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Part 1
Find the standard deviation of this data.
Mean=7.8
data numbers are: 10, 7.5, 8, 7, 8, 6.5, 9, 7.5, 8, 8.5, 7, 8, 9, 6, 7.5
Part 2
Use the mean and standard deviation found above to create a normal distribution curve using the graph below. Label the following on the graph:
1) a mean shoe size
2) shoe sizes that are 1, 2, and 3 standard deviations from the mean
3) the percentages in each piece of the normal distribution curve
4) title of the data
Answers
the standard deviation of the data is 0.5013.
Mean shoe size = 7.8
How to find the standard deviation?To find the standard deviation of the given data, we can use the formula for sample standard deviation:
s = (\(\sqrt{(sum(xi - x)^2) / (n - 1)}\))
where x is the mean, xi is each data point, and n is the sample size.
Plugging in the values, we get:
s = (\(\sqrt{((10-7.8)^2 + (7.5-7.8)^2 + (7.5-7.8)^2) / (15 - 1))}\)
s = (\(\sqrt{(4.84 + 0.09 + ... + 0.09) / 14)}\)
s = t\(\sqrt{(1.8429 / 14}\))
s = 0.5013
Therefore, the standard deviation of the data is 0.5013.
Part 2:
To create a normal distribution curve, we first need to find the z-scores for each shoe size using the formula:
z = (x - mu) / s
where x is the shoe size, mu is the mean, and s is the standard deviation.
Plugging in the values, we get:
z10 = (10 - 7.8) / 0.5013 = 4.38
z7.5 = (7.5 - 7.8) / 0.5013 = -0.60
z8 = (8 - 7.8) / 0.5013 = 0.40
z7 = (7 - 7.8) / 0.5013 = -1.60
z6.5 = (6.5 - 7.8) / 0.5013 = -2.62
z9 = (9 - 7.8) / 0.5013 = 2.39
z8.5 = (8.5 - 7.8) / 0.5013 = 1.39
z9 = (9 - 7.8) / 0.5013 = 2.39
z6 = (6 - 7.8) / 0.5013 = -3.59
z7.5 = (7.5 - 7.8) / 0.5013 = -0.60
Using a standard normal distribution table, we can find the percentages of each piece of the normal distribution curve:
About 68.27 percent of shoe sizes are within one standard deviation of the mean.
Approximately 95.45% of shoe sizes are within 2 standard deviations of the mean.
99.73 percent of shoe sizes fall within three standard deviations of the mean.
Mean shoe size = 7.8
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Related Questions
The class mark of the class 90-120 is :
Answers
Hey
here's ur answer ⤵️
Answer= 105
Step-by-step explanation:
The minimum value in a class is it's lower limit and the maximum value in a class is the upper limit. The given class is 90-120. So, the lower limit of this class is 90 and the upper limit is 120
Hence, the class mark of this class is 90-120= 105.
Hope it helps ✌
Find x. I need it ASAP
Answers
Answer:
x = 27°
Step-by-step explanation:
Because of the two parallel lines, we can conclude that
corner DAB = corner FDE = 2x
In ∆DAB
Corner DAB = 2x
Corner BDA = 2x (given)
Corner ABD = 72 (given)
The sum of three corners in any trianle, adds up to 180°.
So if one corner is 72° and the other two corners are the same, then the two corners together, must be 180-72 = 108°.
For each corner that is 108/2= 54
so corner BDA = 54° and also corner DAB = 54°.
Given was BDA = 2x and BDA = 54°
so 2x = 54°
then x = 27°
6. Which of the following is the turning point of the function y = (x-8)²-2?
(1) (8,-2)
(2) (-8, 2)
(3) (-8,-2)
(4) (8, 2)
Answers
Answer:2
Step-by-step explanation:bc
If 18 g of air has 48 J of heat added to it, what will be the change temperature? (C = 0.25 J/g x°C)
Answers
Explanation is in the file
tinyurl.com/wpazsebu
Given g(x) =5x+4 determine x for g(x)=-36
Answers
Answer:
x = -8
Step-by-step explanation:
Set one side of the equation to be -36, and the other side to be the actual equation for g(x) and solve for x.
-35 = 5x + 4
Subtract 4 from both sides.
-40 = 5x
Divide both sides by 5
-8 = x
x = -8
an oil tank has to be drained for maintenance. The tank is shaped like a that is ft long with a diameter of 2.2 Suppose is drained at a rate of 2.1 ft ^ 3 per minutethe tank starts completely full , how many minutes will it take to empty the tank? Use the value 3.14 for and round your answer to the nearest minutenot round any intermediate computations
Answers
The given information is:
- The tank has the shape of a cylinder
- The dimensions of the cylinder are 5 ft long and diameter 2.2 ft.
- The tank is drained at a rate of 2.1 ft^3 per minute.
The volume of the tank is given by the formula:
\(V=\pi *(\frac{d}{2})^2*h\)Where d is the diameter and h is the height.
By replacing the known values we obtain the initial volume:
\(\begin{gathered} V=3.14*(\frac{2.2ft}{2})^2*5ft \\ V=3.14*(1.1ft)^2*5ft \\ V=3.14*1.21ft^2*5ft \\ V=18.997ft^3 \end{gathered}\)As the drain rate is 2.1 ft^3 per minute, the time that is needed to empty the tank is:
\(\frac{18.997ft^3}{2.1ft^3\text{ / min}}=9.04\text{ min}\)The answer is 9 minutes.
two trains are moving towards each other on the same railroad track. From this track there's an offshot peice of railroad- the length of whice is shorter than the length of the train but longer than the length of one train car. How can the trains pass eash other?
Answers
If the length of whice is shorter than the length of the train but longer than the length of one train car then the train can pass one car at a time.
Given that two trains are moving towards each other on the same railroad track. From this track there's an offshot peice of railroad- the length of whice is shorter than the length of the train but longer than the length of one train car.
We are required to find how the trains pass each other.
Two cases are there:
For each car in the shorter train
Train A leaves one of its cars on the offshot.Both trains move until train B car move the car from the offshoot the portion of track away from train A.Train B moves to allow the cycle to repeat.We assume that cars can be decoupled at any point in the train,so that any required order of cars can be preserved.We further assume that train can move any one of the A's car in addition to all of them.
The total number of cars lengths that must pass the off shoot is the product of the number of cars in both the trains.So,it does not seems to matter which train makes use of the offshoot.
Hence if the length of whice is shorter than the length of the train but longer than the length of one train car then the train can pass one car at a time.
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The diameter of the cylindrical barrel was 20 inches. When the barrel was lifted away, it left an imprint of a circle on the ground. What is the area, in square inches, of the circle? Use 3.14 for ñ
Answers
The area of the circle left by the cylindrical barrel on the ground is 314 square inches.
Given that the diameter of the cylindrical barrel is 20 inches, we need to find the radius, which is half the diameter. Radius = Diameter / 2 = 20 inches / 2 = 10 inches.
Now, we will use the formula for the area of a circle, which is Area = π * (radius^2). We're given π = 3.14, so the area is:
Area = 3.14 * (10 inches)^2
Area = 3.14 * 100 square inches
Area = 314 square inches
So, The area of the circle left by the cylindrical barrel on the ground is 314 square inches.
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The graph of f(x) = x^2 was transformed to create the graph of g(x) = f(x) - 9. Which statement about the graphs is true?
A.The graph of g is a reflection of the graph of f across the x-axis.
B. The vertex of the graph of g is 9 units to the right of the vertex of the graph of f
C. The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.
D. The graph of g is a reflection of the graph of f across the y-axis.
Answers
Answer:
C. The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.
Step-by-step explanation:
It's a given that f(x) = x^2 so that means g(x) = f(x) - 9 means g(x) = x^2 - 9
in slope intercept form y = mx + b, b is the y-intercept
since g(x) is just f(x) with the y-intercept as -9 we know that the vertex of the parabola moves downwards 9 units
---
Hope this helps! :) If so, please mark my answer as brainliest
Function g(x) is the translation of function f(x). The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f(x). The correct statement is C.
Given,\(f(x)=x^{2}\).
\(g(x) = f(x) - 9.\)
From the above functions it is clear that the equation for the graph of g(x) will be,
\(g(x)=x^{2} -9\).
What is intercept?The equation \(y=mx+c\) is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
Since The y intercept of function f(x) is zero.
Hence in the function g(x), it is 9 units below the intercept of the function f(x). Thus the correct option is C.
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What is the domain of the function f(x) - 50 ? 5 + 720-2 {x: 0 < 20) {0, 1, 2, 3,.20} {a: 2 < 20} {0, 1, 2, 3,....19
Answers
The domain of a function f(x) is the set of values of the variable x for which the function is defined (has a defined finite value).
In the case of rational functions like this one, the function becomes undefined when the denominator is 0, so we can write:
\(\begin{gathered} 5+\sqrt[]{20-x}=0 \\ \sqrt[]{20-x}=-5\longrightarrow\text{ there is no real value for x that will satisfy this condition} \end{gathered}\)As the square root will only give positive values or zero, there is no value of x that will make the square root be equal to -5. Then, this condition does not give us any discontinuity for f(x).
We have now to consider that the square root of (20-x) will not accept negative arguments in order to be in the realm of real numbers. So then, we have the condition:
\(\begin{gathered} 20-x\ge0 \\ 20\ge x \\ x\le20 \end{gathered}\)Then, f(x) will not be defined for x that do not satisfy this condition.
We can conclude that f(x) is defined for all values of x that are equal or less than 20.
Answer: The domain is {x: x<=20}
Then
What is 0.35714285714 as a fraction?
Answers
Answer:
0.35714285714 as a fraction equals 35714285714/100000000000
Step-by-step explanation:
To write 0.35714285714 as a fraction you have to write 0.35714285714 as numerator and put 1 as the denominator.
Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.35714285714 = 0.35714285714/1 = 3.5714285714/10 = 35.714285714/100 = 357.14285714/1000 = 3571.4285714/10000 = 35714.285714/100000 = 357142.85714/1000000 = 3571428.5714/10000000 = 35714285.714/100000000 = 357142857.14/1000000000 = 3571428571.4/10000000000 = 35714285714/100000000000
I hope this helps :)
What is the slope of the line on the graph?
Answers
Answer:
5,-1,-7
Step-by-step explanation:
If f(x) = x + 8. find f(6)
Answers
Answer: 14?
Step-by-step explanation:
not sure cause you didn’t put options but i typed it in symbolab functions calculator and that’s what it said..
Find dy/dx if y = ln(e^x^2+1)+e sin x
Answers
dy/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x) + e*cos(x)
This is the derivative of the given function y with respect to x.
We want to find the derivative dy/dx of the function y = ln(e^(x^2)+1) + e*sin(x). To do this, we will apply the rules of differentiation.
First, we'll differentiate the function term-by-term. For the natural logarithm function, the derivative is (1/u) * du/dx, where u is the function inside the natural logarithm. In our case, u = e^(x^2) + 1.
The derivative of e^(x^2) is found by applying the chain rule, which gives us (e^(x^2) * 2x). The derivative of 1 is 0. Therefore, the derivative of u is (e^(x^2) * 2x). Now we can find the derivative of ln(u):
d[ln(u)]/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x)
Next, we will differentiate e*sin(x). The derivative of e*sin(x) is found by applying the product rule. The derivative of e is e, and the derivative of sin(x) is cos(x). Applying the product rule, we have:
d[e*sin(x)]/dx = e*cos(x) + e*sin(x) * 0 = e*cos(x)
Now, adding the derivatives of both terms, we get:
dy/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x) + e*cos(x)
This is the derivative of the given function y with respect to x.
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Estimate the answer by rounding each fraction to the nearest whole or half and then adding.
15 9/10 + 5 3/7 = ??
Answers
The estimate of the given fraction, 15 9/10 + 5 3/7, is 21
Estimating the value of the fraction expressionFrom the question, we are to estimate the answer of the given expression
From the given information, we have a fraction expression.
The given expression is
15 9/10 + 5 3/7
To estimate the answer, we will add the fractions
First,
Convert the fractions from mixed to improper fractions
159/10 + 38/7
Find the LCM of 10 and 7
LCM of 10 and 7 = 70
Using the LCM, add the fractions
[7(159) + 10(38)]/70
(1113 + 380)/70
1493/70
= 21 23/70
≈ 21
Hence,
The estimate is 21
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Which number line shows all the values of x that make the inequality -3x+1<7
true?
Answers
Answer:
D
Step-by-step explanation:
Firstly, we need to get the value of x 1-7 < 3x
-6 < 3x
-2 < x
or x > -2
So we need a number line that has the unshaded circle placed at 2 ( since the inequality sign is single) and it faces the right (arrow face right)
If AFGH
AQRS, find the measure of Q.
Answers
Answer:
D. 28°
Step-by-step explanation:
Since ∆FGH is congruent to ∆QRS, it follows that:
\( m\angle F = m\angle Q \)
Thus:
\( 2x + 10 = 3x + 1 \) (Substitution)
Collect like terms
\( 2x - 3x = -10 + 1 \)
\( -x = -9 \)
Divide both sides by -1
x = 9
\( \angle Q = 3x + 1 \)
Plug in the value of x
\( \angle Q = 3(9) + 1 \)
\( \angle Q = 28 degrees \)
What is the area of the triangle?
10 km
10 km
square kilometers
Answers
A block of wood has a mass of 120g and a volume of 200cm3. What is the density of the wood?
Answers
Answer:
The density of the wood is 0.6 g/cm^3
Step-by-step explanation:
The density of an object can be calculated by dividing the mass of the object by its volume. In this case, the mass of the block of wood is 120g and its volume is 200cm^3.
Density = mass / volume
Density = 120g / 200cm^3
Density = 0.6 g/cm^3
Therefore, the density of the wood is 0.6 g/cm^3.
Rewrite (-5)^-2 without using negative exponents
Answers
Answer:
-0.04
Step-by-step explanation:
Just find the value of it with the exponent, and then your answer will be without a negative exponent.
Hope this helps!
The graph of g is a vertical translation of the graph of f.
If f(x) = mx + b and g(x) = (mx + b) + k. What value
for k transforms the function finto g?
k=
Answers
Answer:
-3
Step-by-step explanation:
I took the test and it was correct, (I also use MyPascoConnect)
the within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Group of answer choices
Scores in each of the actual groups studied
Mean of the groups minus the mean of the scores of the actual groups
Equal to the between-groups estimate of population variance
Means of the groups studied
Answers
The within-group estimate of variance is the estimate of the variance of the population of individuals based on the variation among the scores in each of the actual groups studied.
The within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Scores in each of the actual groups studied.
This estimate represents the variation within each group and helps in understanding the population's variance by looking at individual differences within the groups.
The estimated within-group variance is the sum of the within-group variances for each group in the model. Effectively, this is the sum of the variance of each value (j) from its group (i) divided by the sample size minus one.
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
Y - x = -8
Answers
Answer:
Y=x-8
Step-by-step explanation:
A scale drawing of an American flag is 5 inches long and 3 inches tall. The actual flag is 3 feet tall. What is the scale of the drawing?
Answers
Answer: 1 inch:1 feet
Step-by-step explanation:
Since we are informed that the scale drawing of an American flag is 5 inches long and 3 inches tall and the actual flag is 3 feet tall.
To calculate the scale of the drawing, we should note that the height of the drawing is 3 inches tall while the height of the actual flag is 3 feet tall. It simply means that (3/3 = 1 inch represents 1 feet
9. TOLL ROADS Some toll highways assess tolls based on where a car
entered and exited. The table shows the highway tolls for a car
entering and exiting at a variety of exits. Assume that the toll for the
reverse direction is the same.
Entered Exited Toll
Exit 8 Exit 10 $0.25
Exit 10 Exit 15 $1.00
Exit 15 Exit 18 $0.50
Exit 18 Exit 22 $0.75
a. Julio travels from Exit 8 to Exit 15. Which quantity is equivalent to
Exit 8 to Exit 15?
b. What property would you use to determine the toll?
Answers
Answer:
Step-by-step explanation:
how many days could a 60kg deer survive without food at -20 degrees - has 5kg of fat
18 days
Answers
The survival time of a 60kg deer without food at -20 degrees Celsius depends on various factors, including its age, sex, and physical condition. However, assuming the deer is healthy and has 5kg of fat, it could potentially survive for around 30 to 50 days without food.
The exact survival time can vary depending on several factors, such as the deer's level of physical activity, environmental conditions, and how much energy it is expending to stay warm in the cold temperature. Additionally, if the deer is able to find sources of water, this can also increase its chances of survival.
It's important to note that this is just an estimate and that the actual survival time may vary. If the deer is injured or sick, its chances of survival may be reduced, and it may not be able to survive as long without food.
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Complete Question
How many days could a 60kg deer survive without food at -20 degrees Celsius if it has 5kg of fat?
√2a-3-10=-7 i need help pls
Answers
Answer:
the solution to the equation √2a-3-10=-7 is a = 18.
Step-by-step explanation:Starting with the given equation:
√2a - 3 - 10 = -7
First, let's simplify the left-hand side by combining like terms:
√2a - 13 = -7
Next, we can isolate the variable term (√2a) by adding 13 to both sides:
√2a = 6
To solve for a, we need to square both sides of the equation:
(√2a)^2 = 6^2
2a = 36
Finally, we can solve for a by dividing both sides by 2:
a = 18
Therefore, the solution to the equation √2a-3-10=-7 is a = 18.
Answer:
Step-by-step explanation:
√2a-3-10=-7
We add 10 to both sides:
√2a - 3 = 3
Now we add 3 to both sides to isolate the radical term:
√2a = 6
Then, square both sides
(√2a)^2 = 6^2
2a = 36
Divide both sides by 2
a = 18
Therefore, the solution is a = 18.
1. What is the sum of 4x²y + 2x²y³ and -2xy + x²y³?
A. 4x2y + 3x²y³ - 2xy
B. 2x2y - 4x2y³ - 2xy³
C. 4x2y + 2x2y³ - 2x²y³
D. 2x²y + 2x²y³ + xy
Answers
The sum of the two expressions 4x²y + 2x²y³ and -2xy + x²y³ is 4x²y + 3x²y³-2xy. The correct option is option A.
What is meaning of expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
What is the meaning of like terms?
The term "like terms" in algebra refers to terms that have the same variable raised to the same power. Only the numerical coefficients can vary in terms that are similar to algebra. We can combine similar terms to make algebraic expressions simpler, making it much simpler to determine the expression's outcome.
Given expressions are 4x²y + 2x²y³ and -2xy + x²y³
Add the given expressions:
4x²y + 2x²y³ + (-2xy + x²y³)
Combine like terms:
= 4x²y + (2x²y³+ x²y³)+ (-2xy)
Add like terms:
= 4x²y + 3x²y³-2xy
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the angle measures of a quadrilateral are in a ratio of 4 : 5 : 6 : 9. find the measure of the smallest angle.
Answers
The measure of the smallest angle of the quadrilateral is 60° .
In the question ,
it is given that ,
the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .
So , the measure of the largest angle is = 9x
and the measure of the smallest angle is = 4x .
we know that the sum of the measure of all the angles of the quadrilateral is 360° .
that means ,
4x + 5x + 6x + 9x = 360°
24x = 360
dividing both sides by 24 ,
x = 360/24
x = 15 .
the smallest angle is = 4(15) = 60°
Therefore , The measure of the smallest angle of the quadrilateral is 60° .
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Answers
Answer:
A. 8
Step-by-step explanation:
We are given the functions:
\(f(x)=\sqrt{x}\\\\g(x)=7x+b\)
We are told that on a standard (x, y) coordinate plane that y = f(g(x)) passes through the point (4, 6). In order to solve for b, we need to figure out what f(g(x)) is equal to.
As with a regular function like the two above, f(g(x)) means you are substituting x with g(x) in function f. The problem gave us the two functions, so I will demonstrate what I mean.
\(f(g(x))=\sqrt{(7x+b)}\)
The problem again tells us that y = f(g(x)) goes through (4, 6). Substitute those values for their respective variables and solve for b.
\(y=f(g(x))\\\\y=\sqrt{(7x+b)}\\\\6=\sqrt{(7(4)+b)}\\\\6=\sqrt{(28+b)}\\\\(6)^2=(\sqrt{(28+b)})^2\\\\36=28+b\\\\36-28=28+b-28\\\\8=b\)
Therefore, the value of b is equal to 8.