The following is a code in python.
What is Python and why it is used?Python is a popular computer programming language used to create software and websites, automate processes, and analyze data. Python is a general-purpose language, which means it can be used to make many different types of programs and isn't tailored for any particular issues.
What are the advantages of Python?One of Python's biggest benefits is the variety of libraries and frameworks it offers. Everything from data visualization, machine learning, data science, natural language processing, and complex data analysis uses the Python Library, from NumPy to TensorFlow.
#Specify the function in
DefinedSum(tu)
# Verify whether the tuple contains 0
if len(tu) == 0
#Then, give back 0
return 0
#Otherwise
else:
#invoke the recursive function.
return tu[0]+Sum (tu[1:])
Set a variable of the tuple type
tu=(2,5,1,8,10)
#print, then invoke the function.
print("The total of tuple is:"), sum(tu),
Output:
The sum of tuple is: 26
Here, we define the method "sum()" and send the parameter "tu" to the function, which saves the value of the tuple type.
If the length of the tuple is 0, then the if conditional expression should verify the condition and return 0.
If not, invoke the function, return the tuple's total (which is determined recursively), and exit.
Last but not least, initialize the "tu" variable of the tuple type, print, then run the sum function.
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ghghghghghghghghghghghghghghghgh circle.
Answer:
yass
queen
Step-by-step explanation:
If each quadrilateral below is a rectangle find the missing measure in #4
The missing measures of the angles are as follows:
m∠BCD = 90°m∠ABD = 16°m∠CBE = 74°m∠ADE = 74°m∠AEB = 148°m∠DEA = 32°How to determine the measures of the angles?The figure that completes the question is added as an attachment
From the figure of the rectangle, we have:
m∠BDC = 16°
A rectangle has four (4) interior angles that are 90 degrees each.
This means that
m∠ADE = 90 - 16
m∠ADE = 74°
Also, we have:
m∠ABD = m∠BDC = 16° by the alternate interior angles
By the complementary angle, we have:
m∠CBE = 90 - 16 = 74°
By the alternate interior angles, we have
m∠ADE = m∠CBE = 74°
Solving further, we have the following equations:
m∠AEB = 180 - 2(16)
m∠AEB = 148°
m∠DEA = 180 - m∠AEB
m∠DEA = 180 - 148
m∠DEA = 32°
Hence, the measure of the angle DEA is 32 degrees
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find the area (in cm2) of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 8 cm if two sides of the rectangle lie along the legs.
The area of the largest rectangle that can be inscribed in the right triangle is calculated to be 6 cm^2
As we know that for a rectangle of width W and length L the area is given as;
A = L × W
Now let's say that L is along the 8 cm side and W is along the 3 cm side, let's find a relation between these two.
When we inscribe the rectangle in the larger triangle the quotient between the catheti of the right triangle must be equal to the quotient of the catheti of the right triangle that is generated.
Therefore that new triangle will have legs equal to the;
8cm - L and W.
Then we have that:
8cm - L / W = 8 cm / 3 cm
L = 8 cm - 8/3 × W
Now we can write L in terms of W so that we can replace that in the area equation to get
A = (8cm - (8/3)×W)×W = 8cm×W - (8/3)×W^2
This is the equation we have to maximize, also this is a quadratic polynomial of negative leading coefficient, which means that the maximum is at the vertex.
As we know the vertex of the general quadratic polynomial;
a × x^2 + b × x + c
is at:
x = -b / 2a
Then, in this scenario, the vertex is at;
W = (-8 cm) / (2 × 8/3) = 1.5 cm
Then the length is given by:
L = 8cm - (8/3) × 1.5cm = 4 cm
Therefore the area of the largest rectangle that can be inscribed in the given right triangle is;
A = 1.5 cm × 4 cm = 6 cm^2
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beth wants to determine a 90 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. how large of a sample must she have to get a margin of error less than 0.03?
The size of the sample that she would have to get a margin of error less than 0.03 is 752
How to solve for the sample sizeWe have the margin of error E = 0.03
The confidence interval C I = 90 percent
p = 1 - p = 0.5
z α / 2 = 1.645
The formula for the sample size is given as
(z α / 2 / E)² * p * (1 - p)
(1.645 / 0.03)² * 0.5 * 0.5
= 54.833² * 0.5 *0.5
= 752
Hence n is given as 752. The size of the sample would have to be 752.
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Hellloooo helpppp meeee
70 + 60 + 8x + 2 = 180
132+8x= 180
8x= 180-132
8x=48
x= 6
plug in x
8(6)+2 = 50
Answer:
x = 6
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180°.
To find the value of x, we can use the following equation:
70 + 60 + 8x + 2 = 180
Add like terms132 + 8x = 180
Subtract 132 from both sides8x = 48
divide both side by 8x = 6
Add 0.75 and 0.18. How many tenths are in the sum?
Answer:
Step-by-step explanation:
EXPLANATIONDETAIL STEPSforward
Based on the given conditions, formulate::
Calculate : :
Thanks (77)
Answer: 2 or 100 tenths
Step-by-step explanation:
0.75 + 0.18
You need to do it in the vertical way yo make it easier here i will show you.
0.75
+ 0.18
______
0.93
YOU MUST ALIGN THE DECIMALS TO GET IT RIGHT
At top speed, cheetahs can run 80 miles per hour. How fast would that be in meters/second?
Answer:
The top speed of a cheetah is around 69 to 75 mph. However, the cat can only sprint a short distance of around 0.28 miles. A cheetah is about 2.7 times faster than the fastest human runner. A cheetah accelerates very quickly, allowing it to overtake prey at close range. The fastest cheetah on record is Sarah. Sarah lives at the Cinncinati Zoo in Ohio.
Step-by-step explanation:
Answer:
35.7632
Step-by-step explanation:
multiply the value in miles per hour by the conversion factor '0.44704'.=35.7632 meters per second
One year, the population of a city was 312,000. Several years later it was 274,560. Find the percent decrease.
The percent decrease will be;
⇒ 12%
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
One year, the population of a city was 312,000.
Several years later it was 274,560.
Now,
Since, One year, the population of a city was 312,000.
Several years later it was 274,560.
Hence, The percent decrease is find as;
⇒ Percent = (312,000 - 274,560) x 100 / 312,000
= 12 %
Thus, The percent decrease will be;
⇒ 12%
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11.30 fcat scores and poverty. in the state of florida, elemen- tary school performance is based on the average score obtained by students on a standardized exam called the florida comprehensive assessment test (fcat). an analysis of the link between fcat scores and sociodemo- graphic factors was published in the journal of educational and behavioral statistics (spring 2004). data on average math and reading fcat scores of third graders, as well as the percentage of students below the poverty level, for a sample of 22 florida elementary schools are listed in the table on p. 629.
Math: s=11.2996s=11.2996, Reading: s=14.4128s=14.4128 for the performance in the elementary school of Florida.
What is meant by statistics?The study of data collection, analysis, presentation, and interpretation is known as statistics. Much of the early push for the subject of statistics came from government needs on census in addition to data on a range of economic operations. The current requirement to convert vast volumes of data accessible in many applied disciplines into valuable information has driven both theoretical and practical breakthroughs in statistics.
The facts and statistics that are gathered, standardized, and condensed for presentation and interpretation are known as data. The two types of data are quantitative and qualitative, respectively. Quantitative data quantify how much or how many of something exists, whereas qualitative data offer labels or names for groups of similar objects.
How to solve?
We need to determine whether the math core or the reading score better predicts the percentage of students below the poverty level.
The standard error s=11.2996s=11.2996 for the math scores is less than the standard error s=14.4128s=14.4128 for the reading scores, thus the math scores will result in better prediction.
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What is the solution to the inequality below? 5−10≥−3+14
Answer:
5≥17
Step-by-step explanation:
in a survey about a new cleaning product, 75% of respondents report they would buy the product again. the margin of error for the survey is 5%. based on the margin of error, what percentage range reflects the population's true response?
Answer:80% - 70%
Step-by-step explanation:
If the margin for the error is 5% im guessing that means 5% backwards or forwards so i believe that my answer is correct
ps if im right brainliest please
The percentage range that reflects the population's true response, considering the margin of error, is from 70% to 80%.
Given, a margin of error of 5%, we can determine the range that reflects the population's true response.
To find the range, we consider the maximum and minimum values within the margin of error.
Maximum Value: 75% + 5% = 80%
Minimum Value: 75% - 5% = 70%
Therefore, the percentage range that reflects the population's true response, considering the margin of error, is from 70% to 80%.
This means that we can be 95% confident that the actual percentage of people who would buy the product again lies within this range.
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a research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. the sample mean and standard deviation are 60,139.7 and 3505.42 kilometers. can you conclude, using ????
There is no sufficient evidence to indicate the true standard deviation is less than 4000.
What is the standard deviation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
given that n = 16
x = 60139.7
s = 3718.06
∝ = 0.05
To test the hypothesis
H0 : = 4000
H1 : < 4000 (claim)
test statistics
x² = ((n-1)s²) / H0²
= (15 * 13823970.16) / (16000000)
= 12.96
P- value = P [x² < 12.96] DF = n-1 = 15
= 0.3946
0.1 < P-value <0.5
Hence, there is no sufficient evidence to indicate the true standard deviation is less than 4000.
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g how many ways are there to choose the exec board so that there is at least one masters student and one phd student? (for any of the 4 positions)
The board has a total of 78960006 options from which to select at least one master's and one PhD candidate.
Given,
Total number of students = 8000
Number of Phd students = 5000
Number of masters students = 3000
Number of members in Student Government Executive Board = 4
We have to find the number of ways to choose the exec board so that there is at least one masters student and one Phd student;
Here,
There are 3,000 different ways to have one Master student on the board.
After choosing a masters student, there are 5,000 different methods to have a PhD student on the board.
The number of possible ways to choose the final two members = 7998!/(7998 - 2)!
That is,
5,000 3,000 + 7998!/(7998 - 2) = 78960006
Therefore,
78960006 is the total number of ways the board can choose at least one masters and one PhD.
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Classify each number according to its value. 2.1 × 10-4 9.2 × 10-4 3.4 × 10-5 2.1 × 10-3 2.8 × 10-7 8.3 × 10-5 7.2 × 10-5
According to the information, the numbers are classified as follows: Greater than 8.2 x 104 = None; between 8.2 x 10⁴ and 8.2 x 10⁻⁶ : 2.1 x 10⁻⁴, 9.2 x 10⁻⁴, 3.4 x 10⁻⁵, 2.1 x 10⁻³, 8.3 x 10⁻⁵, 7.2 x 10⁻⁵; and less than 8.2 x 10⁻⁵: 2.8 x 10⁻⁷.
How to find the classification of numbers?To find the classification of numbers we must know how scientific notation works and know how to classify these numbers. According to its scientific notation, if we want to classify numbers greater than 8.2 x 10⁴ we must take the following into account:
All numbers with a power greater than 10⁴ would be greater than 8.2. Therefore, none of the options would be greater than this number.
In the second case, to find the numbers that are between 8.2 x 10⁴ and 8.2 x 10⁻⁶ we must look at the same element, that is, the numbers that have a power less than 10⁴ and greater than 10⁶ would be in the range of this exercise. So the numbers in this range would be:
2.1 x 10⁻⁴9.2 x 10⁻⁴3.4 x 10⁻⁵2.1 x 10⁻³8.3 x 10⁻⁵7.2 x 10⁻⁵In the third case, to identify the numbers that are less than 8.2 x 10⁻⁵ we must take into account the same element. If power is less than 10⁻⁵, they would classify in this interval. So the values that classify are:
8.2 x 10⁻⁷Note: This question is incomplete because there is some information missing. Here is the complete information:
Greater than 8.2 x 104
Between 8.2 x 104
and 8.2 x 10-6
Less than 8.2 x 10-5
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a particular football team is known to run 30% of its plays to the left and 70% to the right. a line backer on an opposing team note that the right guard shifts his stance most of the time (80%) when plays go to the right and he uses a balanced stance the remainder of the time. when plays go to the left, the guard takes a balanced stance 90% of the time and the shift stance the remaining 10%. on a particular play, the line backer notes that the guard takes a balanced stance. i) find the probability that the play will go the left ii) find the probability that the play will go the right iii) if you were the line backer, which direction would you prepare to defend if you saw the balanced stance.
i)The probability that the play will go to the left is 0.659
ii)the probability that the play will go the right is 0.341
iii) The direction I would prepare to defend if I saw the balanced stance if I were the line breaker is It's better to be ready to protect the left side since the likelihood of a play coming via that side so when the right tackle has a balancing stance is nearly double that of a play going it through right because when right guard maintains a neutral position.
Taking the left first
When play travels via the left 30% of the time, the right guard assumes a balanced stance 90% of the time, for a total of 0.9 0.3 = 27%.
- He adopts a new posture. 10% of the time, play goes through the left = 0.1 0.3 = 3% of the time.
70% of the time, play goes through the right.
- He takes a balanced posture 20% of the time that play travels through the right, for a total of 0.7 0.2 = 14%.
- He assumes a shift stance 80% of the time that play travels via the right, for a total of 0.7 0.8 = 56%.
The right guard then assumes a balanced posture 27% of the time + 14% of the time = 41% of the time.
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A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?.
6000FT, is the shortest length of fence that the rancher can use.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
Let the rectangular field's length be x.
rectangle field width = y
square feet of a rectangular field's area
Because length is always positive, it is always positive.
Once more, discriminate with respect to x
replace x=1500
Therefore, at x=1 500, fencing is minimal.
Change x to 1 500.
the rectangular field is 1500 feet long.
rectangle field's width is 1000 feet.
Replace the values
shortest used fence length =6000ft
Hence, 6000FT, is the shortest length of fence that the rancher can use.
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Plot the points (2, -1) and (7,-1) and find the slope.
Answer:
slope = 0Step-by-step explanation:
Slope =
[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]
X1=2 X2=7
Y1=-1 Y2=-1
hence
[tex] \frac{ - 1 - ( - 1)}{7 - 2} [/tex]
[tex] \frac{ - 1 + 1}{7 - 2} [/tex]
[tex] \frac{0}{5} [/tex]
[tex]slope = 0[/tex]
a student at another business school surveys 100 of 1000 graduates from last year and asks about their salaries. the researcher finds that the average income is $65, 000, with a standard deviation of $8000. if you wanted to be 95% sure that the real mean of all 1000 students is within a range of the sample mean, what would you set your confidence interval lower and upper bounds to be?
As per the given standard deviation, the confidence interval is 495.84, upper bound is $65,495.8 and the lower bound is $64,504.2
Confidence interval
Confidence interval means a range of values, bounded above and below the statistic's mean, that likely would contain an unknown population parameter.
Given,
A student at another business school surveys 100 of 1000 graduates from last year and asks about their salaries. the researcher finds that the average income is $65, 000, with a standard deviation of $8000.
Here we need to find the confidence interval lower and upper bounds if you wanted to be 95% sure that the real mean of all 1000 students is within a range of the sample mean.
While we looking into the given question, we have identified the following values,
standard deviation = $8,000
Average income = $65,000
Sample size = 1000
Confidence level = 95%
Then the value of confidence interval is calculated by the formula,
Then we get the value of
Lower bound = 64504.2
Upper bound = 65495.8
Confidence interval (±) = 495.84
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Using Pythagoras' theorem, calculate the length of YZ.
Give your answer in centimetres (cm) to 1 d.p.
17 cm
5 cm
The length of two sides is given as 17 cm and 5 cm, then the length of side YZ by Pythagoras' theorem will be equal to 16.25 cm.
What is a Pythagoras' Theorem?According to the Pythagoras theorem, the square on the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of squares of the remaining two sides.
As per the given values in the question,
The length of two sides is given as 17 cm and 5 cm.
As per Pythagoras' theorem,
h² = p² + b²
17² = 5² + b²
b² = 289 - 25
b = √264
b = 16.25 cm.
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the manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the capital district. in order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2. the hypotheses to be tested are: h subscript 0 : mu equals 9 h subscript 1 : mu not equal to 9 assume that the actual average is $8.8. what is the probability of type ii error at the 5% significance level?
The probability of type ii error at the 5% significance level is 49.5%
Probability:
In statistics, the number of possible way of occurring an particular event is referred as probability.
Given,
The manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the capital district. in order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2. the hypotheses to be tested are: h subscript 0 : mu equals 9 h subscript 1 : mu not equal to 9 assume that the actual average is $8.8.
Here we need to find the probability of type ii error at the 5% significance level.
While we looking into the give question, we have identified the following,
Semi skilled worker hourly wages = $9
Number of samples = 100
sample mean = $8
Standard deviation = $2
Hypotheses
H₀ : μ = 9
H₁ : μ ≠ 9
Significance level = 5%
Therefore, the type II error is calculated as,
=> P [(100 - 9/(2/√100)) ≥ (9 - 8)/(2/√100))] = 1 - 5
When we simplify this one then we get, the probability as 49.5%.
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The bottom of a swimming pool is 12 feet below the surface of the water.
What is the pool's depth in feet?
Enter your answer as an integer.
If it is negative, enter it like this: -42
Answer:12 feet
Step-by-step explanation:
Solve this equation by undoing
AKA solve for x
2x + 8 = 26
Step-by-step explanation:
[tex]2x + 8 = 26 \\ [/tex]
[tex]2x + 8 - 8 = 26 - 8[/tex]
[tex]2x = 18[/tex]
[tex]x = \frac{18}{2} \\ [/tex]
[tex]x = 9[/tex]
Answer:
[tex]\boxed{\tt x=9}[/tex]Step-by-step explanation:
[tex]\tt 2x + 8 = 26[/tex]
Subtract 8 from both sides:-
[tex]\tt 2x+8 \bf{-8}= \tt 26 \bf{-8}[/tex]
[tex]\tt 2x=18[/tex]
Divide both sides by 2:-
[tex]\tt \cfrac{2x}{\bf2}=\cfrac{18}{\bf2}[/tex]
[tex]\tt x=9[/tex]
___________________
Hope this helps!
Have a great day!
Help me out please thank you
answers:
-3/4
-4/3
4\3
3/4
Answer:
Slope: -4/3
y-intercept: -9
Step-by-step explanation:
hope it helps!
Do you prefer taking tests on paper or online? a college instructor gave identical tests to two randomly sampled groups of 45 students. One group took the test on paper and the other took it online. Those who took the test on paper had an average score of 68. 4 with a standard deviation of 12. 1. Those who took the test online had an average score of 71. 3 with a standard deviation of 14. 2. Can you conclude that the mean scores differ between online and paper tests? find the p-value and state a conclusion
As per the given standard deviation, the mean scores difference between online and paper tests is 2.9 and the p value of the test is 0.2999
Standard deviation:
In statistics, standard deviation is a quantity expressing by how much the members of a group differ from the mean value for the group.
Given,
A college instructor gave identical tests to two randomly sampled groups of 45 students. One group took the test on paper and the other took it online. Those who took the test on paper had an average score of 68.4 with a standard deviation of 12.1. Those who took the test online had an average score of 71.3 with a standard deviation of 14.2.
Here we need to find the mean scores difference between online and paper tests and the p value of the test.
While we looking into the given question we have identified the following values,
Test on paper:
Average score = 68.4
Standard deviation = 12.1
Online test
Average score = 71.3
Standard deviation = 14.2
Total number of students = 45
So, the difference between the mean scores differ between online and paper tests is calculated as,
=> 71.3 - 68.4 = 2.9
And the p - value is 0.2999.
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a spinner has six equal parts labeled from 1 to 6. the spinner is spun twice. what is the probability of getting a 3 twice in a row?
The probability of getting 3 twice in a row is 1/36
A spinner has 6 equal parts labeled from 1 to 6.
The spinner is spun twice.
First time what is the conditions {1,2,3,4,5,6}
Second time choices are
{1,1} {1,2} {1,3} {1,4} {1,5} {1,6}
{2,1} {2,2} {2,3} {2,4} {2,5} {2,6}
{3,1} {3,2} {3,3} {3,4} {3,5} {3,6}
{4,1} {4,2} {4,3} {4,4} {4,5} {4,6}
{5,1} {5,2} {5,3} {5,4} {5,5} {5,6}
{6,1} {6,2} {6,3} {6,4} {6,5} {6,6}
So we have total 6*6 = 36 choices
{3,3} comes only 1 times.
We know the formula for probability:
Probability(Event) = Favorable Outcomes/Total Outcomes.
Favorable Outcomes = 1.
Total Outcomes=36.
So the probability of getting a 3 twice in a row is 1/36.
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what is the probability of getting either a spade or an ace when drawing a single card from a deck of 52 cards?
When drawing one card from a deck of 52 cards, the probability of obtaining either a spade or an ace are 4/13.
Given,
Number of cards in a deck = 52
Number of spades = 13
Number of aces = 4
Number of ace of spade = 1
We have to find the probability of getting either a spade or an ace when drawing a single card from the deck;
Here,
Probability of either a spade or an ace :
P(spade or ace) = P(spade U ace)
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
Now,
Probability = required outcome / Total possible outcomes
P(spade) = 13 / 52
P(ace) = 4 / 52
P(spade n ace) = 1 / 52
Then,
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
= 13/52 + 4/52 - 1/52
= 16 / 52 = 4 /13
That is,
The probability of getting either a spade or an ace when drawing a single card from a deck of 52 cards is 4/13
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Nth for the leaner sequence 22,18,14,10,6
The nth term of the sequence is aₙ = 26 - 4n.
How to find the nth term of a sequence?A sequence is defined as an arrangement of numbers in a particular order.
The sequence is an arithmetic sequence. Therefore, the nth term of the sequence can be found as follows:
aₙ = a + (n - 1)d
where
a = firs termd = common differencen = number of termTherefore,
a = 22
d = 18 - 22 = -4
n = number of terms
Hence,
aₙ = 22 + (n - 1)-4
aₙ = 22 - 4n + 4
aₙ = 22 + 4 - 4n
aₙ = 26 - 4n
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Mrs. Smith had 5/6 of a sack of garden soil for
plants. She used 2/3 of it for planting 6 pots
How much garden soil did she use?
Answer:
1/6
Step-by-step explanation:
convert them both to the same denominator (bottom number)
2/3 is 4/6
5/6-4/6 is 1/6
Dear Math Students, I have to divide 5 cups in half for a recipe. Here's what I did: 5÷1/2= 5 x 2/1 =10 I know I did the division correctly, but my answer should be less than 5, not more. Can you explain my mistake and help me fix it? Your friend, Puzzled Penguin
Answer: your first step was right5
Step-by-step explanation:
5/2 =2.5
the sum of ellies's age and genya's age is 60. in six years, genya will be eigth times as old as ellie will be. how old is ellie now
The sum of ellies's age and genya's age is 60. in six years, genya will be eigth times as old as ellie now ellie old is 2 years.
Given:
the sum of ellies's age and genya's age is 60. in six years, genya will be eigth times as old as ellie will be.
Let x and y be the ellie's and genya's ages.
x + y = 60
After 6 years x+6 and y +6.
8(x + 6) = y + 6
8x + 48 = y + 6
8x + 42 = y
8x - y = -42
sum of two equations
x + y + 8x - y = 60 + (-42)
x + 8x = 60 - 42
9x = 18
divide by 9 on both sides
9x/9 = 18 / 9
x = 2
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