1) n²+n is always an even integer
2. n² +n is always an even integer when n is even
3. n² +n is always an even integer when n is odd
How to solveSince, if n is an integer,
Then n = even or odd,
If n = even ⇒ = even
⇒ = even+ even = even
Now, If n = odd ⇒ = odd ( square of a odd number is always odd )
⇒ = odd + odd = even
Hence, however, n is odd or even,
is always an even number.
⇒ Options 1), 2) and 3) are correct.
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if the height of a cone is halved , how will this change the volume of a cone?
if the height of a cylinder is tripled, how will this change the volume of the cylinder?
(explain answer)
The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The volume of a cone is a third of the volume of a cylinder, hence:
V = πr²h/3.
For both cases, the height variable h has an exponent of one, hence:
If the height of a cone is halved, the volume of the cone is halved.If the height of a cylinder is tripled, the volume of the cylinder is tripled.If we had doubled the radius for example, the volume would be multiplied by 2² = 4, as the radius is squared.
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Select the acceptable conclusions to a hypothesis test. a The value of the test statistic lies in the nonrejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true. b The value of the test statistic does not lie in the rejection region. Therefore, we accept the null hypothesis. c The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true. d The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true. e The value of the test statistic does not lie in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is true. f The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.
The acceptable conclusions to a hypothesis test are option a, c, d, f.
What is hypothesis test?
Hypothesis Testing is a way of statistical analysis in which a person can put his assumptions about a population parameter to the test. It usually used to estimate the relationship between two statistical variables.
By the property of hypothesis test the following can be stated.
⇒The value of the test statistic lies in the non rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.
⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true.
⇒The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.
⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.
Hence the correct options are a, c, d, f.
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find out the perimeter of the semicircle
take pie to be 3.142 and write down all the digits in the calculator
the radius of the semicircle is 11cm
Answer:
P = 11 + (1/2)π(11) = 11 + 5.5π = 28.279 cm
Letting π = 3.142:
P = 11 + (1/2)(3.142)(11) = 28.281 cm
Claire spins two spinners, each divided into equal sections labeled 1-8.
What is the probability that Claire spins a sum of 8? State what strategy you will use to answer the question, explain your choice, and then find the answer.
The probability that Claire spinning an 8 is around 0.078, or 7.8%.
How to calculate the favorable outcomes?We may use the strategy of calculating favorable results over total outcomes to get the likelihood that Claire spins a sum of 8. We must specifically determine how many possibilities there are to reach a sum of 8 when spinning the two spinners and divide that number by the total number of possible outcomes.
To illustrate, we can use a table to display all of the possible results for spinning two spinners labeled 1-8, and then compute the sum of each outcome:
There are 64 possible outcomes (8 spinners 1 choice times 8 spinner 2 choices), and we can see that there are 5 methods to reach a sum of 8: (2,6), (3,5), (4,4), (5,3), and (6,2). As a result, the likelihood of getting an 8 is:
P(sum of 8) = number of favorable outcomes / total number of outcomes
= 5 / 64
= 0.078125
So the likelihood of Claire spinning an 8 is around 0.078, or 7.8%.
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solve this. and you will get brainlst.
Step-by-step explanation:
Tan 20 = 50 / d
d = 50 / tan 20 = 137 m
Pls help for 10 pts :)) (Caeser Cipher)
The sixth and seventh letters "NO" become the 15th and 14th letters in the alphabet respectively when shifted by 11 positions, decrypt to "E" and "N" respectively. Therefore, the decrypted plaintext is "CSPAEN".
what is decrypted plaintext ?
The decrypted plaintext is the original message that was encrypted using a cipher, which has now been converted back to its original form using the appropriate decryption technique.
In the given question,
The given ciphertext "ZYJGKNO" can be decrypted using a times-11 cipher as follows:
The first letter "Z" becomes the third letter in the alphabet when shifted by 11 positions, so it decrypts to "C".
The second letter "Y" becomes the 24th letter in the alphabet when shifted by 11 positions, so it decrypts to "T".
The third letter "J" becomes the 18th letter in the alphabet when shifted by 11 positions, so it decrypts to "S".
The fourth and fifth letters "GK" become the 16th and 10th letters in the alphabet respectively when shifted by 11 positions, so they decrypt to "P" and "A" respectively.
The sixth and seventh letters "NO" become the 15th and 14th letters in the alphabet respectively when shifted by 11 positions, so they decrypt to "E" and "N" respectively.
Therefore, the decrypted plaintext is "CSPAEN".
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a student performs an experiment where they flip a coin 3 times . if they perform this experiment 200 times, predict the number of repetitions the experiment that will results in exactly two of the three flips landing on tails
We can predict that out of 200 repetitions of the experiment, approximately 75 of them will result in exactly 2 of the 3 flips landing on tails.
Describe Probability?Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is used to quantify the uncertainty associated with a particular event or outcome. In simpler terms, probability is a measure of the likelihood that a certain event will occur, expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
There are different types of probability, including classical probability, empirical probability, and subjective probability. Classical probability is based on the assumption of equally likely outcomes, while empirical probability is based on actual observations or experiments. Subjective probability, on the other hand, is based on personal judgment or belief.
The probability of getting tails on any single flip of a fair coin is 1/2. Since we are flipping the coin three times, the probability of getting exactly two tails is given by the binomial probability formula:
P(exactly 2 tails) = (number of ways to get 2 tails out of 3) * (probability of getting tails)² * (probability of getting heads)¹
The number of ways to get 2 tails out of 3 is given by the binomial coefficient "3 choose 2", which is 3. So we have:
P(exactly 2 tails) = 3 * (1/2)² * (1/2)¹ = 3/8
This means that the probability of getting exactly 2 tails in one trial of flipping the coin 3 times is 3/8.
To predict the number of repetitions out of 200 that will result in exactly 2 tails, we can multiply the probability of getting exactly 2 tails in one trial by the total number of trials:
Number of repetitions with exactly 2 tails = P(exactly 2 tails) * total number of trials
Number of repetitions with exactly 2 tails = (3/8) * 200
Number of repetitions with exactly 2 tails = 75
Therefore, we can predict that out of 200 repetitions of the experiment, approximately 75 of them will result in exactly 2 of the 3 flips landing on tails.
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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15). Determine the scale factor used.
5
one fifth
12
one twelfth
Tina collects cans to recycle at the supermarket. Last week, on Monday,Wednesday and Thursday , she collected 37 cans each day. On Tuesday,Friday,Saturday and Sunday sh collected 43 cans each day. Tina gets 5 cents for every can she recycles
If on Tuesday, Friday, Saturday, and Sunday, she collected 43 cans each day. Tina got $14.15 for her cans last week.
Tina collected 37 cans on Monday, Wednesday, and Thursday, which is a total of 37 x 3 = 111 cans. She collected 43 cans on Tuesday, Friday, Saturday, and Sunday, which is a total of 43 x 4 = 172 cans. The total number of cans she collected last week is 111 + 172 = 283 cans.
Since Tina gets 5 cents for every can she recycles, she made 5 x 283 = $14.15 for recycling all of the cans she collected last week.
Therefore, Tina got $14.15 for her cans last week.
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Complete question is:
Tina collects cans to recycle at the supermarket. Last week, on Monday, Wednesday and Tursday, she collected 37 cans each day. On Tuesday, Friday, Saturday, and Sunday, she collected 43 cans each day. Tina gets 5 cents for every can she recycles. How much money did Tina get for her cans last week?
I need some help please
Answer:
A. 2
Step-by-step explanation:
Let's interpret the function.
First, let's look at the top section:
[tex]f(x)=x+2[/tex] if [tex]x < 1[/tex]
So, if the value of x is less than 1, to find f(x), we should add 2 to x.
Let's check if x is less than 1:
[tex]x=3\\x < 1\\3 < 1[/tex]
3 is not less than one, so to find f(x), we cannot add 2 to x.
The second part of the function is:
[tex]f(x)=x-1[/tex] if [tex]x\geq 1[/tex]
So, if the value of x is greater than or equal to 1, to find f(x), we should subtract 1 from x.
Let's check if x is greater than or equal to 1:
[tex]x=3\\x\geq 1=\\3\geq 1[/tex]
3 is greater than or equal to 1, so to find f(x), we should use x-1.
[tex]x-1=\\3-1=\\2[/tex]
Thus, f(3) = 2; the answer is A.
FIND Z OF THIS CIRCLE
Answer:
Step-by-step explanation:
Round to 1 significant figure:
The rounded number to 1 significant figure is 10000m.
Significant figures are a way of indicating the precision of a measurement or calculation. They represent the digits in a number that are known with certainty, plus one additional digit that is estimated. The rules for determining significant figures include:
Non-zero digits are always significant.Zeros between non-zero digits are significant.Leading zeros (zeros before the first non-zero digit) are not significant.Trailing zeros (zeros at the end of a number, after the last non-zero digit) are significant if there is a decimal point.Significant figures are important because they allow us to communicate the accuracy and precision of a measurement or calculation. By using the appropriate number of significant figures, we can avoid misleading others with inaccurate or imprecise information.
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Anumeha mows lawns. She charges an initial fee and a constant fee for each hour of work.F represents Anumeha's fee (in dollars) for working t hours. F = 6 + 12t How much does Anumeha charge for each hour of work?
Answer:
if she worked 2h it would be 2×12 for the hourly charge which would be 24and then the 24+6where 6 is the base charge.
Step-by-step explanation:
The intial few would be 6.as we can see in the equation
f(t)=6+12t
t would be the amount of hours and 12 is the rate per hour.
!!PLEASE HELLPPP MEEEE!!
It will take approximately 25 years for $7,000 to double in an account that pays 2.8% simple interest.
How long it take for $7,000 to double with 2.8% S.I?The 70 rule is a helpful shortcut for calculating the number of years it will take an investment to double in value using simple interest. The formula is 70 divided by the interest rate.
In this case, we have an interest rate of 2.8%, so we can calculate that it will take approximately 70/2.8 = 25 years for $7,000 to double in value. It's important to note that this rule assumes the interest rate remains constant over the entire period, which may not always be the case in real-world investments.
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What is the unit price for a piece of cheese if 1. 24 pounds costs $11. 25
The unit price for a piece of cheese is $0.11 per pound.
To find the unit price, we need to divide the total cost by the total weight. In this case, we have 1.24 pounds of cheese that costs $11.25.
So, we can set up a proportion
1.24 pounds / $11.25 = x pounds / $1
To solve for x, we can cross-multiply
1.24 pounds * $1 = $11.25 * x pounds
1.24 = $11.25 * x
x = 1.24 / $11.25
x = 0.11
So, the unit price is $0.11 per pound.
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Can i please have help with this
Answer:
linear
Step-by-step explanation:
its linear because the data shows a straight line:)
Answer:
Linear
Step-by-step explanation:
linear equation forms a straight line on the graph. A nonlinear equation forms a curve on the graph.
Find two numbers having a difference of 16 such that the result of adding their sum and their product is a minimum
Answer:
-8.5 and 7.5
Step-by-step explanation:
Let's call the two numbers x and y. We know that their difference is 16, so we can write:
x - y = 16 or x = y + 16
We want to find the values of x and y that minimize the expression:
x + y + xy
Substituting x = y + 16, we get:
(y + 16) + y + (y + 16)y
Simplifying and expanding, we get:
y^2 + 17y + 16
To minimize this expression, we can take its derivative with respect to y and set it equal to 0:
d/dy (y^2 + 17y + 16) = 2y + 17 = 0
Solving for y, we get:
y = -8.5
Substituting y = -8.5 into x = y + 16, we get:
x = 7.5
Therefore, the two numbers with a difference of 16 such that the result of adding their sum and their product is a minimum are -8.5 and 7.5.
Please help this is the last question I can't get it wrong
Answer:10g-3
Step-by-step explanation:
Answer:
g=0.5
Step-by-step explanation:
2(5—1)=3
10g—2=3
10g—2+2=3+2
10g=5
10g/10=5/10
g=0.5
please help me I've been stumped on this problem
The Results:
a) The measure of ∠BDC = 67°
b) The measure of arc DAC = 46°
How to measure angles?a) The measure of ∠BDC
Since DC ⊥ AB, ∠DCB is a right angle, which means it measures 90°. Also, given that m∠DCB = 23, we can use the fact that the angles in a triangle sum to 180° to find ∠DBC.
∠DBC + ∠DCB + ∠B = 180 (angles in a triangle sum to 180)
∠DBC + 90 + 23 = 180 (substituting values)
∠DBC = 180 - 90 - 23 = 67°.
Thus, the measure of ∠BDC = 67°
b) The measure of arc DAC:
Since AB = AC, it implies that ∠ABC = ∠ACB (angles opposite to equal sides of an isosceles triangle are equal). Therefore, ∠ACB is also 23°.
Now, since ∠ACB is an inscribed angle that intercepts the arc DAC, the measure of the arc DAC is twice the measure of ∠ACB.
Arc DAC = 2 × ∠ACB = 2 × 23 = 46°.
Therefore, the measure of arc DAC is 46°.
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Is ΔABC ~ ΔDEF? Explain.
Answer:
ΔABC and ΔDEF are similar by (AA).
option (2)
Step-by-step explanation:
Here to test if the two triangles are similar based on the information given I will attempt to see if they are similar using
Angle-Angle (AA) Similarity Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Δ = 180°
therefore using the givens:
m∠CAB = 18°
m∠ABC = 110°
m∠ACB = 180°-110°-18° = 52°
now for ΔDEF
because we know corresponding parts of similar triangles are proportional
∠DEF ≅ ∠CAB
and because m∠ACB = 52° and m∠FDE = 52°
∠FDE ≅ ∠ACB
Therefore by AA, we have proven that these two triangles ΔABC and ΔDEF are similar.
so option (2)
Compare these rational numbers. Which of the following are true?
i. -2.3 - 1.3
ii. -2.3 -1.3
iii. -2.3> - 3.3
iv. -2.3 -3.3
a.ii and iv
b.ii and iii
c.i and iii
d.i and iv
The correct options for the given rational numbers are (a) ii and iv.
What are rational numbers?P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. The natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers.
To compare the rational numbers, we need to perform the given operations and determine their relative magnitudes:
i. -2.3 - 1.3 = -3.6
ii. -2.3 -1.3 = -3.6
iii. -2.3 > -3.3
iv. -2.3 -3.3 = -5.6
Comparing i and ii, we see that they are equal. Therefore, both options i and ii are true.
Comparing iii, we see that -2.3 is greater than -3.3. Therefore, option iii is true.
Comparing iv, we see that -5.6 is less than both -2.3 and -3.3. Therefore, option iv is false.
So, the correct options are (a) ii and iv.
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Sue and 4 friends share half a pizza. Each piece of pizza is the same size. Sue believes each piece of pizza has an angle measure of 30º. Is Sue correct? Explain.
Sue statement that each piece of pizza has an angle measure of 30º is incorrect
Stating if Sue's statement is correctAssuming the pizza is circular, we know that the total angle measure of a circle is 360 degrees.
If we cut the pizza into halves, we have two equal pieces, each with an angle measure of 180 degrees.
If Sue and her 4 friends share half a pizza, they are sharing one of these equal pieces.
If we divide the 180 degree angle of the piece of pizza by 5 (Sue and her 4 friends plus Sue herself), we get an angle measure of 36 degrees, which is what Sue believes.
Therefore, Sue is incorrect.
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Which theme park would you choose for yourself and your friends? Explain why.
#3
Water slides are overrated and roller coasters are dangerous, id rather check out the vr
The highest point of a normal curve occurs at Group of answer choices the mean. two standard deviations to the right of the mean. approximately three standard deviations to the right of the mean. one standard deviation to the right of the mean.
The highest point of a normal curve, also known as a Gaussian distribution or bell curve, always occurs at the mean. This is because the normal curve is symmetrical around the mean, with the same number of values on either side of the mean. Therefore, the peak of the curve must be directly above the mean.
The standard deviation is a measure of how spread out the values in a distribution are. For a normal distribution, approximately 68% of the values fall within one standard deviation of the mean, 95% fall within two standard deviations of the mean, and 99.7% fall within three standard deviations of the mean. Therefore, while the highest point of the normal curve occurs at the mean, the curve does extend out to both sides of the mean, with the height of the curve gradually decreasing as the distance from the mean increases.
Specifically, the point at which the curve begins to flatten out on either side of the peak is approximately one standard deviation away from the mean. At two standard deviations away from the mean, the curve has flattened out significantly, and at three standard deviations away from the mean, the curve is almost entirely flat. This is known as the empirical rule, or the 68-95-99.7 rule.
Understanding the normal curve and its characteristics is important in statistics and data analysis, as many real-world phenomena can be approximated using a normal distribution. By knowing the mean and standard deviation of a distribution, we can make predictions about the likelihood of various outcomes occurring.
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Jason is a high school basketball player. In a particular game, he made some free throws (worth one point each) and some two point shots. Jason made a total of 13 shots altogether and scored a total of 20 points. Write a system of equations that could be used to determine the number of free throws Jason made and the number of two point shots he made. Define the variables that you use to write the system..
The system of equations that could be used to determine the number of free throws Jason made and the number of two point shots he made are: x + y = 13 and 1x + 2y = 20
How to answer the aforementioned questionsLet x be the number of free throws Jason made and y be the number of two-point shots he made.
Then, we can write a system of equations based on the given information:
x + y = 13 (total number of shots made)
1x + 2y = 20 (total number of points scored)
The first equation shows Jason's total number of shots, which include both free throws and two-point attempts.
The second equation indicates Jason's total amount of points, taking into account that two-point shots are worth twice as much as free throws.
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On March 30, Century Television received an invoice dated March 28 from ACME Manufacturing for 51 televisions at a cost of $100 each. Century received a 8/5/5 chain discount. Shipping terms were FOB shipping point. ACME prepaid the $91 freight. Terms were 5/10 EOM. When Century received the goods, 3 sets were defective. Century returned these sets to ACME. On April 08, Century sent a $275 partial payment. Century will pay the balance on May 06. What is Century’s final payment on May 06? Assume no taxes
Century's final payment will be on May 06 is $4,028.
Total cost of televisions:
51 TVs at $100 each = $5,100
8% discount = $100 x 8% x 10 = $80
5% discount = $100 x 5% x 10 = $50
5% discount = $100 x 5% x 31 = $155
Total discount = $80 + $50 + $155 = $285
Cost after discount = $5,100 - $285 = $4,815
Shipping cost: no additional cost
Returned sets:
3 *$100 = $300
ACME will issue a credit to Century for $300
Total cost:
$4,815 + $0 - $300 = $4,515
Partial payment:
$275
Final payment:
Balance after partial payment = $4,515 - $275 = $4,240
5% discount if paid within 10 days after the end of the month = $4,240 x 5% = $212
Final payment on May 06 = $4,240 - $212 = $4,028
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On the way to her babysitting job, Mary rode her bike for the first mile. She stopped at a traffic light and waited a few minutes for the traffic light to turn green. She then walked her bike across the street and up a short steep hill. Finally, she rode the bike at a constant speed for one more mile. If Mary created a graph of her time and distance, which statement describes the part of her graph that would show no change in distance?
Mary used her bike to ride the first mile.
Mary stopped and waited for the traffic light to turn green.
Mary walked her bike across the avenue and up a short hill.
Mary rode her bike at a constant speed for one mile.
The part of the graph that would show no change in distance is when Mary stopped and waited for the traffic light to turn green.
Statement B is correct.
How do we calculate?We know that during this time, Mary did not move forward or cover any distance. Hence, the graph would show a flat line at this point, indicating no change in distance.
Distance is described as a numerical or occasionally qualitative measurement of how far apart objects or points are.
In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
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Solve for X. Round to the nearest tenth
Answer:
x=7.9*tan(54°)=10.87
BUNGEE JUMPING Trevor is bungee jumping off of a bridge into a canyon that is 400 feet deep. Trevor's bungee cord is 9 feet more than ten times the distance between Trevor and the bottom of the canyon at the end of his jump. If Trevor is 6 feet tall and the bungee cord is attached to his feet, what will be his height above the bottom of the canyon at the end of his jump? Measure the height from Trevor's head to the bottom of the canyon.
The height above the bottom of the canyon at the end of his jump is 385 feet.
we have,
Canyon depth = 400 feet
Trevor's height= 6 feet
cord length = 9 feet
So, Trevor height to end of jump is
= 400 - (9+6)
= 400 - 15
= 385 feet
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23=J+68/5 solve this problem I will give you about 11 points
Answer:
PEMDAS. Division first. 68/5 is 13.6. Subtract 13.6 from 23 and the answer is 9.4. Therefore J = 9.4
Step-by-step explanation: