Calculation the variance and standard deviation of the discrete random variable is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation is the square root of Variance 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].
As given in the question,
Variance is used to represent the dispersion of the values in the data from the calculated mean.[tex]( x_{i} - \bar{x})[/tex] represent the dispersion of the given data values from the mean.Variance is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] Standard deviation is the square root of the variance it represents the amount of dispersion of all the given data values.Standard deviation is given by 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].Therefore , the variance and standard deviation of the discrete random variable is calculated with the help of the following formulas:
Variance 'σ²' = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].
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** h(x) = 2f(x).g(x)
Find the value of h’(1), if f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1.
The value of h’(1) is = 22
How may the chain rule example be used?
Solution: Since f′(x)=ex, the exponential function with base e's derivative is simply the function itself. G′(x)=4 is the derivative of g. The chain rule states that h′(x)=f′(g(x))g′(x)=f′(4x)4=4e4x. It was crucial that we assessed f's derivative at 4x in this example.
Given that :
h(x) = 2f(x).g(x)
f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1
h’(x) = 2 f'(x)g(x) + g'(x)f(x) by chain rule
h’(1) = 2 f'(1)g(1) + g'(1)f(1)
= 2 * (4 * 2 + 1 * 3)
= 2* (11)
= 22
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6x-7=1-3x[tex]6x-7=1-3x[/tex]
Answer:
x=8/9
Step-by-step explanation:
step one: move x to one side. to do this, we are going to use inverse operations which means adding 3x to both sides.
3x+-3x cancels itself out and 3x+6x=9x.
now, the equation looks like: 9x-7=1
step two: isolate the variable, x. we want to just get x to be by itself so we need to get rid of the -7 next to it by using inverse operations again. this means we're going to add 7 to both sides.
7+-7 cancels itself out and 7+1=8.
now, the equation looks like 9x=8
step three: divide to get x by itself. we want to know what x alone is, not 9x. to do this we are going to use inverse operations one last time. this means dividing each side by 9, because 9x means "9 times x".
9x/9= x, 8/9
so the answer is x=8/9
hope this helped!!
Solve for c.
4(c + 17) = 16
C =
Please help
Which polynomial is prime?
O x² +7
Ox²-25
O3x²-27
O 2x²-8
Explanation:
All of the polynomials listed are quadratic polynomials, which have the general form ax^2 + bx + c, where a, b, and c are constants and x is a variable. A polynomial is considered prime if it cannot be factored into the product of two or more polynomials with integer coefficients.It is not possible to determine whether any of the given polynomials are prime without further information, such as the values of the constants a, b, and c. For example, the polynomial x^2 + 7 could be prime, but it could also be factored into the product of two linear polynomials (x + 3)(x + 3), which would make it composite. Similarly, the polynomial x^2 - 25 could be prime, but it could also be factored into the product of two polynomials of the form (x + 5)(x - 5), which would make it composite. Without more information, it is not possible to determine whether any of the given polynomials are prime.
Justin is going to invest $90,000 and leave it in an account for 19 years. Assuming
the interest is compounded quarterly, what interest rate, to the nearest hundredth of
a percent, would be required in order for Justin to end up with $216,000?
Answer:
4.63%
Step-by-step explanation:
You want the interest rate that, compounded quarterly, will result in a balance of $216,000 for an investment of $90,000 after 19 years.
Compound interestThe formula for the balance of an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.
ApplicationFilling in the given values, we can solve for r:
216000 = 90000(1 +r/4)^(4·19)
2.4 = (1 + r/4)^76 . . . . . divide by 90,000
2.4^(1/76) = 1 +r/4 . . . . . . take the 76th root
(2.4^(1/76) -1) = r/4 . . . . . . subtract 1
r = 4(2.4^(1/76) -1) ≈ 0.0463437 ≈ 4.63%
The required interest rate is about 4.63%.
Given the Trapezoid, BATS, where B (-4, 2), A (-2, 6), T (6, 6), S (8, 2). Graph and find the approximate area of BATS.
The graph of the trapezoid is shown below. The area is calculated as: D. 40 square units.
How to Find the Area of a Trapezoid?To find the area of a trapezoid, the formula used is given below:
Area of a trapezoid = 1/2 * (a + b) * h, where,
a = length of one of the basesb = length of one baseh = height of the trapezoid.The trapezoid BATS with the following vertices, B (-4, 2), A (-2, 6), T (6, 6), S (8, 2), ahs been plotted in the graph shown in the image attached below.
1 unit = 1 box, therefore, we have the following:
a = length of AT = 8 units.
b = length of BS = 12 units
h = 4 units
Plug in the values:
Area of trapezoid BATS = 1/2 * (8 + 12) * 4
Area of trapezoid BATS = 1/2 * (20) * 4
= 10 * 4
Area of trapezoid BATS = 40 square units.
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If f(x) = x2, g(x) = 5x, and h(x) = x + 4, find each value. 17. f[g(–2)]
a. 7 b. 10 c. 30 d. 100
Answer:
d.) 100
Step-by-step explanation:
To solve, first find the value of g(-2):
[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]
Next, use this value to find f(-10):
[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]
how is (-7.5)-21.04 and (-7.5)+21.04 the same value?
The values (-7.5)-21.04 and (-7.5)+21.04 are not the same
What is a decimal?A decimal can be defined as a number consisting of a whole number and also a fractional part.
These numbers are separated by a dot known as the decimal point
The decimal numeral system is seen as a standard system that denotes integer and non-integer numbers.
It is important to note the following operations;
+ × + = ++ × - = -- × + = -- × - = +From the information given, we have;
(-7.5)-21.04
Multiply the operation
+ 157. 8
Then,
(-7.5)+21.04
Multiply the operation
- 157. 8
Hence, the values are either negative or positive.
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Which equation, when paired with y = 2x 5, creates an inconsistent system? 2x y = 5 y = 2x 5 2x – 4y = 10 2y – 4x = –10
The equation that creases an inconsistent system when paired with y = 2x + 5 is given as follows:
2y - 4x = -10.
What is an inconsistent system?A system of equations is called inconsistent when the number of equations of the system is of zero.
The system in this problem is composed by linear equations, which have the following format:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For inconsistent system, we have that the equations:
Have the same slope.Have different intercepts.The function in this problem is given as follows:
y = 2x + 5.
Hence the inconsistent system is formed with:
2y - 4x = -10.
Which is simplified by 2 as follows:
y - 2x = -5.
y = 2x - 5.
Having the same slope of 2, but a different intercept.
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Answer: 2y – 4x = –10
Step-by-step explanation: trust.
The formula for the volume of a cylinder is V=\pi r^2 h,V=πr
2
h, where rr is the radius of the cylinder and hh is the height of the cylinder. Rewrite the formula to solve for hh in terms of rr and V.V.
The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V / π r².
What is volume?An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.
Given:
V = π r² h
Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.
Take the remaining term of the right side to the left as shown below,
V / π r² = h
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Explain how to solve 2^(x + 1) = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth
The solution of the given expression is equal to 2.17.
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 the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,
[tex]2^{x+1}=9[/tex]
Take logs on both sides,
(x+1) ln(2) = ln(9)
(x+1) = ln(9) / ln(2)
x + 1 = 3.17
x = 2.17
Hence, the expression will be solved by taking log on both sides.
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read the picture plsss
Answer:
Step-by-step explanation:
for what values of x and y are the triangles congruent by HL?
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
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what is the volume of the shape
Answer:
Step-by-step explanation:
Hope it helps!
When Lisa increased her speed in letter c,
the increase took two seconds. What was her acceleration?
Lisa's change in speed is 4 miles per hour.Lisa's acceleration is 2 miles per hour.
What was her acceleration?According to the question,
The speed of Lisa is = 3 miles per hour
A dog starts to chase her, and she speeds up to seven miles per hour.
The change in speed after dog chase her is,
= 7 miles per hour - 3 miles per hour
= 4 miles per hour
Lisa's change in speed is 4 miles per hour.
When Lisa increased her speed in letter c, the increase took two seconds.
Then,
The Lisa acceleration is,
Acceleration = Change in speed/Change in time
Acceleration = 4/2
Acceleration = 2 per mail.
Hence, Lisa's acceleration is 2 miles per hour.
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x^4-2x^2-16x-15=0 find the zeros with work please
ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)
steps
find the zeros JUST MEANS SOLVE FOR X
x⁴-2x²-16x-15=0
break it up
let u = x²
x⁴ = (x²)² = u²
-16x+u²-2u-15=0
hold off on -16x
u²-2u-15=0
what 2 numbers when multiplied give you -15 & when added give you -2?
-5 and 3
(u-5) (u+3)
-16x + (u-5) (u+3) = 0
go back x
-16x + (x²-5) (x²+3) = 0
factor -1 out
( looks horrible so far lol )
-1 ((- x²+ 5) (x²+3) + 16x) = 0
multiply (- x²+ 5) with ( x² + 3 )
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0
-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0
21. Is the following ordered pair (3, 6) a solution of the linear inequality y < -5x + 1?
The pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
What is linear inequality?
A linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
y < -5x + 1
Substitute the points and see if they are true
(3, 6)
6 < -5*(3) + 1
6 < -15 + 1
6 < -14
Not true not a solution
Hence, the pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
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2) the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. the bls reported in february 2012 that the labor force participation rate in the united states was 66.9% (calculatedrisk). a marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. what are the expected value and the standard error for a labor participation rate in the company's sample?
The expected value and the standard error for a labor participation rate in the company's sample is 0.0043
In the given question, the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.
The BLS reported in February 2012 that the labor force participation rate in the united states was 66.9% (calculate risk).
A marketing company asks 120 working-age people if they either have a job or are looking for a job, or the labor force.
We have to find the expected value and the standard error for a labor participation rate in the company's sample.
Working age people sample n = 120
The labor force participation rate in the United States was 66.9% = 0.669
The Expected value is μ = p = 0.669
The standard error:
SE = √p(1-p)/n
SE = √0.669(1-0.669)/120
SE = √0.669*0.331/120
SE = √0.2214/120
SE = √0.001845
SE = 0.043
Hence, the expected value and the standard error for a labor participation rate in the company's sample is 0.0043.
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Deposited (dollars)
12,500
10,000
7,500
$5,000
rate of change=
2,500 initial value=
Time (years)
y
dollars per year
dollars
The rate of change is $2500 per year.
The initial amount is $5000.
What is slope?The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.
The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,
m = (y₂ - y₁)/(x₂ - x₁)
In the given graph,
The initial value that deposited at x = 0 is $5000.
To find the rate of change in amount per year,
Find slope of the line, because rate of change will be equal to slope.
Let two points are (0, 5000) and (1, 7500)
The slope = (7500 - 5000 / 1 - 0) = 2500
The rate of change is $2500 per year.
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suppose a juice box contains 30% juice with the remaining portion of the drink composed of water. what is the solute in this type of juice box?
Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.
Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.
Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.
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Write the coordinates of the vertices after a reflection over the line y=-5.
The coordinates of the vertices after a reflection over the line y = -5 is given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
How to obtain the coordinates of the vertices after the reflection?The vertices of the original quadrilateral are given as follows:
T(-2,-5), U(2,-3), V(-2,-1), W(-3,-3).
The reflection line y = -5 is an horizontal line, meaning that after the reflection:
The x-coordinate remains constant.The y-coordinate will be equidistant to y = -5, however in an opposite direction.For example, the distance of the y-coordinate of the vertex U from -2 is of:
2 units above.
Then the y-coordinate of the vertex U' will be also 2 units from -5, just two units below, hence:
U'(2,-7).
Applying this rule for all the other vertices, they will be given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
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A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do
not have brown hair, while 80% of the people who have brown eyes have brown hair. A relative frequency table was constructed for this data. What is the largest
marginal relative frequency and its interpretation?
A. 0.56; Individuals with brown eyes
B. 0.70; Individuals with brown eyes
C. 0.80; Individuals with brown hair
D. 0.83; Individuals with brown hair
A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do not have brown hair, while 80% of the people who have brown eyes have brown hair. 0.80; Individuals with brown hair. Option C
What is the marginal relative frequency?Generally, The largest marginal relative frequency is 0.80, which corresponds to individuals with brown hair. This means that out of all the individuals in the city, 80% of them have brown hair.
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a company makes wax candles in the shape of a cylinder. each candle has a diameter of 4 inches and a height 8 of inches. if the company used of wax, how many candles did it make? use for , and do not round your answer.
If the company has made 6732.16 in³ wax , Total number of candles made is 67
According to the question,
It is given that a wax candle is in cylindrical shape
Diameter of candle = 4 in
Radius will be = 4 / 2
=> 2 in
Height of each candles = 8 in
Company has used 6732.16 in³ of wax
We have to calculate number of candles company has made
Volume of cylinder = πr²h
Where r is radius and h is height
Substituting all the values,
Volume of candle = π (2)² (8)
=> V = 3.14 × 4 × 8 (putting π = 3.14)
=> V = 100.48
Therefore , Number of candles made = Total volume /volume of one candles
=> 6732.16 / 100.48
=> 67 candles are made by company
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Sadie is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Sadie will earn $40 every time one of her songs is played in a commercial and she will earn $120 every time one of her songs is played in a movie. Sadie's songs were played on 3 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $440. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Sadie's songs were played. Define the variables that you use to write the system.
The number of commercials and movies on which the songs were played are 5 and 2.respectively
How to determine the number of commercials and movies on which the songs were played.From the question, we have the following parameters that can be used in our computation:
Earnings from songs played in commercial = $40Earnings from songs played in movie = $120Total earnings = $440The number of commercials is x, and the number of movies is y
The above parameters when represented as an equation is as follows
40x + 120y = 440
x = y + 3
Substitute x = y + 3 in 40x + 120y = 440
40(y + 3) + 120y = 440
Expand
40y + 120 + 120y = 440
Evaluate the like terms
160y = 320
Divide by 160
y = 2
Recall that
x = y + 3
So, we have
x = 2 + 3
x = 5
Hence, the number of commercials is 5 times
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7x+14y=21,-7x+7y=7 using elimation
Answer:(x,y)=(1/3 , 4/3)
Step-by-step explanation:
What is the radius of the circumscribed circle of ABC?
Answer:
Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle
Step-by-step explanation:
:]
Fatimah ate f cookies. Satvinder ate six fewer than two times the number that Fatimah ate. If Satvinder ate 4 cookies, write and solve an equation to find f, the number of cookies Fatimah ate.
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Fatimah ate f treats. Satvinder ate six less than twice the number that Fatimah ate.
Let 's' be the number of cookies eaten by Satvinder. Then the equation is given as,
s = 2f - 6
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be given as,
4 = 2f - 6
2f = 10
f = 5
On the off chance that Satvinder ate 4 treats, the number of treats that Fatimah ate will be 5.
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a study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. one hundred participants are recruited to participate, and half are randomly assigned to participate in the intervention while the others serve as a control group. what study design is being used?
A study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. The study design being used is a randomized controlled trial (RCT).
What is a randomized controlled trial?Generally, In an RCT, the study participants are randomly assigned to either the intervention group or the control group. This helps to ensure that any differences between the two groups are not due to preexisting differences between them, but rather are due to the intervention being tested.
In this case, the intervention is a daily exercise intervention, and the outcome being measured is blood pressure among people with pre-hypertension.
The control group serves as a comparison group, and any changes in blood pressure observed in the intervention group can be attributed to the intervention rather than other factors.
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AB and CD bisect each other at E m/CAE 80 and m/BDE 60 Amy says that mZCEA = 20°, Brent says that it is 30", Carlos says that it is 40", and Debra says that it is 50" Which
student is correct?
The only person that is correct with respect to the measurement of ∠CEA of the congruent triangles is; Carlos
How to Interpret Congruent Angles?From the diagram attached, we are given that;
The measure of ∠CAE = 80°
∠BDE = 60°
Amy says that m∠CEA = 20°
Brent says that it is 30°
Carlos says that it is 40°
Debra says it is 50°
Now, by inspection, it is clear that ΔCAE is congruent to ΔBDE by SAS Congruency postulate and as such we can say that;
∠A = ∠B and ∠C = ∠D
Thus;
∠B = 80° and ∠C = 60°
Sum of angles in a triangle is 180 degrees and so;
∠CEA = 180 - (80 + 60)
∠CEA = 180 - 140
∠CEA = 40°
Which means that Carlos is correct.
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Rachel van Dressler earns 3% commission on all sales. What was her total sales amount if she earns a commission of $3652
Answer:
Van Dressler's total sales amount is $12,166.6666667
Step-by-step explanation:
3% = $365
365/3*100 =$12,166.6666667
