VARIABILITY
Variability (also called spread or dispersion) refers to how spread out a set of data is. Variability gives you a way to describe how much data sets vary and allows you to use statistics to compare your data to other sets of data.
The variability can be analyzed using the range. The range is the amount between your smallest and largest item in the set. You can find the range by subtracting the smallest number from the largest.
Range of Quiz 1
Highest score: 91
Lowest score: 70
Therefore, the range is:
\(R=91-70=21\)Range of Quiz 2
Highest score: 96
Lowest score: 75
Therefore, the range is:
\(R=96-75=21\)Therefore, the variability of both quizzes is the same.
MEAN
The mean is a measure of central tendency of a probability distribution along median and mode. It is also referred to as an expected value.
It can be calculated as the total sum of all values in a collection of numbers divided by the number of numbers in a collection. Therefore, the formula is:
\(Mean=\frac{\text{Sum of numbers}}{Number\text{ of numbers}}\)Mean of Quiz 1
\(M=\frac{70+91+85+87+73+74+77+83}{8}=\frac{640}{8}=80\)Mean of Quiz 2
\(M=\frac{75+82+78+96+92+79+90+88}{8}=\frac{680}{8}=85\)Therefore, the mean of Quiz 2 is greater than that for Quiz 1.
ANSWER
The correct option is OPTION C: The mean of Quiz 2 scores is greater than the mean of Quiz 1 scores, but the variability is the same.
40% of the problems is 32 problems.
Answer:
80
Step-by-step explanation:
Change 40% to a decimal by moving the decimal 2 places left or divide 40 by 100. Write an equation.
\(.4p = 32\)
divide both sides by .4
\(p = 80\)
6 divided by 7215 and i need help its to hard????
Answer:
If you mean 6 / 7215 it is 0.00083
but if you meant 7215 / 6 it is 1202.5
Step-by-step explanation:
Could use help on this thank you in advance!
Answer:
what exactly do i need to do ?????
Step-by-step explanation:
Problem
Circles \(K\) and \(L\) touch externally at point \(P\). Line \(ABC\) cuts \(K\) at points \(A\) and \(B\) and is tangent to \(L\) at \(C\). The line through \(A\) and \(P\) meets \(L\) at a second point \(D\).
Prove that \(PC\) bisects angle \(BPD\).
Step-by-step explanation:
Using the various theorems relating inscribed and external angles to intercepted arcs, we can write the following relations:
angle A = 1/2(arc BP) . . . . . . . . . . . inscribed angle
angle A = 1/2(arc CD -arc CP) . . . external angle at tangent/secant
angle CPD = 1/2(arc CD) . . . . . . . inscribed angle
angle CPB = 1/2(arc CP) + 1/2(arc BP) . . . . . sum of angles at the mutual tangent
ProofEquating the expressions for angle A, we have ...
1/2(arc BP) = 1/2(arc CD -arc CP)
Adding arc CP gives ...
1/2(arc BP +arc CP) = 1/2(arc CD)
Substituting the last two equations for angles from above, this gives ...
angle CPB = angle CPD
Hence PC bisects angle BPD.
Please Solve
F/Z=T for Z
Answer:
F /T = Z
Step-by-step explanation:
F/Z=T
Multiply each side by Z
F/Z *Z=T*Z
F = ZT
Divide each side by T
F /T = ZT/T
F /T = Z
Answer:
\(\boxed{\red{ z = \frac{f}{t} }}\)
Step-by-step explanation:
\( \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} \)
What is -20/2(7 2/3)
The simplified form of -20/2(7 2/3) is -230/3.
To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.
First, let's convert the mixed number 7 2/3 to an improper fraction.
7 2/3 = (7 * 3 + 2) / 3 = 23/3
Now, let's substitute the value back into the expression:
-20/2 * (23/3)
Next, we simplify the multiplication:
-10 * (23/3)
To multiply a fraction by a whole number, we multiply the numerator by the whole number:
-10 * 23 / 3
Now, we perform the multiplication:
-230 / 3
Therefore, the simplified form of -20/2(7 2/3) is -230/3.
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From a group of 6 people, you randomly select 3 of them. What is the probability that they are the 3 oldest people in the group
Answer:
\(Probability = \frac{1}{20}\)
Step-by-step explanation:
Given
\(People = 6\)
\(Selection = 3\)
Required
Determine the probability of selecting the oldest 3
First, we need to determine the total possible selection.
Since it's a selection, we make use of combination as follows:
\(^nC_r = \frac{n!}{(n-r)!r!}\)
In this case:
\(n = 6\)
\(r = 3\)
So:
\(^nC_r = \frac{n!}{(n-r)!r!}\)
\(^6C_3 = \frac{6!}{(6-3)!3!}\)
\(^6C_3 = \frac{6!}{3!3!}\)
\(^6C_3 = \frac{6*5*4*3!}{3!3*2*1}\)
\(^6C_3 = \frac{6*5*4}{3*2*1}\)
\(^6C_3 = \frac{5*4}{1}\)
\(^6C_3 = 20\)
In the combination, there can be only 1 set of oldest people.
So:
\(Probability = \frac{1}{20}\)
-1/4 plus 3/5
Answer or else
The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.
To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.
The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:
-1/4 = -5/20
3/5 = 12/20
Now that the fractions have the same denominator, we can add them:
-5/20 + 12/20 = (-5 + 12)/20 = 7/20
Therefore, -1/4 + 3/5 is equal to 7/20.
To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.
Thus, the final answer is 7/20.
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Compare the best estimate for 1.789/178 and 0.05. Which is less?
Answer:
The smaller number in 0.01
Step-by-step explanation:
To find this answer, just take the fraction and find the quotient of both numbers.
1.789/178 = 0.01005056179
Now take the quotient and compare it to 0.05.
Is 0.01 larger or 0.05 - the answer is 0.01.
Please help me out
Find the height of the pyramid using the given diagram.
?? Inches
Check the picture below.
Find the measure of each angle of the quadrilateral.
all work should be in the picture, lmk if theres anything confusing
If 25% of a number is 100, what is the number?
OA. 50
OB.
100
O c.
150
OD.
200
O E.
400
Answer:
400
Step-by-step explanation:
25% is a fourth 100 ×4 is 400
Which is equivalent to V180x11 after it has been simplified completely?
© 3x10653
O 3x® v5x
O 6x10/5x
O 6x55x
Question:
Which is equivalent to \(\sqrt{180x^{11}}\) after it has been simplified completely?
Answer:
\(\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}\)
Step-by-step explanation:
Given
\(\sqrt{180x^{11}}\)
Required
Simplify
We start by splitting the square root
\(\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}\)
Replace 180 with 36 * 5
\(\sqrt{180x^{11}} = \sqrt{36 * 5} * \sqrt{x^{11}}\)
Further split the square roots
\(\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} * \sqrt{x^{11}}\)
\(\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{11}}\)
Replace power of x; 11 with 10 + 1
\(\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10 + 1}}\)
From laws of indices; \(a^{m+n} = a^m * a^n\)
So, we have
\(\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x^1}\)
\(\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x}\)
Further split the square roots
\(\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10}} * \sqrt{x}\)
From laws of indices; \(\sqrt{a} = a^{\frac{1}{2}}\)
So, we have
\(\sqrt{180x^{11}} = 6*\sqrt{5} * x^{10*\frac{1}{2}} * \sqrt{x}\)
\(\sqrt{180x^{11}} = 6*\sqrt{5} * x^{\frac{10}{2}} * \sqrt{x}\)
\(\sqrt{180x^{11}} = 6*\sqrt{5} * x^{5} * \sqrt{x}\)
Rearrange Expression
\(\sqrt{180x^{11}} = 6 * x^{5} * \sqrt{5} * \sqrt{x}\)
\(\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}\)
From laws of indices; \(\sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}\)
So, we have
\(\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}\)
\(\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}\)
\(\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}\)
The expression can no longer be simplified
Hence, \(\sqrt{180x^{11}}\) is equivalent to \(6x^{5}\sqrt{5x}\)
Answer:
D on edg
Step-by-step explanation:
6x^5 V5x is correct
Find the area of this circle
Answer:113.04ft^2
Step-by-step explanation:
6. What is the area of a rectangular floor that is 7-3" long
and 4-2” wide?
The area of the rectangle will be 4350 Inches squared.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that a rectangular floor is 7-3" long and 4-2” wide. Here 7 ft 3 in = 87 in. 4ft 2 in = 50 in.
The area of the rectangle is calculated by using the formula below:-
Area = Length x Width
Area = 87 x 50
Area = 4350 Inches
Therefore, the area of the rectangle will be 4350 Inches squared.
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JFDKGJNREITFHROIHTJFMNORHCTGJK,MV JIOKVMNTRH HTR OIMTGR
The multiples of 5 and 6 based on the information have been illustrated below.
How to illustrate the multiple?It should be noted that a multiple is a number that can be divided by another number without a remainder.
Here, the multiples of 5 will be:
5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
In this case, the multiples of the numbers have been illustrated.
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Use the system of equations and graphs below to complete the sentence.
Answer:
id say graph d solve it out and thats the only thing i got close to
Step-by-step explanation:
Answer:
it's the one in the top right(graph B), the soultion to graph b is (3,-1)
Step-by-step explanation:
Like the other answer says you solve it out, then you look at the intercepts and use the prosses of elimanation.
the top equation is: y= -1/2x -2.5
the bottom equation is: y= -1/5x -0.4
fill in the mission numbers to make the fractions equivalent. 1/2 and /8= 4/12 and /60= 2/3 and /12= 4/4 and /8=
To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:
1/2 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
1/2 and 4/8
Now, the fractions are equivalent.
---
4/12 and __/60
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:
4/12 and 20/60
Now, the fractions are equivalent.
---
2/3 and __/12
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
2/3 and 8/12
Now, the fractions are equivalent.
---
4/4 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:
4/4 and 8/8
Now, the fractions are equivalent.
What is the answer pleaseee
Answer: 803.84cm3
Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.
To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.
4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.
Now, we have the area of the circle. 50.24cm squared!
The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,
16cm x 50.24cm squared = 803.84cm cubed.
The volume of the can of soup is 803.84cm cubed.
If 3 3/4m of cloth was used for one suit, how many suits can be made with 30m cloth
Answer:
8 suits
Step-by-step explanation:
Divide 30 m by 3 \(\frac{3}{4}\) m , or 30 ÷ 3.75 , then
30 ÷ 3.75 = 8
Then 8 suits can be made from 30 m of cloth
Which two equations can you use to find the adult and child admission fees for a puppet show? Let a represent the fee for adults and c represent the fee for children.
Adults Children Admissions Collected
Day 1
45
30
$315
Day 2
50
40
$370
45c + 30a = 315
45a + 50c = 315
45a + 30c = 315
50c + 40a = 370
50a + 40c = 370
Step-by-step explanation:
45a + 30c = 315
50c + 40a = 370
Answer:
C 45a + 30c = 315
E 50c + 40a = 370
Step-by-step explanation:
give me my Volkswagen Golf GTI 89'
When sales of a particular hybrid automobile reach 60,000 units, federal income tax credits begin to phase out. One year after
reaching this threshold, buyers are still eligible for 15% of the original $2500 credit. What tax credit would buyers receive if they
purchased the vehicle at this time?
(Type a whole number or a decimal)
Answer:
The original tax credit was $2500, so 15% of that is:
0.15 x $2500 = $375
Therefore, buyers would receive a $375 tax credit if they purchased the vehicle one year after the sales reached the 60,000 unit threshold.
If random variable X has a binomial distribution with n=15 and P(success) =p= 0.6, find the mean of X. That is, find E(X). Round to the whole number. Do not use decimals. Answer:
Answer:
9
Step-by-step explanation:
E(X) = np
E(X) = (15) (0.6)
E(X) = 9
The mean of the X is 9.
What is the mean of the binomial distribution?The mean of a binomial distribution is the expected value (long-run average) of the number of successes in the given number of trials.
Formula for calculating mean of binomial distribution\(\mu_{x} = n.p\)
where,
\(\mu_{x}\) is the mean of the binomial distribution
n is the number of trials
and, p is the probability of success
According to the given question.
We have
Number of trials, n = 15
Probability of success, p = 0.6
Therefore, the mean of X is given by
\(E(X) = 15(0.6)\)
⇒ \(E(X) = 9\)
Hence, the mean of the X is 9.
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Desmond is 5 inches taller than Niki.
If we let
represent Niki's height in inches, write an algebraic expression for Desmond's height.
The algebraic expression for Desmond's height is x + 5.
write an algebraic expression for Desmond's height.If we let "x" represent Niki's height in inches, then Desmond's height can be represented by "x + 5", since Desmond is 5 inches taller than Niki.
So the algebraic expression for Desmond's height is x + 5.
What are algebraic expression?Algebraic expressions is consist of variables, numbers, and mathematical operations (such as addition, subtraction, multiplication, and division).
They can contain one or more variables and can be evaluated for different values of the variables.
For example, the expression 3x + 5y - 2z is an algebraic expression that contains three variables (x, y, and z) and three coefficients (3, 5, and -2) that are multiplied by those variables. Algebraic expressions are commonly used in algebra to represent mathematical relationships and solve problems.
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Graphs of a function and its inverse are shown on the same coordinate grid.
Which statements accurately compare the function and its inverse? Check all that apply.
The domains of the two functions extend to positive infinity.
The ranges of the two functions are all real numbers.
The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.
The point of intersection of the two functions indicates that the functions are inverses.
Neither function has a minimum.
The correct statements are;
The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.
The point of intersection of the two functions indicates that the functions are inverses.
Option C and D
How to determine the correct statementsTo accurately compare a function and its inverse based on the graphs, we have to know the following;
The domains of the two functions extend to positive infinity if the domain of the inverse function is equivalent to the range of the original function.The ranges of the two functions are all real numbers if the graphs cover the entire y-axis without any gaps or discontinuities.If the graphs intersect at the point (a, b), it means that f(a) = b and f^(-1)(b) = a, indicating that the functions are inverses of each other.
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3h=-8 solve equation
Answer:
h= -2.6
Step-by-step explanation:
Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales orice Zion Sun
Chairs must sell each chair for to earn a monthly profit of $65,000, if of the total monthly fixed costs are $17,363.50
and the variable cost per chair is $52.17.
• $71.49
• $75.21
O $23.04
O $25.67
Zion Sun Chairs must sell each chair for at least $75.21 to earn a monthly profit of $65,000.
To determine the minimum sales priceTo determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of $65,000, we can use the following formula:
Total Profit = Total Revenue - Total Cost
We know that the monthly fixed costs are $17,363.50, and the variable cost per chair is $52.17. Therefore, the total cost to produce 3,575 beach chairs each month can be calculated as follows:
Total Cost = Fixed Cost + (Variable Cost per Chair x Number of Chairs)
Total Cost = $17,363.50 + ($52.17 x 3,575)
Total Cost = $203,871.25
To earn a monthly profit of $65,000, we can set up the equation as follows:
$65,000 = Total Revenue - $203,871.25
Total Revenue =$268,871.25
To find the minimum sales price per chair, we can divide the total revenue by the number of chairs:
Minimum Sales Price per Chair = Total Revenue / Number of Chairs
Minimum Sales Price per Chair = $268,871.25 / 3,575
Minimum Sales Price per Chair ≈ $75.208
Therefore, Zion Sun Chairs must sell each chair for at least$75.21 to earn a monthly profit of $65,000, given the monthly fixed costs, variable cost per chair, and production quantity.
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what is a negative minus a negative
Answer:
It would be a negative or positive depending on the situation.
Step-by-step explanation:
A negative minus a negative would result in either a positive or negative. For example, -8 - (-9) would be 1 while -8 - (-7) would be -1. If the negative number your subtracting is greater than the number you're subtracting from then it will be positive, vice versa.
Find the distance between (-2, 6) and (1, 3).
Answer:
3√2
Step-by-step explanation:
Distance (d) = \(\sqrt{((1 - -2)^2 + (3 - 6)^2)}\)
= \(\sqrt{((3)^2 + (-3)^2)}\)
= √18
= 3√2
Solve the system of equations by the addition method.−2x−y=0 10x+y=−8
Answer:
(-1, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
-2x - y = 0
10x + y = -8
Step 2: Solve for x
Elimination
Combine equations: 8x = -8Isolate x: x = -1Step 3: Solve for y
Define equation: -2x - y = 0Substitute in x: -2(-1) - y = 0Multiply: 2 - y = 0Isolate y term: -y = -2Isolate y: y = 2Answer:
Step-by-step explanation:
-2x -y = 0
10x+ y= -8
8x = -8
x = -1
-10 + y = -8
y = 2
(-1, 2)