The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.
What is the perimeter of the regular polygon?All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.
P = (Side length) x n
The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,
tan (360° / (2 × 8)) = (n/2) ÷ 4
tan 22.5° = n / 8
n = 3.3137
Then the perimeter is given as,
P = 8 x 3.3137
P = 26.51 units
The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.
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Determine the sixth term of the
sequence
A(n) = -2.5^(n-1)
in words: (A of n is equal to negative two
times 5 raised to the (n-1) power)
The 6th term of the sequence is -97.65625
How to determine the 6th term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
A(n) = -2.5^(n-1)
In the sixth term, we have
n = 6
Substitute the known values in the above equation, so, we have the following representation
A(6) = -2.5^(6-1)
Evaluate
A(6) = -97.65625
Hence, the 6th term is -97.65625
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the red outer shape is a regular hexagon. Decide whether the hexagons are similar.
Answer:
Yes they are similar since it is a regular shape
Yes, the red outer shape is a regular hexagon. the hexagons are similar. red outer shape is a regular hexagon can be seen as regular hezagon, whereby the hezagon are been considered to be similar.
What is regular hexagon ?NOTE; We can see that from the given two regular hexagon, all the interior angle are equal, hence the are similar.
A regular hexagon is a polygon with six equal sides and six equal angles. All the interior angles of a regular hexagon are 120 degrees, and the sum of all interior angles of a regular hexagon is 720 degrees. The regular hexagon is a highly symmetrical shape and is often used in geometry and design.
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A wine producer believes that a new advertisement will increase product sales in LCBO by an average of 50 cases in a week. For a random sample of 20 LCBO stores, it was found that the average sales increase was 41.3 cases, and the sample standard deviation was 12.2 cases.
Test the null hypothesis that the population mean sales increase is at least 50 cases, stating any assumptions you can make. Use 5% as a significant level.
(You NEED to use BOTH the Critical-value approach and p-value approach to get a full mark).
To have a full mark, you NEED to show your calculation and solution (with all the STEPS) in the midterm exam file posted under Assessment-Assignment (Similar to Weekly Quizzes).
Do NOT use EXCEL
a) Reject the null hypothesis
b) Do not reject the null hypothesis
c) None of the answers are correct
we can reject the null hypothesis
Null Hypothesis (H₀): μ ≥ 50
Alternative Hypothesis (H₁): μ < 50
Assumptions:
- A normal distribution for the population of LCBO stores
- A random sample of 20 stores
- A significance level of 0.05
Critical-value approach:
First, calculate the test statistic using the formula:
Test statistic = (Sample Mean - Population Mean) / (Standard Deviation / √Sample Size)
= (41.3 - 50) / (12.2 / √20)
= -2.6
Then, compare this test statistic to the critical-value.
The critical-value is the value that divides the acceptance and rejection regions of the distribution. The critical-value for a two-tailed test with a significance level of 0.05 is ±1.96.
Since -2.6 is less than -1.96, the test statistic falls into the rejection region and we reject the null hypothesis.
p-value approach:
Calculate the p-value using the formula:
p-value = 1 - CDF(test statistic)
Where CDF is the cumulative distribution function.
= 1 - CDF(-2.6)
= 0.004
Since 0.004 is less than 0.05, we reject the null hypothesis.
In conclusion, based on the critical-value approach and the p-value approach, we can reject the null hypothesis and conclude that the population mean sales increase is less than 50 cases.
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Feb 23, 11:43:37 AM Write the augmented matrix for the following system of equations. -2+5x=-2z 4y-6+8z+3x=0 0=6y-6x-3z
The augmented matrix for the given system of equations is [[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]
An augmented matrix is a matrix that includes the coefficients of the variables and the constants in a system of equations. Each row of the matrix corresponds to one equation, and each column corresponds to one variable or the constant.
To write the augmented matrix for the given system of equations, we can start by rearranging the equations so that the variables are on the left side and the constants are on the right side:
5x + 2z = 2
3x + 4y - 8z = -6
-6x + 6y - 3z = 0
Next, we can write the coefficients of the variables and the constants in a matrix, with each row corresponding to one equation:
[5, 0, 2, 2]
[3, 4, -8, -6]
[-6, 6, -3, 0]
Finally, we can combine these rows into a single matrix to get the augmented matrix:
[[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]
This is the augmented matrix for the given system of equations.
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Given I(-4,17), J(1, -3), K(b,3) and L(-5,4) Find the value of b so that IJ is parallel to KL
The lines IJ and KL are parallel , so the slopes of the lines are equal and the value of b is -4.75
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be I ( -4 , 17 )
Let the second point be J ( 1 , -3 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m₁ = ( 17 - ( -3 ) ) / ( -4 - 1 )
Slope m₁ = -20/5
Slope m₁ = -4
Now , the lines IJ and KL are parallel , so the slopes are equal
Let the third point be K ( b , 3 )
Let the fourth point be L ( -5 , 4 )
Slope m₂ = ( 4 - 3 ) / ( -5 - b )
Slope m ₂ = 1/ ( -5 - b )
where m₁ = m₂
On simplifying , we get
1/ ( -5 - b ) = -4
Multiply by ( -5 - b ) on both sides , we get
1 = 20 + 4b
Subtracting 20 on both sides , we get
4b = -19
Divide by 4 on both sides , we get
b = -4.75
Therefore , the value of b is -4.75
Hence , the slope of the lines is m = -4
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OC EXPLANATION Two inequalities joined by the word and or the word or form a compound inequality. To solve the compound inequality, we first solve each inequality. 3u-2<=-14 or 4u+4<28
The solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.
Determine the compound inequalityA compound inequality is an equation that combines two inequalities with the word "and" or "or".
To solve a compound inequality, we need to solve each inequality separately and then combine the solutions.
For the compound inequality 3u-2<=-14 or 4u+4<28, we will solve each inequality separately.
First, we will solve 3u-2<=-14: 3u-2<=-14 3u<=-14+2 3u<=-12 u<=-4
Next, we will solve 4u+4<28:
4u+4<28 4u<28-4 4u<24 u<6
Now, we will combine the solutions.
Since the word "or" is used in the compound inequality, the solution is the union of the two solutions. This means that the solution is any value of u that satisfies either inequality.
The solution is u<=-4 or u<6. This can also be written in interval notation as (-∞,-4] U (-∞,6).
So, the solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.
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If someone could help me out on this!
The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;
(f- g)(x) = -2x² - 9x + 9
(g-f)(x) = 2x² + 9x - 9
(f + g)(x) = 4 x² - x + 5
What is a function?A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.
here, we have,
The general mathematical representation of a function is y = f(x).
f(x)=x²- 5x+7
g(x)=3x² + 4x - 2
so, we get,
(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)
(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2
(f- g)(x) = -2x² - 9x + 9
(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)
(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7
(g-f)(x) = 2x² + 9x - 9
(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2
(f + g)(x) = 4 x² - x + 5
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Use the fact that 1 square mile = 640 acres to find the area of the national park below to the nearest square mile.
National Park A: 1,505,011 acres
1,505,011 acres N square miles (Round to the nearest integer as needed.)
The area in square miles (rounded to the nearest integer) is:
area = 2,492 square miles.
How to find the area in square miles?Here we need to perform a change of units from acres to square miles. We know the relation:
1 square mile = 640 acres.
And we want to find the area of a park with 1,505,011 acres in square miles.
We can rewrite the relation above as:
1 acre = (1/604) square miles.
Then the area of the park will be:
Area = 1,505,011 acres = 1,505,011*(1/604) square miles
Area = 2,491.74 square miles.
Rounding to the nearest integer we will get:
area = 2,492 square miles.
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Please scroll to the bottom of page for END of question.
(ix) (1 mark)
Answer:
(x) (1 mark)
Answer:
(xi) (1 mark)
Answer:
(xii) (1 mark)
Please choose one:
a)
b)
c)
d)
I apologize, but it seems that the question is incomplete or has not been properly formatted. Please provide the full question and any additional details or context so that I can accurately and effectively answer it. Thank you.
graph: f(x)=1/2(2)^x
Answer:
Step one: The parent absolute value function will be reflected across the x-axis and translated down four units.
Step two: The vertex of the parent is (0,0). A reflection does not change the vertex, but the translation will move the vertex (plot 0,-4)
Step three: Evaluate the function at two more points on either side of the vertex. f(-1)=-5 f(1)=-5
Step-by-step explanation:
sorry if im wrong =/
tear production rate reduced normal none astigmatism no yes soft spectacle prescription myope hypermetrope hard none Decision trees for the labor data wage increase Ist year <= 2.5 > 2.5 bad statutory holidays >10 < 10 wage increase Ist year good wage increase 1st year <= 2.5 > 2.5 working hours per week statutory holidays bad good <= 36 > 36 > 10 <= 10 bad health plan contribution good wage increase Ist year none half full <%3D4 bad good bad bad good 17 2nd_Heart Attack Yes Yes Q1. Given the following data table, answer the questions: (5 Marks) Marital Weight Stress Trait Age Gender Cholesterol Status Category Level Anxiety 60 Yes Female Overweight 150 High 50 69 Yes Male Overweight 170 Normal 60 52 No Female Normal 174 High 35 66 Yes Male Overweight 169 Normal 60 70 Yes Female Overweight 237 Normal 65 52 No Female Normal 174 High 35 58 Yes Male Normal 140 Normal 45 No Yes Yes No No (a) Explain the table with respect to rows and columns. Also, explain what is the meaning of rows and columns in any data table. (b) Which problem can be solved using above data table? (c) Prepare decision table for the above table. NEED ITS ACCURATE SOLUTION. ONLY THEN I WILL UPVOTE IT.
(a) Each row represents a different individual and Each column represents a different variable or characteristic. (b) Identifying the relationship between different variables and the likelihood of a person having a heart attack, this problem can be solved using this data table.
(a) The table is organized into rows and columns. Each row represents a different individual and includes information about their age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait. Each column represents a different variable or characteristic, such as age, gender, weight category, etc. The rows and columns are used to organize the data and make it easier to read and understand.
(b) The problem that can be solved using this data table is identifying the relationship between different variables and the likelihood of a person having a heart attack. For example, the table can be used to determine if there is a correlation between age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait and the likelihood of a person having a heart attack.
(c) Decision table for the above table:
| Age | Gender | Weight Category | Cholesterol Level | Marital Status | Stress Level | Anxiety Trait | Heart Attack |
|-----|--------|-----------------|-------------------|----------------|--------------|---------------|--------------|
| 60 | Female | Overweight | 150 | Yes | High | Yes | Yes |
| 69 | Male | Overweight | 170 | Yes | Normal | Yes | Yes |
| 52 | Female | Normal | 174 | No | High | Yes | No |
| 66 | Male | Overweight | 169 | Yes | Normal | No | Yes |
| 70 | Female | Overweight | 237 | Yes | Normal | No | Yes |
| 52 | Female | Normal | 174 | No | High | Yes | No |
| 58 | Male | Normal | 140 | Yes | Normal | No | No |
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if you have any more questions let me know i need help
Answer:
x=6
My best attempt
Step-by-step explanation:
The ratio is 4:5.6 from top to bottom.
We have a ratio of x:8.4
We will make an equation.
4:5.6=x:8.4
Cross multiply:
5.6x=4x8.4
5.6x=33.6
Divide both sides by 5.6:
x=6
How many yards of fabric is needed if a choir robe needs 1 2/9 yards of fabric and John plans on making 24 choir robes
Therefore , the solution of the given problem of unitary method comes out to be 29 1/3 yards of fabric.
Describe the unitary method.To finish the job using the unitary method, multiply the measures taken from this microsecond section by two variable. In a nutshell, when a wanted thing is present, the characterized by a group but also colour groups are both eliminated from the unit technique. For expression instance, 40 changeable-price pencils would cost Inr ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
If 1 2/9 yards of cloth are required for each choir robe, then 24 choir robes will require:
=> 1 2/9 * 24 = (1*9+2)/9 * 24 = 11/9 * 24
We add the numerators and denominators together to multiply fractions:
=> 11/9 * 24/1 = (1124)/(91) = 264/9
264/9 yards of cloth will be required to make 24 choir robes. This can be stated simply as:
(Rounded to the closest 1/3 yard) 264/9 = 29 1/3 yards of fabric.
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Which exponential function is equivalent to the geometric sequence
The exponential function that is equivalent to the geometric sequence, aₙ = 9.5 × 5ⁿ is A. f(n) = (0.95)5ⁿ.
What is an exponential function?An exponential function is a mathematical function that calculates the exponential growth or decay of a data set.
There are two types of exponential functions: exponential growth and exponential decay.
The function f(x) = bx where b > 1 represents exponential growth function while f(x) = bx when 0 < b < 1, represents an exponential decay function.
Thus, the equivalent exponential function is Option A.
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Create your own radical inequality that has a solution of x>13. Your equation must have at least 4 terms in it
The answer is true, our inequality has a solution of x > 13. Our final answer is: 4(x^2 - x - 12) > (101 - 2x)^2
To create a radical inequality that has a solution of x > 13 and has at least 4 terms in it, we can start with the basic inequality x > 13 and add terms to both sides to create a more complex equation. For example:
√(x + 3) + 2 > √(x - 4) + 12
Now, we can rearrange the terms and square both sides to get rid of the radicals:
√(x + 3) - √(x - 4) > 10
(√(x + 3) - √(x - 4))^2 > 10^2
x + 3 - 2√(x + 3)(x - 4) + x - 4 > 100
2x - 2√(x + 3)(x - 4) > 101
Now, we can isolate the radical term and square both sides again:
-2√(x + 3)(x - 4) > 101 - 2x
4(x + 3)(x - 4) > (101 - 2x)^2
4(x^2 - x - 12) > 10201 - 404x + 4x^2
0 > 3x^2 - 403x + 10237
Since we want the solution to be x > 13, we can plug in 13 for x and see if the inequality is true:
0 > 3(13^2) - 403(13) + 10237
0 > 507 - 5239 + 10237
0 > 4505
Since this is true, our inequality has a solution of x > 13. Therefore, our final answer is:
4(x^2 - x - 12) > (101 - 2x)^2
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Pamela is 6 years younger than juri. The sum of their ages is 94
Answer:
Step-by-step explanation:
pamela: j - 6 years = juri's age.
juri: j + 6 years.
sum of pamela and juri = 94 years.
j +(j - 6) = 94
2j - 6 = 94
2j = 94 - 6
2j = 88
j = 44
juri age: 44years and pamela age: 44years - 6years = 38years.
Question
What is the expanded form of this number?
204.017
⁰ (2 x 100) + (4 x 1) + (1 x 1/10) + (7 x 1/1000)
⁰ (2 x 100) + (4 x 1) + (1 x 1/100) + (7 x 1/1000)
⁰ (2 x 100) + (4 x 1) + (1 x 1/10) + (7 x 1/100)
⁰ (2 x 100) + (4 x 1) + (1 x 1/100) + (7 x 1/100)
Answer:
B
Step-by-step explanation:
2 is hundred = 2x100
0 is tens =0x10
4 is unit =4 x 1
All numbers after the decimal point to the right are fractions
0 is tenth = 0/10 =0
1 is hundredth =1/100
7 is thousandth 7/1000
Now you can choose the right answer
Factorise : 9x^{2} +4x^{2} +16z^{2} +12xy-16yz-24xz[/tex]
PLEASE HELP ME OUT THIS IS SO DIFFICULT
A rectangular prism has a volume of 109.86 cubic centimeters. The width of the prism is 13.2 cm. The height of the prism is 4.1 cm. What is the length of the rectangular prism? Show work.
A. 0.5 cm
B. 2.1 cm
C. 2.03 cm
D. 6.4 cm
The length of the rectangular box will be 2.03 cm. Then the correct option is C.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,
V = L x W x H
The volume of a rectangular box is 109.86 cubic centimeters. The prism's breadth is 13.2 cm. The prism stands 4.1 cm tall.
The length of the rectangular prism is given as,
109.86 = L x 13.2 x 4.1
109.86 = 54.12L
L = 109.86 / 54.12
L = 2.03 cm
The length of the rectangular box will be 2.03 cm. Then the correct option is C.
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PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
-8=x
Step-by-step explanation:
-6=x+2
take away 2 from each side
-8= x
Answer:
x = -8
Step-by-step explanation:
To solve for x in equation 3(x - 2) = 4x + 2, we need to simplify the expression on the left side of the equation by using the distributive property. This gives:
3x - 6 = 4x + 2
Next, we need to isolate the variable x on one side of the equation. We can do this by adding 6 to both sides of the equation:
3x - 6 + 6 = 4x + 2 + 6
Simplifying this expression, we get:
3x = 4x + 8
Now, we need to isolate x again by subtracting 4x from both sides:
3x - 4x = 4x + 8 - 4x
Simplifying this expression gives:
-x = 8
Finally, we solve for x by multiplying both sides of the equation by -1:
x = -8
Therefore, the solution to the equation 3(x-2) = 4x + 2 is x = -8.
An investor deposits $10,000 per year for 4 years, with the first deposit made 1 year from the present. One year after the last deposit the investor makes the first withdrawal of $10,000. One year later the second withdrawal is 5% smaller than the first payment withdrawn. The third withdrawal one year later is 5% less than the second withdrawal. There are a total of 15 annual withdrawals, each being 5% less than the previous one.
a. Find the effective annual IRR earned on this investment to the nearest percent.
b. If the dollars invested and withdrawn in part (a) are in actual dollars and the inflation rate for the 19-year time span of the investment is 9% per year, what is the inflation-free IRR earned on this investment?
The effective annual IRR (internal rate of return) is 8%. If the dollars invested and withdrawn and the inflation rate for the 19-year time span of the investment is 9% per year the inflation-free IRR is -0.92%.
To calculate this, we need to use the IRR formula: IRR = [Sum of cash flows / (-initial investment)]1/n - 1, where n is the number of periods.
a. To find the effective annual IRR earned on this investment, we can use the following formula:
0 = -10,000/(1+IRR) - 10,000/(1+IRR)^2 - 10,000/(1+IRR)^3 - 10,000/(1+IRR)^4 + 10,000/(1+IRR)^5 + 10,000(1-0.05)/(1+IRR)^6 + 10,000(1-0.05)^2/(1+IRR)^7 + ... + 10,000(1-0.05)^14/(1+IRR)^18
The effective annual IRR earned on this investment to the nearest percent is 8%.
b. To find the inflation-free IRR earned on this investment, we can use the following formula:
Inflation-free IRR = (1 + IRR)/(1 + inflation rate) - 1
Plugging in the values we found in part (a), we get:
Inflation-free IRR = (1 + 0.08)/(1 + 0.09) - 1 = -0.0092
So the inflation-free IRR earned on this investment is approximately -0.92%.
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In triangle ABC, angle B = 44°, IF AB =BC, SO find angle A and C
The value of angle A and C is 68° respectively
What is sum of angle in a triangle?The sum of angle In a triangle is 180°. This means that A+B+C = 180°.
An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as havingat least two sides of equal length.
Since AB = BC, then the triangle is an isosceles triangle.
The sum of angle in a triangle is 180. This means that A+B+C = 180
Since AB = BC , then angle A = angle C
therefore , substitute C for A
C +B + C = 180
2C + 44 = 180
2C = 180-44
2C = 136
divide both sides by 2
C = 136/2
C = 68°
then A= C = 68°
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help me below??? dont guess
Answer:
C is your answer
Step-by-step explanation:
The temperature in Madadeni one morning was -5°C at 08:00 and increased by 2°C every hour until 12:00. What will the temperature be at 11:30
Answer:
Step-by-step explanation:
20c is the answer
Answer:
ans is 14
Step-by-step explanation:
i do not think is this by i know is 14
Susie buys a car on hire purchase. The car costs R130 000. She pays a 10% deposit on the cash price and will have to pay monthly instalments of R4 600 for a period of three years. David buys the same car, but chooses another option where he has to pay a 35% deposit on the cash price and monthly instalments of R3 950 for two years.
3.1.1 Calculate the HP price for both options.
3.1.2 Calculate the difference between the total price paid by Susie and by David
3.1.3 Calculate the interest that Susie and David have to pay as a percentage of the cash price
1. HP price for Susie is R 282600 and David is R 179300
2. The difference between the total price paid by Susie and David is R 103300
3. The interest that Susie and David have to pay as a percentage of the cash price is 117.38% and 37.92%
What is the HP price:The HP price, also known as the hire purchase price, is the total amount that a buyer pays for a product when purchasing it through a hire purchase agreement.
It includes the cash price of the product plus any interest and fees charged by the lender.
Here we have
3.1.1, For Susie:
The cash price of the car is R 130000.
She pays a 10% deposit, which is:
= [10/100] × 130000 = R 13000
=> HP price = the cash price - the deposit
=> 130000 - 13000 = R 117000
She will pay monthly installments of R 4600 for 3 years,
which is 36 months.
Therefore, the total amount she will pay is:
36 x 4600 = R 165600
Therefore, the total amount she will pay is R 165600
The HP price for Susie is,
117000 + 165600 = R 282600
For David:
The cash price of the car is R 130000. He pays a 35% deposit, which is:
=> [ 35/100] × 130000 = R 45500
The HP price = 130000 - 45500 = 84500
He will pay monthly installments of R 3950 for 2 years, which is 24 months. Therefore, the total amount he will pay is:
24 × 3950 = 94800
The HP price for David is, therefore:
=> 84500 + 94800 = R 179300
3.1.2, The difference between the total price paid by Susie and by David
= 282600 - 179300 = R 103300
3.1.3
For Susie:
The total interest she has to pay is the difference between the HP price and the cash price, which is:
=> 282600 - 130000 = R 152600
The interest rate as a percentage of the cash price is:
=> (152600/130000) × 100% = 117.38%
For David:
The total interest he has to pay is the difference between the HP price and the cash price, which is:
=> 179 300 - 130 000 = R 49 300
The interest rate as a percentage of the cash price is:
=> (49 300/130000) × 100% = 37.92%
Therefore,
1. HP price for Susie is R 282600 and David is R 179300
2. The difference between the total price paid by Susie and David is R 103300
3. The interest that Susie and David have to pay as a percentage of the cash price is 117.38% and 37.92%
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Determine the values of a such that the following vectors are i
linearly independent. V1 = {1,2,0}, v2= {1,0 .,1}, v3 ={1,a,4}.
The vectors v1 = {1,2,0}, v2 = {1,0,1}, and v3 = {1,a,4} are linearly independent if a = 8/3, t and linearly dependent for a = 2, and linearly independent for a = 8/3.
For the vectors to be linearly independent, we need to check if the following system of equations has a unique solution:
c1v1 + c2v2 + c3v3 = 0
where c1, c2, c3 are constants, and 0 is the zero vector.
Substituting the given vectors, we get the following system of equations:
c1 + c2 + c3 = 0 (1)
2c1 + ac3 = 0 (2)
c2 + 4c3 = 0 (3)
If we can find values of a for which this system of equations has a non-trivial solution, then the vectors are linearly dependent. Otherwise, they are linearly independent.
To find such values of a, we need to solve the system of equations and find the conditions under which it has non-trivial solutions.
From equations (2) and (3), we get:
c2 = -4c3 (4)
2c1 + ac3 = 0 (5)
Substituting equations (1) and (4) into equation (5), we get:
2(-c2 - c3) + ac3 = 0
Simplifying, we get:
(-2 + a)c3 - 2c2 = 0
Substituting equation (4), we get:
(-2 + a)c3 + 8c3 = 0
Solving for c3, we get:
c3 = 0 if a = 2
c3 = 0 if a = 8/3
For a = 2, the system reduces to:
c1 + c2 = 0
2c1 = 0
c2 + 4c3 = 0
This system has a non-trivial solution: c1 = 0, c2 = 1, c3 = -1/4.
Therefore, the vectors are linearly dependent for a = 2.
For a = 8/3, the system reduces to:
c1 + c2 + c3 = 0
(8/3)c3 = 0
c2 + 4c3 = 0
This system has only the trivial solution: c1 = c2 = c3 = 0.
Therefore, the vectors are linearly independent for a = 8/3.
In summary, the given vectors are linearly dependent for a = 2, and linearly independent for a = 8/3.
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x = 35, x2 = 250, n= 5 then standard deviation of distribution is a. 1 b. 99 c. 3.1254 d. 9.9498
The correct answer is d. 9.9498.
To find the standard deviation of a distribution, we use the formula:
Standard deviation = √[(∑(x - mean)2)/n]
First, we need to find the mean of the distribution. The mean is the sum of all the values divided by the number of values. In this case, the mean is:
mean = (35 + 250)/5 = 57
Next, we need to find the sum of the squared differences between each value and the mean. This is:
∑(x - mean)2 = (35 - 57)2 + (250 - 57)2 = 485 + 37249 = 37734
Finally, we divide this sum by the number of values and take the square root to get the standard deviation:
Standard deviation = √(37734/5) = √7546.8 = 9.9498
So the standard deviation of the distribution is 9.9498.
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the item to the trashcan. Click the trashcan to cle Solve this equation by completing the square. 3x^(2)-4x=-2
The solutions to this 3x^(2)-4x=-2 are x=(2/3)+i*√(2/9) or x=(2/3)-i*√(2/9).
To solve this equation by completing the square, we need to first rearrange the equation and then complete the square for the x terms. Here are the steps:
1. Rearrange the equation:
3x^(2)-4x=-2 becomes 3x^(2)-4x+2=0
2. Divide the entire equation by the coefficient of the x^(2) term:
(3x^(2)-4x+2)/3=0/3 becomes x^(2)-(4/3)x+(2/3)=0
3. Complete the square by adding the square of half the coefficient of the x term to both sides of the equation:
x^(2)-(4/3)x+(2/3)+(4/3)^(2)/4=(4/3)^(2)/4 becomes x^(2)-(4/3)x+(4/9)=(4/3)^(2)/4-(2/3)
4. Simplify the right side of the equation:
(4/3)^(2)/4-(2/3)=(16/9)/4-(2/3)=(4/9)-(2/3)=(4/9)-(6/9)=-(2/9)
5. Factor the left side of the equation:
(x-(2/3))^(2)=-(2/9)
6. Take the square root of both sides of the equation:
x-(2/3)=+/-sqrt(-(2/9))
7. Solve for x:
x=(2/3)+/-sqrt(-(2/9)) becomes x=(2/3)+i*sqrt(2/9) or x=(2/3)-i*sqrt(2/9)
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(a) (20 pts) Let 11 1 1 1 1 1 1 1 1 1 - 1 1 -1 -1 A= 1 1 -1 -1 -1 1 1 3 1 -1 -1 Find a basis and the dimension for each of the following subspaces: (a.1) Col(A), (0.2) Row(A), (a.3) Nul(A). 1 (b) (b.1
For subspace (a.1) basis for Col(A) is the first four columns of A and dimension is 4. For (a.2) basis for Row(A) is the first four rows of A and dimension is 4. A basis for (a.3) Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0 and dimension is 7.
A basis for a subspace is a set of vectors that are linearly independent and span the subspace. The dimension of a subspace is the number of vectors in a basis for that subspace.
(a.1) Col(A) is the subspace of R^4 spanned by the columns of A. To find a basis for Col(A), we can reduce A to its reduced row echelon form (RREF) and find the columns of A that correspond to the pivot columns in the RREF. The RREF of A is:
1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0
The pivot columns are the first four columns, so a basis for Col(A) is the first four columns of A:
{[1, 1, 1, 1], [1, 1, -1, -1], [1, -1, 1, -1], [1, -1, -1, 1]}
The dimension of Col(A) is the number of vectors in the basis, which is 4.
(a.2) Row(A) is the subspace of R^11 spanned by the rows of A. To find a basis for Row(A), we can reduce A to its RREF and find the nonzero rows. The RREF of A is the same as above, so a basis for Row(A) is the first four rows of A:
{[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1, -3, 3, 0, 0]}
The dimension of Row(A) is the number of vectors in the basis, which is 4.
(a.3) Nul(A) is the subspace of R^11 consisting of all vectors x such that Ax = 0. To find a basis for Nul(A), we can reduce A to its RREF and find the solutions to the homogeneous equation Ax = 0. The RREF of A is the same as above, and the general solution to Ax = 0 is:
x1 = 0
x2 = 0
x3 = 0
x4 = 0
x5 = free
x6 = free
x7 = free
x8 = free
x9 = free
x10 = free
x11 = free
A basis for Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0:
{[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]}
The dimension of Nul(A) is the number of vectors in the basis, which is 7.
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Answer:
1+1= 2
Step-by-step explanation:
im a genuis