In mathematics, central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data? Explain.

Answers

Answer 1

Variability tells us how spread out the data points are around the center. The smaller the variability, the more clustered the points are to the center. In terms of a bell curve, the smaller the variability, the taller and skinnier it will get where its tallest point is at the center. In contrast, a larger variability makes the distribution curve wider and flatter.

Related Questions

Can you please help me out ?

Answers

45 45 90 triangle
ratio
leg:leg:hypo = x : x : x√2
hypo = 22√2 (x = 22)

so leg = 22

answer
22 units

What you can do for this case is to use the following trigonometric definition.sine (45) = a / h
Where,
a: side of the triangle.
h: hypotenuse.
We then have to clear the value of a:
a = sine (45) * h
Substituting:
a = sine (45) * (22 * root (2))
a = (root (2) / 2) * (22 * root (2))
a = 22
Answer:
22 (option 3)

The ice rink sold 95 tickets for the afternoon skating session, for a total of $828. answer General admission tickets cost $10 each and youth tickets cost $8 each. How many general admission tickets and how many youth tickets were sold?
I think it is 34 general and 61 youth

Answers

i just answered this question few minutes ago
yes, you are right

How do I double the volume of a pyramid

Answers

Any one of ...
1) double the height, or any other single dimension
2) multiply the base edge lengths, or any other pair of dimensions, by √2
3) multiply every dimension by ∛2
4) multiply the dimensions by any combination of numbers whose product is 2.

Maya added 10 grams of salt to 40 grams of water.
She made ___ grams of ___% solution.

Please help
*show work*

Answers

Answers:
She made __50__ grams of __20__% solution

-------------------------------------------------------------------

Work Shown:

There's 10+40 = 50 grams of stuff overall (that "stuff" being salt and water). Of this total, 10 grams are salt so 10/50 = 1/5 = 0.20 = 20% is salt. Therefore this is a 20% salt solution.

We can say "20% solution" or "20% salt solution" to be more specific of what kind of chemical mix it is.

Answers:

She made __50__ grams of __20__% solution

-------------------------------------------------------------------

Work Shown:

There's 10+40 = 50 grams of stuff overall (that "stuff" being salt and water). Of this total, 10 grams are salt so 10/50 = 1/5 = 0.20 = 20% is salt. Therefore this is a 20% salt solution.

We can say "20% solution" or "20% salt solution" to be more specific of what kind of chemical mix it is.

a rectangle is 1/3 yards long and 2/3 yards wide.

what is the area of the rectangle?

enter your answer in the box as a fraction in simplest form

[tex] \frac{?}{?} \: {yd}^{2} [/tex]

Answers

Area of a rectangle is the product of its length and width. So,

Area = Length x Width

Length of rectangle = 1/3 yards
Width of rectangle = 2/3 yards

So, the area A of the rectangle will be:

[tex]A = \frac{1}{3}* \frac{2}{3} = \frac{2}{9} [/tex]

So, the Area of rectangle will be [tex] \frac{2}{9} [/tex] square yards.

Final answer:

The area of a rectangle with dimensions of 1/3 yards by 2/3 yards is calculated using the formula length × width, resulting in an area of 2/9 square yards. This value is already in simplest form.

Explanation:

The question asks us to find the area of a rectangle that is 1/3 yards long and 2/3 yards wide. The formula to calculate the area of a rectangle is length × width. Therefore, to find the area, we multiply 1/3 yards by 2/3 yards.

Area = (1/3) yd × (2/3) yd = 2/9 yd²

This calculation shows that the area of the rectangle is 2/9 square yards. It is important to express the answer in simplest form, as the question requests, and 2/9 is already in its simplest form.

alvin's age is two times elga's the sum of their ages is 87 what is elga's age?

Answers

Hey there! :D

87= 2x+x <== let x equal Elga's age.

Since Alvin's is 2 times Elga's, then you can represent that by 2x. They add up to 87.

87= 2x+x

87= 3x

Divide both sides by 3.

x=29

Elga is 29.

I hope this helps!
~kaikers

Final answer:

By forming an algebraic equation based on the given information, we find that Elga's age is 29 years.

Explanation:

This question belongs to the category of Algebraic equations. We know that Alvin's age is two times Elga's, so we could represent Alvin's age as 2E, where E represents Elga's age.

The problem also tells us that the sum of their ages equals 87. That means we can form this equation: E + 2E = 87.

Combining like terms, we get 3E = 87. Finally, dividing each side by 3, we find the value of E (Elga's age).

So, Elga's age is 87 / 3, which equals 29 years.

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For each pair of numbers, tell: By what percent of the first number is the second number larger? By what percent of the second number is the first number smaller? 15 and 20

Answers

The answer for the first question is 33.33%.
Reason: The second number (20) is larger than the first number (15) by 5 and 5 is 33.33% the first number.
.
The answer for the second question is 25%, also.
Reason: The first number (15) is smaller than the second number (20) by 5 and it is 25 percent of the second number.
:)

By using a rule of 3, we will see that:

The second number is 33.33% larger than the first one.The first number is 25% smaller than the second one.

How to find the percentages?

In the first case, we want to know by what percent of the first number is the second larger.

Then the 100% will be taken as the first number, so we have the relation:

100% = 15

And the other number will represent a percentage X, so we write:

X = 20

By taking the quotient of these two equations, we get:

X/(100%) = 20/15

Solving this for X, we get:

X = (20/15)*100% = 133.33%

We can conclude that the second number is 33.33% larger than the first number.

For the second part, we take 20 as our 100%, and we do the same thing:

X = (15/20)*100% = 75%

Then 15 is (100% - 75% = 25%) 25% smaller than 20.

As you can see the percentages are different. Why does this happen? because in each case the 100% represents a different number.

Finally, we can conclude that:

The second number is 33.33% larger than the first one.The first number is 25% smaller than the second one.

If you want to learn more about percentages, you can read:

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122% in simplest form

Answers

For this case we have the following decimal expression:
122%
To write it in a simple numerical value, we must divide the given value by 100.
We have then:
[tex](122/100) [/tex]
Simplifying we have:
[tex]61/50 [/tex]
In decimal form we have:
1.22
Answer:
Two options:
1) as a decimal: 1.22
2) as a fraction: 61/50
Both answers are equivalent.

Answer: The simplest form of 122% is [tex]\frac{61}{50}[/tex] in fraction and [tex]1.22[/tex] in decimal.

Step-by-step explanation:

We know that to simplify percentage into fractions or decimals, we need to divide it by 100.

The percent value = 122%

Therefore , to simplify it into the simplest form we divide it by 100, we get

[tex]122\%=\frac{122}{100}=\frac{61}{50}[/tex]

In decimal , [tex]122\%=\frac{122}{100}=1.22[/tex]

Hence, the simplest form of 122% is [tex]\frac{61}{50}[/tex] in fraction and [tex]1.22[/tex] in decimal.

The size of a laptop monitor is usually measured along the diagonal. A rectangular monitor is 12 inches long and 7 inches tall. What is the length of the diagonal of this monitor, to the nearest tenth of an inch? Enter your answer, as a decimal, in the box.

Answers

14.

a^2 + b^2 = c^2
12^2 + 7^2 = c^2
144 + 49 =c^2
193 = c^2
c= 13.89
14

The length of the diagonal of this monitor, to the nearest tenth of an inch, would be 14.

What is Pythagoras Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

The size of a laptop monitor is usually measured along the diagonal. A rectangular monitor is 12 inches long and 7 inches tall.

[tex]a^2 + b^2 = c^2\\12^2 + 7^2 = c^2\\144 + 49 =c^2\\193 = c^2\\c= 13.89 14[/tex]

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Write an expression using variables for the sum of two consecutive numbers

Answers

Let the first consecutive number = n
Then the second one will be n+1
The sum will be n + n+1 = 2n + 1

Question is 2n + 1 always odd or always even?

The answer is always odd.

Quadrilateral ABCD is inscribed in this circle.

What is the measure of ∠A ?

Enter your answer in the box.

____°

Answers

Answer:

Measure of ∠A is 106°

Step-by-step explanation:

We are given that, 'Quadrilateral ABCD is inscribed in the circle'.

So, we get that,

'ABCD is a cyclic quadrilateral' i.e. The sum of the opposite interior angles is 180°.

Thus, we have,

∠A +∠C = 180°

i.e. ∠A + 74° = 180°

i.e. ∠A = 180° - 74°

i.e. ∠A = 106°

Thus, the measure of ∠A is 106°.

What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.

Answers

Given x^4+95x^2-500=0
set u=x^2, and substitute
u^2+95u-500=0

Since -5*100=-500, and -5+100=95, we factor equation as
(u-5)(u+100)=0
=> u=5 or u=-100
Back-substitute,
u=5 => x= &pm; √ 5
u=-100 => x= &pm; 10i (if you work with complex roots)

So
answer: the real roots of given equation are &pm; √ 5
the complext roots are: x= &pm; 10i

Using factorization, the factors of the given equation are; ±√5 and ±10i.

What is Factorization?

In mathematics, factorization or factoring consists of writing a number or any mathematical item as a product of several factors, typically small or easier objects of the same.

we have been given the equation:

x⁴ + 95x² – 500 = 0

Factorizing the above equation,

x⁴ + 100x² - 5x² - 500 = 0

x²(x² + 100) - 5(x² + 100) = 0

(x² - 5)(x² + 100) = 0

Solving further:

x² = 5

x² = -100

x = ±√5

x = √-100

Factors : ±√5 and ±10i

Therefore, we know that the factors of the given equation are; ±√5 and ±10i.

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3/10n = 4/5

what value of n will make this equation correct?

Answers

Answer:

the answer is 2 and 2/3 if that doesn't pop up then 8/3 also works.

Step-by-step explanation:

Which of the following is a perfect square?
A. 127
B. 100
C. 13
D. 102

Answers

A perfect square is in the form x^2

We can find the perfect square by taking the square root of each number. The number that reduces to a whole number when the square root is taken is your answer.

sqrt(100) = 10 so B. 100 is your answer.

The answer is B all of the perfect squares are1, 4, 9, 16, 25, 36, 49, 64, 81, 100

you are starting your own small business in Albuquerque. you borrow $10,000 from a bank at 9% rate for 5 years find the interest you will pay on this loan

Answers

A=P
10,000(1+0.09.5) = 14,500
=$4,500 interest

I will have to pay $4500 interest for the loan I have taken to start a small business.

What is simple interest?

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, P = $10,000, r = 9% and t = 5.

∴ SI = (10000×9×5)/100.

SI = 100×45.

SI = 4500.

So, I need to pay $4500 for the loan.

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A: 2x + 8y = 5 B: x + 9y = 10 To solve this system of equations by elimination, what could you multiply equation B by if you want to add the equations together and have a resulting equation with only the y-variable (the x-variable is eliminated)?

Answers

Ans: multiply by -2

A: 2x + 8y = 5
B: x + 9y = 10
B x (-2) : -2x - 18y = -20

A + B:
8y - 18y = 5 - 20
- 10y = -15
y = 1.5

To solve for x
B: x + 9y = 10
x + 9(1.5) = 10
x + 13.5 = 10
x = 10 - 13.5
x = -3.5

A: 2x + 8y = 5
B: x + 9y = 10

You can multiply equation B by -2 to be able to eliminate the x variable in both equations when you add them together.
B) -2(x + 9y)= 10
-2x - 18y= -20

Add both equations together:
2x + 8y = 5
+(-2x - 18y= -20 )
the x variable is eliminated
-10y= -15
divide both sides by -10
y= -15/-10
y= 1 1/2

Solve for x:
x + 9y= 10
x + 9(1 1/2)= 10
x + 13.5= 10
x= -3.5

ANSWER: multiply equation B by -2

Hope this helps! :)

What is the length of YX¯¯¯¯¯¯? Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth. m_https://static.k12.com/nextgen_media/assets/8107298-NG_GMT_SemB_10_UT_06.png'

Answers

1. You can solve this problem by applying the Tangent Secant Theorem. Then, you have:

YX²=(YZ)(YV)
YX=√(YZ)(YV)

YZ=9+19
YV=9

2. When you substitute the values of YZ and YV into YX=√(YZ)(YV), you obtain:

YX=√(YZ)(YV)
YX=√(9+19)(9)
YX=√(28)(9)
YX=√252
YX=15.87

What is the length of YX?

The answer is: The lenght of YX is 15.87

Final answer:

To find the actual length represented by YX, we set up a proportion using the given scale length and solve for the unknown length x. Using one of the provided scale ratios, such as 0.5 inches representing 2000 miles, we perform cross-multiplication to solve for x and determine the accurate length after calculations.

Explanation:

The student is asked to find the actual length represented by the segment YX on a map or a diagram when given a scale length. To solve the problem, we set up a proportion based on the scale provided and solve for the unknown length x. There are different given scales in the prompts such as 0.5 inches representing 2000 miles, 8 inches representing an unknown number of miles, and 3 inches also representing an unknown number of miles.

Example with a Scale Ratio of 0.5 inches to 2000 miles

To solve for x when the scale is 0.5 inches on the map corresponds to 2000 miles in reality, we use a proportion: 1 inch/2000 miles = 0.5 inches/x miles. After cross-multiplication, we get x = 0.5 inches * 2000 miles, which after calculation will give us the value of x rounded to the nearest hundredth.

Example with a Scale Ratio of 0.25 inches to 2000 miles

Similar steps are taken if the scale is 0.25 inches. We set up the proportion 1 inch/2000 miles = 0.25 inches/x miles and solve for x after cross-multiplication.

what is the radius and center of this circle?
[tex] {x}^{2} + {y}^{2} + 2x - 4y - 2 = 0[/tex]

Answers

the center is (-1,2)
the radius is
[tex] \sqrt{7} \: or \: 2.646[/tex]

PLEASE HELP BABES!!

Heather is trying to decide what classes to take next year. She must take one of each and can choose from 3 math classes, 2 science classes, 4 history classes, and 3 English classes. How many different schedules can she have?
A) 4
B) 12
C) 48
D) 72

Answers

d)72 is the answer. It might also be c)48 but im not sure.

It took the race car 22 minutes to travel 114.4 kilometers. At what rate did the car travel?Use the formula r = d/t, where r is the rate, d is the distance, and t is the time. Round your answer to the nearest tenth.

Answers

D=114.4 kilometers
T=22 minutes

R= 114.4 km /22 min
R= 5.2 km/min

3(p+8) = -6 ( p + 6 )

Answers

The answer is

P= -20
-----
3

Hope this helps:)

*GilmoreGirl01*

What is the general term for the sequence 1, 6, 11, 16

Answers

[tex]a_1=1 \\ d=a_2-a_1=6-1=5 \\ \\ a_n=a_1+d(n-1) \\ {} \ \ \ =1+5(n-1)\\ {} \ \ \ =1+5n-5\\ {} \ \ \ =5n-4[/tex]

The general term of the sequence is an = 5n - 4

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 5 to the previous term in the sequence gives the next term.

The functions f and g are defined as follows f(x)=5x+3/6x+7 and g(x)= square root sign x^2-4x

find f(6/x) and g(x-4)

Answers

f(x)=5x+3/6x+7

This means that f(6/x) = [5(6/x)+3] / [6(6/x)+7] = [ 30/x +3 ] / [36/x +7]

If we assume x≠0 , f(6/x) = [30 +3x]/ [36 + 7x]

g(x)=√ [ x^2-4x ]

g(x-4) = √ [ (x-4)^2-4(x-4) ] = √ [ x² -8x +16 -4x +16 ] = √ [ x^2-12x +32]

I am an odd number. I am less than 100. The sum of my fights is 12. I am a multiple of 15. What number am I?

Answers

Try this option:
1. Odd numbers, which are multiple of 15 and less then 100, are: 15, 45 and 75.
2. the sums of digits are: for 15 is 6, for 45 is 9, for 75 is 12.
3. this number is 75.

David and Josh are both practicing for an upcoming swim tournament. Every week, David swims for 3x hours at an average speed of x laps per hour. Josh swims 5 more hours per week than David, but at an average speed that is 4 laps per hour less than David's average speed.

Which of the following functions will give the total distance, in laps, that Josh swims each week?

Answers

Answer: 3x^2 - 7x - 20

Explanation:

This questions has 4 answer choices to select the right one.

These are the answer choices:

A) f(x) = 3x^2 - 17x + 20
B) f(x) = 3x^2 + 7x - 20
C) f(x) = 3x^2 - 7x - 20
D) f(x) = 3x^2 + 17x + 20

Solution:

Translate the given word statements into algebraic expressions:

1) Every week, David swims for 3x hours at an average speed of x laps per hour =>

time = 3x
speed = x

2) Josh swims 5 more hours per week than David =>

time = 5 + 3x

speed that is 4 laps per hour less than David's average speed =>

speed = x - 4

3) distance, in laps, that Josh swims each week, equal time * speed

=> distance = (3x + 5) (x - 4)

4) Expand the parenthesis:

a) distributive property: (3x)(x) + (3x)(-4) + 5(x) + 5(-4) = 3x^2 - 12x + 5x - 20 =

= 3x^2 - 7x - 20

Answer: 3x^2 - 7x - 20 (option C)

Among 81678167 cases of heart pacemaker malfunctions, 457457 were found to be caused by firmware, which is software programmed into the device. if the firmware is tested in 33 different pacemakers randomly selected from this batch of 81678167 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? is this procedure likely to result in the entire batch being

Answers

(Note: This seems when question was pasted from its source the in text box, the numbers were pasted twice. Solving the question considering only one occurence of number i.e using 8167 instead of 81678167. However, method will be same regardless of the numbers listed)

Part a)
Total number of cases = 8167
Number of Malfunctions due to firmware = 457

Probability that a malfunction is because of firmware = [tex] \frac{457}{8167}[/tex]

Probability that the malfunction is not because of firmware = 1 - Probability that a malfunction is because of firmware = [tex]1- \frac{457}{8167}= \frac{7710}{8167} [/tex]

Probability of selecting 3 pacemakers without a malfunction because of firmware = [tex] ( \frac{7710}{8167} )^{3} = 0.841[/tex]

Part b)
The probability of selecting 3 pacemakers without any malfunction because of firmware is 0.841, which is a high probability. So we can say, yes this procedure is very likely to result in entire batch being accepted. The probability near 1 is considered a very higher probability for an event and the probability near 0 is considered a very lower probability for an event.

ordered: 0.5 mg
Available: 2 mg/ml
how many mls should be given?

Answers

2 mg per 1 ml. divide everything by 4 to give you 0.5 mg / 0.25 ml

Final answer:

The patient should be given 0.25 mls of the medication.

Explanation:

To calculate the volume of medication a patient should be given, we can use a basic formula that relates the ordered dose, the concentration of the medication available, and the volume required to deliver the ordered dose. In this case, the student has been asked to determine how many milliliters (mls) of medication to administer when 0.5 mg is ordered and the medication concentration available is 2 mg/ml.

The formula to use is:

Dose ordered (mg) / Concentration of medication (mg/ml) = Volume to administer (ml)

So for this problem:

0.5 mg / 2 mg/ml = 0.25 ml

Therefore, the patient should be given 0.25 mls of the medication.

The total land area of the United stated is about 3483511 square miles more than the total land area of Tennessee, which is about 53927 square miles. Write and solve an equation to find the total land area of the United stayed.

Answers

Let us denote the total land area of Tennessee by [tex] T [/tex].

Now, It has been given to us that the total land area of Tennessee is about 53927 square miles.

Therefore, [tex] T=53927 [/tex]

It has also been given to us that the total land area of the United States is about 3483511 square miles more than the total land area of Tennessee.

Let us denote the total land area of the United States by [tex] U [/tex].

Now, if the total land area of the United States (denoted by [tex] U [/tex]) is 3483511 square miles more than the total land area of Tennessee (which is 53927 square miles and is denoted by [tex] T [/tex]), then that means that we have to add 3483511 square miles to the total land area of Tennessee to get the total land area of the United States. This can be written in the equation form as:

[tex] U=3483511+T=3483511+53927=3537438 [/tex]

Thus the total area of the United States is 3537438 square miles.

Final answer:

The total land area of the United States is calculated by adding the land area of Tennessee to the difference given in the question. The equation is US Area = 53,927 + 3,483,511. Solving this equation, the total land area of the United States is approximately 3,537,438 square miles.

Explanation:

To find the total land area of the United States, we can use the given information and set up an equation. The total land area of Tennessee is about 53,927 square miles. The question states that the total land area of the United States is about 3,483,511 square miles more than Tennessee's land area. We can express this relationship with the following equation:

Total land area of the United States = Land area of Tennessee + 3,483,511 square miles

US Area = 53,927 + 3,483,511

Solving for the total land area of the United States:

US Area = 3,537,438 square miles

Therefore, the total land area of the United States is approximately 3,537,438 square miles.

Find a1 for the arithmetic series with s20 = 80 And d = 2

Answers

we know that
the formula of the arithmetic series is
Sn=n[2(a1) + (n - 1)d]/2
where
Sn=80
n=20
d=2
a1=?
then
80=20*[2*a1+19*2]/2----------------> 160=[40*a1+760]
160=[40*a1+760]----------> a1=(160-760)/40------------> a1=-15

the answer is
a1=-15

To solve this, we are going to use the standard formula for arithmetic series [tex]S _{n} = \frac{n}{2} [2a_{1} +(n-1)d][/tex]
where:
[tex]S_{n} [/tex] is the sum of the arithmetic sequence
[tex]n[/tex] is the number of terms
[tex]d[/tex] is the difference
[tex]a_{1} [/tex] is the first term
From our problem we know that [tex]S_{n} =80[/tex], [tex]n=20[/tex], and [tex]d=2[/tex]. Lets replace those values in our formula to find [tex]a_{1} [/tex]:
[tex]80= \frac{20}{2} [2a_{1} +(20-1)2][/tex]
[tex]80=10(2a_{1} +38)[/tex]
[tex]80=20a_{1} +380[/tex]
[tex]20a_{1} =-300[/tex]
[tex]a_{1} = \frac{-300}{20} [/tex]
[tex]a_{1} =-15[/tex]

We can conclude that the first term [tex]a_{1} [/tex] of the arithmetic series is [tex]-15[/tex]

Which of the following statements is true about lines 3y + 2x - 9 = 0 and 12y + 8x - 5 = 0? They are parallel They are perpendicular They are parallel to the x-axis They are parallel to the y-axis

Answers

i think c is the answer

Answer:

The statement "They are parallel" is true.

Step-by-step explanation:

The general form of the equation of a straight line is:

[tex]Ax+By+C=0[/tex]

where A, B, and C are three real numbers.

A line parallel to the x-axis has this form [tex]y=C[/tex] where C is a real number.

A line parallel to the y-axis has this form [tex]x=C[/tex] where C is a real number.

From the lines given none of these have the form of a line parallel to the x-axis or the y-axis. Therefore the statements "They are parallel to the x-axis" and "They are parallel to the y-axis" are false.

Two non-vertical lines in a plane are parallel if they have both:

the same slopedifferent y-intercepts

Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other.

To check if the lines are parallel of perpendicular you must transform these lines into the slope/intercept form

[tex]y=mx+b[/tex]

where m represents the slope and b represents the y-intercept.

The slope/intercept form for the first line is:

[tex]3y+2x-9=0\\\\3y+2x-9-2x=0-2x\\\\3y-9=-2x\\\\3y-9+9=-2x+9\\\\3y=-2x+9\\\\y=\frac{-2x+9}{3}\\\\y=\frac{-2}{3}x+3[/tex]

The slope/intercept form for the second line is:

[tex]12y+8x-5=0\\\\12y+8x-5-8x=0-8x\\\\12y-5=-8x\\\\12y-5+5=-8x+5\\\\12y=-8x+5\\\\y=\frac{-8x+5}{12}\\\\y=\frac{-2}{3}x+\frac{5}{12}[/tex]

We can see that the lines have the same slope and different y-intercepts. Therefore the statement "They are parallel" is true.

We can check our work with the graph of the lines.

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