Consider the given set of numbers 70, 81, 91, 83, 88, and 55. A new number equal to a 12% increase in the median of this set is added to the list. What percentage larger is the mean of the new list in comparison with the original

Answers

Answer 1

New mean is 2.53% larger than the original mean.

What is mean?

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

We can find the percentage larger is the mean of the new list in comparison with the original as shown below:

Given, set of number 55, 70, 81, 83, 88, 91

Median= (81+83)/2

= 164/2

= 82

Mean = (55+70+81+83+88+91)/6

= 468/6

= 78

New value which is added = 82*1.12

= 91.84

New Mean = (55+70+81+83+88+91+91.84)/7

= 559.84/7

= 79.97

Increase in mean = 79.97-78

=1.97

increase percentage (1.97/78) *100

= 2.53%

Hence, new mean is 2.53% larger than the original mean.

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Related Questions

A new Concept XI bicycle cost a bike shop $800. The shop set the original list price of the bicycle at a price greater than $800. During the shop’s 30th anniversary sale, every list price in the store was marked down 30%. The shop sold this bicycle during its anniversary sale. Given that the shop made a 40% profit on the sale of this bicycle, what was the bicycle’s original list price?

Answers

Based on the fact that the shop still made a 40% profit on the concept xi bicycle, the original listing price must have been $1,600.

what price was the bicycle originally listed at?

assuming the list price is x, the formula would be:

800 x 1.40 = (x × 0.7)

solving gives:

1,120 = 0.7x

x = 1,120 / 0.7

= $1,600

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Solve the equation: √2 + 4 - 1 = 2
A) ±x= √5
B) ±x = √13
OC) x= 3
D) x = 5

Answers

Answer:

Step-by-step explanation:

1) Separate terms with roots from terms without roots.

[tex]x^2+4=\sqrt[\frac{1}{2} ]{4+1}[/tex]

2) Simplify 4 + 1 to 5.

[tex]x^2+4=\sqrt[\frac{1}{2} ]{5}[/tex]

3) Invert and multiply.

[tex]x^2+4=5^2[/tex]

4)  Simplify  [tex]5^2[/tex] to 25.

[tex]x^2+4=25[/tex]

5) Subtract 4 from both sides.

[tex]x^2=25-4[/tex]

6) Simplify 25 - 1 to 24.

[tex]x^2=21[/tex]

7)  Take the square root of both sides.

[tex]x=\pm\sqrt{21}[/tex]

Answer:

A

Step-by-step explanation:

[tex]\sqrt{x^{2}+4}-1=2\\\sqrt{x^{2}+4}=3\\x^{2}+4=9\\x^{2}=5\\x=(plus/minus) \sqrt{5}[/tex]

What is the value of the function at x=−2? y=−4 y equals negative 4 y = 0 y, = 0 y = 2 y = 2, y = 3

Answers

Based on the graph which models the function at x = -2 (see attachment), the corresponding y-value is y = 3.

What is a function?

In Mathematics, a function can be defined as a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.

In this scenario, there are several values (points) on the given linear graph expressed as a coordinate (x, y). Hence, the x-values on the x-axis is directly proportional to the y-values on the x-axis.

By critically observing the graph which models the function at x = -2 (see attachment), we can logically deduce that the corresponding y-value is three (3).

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Answer:

Ik im late but yea

Step-by-step explanation:

I took the test :O

1/2a+2/3b=50 when b=30?

Answers

The given equation is (1/2)a + (2/3) b = 50

and b = 30

Substituting the given value of b is above the equation we get

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a+\left(\frac{2}{3}\right)\times30=50 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow \left(\frac{1}{2}\right)a+20=50 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a=50-20=30 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow a = 30 \times 2 = 60 } \end{gathered}$}[/tex]

Therefore, a = 60 and b = 30 is a solution of the given equation.

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Find the circumference of a circle with diameter, d = 8.92m. give your answer rounded to 2 dp.

Answers

Answer:

Step-by-step explanation:

circumference is 2πr

r=d/2

r=4.46m

C=2π(4.46)=28.02

The vectors are linearly independent if and only if?

Answers

The vectors are linearly independent if and only if k ≠ -11

How to solve the vector

In mathematics, the definition of a vector is a quantity that is made up of both magnitude and also have direction. This type of quantity is not one that is considered based on its position. A very good example of such a quantity with magnitude and direction is acceleration.

Vectors are used to represent items such as position, velocity, physical quantities and others in mathematics and in physics.

In this question,

We have 2v - 3w

We have to multiply 2 by the values of v and multiply 3 with the values of w

this would produce

[2,6,8]-[6,6,12]

subtract w from v

= [-4, 0, -4]

We u as -1, 0 and 10+k

It is not possible to -1 = 10 + k

-11 = k

Hence we have to conclude that they are linearly independent if and only if k ≠ -11

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Find the maximum or minimum value of the product of two numbers whose difference is 14.

Answers

The maximum value of the product of two number whose difference is 14 is 49.

What is the maximum or minimum value of a function?

The maximum or minimum value of a function is the highest or lowest value of that function.

How to determine the maximum or minimum of the product of two numbers?

Let the numbers be x and y

Their product f(x,y) = xy

Since their difference is 14, x - y = 14

So, x = 14 - y

Substituting x into f(x,y), we have

f(x,y) = xy

= (14 - y)y

= 14y - y²

To find the maximum or minimum value of f(x,y) we differentiate it with respect to y and equate to zero.

So, f(x,y) = f(y) = 14y - y²

df(y)/dy = d(14y - y²)/dy

df(y)/dy = d(14y)/dy - dy²/dy

df(y)/dy = 14 - 2y

Equating to zero, we have

df(y)/dy = 0

14 - 2y = 0

14 = 2y

y = 14/2

y = 7

To determine if this gives a maximum or minimum for f(y) = f(x,y), we differentiate f'(y) again

So, df'(y)/dy = d(14 - 2y)/dy

= d14/dy + d(-2y)/dy

= 0 - 2

= -2 < 0.

Since f"(y) = -2 < 0, then y = 7 gives a maximum for f(x,y)

So, since y = 7,

x = 14 - y = 14 - 7 = 7

So, f(x,y) is maximum at x = 7 and y = 7

So, f(7,7) = 7 × 7

= 49

So, the maximum value of the product of two number whose difference is 14 is 49.

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Find AC please help trig is so hard

Answers

I hope this helps, I tried to make my handwriting as easy to read and to explain as much, I just used a calculator to compute all those values to find AC

If the sum of the interior angle of a polygon is 1800 how many sides does it have

Answers

Answer: 12 sides

Step-by-step explanation:

The sum of the interior angles of a polygon is 180(n-2), where n is the number of sides

[tex]180(n-2)=1800\\\\n-2=10\\\\n=12[/tex]

A linear expression does not have a squared variable.

Answers

it is true that a linear expression does not have a squared variable.

How to determine the true statement?

The following are the forms of a linear expression

y = mx + c

Ax + By = C

x = a

Notice that none of the above expressions have a squared variable

This means that, a linear expression does not have a squared variable.

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Can someone help me with this problem and show work please !

Answers

Answer: Length - 20, Width - 10

Step-by-step explanation:

First we will use the formula to find area:

Area = Length * Width --- However, since it's double the length we will do 2Length.

Area = 2x*x

Given Area = 200

Next we will solve to find Width:

[tex]2x^{2} =200[/tex]

Divide by 2:

[tex]x^{2} =100[/tex]

Take square root:

[tex]x=10[/tex]

Width = 10

Now we multiply 10 by 2, as length is twice it's width:

[tex]2*10=20[/tex]

Length = 20

Final answer: Width = 10, Length = 20

I hope this helps!

There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter?

Answers

Using the combination formula, the coach can make 5,005 different groups.

The position does not matter, hence the combination formula is used.

What is the combination formula?

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 6 students are taken from a set of 15, hence the number of groups is:

[tex]C_{15,6} = \frac{15!}{6!9!} = 5005[/tex]

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WILL GIVE BRAINLEST!!!
Find the length of the base.

Answers

Answer:

32

Step-by-step explanation:

The length of segment AB is the average of XY and WZ.

(22 + x)/2 = 27

22 + x = 54

x = 32

Answer this one please!

Answers

Using simultaneous equation,

a=-1, b=1, x=1, y=0
OR
a=1, b=-1, x=1, y=0.

Evaluate the piecewise function at the indicated values from the domain:

ƒ(−1) = 1

ƒ(−1) = −1

ƒ(−1) = −2

ƒ(−1) = 0

Answers

The value of the piecewise function at the domain is f(-1) = 1

How to evaluate the piecewise function?

The complete question is added as an attachment

At x = -1, the function is

f(x) = x^2

So, we have:

f(-1) = (-1)^2

Evaluate

f(-1) = 1

Hence, the value of the piecewise function at the domain is f(-1) = 1

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Which points lie on the graph of f(x) = -√-x?
□(-9,3)
□(-4,-2)
□ (-1, 1)
□(0,0)
□ (1,1)
□(2,-4)
□(9,3)

Answers

Answer:

(-4, -2).

(0, 0).

Step-by-step explanation:

Both coordinates will be negative or (0.0).

It's these followings:

□(-4,-2)

□(0,0)

Hope this helps!

Is 1/11 a irrational number?

Answers

Answer:

No

Step-by-step explanation:

Am irrational number is a number that can't be expressed by a ratio (fraction). 1/11 is a fraction so it is rational, not irrational.

60÷8 explained well and not in a decimal form

Answers

Answer: 15/2

Step-by-step explanation: if you fraction it, it'll be 60/8 so you can simplify it by 4. So 60÷4/8÷4 will be 15/2. So the answer is 15/2

Answer:

15/2 or 7 1/2.

Step-by-step explanation:

60 / 8      divide top and bottom by 4:-

= (60/4)  /  (8/4)

= 15/2.

1. A committee of 3 men and 4 women is to be formed from 5 men and 6 women. If a particular woman is not to be included, how many different committees are possible​

Answers

Step-by-step explanation:

Taking the men first: there are 5 ways to form a 4-man committee out of 5 men.

Taking the women now: There are 20 ways to form a 3-woman committee out of 6 women.

Each of the 5 possible male groups can be combined with any of the 20 possible female groups.

So: 100.

The volume of a sphere is 500/3π cm3.
Work out the surface area of the sphere.
Give your answer in terms of π.

Answers

The answer is 100π cm².

Since we are given the volume, equate it to the formula of a sphere to find the radius.

500/3π = 4/3πr³r³ = 500/4r³ = 125r = 5 cm

Now, substitute this in the formula to find surface area.

A = 4πr²A = 4π × (5)²A = 100π cm²

What is the size of exterior angle of regular polygon which has interior angle of 120 degree?

Answers

Answer: 60 degrees

Step-by-step explanation:

An interior angle of a polygon and its corresponding exterior angle are supplementary (add to 180 degrees).

what is the volume of the sphere shown below with a radius of 9

Answers

Answer:

972π  or 3052.08 if π=3.14(remember to label the answer with your units)

Step-by-step explanation:

The formula for the volume of a sphere is [tex]\frac{4}{3}\\[/tex]π[tex]r^{3}[/tex]. So, just plug the radius into the formula. [tex]r^{3}[/tex] in this case is [tex]9^{3}[/tex] which is 729. For, [tex]\frac{4}{3}[/tex]×729, the 3 and 729 cancel out to create 4×243 which is 972. Just add π to this and you get 972π. If π is 3.14 just multiple 972 and 3.14 to get 3052.08.

Identify the perimeter of a rectangle in which h = 8 ft and a = 144x ft^2. please help asap

Answers

Here, Given

h= 8ft

a=144 * ft^2

then,

A=L*H

144=L*8 or 144/8 =L

L=18

now, P=2(L+H)

P=2(18+8)

P=52m

Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.

The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.

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Hi having a bit of trouble.

Answers

Answer:

  P = 160/A

Step-by-step explanation:

For P to vary inversely with A, we must have P be proportional to the reciprocal of A. The constant of proportionality is given.

Inversely proportional

Two quantities are directly proportional if there is a constant of proportionality (k) that multiplies one of them to give the value of the other:

  y = kx

They are inversely proportional if the inverse of one of them can be multiplied by a constant of proportionality to give the value of the other:

  y = k(1/x) = k/x

In this problem, the variables P and A are said to be inversely proportional. That means the equation that relates them will be of the form ...

  P = k/A

You are given such a form with k=160, which is an appropriate value for the relation given by the problem. All you need to do is fill in the variable:

  P = 160/A

What number is represented by point B? A number line going from 1 to 2 with 5 equal spaces between 1 and 2. Point B is one mark to the left of 2. StartFraction 4 Over 5 EndFraction 1 and StartFraction 4 Over 5 EndFraction 1 and StartFraction 5 Over 4 EndFraction 2 and StartFraction 1 Over 5 EndFraction

Answers

Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2the number represented by point B is 1⁴/₅

The question has to deal with proportion

What is proportion?

Proportion is the measure of a variable or quantity relative to another.

How to calculate which number represents point B?

Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2, the measure of a sub-unit between 1 and 2 is

= 1/5

So, each sub-unit measure 1/5

Since point B is one mark to the left of 2, we have that point B is y = 2 - 1/5 = (10 - 1)/5

= 9/5

= 1⁴/₅

So, the number represented by point B is 1⁴/₅

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When rolling a single number cube, what are the odds, in simplest form, in favor of rolling a 4 or a 5?
A. 1:1
B. 1:2
C. 1:3
D. 1:5

Answers

Answer:

C

Step-by-step explanation:

You have a total of 6 outcomes (1,2,3,4,5,6).  That is your numerator.  Out of those numbers, you only want 2 of them (4 or 5), so the fractions would be 2/6 or 1/3 which can also be written 1:3

5 roses in a vase 12 flowers what is the ratio of all flowers in the vase of daisies

Answers

The ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.

The number of flowers in the vase = 12 flowers

The number of roses in the vase = 5 roses.

Therefore, the number of daisies in the vase = The number of flowers in the vase - The number of roses in the vase,

or, the number of daisies in the vase = 12 - 5 = 7.

Thus, the number of daisies in the vase = 7.

We are asked to find the ratio of the total number of flowers in the vase, to the number of daisies in the vase.

Thus, the ratio = The number of flowers in the vase/The number of daisies in the vase,

or, the ratio = 12/ = 12:7.

Thus, the ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.

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Geroge is bringing garonla bars and apples for his classmate at school apples cost 0.75 each qnd garonla bars cost 0.15 each geroge will bring 60 total items too school and spend a total of 21$ whixh system of equations best respesents the number of apples a and the number of garonla bars g?

Answers

The system of equations best represents the number of apples a and the number of garonia bars g be a+b=60, 0.75x+0.15y=21.

Given that cost of 1 apple is $0.75, cost of 1 gargonia bars be $0.15 ,total things are 60 and total money paid be $21.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be a linear equation,quadratic equation, cubic equation.

Because we have been told that there are 60 total things and a represents the number of apples and g represents number of garonia represents the number of garonia bars.

a+b=60--------1

Money paid by consumers is cost per units*number of units

So,

0.75a+0.15b=21

Hence the system of equations best represent the number of apples and the  number of garonua bars g are a+b=60, 0.75a+0.15b=21.

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5x=3125 how do i solve that

Answers

Answer:

just divide 3125 by 5 and your answer is 625

Step-by-step explanation:

Using division, 3125 by 5 and get answer 625.

How can we interpret the division?

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

If 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus,  a / b = a divided in b equal parts.

We have been given 5x = 3125

Divide by 5 each sides;

x = 3125/5

x = 645

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2. (4)1 point possible (graded, results hidden)Recall for Define the kernel function Write as a function of the dot product . To answer, let , and enter in terms of . z^2 submitted

Answers

The Kernel Function K (x,x') written as a function of the dot product x *x' is  K (x, x') = Z². See the working below.

What is a Kernel Function?

A kernel function is a way for taking input data and transforming it into the needed form of processing data.

The term "kernel" refers to a collection of mathematical functions used in Support Vector Machine to provide a window to alter data.

What is the solution deriving the expression given above?

Given x = [x₁, x₂][tex]^{T}[/tex]

β(x) = [x²₁, √2 x₁ x₂, x²₂]

K (x₁, x') = β(x)[tex]^{T}[/tex] β(x')[tex]^{T}[/tex]

Hence, X' =  [x₁, x₂][tex]^{T}[/tex]

→ β(x') = [x'²₁, √2 x'₁ x'₂, x'²₂]

K (x, x') = [x²₁, √2 x₁ x₂, x²₂][tex]^{T}[/tex]  [x'²₁, √2 x'₁ x'₂, x'²₂]

K (x, x') = [x²₁, [x'²₁ + 2x₁ x₂ x'₁ x'₂ + x²₂ x'²₂

Because Z = x · x' (dot product of x·x')

= x₁ x'₁ + x₂x₂'

Expressing K (x,x') as a function of Z, we have

K (x₁, x') =  x²₁ x'²₁ + 2x₁x₂ x'₁ x'² + x²₂ x'²₂

Simplified, we have

(x₁ x₁¹ + x₂x¹₂)² =  Z²; and

[(a+b)² = a²+2ab+b₂] = z x₁x₁¹ + x₂x₁²

Therefore,

K (x, x¹) = Z²

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