The mean is 79.5.
The standard deviation is 3.99
What is the mean and standard deviation?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
(82 + 78 + 80 + 72 + 85 + 80) / 6 = 477 / 6 = 79.5
Standard deviation is used to determine how the values in a group differs from the mean of the values in the group.
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation:79.50
Determine the difference between each value and the mean and then square the result: (82 - 79.5)² + (78 - 79.5)² + (80- 79.5)² + (72- 79.5) ²+ (85- 79.5)² + (80- 79.5)² = 6.25 + 2.25 + 0.25 + 56.25 + 30.25 + 0.25 = 95.5
Determine the mean of the sum of the squared differences and then find the square root of the mean:
√95.5 / 6 = 3.99
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HELP!
Can someone explain to me how to find scaled factors as simply as they can?
Answer:
The formula for scale factor is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape
To simplify the ratio just reduce it to the simplist form.
Divide each number in the ratio by the same amount to get the answer.
Step-by-step explanation:
hope this helps :)
a fighter jet traveled k miles in its first 96 minutes of flight time. if it completed the remaining 300 miles of the trip in t minutes, what was the average speed, in miles per hour for the entire trip?
The average speed was 60[tex]\frac{k+300}{96+t}[/tex]
We are given that a plane travelled k miles in 96 minutes. Since we need the average speed in miles per hour we can convert 96 minutes to hours.
96 minutes = 96/60 =8/5 hours
We are also given that the Plane completed the remaining 300 miles in t minutes. We must also convert t minutes to hours.
t minutes = t/60 hours
Now we can calculate the average speed for the entire trip, using the formula for average speed.
Average Speed = total distance/ total time
Average Speed = (k +300)/(8/5 + t/60)
Average speed = (k + 300) / ((96 + t)/60)
Hence, Average Speed = 60(k + 300)/ (96 + t)
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NEED HELP ASAP look at picture
The required simplified value of the function is (f/g)(x) = (x - 3) / (x + 2). Option C is correct.
Given that,
f(x) = 2x² - 5x - 3
g(x) = 2x² + 5x + 2
(f / g)(x) = To be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here.
f(x) = 2x² - 5x - 3
f(x) = (2x + 1) (x - 3 )
g(x) = 2x² + 5x + 2
g(x) = (2x + 1)(x + 2)
(f / g)(x) = (2x + 1) (x - 3 ) / (2x + 1)(x + 2)
(f/g)(x) = (x - 3) / (x + 2)
Thus, the required simplified value of the function is (f/g)(x) = (x - 3) / (x + 2). Option C is correct.
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Can someone please send the answers to these questions with explanation? (Attachment) (30 POINTS)
Answer:
Step-by-step explanation:
a) this graph is that of a parabola that opens up. As is the case for all parabolas, the domain is the set of all real numbers. The range begins with the smallest y-value, which is -4, extending upwards from there: [-4, infinity)
b) this graph's shape most closely resembles that of a polynomial; as we move from left to right, y increases, reaches a local maximum, decreases to a local minimum, and then continues to increase with x. As is the case for all polynomials, the domain is the set of all real numbers. As we move from x = 0 to the left, y decreases without bound; from x ≥ 12 onward, y increases without bound; thus, the range is (-infinity, +infinity).
c) The graph represents a quarter of an ellipse for which x begins at -40 and ends at [4, -16]. Thus, the domain is [-40, 4]. By inspection we see that the smallest y value is -16 and the largest is 4; thus, the range is [-40, 4].
If a=-5, find the value of 2a² - 5a - 10
Answer:
= 65
Step-by-step explanation:
= 2×(-5)² - 5×(-5) - 10
= 2×25 + 25 - 10
= 50 + 15
= 65
Answer:
65
Step-by-step explanation:
HELP ANSWER PLSSSSSSSSSSSS
The degrees of the whole segment is 90 because we know that a right angle is 90 degrees and can be shown with a square in the corner. One angle inside the 90 degrees is 50 degrees and the other two values are the same. Since 90 - 50 = 40, we know that the remaining is 40 degrees. Since x is the same, we divide 40 by 2, getting 20 degrees.
ANSWER: x = 20 degrees
Explain how you can use a graphing calculator to determine if a table of values represents a proportional function.
Table: x and y increments must be the same. X and y increments need not be the same.
The x and y exponents should be 1. Linear equation.
Graphs should be straight.
This is further explained below.
Explain how you can use a graphing calculator to determine if a table of values represents a proportional function:Generally, Based on the table, you need to ensure that the increments for the x values and the y values are the same.
It is not necessary for the increment to be the same for both the x and y values.
The following conclusion may be drawn from an equation: both the x and y exponents should be set to 1.
It seems like we need a line equation for this problem.
In conclusion, Inferred from a graph: the shape of the graph ought to be that of an unbroken line.
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Calculate the distance between the points P= (-7, 8) and J =(-3, 1) in the coordinate plane.
Give an exact answer (not a decimal approximation).
Distance:
The distance between the given points P(-7,8) and J(-3,1) is √65 = 8.06225775
Given that, The points are P=(-7,8) and J = (-3,1).
A coordinate plane is a surface formed by two dimensional lines .
The distance between the points is calculated using the distance formula that is, distance between A(x1,y1) and B(x2,y2) is,
√[(x2-x1)²+(y2-y1)²], by using this formula you can find the distance between any two points on the plane.
Therefore the distance between the given points P and J is ,
PJ = √[(-3+7)²+(1-8)²]
= √[(4)²+(-7)²]
= √[(16) + (49)]
= √[16+49]
= √[65]
= 8.06225775
PJ = 8.06225775
Therefore the distance between the given points P(-7,8) and J(-3,1) is 8.06225775
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50,500-35,675 and work for it
Answer: 14,825 is the answer
Step-by-step explanation:
Answer: 14,825
Step-by-step explanation:
its easy.
The sum of two numbers is 172. The first is 8 less
than 5 times the second. Find the first number.
Answer:
X+Y=172 OE X=172-Y
X=5Y-8
5Y-8=172-Y
5Y+Y=172+8
6Y=180
Y=180/6
Y=30 ANS
X=172-30
X=142 ANS.
Step-by-step explanation:
Some friends are going to be driving to a city 900 miles away from home. They are planning to stay the night in a city 420 miles away, then drive the rest of the distance the following day. If they plan to drive on average 60 miles per hour, how long will they be driving the second day?
The total time they will be driving the second day is 8 hours
The total distance they are planning to go = 900 miles
Distance travelled on first day = 420 miles
Distance yet to be travelled on second day = Total distance - distance covered = 900 miles- 420 miles= 480 miles
The speed of the car = 60 miles per hour
60 miles of distance covered in time = 1 hour
1 mile of distance covered in time = 1 hour /60 miles = 1 minute
This is solved using Unitary Method
1 hour = 60 minutes
480 miles can be covered in time = 1 minute × 480 miles
= 480 minute
=8 hours
Hence, The total time they will be driving the second day is 8 hours
Distance and displacement are two quantities that appear to mean the same thing but have very different meanings and definitions. Distance is defined as "how much ground an object has covered during its motion," whereas displacement is defined as "how far out of place an object is."
Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point.
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Simplify to a single power of 2:
(2²)^4
Answer:
[tex]\sf 2^{8}[/tex]
Step-by-step explanation:
Exponent rule:[tex]\sf \boxed{(a^m)^n=a^{m*n}}[/tex]
To convert to single power, multiply the powers.
[tex]\sf (2^2)^4= 2^{2*4}[/tex]
[tex]\sf =2^8[/tex]
[tex] \bf\implies \: {2}^{8} [/tex]
Step-by-step explanation:We know that,The exponent (^) rule to solve this problem that is :
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \bf \longrightarrow \: {(a^{m})}^{n} = {(a)}^{m \times n} [/tex]
According to the question :-
[tex] \bf \longrightarrow \: {(2^{2}) }^{4} [/tex]
[tex] \bf \longrightarrow \: (2)^{2 \times 4} [/tex]
[tex] \bf\longrightarrow \: {2}^{8} \: \boxed { \bf \: \red{ ans.}}[/tex]
What is the value of x² + 2x + 3 when x = 3/4
27/4
81/16
6
69/16
the product of two consecutive integers is 420. which quadratic equation can be used to find x, the lesser number? x2 1
The quadratic equation, x(2) + 2 =420 can be used to find x.
you can use trial and error
x(2) + 2 =420
210(2)=420 but we need to add the two so lower the [tex]120[/tex]
209(2)=418+2 = 420
so, the x value must less than 21.
How do you write a quadratic equation in standard form?A quadratic equation with variable x is written in standard form as [tex]ax2 + bx + c = 0[/tex], where a, b, and c are constants such that the value of an is non-zero but the values of b and c can both be zeros.
Let's change [tex]ax2 + bx + c = 0[/tex] from its standard form to its vertex form, which is [tex]a (x - h)2 + k = 0[/tex], where (h, k) is the vertex of the quadratic function [tex]f(x) = a (x - h)2 + k[/tex]. Keep in mind that 'a' has the same value in both equations. Just set them equal so we can determine how the variables relate to one another.
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Parallel to 4x — 6y = -36 passing through (2,3)
An equation which is parallel to 4x - 6y = -36 passing through points (2, 3) is y = 2x/3 + 5/9.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.
This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
Simplifying the equation, we have:
4x - 6y = -36
6y = 4x + 36
Dividing both sides by 6, we have:
y = 2x/3 + 6
m₁ = m₂ = 2/3.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
At point (2, 3), we have:
y - 3 = 2/3(x - 2)
y - 3 = 2/3(x - 2)
y - 3 = 2x/3 - 4/3
y = 2x/3 - 4/3 + 3
y = 2x/3 + 5/9
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Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42, find Julia’s age
Answer:
Julia is 15
Step-by-step explanation:
13 + 14 + 15 = 42
Julia is the oldest and 15 is the greatest of the 3 numbers
therefore Julia is 15
Julia's age out of the three is equal to 15 years.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42.
Julia's age will be calculated as,
13 + 14 + 15 = 42
Julia is the oldest and 15 is the greatest of the 3 numbers.
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" .
8x + 4 = -28
solve for x
Answer:
x=-4
Step-by-step explanation:
8x+4=-28
8x=-28-4
8x=-32
x=-4
Find the value of f(-2)
Answer:
y= -3 or just -3
Step-by-step explanation:
Find the product.
2 1/3 ⋅ 3 1/2
Write the answer as a mixed number.
What is 0.904 subtract 0.01?
Answer:
0.894 is your correct answer.
Answer:
0.894 because the 0.01 will affect the hundredths so the 0 will be affected in 0.904 and the 9 will change to an 8 because there's nothing left in 0 so you have to substitute.
Is it possible to calculate the cube root of a negative number?
Answer:
Yes, the cube root of a negative number can be calculated.
Step-by-step explanation:
plss help(image attached que 5)
Answer:
3300cm² is the answer of this question i guess so
a cylindrical container must hold 2l or 2,000 cm^3 of liquid. find the dimensions of the container which will minimize the amount of material needed.
The dimensions of the container is r = 6.828 cm and h = 13.656 cm.
Volume of the Cone:
Volume of the cone is define the space or the capacity of the cone.
The formula for the volume of the cone is,
V = πr²h
Where
r represents the radius of the cone
h represents the height of the cone
Given,
Cylindrical container must hold 2l or 2,000 cm³ of liquid.
Here we need to find the dimensions of the container which will minimize the amount of material needed.
Let height = h and radius of the base = r.
We know that the volume of the container,
V = 2000
We know the formula of volume of the cone is,
V = πr²h
2000 = πr²h
Here we need the value of h,
So,
h = 2000/πr²
and surface area of the can
S = 2πr² + 2πrh
Apply the value of h,
S = 2πr² + 2πr (2000/πr²)
S = 2πr²+ (4000/r)
S = 2πr²+ 4000 x r⁻¹
S′=(−1)(4000r⁻²)+4πr
S′=4πr−(4000/r²)
Consider,
4πr−(4000/r²) = 0
4πr³−4000 = 0
πr³−1000 = 0
πr³ = 1000
r³ = 1000 / π
r = √1000 / π
r = 6.828 cm
Apply the value of r on the equation to find the value of h,
h = 2000/(π∗(6.828)²)
h = 2000/146.46
h = 13.656
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5y + 7x = -1
-2y = -5x - 23
Elimination
Step-by-step explanation:
+25y + 35x = -1. × 5
+35x - 14y = -161. × 7
-. +. +
39y = 156
y=4
putting value of y in 5y + 7x =-1
5×4+7x =-1
7x = -21
x= -3
What is the solution to this equation?
x + 4(x + 5) = 40
A. X= 4
B. X= 7
C. x=9
D. x = 12
Answer:
A
Step-by-step explanation:
x + 4(x + 5) = 40 ← distribute parenthesis and simplify left side
x + 4x + 20 = 40
5x + 20 = 40 ( subtract 20 from both sides )
5x = 20 ( divide both sides by 5 )
x = 4
PLEASE HELP
question down below
Answer:
Draw a line going down from the 300, with a break in the middle and finish it out at the 6 hr mark.
Step-by-step explanation:
Start at the 300 and draw that line down to the 180 mark lined up with the 2 hour dot. Then draw a horizontal line from there to the middle of the 2 and the 4. Then draw a line from where you ended the break with the same slope as the beginning.
Hope this helps!
what is the step-by-step answer to
-3(X + 2)=-18
Answer:
x = 4Step-by-step explanation:
Simplify both sides of the equation:−3 (x+2) = −18
(−3) (x) + (−3) (2) = −18 (Distribute)
−3x + −6 = −18
−3x −6 = −18
Add 6 to both sides:−3x −6 +6 = −18 + 6
−3x= −12
Divide both sides by -3:−3x/−3 = −12/−3
x = 4
Moo berry creamery uses 2 cups of ice cream in each milkshake. How many milkshakes can they make with 1 gallon of ice cream?
Moo berry can make 8 milkshakes with 1 gallon of ice cream.
How to calculate the number of milkshakes ?Moo uses 2 cups of ice cream in each milkshake
He is using 1 gallon of ice cream
Therefore the number of milk shakes he can produce can be calculated as follows
16 cups makes 1 gallon
= 16/2
= 8
Hence 8 milkshakes can be made with one gallon of ice cream
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ALGEBRA 1 QUESTION PLEASE HELP!!
Solve this literal equation:
V = 4/3 x pi x r^3
(x being a multiplication symbol, not a variable)
**PLEASE SHOW STEPS TO SOLVE**
Answer:
[tex]\sf \pi = \dfrac{3V}{4r^3}[/tex]
Explanation:
Equation:
[tex]V = \dfrac{4}{3} \pi r^3[/tex]
Task: make pie the subject.
cross multiply
[tex]\sf \dfrac{3V}{4} = \pi r^3[/tex]
divide both sides by r³
[tex]\sf \dfrac{3V}{4} \div r^3= \pi r^3 \div r^3[/tex]
simplify following
[tex]\sf \dfrac{3V}{4r^3} = \pi[/tex]
Hence:
[tex]\sf \pi = \dfrac{3V}{4r^3}[/tex]
Determine the translation.