 and P(A2)=0.38. It is also known that P(A1∩A2)= 0. Suppose P(B|A1)=0.14 and P(B|A2)=0.09. Answer the following questions. (**Using Excel**)
(a) Are A1 and A2 are mutually exclusive? Explain.
(b) Calculate P(A1∩B) and P(A2∩B).
(c) Calculate P(B).
(d) Apply Bayes’ theorem to compute P(A1|B) and P(A2|B).
(e) Draw the corresponding Venn diagram or the probability tree
The overlapping area between A1 and B, and the probability of A2∩B is represented by the overlapping area between A2 and B.
(a) A1 and A2 are not mutually exclusive since their intersection probability P(A1∩A2) is not equal to zero.
(b) To calculate P(A1∩B), we can use the formula:
P(A1∩B) = P(B|A1) * P(A1)
P(A1∩B) = 0.14 * 0.62
P(A1∩B) = 0.0868
To calculate P(A2∩B), we can use the formula:
P(A2∩B) = P(B|A2) * P(A2)
P(A2∩B) = 0.09 * 0.38
P(A2∩B) = 0.0342
(c) To calculate P(B), we can use the formula for the total probability:
P(B) = P(B|A1) * P(A1) + P(B|A2) * P(A2)
P(B) = 0.14 * 0.62 + 0.09 * 0.38
P(B) = 0.1228 + 0.0342
P(B) = 0.157
(d) To apply Bayes’ theorem, we can use the formula:
P(A1|B) = P(B|A1) * P(A1) / P(B)
P(A1|B) = 0.14 * 0.62 / 0.157
P(A1|B) = 0.553
To calculate P(A2|B), we can use the formula:
P(A2|B) = P(B|A2) * P(A2) / P(B)
P(A2|B) = 0.09 * 0.38 / 0.157
P(A2|B) = 0.217
(e) Here is a Venn diagram to represent the events A1, A2, and B:
+------------+
| |
| A1 |
| |
+------+-----+
| P(B|A1) = 0.14
+------|-----+
| | |
| B | A1∩B|
| | |
+------+-----+
| P(B|A2) = 0.09
+------+-----+
| | |
| A2 | B∩A2|
| | |
+------+-----+
| |
| A1∩A2 |
| |
+------------+
The left circle represents A1, the right circle represents A2, and the intersection represents A1∩A2. The probability of B given A1 is represented by the line connecting B and A1, and the probability of B given A2 is represented by the line connecting B and A2. The probability of A1∩B is represented by the overlapping area between A1 and B, and the probability of A2∩B is represented by the overlapping area between A2 and B.
To learn more about represented visit:
https://brainly.com/question/19000815
#SPJ11
Tally's teacher divides her class of 16 students into 4 equally sized teams: red team, yellow team, green team and the blue team. She assigns a students to each team. What is the probability that Tally is on the red team? Enter your answer as a simplified fraction.
The probability that Tally is on the red team is 1/4.
We have,
Total students = 16
Students in each group = 16/4 = 4
Total Teams = Red, Yellow, Green and Blue.
So, the probability that Tally is on the red team
= 4 / 16
= 1/4
Thus, the probability is 1/4.
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ1
Michael read 135 pages in 90 minutes. Select all the rates that have the same constant rate of change as michael's
The same constant rate of change as Michael's is depicted in following ratio - 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.
The rate of reading Michael is -
Rate = 135/90
Rate = 3:2
Now, we will check the options to see if they have same ratio.
Option 1 180 page in 2 hours
As known about time conversion that 1 hour has 60 minutes, 2 hours = 120 minutes
So, Rate = 180/120
Rate = 3:2
Option 2 60 pages in 30 minutes
Rate = 60/30
Rate = 2:1
Option 3 108 pages in 2 and half hours
Time = 2.5 hours
Time = 150 minutes
Rate = 108/150
Rate = 18:25
Option 4 150 page in 1 hour
Rate = 150/60
Rate = 5:2
Option 5 225 pages in 150 minutes
Rate = 225/150
Rate = 3:2
Option 6 210 pages in 2 hour 20 minutes
Time = 140 minutes
Rate = 210/140
Rate = 3:2
Hence, the same rate options are 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.
Learn more about rate -
https://brainly.com/question/29023704
#SPJ4
The complete question is -
Michael read 135 pages in 90 minutes. Select all of the rates that have the same constant rate of change as Michael's rate. 180 pages in 2 hours, 60 pages in 30 minutes, 108 pages in 2 and half hours, 150 pages in 1 hour, 225 pages in 150 minutes, 210 pages in 2 hour 20 minutes
Trials in an experiment with a polygraph include 99 results that include 22 cases of wrong results and 77 cases of correct results. use a 0.05 significance level to test the claim that such polygraph results are correct less than 80% of the time. identify the null hypothesis, alternative hypothesis, test statistic, p-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. use the p-value method. use the normal distribution as an approximation of the binomial distribution.
Using a 0.05 significance level, a hypothesis test was conducted to determine if polygraph results are correct less than 80% of the time. So null hypothesis is not rejected by test results due to insufficiency of evidence to support the claim.
Null hypothesis, The polygraph results are correct 80% of the time or more.
Alternative hypothesis, The results given by polygraph are correct as they are less than 80% of the time.
Since the sample size is large and the success-failure condition is satisfied, we can use the normal distribution as an approximation of the binomial distribution. we can calculate the test statistic from formula
z = (p - P) / √(P(1-P)/n)
where p is the sample proportion of correct results, P is the hypothesized proportion of correct results (0.80), and n is the sample size.
p = 77/99 = 0.7778
z = (0.7778 - 0.80) / √(0.80(1-0.80)/99) = -0.6318
Using a standard normal distribution table, the p-value is found to be 0.2646.
Since the p-value (0.2646) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to conclude that the polygraph results are correct less than 80% of the time.
Therefore, we can conclude that at a 0.05 significance level, there is not enough evidence to support the claim that such polygraph results are correct less than 80% of the time.
To know more about Null hypothesis:
https://brainly.com/question/28920252
#SPJ1
The coordinates of points A and B are A(4, −2) and B(12, 10). What are the coordinates of the point that is 14 of the way from A to B? A. (1, −0.5) B. (6, 1) C. (10, 7) D. (3, 2.5)
The coordinate of the point is given as: (x,y) = (28/5, 2/5)
Why is this so?Given
A = (4,-2)
B = (12,-10)
Ration = 1/4
We apply the following formula:
(x,y) = [((mx2 + nx1)/(m+n)), ((my2 + ny1)/(m+n)),
Where:
m and n are the ratios. That is:
m/n = 1/4
m : n = 1 : 4
Where A(4,-2) and B(12,10); we have
(x,y) = [((1 * 12 + 4x4)/(4+1)), ((1*10 + 4 *-2)/(4+1)),
(x,y) = (12 + 16/5), ((10-8)/5))
Simplified, this yeild:
(x,y) = (28/5, 2/5)
Thus, the coordinate of the point is (x,y) = (28/5, 2/5).
Learn more about coordinates:
https://brainly.com/question/16634867
#SPJ1
select the domain and range of each relation. { ( 0 , 2 ) , ( 1 , 3 ) , ( 2 , 4 ) , ( 3 , 5 ) , ( 4 , 6 ) }
The domain and range of the given relation { ( 0 , 2 ) , ( 1 , 3 ) , ( 2 , 4 ) , ( 3 , 5 ) , ( 4 , 6 ) } are as follows: Domain: {0, 1, 2, 3, 4}, Range: {2, 3, 4, 5, 6}.
The domain represents the set of all input (x) values, while the range represents the set of all output (y) values in the relation. The given set of ordered pairs is a relation. The first coordinate in each pair is the input, also known as the domain, and the second coordinate is the output, also known as the range.
Domain: { 0, 1, 2, 3, 4 }
Range: { 2, 3, 4, 5, 6 }
Learn more about the range here: brainly.com/question/30067462
#SPJ11
An object has a mass of 613 kg and a volume of 11 m³. Find the density of the object in kg/m³. Give your answer rounded to 1 decimal place.
Answer:
55.7 kg/m^3
Step-by-step explanation:
Density= Mass ÷ Volume
D=613÷ 11
D=55.72727...
Rounded to 55.7
There ya go
One of the support wires for a radio tower is 100 feet long. One end of the wire is 40 feet from the base of the tower, as shown in the diagram below.
What angle (x), in degrees, does the support wire make with the ground?
Show all work
The required support wire makes an angle of approximately 67.54° degrees with the ground.
We can use trigonometry to find the angle x. In the diagram, we can see that the support wire, the height of the tower, and the ground form a right triangle. The length of the support wire is the hypotenuse of this triangle, and the distance from the base of the tower to the point where the wire touches the ground is the adjacent side. We can use the tangent function to find the angle x:
tan(x) = opposite / adjacent
In this case, the opposite side is the height of the tower, which we don't know yet. However, we can use the Pythagorean theorem to find it:
height² = support wire² - adjacent²
height² = 100² - 40²
height ≈ 96.8
Now we can plug in the values to find x:
tan(x) = opposite / adjacent
tan(x) = 96.8 / 40
x ≈ 67.54°
Therefore, the support wire makes an angle of approximately 67.54° degrees with the ground.
Learn more about trig ratios here;
https://brainly.com/question/14977354
#SPJ1
the cost of producing smartphones has fallen over the past decade. consider some implications of this change.show the effect of falling production costs on the market for smartphones.
As the cost of producing smartphones has fallen over the past decade, several implications and effects on the market for smartphones can be observed:
1. Lower prices: Falling production costs have led to lower prices for consumers, making smartphones more affordable and accessible to a broader population.
2. Increased demand: Lower prices have also resulted in increased demand for smartphones, as more people can now afford them. This has led to a higher sales volume in the market.
3. Market expansion: The accessibility and affordability of smartphones have led to market expansion, as smartphones become more prevalent in both developed and developing countries.
4. Greater competition: The lower production costs have enabled more companies to enter the smartphone market, increasing competition and leading to more product variety for consumers.
5. Innovation and improvement: Due to the increased competition, companies are constantly seeking ways to differentiate their products through innovative features, improved design, and better performance.
Overall, the falling production costs of smartphones have positively impacted the market by lowering prices, increasing demand, and driving innovation and competition.
Know more about cost here:
https://brainly.com/question/30045916
#SPJ11
show that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3
we have shown that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.
Let n be a positive integer and let d1, d2, ..., dm be its decimal digits, where dm is the leftmost (most significant) digit and d1 is the rightmost (least significant) digit. Then n can be written as:
n = [tex]d1 * 10^{(m-1)} + d2 * 10^{(m-2)} + ... + dm-1 * 10 + dm[/tex]
We want to show that n is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.
First, suppose that n is divisible by 3. Then we have:
n = 3k
for some integer k. Substituting the expression for n, we have:
[tex]d1 * 10^{(m-1)} + d2 * 10^{(m-2)} + ... + dm-1 * 10 + dm = 3k[/tex]
Taking both sides modulo 3, we obtain:
d1 + d2 + ... + dm-1 + dm ≡ 0 (mod 3)
which means that the sum of the decimal digits of n is divisible by 3.
Conversely, suppose that the sum of the decimal digits of n is divisible by 3. Then we have:
d1 + d2 + ... + dm-1 + dm = 3k
for some integer k. Substituting this expression into the equation for n, we obtain:
n =[tex]d1 * 10^{(m-1)} + d2 * 10^{(m-2)} + ... + dm-1 * 10 + dm[/tex]
= [tex]d1 * (10^{(m-1)} - 1) + d2 * (10^{(m-2)} - 1) + ... + dm-1 * (10 - 1) + (d1 + d2 + ... + dm-1 + dm)[/tex]
= [tex]d1 * (10^{(m-1)} - 1) + d2 * (10^{(m-2)} - 1) + ... + dm-1 * (10 - 1) + 3k[/tex]
The first m-1 terms on the right-hand side are all divisible by 3, since 10^n - 1 is divisible by 3 for any positive integer n. Therefore, we have:
n ≡ dm + 3k (mod 3)
Since the sum of the decimal digits of n is divisible by 3, we have dm + d1 + d2 + ... + dm-1 ≡ 0 (mod 3). Therefore, we have:
n ≡ 0 (mod 3)
which means that n is divisible by 3.
Therefore, we have shown that a positive integer is divisible by 3 if and only if the sum of its decimal digits is divisible by 3.
To know more about positive integer refer here:
https://brainly.com/question/18380011
#SPJ11
caputo fractional integral and derivativefal k b(- b) "D. f(x) = f(x)- **f(0+), a ER+. k! k=0
The Caputo fractional integral and derivative are mathematical operations used to describe the behavior of a function. The Caputo fractional derivative is a generalization of the traditional derivative and measures the rate of change of a function with respect to a fractional order. The Caputo fractional integral is the inverse operation of the fractional derivative and measures the accumulation of a function over a fractional order.
In the given equation, "D" represents the Caputo fractional derivative, and "f(x)" is the function being differentiated. The "k" and "k!" terms in the equation correspond to the order of the derivative being taken. The "a" and "b" terms are constants that determine the interval over which the derivative is being taken.
The notation "f(0+)" represents the limit of the function as it approaches zero from the right-hand side. This is necessary in fractional calculus because the behavior of a function near zero can be different from its behavior at other points.
Overall, the Caputo fractional integral and derivative are powerful tools for analyzing the behavior of complex functions and systems. They allow us to extend traditional calculus to include fractional orders and better understand phenomena like fractals and self-similar patterns.
derivativehttps://brainly.com/question/23819325
#SPJ11
martin has read 10% of a book. He has 27 more pages to finish. How many pages are there in the book?
Concert tickets go on sale for $34. 00 each
The required amount will be earn is $3400.
This calculation only takes into account the revenue earned from ticket sales and does not include any additional revenue streams such as merchandise sales or sponsorships.
The total earnings will depend on various factors such as ticket pricing strategy, marketing efforts, and concert attendance.
Here given concert tickets are selling for $34.00 each and it is also given a total number of 100 tickets are sold.
the total earnings will be calculated by multiplying the ticket price by the number of tickets sold.
So,total amount earn = $34×100 = $3400.
This is a problem of Multiplication.
Learn more about Multiplication here,
https://brainly.com/question/10873737
#SPJ4
Correct question is " Concert tickets go on sale for $34. 00 each . Now total number of sold tickets are 100 . Count how many money will earn ."
What is the tallest and shortest plant heights ?
In general, the tallest and shortest plant heights can vary widely depending on the species of plant being considered.
For example, some species of trees can grow over 300 feet tall, while certain species of mosses may only grow a few millimeters in height. The specific environmental conditions, such as the availability of water, sunlight, and nutrients, can also impact the growth and height of plants. Therefore, without more specific information, it is difficult to provide a more precise answer.
Learn more about heights
https://brainly.com/question/28122539
#SPJ4
Using white paper, wyatt created a cube with a side length of 4 inches. He wants to color all sides of the cube. How many square inches will wyatt color.
Wyatt will color a total of 96 square inches on all sides of the cube.
A cube has six sides, and each side will be a square. To find the total area of all the sides that Wyatt will color, we need to multiply the area of one side by the total number of sides.
Given that the side length of Wyatt's cube is 4 inches, the area of one side would be;
Area of one side = side length × side length
= 4 inches × 4 inches
= 16 square inches
Since there are six sides in total, the total area of all the sides would be;
Total area of all sides = Area of one side × Number of sides = 16 square inches × 6
= 96 square inches
Therefore, total 96 square inches will wyatt color.
To know more about square inches here
https://brainly.com/question/6754997
#SPJ1
Number graph ranging from negative two to ten on the x and y axes. A line labeled y equals begin fraction three over two end fraction times x is drawn on the graph. A second line, labeled y equals begin fraction negative one over two end fraction x plus four, is drawn on the graph. What is the solution to the system of equations represented by these two lines? Responses (2, 0) (2, 0) (0, 4) (0, 4) (4, 2) (4, 2) (2, 3)
Answer:
Step-by-step explanation:
To find the solution to the system of equations represented by the two lines, we need to find the point where they intersect on the graph.
First, let's find the coordinates of the intersection point by solving the system of equations. We have:
y = (3/2)x (Equation 1)
y = (-1/2)x + 4 (Equation 2)
To find the intersection point, we need to set the two equations equal to each other:
(3/2)x = (-1/2)x + 4
Simplifying this equation, we get:
2x = 8
x = 4
Now that we know x = 4, we can substitute this value into either Equation 1 or Equation 2 to find the corresponding value of y:
y = (3/2)x
y = (3/2)(4)
y = 6
Therefore, the solution to the system of equations represented by the two lines is (4, 6).
determine whether this argument, taken from kalish and mon- tague [kamo64], is valid. if superman were able and willing to prevent evil, he would do so. if superman were unable to prevent evil, he would be impotent; if he were unwilling to prevent evil, he would be malevolent. superman does not prevent evil. if superman exists, he is neither impotent nor malevolent. therefore, superman does not exist
Answer: i think it b
Step-by-step explanation:
b
The argument is not valid.
The argument commits a fallacy known as the false dilemma or false dichotomy, which presents only two options when there may be more. In this case, the argument assumes that if Superman does not prevent evil, then he must either be impotent or malevolent.
However, there could be other reasons why Superman does not prevent evil, such as a lack of knowledge or resources.
Furthermore, the argument assumes that if Superman exists, then he must either prevent evil or be impotent/malevolent, but this assumption is not necessarily true. It is possible for Superman to exist and not have the ability or inclination to prevent all evil.
Therefore, the conclusion that Superman does not exist does not necessarily follow from the premises. The argument is not valid.
To know more about argument, refer here:
https://brainly.com/question/30637036#
#SPJ11
The length of a cell phone is
1.4
1.4 inches and the width is
4.4
4.4 inches. The company making the cell phone wants to make a new version whose length will be
1.96
1.96 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
The width of the new phone is 6.16 inches.
How to find the width of the new phone?The length of a cell phone is 1.4 inches and the width is 4.4 inches. The company making the cell phone wants to make a new version whose length will be 1.96 inches.
The side length of the new phone are proportional to the old phone. Therefore, the width of the new phone can be calculated as follows:
let
x = width of the new phone
1.4 / 1.96 = 4.4 / x
cross multiply
1.4x = 4.4 × 1.96
1.4x = 8.624
divide both sides by 1.4
x = 8.624 / 1.4
x = 6.16
Therefore,
width of the new phone = 6.16 inches
learn more on width here: https://brainly.com/question/20390545
#SPJ1
which graph represents -5x+3y>9
A graph which represent the inequality -5x + 3y > 9 is shown below.
How to graph the solution to this linear inequality?In order to to graph the solution to the given linear inequality on a coordinate plane, we would use an online graphing calculator to plot the given linear inequality and then take note of the points that lie on its line;
-5x + 3y > 9
3y > 9 + 5x
y > 9/3 + 5x/3
y > 5x/3 + 3
Next, we would use an online graphing calculator to plot the given linear inequality as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that a possible solution for the linear equation is the ordered pairs (0, 3) and (-1.8, 0), with a dashed line that is shaded above to indicate the solution, and this must be represented with the greater than or equal to (>) inequality symbol.
Read more on inequality here: brainly.com/question/27976143
#SPJ1