What is the solution to this system of equations?
4x-3y=26
3x+2y=11
A:(5,-2)
B:(-2,5)
C:(5,2)
D(8,2)
Answer:
Option A: (5,-2)
Step-by-step explanation:
4x - 3y = 26
3x + 2y = 11
from equ 1 make x the subject formular | equ means equation
4x - 3y = 26
4x = 26 + 3y
x = (26 + 3y)/4
Substitute x = (26 + 3y)/4 into equ 2
3((13+3y)/4) + y = 11
(39+17y)/4 + y = 11
39/4 + 17y/4 + y = 11
39/4 + 17y/4 = 11
17y/4 = 11 - 39/4
17y/4 = -17/2
17/4y/17/4 = -17/2/17/4
y = -2
Substitute y = -2 into equ 2
3x + 2y = 11
3x + 2(-2) = 11
3x - 4 = 11
3x = 11 + 4
3x = 15
3x/3 = 15/3
x = 5
(x,y) = (5,-2)
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For each part, compare distributions (1) and (2) based on their means and standard deviations. You do not need to calculate these statistics; simply state how the means and the standard deviations compare. Make sure to explain your reasoning. Hint: It may be useful to sketch dot plots of the distributions.
(a) (1) 3, 5, 5, 5, 8, 11, 11, 11, 13
(2) 3, 5, 5, 5, 8, 11, 11, 11, 20
(b) (1) -20, 0, 0, 0, 15, 25, 30, 30
(2) -40, 0, 0, 0, 15, 25, 30, 30
(c) (1) 0, 2, 4, 6, 8, 10
(2) 20, 22, 24, 26, 28, 30
(d) (1) 100, 200, 300, 400, 500
(2) 0, 50, 300, 550, 600
We have compared the given standard distributions based on their means and standard deviations.
What is the standard deviation?
Standard deviation is a statistical measure of the spread of a dataset, defined as the square root of its variance. It is a way to quantify the amount of variation or dispersion of a set of data values.
(a) The means and the standard deviations of both distributions (1) and (2) are the same. The only difference is that there is an outlier in (2) with the value of 20 that doesn't exist in (1)
(b) The means of both distributions (1) and (2) are the same. However, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)
(c) The means of both distributions (1) and (2) are different, Distribution (2) has larger mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)
(d) The means of both distributions (1) and (2) are different, Distribution (2) has smaller mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)
Hence, we have compared the given standard distributions based on their means and standard deviations.
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given the list of item ids and a maximum number o fitem deletion m return the number of unique items remained in bag
The function uniqueItems takes a list of items and a maximum number of item deletions and returns the number of unique items remained in the bag.
def uniqueItems(items, m):
uniqueItems = set(items)
return len(uniqueItems) - m
items = [1,2,3,4,5,6]
m = 2
print(uniqueItems(items, m)) # 4
# First, we create a set using the items list to get a collection of unique items
uniqueItems = set(items) # {1, 2, 3, 4, 5, 6}
# Then, we subtract the maximum number of items to be deleted from the length of the set to get the number of unique items remained
return len(uniqueItems) - m # 4
The function uniqueItems takes a list of items and a maximum number of item deletions and returns the number of unique items remained in the bag.
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A doctor prescribes an ointment that is 4% hydrocortisone. A pharmacist has 1% and 5% concentrations in stock. How many ounces of each should the pharmacist use to make a 1-ounce tube?
To make a 1-ounce tube of the ointment that is 4% hydrocortisone, the pharmacist needs to use 0.04 ounces of the active ingredient (hydrocortisone).
The pharmacist has 1% and 5% concentrations in stock, therefore he needs to use 0.96 ounce of the 1% concentration and 0.04 ounces of the 5% concentration.
The pharmacist should use 0.96 ounces of the 1% concentration and 0.04 ounces of the 5% concentration to make a 1-ounce tube of the ointment with the correct percentage of hydrocortisone.
It's important to note that it's important that the pharmacist needs to mix the correct amount of hydrocortisone to get the desired percentage, and also that the pharmacist needs to check the final percentage of the ointment before dispensing to ensure the safety and efficacy of the medication.
If G is a group of order pq, where p and q are primes. How could I prove that any nontrivial subgroup of G must be cyclic?
Let H be a nontrivial subgroup of G.
Since p and q are coprime, the only possible divisors of pq are p and q. Thus we must have either |H|=p or |H|=q. Now, by Cauchy's theorem, H must contain an element of order p or q respectively. Then, by Lagrange's theorem, the order of any element in H must divide p or q, i.e. H must be cyclicThen, H has an order of m, where m is a divisor of pq. By Lagrange's Theorem, m divides both p and q. Since p and q are prime, m must be equal to either p or q. This implies that the order of H is either p or q.
Therefore, H must be cyclic, because the order of a cyclic group is always equal to its number of elements. Thus, any nontrivial subgroup of G must be cyclic.
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Complete question:If G is a group of order pq, where p and q are primes, how could I prove that any nontrivial subgroup of G must be cyclic?
In a group of nine people each person shakes hands with exactly two of the other people from the group. Let N be the number of ways this handshaking can occur. Consider two handshaking arrangements different if and only if at least two people who shake hands under one arrangement do not shake hands under the other arrangement. Find the remainder when N is divided by 1000
Answer:
We can solve this problem using the principle of counting, specifically the handshaking lemma.
The handshaking lemma states that in a group of 2n people, where each person shakes hands with exactly one other person, the number of handshaking arrangements is equal to n!.
In this case, we have 9 people, so n = 4.5. Each person shakes hands with exactly two other people, so the number of handshaking arrangements is (4.5!) / (2!)^4 = 945.
Finally, the remainder when N is divided by 1000 is 945 % 1000 = 945.
Step-by-step explanation:
A rectangular paperboard measuring 26 in long and 20 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed?
The perimeter of a two-dimensional shape is the distance around the shape. In this case, the paperboard has a semicircle cut out of it, so the perimeter of the paperboard that remains after the semicircle is removed is the distance around the remaining rectangular shape.
To calculate the perimeter of the remaining rectangular shape, you can use the formula: 2(length + width) = 2(26 in + 20 in) = 2(46 in) = 92 in.
It is important to note that the perimeter is a measure of the distance around a two-dimensional shape and it doesn't take into account the area inside the shape. Also it is measured in units, in this case inches.
I hope this helps :)
Let S be the set of all positive integers having at most 4 digits and such that each of the digits is 0 or 1. What is the greatest prime factor of the sum of all the numbers in S ?
A. 11
B. 19
C. 37
D. 59
E. 101
The greatest prime factor of 2516 is 11, so the answer is A. 11
What is the prime factor?
A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11,
We can use the process of counting to find the sum of all the numbers in S.
For one-digit numbers, there are 2 possibilities (0 or 1).
For two-digit numbers, there are 2 x 2 = 4 possibilities (00, 01, 10, 11).
For three-digit numbers, there are 2 x 2 x 2 = 8 possibilities (000, 001, 010, 011, 100, 101, 110, 111).
For four-digit numbers, there are 2 x 2 x 2 x 2 = 16 possibilities (0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111).
So, the sum of all the numbers in S is
2 + 4(1+2+3+4) + 8(1+2+3+4+5+6+7+8) + 16(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16)
We can simplify this expression as
2 + 4(10) + 8(36) + 16(136)
The sum of all the numbers in S is equal to 2 + 40 + 288 + 2176 = 2516.
Hence, The greatest prime factor of 2516 is 11, so the answer is A. 11
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Recognizing the measurement scale of the data collected on each variable is important because the type of data dictates the appropriate data summary methods and statistical procedures. Which variable(s) in the data set are measured using a nominal scale?
The data set's environment variable(s) are quantified on a nominal scale.
Describe data sets?
A data set is created from collected data. When working with tabular data, a data set is equivalent to one or more database tables, each of whose columns and rows correspond to various variables and each of which corresponds to a particular record of the corresponding data set. A data set is a collection of interconnected, unique pieces of interconnected data that can be accessed separately, together, or under a single control.A particular type of data structure is used to organize a data set. A few examples of the enormous amount include numerous medical data, various measures, financial data, statistical data, demographic data about specific populations, and insurance data.To learn more about data sets refer to:
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solve the equation , 3/4x-5=x
Answer: x= 0.146 or x= -5.15
(refer to the steps I wrote down, check the image)
I collect an SRS of size n from a population and compute a 95% confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data? (a) Use a larger confidence level. (b) Use a smaller confidence level. (c) Increase the sample size. (d) Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger. (e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is 0.05.
Use a larger confidence level would produce a new confidence interval with larger width (larger margin of error) based on these same data.
How do you calculate the population proportion's 95% confidence interval?
We must determine p′ and q′ in order to construct the confidence interval. p′ = 0.842 is the sample percentage; this is the point estimate of the population proportion.
Since CL = 0.95 is the requested confidence level, the calculation is as follows: = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.
What does confidence interval mean?
When you conduct your experiment again or resample the population in the same way, you may anticipate your estimate to fall inside a specific range of values a certain proportion of the time. This is known as the confidence interval.
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^UVW & ^ UXY are shown below.
Which statement is true ?
Answer:
They have to be similar because careful inspection will show all of their angles (the two triangles) are equal.
One can start with the fact that the two triangles have a common angle.
CAll it x.
x * 40 + q = 180
x + 50 + r = 180
q and r must equal 50 and 40 to satisfy the sum of the interior angles must sum to 180.
A triangle has a side lengths of 17 feet, 26 feet, and 16 feet. Is it a right triangle
Answer: No, it is not a right triangle
Step-by-step explanation:
a=17
b=16
c=26
a^2 + b^2 = c^2 (C will always be the longest side)
17^2 + 16^2 = 26^2
49 + 256 = 676
305 is not equal to 676
Answer:
to test if this is a right triangle, test the side lengths with the Pythagorean theorem
a^2 + b^2 = c^2
Step-by-step explanation:
c is the hypothenuse, the longest side of a right triangle
a and b are the legs of the right triangle.
a = 16
b = 17
c = 26
16^2 + 17^2 = 26^2 ?
256 + 289 = 676?
545 ≠ 676
NO, this triangle is NOT a right triangle
Can someone help me solve this and explain it?
Answer:
a. -0.004
b. -sqrt(20)/70
Step-by-step explanation:
a.
We are given that y = a(x - 70)^2 + 20
And we know that x=0 and y=0
We can substitute these values into the equation:
0 = a(-70)^2 + 20
Simplifying we get:
0 = a(4900) + 20
Subtracting 20 from both sides we get:
-20 = a(4900)
Dividing both sides by 4900 we get:
a = -20/4900
a = -20/4900 = -0.004
So the value of a is -0.004
b.
We are given that y = a(x - 70)^2 + 20
And we know that x=140 and y=0
We can substitute these values into the equation:
0 = a(140-70)^2 + 20
Simplifying we get:
0 = a(70)^2 + 20
Subtracting 20 from both sides we get:
-20 = a(70)^2
Taking the square root of both sides:
sqrt(-20) = a(70)
Dividing both sides by 70:
-sqrt(20)/70 = a
a = -sqrt(20)/70
So the value of a is -sqrt(20)/70
PLEES HELP ME WITH MY HOMEWORK
Answer:
Step-by-step explanation:
2. 63
3. 0
4. 6
5. 9
6. 10
7. 4
8. 8
9. 0
10. 5
11. 10
12. 7
13. 9
14. 5
15. 5
16. 3
17. 8
18. 0
The sum of 11 and three-fourths of a number is less than 112. What are the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter, "x" as a variable and write the inequality so that the term, "x" term comes first. Where necessary, write numbers as fractions (rather than decimals)
The inequality that can be used to solve the possible values of the number is 11 + 3/4x < 112 where the number x is x < 134 2/3
How to write inequality?sum of 11 and three-fourths of a number is less than 112.
Let
The unknown number = x
11 + 3/4x < 112
Subtract 11 from both sides
3/4x < 112 - 11
3/4x < 101
divide both sides by 3/4
x < 101 ÷ 3/4
multiply by the reciprocal of 3/4
x < 101 × 4/3
x < 404/3
x < 134 2/3
Therefore, the inequality which represents the situation is 11 + 3/4x < 112.
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Please hurry!
A box of apples sells for $17. At this rate, which expression represents the cost, in dollars, of 100 apples?
A) 5/17•20
B)5/20•17
C)100/17•20
D)100/20•17
E)17•5•20
Answer: D
Step-by-step explanation: A box of apples consists of 20 apples. Since there are a total of 100 apples, you want to find how many boxes makeup 100 apples. 100/20. Then, you would want to multiply that by the cost of each box (i.e. 5 boxes times 17). This is what is done in D when the order of operations is followed.
methods for solving systems of linear equations
( graphing )
how to graph
Y= 2x+6
Y=2x+2
locate the point of the intersection of the two lines
( , ) ?
Answer: imma be honnest im just trying to get points rn.
Step-by-step explanation: i have no idea but thank you for your time reading my nonescence.
use what you know about inverse functions to determine the derivative of the inverse function beginning with f ( f -1(x)).
The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.
To find the inverse of the given function as it is not a one to one function (has the same value f(x) for more that one value of x) you restrict the domain to get a function one to one.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
f (x) = 1/3x - 2
Find its inverse as shown below,
Add 2 to x and then divide by 1/3 as shown below,
f⁻¹(x) = (x + 2) / 1/3
f⁻¹(x) = 3(x + 2)
compare with f⁻¹(x) = a (x + 2)
a = 3
Calculate the x-intercept by putting f(x) = 0
0 = x + 2
x = -2
In a quadratic function as given use the vertex to restrict the domain; restrict the domain using coordinate x of the vertex.
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determin the median for each of the following sit of data 11, 12, 14, 16, 20, 13, 18, 15, 11, 16
I am pretty sure the answer is 14.5
Answer:
14.5
Step-by-step explanation:
Arrange the numbers from small to big
11, 11, 12, 13, 14, 15, 16, 16, 18, 20
If the set of data is an even number, like in this case,
Take 2 of the middle numbers:
14 and 15
Add them and divide by 2:
14+15= 29
29 ÷ 2= 14.5
The sports program has a balance of $500 Kenny needs to buy basketballs that cost $25 per practice Kenny hopes to have at least $200 after purchasing the necessary basketballs which inequality represents Kenny’s situation.
The inequality that represents Kenny's situation is 25x ≤ 500 − 200
What is inequality ?In mathematics, inequality is describe about the relative size or order of two values.
It states that one value is either greater than, less than, or not equal to the other value.
It is usually represented by symbols such as > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), and ≠ (not equal to).
In this question ,
Let x be the number of basketballs Kenny needs to buy.
The inequality that represents Kenny's situation is:
25x ≤ 500 − 200
This inequality states that the total cost of purchasing the basketballs (25x) must be less than or equal to the available balance minus the desired amount after purchase (500 − 200 = 300).
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In each of the following cases, would the mean or the median probably be higher, or would they be about equal? a. Prices of all new cars sold in 1 month in a large city. b. Heights of all 7-year-old children in a large city. c. Shoe sizes of adult women.
In the case of prices of all new cars sold in a month in a large city, the mean is likely to be higher than the median.
The reason is, new car prices range from economy to luxury, and there are high-end cars that are more expensive than the average/median cars, which will pull the mean value to a higher level.
In the case of the heights of all 7-year-old children in a large city, the mean and median are likely to be about equal. The reason is, children's heights are likely to be distributed relatively evenly, and the mean and median are typically close together for a normal distribution.
In the case of shoe sizes of adult women, the median is likely to be higher than the mean. The reason is, the distribution of shoe sizes among adult women is likely to be skewed, with more women having shoe sizes near the middle of the distribution, and fewer women having sizes that are either very small or very large. This will pull the median to a higher level than the mean.
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Timmykat wants to start losing some weight. He goes to the doctor and the doctor tells him that he needs to burn off 600 calories a day or more. TK loves riding his bike but he only burns 10 calories a minute that way. When TK runs he loses 15 calories a minute.
a) Make an inequality where x represents the number of minutes biking and y represents the number of minutes running. b) If Timmykat bikes for 30 minutes and doesn’t run at all will he burn enough calories?
c) If Timmykat runs for 30 minutes and doesn’t bike at all will he burn enough calories?
d) Graph the inequality.
e) What are three different scenarios where Timmykat will burn at least 600 calories a day?
The total number of calories burned can be represented by the inequality 10x + 15y ≥ 600
Timmykat will not burn enough calories in the two scenariosThe graph is attachedThe three different scenarios are explained belowThe inequality of the scenarioUsing the following parameters:
x represents the number of minutes biking y represents the number of minutes runningThe inequality is
10x + 15y ≥ 600
Will he burn enough calories?In this case, x = 30 and y = 0.
Plugging in these values into the inequality:
10(30) + 15(0) = 300
Since 300 is less than 600, Timmykat will not burn enough calories if he only bikes for 30 minutes and doesn't run at all.
Will he burn enough calories?In this case, x = 0 and y = 30.
Plugging in these values into the inequality:
10(0) + 15(30) = 450
Since 450 is less than 600, Timmykat will not burn enough calories if he only runs for 30 minutes and doesn't bike at all.
The graph of the inequalitySee attachment
Three different scenariosThree different scenarios where Timmykat will burn at least 600 calories a day are:
Biking for 40 minutes and running for 20 minutes: 10(40) + 15(20) = 400 + 300 = 700, which is greater than 600.Biking for 45 minutes and running for 15 minutes: 10(45) + 15(15) = 450 + 225 = 675, which is greater than 600.Biking for 50 minutes and running for 10 minutes: 10(50) + 15(10) = 500 + 150 = 650, which is greater than 600.Read more about inequality at
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which of the following actions would cause alex's set of ordered pairs to no longer define a function?
Alex's set of ordered pairs would no longer define a function if any of the following actions were taken:
Adding a second ordered pair with the same first coordinate but a different second coordinateRemoving an ordered pair from the setModifying an ordered pair so that the first coordinate is different from its original valueReordering the ordered pairs in the setChanging the domain or range of the function
A set of ordered pairs defines a function if, for every element in the domain (the set of first coordinates), there is exactly one element in the range (the set of second coordinates).
For example, if Alex's set of ordered pairs is {(1,2), (2,3), (3,4)}, it would no longer define a function if a new ordered pair of (2,5) is added to it, as it would mean that there are now two different second coordinates (3,5) for the first coordinate 2. This would violate the rule that every element in the domain must have exactly one corresponding element in the range. Similarly, removing one of the ordered pairs, changing the order of the ordered pair, or changing the domain or range would cause the set to no longer to define a function.
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Provide the equation of all vertical line that violate the vertical line test. Please help
The vertical line that violates the vertical line test is given as follows:
x = -3.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
For the relation graphed, we have that at x = -3, there are two closed bounds of the function, meaning that the input x = -3 is mapped to multiple outputs and thus the relation is not a function.
This also means that a vertical line traced at x = -3 would cross the graph of the function at two points, thus violating the vertical line test.
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A teacher’s cabinet has 56 black dry erase markers and 14 red dry erase markers. Which proportion can be used to determine p, the percent of dry erase markers that are red?
The percent of dry erase markers that are red is 25
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
Number of black dry erase markers= 56
Number of red dry erase markers= 14
Now,
14/56=x/100
56x=1400
x=25
Therefore, the value of red marker in percent will be 25%
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write the equation of the trigonometric graph. use a positive coefficient on sine for this activity.
The different values of x in the equation y = 3 sin (x + π/2) to determine the values of y for different values of x.
The equation of the trigonometric graph is given by y = A sin (Bx + C).
Here, A is the amplitude, B is the angular frequency, and C is the phase shift.
Let's assume that A = 3, B = 1, and C = π/2.
Therefore, the equation of the trigonometric graph is given by y = 3 sin (x + π/2).
To calculate the value of y, we can substitute values of x in the equation.
Let's consider x = 0.
Therefore, the value of y is given by y = 3 sin (0 + π/2).
Using the trigonometric identity sin (π/2 + x) = cos x, we get y = 3 cos 0.
Since cos 0 = 1, y = 3.
Hence, the value of y for x = 0 is 3.
Similarly, we can substitute different values of x in the equation y = 3 sin (x + π/2) to determine the values of y for different values of x.
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A submarine is 575 feet below sea level. It is ascending at a rate of 325 feet per minute
If a submarine is 575 feet below sea level and is ascending at a rate of 325 feet per minute, we can use that information to determine how long it will take for the submarine to reach the surface.
The distance the submarine needs to travel to reach the surface is:
Distance = Sea level - Current depth
Distance = 0 feet - (-575 feet) = 575 feet
We can use the rate of ascent and distance to find the time it will take for the submarine to reach the surface.
Time = Distance / Rate
Time = 575 feet / 325 feet per minute
Time = 1.77 minutes
So it will take the submarine 1.77 minutes to reach the surface, assuming it continues to ascend at a rate of 325 feet per minute.
What is the answer for this equation 4x+5x+7+x+2
it depends on what x is but simplified that equation is 9x+9+x
IMC 2018 5th grade question 14
Answer: 69
Step-by-step explanation:
