Answer:
$12,000
Step-by-step explanation:
By paying the minimum rent, the tenant would pay $1000 * 12 = $12,000.
Rent cannot be less than $12,000.
If the 2% of sales is greater than $12,000, then 2% of sales becomes the rent.
Now we calculate 2% of annual sales.
2% * $435,000 = $8,700
Since the minimum rent, $12,000, is greater than 2% of sales, then rent is $12,000.
What is the relationship between angle a and angle b A) Vertical Angles B) Complementary Angles C) Supplementary Angles D) None of the above
Answer:
C. Supplementary
Step-by-step explanation:
Angle a and angle b are on the line CZA.
We can assume that line CZA is a straight line, which is equal to 180 degrees.
Since angle a and b are on the straight line together, they must add to 180 degrees. Therefore, they are supplementary angles.
So, choice C. Supplementary angles is correct.
simplify (3+3 / x(x+1) )(x-3 / x(x-1) )
Answer:
I think it is [tex]\frac{6x-18}{x^{4} }[/tex]
Step-by-step explanation:
Part 1 You will need to measure five different people. Record your measurements on a piece of paper. Using a tape measure or ruler, measure the length (in inches) of a person’s left foot and then measure the length (in inches) of that same person’s forearm (between their wrist and elbow). Refer to the diagrams below. You will have two measurements for each person. (An easy way to measure the length of a foot is to have your subject stand on a piece of paper. Then, trace their foot and measure the outline once they move off the paper.) To measure the forearm, measure inside the arm, between the wrist and the elbow. Part 2 Organize your data and find the rate of change. Create a table of the measurements for your data. Label the forearm measurements as your input and the foot measurements as your output. Select two sets of points and find the rate of change for your data. Describe your results. If you had to express this relation as a verbal statement, how would you describe it? Part 3 Compare rates of change. The equation below can be used to find the length of a foot or forearm when you know one or the other. (length of the foot) = 0.860 • (length of the forearm) + 3.302 If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302. Using this equation, how long would the foot of a person be if his forearm was 17 inches long? What is the rate of change of the equation from Part A? Compare the equation from Part A to your data. Are they the same? Which has a greater rate of change? Why do you think the values are different? Is the relation in your data a function? Why or why not? Could the equation in Part A represent a function? Why or why not? Explain your answer. For this option you will submit the details from all three parts. Submit your measurements, the table, and description that you created in Parts 1 and 2. Submit your answers to the questions from Part 3. Measurement of forearm (x) 10in. , 15in , 10in, 11in. , 12in. Measurement of left foot (y) 9in. 11in. . 8in. 9 11/16in. 11 1/4in.
Answer:
to be honest I'm not sure how to do this question plz answer my question plz
Step-by-step explanation:
to be honest I'm not sure how to do this question plz answer my question plz I'm so much home workout
Please answer this correctly without making mistakes
Answer:
1/2
Step-by-step explanation:
There are eight equal pieces. Oliver used four pieces to make toast. Since the total is eight pieces, the fraction he used to make toast is 4/8, which simplifies to 1/2
Answer:
4/8
Step-by-step explanation:
He cut the bread into 8 equal pieces, so the denominator is 8.
He used 4 pieces for making toast.
He saved 4 pieces for later.
Hope this helps ;) ❤❤❤
What is 36/100 added with 4/10
Answer:
0.76 or 19/25
Step-by-step explanation:
Convert 4/10 so that it has a common denominator with 36/100.
4/10 x 10/10 = 40/100
Now that the denominator is the same, just add the top values.
40/100 + 36/100 = 76/100
We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.
Answer:
19/25Step-by-step explanation:
[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]
[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]
A large study of over 2000 parents and children in Norway found that toddlers who regularly slept less than 10 hours per night or woke frequently (three or more times) at night tended to experience more emotional and behavioral problems when they reached age five. The study involved a large random sample of mothers and children and was conducted over several years. What is the population of interest in this survey
Answer: Parents and children ( till the age of 5) of Norway
Step-by-step explanation:
The population in a survey is the group of people sharing common features or characteristics as per the researcher point of view.Here, A large study of over 2000 parents and children in Norway found that toddlers who regularly slept less than 10 hours per night or woke frequently (three or more times) at night tended to experience more emotional and behavioral problems when they reached age five.
Since the study involved a large random sample of mothers and children and was conducted over several years.
So, the population of interest in this survey is "Parents and children ( till the age of 5) of Norway".
A rectangular vegetable garden will have a width that is 4 feet less than the length and an area of 140 square feet if x represents the length then the length can be found by solving the equation:
If x represents the length, then the length can be found by solving the equation: x(x-4)=140
Answer: x(x-4) = 140 This equation can be solve to find the length.
Step-by-step explanation:
If the width of the rectangle will be 4 less than the length and the length is represented by x then we could have the equation w=x - 4 for the width and the length is just x. And to find the area of a rectangle we multiply the length by the with so multiply x-4 by x for it to equal 140 because 140 is the area.
x(x-4) = 140 solve for x
[tex]x^{2}[/tex] - 4x = 140 subtract 140 from both sides
x^2 - 4x - 140 = 0 find a number that the product is 140 and the sum is -4
-14 and 10 works out.
[tex]x^{2}[/tex] - 14x + 10x - 140 = 0 factor by grouping
x(x -14) 10(x-14) = 0 factor out x-14
(x-14) ( x+10) = 0 set them both equal zero.
x-14= 0 or x+10 = 0
x = 14 or x= -10
Since -10 can't represent a distance, the answer is 14.
Check.
In this case the length is 14 and if the width is 4 less than the length then we will subtract 4 from 14.
14- 4 = 10 so the width is 10.
14 * 10 = 140
Help with 18 - 22
18 4 x 1 =
— —
7 2
A. 8
—
7
B. 4
—
14
C. 28
—
2
19. 15 X 2 =
— —
2 20
A. 4
—
300
B. 30
—
40
C. 30
—
4
20. 3 x 7 =
— —
6 8
A. 18
—
56
B. 24
—
42
C. 21
—
48
21. 9 x 1 =
— —
10 2
A. 9
—
20
B. 18
—
10
C. 8
—
18
22. 3 x 2 =
— —
6 4
A. 6
—
24
B. 18
—
8
C. 8
—
18
Answer:
18. b. 4/14
19. b. 30/40
20. c. 21/48
21. a. 9/20
22. a. 6/24
Step-by-step explanation:
So in these questions all we do is multiply the fractions.
18)
[tex]\frac{4}{7} * \frac{1}{2}[/tex]
4*1 = 4
7*2 = 14
b. 4/14
19)
[tex]\frac{15}{2}*\frac{2}{20}[/tex]
15*2 = 30
2*20 = 40
b. 30/40
20)
[tex]\frac{3}{6}*\frac{7}{8}[/tex]
3*7 = 21
6*8 = 48
c. 21/48
21)
[tex]\frac{9}{10}*\frac{1}{2}[/tex]
9*1 = 9
10*2 = 20
a. 9/20
22)
[tex]\frac{3}{6}*\frac{2}{4}[/tex]
3*2 = 6
6*4=24
a. 6/24
Hope this helps :)
What does the symbol in the image on number 39 mean
Answer:
It means direct sum.
Step-by-step explanation:
TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streaming is gaining in popularity. A poll reported that 54% of 2348 American adults surveyed said they have watched digitally streamed TV programming on some type of device.
1) Calculate and interpret a confidence interval at the 99% confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time.
A) We are 99% confident that this interval does not contain the true population proportion.
B) We are 99% confident that this interval contains the true population proportion.
C) We are 99% confident that the true population proportion lies below this interval.
D) We are 99% confident that the true population proportion lies above this interval.
2) What sample size would be required for the width of a 99% CI to be at most 0.03 irrespective of the value of p?
Answer:
1
Option B is the correct answer
2
[tex]n = 9418[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 2348[/tex]
The sample proportion is [tex]\r p = 0.54[/tex]
Given that the confidence level is 99% then the level of significance is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1[/tex]%
[tex]\alpha = 0.01[/tex]
Next we obtain the critical values of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table. The values obtained is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason we are obtaining values for is because is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while is the area under the normal distribution curve for just one tail and we need the value for one tail in order to calculate the confidence interval .
Next is to calculate the margin of error which is mathematically evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p ( 1 - \r p )}{n } }[/tex]
substituting values
[tex]MOE = 2.58 * \sqrt{ \frac{0 .54( 1 - 0.54 )}{2348 } }[/tex]
[tex]MOE = 0.0265[/tex]
Now the interval for the 99% confidence level is evaluated as
[tex]\r p - MOE < \r p < \r p + MOE[/tex]
substituting values
[tex]0.514 < \r p <0.567[/tex]
Looking at the Confidence interval we see that the proportion of Americans that watched streamed program up to that point in time is between
51.4% and 56.7%
Hence we are 99% confident that this interval contains the true population proportion.
The sample size that will be required for the width o 99% Cl is mathematically evaluated as
[tex]n = \frac{4 *[Z_{\frac{\alpha }{2} }]^2 * \r p (1- \r p )}{MOE^2}[/tex]
substituting values
[tex]n = \frac{4 *2.58^2 * 0.54 (1- 0.54 )}{0.0265^2}[/tex]
[tex]n = 9418[/tex]
A nut-raisin mix costs $5.26 a pound. Rashid buys 15.5 pounds of the mix for a party. Rashid’s estimated cost of the nut-raisin mix is A.$16 B.$22 C.$61 D.$80
Answer:
D.$80
Step-by-step explanation:
$5.26 x 15.5= $81.53
The closest amount to $81.53 is D.$80
Find the 50th term of the following arithmetic sequence.
6, 13, 20, 27, ...
Answer:
349
Step-by-step explanation:
We know that a₁ (the first term) is 6 and d (the common difference) is 13 - 6 = 7.
Explicit formula: aₙ = a₁ + (n - 1)d = 13 + (n - 1) * 7 = 7n - 1
Therefore, a₅₀ = 7(50) - 1 = 349
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ∗ = 22 % . You would like to be 95% confident that your esimate is within 1% of the true population proportion. How large of a sample size is required?
Answer:
The large of a sample size is required is 6,592
Step-by-step explanation:
In order to calculate large of a sample size is required we would have to calculate the following formula:
large of a sample size is required=(Z∝I2/E)∧2* P(1-P)
According to the given data we have the following:
E= margin of error= 1%=0.01
95% confident that your esimate is within 1% of the true population proportion, therefore, level of significance=∝=1-0.95=0.05
Z value for the 95% confident is 1.960, therefore, Z∝I2=1.960
Therefore, large of a sample size is required=(1.960/0.01)∧2* (0.22)(1-0.22)
large of a sample size is required=6,592
The large of a sample size is required is 6,592
For the functions f(x)=2x^2+3x+9 and g(x)=−3x+10 find (f⋅g)(x) and (f⋅g)(1)
Step-by-step explanation:
f(x)=2x²+3x+9
g(x) = - 3x + 10
In order to find (f⋅g)(1) first find (f⋅g)(x)
To find (f⋅g)(x) substitute g(x) into f(x) , that's for every x in f (x) replace it by g (x)
We have
(f⋅g)(x) = 2( - 3x + 10)² + 3(- 3x + 10) + 9
Expand
(f⋅g)(x) = 2( 9x² - 60x + 100) - 9x + 30 + 9
= 18x² - 120x + 200 - 9x + 30 + 9
Group like terms
(f⋅g)(x) = 18x² - 120x - 9x + 200 + 30 + 9
(f⋅g)(x) = 18x² - 129x + 239
To find (f⋅g)(1) substitute 1 into (f⋅g)(x)
That's
(f⋅g)(1) = 18(1)² - 129(1) + 239
= 18 - 129 + 239
We have the final answer as
(f⋅g)(1) = 128Hope this helps you
Iris has 120 songs on her playlist. each week, she downloads 4 new songs
Answer:
120 + 4w
Step-by-step explanation:
I am indeed doing it aswell
According to the National Health Statistics Reports, the standard deviation of the weights of all one-year-old baby boys born in the U.S. is 5.3 pounds. A random sample of 360 one-year-old baby boys born in the U.S. had a mean weight of 25.5 pounds.
a) Construct a 90% confidence interval for the mean weight of all one-year-old baby boys in the U.S. Write a sentence that interprets this interval.
b) Should this confidence interval be used to estimate the mean weights of all one-year-old babies in the U.S.? Explain.
Answer: A) At 90% confidence interval estimate of the population mean
is,( 25.0405 , 25.9595 )
B) YES
Step-by-step explanation:
Given that,
Point estimate = sample mean Ж = 25.5
Population standard deviation α = 5.3
Sample size = n =360
At 90% confidence level the z is ,
∝ = 1 - 90% = 1 - 0.90 = 0.1
∝ / 2 = 0.1 / 2 = 0.05
Z∝/2 = Z0.05 = 1.645 ( WHEN WE USE THE Z TABLE )
Margin of error E = Z∝/2 * ( α/√n)
E = 1.645 * (5.3 / √360 ) = 0.4595
At 90% confidence interval estimate of the population mean
is
Ж - E < ц < Ж + E
25.5 - 0.4595 < ц < 25.5 + 0.4595
25.0405 < ц < 25.9595
( 25.0405 , 25.9595 )
At 90% confidence interval estimate of the population mean
is,( 25.0405 , 25.9595 )
B) This confidence interval can be used to estimate the mean weight of all one - year old babies in the US since the mean value of 25.5 falls within the confidence values, we have sufficient evidence to
conclude that the mean weight of all one-year-old boys is 25.5
Question Help
During the morning rush, entering travelers can fill a station in 30 minutes. Fortunately, departing trains can empty it in 40 minutes.
rush-hour pace, how long will it take for the station to fill with travelers?
Answer:
One hour ten minutes
Step-by-step explanation:
departing trains can empty it in 40 minutes.
entering travelers can fill a station in 30 minutes.
Time it will take travellers to fill the train
= Time for departing train + time for filling a station
= 40 minutes+ 30 minutes
= 70 minutes
= One hour ten minutes
Find the length of AG
Answer:
[tex]AG=22[/tex]
Step-by-step explanation:
Follow the next steps:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F} =\frac{C-D}{F-G} =\frac{A-C}{A-F} =\frac{B-D}{E-G} =\frac{A-D}{A-G}[/tex]
Let:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F}\\ \\\frac{4}{A-E} =\frac{5}{10x}\\ \\Solving\hspace{3}for\hspace{3}A-E\\\\A-E=8x[/tex]
Now:
[tex]\frac{C-D}{F-G} =\frac{A-C}{A-F} \\\\\frac{2}{F-G} =\frac{9}{18x} \\\\Solving\hspace{3}for\hspace{3}F-G\\\\F-G=4x[/tex]
Hence:
[tex]A-G=(A-E)+(E-F)+(F-G)=22x[/tex]
Finally:
[tex]\frac{B-D}{E-G} =\frac{A-D}{A-G}\\\\\frac{A-D}{B-D} =\frac{A-G}{E-G}\\[/tex]
[tex]\frac{11}{7} =\frac{22x}{14x} \\\\\frac{11x^{2} }{7} -\frac{11}{7} =0\\\\[/tex]
Hence:
[tex]x=1\\x=-1[/tex]
Since it would be absurd for [tex]x=-1[/tex], the real solution is [tex]x=1[/tex]
Therefore:
[tex]AG=22[/tex]
A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 11% chose chocolate pie, and the margin of error was given as plus or minus5 percentage points. What values do ModifyingAbove p with caret, ModifyingAbove q with caret, n, E, and p represent? If the confidence level is 95%, what is the value of alpha?
Answer:
[tex]\r p = 0.11[/tex]
[tex]\r q = 0.89[/tex]
n = 2000
[tex]E = \pm 5[/tex]
p - population proportion
[tex]\alpha = 5[/tex]%
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 2000[/tex]
The proportion of the population for chocolate pie is [tex]p_c = 0.11[/tex]
The margin of error is [tex]E = \pm 5[/tex]%
Now in the question we are asked to provide the meaning of
[tex]\r p , \r q , n , E , and\ p[/tex]
Now [tex]\r p[/tex] is the sample proportion of the population that those chocolate pie as favorite pie of which is given from the question as 0.11
Now
[tex]\r q[/tex] is the sample proportion of the population that choose other pies apart from chocolate pie as their favorite and it is evaluated as
[tex]\r q = 1 - \r p[/tex]
[tex]\r q = 1 - 0.11[/tex]
[tex]\r q = 0.89[/tex]
n is the sample size which is given as n = 2000
E is the margin of error which given as [tex]E = \pm 5[/tex]%
p is the population proportion
Given that the confidence level is 95 % then the level of significance is mathematically evaluated as
[tex]\alpha =(100 - 95)[/tex]%
[tex]\alpha =[/tex]5%
3) The chance that a salmon jumps up the waterfall to upstream successfully 35%. We have a group of 9 salmon. What is the chance that none of them jump up successfully? What is the chance that all of them reach up-stream? What is the chance that at least 2 of them reach up-stream? What is the chance that at most 1 of them reaches up-stream? Is “at least 1” complement of the event “at most 1”?
Answer:
(a) P(0,9) = 0.0207
(b) P(2-9,9) = 0.1004
(c) P(0-1,9) = 0.1211
(d) "at least 1" and "at most 1" are not complements of each other because there is an overlap of "1" in both cases.
Step-by-step explanation:
With appropriate assumptions, this can be solved using the binomial distribution.
Probability of success for each trial, p = 35%
Number of trials, n = 9
using formula for x successes out of n trials, each with probability p
P(x,n) = C(n,x) p^x (1-p)^(n-x)
where C(n,x) = n!/(x!(n-x)!)
(a) zero success
n=9
p=0.35
x = 0
P(0,9) = 9!/(0!9!) 0.35^0 * 0.65^9
= 1*1* 0.0207
= 0.0207
(b) 2 or more successes
We need the sum of probabilities of 2,3,4,5,6,7,8,9 successes, which is easier calculated by (1-P(0,9)-P(1,9))
P(1,9) = C(9,1) * p^1 * p^8
= 9 * 0.35 * 0.65^8
= 9 * 0.35 * 0.3186
= 0.1004
Therefore
P(2 to 8, 9)
= 1 - P(0,9) - P(1,9)
= 1 - 0.0207 - 0.1004
= 0.8789
(c) at most 1 success
P(0,9) + P(1,9)
= 0.0207 + 0.1004
= 0.1211
Find the y-intercept and x-intercept of the line.
– 3x+9y= 14
Answer:
[tex]\huge\boxed{x-intercept=-\dfrac{14}{3}=-4\dfrac{2}{3}}\\\boxed{y-intercept=\dfrac{14}{9}=1\dfrac{5}{9}}[/tex]
Step-by-step explanation:
[tex]-3x+9y=14\\\\x-intercept\ \text{for}\ y=0:\\\\-3x+9(0)=14\\-3x+0=14\\-3x=14\qquad\text{divide both sides by (-3)}\\\boxed{x=-\dfrac{14}{3}=-4\dfrac{2}{3}}}[/tex]
[tex]y-intercept\ \text{for}\ x=0:\\\\-3(0)+9y=14\\0+9y=14\\9y=14\qquad\text{divide both sides by 9}\\\boxed{y=\dfrac{14}{9}=1\dfrac{5}{9}}[/tex]
94. A tin of peas & carrots and two mangoes weighing 300 grams each are placed on one
side of a scale. To balance the scale, 4 tins of condensed milk each weighing 250g are
placed on the other side. Determine the mass of the peas & carrots.
Answer:
400 g
Step-by-step explanation:
Let p represent the mass of the peas & carrots. The scale is balanced when the mass on one side is equal to the mass on the other side.
p + 2(300 g) = 4(250 g)
p = 1000 g -600 g . . . . . subtract 600 g
p = 400 g
The mass of the peas & carrots is 400 grams.
A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses. How many courses worth 3 credits did the student complete?
Answer:
They completed 13, 3 credit classes
Step-by-step explanation:
1. Make 2 formulas. In this case: x+y=18
and 3x+4y=59
2. Then multiply x+y=18 by 3 and subtract the two equations.
Find y which is 5 and input into the equations. Then find your answer.
What is a3 if an=64(12)n−1
Answer:
[tex]\huge\boxed{a_3=9,216}[/tex]
Step-by-step explanation:
[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]
Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and y are related by the equation =y+115025x. Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
Answer:
Change in the cost of each book printed = $25
Cost to get started = $1150
Step-by-step explanation:
Equation representing the relation between number of copies of the books (x) and total cost of publishing a book (y) is,
y = 1150 + 25x
This equation is in the form of a linear equation,
y = mx + b
Where m represents the change in cost of printing each book and y-intercept of the line 'b' represents the cost before any book is printed.
By comparing these equations,
m = 25
Therefore, change in the cost of each book printed = $25
b = 1150
Which represents the cost to get started = $1150
In year 3 it is expected that the total value of clothing sales will reach 32 million if the total value of ASCO sells Remains the Same as year 2what percentage of sales clothing account for in year three
Answer:
The sales account for year 3 is [tex][\frac{32\ \text{mn}-x\ \text{mn}}{x\ \text{mn}}\times 100\%][/tex].
Step-by-step explanation:
As the sales for year 2 is not provided, assume it is x million.
The total sales in year 3 is, 32 million.
Compute the sales account for year 3 as follows:
[tex]\text{Percentage of sales for year 3}=\frac{\text{Total Sales in year 3}-\text{Total Sales in year 2}}{\text{Total Sales in year 2}}\times 100\%[/tex]
[tex]=\frac{32\ \text{mn}-x\ \text{mn}}{x\ \text{mn}}\times 100\%[/tex]
TEST ITEMS
Nathan purchased a square sheet of kite paper to make a kite.
The area of the kite paper was 1600cm. While making the kite
he realised that the sheet of kite paper was 4cm short on one
side. What would be the dimensions of kite paper Nathan need
to properly make the kite?
Answer:
40 cm by 44 cm
Step-by-step explanation:
A square sheet of paper has area 1600 cm^2.
area = s^2
1600 cm^2 = s^2
s = sqrt(1600 cm^2)
s = 40 cm
The side of the square was 40 cm, so the square measured 40 cm by 40 cm.
One side of 4 cm short, so the paper should have been 40 cm by 44 cm.
Write a short statement that expresses a possible function between the given variables.(price of a DVD player, demand for DVD player)
Answer:
When the price of DVD player increases, the demand will decrease.
Step-by-step explanation:
The price and demand function have an inverse relationship. When the price of good increases its demand will decrease. This is law of demand. If the price of goods increase to a certain level its demand will start decreasing. The people will start buying lesser good and will consume less. The propensity to consume will decline and less economic goods will be consumed. When the price of DVD player is increased then the demand will decline for DVD players and people will drop the decision to buy the DVD player.
Prove that a cubic equation x 3 + ax 2 + bx+ c = 0 has 3 roots by finding the roots.
That's a pretty tall order for Brainly homework. Let's start with the depressed cubic, which is simpler.
Solve
[tex]y^3 + 3py = 2q[/tex]
We'll put coefficients on the coefficients to avoid fractions down the road.
The key idea is called a split, which let's us turn the cubic equation in to a quadratic. We split unknown y into two pieces:
[tex]y = s + t[/tex]
Substituting,
[tex](s+t)^3 + 3p(s+t) = 2q[/tex]
Expanding it out,
[tex]s^3+3 s^2 t + 3 s t^2 + t^3 + 3p(s+t) = 2q[/tex]
[tex]s^3+t^3 + 3 s t(s+t) + 3p(s+t) = 2q[/tex]
[tex]s^3+t^3 + 3( s t + p)(s+t) = 2q[/tex]
There a few moves we could make from here. The easiest is probably to try to solve the simultaneous equations:
[tex]s^3+t^3=2q, \qquad st+p=0[/tex]
which would give us a solution to the cubic.
[tex]p=-st[/tex]
[tex]t = -\dfrac p s[/tex]
Substituting,
[tex]s^3 - \dfrac{p^3}{s^3} = 2q[/tex]
[tex](s^3)^2 - 2 q s^3 - p^3 = 0[/tex]
By the quadratic formula (note the shortcut from the even linear term):
[tex]s^3 = q \pm \sqrt{p^3 + q^2}[/tex]
By the symmetry of the problem (we can interchange s and t without changing anything) when s is one solution t is the other:
[tex]s^3 = q + \sqrt{p^3+q^2}[/tex]
[tex]t^3 = q - \sqrt{p^3+q^2}[/tex]
We've arrived at the solution for the depressed cubic:
[tex]y = s+t = \sqrt[3]{q + \sqrt{p^3+q^2}} + \sqrt[3]{ q - \sqrt{p^3+q^2} }[/tex]
This is all three roots of the equation, given by the three cube roots (at least two complex), say for the left radical. The two cubes aren't really independent, we need their product to be [tex]-p=st[/tex].
That's the three roots of the depressed cubic; let's solve the general cubic by reducing it to the depressed cubic.
[tex]x^3 + ax^2 + bx + c=0[/tex]
We want to eliminate the squared term. If substitute x = y + k we'll get a 3ky² from the cubic term and ay² from the squared term; we want these to cancel so 3k=-a.
Substitute x = y - a/3
[tex](y - a/3)^3 + a(y - a/3)^2 + b(y - a/3) + c = 0[/tex]
[tex]y^3 - ay^2 + a^2/3 y - a^3/27 + ay^2-2a^2y/3 + a^3/9 + by - ab/3 + c =0[/tex]
[tex]y^3 + (b - a^2/3) y = -(2a^3+9ab) /27 [/tex]
Comparing that to
[tex]y^3 + 3py = 2q[/tex]
we have [tex] p = (3b - a^2) /9, q =-(a^3+9ab)/54 [/tex]
which we can substitute in to the depressed cubic solution and subtract a/3 to get the three roots. I won't write that out; it's a little ugly.
2a+3a what matche sthis equation
Answer:
5a
Step-by-step explanation:
Answer:
5a.
Step-by-step explanation:
2a + 3a
= (2 + 3)a
= 5a.
Hope this helps!