After two numbers are removed from the list $$9,~13,~15,~17,~19,~23,~31,~49,$$ the average and the median each increase by $2$. What is the product of the two numbers that were removed?
Answer:
The removed numbers are 13 and 19, and the product is:
13*19 = 247
Step-by-step explanation:
We have the set:
{9, 13, 15, 17, 19, 23, 31, 49}
The original median is the number that is just in the middle of the set (in a set of 8 numbers, we take the average between the fourth and fifth numbers)
then the median is:
(17 + 19)/2 = 18
and the mean is:
(9 + 13 + 15 + 17 + 19 + 23 + 31 + 49)/8 = 22
We want to remove two numbers such that the mean and the median increase by two.
Is immediate to notice that if we want the median to increase by two, we need to remove the number 19 and one number smaller than 17.
Then the median will be equal to:
(17 + 23)/2 = 20
which is 2 more than the previous median.
because 19 assume that we remove the 19 and number N.
To find the value of N, we can solve for the new mean:
((9 + 13 + 15 + 17 + 23 + 31 + 49 - N)/6 = 22 + 2
(this means that if we remove the number 19 and the number N, the mean increases by 2.
(9 + 13 + 15 + 17 + 23 + 31 + 49 - N)/6 = 22 + 2
(9 + 13 + 15 + 17 + 23 + 31 + 49 - N) = 24*6 = 144
157 - N = 144
157 - 144 = N = 13
This means that the other number we need to remove is 13
Then we remove the numbers 13 and 19
The product of the two removed numbers is:
13*19 =247
Answer:
247
Step-by-step explanation:
The average of the original numbers is 176/8 = 22. The median of the original numbers is the average of the middle two numbers: 17 + 19/2 = 18.
Thus, after removing two numbers, we should obtain a list of six numbers whose average is 24 and whose median is 20.
For the median of six numbers to be 20, the middle two numbers in that list must add up to 40. Searching our original list for pairs of numbers that add up to 40, we find two such pairs: 9, 31 and 17, 23. But 9 and 32 can't be the middle numbers after we remove two numbers, so 17 and 23 must be the middle numbers. This tells us that one of the removed numbers must be 19.
For the average of six numbers to be 24, the sum of the six numbers must be 6 ∙ 24 = 144. This is 32 less than the original sum of 176, so if one of the removed numbers is 19, the other must be 32 - 19 = 13.
Therefore, the product of the two removed numbers is 13 ∙ 19 = 247.
Show f(x)=e" and g(x) : = ze linearly independent by finding its Wronskian.
The f(x) = [tex]e^x[/tex] and g(x) = x form a linearly independent set of functions.
To show that the functions f(x) = [tex]e^x[/tex] and g(x) = x are linearly independent, we can calculate their Wronskian and verify that it is nonzero for all values of x.
The Wronskian of two functions f(x) and g(x) is defined as the determinant of the matrix:
| f(x) g(x) |
| f'(x) g'(x) |
Let's calculate the Wronskian of f(x) = [tex]e^x[/tex] and g(x) = x:
f(x) = [tex]e^x[/tex]
f'(x) = [tex]e^x[/tex]
g(x) = x
g'(x) = 1
Now we can form the Wronskian matrix:
| [tex]e^x[/tex] x |
| [tex]e^x[/tex] 1 |
The determinant of this matrix is:
Det = ([tex]e^x[/tex] * 1) - ([tex]e^x[/tex] * x)
= [tex]e^x[/tex] - x[tex]e^x[/tex]
= [tex]e^x[/tex](1 - x)
We can see that the determinant of the Wronskian matrix is not zero for all values of x. Since the Wronskian is nonzero for all x, it implies that the functions f(x) = [tex]e^x[/tex]and g(x) = x are linearly independent.
Therefore, f(x) = [tex]e^x[/tex] and g(x) = x form a linearly independent set of functions.
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Heya!
[tex] \underline{ \underline{ \text{question}}} : [/tex] In the adjoining figure , PQRS is a parallelogram and X , Y are points on the diagonal QS such that SX = QY. Prove that the quadrilateral PXRY is a parallelogram.
Answer:
See Below.
Step-by-step explanation:
We are given that PQRS is a parallelogram, where X and Y are points on the diagonal QS such that SX = QY.
And we want to prove that quadrilateral PXRY is a parallelogram.
Since PQRS is a parallelogram, its diagonals bisect each other. Let the center point be K. In other words:
[tex]SK=QK\text{ and } PK = RK[/tex]
SK is the sum of SX and XK. Likewise, QK is the sum of QY and YK:
[tex]SK=SX+XK\text{ and } QK=QY+YK[/tex]
Since SK = QK:
[tex]SX+XK=QY+YK[/tex]
And since we are given that SX = QY:
[tex]XK=YK[/tex]
So we now have:
[tex]XK=YK\text{ and } PK=RK[/tex]
Since XY bisects RP and RP bisects XY, PXRY is a parallelogram.
please use calculus 2 and show all work thank you
Evaluate (f¹)' (2) for the function f(x) = √√√x³ + x² + x + 1. Explain your reasoning and write the solution in exact form. Do not use a decimal approximation.
Given function is `f(x) = √√√x³ + x² + x + 1`. Now, we are going to find out the first derivative of f(x).f(x) = √√√x³ + x² + x + 1
Take the logarithmic derivative of both sides: ln(f(x)) = ln(√√√x³ + x² + x + 1)Differentiate both sides of the equation with respect to x using the chain rule:1/f(x) * f'(x) = (1/2) * (1/3) * (1/4) * (3x² + 2x + 1) * (x³ + x² + x + 1)-1/2The first derivative of f(x) can be obtained by rearranging the equation: f'(x) = (x³ + x² + x + 1) * (3x² + 2x + 1) / 2 * f(x)We need to find f'(2)Now, substituting x = 2 in f'(x), we get f'(2) = (2³ + 2² + 2 + 1) * (3 * 2² + 2 * 2 + 1) / 2 * √√√2³ + 2² + 2 + 1Taking the value of f(x) and f'(2) in exact form, we get f'(2) = 693 / 16√√√2
Therefore, `(f¹)' (2) = 693 / 16√√√21`This is how the value of `(f¹)' (2)` for the function `f(x) = √√√x³ + x² + x + 1` is evaluated.
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In a controversial election district, 73% of registered voters are democrat. a random survey of 500 voters had 68% democrats. are the bold numbers parameters or statistics?
Answer:
73% = parameter
68% = statistic
Step-by-step explanation:
Parameter and statistic differs from one another in statistical parlance in that, parameter refers to nemwrical characteristic derived from the population data. In the scenario described above, 73% describes the percentage of all registered Voters (population of interest). On the other hand, statistic refers to numerical characteristic derived from the sample data. 68% represents the percentage of democrats from the sample surveyed from the the larger population.
Hence,
68% is a sample statistic and 73% is a population parameter.
Image is above
What is the area?
15 cm
20 cm
square centimeters
Please help!
Goes through the points (1, 11) and (1, -2)
Use the slope formula
Y2 - Y1
m=————-
X2 - X1
Darius finds a leaf that is 6 cm long. Which measurement is equivalent to 6 cm?
OA. 0.6 mm
OB. 60 mm
OC. 0.06 mm
OD. 600 mm
Answer:
B: 60mm
Step-by-step explanation:
Answer:
B. 60 mm
Step-by-step explanation:
1 cm = 10 mm
6 cm = 6 * 1 cm = 6 * 10 mm = 60 mm
Answer: B. 60 mm
Perform the indicated calculation. 5_P_2/ 10_P_4 (Round to four decimal places as needed.) 10 P
The permutations value of ₅P₂/₁₀P₄ is 1/252.
To perform the indicated calculation of ₅P₂/₁₀P₄, we need to evaluate the permutations.
The formula for permutations is given by nPr = n! / (n - r)!, where n is the total number of items and r is the number of items selected.
Let's calculate each permutation separately:
₅P₂ = 5! / (5 - 2)!
= 5! / 3!
= (5 * 4 * 3!) / 3!
= (5 * 4)
= 20
₁₀P₄ = 10! / (10 - 4)!
= 10! / 6!
= (10 * 9 * 8 * 7 * 6!) / 6!
= (10 * 9 * 8 * 7)
= 5,040
Now we can substitute the values into the expression:
₅P₂ / ₁₀P₄ = 20 / 5,040
Simplifying the division:
₅P₂ / ₁₀P₄ = 1 / 252
Therefore, the value of ₅P₂/₁₀P₄ is 1/252.
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Complete question:
Perform the indicated calculation: ₅P₂/₁₀P₄
Describe how oral traditions, proverbs, and music are key features of Africa's cultural legacy.
==================================================================
Even if you spam the question or just use it for points GodBless you!! : 3
Answer:
like egip
Step-by-step explanation:
A line segment has endpoints S(-9,-4) and T(6,5). Point R lies on ST such that the ratio of SR to RT is 2:1. What are the coordinates of point R?
Answer:
Coordinates of R = (1,2)
Step-by-step explanation:
Let the coordinate of R be (x, y)
Since coordinates of S and T are S(-9,-4) and T(6,5). Then we can use the Formula for length of line from coordinates to find coordinates of R since SR/RT = 2/1
Thus; 1(S) = 2(T)
Coordinates of R = [(1(-9) + 2(6))/(1 + 2)], [(1(-4) + 2(5))/(1 + 2)
Coordinates of R = (3/3), (6/3)
>> (1, 2)
If f(x) - 2x2 +5./(x-2), complete the following statement:
The domain for f(x) is all real numbers
than__or equal to 2.
Answer: Greater than or equal to 2.
Step-by-step explanation:
Given
Function is [tex]f(x)=2x^2+5\sqrt{x-2}[/tex]
The entity inside a square root is always positive i.e. greater than equal to zero
[tex]\therefore \ x-2\geq 0\\\Rightarrow x\geq2[/tex]
So, the domain of the function is all real numbers greater than or equal to 2.
What is the twelfth term in the sequence with nth term formula 5/6+1/2n? Give your answer as a top-heavy fraction in its simplest form.
Given:
The formula for nth term of a sequence is:
[tex]\dfrac{5}{6}+\dfrac{1}{2}n[/tex]
To find:
The 12th term in the given sequence.
Solution:
Consider the formula for nth term of a sequence:
[tex]a_n=\dfrac{5}{6}+\dfrac{1}{2}n[/tex]
Putting [tex]n=12[/tex], we get
[tex]a_{12}=\dfrac{5}{6}+\dfrac{1}{2}{12}[/tex]
[tex]a_{12}=\dfrac{5}{6}+6[/tex]
[tex]a_{12}=\dfrac{5+36}{6}[/tex]
[tex]a_{12}=\dfrac{41}{6}[/tex]
Therefore, the 12th in the given sequence is [tex]\dfrac{41}{6}[/tex].
help, please Ill mark brainliest!
Answer:
the answers are 12.5, 5, 2, 0.8 and 0.32
Step-by-step explanation:
2(0.4)^-2
=2(6.25)
= 12.5
2(0.4)^-1
= 2(2.5)
=5
2(0.4)^0
=2(1)
=2
2(0.4)^1
=2(0.4)
=0.8
2(0.4)^2
=2(0.16)
=0.32
Sarah competes in a long jump competition.
Her first jump is 4.25 m.
I
Her best jump is 12% more than this.
However, her best jump is 15% lower than the winning jump.
Work out the length of the winning jump.
One of the legs of a right triangle measures 8 cm and its hypotenuse measures 14 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
about 11.5 cm.
Step-by-step explanation:
I know the measurement of the other leg is about 11.5 cm. I know because I used the Pythagorean theorem.
a^2+b^2=c^2.
"a" and "b" are the values of the legs of the triangle, while "c" is the measure of the hypotenuse. We know that 8cm is the measure of one of the legs, and 14 cm is a measure of the hypotenuse.
8^2+b^2=14^2 simplified: 64+b^2=196
Then, I subtracted 64 on both sides, so I would have "b" by itself.
b^2=132
Next, I found the square root of both b^2 and 132, so I would find the true value of "b."
b=11.4891252931
So, the measure of the other leg rounded to the nearest tenth is about 11.5.
6x²-15x=0
If possible use the quadratic formula
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
if ur lucky u get 25 points!
Answer:
What do you mean lucky?
Answer:
Yes
Step-by-step explanation:
John bought a $2,910 car on the installment plan.The installment agreement included a 15% down payment and 18 monthly installment payments of $161.56 each. A) How much is the down payment.B) What is the total amount of the monthly payments. C) what is the total cost he paid for the car. D) What is the finance charge.
9514 1404 393
Answer:
down: $436.50
payment total: $2,908.08
total paid: $3,344.58
finance charge: $434.58
Step-by-step explanation:
A) The down payment is 15% of the cost, so is ...
0.15 × $2910 = $436.50
__
B) The total of the 18 monthly payments of $161.56 each is ...
18 × $161.56 = $2908.08
__
C) The total amount paid for the car is the sum of the down payment and the monthly payments:
$436.50 +2,908.08 = $3,344.58
__
D) The finance charge is the difference between the amount paid and the original cost of the car:
$3,344.58 -2,910 = $434.58
THE FASTER THE BETTER PLEASE HURRY 10 POINTS
Answer:
48in^2
Step-by-step explanation:
The area of a triangle is calculated by the formula A= b*h1/2. Substitute b for 24, h for 4, and solve.
which is the next leap year after to 2017
Answer:
2020
Step-by-step explanation:
Answer:
2020 i think i hope it is the right answer for you
Ashleigh can choose from one of 6 different routes to get to work. The routes are listed below.
• Main St.
• Route 6
• Hilltop Drive
• Medical Avenue
• Highway 220
• Friendship Boulevard
If she chooses one route at random, what is the probability that she will choose either Hilltop Drive or Medical Avenue to get to work?
Answer:
1 /3
Step-by-step explanation:
Total Number of routes = 6
Probability = required outcome / Total possible outcomes
Probability of any one of the routes :
Required outcome / Total possible outcomes
Probability of choosing any one of the routes = 1/6
Hence,
Probability of choosing either Hilltop. Drive or medical avenue =
1/6 + 1/6 = (1 + 1) / 6 = 2 /6 = 1/3
Can some plz help me
Answer:
I think 60 s.sq m
What is the equation of the graph?
5
---- is the answer to the question
-6
Answer:
y= 4/6x + 4
Step-by-step explanation:
The "rise" of the slope is 4 and the "run" of the slope is 6.
Two rectangles are similar. The area of the first rectangle is 20m2. The second rectangle is similar by a scale factor 4. What is the area of the second rectangle?
options
300 m2
340 m2
320 m2
380 m2
Answer:
320 m2
Step-by-step explanation:
I think the answer would be B) 340 m2
1%
The positions of towns A, B and C are shown in the scale diagram below.
.B
.
A
Scale: 1 cm represents 10 miles
Ismael's house is the same distance
from town A and town B.
His house is exactly 20 miles from town C.
Use the x tool to show all the possible positions of Ismael's house.
You must show all your construction lines.
[5]
There are no possible positions for Ismael's house.
In this case, we need the following geometrical constructions:
1) Given that Ismael's house has the same distance from towns A and B, we must create a line segment between A and B and perpendicular line passing through the midpoint of line segment AB.
2) Since Ismael's house is 20 miles away from town C, we must create a circle centered at C.
All possible positions of Ismael's house are the set of points where both the perpendicular line and the circle intercepts each other. After making all operations defined above, we conclude that there are no possible positions for Ismael's house.
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The verbal part of the GRE exam score can be modeled by a normal distribution with mean 160 and a standard deviation of 8. If a student who took this exam is selected at random, what is the probability that he/she obtained a score between 150 and 162? What is the score of a student who scored in the 82th percentile on the verbal part of the GRE?
The probability that a randomly selected student obtained a score between 150 and 162 on the verbal part of the GRE exam is approximately 0.383, or 38.3%.
To find the probability that a student obtained a score between 150 and 162, we need to calculate the area under the normal distribution curve between these two scores. Since the distribution is normal with a mean of 160 and a standard deviation of 8, we can use the Z-score formula to standardize the scores.
First, we calculate the Z-score for a score of 150:
Z1 = (150 - 160) / 8 = -1.25
Next, we calculate the Z-score for a score of 162:
Z2 = (162 - 160) / 8 = 0.25
Using a standard normal distribution table or a statistical calculator, we can find the area under the curve between these two Z-scores. The probability of obtaining a score between 150 and 162 is equal to the area to the right of Z1 minus the area to the right of Z2.
P(150 ≤ X ≤ 162) = P(Z1 ≤ Z ≤ Z2) ≈ P(Z ≤ 0.25) - P(Z ≤ -1.25)
Looking up these values in the standard normal distribution table, we find that P(Z ≤ 0.25) is approximately 0.5987 and P(Z ≤ -1.25) is approximately 0.1056. Subtracting the second probability from the first, we get:
P(150 ≤ X ≤ 162) ≈ 0.5987 - 0.1056 ≈ 0.4931
Therefore, the probability that a randomly selected student obtained a score between 150 and 162 is approximately 0.4931, or 49.3%.
To find the score of a student who scored in the 82nd percentile, we need to find the Z-score that corresponds to the 82nd percentile. The Z-score can be found using the inverse standard normal distribution (also known as the Z-score table or a statistical calculator).
The Z-score corresponding to the 82nd percentile is approximately 0.905. We can use this Z-score to find the corresponding score on the distribution using the formula:
X = Z * σ + μ
Substituting the values, we get:
X = 0.905 * 8 + 160 ≈ 167
Therefore, the score of a student who scored in the 82nd percentile on the verbal part of the GRE is approximately 167.
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Please help me solve these, I tried solving them but I got confused with the signs,
a) -6x = 30 b) -3x = -9
c)-5x = 25
Answer:
a) x= -5
b) x= 3
c) x= -5
2,000(1 + 1)^5
Can you answer my question please
Answer:
2,000(1 + 1)⁵ = 64000, or in alternate form, 40³
A fair die is tossed 180 times .A one refers to the face with one dot. Thou, P(one = 1/6. computer the approximate probability of obtaining at least 37. ones
The approximate probability of obtaining at least 37 ones is -0.000005.
Given that, a fair die is tossed 180 times. A one refers to the face with one dot.
Thus, P(one) = 1/6.The probability of obtaining at least 37 ones can be approximated using the normal distribution.
Using the central limit theorem, we have,μ = n * P = 180 * (1/6) = 30 andσ² = n * P * (1 - P) = 180 * (1/6) * (1 - 1/6) = 25/6
Since we cannot use a normal distribution directly since we need to find the probability of at least 37 ones, we use a continuity correction by considering the range from 36.5 to 37.5 ones.
Now, using the standard normal distribution, we have, z = (37.5 - 30) / √(25/6) = 5.40 and z = (36.5 - 30) / √(25/6) = 4.87
Using a table of standard normal distribution, the probability corresponding to z = 5.40 and z = 4.87 are 0.0000034 and 0.0000084, respectively.Using continuity correction, the approximate probability of obtaining at least 37 ones is given by,P(X ≥ 37) ≈ P(36.5 ≤ X ≤ 37.5) = P( z ≤ 5.40) - P(z ≤ 4.87)= 0.0000034 - 0.0000084= -0.000005
Therefore, the approximate probability of obtaining at least 37 ones is -0.000005.
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The approximate probability of obtaining at least 37 ones is 0.8051.
Given that a fair die is tossed 180 times where the probability of getting a one is 1/6.
We need to find the approximate probability of obtaining at least 37 ones.
Using the binomial probability distribution, the probability of getting r successes in n independent trials can be given by:
[tex]P(r) = nCr x (p^r) x (1-p)^(n-r)[/tex]
Where n = 180, p = 1/6, q = 1- p = 5/6
We want to find the probability of getting at least 37 ones.
Therefore, we can subtract the probability of getting less than 37 ones from 1.
[tex]P(X≥37) = 1 - P(X<37) = 1 - P(X≤36)So, P(X≤36) = P(X=0) + P(X=1) + P(X=2) + .....+ P(X=36)P(X= r) = nCr x (p^r) x (q)^(n-r)[/tex]
On substituting the given values, we get:
P(X≤36) = ∑P(X = r)
n = 180
r = 0 to 36
p = 1/6, q = 5/6
[tex]P(X≤36) = ∑(nCr) × (p^r) × (q)^(n-r)[/tex]
n = 180, p = 1/6, q = 5/6= 0.1949
On subtracting it from 1, we get:
[tex]P(X≥37) = 1 - P(X<37) = 1 - P(X≤36)≈ 1 - 0.1949≈ 0.8051[/tex]
Therefore, the approximate probability of obtaining at least 37 ones is 0.8051.
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