The average of the data is 3.5, indicating the central tendency. The population standard deviation is approximately 1.71, representing the spread or variability of the data.
To compute the histogram, average, and population standard deviation of the data {1, 2, 3, 4, 5, 6}, we can follow these steps:
Histogram: A histogram represents the frequency distribution of the data. Since the data is already given, we can directly compute the histogram by counting the number of occurrences of each value.
Data: {1, 2, 3, 4, 5, 6}
Histogram:
1: |
2: ||
3: |||
4: |||
5: ||
6: |
Average (Mean): To calculate the average, we sum up all the values and divide by the number of data points.
Average = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 3.5
Therefore, the average of the given data is 3.5.
Population Standard Deviation: The population standard deviation measures the spread of the data points around the average. It can be calculated using the formula:
Standard Deviation = √[(Σ(x - μ)^2) / N]
where Σ denotes the sum, x represents each data point, μ represents the average, and N represents the number of data points.
Standard Deviation = √[((1 - 3.5)^2 + (2 - 3.5)^2 + (3 - 3.5)^2 + (4 - 3.5)^2 + (5 - 3.5)^2 + (6 - 3.5)^2) / 6]
Standard Deviation ≈ √[17.5 / 6] ≈ √2.9167 ≈ 1.71
Therefore, the population standard deviation of the given data is approximately 1.71.
Comparing to Roll Data:
To provide a comparison with the roll data, the roll data must be provided or specified. Please provide the roll data so that a meaningful comparison can be made.
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How doe the definition of percent help you wright fraction and decimal equivalent
The definition of percent helps you write fraction and decimal equivalents by understanding that "per cent" means "per hundred".
For example, if you are asked to write the fraction and decimal equivalent of 25%, you would divide 25 by 100 to get the fractional equivalent of ¼, and divide 25 by 100 to get the decimal equivalent of 0.25.
The decimal equivalent of a fraction or percentage is the numerical value expressed in decimal form. For example, the decimal equivalent of 1/2 is 0.5 and the decimal equivalent of 25% is 0.25. Decimal equivalents are useful for calculations and can be used to convert fractions and percentages into decimal form.
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Which of the following quadrilaterals always have diagonals thats are congruent? check all that apply
Parallelogram
Rectangles
Rhombi
Squares
Isosceles trapezoid
Answer: Rectangles, Squares, Isosceles Trapezoid
The following quadrilaterals always have diagonals that are congruent :
RectanglesSquaresIsosceles TrapezoidLearn more about Congruency:
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Given
fx=4x+5, find f(3).
19
17
12
35
Answer:
17
Step-by-step explanation:
Plug in 3 for x and you'll get
\(4(3) + 5\)
Which is 17.
Answer:
I think it is 19
Step-by-step explanation:
A bag contains 24 ounces of soil. You use 2 7/8 ounces of soil to plant 1 herb.Is there enough soil in the bad to plant 8 herbs?
Answer:
There's enough soil to plant 8 herbs.
Step-by-step explanation:
24 ÷ 2 7/8 = 8.3
This shows that there's enough soil to plant 8 herbs.
5
A Petri dish is filled with 250 bacterial cultures. The number of bacteria in the dish triples
every hour.
Select the recursive and explicit formulas that model the scenario.
The recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹
Calculating the recursive and explicit formulas that model the scenario.From the question, we have the following parameters that can be used in our computation:
Initial = 250 bacterial cultures.Rate = triples every hour.This means that
Initial, a = 250 bacterial cultures.
Rate = 3
So, the recursive formulas is
f(n) = 3f(n - 1), where f(1) = 250
For the explicit formula, we have
f(n) = 250(3)ⁿ‐¹
Hence, the recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹
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6. 10 brown eggs to 12 white eggs
ratios
Answer:
10/12 or you can simplify 5/6
Step-by-step explanation:
Help ASAP! I need this badly, my last question!
Answer:
Step-by-step explanation:
...... The problem is glitched re send the image/
A company that makes hair-care products had 7,000 people try a new shampoo. Of the 7,000 people, 28 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answer: 0.4%
Step-by-step explanation:
First, a porportion needs to be set up.
part/whole = percent/100
28/7,000 = x/100
Second, cross multiply.
2800=7,000x
x=0.4
what is the value of 11²
Answer: 121
11^2 = 11 x 11 = 121
Answer:
121
Step-by-step explanation:
To square a number, we have to multiply the number by itself. This means we'll multiply 11 by 11.
11 · 11 = 121
So, 11² = 121.
I hope this helps :)
Can you please solve what is a constant and what is a term I’m just too lazy
3x+8-x=42
And can you please include a step-by step? I can't figure this out.
Answer:
x=17
Step-by-step explanation:
3x - x is 2x so 2x + 8 = 42
minus 8 from both sides is 2x = 34
divide 2 from both sides x = 17
The sum of the angle measures of a triangle is 180°. Two angles of a triangle measure 40°and 60°, so Juan concludes that the third angle measures 80°. What do you notice about the how the conclusions were made from the statement above?
Answer:
Step-by-step explanation:
Third angle = 180 - (40 + 60)
= 180 - 100
= 80°
When you subtract the sum of 40 and 60 from 180, you will get the third angle.
The Cooper family has a monthly income of $4,000.
How much money do the Coopers spend on food each month?
Answer:
$440
Step-by-step explanation:
4000×11% = 440
since on average 11% of overall income is spent on food
You want to develop a three-sigma R-chart.
You know the average range is 14 based on several samples of size
6. Which of the following is the resulting LCL?
The resulting LCL for the three-sigma R-chart is approximately 8.08.
To determine the lower control limit (LCL) for a three-sigma R-chart, we need to calculate the control limits using the average range and the appropriate factors. In this case, the average range is given as 14.
The control limits for an R-chart can be calculated using the formula:
LCL = D3 * Average Range
For a three-sigma R-chart, the factor D3 is 0.577.
Substituting the values into the formula, we get:
LCL = 0.577 * 14
LCL ≈ 8.08
Therefore, the resulting LCL for the three-sigma R-chart is approximately 8.08.
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consider the vector field. f(x, y, z) = 2ex sin(y), 8ey sin(z), 3ez sin(x) (a) find the curl of the vector field.
The curl of the vector field F = 2e^x sin(y)i + 8e^y sin(z)j + 3e^z sin(x)k is given by curl(F) = (cos(x) + 2)j - (3cos(x) - 2e^z)k.
To find the curl of a vector field, we need to compute the cross product of the del operator (∇) with the vector field. The del operator in Cartesian coordinates is given by ∇ = ∂/∂x i + ∂/∂y j + ∂/∂z k.
Let's calculate the curl of the vector field F:
curl(F) = (∇ x F)
Using the del operator, we can calculate the cross products of the del operator with the vector field components:
∇ x (2e^x sin(y)i) = (∂/∂y(2e^x sin(y)) - ∂/∂z(2e^x sin(y)))j + (∂/∂z(2e^x sin(y)) - ∂/∂x(2e^x sin(y)))k
= (2e^x cos(y))j - 0k
= 2e^x cos(y)j
∇ x (8e^y sin(z)j) = (∂/∂z(8e^y sin(z)) - ∂/∂x(8e^y sin(z)))k + (∂/∂x(8e^y sin(z)) - ∂/∂y(8e^y sin(z)))i
= (8e^y cos(z))k - 0i
= 8e^y cos(z)k
∇ x (3e^z sin(x)k) = (∂/∂x(3e^z sin(x)) - ∂/∂y(3e^z sin(x)))i + (∂/∂y(3e^z sin(x)) - ∂/∂z(3e^z sin(x)))j
= 0i - (3e^z cos(x))j
= -3e^z cos(x)j
Adding these results together, we get:
curl(F) = 2e^x cos(y)j + 8e^y cos(z)k - 3e^z cos(x)j
= (cos(x) + 2)j - (3cos(x) - 2e^z)k
Therefore, the curl of the vector field F is given by curl(F) = (cos(x) + 2)j - (3cos(x) - 2e^z)k.
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A distribution has a mean of 16 and a standard deviation of 6. What is the z score that corresponds with 25?.
Using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.
What is a normal distribution?A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
The characteristics of normal distributions are as follows: Bell-like in its symmetry.
The distribution's mean and median, which are both at its center, are equal.
68 percent of the data, or approximately, falls within one standard deviation of the mean.
So, the formula is used to determine the Z score for a data point x in a normal distribution:
Z = z - mean/standard deviation
Now, use the formula to calculate the z value as follows:
Z = z - mean/standard deviation
Z = 25 - 16/6
Z = 9/6
Z = 3/2
Z = 1.5
Therefore, using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.
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Look at the pattern below. step 1 with 1 square step 2 with 3 squares step 3 with 6 squares step 4 with 10 squares How many squares will be in the pattern in step 6
Answer:
21 squares
Step-by-step explanation:
Here in this question, we are given a pattern and we want to determine what the values in that pattern will be at a specific step.
We proceed as follows;
What we can see in this pattern is that the difference in number of squares between a pattern and the next pattern increases by the addition of the next integer to the number of squares we have in the last pattern.
Thus for step 5, we shall be adding the next integer( 5) to the number of squares ;
That would be 10 + 5 = 15 squares
For step 6, we shall be adding the next integer (6) to the number of squares in step 5.
That would be 15 + 6 = 21 squares
How we got the initial next integer?
step 1 = 1 square
step 2 = 3 squares ( integer difference of 2)
step 3 = 6 squares ( integer difference of 3)
step 4 = 10 squares ( integer difference of 4)
so;
step 5 = 15 squares ( integer difference of 5)
step 6 = 21 squares( integer difference of 6)
Convert.
ounces
1
pound
8
Answer:
2 ounces
\(0.125*16=2\)
Multiply mass by 16 to find.
Franklin has a grade of 60 and wants to raise it to 80. What percent increase is this?
Answer:
33.4%
Step-by-step explanation:
60+33.4%=80
60x1.334=80
I really need help on my math hw
IT IS DUE TOMORROW!
According to the information the triangle would be as shown in the image.
How to draw the correct triangle?To draw the correct triangle we have to consider its dimensions. In this case it has:
AB = 3cmAC = 4.5cmBC = 2cmIn this case we have to focus on the internal angles because this is the most important aspect to draw a correct triangle. In this case, we have to follow the model of the image as a guide to draw our triangle.
To identify the value of the internal angles of a triangle we must take into account that they must all add up to 180°. In this case, we took into account the length of the sides to join them at their points and find the angles of each point.
Now, we can conclude that the internal angles of this triangle are:
Angle A ≈ 51.23 degreesAngle B ≈ 59.64 degreesAngle C ≈ 69.13 degreesTo find the angle measurements of the triangle with side lengths AB = 3cm, AC = 4.5cm, and BC = 2cm, we can use the trigonometric functions and the laws of cosine and sine.
Angle A:
Using the Law of Cosines:
cos(A) = (b² + c² - a²) / (2bc)cos(A) = (2² + 4.5² - 3²) / (2 * 2 * 4.5)cos(A) = (4 + 20.25 - 9) / 18cos(A) = 15.25 / 18Taking the inverse cosine:
A ≈ arccos(15.25 / 18)A ≈ 51.23 degreesAngle B:
Using the Law of Cosines:
cos(B) = (a² + c² - b²) / (2ac)cos(B) = (3² + 4.5² - 2²) / (2 * 3 * 4.5)cos(B) = (9 + 20.25 - 4) / 27cos(B) = 25.25 / 27Taking the inverse cosine:
B ≈ arccos(25.25 / 27)B ≈ 59.64 degreesAngle C:
Using the Law of Sines:
sin(C) = (c / a) * sin(A)sin(C) = (4.5 / 3) * sin(A)Taking the inverse sine:
C ≈ arcsin((4.5 / 3) * sin(A))C ≈ arcsin(1.5 * sin(A))Note: Since we already found the value of A to be approximately 51.23 degrees, we can substitute this value into the equation to calculate C.
C ≈ arcsin(1.5 * sin(51.23))C ≈ arcsin(1.5 * 0.773)C ≈ arcsin(1.1595)C ≈ 69.13 degreesAccording to the above we can conclude that the angles of the triangle are approximately:
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Question 11 of 19
On Monday, stock XYZ opened at $8.94. On Friday, it closed at $10.12. What
is the rate of change of stock XYZ for this particular week?
OA. 13.2%
B. 10.1%
C. 1.2%
D. 8.9%
The rate of change of stock XYZ for this particular week is 13.2%, which is option A.
To calculate the rate of change of stock XYZWe need to find the percentage change from the opening price to the closing price.
The percentage change is calculated as follows:
Percentage change = ((closing price - opening price) / opening price) x 100%
Plugging in the given values, we get:
Percentage change = (($10.12 - $8.94) / $8.94) x 100%
Percentage change = ($1.18 / $8.94) x 100%
Percentage change = 0.132 x 100%
Percentage change = 13.2%
Therefore, the rate of change of stock XYZ for this particular week is 13.2%, which is option A.
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Translate (-2,-2) up 1 unit. Then reflect the result over the x-axis. What are the coordinates of the final point?
Answer:
The coordinates should be (2,-1) also theres a website my friend showed me called mathaway it answers any question except word problems :)
Step-by-step explanation:
Please help !!!! ASAP
Answer:
Solution given:
length of arc LM={angle}/360*2*π*r
=here π=180 for angle and π for length
=(3π/4)/360*2*π *6
=(3*180/4)/360*2*π*6
=9/2π
option C
9/2π is a required answer.
Force f acts between a pair of charges, q1 and q2, separated by a distance d. for each of the statements, use the drop-down menus to express the new force in terms of f. q1 is halved, q2 is doubled, but the distance between the charges remains d. q1 and q2 are unchanged. the distance between the charges is doubled to 2d. q1 is doubled and q2 is tripled. the distance between the charges remains d.
The initial force between the two charges is given by:
\(F=k\frac{q_{1} q_{2} }{d^2}\)
where k is Coulomb's constant, q1 and q2 are the two charges, and d is their separation. Let's analyze now the other situations:
1. F
In this case, q1 is halved, q2 is doubled, but the distance between the charges remains d.
So, we have:
q'₁=q₁/2
q'₂=2q₂
d'=d
So, the new force is:
\(F'=k\frac{q'_{1}q'_{2} }{d^2} \\\\F'=k\frac{(\frac{q_{1} }{2})(\frac{q_{2} }{2}) }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{d^2} =F\)
So the force has not changed.
2. F/4
In this case, q1 and q2 are unchanged. The distance between the charges is doubled to 2d.
So, we have:
q'₁=q₁
q'₂=q₂
d'=2d
So, the new force is:
\(\\F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{2d^2} \\\\F'=\frac{1}{4} k\frac{q_{1}q_{2} }{d^2} \\\\F'=\frac{F}{4}\)
So the force has decreased by a factor of 4.
3. 6F
In this case, q1 is doubled and q2 is tripled. The distance between the charges remains d.
So, we have:
q'₁=2q₁
q'₂=3q₂
d'=d
So, the new force is:
\(F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{2q_{1}3q_{2} }{d^2}\\ \\F'=6k\frac{q_{1}q_{2} }{d^2} =6F\)
So the force has increased by a factor of 6.
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Answer:
1. F
2. F/4
3. 6F
Please help!! I have 10 minutes left!!
Which values will be part of the sequence?
3, 4.5, 6, 7.5, …
A. 9
B. 11.5
C. 15
D. 19.5
Answer:
9
just add 1.5 to each of the numbers
Answer:
9
Step-by-step explanation:
because 3, 4.5, 6, 7.5
3 to 4.5 it skips over 4 then 4.5 to 6 it skips over 5 and 5.5 and because the pattern i see it is 9 because it is gonna skip 8 and 8.5
Find the Surface area of the trapezoid
please help
show work
Answer:
259.5
Step-by-step explanation:
8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5
Kellen cuts a foam block along the red line. When he looks at the newlyexposed face, what is the shape of the cross-section?9 cm7 cm5 cmA. A square, 7 cm by 7 cmB. A rectangle, 7 cm by 5 cmC. A rectangle, 9 cm by 5 cmD. A rectangle, 9 cm by 7 cmSUBMIT
The answer is B, A rectangle, 7 cm by 5 cm
Carlton is a project manager for a landscape design company. He is analyzing the duration of four current projects. Which graph best shows how many days each project has lasted? A. B. C. D.
Answer:i am pretty sure it is c
Step-by-step explanation:
this is because it says Which graph best shows how many days each project has lasted? and c is the only one that is talking about days
Find x rounded to the nearest while number
Answer:
10.35
Step-by-step explanation:
The given triangle is a right angled ∆ .The data given is ,
Base = x Hypontenuse = 23 Angle = 63° .We can use ratio of cosine here , as ,
=> cos∅ = b/h
=> cos 63° = x/23
=> 0.45 = x/23
=> x = 23 × 0.45
=> x = 10.35
Hence the value of x is 10.35