The average charitable contribution itemized per income tax return in a certain state is $792. Suppose that the distribution of contributions is normal with a standard deviation of $103. Find the limits for the middle 80% of contributions. Round z-value calculations and final answers to 2 decimal places.
Answers
So here we have a typical problem with a normal distribution. The curve defined by a normal distribution looks like this:
We are being asked to find the limits for the middle 80% contributors. This basically means that we'll have to find two values in the horizontal axis. The consition these two values have to met is that 0 is their mid value and the area of the curve limited by them has to be the 80% of the total area under the curve. In order to find these values we will have to use what is known as a z-values table.
Before continuing let's think about the following. We want to find an area centered around z=0 that is the 80% of the total area under the curve. This means that the areas at the left and at the right of this area must have the 10% of the total are each. The z-values table gives us the % of the area under the curve between -∞ and a given z. This means that we have to find the z-values for which this percentage is 10 and 90. So basically in the table we have to find the z's that have 0.10 and 0.90. These are those z-values in the table:
The z-values are given by the sum of the numbers in the rows and those in the columns so basically the values we are looking for are z=-1.28 and z=1.28.
In summary, the 80% of the area under the curve is equal to the are under the curve between z=-1.28 and z=1.28. However these are not the limits we are looking for. We still need to make a transformation. These z-values meet the following relation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where μ is the mean of the normal distribution (in this case this is the the average charitable contribution that is equal to $792), σ is the standard deviation (here it's $103) and x are going to be the limits we are looking for. Then if we use the 2 z-values we found we have:
[tex]\begin{gathered} -1.28=\frac{x-792}{103} \\ 1.28=\frac{x-792}{103} \end{gathered}[/tex]We can multply both sides of each equation by 103 and then substract 792 from both sides:
[tex]\begin{gathered} -(1.28\cdot103)+792=x \\ 660.16=x \\ (1.28\cdot103)+792=x \\ 923.84=x \end{gathered}[/tex]Which means that the middle 80% contributions are between $660.16 and $923.84.
Related Questions
Expand: (m + 4) 0 m2 + 8m + 16 0 m2 + 4m + 16 O mp + m +- 8
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we have the next squared binomial
[tex](m+4)^2[/tex]we have the next formula in order to expand a squared binomial
[tex](a+b)^2=a^2+2ab+b^2[/tex]So we can expand
[tex](m+4)^2=m^2+2(4)(m)+4^2=m^2+8m+16[/tex]so the correct answer is the first one
YOU HAVE TO FIND THE PRODUCT AND THEN SIMPLIFY IT THANK YOU :)
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To find the product of 6 x 3 2/3
First change the mixed number to an improper fraction
That is;
6 x 11/3
we can now proceed to multiply
= 66/3
=22
The question is : what number makes this equation true
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Given
[tex]\frac{2}{3}\div\frac{\placeholder{⬚}}{7}=\frac{14}{21}[/tex]Find
what makes the equation true
Explanation
Let the number be x.
so , the equation becomes
[tex]\frac{2}{3}\div\frac{x}{7}=\frac{14}{17}[/tex]then , by solving this
[tex]\begin{gathered} \frac{2}{3}\div\frac{x}{7}=\frac{14}{21} \\ \\ \frac{2}{3}\times\frac{7}{x}=\frac{14}{21} \\ \\ \frac{14}{3x}=\frac{14}{21} \\ \\ x=7 \end{gathered}[/tex]Final Answer
Therefore ,
[tex]\frac{2}{3}\div\frac{7}{7}=\frac{14}{21}[/tex]A home is on the market for $315,00, After 90 days, the seller reduces the price by 8%. What is the new price of the home Whats the anwser
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315,000 x 0.08 = 25,200
Subtract product from original price
Answer: 289,800
PLEASE. HELP
The table shows the number of gallons of paint Mrs. Brown used to paint the of rooms in her house. Find the slope of the line
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Answer: 2/3
Step-by-step explanation:
solve equations by factoring:4x^2-81=0
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We have the equation:
[tex]4x^2-81=0[/tex]We can see that there is a differnce of squares:
[tex]4x^2-81=(2x)^2-9^2[/tex]And then we can rewite the difference of squares as:
[tex](2x)^2-9^2=(2x-9)(2x+9)[/tex]And this is equal to 0:
[tex](2x-9)(2x+9)=0[/tex]Now, there are two possibilities:
[tex]\begin{gathered} 2x-9=0 \\ Or_{\colon} \\ 2x+9=0 \end{gathered}[/tex]Then, we need to solve this two equatiions:
[tex]\begin{gathered} 2x-9=0 \\ x=\frac{9}{2} \end{gathered}[/tex][tex]\begin{gathered} 2x+9=0 \\ x=-\frac{9}{2} \end{gathered}[/tex]The two solutions for the equation are:
[tex]\frac{9}{2}\text{ and}-\frac{9}{2}[/tex]Graph 2x+y<1Y>1/2x+2
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We need to graph the next given inequalities:
[tex]\begin{gathered} 2x+y<1 \\ \text{and} \\ y>1/2x+2 \end{gathered}[/tex]For 2x+y<1.
We need to find the x-intercept and y-intercept
To find the y-intercept, set x=0
[tex]\begin{gathered} 2(0)+y<1 \\ \text{Then} \\ y<1 \\ \text{The y-intercept is the point (0,1)} \end{gathered}[/tex]To find the x-intercept, set y=0
[tex]\begin{gathered} 2x+0<1 \\ \text{solve for x} \\ x<\frac{1}{2} \end{gathered}[/tex]The symbol "<" means less than, so we get the next graph:
For the second inequality y>1/2x+2
To find the y-intercept, set x=0
Transform each graph as specified below.(a) The graph of y=f(x) is shown. Draw the graph of y=2(x).(b) The graph of y=g(x) is shown. Draw the graph of y=ry=g(2x)
Answers
(a)
In order to graph y = 2f(x), we just need to use the values of y two times higher than the values of y = f(x), that is, a vertical stretch. So we have:
(In black: y = 2f(x), in red: y = f(x))
(b)
In order to graph y = g(2x), we just need to use half the values of x from y = g(x), that is, a horizontal compression. So we have:
(in green: y = g(2x), in blue: y = g(x))
If c(x) = 4x-2 and d(x) = x2 + 5x, what is (c.d)(x)?
O 4x³ + 18x² - 10x
O x² +9x-2
O 16x² + 4x - 6
O4x² + 20x - 2
Answers
In a case whereby c(x) = 4x-2 and d(x) = x2 + 5x, is two different equation, then the value of c(d(x)) is 4x2 + 20x - 2.
How can the value of the expression c(d(x)) be calculated?the first equation is been given as c(x) = 4x-2
And the second equation is been given as d(x) = x2 + 5x
Then to know the value of c(d(x)) then we will need to find the multiplication of the values that is been associated with c and d and this can be done as:
c(d(x)) = [c(x2 + 5x)]
And this will give us
=[ 4(x2 + 5x) - 2]
then after expansion we will have 4x2 + 20x - 2, going through the solution, we can see that the function that is given is been followed and the values for each of the function is been substituted so that the the value of c(d(x)) can be gotten.
Therefore, option D is correct.
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what is the function of matrices in Algebra 1?
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EXPLANATION
The major application of matrices is to represent linear transformations, that is, generalization of linear functions.
2. Which statement best describes the relationship based on the graph?
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Sandsher, this is the solution to the exercise:
As you can see in the image, when the outside temperature increases, there is also an increase in the number of cars sold. However, we are not sure if the outside temperature is the only cause to explain such trend, and the increase is not constant and steady.
In consequence, the correct answer to this exercise is:
C. An increase in temperature is related to an increase in cars sold.
Question 1 (1 point) page 6 #1 Match each spinner with its likelihood to land on black. Column A Column B 1. impossible a 2. unlikely 3. equally likely 4. likely 5. certain b. - o Type here to search
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Answer:
1.......c
2.....a
3.....b
4......e
5.....d
Because of the size of the black section,
A track coach is standing in the center of a circular track whose diameter is 70 meters and she has to rotate 280 degrees to watch her runner. how far has the runner traveled?
Answers
Diameter is 70m
Thus radius = half of diameter= 70/2 = 35meters
Angle of rotation (teta) = 280 degrees
The distance covered will be
[tex]\begin{gathered} \text{Distance = }\frac{\theta}{360^0}\times2\times\pi\times r \\ =\text{ }\frac{280}{360}\times2\times3.142\times35 \\ =\frac{61583.2}{360} \\ =171.06\text{ meters} \end{gathered}[/tex]The runner has traveled 171.06 meters
A plant is 6.2cm tall.
The height of the plant increases by 11% each week
Find how tall the plant will be after 2 weeks
Answers
If A plant is 6.2cm tall. The height of the plant increases by 11% each week. Then 7.564 cm is the height of plant after two weeks.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
A plant is 6.2cm tall
The height of the plant increases by 11% each week
Let us convert 11% to the decimal value by dividing 11 with 100.
11/100=0.11
Now we have to find height plant will be after 2 weeks.
The increase of plant length in 1 week will be
0.11×6.2=0.682 inches
For 2 weeks it is 2×0.682
=1.364
Now add the initial length with increment of height to find the height after 2 weeks.
6.2cm+1.364m=7.564cm
Hence 7.564 cm tall the plant will be after 2 weeks
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Excuse the quality of my picture. I am trying to find which piecewise functions are represented by this graph.
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Let's begin with the line that goes from minus infinity to zero
the equation of this line is
[tex]y=x+2[/tex]because of the filled circle we know that this interval touch the zero
[tex](-\infty,0\rbrack[/tex]in inequality, this will be
[tex]x\le0[/tex]then for the line that is between 0 and 2, we have a filled circle in the number two therefore we can touch this number
the interval will be
[tex](0,2\rbrack[/tex]in inequality notation
[tex]0 for the line that starts in 2 we have an emptythe interval
[tex](2,\infty)[/tex]in inequality notation
[tex]x>2[/tex]Therefore the piecewise function i
[tex]f(x)=f(x)=\begin{cases}x+2,ifx\le0 \\ \frac{x}{3}+1,if02\end{cases}[/tex]the correct option is the second one
someone help i’m stuck on this :c
Answers
Answer:
40 m × 7 m28 m × 10 mStep-by-step explanation:
You want possible dimensions of a field that is 280 square meters in area and has a 3-sided perimeter of 54 meters or less.
DefinitionsFor the purpose here, we can define the length of the field as the distance parallel to the river. Then the width is the distance out from the river.
DimensionsPossible whole-number dimensions of the field can be found by considering factor pairs of 280. Listing length first, we could have ...
280 = (280)(1) = (140)(2) = (70)(4) = (56)(5) = (40)(7) = (35)(8) = (28)(10) = (20)(14) . . . and the reverse of these
Perimeter fenceThe length of the fence required will be the length plus 2 times the width. For the factor pairs shown, the fence lengths, respectively, are ...
282, 144, 78, 66, 54, 51, 48, 48, 54, 66, 78, 87, 117, 144, 282, 561 . . . meters
The highlighted values are 54 meters or less, corresponding to dimensions ...
40 m × 7 m35 m × 8 m28 m × 10 m20 m × 14 m14 m × 20 mPossible dimensions are 40 m by 7 m, and 28 m by 10 m.
__
Additional comment
As you have noted, other values of dimensions are possible, for example, 22.4 m × 12.5 m, a size requiring a fence 47.4 m long.
I need help with math
Answers
Frank's Hardware's store has a rectangular logo with a width of 3.4m
and area 13 square meters, we are to obtain the length,
[tex]\begin{gathered} \sin ce\text{ Area=L}\times B \\ The\text{ equation becomes;} \\ L=\frac{13}{3.4} \end{gathered}[/tex]hi I need help with this question because my math teacher explains it very hardly for me to understand
Answers
The reflection image is as follows,
Write the equation of the line that passes through the points (-3,1) and (-5,8).Put your answer in fully reduced point-slope form
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Answer:
y - 1 = -7/2 (x + 3 )
Explanation:
The point-slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]where (x_1, y_1) is a point on the line and m is the slope.
Let us first find the slope.
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{8-1}{-5-(-3)}[/tex][tex]m=-\frac{7}{2}[/tex]A point on the line we are told is (-3, 1); thereofore, (x_1, y_1) = (-3, 1); hence
[tex]y-1=-\frac{7}{2}(x+3)[/tex]In the figure, KM is perpendicular to JL Point Pis the midpoint of JL.KMGiven AJPKALPK and AJPM - ALPM, which criterion can be directly applied to show that AKIM AKLM?CAGReview progres
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In this problem we have that
JK=KL
JM=LM
and
KM is a common side
therefore
triangle KJM and triangle KLM are congruent by SSS
Help find the volume and write in terms of Pi
Answers
Answer:
The volume of the cylinder is 3584π cubic yards.
Explanation:
The given figure is a cylinder. The volume of a cylinder, V is calculated using the formula below:
[tex]V=\pi r^2h[/tex]From the diagram:
• The radius of the cylinder, r = a = 8 yd.
,• The height of the cylinder, h = b = 56 yd.
Substitute these values into the formula above:
[tex]\begin{gathered} V=\pi\times8^2\times56 \\ =3584\pi\:cubic\;yards \end{gathered}[/tex]The volume of the cylinder is 3584π cubic yards.
The cost of a taxi ride is $1.451.45 for the first mile and $1.251.25for each additional mile or part thereof. Find the maximum distance we can ride if we have $42.742.7. Enter your answer as an integer or a decimal. If needed, round to the nearest tenths of miles.
Answers
The maximum distance is 34.4 miles
Explanation:Given that:
The ride costs $1.45 for the first ride, and $1.25 for each additional mile or part thereof.
Having $42.7, the maximum distance we can ride is given as:
[tex]\begin{gathered} 42.7=1.45+1.25x \\ \\ 1.25x=42.7-1.45 \\ x=\frac{42.7-1.45}{1.25}=34.4 \end{gathered}[/tex]The maximum distance is 34.4 miles
A survey was conducted to find the possible relationship between age groups and the most favored of three book genres. The data is representedin the frequency table.MotivationalDo-It-YourselfTotalBiographies1101134026321-30 years31-40 years804421995· 10741-50 years9269268Total285153312750To the nearest tenth, what percentage of people were in the 41 – 50 age group and favored the Do-It-Yourself books?
Answers
The Solution.
The total number of people surveyed = 750.
The number of age group 41 - 50 that favored the Do-It-Yourself books = 69
The percentage of the people in age group 41 - 50, and favored the Do-It-Yourself books is calculated as below:
[tex]\frac{69}{750}\times100=9.2\approx9\text{ \%}[/tex]Hence, the correct answer is 9 percent.
describe the transformation.
[tex]y = x {}^{2} \: to \: y = 2(x - 3) {}^{2} + 4[/tex]
Answers
Answer:
A translation of 3 units to the right, followed by a vertical stretch by a factor of 2, followed by a translation of 4 units up.
Step-by-step explanation:
Transformations
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]\begin{aligned} y =a\:f(x) \implies & \textsf{$f(x)$ stretched/compressed vertically by a factor of $a$}.\\& \textsf{If $a > 1$ it is stretched by a factor of $a$}.\\& \textsf{If $0 < a < 1$ it is compressed by a factor of $a$}.\end{aligned}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
Therefore, the series of transformations of:
[tex]y=x^2 \quad \textsf{to} \quad y=2(x-3)^2+4\quad \textsf{is}:[/tex]
Translated 3 units to the right:
[tex]f(x-3)\implies y=(x-3)^2[/tex]
Stretched vertically by a factor of 2:
[tex]2f(x-3)\implies y=2(x-3)^2[/tex]
Translated 4 units up:
[tex]2f(x-3)+4\implies y=2(x-3)^2+4[/tex]
Therefore, the series of transformations is:
A translation of 3 units to the right, followed by a vertical stretch by a factor of 2, followed by a translation of 4 units up.
How much would $150 invested at 8% interest compounded continuously beworth after 17 years? Round your answer to the nearest cent.
Answers
Answer: A. $584.43
Explanation
Given
[tex]A(t)=P\cdot e^{rt}[/tex]where A(t) is the amount obtained, P is the initial amount, e is a mathematical constant, r is the rate, and t is the time.
Thus, we are also given that:
• P = $150
,• r = 8% = 0.08
,• t = 17
Therefore, replacing the values:
[tex]A(17)=150\cdot e^{0.08(17)}[/tex][tex]A(17)=150\cdot e^{1.36}[/tex][tex]A(17)\approx584.43[/tex]Find the distance between the pair of points,(9, 3), (9,7)Set up the problem here:
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We are given the following two points.
[tex]\mleft(9,3\mright)\: and\: (9,7)[/tex]Let us find the distance between these two points.
Recall that the distance formula is given by
[tex]undefined[/tex]A scatter plot could have a positive and negative relationship.O TrueO False
Answers
Remember that
We often see patterns or relationships in scatterplots. When the y variable tends to increase as the x variable increases, we say there is a positive correlation between the variables. When the y variable tends to decrease as the x variable increases, we say there is a negative correlation between the variables
therefore
The answer is TrueI need some help finding slope from an equation6x-5y=20
Answers
Okay, here we have this:
Considering that the slope of a line with the form Ax+By=C is equal to -A/B, we obtain the following:
m=-6/-5
m=6/5=1.2
Finally we obtain that the slope is 6/5 or 1.2.
Let's solve the exercise in another way, solving for "y", and the coefficient that we obtain from x will be our slope:
6x-5y=20
-5y=-6x+20
y=(-6x+20)/-5
y=-6x/-5-4
y=6/5x-4
Here we can see that the slope is 6/5.
Draw ALMN with vertices L(3,-1), M(7,-3), and N(6,3). Find the coordinates of the vertices after a 90° rotation about the origin and about each of the points L, M, and N. what are the coordinates of the points after a 90° rotation about the origin? L=? M=? N=?
Answers
Answer:
The coordinates of the image are;
[tex]\begin{gathered} L^{\prime}=(-1,-3) \\ M^{\prime}=(-3,-7) \\ N^{\prime}=(3,-6) \end{gathered}[/tex]Explanation:
Given the coordinates of L,M and N as;
[tex]\begin{gathered} L=(3,-1) \\ M=(7,-3) \\ N=(6,3) \end{gathered}[/tex]A 90 degree clockwise rotation can be represented as;
[tex](x,y)\rightarrow(y,-x)[/tex]Applying this rule to the given coordinates we have;
[tex]\begin{gathered} L(3,-1)\rightarrow L^{\prime}(-1,-3) \\ M(7,-3)\rightarrow M^{\prime}(-3,-7) \\ N(6,3)\rightarrow N^{\prime}(3,-6) \end{gathered}[/tex]Therefore, the coordinates of the image are;
[tex]\begin{gathered} L^{\prime}=(-1,-3) \\ M^{\prime}=(-3,-7) \\ N^{\prime}=(3,-6) \end{gathered}[/tex]To install an outdoor swimming pool will cost you £800 in England. how much will it cost you to install a swimming pool of the same capacity in South African Rand?
Answers
Answer:
It would cost you approximately R15836.13