The outlier does not affect the mode
The outlier will increase the mean.
The outlier will not affect the median.
How does outlier affect the mean, median and mode?The outlier will increase the mean because it will significantly increase the sum of the values.
The presence of an outlier will not affect the median, as it only changes the position of the middle value.
The mode is the value that occurs most frequently in a data set. In this case, the mode will not be affected because the outlier is not the most frequent in the data set and only appears once.
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What are the values of x and y?
X=
Y=
Answer:
X = 6
Y = 17
Step-by-step explanation:
The points GHIJ for a cyclic quadrilateral.
The sum of opposite angles of a cyclic quadrilateral is 180°
So
∠J + ∠H = 180°
⇒ 6y + 78° = 180°
⇒ 6y = 180° - 78°
⇒ 6y = 102°
⇒ y = 102°/6
⇒ y = 17°
Similarly for angle x
∠I + ∠G = 180°
⇒ 16x + 14x = 180°
⇒ 30x = 180°
⇒ x = 180°/30
⇒ x = 6°
What is the difference between a formal and informal proof?
A) A formal proof is much shorter, whereas an informal proof is longer.
B) A formal proof provides the reasons for steps, whereas an informal proof does not.
C) A formal proof uses equations, whereas an informal proof only uses text.
D) A formal proof uses a table or a list of steps, whereas an informal proof uses paragraphs.
Answer: D
Step-by-step explanation: formal proofs deeply uses tables or a list of steps where informal proofs are proven in paragraphs.
[5 (8^1/3 + 27^1/3)^3]^1/4 simplify
Answer
5
Solution
[5 (8^1/3 + 27^1/3)^3]^1/4
= [5 ((2^3)^1/3) + (3^3)^1/3)^3]^1/4
= [5((2+3)^3)1/4
= (5×5^3)^1/4
= (5^4)^1/4
= 5
help me please How would you informally prove that you are taking courses online?
A) You could show a registrar’s receipt with the current date.
B) You could show your course notes with the current date.
C) You could repeat all the material you learned.
D) You could ask for an enrollment verification notice from the school.
The conditional statement is solved and you could ask for an enrollment verification notice from the school
Given data ,
Let the statement be informally proven that you are taking courses online
And , To informally prove that you are taking courses online, you can contact the professors of the courses via email and obtain informal permission from them first.
Then you can initiate the request using the new online information system of the school to obtain an enrollment verification notice
It is a legitimate document that the school has produced that may be utilized for a number of things, including debt deferments, employment, and insurance.
Hence , the conditional statement is solved
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−9⋅(5j+k)
Apply the distributive property to create an equivalent expression.
Answer:
-45j - 9k
Step-by-step explanation:
-9(5j + k)
-9(5j) + -9(k)
-45j - 9k
Helping in the name of Jesus.
Study the system of equations below.
x + y =-4
x - y = 10 What is the solution to the system of
equations?
A (-4, 10)
B (10, 4)
C(3,-7)
D(7,-3)
Answer:
Option C
Step-by-step explanation:
To solve this system of equations, we can use the method of elimination. Adding the two equations together eliminates the y variable, and we get:
2x = 6
Simplifying, we get:
x = 3
Substituting x = 3 into either of the original equations, we get:
3 + y = -4
Solving for y, we get:
y = -7
Therefore, the solution to the system of equations is (3, -7), which is option C.
100 Points!!! Algebra question. Find the third term of (11x+3y)^6. Photo attached. Please show as much work as possible. Thank you!
Answer: If you are trying to find the third derivative
It would be f'''(x)=159720(11x+3y)^3
Step-by-step explanation:
The third term of the given expression [tex](11x+3y)^6[/tex] is 135[tex]x^4y^2[/tex].
The binomial theorem states that [tex](a+b)^n[/tex] can be expanded as follows:
[tex](a+b)^n[/tex] = nC0*[tex]a^n[/tex] + nC1*[tex]a^{n-1[/tex]*b + nC2*[tex]a^{n-2[/tex]*[tex]b^2[/tex] + ... + nCn*[tex]b^n[/tex]
where nCk is the binomial coefficient, which is defined as n! / k!(n-k)!.
In this case, we have [tex](11x+3y)^6[/tex], so n = 6.
The third term of the expansion is given by nC2[tex]a^{n-2[/tex][tex]b^2[/tex], which is equal to 6C211[tex]x^4[/tex]3[tex]y^2[/tex].
6C2 is equal to 6! / 2!4! = 15, so the third term is equal to 1511[tex]x^4[/tex]3[tex]y^2[/tex] = 135[tex]x^4y^2[/tex].
Therefore, the third term of [tex](11x+3y)^6[/tex] is 135[tex]x^4y^2[/tex].
Here is a breakdown of the steps:
Find the binomial coefficient nC2.
Multiply nC2 by 11[tex]x^4[/tex] and 3[tex]y^2[/tex].
Simplify the expression.
The answer is 135[tex]x^4y^2[/tex].
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During a game, a spinner landed on several different colors. During a game, a spinner landed on several different colors.
Considering this data, how many of the next 13 spins should you expect to land on purple?
First, we need to find the experimental probability (probability using the provided data) of landing on purple.
Experimental probability of purple = # of purple / total #
Experimental probability of purple = 2 / 26 = 1 / 13 (simplified)
Next, we need to consider the probability in the context of 13 spins, as per the question. Our experimental probability tells us that 1 out of every 13 spins will be purple. Therefore, we can expect 1 of the next 13 spins to land on purple.
Answer: 1 spin
Hope this helps!
Need the right answer for problem 12
The distance of the point from the line is d =
Given data ,
Let the point be P ( 1 , 1 )
Let the equation of line be represented as e
where A ( -5 , 0 ) and B ( 1 , -2 ) lies on the line
So , slope m = ( 0 + 2 ) / ( -5 - 1 )
m = 2/-6
m = -1/3
So , the equation of line is
y - 0 = ( -1/3 ) ( x + 5 )
y = ( -1/3 ) ( x + 5 )
( 1/3 )x + y + 5/3 = 0
Now , the Distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )
On simplifying , we get
D = | ( 1/3 )( 1 ) + ( 1 ) ( 1 ) + ( 5/3 ) | / √[ ( 1/3 )² + ( 1 )² ]
D = | ( 6/3 ) + 1 | / √ [ ( 1/9 ) + 1 ]
D = 3 / ( 10 ) / 9
D = 27/10
D = 2.7 units
Hence , the distance is 2.7 units
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A local maximum of the function f(x) occurs for which x-value? A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 16, negative 2, 0, 6, 0, negative 2. Group of answer choices –4 –3 –2 –1
There is a local maximum at the point (-1,6), therefore, for x = -1
option D is correct
What do we mean by local maximum point?A local maximum point on a function is described as a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).
We see that the function adopts values smaller than 6 to the left of x = -1, and to the right of it:
(-3, -2), (-2, 0) to the left of x = -1 where the function's value is 6
and (0, 0), and (1, -2) to the right of x = -1
Therefore, we can say that the pints (-1, 6) is a maximum, that is for x = -1, where the function renders a value of 6.
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write 68.19 to one significant figure
Answer:
70...............................
Reason:
The left-most digit is the most significant when it comes to rounding. We bump the 6 up to 7 since 68 is closer to 70 (compared to 60). The other digits turn to 0 and become insignificant.
Do not write any of the following:
70.70.070.00because that would mean we would have 2, 3, and 4 sig figs respectively. We simply write 70 without a decimal point.
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 150 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Use the calculator provided and round your answer to the nearest gram.
grams
7. The plot of land modeled below is composed of a right triangle and a rectangle. If Patrick wants to install a fence around the perimeter of the plot of land, how many feet of fencing will be needed
The number of feet of fencing that will be needed is illustrated below
How many feet of fencing will be needed The feet of fencing that will be needed is the perimeter of the fence
To find the perimeter of a composite figure, we need to add up the lengths of all the sides of the figure.
In this case, we add the side lengths of the rectangle to the side lengths of the right triangle and subtracting the common lengths between both shapes
Take for instance, we have
Right triangle: 3 units, 4 units and 5 unitsRectangle: 4 by 5 unitsCommon segment: 4 unitsSo, we have
Fencing = 2 * (4 + 5) + 3 + 4 + 5 - 2 * 4
Fencing = 22 units
So, the amount of fencing for the assumed dimensions is 22 units
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29 Given: A = √363 and B = √27
Explain why A + B is irrational.
Explain why A B is rational.
To explain why A + B is irrational, we need to show that it cannot be expressed as a ratio of two integers.
Suppose that A + B is rational, which means we can write it as the ratio of two integers p and q (where q is not zero):
A + B = p/q
Now, we can substitute the values of A and B and simplify:
√363 + √27 = p/q
We can then rearrange the terms to isolate one of the square roots:
√363 = p/q - √27
We can square both sides of this equation to eliminate the square roots:
363 = p^2/q^2 + 27 - 2(p/q)√27
Notice that the right-hand side of this equation has a term with a square root. This means that if we assume that A + B is rational, we arrive at a contradiction: we have shown that √363 (which is equal to A) is irrational, which means that p^2/q^2 + 27 must also be irrational. However, the left-hand side of the equation is rational. Therefore, our assumption that A + B is rational must be false, and we conclude that A + B is irrational.
To explain why AB is rational, we can use the fact that the product of two rational numbers is rational.
We can rewrite A and B as follows:
A = √(363) = √(121 x 3) = √(11^2 x 3) = 11√3
B = √(27) = √(9 x 3) = √(3^2 x 3) = 3√3
Therefore, AB = 11√3 x 3√3 = 33 x 3 = 99.
Since 99 is a rational number (which can be expressed as the ratio of the integers 99 and 1), we conclude that AB is rational.
The formula A = 252e^.049t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 373 thousand?
Answer: Approximately the year 2006
Roughly 8 years after 1998
================================================
Work Shown:
A = 373 represents a population of 373 thousand.
Plug in this value of A and solve for t. We'll need natural logs (LN) to isolate the variable.
[tex]A = 252e^{0.049t}\\\\373 = 252e^{0.049t}\\\\373/252 = e^{0.049t}\\\\1.4801587 \approx e^{0.049t}\\\\[/tex]
Apply natural logs to both sides.
[tex]\text{Ln}(1.4801587) \approx \text{Ln}\left(e^{0.049t}\right)\\\\\text{Ln}(1.4801587) \approx 0.049t*\text{Ln}\left(e\right)\\\\\text{Ln}(1.4801587) \approx 0.049t*1\\\\\text{Ln}(1.4801587) \approx 0.049t\\\\t \approx \text{Ln}(1.4801587)/0.049\\\\t \approx 8.0030472\\\\[/tex]
It takes about 8 years for the population to reach 373 thousand.
Since t = 0 starts at 1998, we get to the year 1998+8 = 2006.
The whole page Tysm plsssssss step by step btw
The sum of all the pets in the list is 11.
The average number of pets that the students own is 1.375.
How to calculate the sumIt should be noted that to find the sum of all the pets in the list, we simply add up all the values:
0 + 1 + 2 + 3 + 1 + 2 + 0 + 2 = 11
Therefore, the sum of all the pets in the list is 11.
Since Cameron asked eight of his classmates, we divide the sum of pets by 8 to find the mean:
11 ÷ 8 = 1.375
Therefore, the average number of pets that the students own is 1.375.
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The measures of center can be used to summarize the number of pets that students own. Cueton asked eight of his classmates how many pets they own. The results are listed below.
0 1 2 3 1 2 0 2
What is The sum of all the pets in the list
What is the average number of pets that the students own
PROJECT: INSCRIBED POLYGONS
You've learned about the different parts of a circle, as well as regular polygons and their angle measures. You've also learned how to use a protractor to measure angles.
In this project, you will apply this knowledge to inscribe regular polygons in a circle. If a polygon is inscribed in a circle, all of its vertices touch the circle. Here is an example of an equilateral triangle inscribed in a circle.
OBJECTIVES
Inscribe regular polygons in circles using a protractor, compass, and straight edge.
Materials
pencil and paper
protractor
compass
straight edge
Mr. McGill is buying a car worth $35,000 and taking out a loan for the full amount. If
it is increasing at 2.5 percent yearly. How much will the loan increase to in 5 years?
A.) $39,599.29
B.)$36,599.29
C.)$18,382,656.25
D.)$40,269,30
The loan will increase to $39599.29 in 5 years
How much will the loan increase to in 5 years?From the question, we have the following parameters that can be used in our computation:
Mr. McGill is buying a car worth $35,0002.5% interest compounded annualyUsing the above as a guide, we have the following:
Amount = P * (1 + r)ᵗ
Where
P = Principal = 35000
r = Rate = 2.5%
t = time = 5
Substitute the known values in the above equation, so, we have the following representation
Amount = 35000 * (1 + 2.5%)⁵
Evaluate
Amount = 39599.29
Hence, the amount is 39599.29
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A $162,000 trust is to be invested in bonds paying 9%, CDs paying 7%, and mortgages paying 10%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $14,650 annual income from the investments, how much should the bank invest in bonds? (It's okay to use your calculator to solve the system you set up on this problem.
The bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
How to solve for the amount(162,000 - 2x) is invested in mortgages.
The annual income earned from the bond investment is:
0.09x
The annual income earned from the CD investment is:
0.07x
The annual income earned from the mortgage investment is:
0.10(162,000 - 2x) = 16,200 - 0.20x
The total annual income earned from the investments is:
0.09x + 0.07x + 16,200 - 0.20x = 14,650
Simplifying and solving for x, we get:
-0.04x + 16,200 = 14,650
-0.04x = -1,550
x = 38,750
Therefore, the bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
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Rewrite the quadratic function as a product of linear factors.
f(x) = 16x^2 - 3
help pls
Answer: (4x - √3)(4x + √3).
Step-by-step explanation: Use factoring. The equation (when factored out) is: ax^2 + bx + c. Hence, the equation you wrote rewritten is: 16x^2 + 0x - 3. (√3)(√3) = 3 and (4x)(4x) = 16x^2. It is divisible.
So, the quadratic function f(x) = 16x^2 - 3 can be expressed as a product of linear factors as (4x - √3)(4x + √3).
using the table feature of a graphing utility what would be the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds?
Using the table feature of a graphing utility the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds would be 2.16 x 10¹⁴ joules/second/meter².
How did we get this ?First, note that the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds can be calculated using the formula..
I = (1/2)ρv²
Here I Intensity
ρ = density of the medium - this is a constatnt
v = velocity of the S-waves
If we used a graphing tool
a coumun ffor v will be created
a column for the formula for velocity will also be created.
The formula for velocity is
V = A/ T
A = amplitude
T = time or period in seconds
Since A = 200,000 micrometers; and
T = 0.05 secons
v = 200,000 / 0.5
v = 400,000 micrometer/sec
Back o the table, we ahve to add another oclumn for V²
then enter the values for V²
V² = 400,000²
v² = 160,000,000,000 micrometer²/sec²
Nowe we add another column which is
I = 1/2(pv²)
I = 2.16 x 10¹⁴ joules/second/meter².
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Solve for x. Round to the nearest tenth, if necessary.
Answer:
9.6
Step-by-step explanation:
sin(angle)= opposite/hypotenuse
sin(42°)=6.4/X
X*SIN(42°)=6.4
X=6.4/SIN(42)
X=9.6
Answer:
Step-by-step explanation:
sin(42°)=6.4/X
X*SIN(42°)=6.4
X=6.4/SIN(42)
sin(42°)=6.4/X
X*SIN(42°)=6.4
X=6.4/SIN(42)
X=9.6
‼️‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️‼️
Answer:
2π(10^2) + 2π(10)(16)
= 2π(100) + 2π(160)
= 200π + 320π
= 520π ft^2
There are 15 tables at a wedding reception,
5 of which have purple centerpieces.
1) What is the probability that a randomly
selected table will have a purple centerpiece?
◄) Write your answer as a fraction or whole
number.
Answer:
1/3
Step-by-step explanation:
There are 15 tables and 5 have a purple centerpiece. Divide 15 by 5 to get the probability of a randomly selected table being purple.
5/15 is 5 out of 15. 5/15 simplifies to 1/3.
The reciprocal of h.C.F and lcm of two number are 1/12 and 1/312 respectively. If one of the number is 24. Find the other number?
The other number is 156.
Let a and b be two numbers, with a = 24.
We know that the product of two numbers' HCF and LCM is equal to the product of the two numbers.
So, we have:
HCF × LCM = a × b
We are given that the reciprocal of HCF is 1/12.
So, HCF = 1 / (1/12) = 12.
We are also given that the reciprocal of LCM is 1/312.
So, LCM = 1 / (1/312) = 312.
12 × 312 = 24 × b
Simplifying, we get:
b = (12 × 312) / 24 = 156
Therefore, the other number is 156.
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ANGELINA
Mr. Black's class sold highlighters and pens to raise money. Every highlighter cost the same amount. Every pen
cost the same amount.
. On day 1, the class made $120 and sold 80 highlighters and 20 pens.
. On day 2, the class made $200 and sold 120 highlighters and 40 pens.
What was the cost per highlighter?
$
1
4
7
0
2
5
8
per highlighter
3
6
9
The cost per highlighter is approximately $1.
To find the cost per highlighter, we can use a system of equations. Let's call the cost per highlighter "h" and the cost per pen "p". Then, we can set up two equations based on the information given;
80h + 20p = 120 (day 1)
120h + 40p = 200 (day 2)
We can simplify these equations by dividing both sides by 20;
4h + p = 6 (day 1)
6h + 2p = 10 (day 2)
Now we can use the first equation to solve for p in terms of h;
p = 6 - 4h
Substitute this expression for p into second equation;
6h + 2(6 - 4h) = 10
Simplify and solve for h;
6h + 12 - 8h = 10
-2h = -2
h = 1
Therefore, the cost per highlighter is $1.
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Please help Thanks
there is a FRACTION symbol two variable symbols y and x
Step-by-step explanation:
The equation of the line (by inspection) is y = 1/2 x
I really need hep please
The valid row-operation which needs to be performed on the given matrix to get "1" in position of row1 and column1 are "R₁ → 2R₁ + R₂" and then "R₁ → R₁/2".
The "row-operation" is a type of matrix operation that involves swapping, scaling, or adding rows in a matrix. These operations are used to transform a matrix into a more reduced form.
The Augmented matrix on which we have to perform the "row-operation" is
⇒ [tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex],
To get "1" in first row and first column,
The first row-operation is R₁ → 2R₁ + R₂
We get,
⇒ [tex]\left[\begin{array}{ccc}7\times 2-12&-4\times 2+7&8\times 2-13\\-12&7&-13\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}14-12&-8+7&16-13\\-12&7&-13\end{array}\right][/tex]
⇒ [tex]\left[\begin{array}{ccc}2&-1&3\\-12&7&-13\end{array}\right][/tex],
The second , row-operation to get a "1", is R₁ → R₁/2,
We get,
⇒ [tex]\left[\begin{array}{ccc}2/2&-1/2&3/2\\-12&7&-13\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}1&-0.5&1.5\\-12&7&-13\end{array}\right][/tex].
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Angles in parallelograms maze
The values of angles x in the parallelogram maze are calculated below
Calculating the angles x in the parallelogram mazeThe question is solved by taking the shapes from left to right on each row
So, we have
x + 65 = 180 --- adjacent angles
x = 115
x + 103 = 180 --- adjacent angles
x = 77
9x = 90 --- angles in a rectangle
x = 10
x + 85 = 180 --- adjacent angles
x = 95
x + 60 = 180 --- adjacent angles
x = 120
2x = 90 --- angles in a rectangle
x = 45
x = 98 -- opposite angles in a parallelogram
3x = 81 -- opposite angles in a parallelogram
x = 27
4x + 76 = 180 --- adjacent angles
x = 26
3x = 78 -- opposite angles in a parallelogram
x = 26
8x + 68 = 180 --- adjacent angles
x = 14
4x = 72 -- opposite angles in a parallelogram
x = 18
x + 126 = 180 --- adjacent angles
x = 54
x = 90 -- opposite angles in a parallelogram
6x = 90 -- opposite angles in a parallelogram
x = 15
2x + 62 = 180 --- adjacent angles
x = 59
6x = 106 --- opposite angles in a parallelogram
x = 17.6
5x = 90 --- angles in a rectangle
x = 18
5x + 80 = 180 --- adjacent angles
x = 20
10x = 90 --- angles in a rectangle
x = 9
2x = 100 --- opposite angles in a parallelogram
x = 50
6x = 96 --- opposite angles in a parallelogram
x = 16
x + 105 = 180 --- adjacent angles
x = 75
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I need help please
I need to answer the white box i don't know the answer
The expression of the matrix row operation is 1/4 Row 1 ⇒ Row 1
Determing the matrix row operation and expressionFrom the question, we have the following parameters that can be used in our computation:
[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]
From the above matrices, we understand that
Dividing the first row of the first matrix by 4 gives the first row of the second matrix Other corresponding row elements of the second and third rows remain unchangedThis means that
row 1 = 1/4(row 1)
This in other words means that
row 1 = (row 1)/4
When these values are evaluated, we have
[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]
This means that we replace -24, -24, 12, and 20 in row 1 with -6, -6, 3 and 5
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