Answers
Using the pythagoras theorem in the given figure, the required length of c is [tex]49\sqrt{6}[/tex].
What is pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean Theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides.
Who is pythagoras theorem named after?The pythagoras theorem is named after the Greek mathematician-philosopher Pythagoras.
To solve for c, first taking the small triangle in the left of the figure,
since one of the angle is 45 degree and another is 90 degree, the unlabelled angle is 45 degree. Which makes this triangle a isosceles triangle, hence the sides a and b are equal in length. i.e a = b
Using pythagoras theorem in this triangle,
[tex](7\sqrt{2} )^{2} = \sqrt{a^{2}+\ a^{2} }[/tex]
Therefore, a = 49[tex]\sqrt{2}[/tex]
Now Taking the small triangle in the right of the given figure,
tan 30 = a/c
or, [tex]\frac{1}{\sqrt{3} }[/tex] *c = 49[tex]\sqrt{2}[/tex]
Therefore , c = 49[tex]\sqrt{6}[/tex]
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Related Questions
In College Park mice, short tails (ss) is recessive to long tails (SS). In the HJP building exterminators found the allele frequency of mice with short tales in the population within the building to be 0.7. In the BioPsyc building exterminators find that the allele frequency of the gene for short tale in mice in the building to me 0.2. Due to construction in the BioPsyc building several of the mice made HJP their new home. The exterminator guessed that about 20% of the mice in HJP now consist of mice from BioPsyc. What will be the new frequency of the short tales among mice in HJP?
a. 0.43.
b. 0.65.
c. 0.57.
d. 0.60.
Answers
The new frequency of short tail mice in HJP is 0.60.
What is Algebra?Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.
Let, initial number of mice in HJP be 'x'
and the number of mice travelling from BioPyc building to HJP be 'ý
So, Total mice in HJP= x+ y
As, [tex]\frac{y}{x+y} = 0.2[/tex]
y= 0.2x + 0.2 y
0.8y =0.2 x
x= 4y
Now, total short tail mice in HJP= 0.7 x + 0.2 y
Thus, New frequency of short tail among mice in HJP
= [tex]\frac{0.7x + 0.2y}{x+y}[/tex]
Put x= 4y in above equation we get,
= [tex]\frac{0.7 * 4y+ 0.2y}{4y+y}[/tex]
= [tex]\frac{3y}{5y}[/tex]
= 0.60
Hence, the new frequency of short tail mice in HJP is 0.60.
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The minute hand of a clock is 7 minutes. How far does the tip of the minute hand move in 50 minutes?
Answers
The distance that the minute hand moves in 50 minutes, given that it started at 7 minutes, is 258 degrees.
How to find the distance moved ?A rotatation around the clock by the minute hand, is a full 360 degrees as it begins at 12 and ends at 12 .
If a minute hand is at 7 minutes, then it means that the degrees moved is:
= 7 / 60 x 360
= 42 degrees
At 50 minutes, the degrees moved is :
= 50 / 60 x 360
= 300 degrees
Seeing as the minute hand started at 7 minutes, the distance moved is :
= 300 - 42
= 258 degrees
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A savings account increased by $75 is now more than $500. What is the least amount of money that was originally put in the savings account?
Answers
The least amount of money that was originally put in the savings account is $426.
What is the least amount of money?The amount of money in the savings account is a function of the money that was originally in the account and the amount by which the account was increased by.
The inequality that represents the total amount of money in the savings account is:
amount originally in the account + amount deposited > 500
x + $75 > $500
x > $500 - $75
x > $425
The least amount would be $426 because this is the smallest number that is greater than $425 that would make the total amount more than $500.
To check:
$75 + $426 = $501
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My question is in the pic
Answers
Answer: 7t+7
Step-by-step explanation: i know
Well, both 4t and 3t have the same variable so add them together to get 7t, then add 4 and 3 to get 7, so your fill in the blank should be 7t+7
What is the value of 9x÷y³?
Answers
Y=0
A survey was given to a random sample of 550 voters in the United States to ask about their preference for a presidential candidate. Of those surveyed, 264 respondents said that they preferred Candidate A. Determine a 95% confidence interval for the proportion of people who prefer Candidate A, rounding values to the nearest thousandth.
Answers
The 95% confidence interval for the proportion of people who prefer Candidate A is given as follows:
(0.438, 0.522).
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]n = 550, \pi = \frac{264}{550} = 0.48[/tex]
Hence the lower bound of the interval is obtained as follows:
[tex]0.48 - 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.438[/tex]
The upper bound of the interval is obtained as follows:
[tex]0.48 + 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.522[/tex]
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31 is what percent of 37?
Answers
Answer: The total answers count 37 - it's 100%, so we to get a 1% value, divide 37 by 100 to get 0.37. Next- calculate the percentage of 31: divide 31 by 1% value (0.37), and you get 83.78% - it's your percentage grade.
hello i need help with my math question one only pease and thank you
Answers
a) The after-tax cost of the vehicle Rachel is buying is $29,368.70.
b) The part of the after-tax cost that Rachel will finance after making the down payment is $25,118.70.
c) The total payments after 5 years are $30,659.60.
d) The total interest Rachel paid is $1,290.90.
What is the interest payment?The interest payment represents the difference between the total monthly payments and the financing part of the after-tax cost of the vehicle.
The total monthly payments ($26,409.60) are obtained by multiplying the monthly payments ($440.16) by the number of payment periods (60).
Value of vehicle = $25,990
Harmonized sales tax (HST) = 13%
After-tax cost of the vehicle = $29,368.70 ($25,990 x 1.13)
Down payment = $4,250
Financing part = $25,118.70 ($29,368.70 - $4,250)
Monthly payments = $440.16
Financing period = 60 months (5 years x 12)
Total monthly payments = $26,409.60 ($440.16 x 60)
The total amount paid for the car = $30,659.60 ($26,409.60 + $4,250)
Total interest = $1,290.90 ($26,409.60 - $25,118.70)
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Alice is buying a
bicycle that regularly
cost $120. It is on
sale for 25% off and
the tax rate is 9.125%.
is the final amount cheaper or more expensive than the original price?
Answers
Answer:
NO
the final amount is 98.21 which is less than 120
Step-by-step explanation:
Price after discount = $120 x (100 - 25%)
$120 x 0.75 = $90
tax = $90 x 0.09125 = $8,21
final amount = $90 + 8.21 = 98.21
Please help asap!
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow
Determine P(not orange) if the spinner is spun once.
25%
12.5%
87.5%
37.5%
(no links)
Answers
Answer:
7/8 = 87.5%
Step-by-step explanation:
You have only one of eight (1/8) evenly divided sections that is orange. The rest is not orange (1 - 1/8 = 7/8).
Therefore, spinning once will yield 7/8 odds of not landing on orange, or 0.875 or 87.5%.
The probability of not getting orange is 87.5%. The correct option is C.
What is probability?Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favourable outcomes to all outcomes.
Probability = Number of favourable outcomes / Number of samples
Given that a spinner with repeated colours numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
You only have one of eight (1/8) evenly divided orange sections.
The rest is not orange,
P = (1 - 1/8
P = 7/8
P = 87.5%
Therefore, spinning once will yield 7/8 odds of not landing on orange or 0.875 or 87.5%.
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What comes after ones column?
Answers
Answer: tens
Step-by-step explanation: after ones comes tens, before ones comes decimal point
what is 16 1/2 as a decimal and fraction?
Answers
Answer:
16 1/2 as a decimal is 16.5.
We convert it to an improper fraction which, in this case, is 33/2 and then we divide the new numerator (33) by the denominator to get our answer.
Answer:
16.5% and 16.5
Step-by-step explanation:
Can someone help me please
Answers
Step-by-step explanation: the awnser is 70 because 69 and 71 is in the outside of 70 therefore it's 70 there u go
Lisa plays soccer 3 out of the 7 days of the week. How many possible schedules are there to play
soccer on Monday or Tuesday or both.
Ex: 5
Answers
Answer:
There are 25 possible schedules.
Step-by-step explanation:
The order in which they play soccer is not important(Monday and Tuesday is the same as Tuesday and Monday), and thus the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Monday but not Tuesday:
Monday(1) and 2 out of the remaining 7 - 2 = 5. So
[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
Tuesday but not Monday:
Tuesday(1) and 2 out of the remaining 7 - 2 = 5. So
[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
Monday and Tuesday:
Monday and Tuesday(1), plus one out of the remaing 5 days. So
[tex]C_{5,1} = \frac{5!}{1!4!} = 5[/tex]
Total:
10 + 10 + 5 = 25
There are 25 possible schedules.
You are a loan officer at the West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a house they want to buy. The house has a market value of $170,000. Your bank requires 1/5
of the market value as a down payment.
(a)
What is the amount (in $) of the down payment?
$
(b)
What is the amount (in $) of the mortgage for which the Bradys are applying?
$
(c)
Your bank offers the Bradys a 30 year mortgage with a rate of 5%. At that rate, the monthly payments for principal and interest on the loan will be $5.37 for every $1,000 financed. What is the amount (in $) of the principal and interest portion of the Bradys' monthly payment?
$
(d)
What is the total amount (in $) of interest that will be paid over the life of the loan?
$
(e)
Your bank also requires that the monthly mortgage payments include property tax and homeowners insurance payments. If the property tax is $1,710 per year and the property insurance is $1,458 per year, what is the total monthly payment (in $) for PITI (principal, interest, taxes, and insurance)?
$
(f)
To qualify for the loan, bank rules state that mortgage payments cannot exceed 1/4
of the combined monthly income of the family. If the Bradys earn $3,750 per month, will they qualify for this loan?
Yes, they will qualify.
No, they will not qualify.
(g)
What monthly income (in $) would be required to qualify for this size mortgage payment?
$
Answers
Answer:
West Elm Savings and Loan
a) The amount of the down payment is:
= $34,000
b) The amount of the mortgage for which the Bradys are applying is:
= $170,000.
c) The amount of the principal of $136,000 ($170,000 - $34,000) and the interest portion of the monthly payment by the Brady's is:
= $730.32
d. The total amount of interest that will be paid over the life of the loan is:
= $126,915.20
e) Total monthly payment = $994.32
f) No, they will not qualify.
g) The monthly income that would be required to qualify for this size of mortgage payment is:
= $3,977.28
Step-by-step explanation:
a) Data and Calculations:
Market value of mortgage house = $170,000
Required down payment = 1/5 or 20%
a) The amount of the down payment = $34,000 ($170,000 * 20%)
b) The amount of the mortgage for which the Bradys are applying is = $170,000.
c) Interest on the loan = $5.37 for every $1,000
The amount of the principal of $136,000 ($170,000 - $34,000) and interest portion of the monthly payment by the Brady's = $730.32 ($5.37 * $136,000/$1,000)
d. The total amount of interest that will be paid over the life of the loan is:
= $126,915.20 ($262,915.20 - $136,000)
Sum of all periodic payments = $262,915.20 = ($730.32 * 12 * 30)
e) Annual Property tax = $1,710
Annual Property insurance 1,458
Total additional annual pyts $3,168
Monthly additional costs = $264 ($3,168/12)
Total monthly payment = $994.32 ($730.32 + $264)
f) Bradys' combined monthly income = $3,750
Qualification threshold = $937.50 ($3,750/4)
No, they will not qualify.
g) The monthly income that would be required to qualify for this size of mortgage payment is:
= $3,977.28 ($994.32/0.25)
The correct answers are given below, based on the available information given.
The amount (in $) of the down payment is:
$34,000
The amount of the mortgage for which the Bradys are applying is:
$170,000.
The amount of the principal of $136,000 ($170,000 - $34,000) and the interest portion of the monthly payment by the Brady's is:
$730.32
The total amount of interest that will be paid over the life of the loan is:
$126,915.20
The total monthly payment
= $994.32
No, they will not qualify.
The monthly income that would be required to qualify for this size of mortgage payment is:
$3,977.28
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roxanne needs 134,000 three years from now. How much should she deposit at the beginning of each 3 months in order to accumulate the desired amount if money is worth 4% coumpounded quarterly?
what is the missing in the given question?
Answers
The amount that Roxanne should deposit at the beginning of each 3 months to accumulate $134,000 at 4% compounded quarterly for three years is $10,461.13.
How is the quarterly deposit determined?The quarterly deposit can be computed using an online finance calculator with the following parameters.
The quarterly deposit shows the periodic investment that must be made to accumulate a future value of $134,000.
N (# of periods) = 12 quarters (3 x 4)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
FV (Future Value) = $134,000
Results:
PMT (periodic deposits) = $10,461.13
Sum of all periodic deposits = $125,533.56
Total Interest = $8,466.44
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ANSWER FAST
NO LINKS
16> f, if f=17
Answers
Answer:
It is False
Step-by-step explanation:
16>17 is not a true statement.
Which data set is represented by the modified box plot 92,88,100,136,106,79,88,86,98,115
Answers
Answer:
One dot mark above one hundred and thirty-six. A) 92, 88, 100, 136, 106, 79, 88, 86, 98, 115. B) 92, 88, 100 ...
Step-by-step explanation:
You are at an altitude of 250 feet in a hot-air balloon. You turn the burner on high and rise at a rate of 20 feet per minute for 5 minutes. Your altitude h after you have risen for t minutes is given by the function h = 250+ 201. (a) Make a table to show the altitude as a function of the number of minutes you have traveled. (b) Graph your data points-make sure to label the units on your axes. (c) Does it make sense to connect the points on the graph? Explain. 400 Altitude # of minutes ( in feet) 350 300 1 250 1.5 200 150 3 100 4 50 1 2 4 5 6 3. 2. Question Name: Date: Page 5 of 6 7. You are at an altitude of 250 feet in a hot-air balloon. You turn the burner on high and rise at a rate of 20 feet per minute for 5 minutes. Your altitude h after you have risen for t minutes is given by the function h = 250 + 20t. (a) Make a table to show the altitude as a function of the number of minutes you have traveled. (b) Graph your data points-make sure to label the units on your axes. (c) Does it make sense to connect the points on the graph? Explain. 400 Altitude # of minutes ( in feet) 350 300 1 250 1.5 200 150 3 100 4 50 5 1 3 4 5 (d) After 5 minutes, you turn the burner to low. This gives just enough heat to keep the balloon from falling but not enough to make it rise any higher. Plot a point on the graph to show how high the balloon is after 6 minutes. (e) Does it make sense to connect the point plotted in part (d) to the rest of the graph? Explain. (f) What is the domain of the function? (g) What is the range of the function? Transcribed Image Text:Name: Date: Page 5 of 6 7. You are at an altitude of 250 feet in a hot-air balloon. You turn the burner on high and rise at a rate of 20 feet per minute for 5 minutes. Your altitude h after you have risen for t minutes is given by the function h = 250 + 20t. (a) Make a table to show the altitude as a function of the number of minutes you have traveled. (b) Graph your data points-make sure to label the units on your axes. (c) Does it make sense to connect the points on the g
Answers
Yes, when we connect the points, we get straight line.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Given that, you are at an altitude of 250 feet in a hot-air balloon. You turn the burner on high and rise at a rate of 20 feet per minute for 5 minutes.
Your altitude h after you have risen for t minutes is given by the function h = 250+ 20t.
a) Make a table to show the altitude as a function of the number of minutes you have traveled.
t h
0 250
1 270
2 290
3 310
b) Graph the points, (0, 250), (1, 270), (2, 290) and (3, 310).
c) Yes, when we connect the points, we get straight line.
Hence, graph the points, (0, 250), (1, 270), (2, 290) and (3, 310).
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1. The radius of a circle is
A. 7 m
B. 5 m
C. 12.6 m
D. 8 m
2. The area of triangle is
A.78.5 m²
B. 7.85 m²
C. 785 m²
D. 87.5 m²
3. The area of a triangle is
A. 88.2 m² B.
52.7 m2
C. 44.1 m²
D. 8.82 m²
4. To compute for the area of the shaded region we
A. add both areas
B. subtract both areas
C. multiply both areas
D. divide both areas
5. What is the area of the shaded region?
A 34.4 m²
B. 56.8 m²
C. 97.2 m²
D.122.6 m²
the shape is in the picture T - T
Answers
Answer:
1. The radius of a circle is 5 m
Option B
2. The area of circle is
A = 3.14*5² = 78.5 m²Option A
3. The area of a triangle is
A = 1/2*12.6*7 = 44.1Option C
4. To compute for the area of the shaded region we
B. subtract both areas
5. What is the area of the shaded region?
78.5 - 44.1 = 34.4 m²Option A
Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in degrees. (Enter your answers as a comma-separated list.) −420°
Answers
Answer:
- 420° = -7/3 π ≈ - 2.333 π
Step-by-step explanation:
- 420° = -7/3 π ≈ - 2.333 π
Coterminal angle in [0, 360°) range:
300°, located in the fourth quadrant.
Positive coterminal angles: 300°, 660°, 1020°, 1380°, 1740°...
Negative coterminal angles: -60°, -420°, -780°, -1140°
I hope this helps!1!!
-420° = -360° - 80° = -80°
-80° = 360° - 80° = 280°
Co terminal angle = 280° and -80°
HELP ASAP!!! IM VERY CONFUSED. THANK YOU!
Answers
Please provide steps. I have a test soon.
Answers
Answer:
B) 5x+15y=30
5x-5y=10
Step-by-step explanation:
First, we solve the top equations by addition. Multiply the first one by -4.
-4x-12y=-24
4x-8y=4
This equals -20y=-20, so y=1. Now we put that back into either equation and find that x=3. So the solution set is (3,1)
Plugging those into each of the possible choices, we find that the answer is
B) 5x+15y=30. 5(3)+15(1)=30 15+15=30. 30=30 CHECK
5x-5y=10 5(3)-5(1)=10. 15-5=10. 10=10. CHECK
You bought a new laptop and paid an initial payment of $150 you will make 12 payments of $69.50 how much would the computer cost if your state tried to 6% sales tax
Answers
The cost of the computer if the sales tax is 6% is 924.96 dollars.
How to find the cost of the computer after sales tax?You bought a new laptop and paid an initial payment of $150. You will make 12 payments of $69.50.
The amount the computer cost if the your state charge 6% sales tax can be calculated as follows;
Install mental payment = 12 × 69.50
Install mental payment = 834 dollars
You already made payment of 150 dollars.
Therefore,
total payment including sale tax = 150 + 834
total payment including sale tax = 984 dollars
Sales tax = 6% of 984
Sales tax = 6 / 100 × 984
Sales tax = 5904 / 100
Sales tax = 59.04 dollars
Therefore,
cost of the computer = 984 - 59.04
cost of the computer = 924.96 dollars
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If the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y intercept of the regression line to three decimal places. X y 2 4101 31029 4 261 5 69 6 21 O A. log(y) = -4.743x+0.575 O B. login) - - 575x +4743 O C. logly) - 4743x+0575 O D. logi) - 0575x+4 743
Answers
The equation of the regression line is given as ŷ = -0.5755X + 4.743
How to solve for the regression line
First we have to find the logarithm of the y variables.
Logarithms of y-values:
log 4101 = 3.613
log 1029 = 3.012
log 261 = 2.417
log 69 = 1.839
log 21 = 1.322
We have to plot the ordered pairs to be in order of the table using the log y parameters.
Using a regression analysis calculator online, the equation of the regression line is ŷ = -0.5755X + 4.743.
The graph and the online calculator is contained in the image attached.
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What is the equation of this graph in slope intercept form
Answers
The slope-intercept form of the two straight lines in the graph of the question are;
y = 4y = 3What is the slope-intercept form of the equation of a straight line?The slope-intercept form of the equation of a straight line is; y = m·x + c
Where;
m = The slope of the line
c = The y-intercept of the line
The values of the ordered pair of the points on the line are in the form (x, y)
The graph consists of two straight lines, therefore the equations that represent the graphs are found as follows;
Points on the blue line graph are (0, 4), (2, 4), and (4, 4)
The slope of the blue line graph is therefore;
m = (4 - 4)/(2 - 0) = 0
The y-intercept of the blue line graph is; c = 4
The slope-intercept form of the equation representing the blue line graph is therefore;
y = 0 × x + 4
y = 4The slope-intercept form of the equation of the blue line graph is; y = 4
Points on the red line graph are; (0, 3), (2, 3), (4, 3)
The sloped of the red line graph is therefore; m = (3 - 3)/(2 - 0) = 0
The y-intercept of the red line graph is; c = 3
The slope-intercept form of the equation of the red line graph is therefore; y = 0 × x + 3
y = 3
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hello i need help with questions 5 please thank you.
Answers
5a) The total cost of buying the car, priced at $32,000 with the harmonized sales tax (HST) of 13%, is $36,160.
5b) Through the lease, the customer saves $14,760.
5c) The lease options for the lessee after returning the car include:
Lease buyoutLease extensionNew lease contractBuying out the vehicle and then reselling it.6a) The after-tax cost of the Honda Civic is $32,199.35.
6b) The value of the vehicle that needs to be financed is $26,199.35.
6c) The monthly payment will be $567.26 for 4 years.
6d) After four years, the total amount paid for the vehicle is $33,228.48.
Financing Options:A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.
A car purchase can also be financed through loans, like home mortgages.
Value of the car = $32,000
Harmonized Sales Tax (HST) = 13%
Cost of the car with HST = $36,160 ($32,000 x 1.13)
Lease Arrangement:Down payment = $1,000
Financing part = $35,160 ($36,160 - $1,000)
Installment payments = 48
Periodic payments = $425
Total lease cost = $21,400 ($1,000 + 48 x $425)
Savings (advantages) from leasing = $14,760 ($36,160 - $21,400)
Jordan's Car:The value of the Honda Civic = $28,495
Harmonized Sales Tax (HST) = 13%
After-tax cost = $32,199.35 ($28,495 x 1.13)
Annual interest rate = 1.9% compounded monthly
Down payment = $6,000
Financing part = $26,199.35 ($32,199.35 -$6,000)
Financing period = 4 years
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 1.9%
PV (Present Value) = $26,199.35
FV (Future Value) = $0
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 12
Results:
Monthly Payments (PMT) = $567.26
Sum of all periodic payments = $27,228.48
Total Interest $1,029.13
Total amount paid over 4 years = $33,228.48 ($27,228.48 + $6,000)
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what values are solutions for inequality -3 < 2x -3
Answers
The values that are solutions to the inequality -3 < 2x -3 are all real numbers greater than 0.
What is the solution to the given inequality?Given the inequality in the question;
-3 < 2x -3
Solve for x, by making it the subject of the formula.
Subtract 2x from both sides
-3 < 2x -3
-3 - 2x < -3
Add 3 to both sides
-3 + 3 - 2x < -3 + 3
-2x < -3 + 3
-2x < -3 + 3
-2x < 0
Next, divide both sides by -2
-2x/-2 > 0/2
x > 0/2
x > 0
Therefore, the solution to the inequality is x > 0.
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29. What is length of x?
Please explain this one too me since I did not understand it thanks
Answers
The value of x is 10 yards. The given shape is a trapezoid.
What are trigonometry ratios?
Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Draw a line parallel to the base.
Name the corner point of the shape.
Assume that ∠ADG = θ.
Consider △BDF:
BD = 6 + x
DF = 8 + 4.8 = 12.8 yrds.
The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.
cos θ = DF/BD
cos θ = 12.8 /(6+x) .....(i)
Consider △CDE:
cos θ = DE/CD
cos θ = 8/x .....(ii)
Now equate equations (i) and (ii):
12.8 /(6+x) = 8/x
Cross multiply:
12.8 × x = 8(6+x)
12.8x = 48 + 8x
12.8x - 8x = 48
4.8x = 48
Divide both sides by 4.8:
x = 48/4.8
x = 10
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The value of x is 10 yards. The given shape is a trapezoid.
What are trigonometry ratios?Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Draw a line parallel to the base.
Name the corner point of the shape.
Assume that ∠ADG = θ.
Consider △BDF:
BD = 6 + x
DF = 8 + 4.8 = 12.8 yrds.
The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.
cos θ = DF/BD
cos θ = 12.8 /(6+x) .....(i)
Consider △CDE:
cos θ = DE/CD
cos θ = 8/x .....(ii)
Now equate equations (i) and (ii):
12.8 /(6+x) = 8/x
Cross multiply:
12.8 × x = 8(6+x)
12.8x = 48 + 8x
12.8x - 8x = 48
4.8x = 48
Divide both sides by 4.8:
x = 48/4.8
x = 10
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A jewelry store has 218.75 ounces of 14-carat gold in stock.
(a) How many custom necklaces can be manufactured if each requires 3 1/8 ounces of gold?
(b) If gold is currently selling for $1,050 per ounce, how much is the gold in each necklace worth (in $)?