a) The range of the given data set is 25.
b) The standard deviation of the given data set is 10.1.
The given data set is 141, 116, 117, 135, 126, 121.
a) The range is the difference between the highest and lowest values within a set of numbers.
Range = Highest value - Lowest value
= 141-116
= 25
So, the range is 25.
b) Set up the formula for sample standard deviation. The standard deviation of a set of values is a measure of the spread of its values.
[tex]s=\sqrt{\frac{(x_i-\bar x)^2}{n-1} }[/tex]
Here, mean ([tex]\bar x[/tex]) = [tex]\frac{141+116+117+135+126+121}{6}[/tex]
= 126
[tex]s=\sqrt{\frac{(141-126)^2+(116-126)^2+(117-126)^2+(135-126)^2+(126-126)^2+(121-126)^2}{6-1}}[/tex]
[tex]s=\sqrt{\frac{(15^2+(-10)^2+(-9)^2+(9)^2+(0)^2+(-5)^2}{5}}[/tex]
[tex]s=\sqrt{\frac{(225+100+81+81+25)}{5}}[/tex]
[tex]s=\sqrt{\frac{512}{5}}[/tex]
s=10.1
So, the standard deviation is 10.1.
Therefore,
a) The range of the given data set is 25.
b) The standard deviation of the given data set is 10.1.
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Which of the following represents the translation of R (-3, 4) along the vector
<7, -6> and then the vector < -1, 3 >?
Pls help lol
By applying concepts of linear algebra, the point P'(x, y) = (-3, 4) represents the translation of P(x, y) = (-3, 4) along the vectors <7, -6> and <-1, 3>.
How to determine the resulting point by applying translations
Translations are a kind of rigid transformation. A transformation is rigid if and only if Euclidean distances are conserved. By linear algebra, an image as a consequence of consecutive translations is described by the following formula:
[tex]P' (x,y) = P(x,y) + \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)[/tex] (1)
Where:
P(x, y) - Original pointP'(x, y) - Image[tex]\left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)[/tex] - Net translation vectorNow we proceed to determine the image of the given point:
P'(x, y) = (-3, 4) + (7, -6) + (-1, 3)
P'(x, y) = (-3 + 7 - 1, 4 - 6 + 3)
P'(x, y) = (3, 1)
By applying concepts of linear algebra, the point P'(x, y) = (-3, 4) represents the translation of P(x, y) = (-3, 4) along the vectors <7, -6> and <-1, 3>.
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Luca shows his work in finding the solution to 2−6=5−5(−1)
. After checking his answer in the original equation, he found that it did not work. Where did he make a mistake?
Regina graphs the relationship between temperature (in °C) degrees and elevation (in M) in 9 different cities (Shown below).
What is the meaning of point A?
Choose 1 answer:
(Choice A)
A city 6m below sea level is 5° C below zero
(Choice B)
A city 6m above sea level is 5° C below zero
(Choice C)
A city 6m below sea level is 5° C above zero
(Choice D)
A city 6m Above sea level is 5° C above zero
The meaning of point A is (d) A city 6m Above sea level is 5° C above zero
How to determine the meaning of point A?From the complete question, the point A is located as:
A = (5,6)
5 and 6 are positive numbers.
This means that A is located 6m above the sea level and 5° C above zero
Hence, the meaning of point A is (d) A city 6m Above sea level is 5° C above zero
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Answer:
ITS CHIOCE C
Step-by-step explanation:
I GOT IT WRONG ON KHAN ACADMEY BC OF THE FIRST ASNWER, AND FOUND OUT THE ACTUAL ANSWER :D
Find the area of the kite
Answer:
180
Step-by-step explanation:
(10×11)+(10×7)=110+70
The area of the kite is expressed as 1/2 × (Product of its diagonals)
In this case, we have;
Diagonal₁ - 10 + 10 feet = 20 feetDiagonal₂ - 7 + 11 feet = 18 feetTherefore, when we substitute the diagonals in the formula, we get;
⇒ 1/2 × (Product of its diagonals)⇒ 1/2 × (20 × 18)When simplified, we get;
⇒ 1/2 × (20 × 18)⇒ 1/2 × (360)⇒ 360/2 = 180 ft²Therefore, the area of the kite is 180 ft².
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What is the equation of a line that has an x-intercept of 5 and a slope of 4?
Answer:
y=4x-20
Explanation:
Since we already have a slope, all we need to do is just find the y-intercept. To do this we can make an XY t-chart.
Using the chart we can see that for every x that decreases, a y decreases 4 times. So if we subtract 5 from x, we will multiply 5 times y. Note that this graph is increasing so the y-intercept is negative. -5 · 4 = -20
X | Y
6 | 4
5 | 0
0 | -20
Hope this Helps!
Figure 1 is similar to figure 2. What is the height of figure 1?
4x 2x
x+1 x
A.1 Units
B.2 Units
C.8 Units
D.4 Units
The calculated value of the height of figure 1 is (d) 4 units
How to calculate the height of figure 1?from the question, we have the following parameters that can be used in our computation:
The figures
The figure 1 is similar to figure 2
So, we have
4x/(x + 1) = 2x/x
When evaluated, we have
4x = 2x + 2
So, we have
2x = 2
Evaluate
x = 1
This means that
Height = 4 * 1
Evaluate
Height = 4
Hence, the height of figure 1 is 4 units
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what is the area of a cylinder
A cylinder's volume is =
π r² h,
and its surface area is =
2π r h + 2π r².
Envision Math 4th grade topic 16-1
simplify 3^-6*(3^4/3^0)^2
Answer:
Thhe simplified form of the expression is 9
Indices are expressed as power or exponent which is raised to a number or a variable.
According to the law of indices
\begin{gathered}a^n \times a^m = a^{n+m}\\a^n \div a^m = a^{n-m}\end{gathered}
a
n
×a
m
=a
n+m
a
n
÷a
m
=a
n−m
Given the expression
3^{-6} \times (\dfrac{3^4}{3^0} )^23
−6
×(
3
0
3
4
)
2
This can also be expressed as:
\begin{gathered}=\dfrac{1}{3^6} \times (\frac{3^4}{1})^2 \ (3^0 =1)\\= \dfrac{1}{3^6} \times 3^8\\=\dfrac{3^8}{3^6}\\=3^{8-6}\\=3^2\\=9\\\end{gathered}
=
3
6
1
×(
1
3
4
)
2
(3
0
=1)
=
3
6
1
×3
8
=
3
6
3
8
=3
8−6
=3
2
=9
This shows that the simplified form of the expression is 9
Bo's family took a road trip to Niagara Falls. Bo fell asleep 84% of the way through the trip. If the total length of the trip was 600 miles, how many miles had they travelled when Bo fell asleep?
Answer:
504
Step-by-step explanation:
Calculate the length of a diagonal of a square with side each 7cm long
Answer:
[tex]7\sqrt{2} \ cm[/tex]
Step-by-step explanation:
Formula ………………………………………………
The length of a diagonal of a square with side of length “a” is :
[tex]a\sqrt{2}[/tex]
======================================================
Since a = 7 (in our case) then
[tex]\text{the length of the diagonal} =7\sqrt{2}[/tex]
Note : you can also use the Pythagorean theorem.
What does the correlation coefficient of a function tell us about the model?
Answer:
the correlation coefficients is a statistical calculation
that used to examine the relationships between two sets of data.
Step-by-step explanation Hope this helps :)
question 4. evaluate the expression [tex]-6^3[/tex]
Answer:
The answer would be ~30~ because 2*2^3 = 2^4= 16 then 3*6=18 then 16+18-4=30
Hope this helps
Have a great day/night
Answer ~
whenever we see an expression in the form of [tex]x^{n}[/tex] we have to multiply x to itself " n " times !
here in the question ,
we're given with the expression ( - 6³ )
so ,
[tex] - 6 {}^{3} = - 6 \times - 6 \times - 6 \\ \dashrightarrow \: - 216[/tex]
hope helpful ~
Which of the following inequalities matches the graph?
Answer:
6x - y < -3
Step-by-step explanation:
When graphing inequalities:
< or > = dashed line
≤ or ≥ = solid line
< or ≤ = shade below the line
> or ≥ = shade above the line
Create an equation for the line
Choose 2 points on the line:
let (x₁, y₁) = (-1, -3)let (x₂, y₂) = (0, 3)Calculate the slope:
[tex]\sf \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-(-3)}{0-(-1)}=6[/tex]
Determine the equation for the line using the point-slope formula:
[tex]\implies\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-(-3)=6(x-(-1))[/tex]
[tex]\implies \sf y+3=6(x+1)[/tex]
[tex]\implies \sf y=6x+3[/tex]
As the shading is above the line:
⇒ y > 6x + 3
Compare with answer options
Rearrange each answer option to make y the subject:
Option (a)
-6x + y < 3
⇒ y < 6x + 3
Option (b)
6x + y < 3
⇒ y < -6x + 3
Option (c)
6x - y < -3
⇒ -y < -6x - 3
⇒ y > 6x + 3
Therefore, as option C matches the calculated inequality, the answer is
6x - y < -3
Answer:
6x - y < 3
Step-by-step explanation:
Finding the equation of the inequality :
Slope :
⇒ m = 3 - (-3) / 0 - (-1)
⇒ m = 6/1
⇒ m = 6
Y-intercept :
⇒ (0, 3)
Equation :
⇒ y = 6x + 3
Here :
⇒ Above the origin, so it is greater than ( > )
⇒ y > 6x + 3
⇒ 6x - y < 3
buffy's beverages has increasing profits each week during the hot summer months. Buffy finds that each week his profits increase by 20% over what they were the previous week. In his first week of business his profits were $200
The exponential function that gives the profit after x weeks is given by:
[tex]P(x) = 200(1.2)^x[/tex].
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem:
Buffy finds that each week his profits increase by 20% over what they were the previous week, hence r = 0.2.In his first week of business his profits were $200, hence A(0) = 200.Thus, the equation is given by:
[tex]A(x) = 200(1 + 0.2)^x[/tex]
[tex]A(x) = 200(1.2)^x[/tex]
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The perimeter of a rectangular field is 354m.
If the width of the field is 81m , what is its length?
Answer:
The length of the field is equal to 96 m.
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Geometry
Perimeter Formula [Rectangle]: P = 2l + 2w
l is lengthw is widthStep-by-step explanation:
Step 1: Define
Identify given.
P = 354 m
w = 81 m
Step 2: Find Length
[Perimeter Formula - Rectangle] Substitute in variables:∴ we have found the length of the field to be 96 meters.
---
Topic: Geometry
Naeema and Giovanna want to see who can run farther in 5 seconds. Naeema ran 9 yards and 8 inches. Giovanna ran 30 feet. Who ran farther? How much farther did they run?
Answer:
giovanna ran farther because naeema ran 9 yards and 8 inches and 9 yards is 27 feet so she ran 27 ft 8 in therefore giovanna ran farther
Step-by-step explanation:
30>27
Mike wants to be elected president of the 7th-grade student council. he wants to determine his chance of winning the election. which would be the best way for mike to determine if he will win the election?
Answer:
B. survey a random sample of 7th-grade students
Step-by-step explanation:
this answer would make the most sense because it is a example of a random statistical question.
If a right circular cylinder and oblique cylinder both have a height of 12 inches and diameter of 6 inches, do they have the same volume? (Use straight pi equals 3.14)
Group of answer choices
Yes, they both have a volume of 339.12 inches cubed.
No, the right circular cylinder has a volume of 339.12 inches cubed and the oblique cylinder has a volume of 1 comma 356.48 inches cubed.
No, the right circular cylinder has a volume of 1 comma 356.48 inches cubedand the oblique cylinder has a volume of 339.12 inches cubed.
Yes, they both have a volume of 1 comma 356.48 inches cubed.
Answer:
Yes, they both have a volume of 339.12 inches cubed.
Step-by-step explanation:
To calculate the volume of an oblique cylinder is very simple, we must multiply π (Pi = ~ 3.14) by the radius to the power of two and then multiply by the height. In this case the height forms a 90 degree angle from the opposite base to the position of the base, but outside of it.
Volume = π × Radius² × Height
The formula for the volume of a regular cylinder or an oblique cylinder is the same, if we imagine a stack of poker chips (forming a cylinder), even when we tilt the chips to one side (forming an oblique cylinder) the volume remains the same.
Now using this information, we must find the volumes of both cylinders.
For the oblique cylinder:
Given
Using the formula,
The volume would be 339.29 m³
Now solving for the other cylinder:
V=πr²h=π·32·12≈339.29201
Rounded, the answer would be 33.29 m³
This therefore proves that they both have the same volume.
Last year, the number of skateboards produced by a skateboard company is normally distributed. The standard deviation of skateboards produced was 20 skateboards. They found they produced up to 280 skateboards on 93.32% of the days last year. Use this information to find the average number of skateboards produced per day last year.
The average number of skateboards produced per day last year is 310.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have:
The standard deviation of skateboards produced was 20 skateboards. They found they produced up to 280 skateboards on 93.32% of the days last year.
Z- score at 93.32% is -1.5
We know:
[tex]\rm Z = \dfrac{(x - \mu)}{\sigma}[/tex]
[tex]\rm -1.5 = \dfrac{(280 - \mu)}{20}[/tex]
μ = 280 + 30
μ = 310
Thus, the average number of skateboards produced per day last year is 310.
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is 0.4285714285714 a rational number
Answer:
No it is not a rational number
Step-by-step explanation:
A rational number is a number that can be written in the form
p
q
, where
p
and
q
are integers and
q
≠
o
.
All fractions, both positive and negative, are rational numbers. A few examples are
4
5
,
−
7
8
,
13
4
,
and
−
20
3
What is the product? 2/3×1/5
Answer:
0.13
Step-by-step explanation:
2/3×1/5 = 0.13
Four friends are playing the board game Hidden Treasure. The game begins with 40 coins
divided evenly among the four players. Each player keeps 2 of their coins on the table and
keeps the rest of the coins inside their bag.
Let b equal the number of coins in each bag.
Which equation represents the total number
of coins the four players have?
4(b+2)=40
4b=40
b+2=49
4b+2=40
Answer:
I hope this helps 40 divided by 4 is 10 10 per person 10-2=8 8 coins in each players bag and the total amount of coins in bags is 8 times 4 which is 32
can someone help me plss ill mark brainliest
Answer: x^44y^16z^44
Step-by-step explanation:
(rounding) 0.46. whats the nearest tenth?
Answer:
0.5
Step-by-step explanation:
4 is in the tenths place and 6 is in the hundredths place
Since the digit in the hundredths place (6) is greater than or equal to 5, add 1 to the digit in the tenths place (4)
1 + 4 = 5, so the digit in the tenths place becomes 5
The digit in the hundredths place is dropped
0.46 rounded to the nearest tenth (one decimal place) = 0.5
Determine the equation for the line of best fit to represent the data.
Answer:
d
Step-by-step explanation:
Noah bowled 3 games for his bowling team. in the second game, he scored 10 points more than in the first game; in the third game, he scored 10 points more than in the second game. his average score was 230 points for the 3 games. how many points did noah score in the third game?
Answer:
240 points game 3
Step-by-step explanation:
use what is given and put everything in variable terms since this asks for the average, you have to divide by the number of games in the end
10 10 x 10 10 x 10x10 x10
Answer:
Step-by-step explanation:
The answer is 10,000,000 because u have to do 10x10x10x10x10x10x10
So basically I did the most easiest way possible with is multiply 1 and 1 and then add the zero and I got 10 so if u add the zeros up 6 more times then we get 10 million or 10,000,000.
PLEASE HELP ASAP
If (x + 3)2 = 42, what is the approximate positive value of x?
A) 0.48
B) 3.48
C) 5.48
D) 6.48
An expression is defined as a set of numbers, variables, and mathematical operations. The value of x is 3.48.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The solution of the expression (x+3)²=41 can be found as shown below,
(x+3)²=42
(x+3)=√42
x+3=6.48
x = 3.48
Hence, the value of x is 3.48.
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Identify the amount (a) and the growth factor (b) in each exponential function. Break B into (1+r) where the rate of growth. Give r as a percentage.
y=1.07 (1.96)x
a
b=
r(as a percentage)
Answer:
a = 1.07
b = 1.96
r = 96%
Step-by-step explanation:
In an exponential function, modeled by f(x) = a(b)ˣ, a is the initial value and b is the growth factor. If we apply this formula to the given function y = 1.07(1.96)ˣ, we can see that the initial value, a, is 1.07, and the growth factor, b, is 1.96.
Now, to break down b, 1.96, into a rate, you simply set it equal to the problem’s given (1 + r) equation to find the rate.
1.96 = 1 + r
So r = .96
Now, we just have to convert .96 into a percentage to get a growth rate of 96%.
