By central limit theorem ,with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.
The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.
Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.
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oncerns about climate change and co2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). random samples of 47 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) if the true mean is .9340 with a standard deviation of 0.0030, within what interval will 98 percent of the sample means fall? (round your answers to 4 decimal places.)
The interval is from 0.9330 to 0.9350
For given condition;
mean = 0.9340
standard deviation = 0.0030
z-score at 98% = 2.33
n = size of sample = 47
Step 1: calculate the standard error of the mean
standard error of mean = z-score * standard deviation/sqrt(n)
= 2.33 * 0.0030/[tex]\sqrt{47}[/tex]
= 0.0010
step 2: upper limit = mean + standard error
= 0.9340 + 0.0010
= 0.9350
lower limit = mean - standard error
= 0.9340 - 0.0010
= 0.9330
Hence, the interval is from 0.9330 to 0.9350
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What is the
intermediate step in the form
(x + a)² = b as a result of completing
the square for the following equation?
-3x² - 35x - 189 = 13x
Using completing the square method (x + 8)2 = +1 is the intermediary step in the equation (x + a)2 = b after the square is complete.
What is completing the square method?A quadratic problem can be solved using the Completing the Square method. In order to do this, the equation's form must be altered so that the left side is a perfect square trinomial. Finding the roots or zeros of a quadratic polynomial or a quadratic equation is the most frequent use of the completing the square method, which also covers factoring quadratic equations.Get the intermediate step:
-3x² - 35x - 189 = 13x-3x² - 35x -13x- 189 = 0-3x² - 48x- 189 =0Divide the equation by 3 into both sides:
-x² - 16x- 63 = 0x² + 16x +63 = 0Adding 1 on both sides to complete the square:
x² + 16x +63 +1 = 1x² + 16x +64 = 1(x + 8)² = +1Therefore, (x + 8)2 = +1 is the intermediary step in the equation (x + a)2 = b after the square is complete.
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The value of x =5 is a solution to each of the following except which ?
A 3x+2=4x-3
B (x+2)(x-5)=0
C4x+2=15
D 3x-10=x
Answer:
The answer is C
Step-by-step explanation:
If you substitute every x value for 5, you know that every equation can have 5 as an answer but C.
A. 3x+2=4x-3
Isolate the x(s) and combine like terms
3x+2-2=4x-3-2
3x=4x-5
3x-4x=4x-4x-5
-x=-5
-x(-1)=-5(-1)
x=5
Therefore A is a solution
B. (x+2)(x-5)=0
Substitution--Substitute every x for a 5
(7)(0)=0
anything multiplied by 0 will be 0
B. Is a solution because it is true.
C. 4x+2=15
Isolating the x(s) and combine like terms
4x+2-2=15-2
4x=13
4x÷4=13÷4
x=3.25
C is not a solution because x should equal to 5 but in this equation x can only be equal to 3.25. C is wrong.
We know our answer so we don't have to keep solving the rest of the equations.
But I'll just do D
D. 3x-10=x
Isolate the x(s) and combine like terms
3x-x-10=x-x
2x-10=0
2x=10
2x÷2=10÷2
x=5
D is a solution.
Area of circle when r is 14
Answer:
The area is 196π, or 615.752160 when evaluated to 6 decimal places.
Step-by-step explanation:
There is an equation for the area of a circle:
A=π[tex]r^{2}[/tex], Where A is the area and r is the radius. π is π, it is its own number. Plugging in the radius stated we can evaluate:
A=π([tex]14^{2}[/tex])
A=196π
If we write out π and evaluate with an (un)reasonable amount of decimal places:
π≅3.1415926536
A=196×(3.1415926536)
A≅615.752160
Answer:
A = [tex]\pi ^{2}[/tex]
Step-by-step explanation:
A≈615.75
PLEASE HELP I NEED THIS ASAP PLEASE!!!!
Answer: Radius (r) 5.99848 in
Diameter 11.99696 in
Circumference (c) 37.68955 in
Area 113.04in²
Radius (r) 5.99848 in
Diameter 11.99696 in
Circumference (c) 37.68955 in
Area 113.04 in²
Radius (r) 0.999493 in
Diameter 1.998986 in
Circumference (c) 6.28 in
Area 3.13841 in²
Radius (r) 8.49569 in
Diameter 16.99138 in
Circumference (c) 53.38 in
Area 226.75 in²
Radius (r) 2.5 cm
Diameter 5 cm
Circumference (c) 15.70796 cm
Area 19.63495 cm²
Radius (r) 1.1 yd
Diameter 2.2 yd
Circumference (c) 6.9115 yd
Area 3.80133 yd²
Radius (r) 2 in
Diameter 4 in
Circumference (c) 12.56637 in
Area 12.56637 in²
Step-by-step explanation: I hope this helps.
what is the size of the angle between north west and south east?
180°
Step-by-step explanation:Size of the angle between:North and South: 180°East and West: 180°North East and South West: 180°North West and South East: 180°North West and North East: 90°South West and South East: 90°Find the distance between the points (10, 1) and (9, -4) using the distance formula. Round to the hundredths
place.
A: 3.16
B: 5.00
C: 3.00
D: 5.10
Please explain.
Answer:
3.16
Step-by-step explanation:
the number after the decimal point you add the and before are added s example0.1=one is tenth1.6=one is tensA line that includes the point (3,10) has a slope of 4. What is its equation in slope intercept form?
The slope intercept form of equation of the line is y = 4x - 2
The slope intercept form of equation of the line that includes the point (3,10) has a slope of 4. is y = 4x - 2
What is equation of a straight line in slope intercept form?This is an equation of the form y = mx + c, where:
the coefficient of x is the slope
c is the intercept
To calculate the equation of the line that include point (3,10) has a slope of 4 we solve as follows
( y - y' ) / ( x - x' ) = 4
( y - y' ) = ( x - x' ) = 4
where y' = 10, and x' = 3
y - 10 = (x - 3 ) * 4
y - 10 = 4x - 12
y = 4x - 12 + 10
y = 4x - 2
The slope intercept form of equation of the line is y = 4x - 2
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If the first term of gp is 1 and 4th is 27 find the ratio term and the 9th term
The ratio term of given geometric progression is 3 and the 9th term of the GP is 6561.
What is Geometric Progression?
A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54,_ _ _ _ has a common ratio of 3.
Given in question,
first term of the GP is 1,
4th term of the GP is 27,
[tex]4^{th} term = ar^3[/tex]
[tex]ar^3 = 27[/tex]
Therefore, the ratio term of geometric progression, r = 3
We know that, [tex]a_n = ar^{n-1}[/tex]
[tex]a_9 = ar^8[/tex]
[tex]a_9 = 3^8[/tex]
a9 = 6561
Therefore, the 9th term of given geometric progression is 6561.
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36. THOUGHT PROVOKING
Describe a function in which the inputs and/or the
outputs are not numbers. Identify the independent
and dependent variables. Then find the domain and
range of the function.
Answer:
A function is a relation where each input value is assigned to only one output value. The domain of a function is the set of all input values, or x-values, for which the function is defined. The range of a function is the set of all output values, or y-values, for which the function is defined. To write the equation y = ax + b in function notation, substitute f(x) for y.
Step-by-step explanation:
Brainlest, Please!
betty and karen have been hired to paint the houses in a new development. working together, the women can paint a house in two-thirds the time that it takes karen working alone. betty takes 4 h to paint a house alone. how long does it take karen to paint a house working alone?
Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour then Karen working alone will paint a house in 3 hours.
How long does it take paint a house working alone?Since Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour.
Karen can even paint 1/x in 1 hour
Both of them will paint the house in 3/2 hours.
We then add them together which gives:
1/6 + 1/x = 3/2x
The lowest common multiple is 6x
1x/6x + 6/6x = 9/6x
We then leave out the denominators
1x + 6 = 9
simplifying the above equation, we get
x = 9 - 6
x = 3
Therefore, the value of x = 3.
Karen working alone will paint a house in 3 hours.
The complete question is:
Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 14 h to paint a house alone. Betty takes 6 h to paint a house alone.
Required:
How long does it take Karen to paint a house working alone?
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15
4. If M is the midpoint of line segment EF. E is located at (10,-8) and M is located at (-6, -2). Find the other
endpoint.
Answer:
The other endpoint is F( - 22, 4)=============================
GivenSegment EF with:
Endpoint E = (10, - 8),Midpoint M = (- 6, - 2),Endpoint F = (x, y).SolutionUse midpoint equation:
x = (x₁ + x₂)/2, y = (y₁ + y₂)/2Find unknown coordinates of the point F:
- 6 = (10 + x)/2 ⇒ -12 = 10 + x ⇒ x = - 12 - 10 = - 22,- 2 = (- 8 + y)/2 ⇒ - 4 = - 8 + y ⇒ y = - 4 + 8 = 4.So the point is F = ( - 22, 4)
Answer:
F = (-22, 4)
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\ \textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.}[/tex]
Given information:
Midpoint = (-6, -2)E = (10, -8)Define the endpoints of the line segment EF:
Let (x₁, y₁) = endpoint E = (10, -8)Let (x₂, y₂) = endpoint FSubstitute the given information into the formula:
[tex]\implies (x_M,y_M)=\left(\dfrac{x_F+x_E}{2},\dfrac{y_F+y_E}{2}\right)[/tex]
[tex]\implies (-6,-2)=\left(\dfrac{x_F+10}{2},\dfrac{y_F-8}{2}\right)[/tex]
Find the x-coordinate of M:
[tex]\implies \dfrac{x_F+10}{2}=-6[/tex]
[tex]\implies x_F+10=-12[/tex]
[tex]\implies x_F=-22[/tex]
Find the y-coordinate of M:
[tex]\implies \dfrac{y_F-8}{2}=-2[/tex]
[tex]\implies y_F-8=-4[/tex]
[tex]\implies y_F=4[/tex]
Therefore, the coordinates of endpoint F are (-22, 4).
which is true about box plots? group of answer choices boxplots show the number of datapoints between any two values boxplots present the shape of the distribution (density curve) boxplots can involve a categorical variable and a continuous numerical variable boxplots show the size of the data set (number of data points) boxplots visually present the mean and standard deviation boxplots show where the peak of the distribution is
Box plots present the shape of the distribution (density curve), Box plots can involve a categorical variable and a continuous numerical variable, Box plots show where the peak of the distribution is are the correct statement.
Instead of showing the raw data points, Box Plots takes the sample data and then present the ranges of values based on the quartiles and also display the asterisks for outliers that generally falls outside the whiskers.
Yes, the shape of distribution can be understood from a Box Plot. It can show whether a statistical data set is normally distributed or skewed.
A Box plot is a graph of the distribution that has Continuous variables. It is also applicable for Categorical variables.
Box Plot generally shows the below parameters: Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.
A size can be determined by using these parameters but is not directly seen in a Box Plot
Generally a Standard Deviation is not visualized by Box Plot. It mainly visualizes Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.
Yes, the peak of the distribution can be analyzed from Box Plot
Generally for Normal Distribution, Mean = Median and this is the point where the peak is seen.
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at a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 20 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate (in ft/min) is the height of the pile changing when the pile is 22 feet high? (hint: the formula for the volume of a cone is v
When the pile is 22 feet high, the height of the pile changes to 20/1089π.
Given (dV)/(dt) = 20, h = 22 feet , dh /dt =?
The volume of cone is V = 1/3 * pi * r ^ 2 * h
d=3h
2r = 3h
r = (3h)/2
V = 1/3 * pi * r ^ 2 * h
= 1/3 * pi * ((3h)/2) ^ 2 * h
= 1/3 * pi((9 * H ^ 2 )/4) * h
= (9pi)/12 * h ^ 3
Differentiate w.r.to t
(dV)/(dt) = (3pi)/4 * (3h * h^ 2) * (dh)/(dt)
(dV)/(dt) = (9pi)/4 * (h ^ 2) * (dh)/(dt)
(dV)/(dt)=20, h=22 feet
20 = (9pi)/4 * (22 ^ 2) * (dh)/(dt)
(dh)/(dt) = 80/ (9pi * (22^ 2))
h^ t = 20/ 1089 *pi ft / min
Therefore, The height of the pile changing when the pile is 22 feet high is 20/1089π
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What is -5/7 times (-1/6)
Answer:
5/42 or 0.1190
hope this helps :)
The first three terms of an arithmetic sequence are as follows.17, 25, 33Find the next two terms of this sequence.17, 25, 33,
The sequence is given by the following formula:
[tex]y_{i+1}=y_{i-1}+8[/tex][tex]\begin{gathered} y_0=17 \\ y_1=17+8=25 \\ y_2=25+8=33 \\ y_3=33+8=41 \\ y_4=41+8=49 \end{gathered}[/tex]Finally, the answers are 41 and 49.
What measure of variance is best to describe Mr. Mack’s 1st period scores?Choose the correct one MeanMedianModeInterquartile range Standard deviation Variance
Step 1
The measures of variance include;
[tex]\begin{gathered} 1)\text{ Interquartie Range} \\ 2)\text{ Range} \\ 3)\text{ Standard deviation} \\ 4)\text{ Variance} \end{gathered}[/tex]Step 2
For a bar chart, we have that;
[tex]undefined[/tex]Which of the following is NOT a misuse of statistics?Choose the correct answer below.A. Utilizing valid statistical methods and correct sampling techniquesB. Making conclusions about a population based on a voluntary response sampleC. Concluding that a variable causes another variable because they have some correlationD. Misleading graphs
Required:
We need to find the statement which is NOT a misuse of statistics.
Explanation:
Recall that misuse of statistics occurs when a statistical argument asserts a falsehood.
Utilizing valid statistical methods and correct sampling techniques is not a misuse of statistics.
Final answer:
A. Utilizing valid statistical methods and correct sampling techniques
Kennedy has $0.81 worth of pennies and nickels. she has 9 more nickels than pennies. write a system of equations that could be used to determine the number of pennies and the number of nickels that kennedy has. define the variables that you use to write the system.
Variable used to write the equation are x, Number of pennies and y, Number of nickels and the system of equations used is x+y=0.81 and x+9=y.
An equation is a mathematical statement that shows that two mathematical expressions are equal.
Let the variables defined to form the system of equation are as follows:
x= Number of pennies
y= Number of nickels
Total worth of pennies and nickels is 0.81
mathematically, x+y=0.81
Given condition, she has 9 more nickels than pennies
mathematically, x+9=y
So, the system of equation which can be used to determine the number of pennies and the number of nickels that Kennedy has are x+y=0.81 and x+9=y, where variables used are x and y.
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Chad doesnt have any money, but he owes his sister $15, owes his brother $9 and owes his friend $24. What integer could be used to represent the amount of money chad has?
Answer:
- 48.00
Step-by-step explanation:
Add all the debt up.
Answer: -48
Step-by-Step Explanation:
Money that Chad owes his Sister = $15
Money that Chad owes his Brother = $9
Money that Chad owes his Friend = $24
Total Money he owes = 15 + 9 + 24 = $48
Hence, Total Money he has = -48 (since he doesn't have any money)
FIND THE MEASURE OF EACH ANGLE<1 and <2 form a linear pair and m<2= 52 degrees.
Linear pair angles are the ones that form a straight line, in other words they will form a 180º angle. Therefore if the angle 2 measures 44 degrees we can find the angle 1 by doing as follows:
[tex]\begin{gathered} \measuredangle1+\measuredangle2=180 \\ \measuredangle1+52=180 \\ \measuredangle1=180-52 \\ \measuredangle1=128 \end{gathered}[/tex]The angle one is equal to 128 degrees.
For which value of x does the graph of the following function F(x) have a
vertical asymptote?
F(x) =
1
X-11
Answer:
x = 1
Step-by-step explanation:
Horizontal asymptotes are the y-values for which a particular function is undefined;
Finding the horizontal asymptote for linear reciprocal function is quite simple;
For this kind of function, where there is no x term in the numerator, the horizontal asymptote is just equivalent to the constant added to the fraction (note: having no added constant is the same as having an added 0);
so:
f(x) = 1/(x - 1) = (1/( - 1 )) + 0
The horizontal asymptote is y = 0 for this function.
If it was F(x) = (1/(x - 1)) + 1, the horizontal asymptote would be y = 1
hope it help!! :)
Solve each equation.
4/7 v = -8 2/3
[tex] \frac{4}{7} v = - \frac{26}{3} \\ - 26(7) = 4v(3) \\ - 182 = 12v \\ \frac{ - 182}{12} = \frac{12v}{12} \\ v = - 15 \frac{2}{12} \\ v = - 15 \frac{1}{6} [/tex]
BE AWARE I USED CROSS MULTIPLICATION.
Mandrel has 15 electronic books and 24 education CDs. He gives 5 books and 12 CDs to his nephew. What
ratio of each did he give to his nephew? Are the ratios proportional?
Answer:
10:12
Step-by-step explanation:
15-5=10
24-12=12
og ratio is 15:24
new ratio is 10:12
+) The expression 5p represents the total price of buying 5 movie tickets. ) What do the parts of the expression 5p represent? • The variable p represents the ? The number 5 represents the ?
Since the expression 5p represents the total price of buying 5 movie tickets, divide the expression 5p by 5 to find the price of a single ticket:
[tex]\frac{5p}{5}=p[/tex]Then, the price of a ticket is p.
Therefore, the variable p represents the ticket price, while the number 5 represents the number of tickets.
need help on this, thanks
The value of question are 65+[tex]\underline{115}[/tex]=180, [tex]11x+\underline{48}=180^o[/tex], [tex]11x=\underline{132}[/tex] and [tex]x=\underline{12}[/tex].
In the given question we have to find the value of missing term.
(1) 65+......=180
(2) 11x+.......=180
(3) 11x=.........
(4) x=........
To solve this question we have to use some theorem.
Firstly solving the first question.
As we know that the angle of straight line is 180[tex]^o.[/tex]
So from the diagram
[tex]65+z=180^o[/tex]
Subtract 65 on both side
[tex]65+z-65=180^o-65[/tex]
[tex]z=115[/tex]
Hence, 65+[tex]\underline{115}[/tex]=180.
Now finding the value of second question.
Using Alternate Exterior Angles Theorem
According to theorem the angle beside 11x - 17 is 65.
As we know that the angle of straight line is 180[tex]^o.[/tex]
So 11x-17+65=180[tex]^o.[/tex]
Simplifying
So [tex]11x+\underline{48}=180^o[/tex]
Now finding the value of third question.
From the second question answer we get [tex]11x+{48}=180^o[/tex]
Now solving this equation to find the value of 11x
Subtract 48 on both side
[tex]11x+{48}-48=180^o-48[/tex]
[tex]11x=132[/tex]
Hence, [tex]11x=\underline{132}[/tex]
Now solving the fourth question.
To find the value of fourth question we further simplify the answer of third question.
[tex]11x=132[/tex]
Divide by 11 on both side
[tex]\frac{11}{11}x=\frac{132}{11}[/tex]
[tex]x=12[/tex]
Hence, [tex]x=\underline{12}[/tex]
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Hi please help me on the q
Answer:
x = 30°
Step-by-step explanation:
The angles of a pentagon add up to 540°
Make an equation adding up the angles to equal 540°
x + 4x + 4x + 135° + 135° = 540°
Simplify
9x = 270°
Divide
x = 30°
5 : it is night. someone who is 4 feet tall is walking away from a street light at a rate of 8 feet per second. the street light is 12 feet tall. the person casts a shadow on the ground in front of them. how fast is the length of the shadow growing when the person is 3 feet from the street light? the length of the shadow is growing at a rate of
When a person is 3 feet from a street light, the length of the shadow grows at a rate of 4 feet per second.
See the figure that illustrates the in question statement, attached.
making use of the related triangle theorem;
4/y = 12/x+y
Cross multiply
4(x+y)=12y
4x+4y = 12y
4x=8y
x/y =2
x=2y
Divide the two sides of the equation by t, where dx/dt = 2 dy/dt. The speed at which the person is walking away from the street light is expressed as dx/dt
The growth rate of the shadow's length is measured by the ratio dy/dt.
Given that dx/dt = 8ft/s
by solving,
dy/dt = 4 ft/s
Hence the rate at which the length of the shadow growing when the person is 3 feet from the street light is 4ft/s
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boxes of nails are stacked on top of each other on a work bench. The table below shows how the height above the floor of the topmost box depends on the number of boxes. What is a rule for the height? Give the rule in words and as an algebraic expression.
The height is the sum of 39 and 9 times the number of boxes, n. The rule is 9n + 39.
What is algebraic expression?An algebraic expression is defined as the type of expression that is made up of a variable, a coefficient and a constant.
From the given box of nails,
The height of 2 boxes of nails = (9× 2) + 39 = 57 In
The height of 3 boxes of nails = ( 9 × 3) + 39 = 66 In
The height of 4 boxes of nails = ( 9× 4) + 39 = 75 ln
That is to say that the height of the box above the floor can be calculated by the sum of 39 and 9 times the number of boxes, n.
Therefore, the rule of heights is 9n + 39 where n is the number of boxes present.
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The ratio of 1.4 to 26 is the same as the ratio of 2.8 to ____.