Answer: b. f(x) is an even function for all even values of m.
Step-by-step explanation:
[tex]f(x)=(x^m +9)^2[/tex]
If m is even, then [tex](-x)^m=x^m[/tex].
This means that [tex]f(-x)=(x^m+9)^2 \implies f(-x)=f(x)[/tex]
Thus, b is the correct answer.
Which of the following are solutions to the equation below?
Check all that apply.
9x² - 6x + 1 =7
O A. x= 2√2
B. x = -√7+1
3
☐ C. X=
□ D. X=
√√7+1
3
+1
□ E. x = 2√2
3
O F. X= -√2+1
Answer: C and B
Step-by-step explanation:
[tex]9x^2 - 6x+1=7\\\\9x^2 - 6x-6=0\\\\x=\frac{-(-6) \pm \sqrt{(-6)^2 - 4(9)(-6)}}{2(9)}\\\\x=\frac{6 \pm \sqrt{252}}{18}\\\\x=\frac{1 \pm \sqrt{7}}{3}[/tex]
Consider the following data on the estimated cost (in millions of dollars) resulting from traffic congestion for different urban areas. The following are the data for the 13 largest U.S. urban areas.
The mean is $5.769 million and the standard deviation is $3.905 million.
What is the mean?The mean is the average of a data set.
What is the standard deviation?The standard deviation shows the measure of the dispersion from the mean.
Data and Calculations:Urban Area Total Cost Squared Difference
(millions of dollars) (x - u)²
New York 16 104.65
Los Angeles 13 52.27
Chicago 7 1.51
Washington, D.C. 5 0.59
Houston 5 0.59
Dallas, Fort Worth 4 3.13
Detroit 4 3.13
Miami 4 3.13
Phoenix 4 3.13
Philadelphia 4 3.13
San Francisco 3 7.67
Boston 3 7.67
Atlanta 3 7.67
13 Total 75 198.27
Mean = 5.769 (75/13) 15.251 (198.27/13)
Standard Deviation = 3.905 (square root of 15.251)
Question Completion:Urban Area Total Cost
(millions of dollars)
New York 16
Los Angeles 13
Chicago 7
Washington, D.C. 5
Houston 5
Dallas, Fort Worth 4
Detroit 4
Miami 4
Phoenix 4
Philadelphia 4
San Francisco 3
Boston 3
Atlanta 3
Calculate the mean and standard deviation for this data set (in millions of dollars). (Round your answers to three decimal places.) mean $ million standard deviation $ million
Thus, the mean is $5.769 million and the standard deviation is $3.905 million.
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Choose the equation for the graph.
a) y = -x - 4 + 1
b) y=-x-4) - 1
c) y = -x + 4 + 1
d) y = -x + 4) - 1
e) y =
|x4| +1
Answer:
a
Step-by-step explanation:
The vertex is at (4,1).
Eliminate b, c, dAlso, the graph opens down, so this eliminates e.
So, the answer is a.
Bailey was practicing karate and kicked the target 6 out of 20 times. Express the number of times she kicked the target as a fraction of the total number of kicks , and reduce the fraction to the lowest terms.
Answer:
ok so here we know that Baily kicked the target 6 times out of 20 that is 6/20 and then you just reduce the fraction dividing it by 2 so it will be 3/10
Step-by-step explanation:
hope it helps :)
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2
3
4
5
6
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive stated, “The revenues for online ads are more than double that of the revenues for printed ads.”
Use the graph below to justify the lead executive’s statement.
Determine the approximate year that the two ad revenues were equal.
See Text Version
Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1995 is represented by year 0:
Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95
Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
The answers are as follows:
What is data?Data is information that has been translated into a form that is efficient for movement or processing.
1. By substituting the values x= 1, 2, 3..
We get the point where f(x)= g(x)
So, f(5)= g(5) =2
Hence, the value of x is 5.
2. As per the given data, during year 14,
revenue from online ads is approximately $4.2 million, whereas revenue from online ads is double than revenue from printed ads.
Also, both line intersect inbetween 7 and 8th year and both online ads and printed ads generated an approximate revenue of $2.2 million.
3. Western Beach erodes from 100 ft to 70 ft.
So, rate of erosion = 30 ft/15 yr = 2 ft/yr.
and, Dunes Beach builds up from 20 ft to 95 ft.
So, rate of buildup = 75 ft/15 yr = 5 ft/yr.
Hence, Dunes beach gets 5 feet every year, and every 5 years the beach loses 25 feet.
b) From the table, beaches will have the same width sometime in year 11 (2006).
c) If the rate remains constant then there is no same width cause of decrease in western beach and increase dunes beach.
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In a relatively pointless survey, the following data was collected on cars in a Costco parking lot: there were 94 white cars; 44 purple cars; 41 dark gray cars; 27 light blue cars; 46 green cars; 19 cars of some other color.
If you were to construct a Pareto chart (using the rule suggested in the book), how would the second bar in the graph be labeled?
color =
If I am to to construct a Pareto chart based on the rule of the chart, the second bar color in the graph be labeled light blue.
What is a Pareto chart?A Pareto chart is known to be a form of a bar graph.
It is made up of different lengths of bars that stands for frequency or cost ( e.g. time or money, and are said to be placed with longest bars on the left and then the shortest are placed to the right.
Since there are 27 light blue cars and this is the first one among the shortest, one can make it to be in the second bar and as such, If I am to to construct a Pareto chart based on the rule of the chart, the second bar color in the graph be labeled light blue.
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Find the y intercept of the line on the graph
Answer: y = -1
Step-by-step explanation:
When x = 0, y = -1
Also, you can think about it as when the graph of the line passes the y axis
John deposits a certain amount that is compounded continuously at 8% interest. Find the number of years it takes to double the amount.
Answer:
about 8.66 years
Step-by-step explanation:
The multiplier of account value when interest is compounded continuously is ...
k = e^(rt)
where r is the annual interest rate, and t is the number of years.
SetupWe want to find t when k=2 and r=0.08. Putting these values in the formula gives ...
2 = e^(0.08t)
SolutionTaking logs of both sides, we have ...
ln(2) = 0.08t
t = ln(2)/0.08 = 0.693147/0.08 ≈ 8.66
It takes about 8.66 years to double the amount.
__
Additional comment
If the interest rate is expressed in integer numbers of percentage points (R%), then the doubling time is ...
t = 100·ln(2)/R ≈ 69.3147/R
Here, that is 69.3147/8 ≈ 8.66.
The "rule of 72" is used to estimate the doubling time for periodically compounded interest at rate R%. That rule tells you the time is t ≈ 72/R. For most interest rates and compounding frequencies in a reasonable range, this gives a time within a reasonable amount of error.
For continuously compounded interest, we have shown the doubling time in years is 69.3147/R. (The exact value of the constant is 100·ln(2).) For the purpose here, a constant of 69.3 gives an estimate accurate to 3 sf.
Which of the following equations has the solution x = all real numbers?
O 4(3-x) + 7x = 4x + 12 + 2x
O 4(4-x) + 6x = x + 16 - 4x
O 3(4-x) + 6x = 4x + 12 - x
O 4(3-c) + 6x = 3x + 8x
Answer: 3(4-x) + 6x = 4x + 12 - x
Step-by-step explanation:
For the solution to be all real numbers, the left hand has to be identical to the right hand side.
1) [tex]4(3-x)+7x=12-4x+7x=12+3x[/tex], so wrong.
2) [tex]4(4-x)+6x=16-4x+6x=16+2x[/tex], so wrong.
3) [tex]3(4-x)+6x=12-3x+6x=12+3x=4x+12-x[/tex], so correct.
4) Wrong variable, so eliminate immediately.
Solve the logarithmic equation...
Answer:
x = 3
Explanation:
[tex]\sf Given \ equation: \ log_{10} (1000) = x[/tex]
Solving steps:
[tex]\rightarrow \sf log_{10} (1000) = x[/tex]
apply rule: logₐ(b) = c then b = aᶜ
[tex]\rightarrow \sf 1000 = 10^x[/tex]
rewrite following
[tex]\rightarrow \sf 10^3= 10^x[/tex]
cancel out bases
[tex]\rightarrow \sf x = 3[/tex]
Answer:
d.) x = 3
Step-by-step explanation:
you simply need to know 10 to power of how many makes 1000 , In case didn't know you can replace the value of x with the given options and see if it can be solved or not .
2.3. Use the following subtraction strategies to calculate 884-597: 2.3.1. breaking up the second number 2.3.2. adding on to the smaller number until you reach the bigger number 2.4. Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition. (4) (3) (3) 2.5. Suppose you want to have the activity in 2.4 marked by peers. Give a marking guideline according to which learners can score each other's work. (2) 2.6. Draw a diagram by which you can visually explain to learners in the Intermediate Phase why the sum of five consecutive numbers is equal to the fifth multiple of the middle number. Choose any set of five consecutive numbers to illustrate your statement. Write down your explanation in four powerful sentences. (5) OW a 2.3 . Use the following subtraction strategies to calculate 884-597 : 2.3.1 . breaking up the second number 2.3.2 . adding on to the smaller number until you reach the bigger number 2.4 . Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition . ( 4 ) ( 3 ) ( 3 ) 2.5 . Suppose you want to have the activity in 2.4 marked by peers . Give a marking guideline according to which learners can score each other's work . ( 2 ) 2.6 . Draw a diagram by which you can visually explain to learners in the Intermediate Phase why the sum of five consecutive numbers is equal to the fifth multiple of the middle number . Choose any set of five consecutive numbers to illustrate your statement . Write down your explanation in four powerful sentences . ( 5 ) OW a
It should be noted that the value of 597 subtracted from 884 is 287.
How to illustrate the subtraction?The information is simply that we should subtract 884 and 597 and also illustrate it.
This will be:
884 - 597 = 287.
A word problem illustrating this is that a man had 884 pens and gave 597 pens to his friends. How many pens does he have left?
This will be:
= 884 - 597 = 287
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Question
Determine an angle between 0° and 360° that is coterminal to an angle with measure of 1524°.
Enter your answer below without a degrees symbol - just enter the numeric answer.
Answer: 84°
Step-by-step explanation:
On a unit circle, coterminal angles are angles that are in the opposite position of the asked angle. 1524° revolves around 127/15π times across the entire unit circle.
84° is the only positive coterminal angle between 0 and 360 that is in the opposite position of 1524°.
Keep in mind, that there are more coterminal angles, namely 444°, 804°, 1164°, and 1524° itself, but they are outside of the range of 0 and 360 degrees.
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is
summarized in the histogram below.
What is the sample size for this data set?
Explanation:
Add up the heights of each bar to get the sample size.
4+4+7+12+11+4+1 = 43
Find the measure of the angle indicated in bold
The measure of the angles in bold are as follows;
25. 90° and 90°
26. 60° and 60°
How to find angles?When two parallel lines are cut by a transversal , angle relationship are formed. They are alternate angles, corresponding angles etc.
Therefore,
x + 96 + x + 96 = 180
2x = 180 - 192
2x = -12
x = -6
Hence, the angles are 90 and 90 degrees.
6x = 5x + 10(corresponding angles)
6x - 5x = 10
x = 10
Therefore, the angles are 60 degrees and 60 degrees
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The following table shows the data collected from a random sample of 100 middle school students on the number of hours they do household chores every week:
Weekly Duration of Household Chores
Time (in hours) 0–1 2–3 4–5 6–7
Number of Students 32 64 3 1
There are 1,500 students in the school. Based on the sample proportion, how many students in the school would be expected to do household chores for at least two hours every week?
A 480
B 960
C 1020
D 1440
The students in the school would be expected to do household chores for at least two hours every week with 1020 students.
We have given
Time (in hours) 0– 1 2–3 4–5 6–7
Number of Students 32 64 3 1
What is the random sample?A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
The keyword is at least, this means anything under that number will not qualify.
So that leaves 68 out of the 100 sample students.
So if you want to have the same thing but with 1,500 students.
Take off the 2 zeros at the end of 1500 and multiply by 68 to get your answer.
This is because there are 2 zeros in 100, so to cancel out the 2 zeros in 100, take out the 2 zeros in 1500 making it a lot easier.
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On July 1, 20x5, Augusta Enterprises issued bonds with a face value of $1,000,000. The bonds carry a face interest rate of 10 percent that is payable each July 1 and January 1.
a. Prepare the entry in journal form without explanation for the issuance assuming the bonds are issued at 97.
b. Prepare the entry in journal form without explanation for the issuance assuming the bonds are issued at 102.
Based on the price that Augusta Enterprises issued the bonds, the journal entries would be:
Date Account title Debit Credit
July 1, 20x5 Cash $97,000
Discount on Bonds payable $3,000
Bonds payable $1,000,000
Date Account title Debit Credit
July 1, 20x5 Cash $1,020,000
Premium on Bonds payable $20,000
Bonds payable $1,000,000
How are bonds recorded at premium and discount?The cash received from the discounted bond is:
= 1,000,000 x 97%
= $970,000
The cash received from the premium bond is:
= 1,000,000 x 102/100
= $1,020,000
The premium is:
= 1,020,000 - 1,000,000
= $20,000
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Draw a histogram and a box-and-whisker plot to represent the combined data, and answer the questions. Be sure to include the new graphs as part of your final submission.
How do the graphs of the combined data compare to the original graphs?
Compared to the original graphs, do the new graphs make it easier or more difficult to estimate the price of a book?
The new graphs would make it more difficult to estimate the price of a book.
How to create the combined graph?To do this, we simply combine the frequencies on Felix and Tyler's table.
When this is done, we have the following dataset
3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7, 8,8,8,8,9,9,9,9,9,9,9,9,9,11,11,13,13,13,13,15,15,15,16,16,18,18,18,18,18,19,19,19,19,19,19,29,32,32,36,36,36,38,38,64,64,66,66,66,68,68,69,75,75,76,76,76,76,76,78,78,79,82,82,86,86,86,89,96,96,97,97,99
Next, we create the box & whisker plot and the histogram using the new dataset
(see attachment for the graphs)
The new graphs would make it more difficult to estimate the price of a book.
This is so because the dataset used to create the graphs do not come from the same source
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In the coin flipping lab, suppose that you simulated the flipping of a weighted coin 30 times and got 5 heads and 25 tails. What is your estimated probability for P(H)?
Answer:
1/6
Step-by-step explanation:
Out of 30 tosses, 5 come up heads. So the estimated probability of heads is 5/30, or 1/6.
Answer: 0.17
Step-by-step explanation:
just got it right on quiz
in the x-y plane, what is the y- intercept of the graph of the equation y=6 (x-1/2) (x+3)
The y-intercept on the x-y plane is (0, -9).
How to get the y-intercept?To get the y-intercept we just need to evaluate in x = 0.
Here we have:
y = 6*(x - 1/2)*(x + 3)
Evaluating the given equation in x = 0 we get:
y = 6*(0 - 1/2)*(0 + 3) = -9
Then the y-intercept on the x-y plane is (0, -9).
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Answer:
-9
Step-by-step explanation:
??????????????????????????????
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2x-20}{3}=2x \end{gathered}$}[/tex]
Multiply both sides of the equation by 3.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20=6x \end{gathered}$}[/tex]
Subtract 6x on both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20-6x=0 \end{gathered}$}[/tex]
Combine 2x and −6x to get −4x.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x-20=0 \end{gathered}$}[/tex]
Add 20 to both sides. Any value plus zero results in its same value.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x=20 \end{gathered}$}[/tex]
Divide both sides by −4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{-4} \end{gathered}$}[/tex]
Divide 20 by −4 to get −5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-5 \ \ \to \ \ \ Answer \end{gathered}$}[/tex]
{ Pisces04 }[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathbf{\dfrac{2x - 20}{3} = 2x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT or DISTRIBUTE:}[/tex]
[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} = 2x}[/tex]
[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} - 2x = 2x - 2x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{- \dfrac{4}{3}x - \dfrac{20}{3} = 0}[/tex]
[tex]\huge\textbf{ADD }\boxed{\rm{\bf \dfrac{20}{3}}}\huge\textbf{ to BOTH SIDES:}[/tex]
[tex]\mathbf{-\dfrac{4}{3}x - \dfrac{20}{3} + \dfrac{20}{3} = 0 + \dfrac{20}{3}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{-\dfrac{4}{3}x = \dfrac{20}{3}}[/tex]
[tex]\huge\textbf{MULTIPLY }\boxed{\rm \bf {\dfrac{3}{-4}}}\huge\textbf{ to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{3}{-4}\times\dfrac{-4}{3}x = \dfrac{3}{-4}\times\dfrac{20}{3}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{x = -5}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -5}}}\huge\chekmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A box with an open top is to be constructed from a 15 inch by 24 inch piece of cardboard by cutting squares of equal sides from the corners and folding up the sides. Find the dimensions of the box of the largest volume that can be constructed.
The dimensions of the box of the largest volume that can be constructed are
D=18,9,3
What are the dimensions?Generally, the equation for the lenght is mathematically given as
Lenght=(24-2x)
Widht= (15-2x)
Therefore
Volume =L*B*H
V=(24-2x)(15-2x)x
V=(360-48x-30x+4x)x
V=4x^3-78x^2+360x
Differnciating we have
dv/dx=12x^2-156x+360
put dv/dx=0
12(x^2-13x+30)=0
x^2-10x-3x+30=0
(x-10)(x-3)=0
root=10,3
Second diiferciation
d^v/dx^2=24x-156
[tex]lim _{x=3} =-84 < 0[/tex]
In conclusion,
L=24-2x
L=24-2x3
L=18in
w= 15-2x
w=15-2*3
w=9in
h=x
h=2in
Dimension=18,9,3
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A garden table and a bench cost $714 combined. The garden table costs $64 more than the bench. What is the cost of the bench?
Answer:
The bench costs $325
Step-by-step explanation:
let garden table = x
let bench = y
x = y+64
x+y = 714
y+y+64 = 714 (we know, x = y+64)
2y + 64 = 714
2y = 650
y = 325
Answer:
Bench: $325
Garden Table: $389
Step-by-step explanation:
g + b = 714 Eq. 1
g = b + 64 Eq. 2
g = cost of the garden table
b = cost of the bench
Replacing Eq.2 in Eq.1
(b+64) + b = 714
2b + 64 = 714
2b = 714 - 64
2b = 650
b = 650/2
b = 325
from the Eq. 2
g = b + 64
g = 325 + 64
g = 389
Check:
from the Eq. 1
g + b = 714
389 + 325 = 714
Draw u – v + w. please help !!!!!!!!!!
Here, we have to perform a sum of vectors and draw the resultant vector and the resultant vector will be <4, 0>.
How to illustrate the vector?If we see the image, we can write the vectors as:
w = <3, 3>
u = <-3, -4>
v = <-4, -1>
Now we want to sum:
u - v + w
u - v + w
= <-3, -4> - <-4, -1> + <3, 3>
= <-3 + 4 + 3, -4 + 1 + 3>
= <4, 0>
The graph of the resultant vector can be seen below.
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QUESTION IS DOWN BELOW 30 points for answer
Answer: a) 25:16 and b) 125:64
Step-by-step explanation:
For simplicity, assume that two spheres have diameters of 5 and 4.
a) 4pi(5^2) and 4pi(4^2)
= 100pi:64pi
= 100:64
= 25:16
b. 4/3 pi(5^3) and 4/3 pi(4^3)
= 166.67pi and 85.33pi
= 500:256
= 125:64
Name this triangle by its sides and angles. This is a(n) ____________________ triangle. a triangle with one right angle and three non-congruent sides obtuse, isosceles obtuse, scalene right, scalene right, isosceles
Answer:
c
Step-by-step explanation:
PLEEEEEEEEEEASSEEEEEEE ANSWER QUESTION IS DOWN BELOW WORTH 15 POINTS each
A ratio shows us the number of times a number contains another number. The ratio of the volume of the model to the volume of the original is 27/2744.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that the scale factor is 3:14. Therefore, the ratios can be written as,
(a) The ratio of the surface area of the model to the surface area of the original is,
Surface area Ratio = (3/14)² = 9/196
(b) The ratio of the volume of the model to the volume of the original.
Volume Ratio = (3/14)³ = 27/2744
(c) The ratio of the width of the model to the width of the original.
Width Ratio = 3/14
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please help me asap thank you so so so much u are the most amazing
The smallest angle would be 19 degrees. So option D is correct.
What is the sum of the octagon?The sum of exterior angles of the regular octagon is 360 degrees.
Given;
The angles
x + 13 + 2x - 1 + 2x + 6 + 2x + 12 + 2x - 17 + 3x - 4 + 3x - 10 + 4x = 360
19x - 1 = 360
19x = 359
x = 18.89
The smallest angle would be
2x - 17 = 2(18.89) - 17 = 19
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Which expression is equivalent to the following complex fraction?
-2/x + 5/y / 3/y - 2/x
Answer: [tex]\frac{5x-2y}{3x-2y}[/tex]
Step-by-step explanation:
[tex]\frac{-\frac{2}{x}+\frac{5}{y}}{\frac{3}{y}-\frac{2}{x}}[/tex]
Multiplying the numerator and denominator by xy,
[tex]=\frac{-2y+5x}{3x-2y}\\\\=\frac{5x-2y}{3x-2y}[/tex]
15. Which one of the following is a geometric sequence?
O A. 0, 1, 2, 3,...
O B. 2, -3, 92, -18/4
O C. -7, 10, 23, 36, ...
O D. 8, 4, 2, 1, 1/2, ¹/4....
in a random sample of 36 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 50 months, with a standard deviation of 5 months. construct and interpret a 90 % confidence interval for the mean length of sentencing for this crime.
The answer is 90% of the crime is between 48.63 and 51.37
How to solve for the confidence intervalThe sd = 5 months
n = 36
Mean length = 50
1- 0.90
= 0.1
Critical value = alpha/2 = 1.645
Margin of error
E = 1.645 x 5/√36
= 1.37
The upper and lower limits are50 - 1.37 + 50 + 1.37
= (48.63, 51.37)
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