Answer:
10083024Step-by-step explanation:
1) The greatest common factor of 72 and 112 is 8, so the least common multiple is ... 72×112/8 = 1008.
The least common multiple of 72 and 112 is 1008.
__
2) The house number will be a multiple of 1008 between 3000/1008 = 2.98 and 4000/1008 = 3.96. The only integer in that range is 3, so Peter's house number is ...
3 × 1008 = 3024
Peter's house number is 3024.
The function f(x) = -X2 - 2x + 15 is shown on the graph.
What are the domain and range of the function?
O
The domain is all real numbers. The range is {yly < 16).
The domain is all real numbers. The range is {yly > 16).
The domain is xxl-5
The domain is {xl-5 5x53). The range is {yly s 16).
Answer:
Step-by-step explanation:
i can't see graph.
[tex]f(x)=-x^2-2x+15=-(x^2+2x+1-1)+15=-(x-1)^2+1+15=-(x-1)^2+16\\domain=all~real~numbers.\\[/tex]
Range≤16
so A
The domain is all real numbers. The range is y less then or equal to 16.
Quadratic functionQuadratic function is a polynomial of degree 2. It is in the form:
f(x) = ax² + bx + c
where a, b, c are constants
The domain of a function is the set of input variables while the range of a function is the set of output variables.
From the image attached, The domain is all real numbers. The range is y less then or equal to 16.
Find out more on quadratic equation at: https://brainly.com/question/25841119
Joe has $4.52 in dimes, nickels, and pennies. If he has one more dime than three times the number of nickels and 10 more pennies than nickels, how many of each type of coin does he have?
Answer:
12 nickels, 37 dimes and 22 pennies
Step-by-step explanation:
Let
x ----> the number of nickels
y ----> the number of dimes
z ----> the number of pennies
we know that
1 nickel=$0.05
1 dime=$0.10
1 pennies=$0.01
so
0.05x+0.10y+0.01z=4.52 -----> equation A
y=3x+1 ----> equation B
z=x+10 ----> equation C
substitute equation B and equation C in equation A and solve for x
[tex]0.05x+0.10(3x+1)+0.01(x+10)=4.52 0.05x+0.30x+0.10+0.01x+0.10=4.52\\0.36x+0.20=4.52\\ 0.36x=4.52-0.20\\x=4.32/0.36\\x=12\ nickels[/tex]
Find the value of y
[tex]y=3(12)+1=37\ dimes[/tex]
Find the value of z
[tex]z=12+10=22\ pennies[/tex]
The population of the United States is about 3.2x10^8 the population of the United States is about 80 times the population of Oregon write the population of Oregon in scientific notation
Answer:
The answer to your question is: 4 x 10 ⁶ = population of Oregon
Step-by-step explanation:
Data
Population of the USA = 3.2 x 10⁸
Population of the USA = 80 population of Oregon
Process
3.2 x 10⁸ = 80 population of Oregon
3.2 x 10⁸ / 80 = population of Oregon
4 000 000 = population of Oregon
4 x 10 ⁶ = population of Oregon
The population of Oregon will be 4 x 10⁶.
What is Division method?
Division method is used to distributing a group of things into equal parts.
Given that;
The population of the United States = 3.2 x 10⁸
And, The population of the United States is about 80 times the population of Oregon.
Let population of Oregon = x
Then, We can formulate;
3.2 x 10⁸ = 80 × x
Solve for x as;
3.2 x 10⁸ = 80 × x
x = 3.2 x 10⁸ / 80
x = 0.04 x 10⁸
x = 4 x 10⁻² x 10⁸
x = 4 x 10⁶
Thus, The population of Oregon will be 4 x 10⁶.
Learn more about the divide visit:
https://brainly.com/question/2263967
#SPJ2
A jogger can jog 3 miles in 15 minutes and 18 miles in 1 1/2 hours. If the number of miles and the time are in a proportional linear relationship, at what rate is the jogger jogging per hour?
Answer: He jogs 12 miles per hour
Step-by-step explanation: Every 15 minutes he jogs 3 miles, there are 60 minutes in an hour, 60/15 = 4, 4 x 3 = 12
math question: (!!please answer right away!!)
1.) "A diver dives 47 ft below the surface of the water and then rises 12 ft. Use addition to find the divers depth."
2.) "The temperature at 6 AM is -6°F. The temperature rises 13 degrees Fahrenheit by noon. Use addition to find the temperature at noon."
For the first problem, the diver's depth after diving 47 feet and then rising 12 feet is -35 feet or 35 feet below the surface. In the second problem, the temperature rose from -6°F to 7°F by noon.
Explanation:Let's answer your mathematics problems one by one.
Problem 1:
A diver dives 47 ft below the surface of the water and then rises 12 ft. We can use addition by understanding that direction matters. A depth of 47 ft below the surface is represented as -47, while rising 12 ft means +12. So, the final depth could be represented mathematically as -47 + 12, which equals to -35 ft. It means the diver is 35 feet below the surface of the water.
Problem 2:
The temperature at 6 AM is -6°F. The temperature rises 13 degrees Fahrenheit by noon. The situation can be mathematically represented as -6 + 13. So, the temperature at noon would be 7°F.
Learn more about Addition here:https://brainly.com/question/35006189
#SPJ2
-81 ÷(-9)
A:729
B:-729
C:-9
D:9
Answer:
9
Step-by-step explanation:
a negative divided by a negative is a positive.
Two parallel lines are crossed by a transversal. Horizontal and parallel lines p and q are cut by transversal m. At the intersection of lines p and m, the bottom left angle is b degrees. At the intersection of lines q and m, the top right angle is 128 degrees. What is the value of b? B = 32 b = 52 b = 118 b = 128
Answer: Last option.
Step-by-step explanation:
Observe the figure attached.
In order to find the value of "b", you need to remember the definition of "Alternate interior angles". These are the pairs of angles located in the interior of the parallel lines and on opposite side of the transversal. They are congruent.
Based on this definition, you can conclude that the angle "b" and the angle that measures 128° are Alternate interior angles; therefore they are congruent.
This means that the value of "b" is:
[tex]b=128\°[/tex]
Answer:
The last answer!
Step-by-step explanation:
edge 2020
3:5, 3 to 5, and 5/3 all represent the same ratio. true or false
Answer:
False.
Step-by-step explanation:
The first two (3:5) & (3 to 5), represents the same ratio.
However, 5/3 does not equal to the others, for it's form would be:
5:3
5 to 3
~
Answer:
false
Step-by-step explanation:
i hope i helped :)
MARK AS BRAINLIESTT
Allie needs at least 50 hours of community service for social studies class. She already has 20. How many more hours does she need? Write an inequality to model this situation.
A)
x + 20 ≤ 50
B)
x + 20 ≥ 50
C)
x - 20 ≥ 50
D)
x + 50 ≥ 20
Answer
B) x + 20 ≥ 50
Step-by-step explanation:
Answer:
B) x + 20 ≥ 50
Step-by-step explanation:
Given,
The hours she already has for social studies = 20,
After getting x more hours,
The total hours she has now = x + 20,
According to the question,
Total hours ≥ 50
[tex]\implies x + 20\geq 50[/tex]
Which is the required inequality to model give situation,
Hence, OPTION B is correct.
It was reported that in 2004, the mean net worth of families in a certain region was $470.2 thousand and the median net worth was $92.3 thousand. Which measure of center do you think is more appropriate? Explain your answer.
Answer:
Median.
Step-by-step explanation:
We have been given that in 2004, the mean net worth of families in a certain region was $470.2 thousand and the median net worth was $92.3 thousand.
We know that mean and median of a symmetric data set is equal.
We also know that when mean of a data set is greater than median, then the data set has a very large valued outlier.
Since mean net wroth of families is approximately 5 times more than median net wroth of families, this means that some of the families has very high net worth as outliers.
Since the net worth of families has very large outliers, therefore, I would prefer median as the appropriate measure of center as median is not affected by outliers.
Professor Green is interested in determining the average SAT score for the entire population of individuals who took the SAT. She wants to know how her class compares to the population of students who took the SAT. She finds that the average SAT score for the population is 1000. Is this score an example of a descriptive or an inferential statistic?
Answer:
Descriptive statistics
Explanation:
The population average is a descriptive statistic. It informs about how the population looks like, in this case, the population looks like having a average of 1000.
If, using her class's average where to infer the population average that is inferential statistic. But that is not the case
You are helping Bobby find the length and width of his garden. He knows that the area of the garden is LaTeX: x^2+8x+15x 2 + 8 x + 15 square feet. The length of his garden is LaTeX: \left(x+5\right)( x + 5 )square feet.
Part 1) What is the width of the garden? Explain how you came to this conclusion and what method you used (algebra tiles, the x-method, another method, etc. )
Part 2) If LaTeX: xx is 3 feet, what would the area of the garden be? Show your work.
Answer:
If the length of the garden is (x + 5) then the width will be (x + 3)
The area of the garden is 48 sq feet
Step-by-step explanation:
The garden is x^2 + 8x + 15 sq feet
Use the factorization method and break the middle term:
x^2+3x+5x+15
Group the first two terms and last two terms:
(x^2+3x)+(5x+15)
Take out the common from each pair.
x(x+3) +5(x+3)
(x+5)(x+3)
We have already been given that x+5 is the length. Then this shows that x+5 is the length and x+3 is the width
If the length of the garden is (x + 5) then the width will be (x + 3)
The method I used is the F.O.I.L. method
The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product.
(x + 5)(x + 3) = x^2 + 3x + 5x + 15
Solve the like terms:
= x^2 + 8x + 15
b) x= 3 feet
(x + 5)(x + 3)
Substitute the value in the expression
(3 + 3)(5 + 3)= (8)(6)= 48 square feet
Area of the garden is 48 sq feet.
Sean plan to join a streaming music service. One plan is $20 down plus monthly payments of $10 a month. The second plan is $40 down and $8 a month. How many month with the total amount paid be the same for both companies? What would the amount be?
Answer:
10 months
Step-by-step explanation:
Let X represent the number of months
The cost equation for the first plan = $20 + 10x
The cost equation for the second plan =$ 40+8x
The number of months at which the cost for the two plans will be equal can be worked out by equating the costs for the two plans and then calculate the value of x.
Thus,
$20+10x = $40 +8x
10x -8x =$40-$20
2x = $ 20
x= 20/2
x= 10
Substituting X in each equation,
$20 +$10(10) = $40 + $8(10)
$ 20 +$100 =$40 +$80
$120 =$120
Thus, the amount after ten months = $120
Freedonia has 50 senators. Each senator is either honest or corrupt. Suppose you know that at least one of the Freedonian senators is honest and that, given any two Freedonian senators, at least one is corrupt. Based on these facts, you can determine how many Freedonian senators are honest and how many are corrupt.
Answer:
There are 49 corrupt senators and 1 honest senator.
Step-by-step explanation:
Freedonia has 50 senators. Each senator is either honest or corrupt. At least one of the Freedonian senators is honest.
As we can see that there are no two senators where both of them are honest. So either there is one senerator who is honest or none.
As given that at least one of the Freedonian senators is honest.
Hence, we can conclude there is one and only one honest senator.
Final answer:
In Freedonia's senate, there must be one honest senator and forty-nine corrupt senators to satisfy the given conditions.
Explanation:
To solve the problem presented, we must work under the conditions that in Freedonia's senate of 50 senators, which implies that there are 50 senators in total, each is either honest or corrupt, at least one senator is honest, and in any pair of senators, at least one is corrupt. This means it's impossible to have two honest senators together, as this would contradict the condition that in any pair of senators, there must be at least one corrupt senator.
Given that there is at least one honest senator, we can use logic to deduce the following: If we were to assume that there are two honest senators, we would have a pair of senators where both are honest, which violates the given condition. Therefore, there can be only one honest senator in Freedonia's senate to meet all the conditions laid out in the problem.
Since the total number of senators is 50, and we have established that there is only one honest senator, it follows that the remaining 49 senators must be corrupt. Hence, the Freedonia's senate consists of one honest senator and forty-nine corrupt senators.
Which property justifies this statement? If x=3, then x−3=0. Subtraction Property of Equality Division Property of Equality Reflexive Property of Equality Multiplication Property of Equality
The statement 'If x=3, then x−3=0' is justified by the Subtraction Property of Equality. This property allows you to subtract the same value from both sides of an equation while maintaining equality.
Explanation:The statement 'If x=3, then x−3=0' is justified by the Subtraction Property of Equality. This property states that if you subtract the same number from both sides of an equation, the equation remains equal. So, in this case, you start with x=3 and then you subtract 3 from both sides to get x-3=0. It's also important to note that the other properties mentioned, Division, Reflexive, and Multiplication, aren't appropriate in this scenario because no division, reflexion or multiplication operation is being performed.
Learn more about Subtraction Property of Equality here:https://brainly.com/question/33218308
#SPJ2
On Tuesday at 2 p.m., the ocean’s surface at the beach was at an elevation of 2.2 feet. Winston’s house is at an elevation of 12.1 feet. The elevation of his friend Tammy’s house is 3 1/2 times the elevation of Winston’s house.
a. What is the elevation of Tammy’s house?
b. How many times greater is the elevation of Tammy’s house than the elevation of the ocean’s surface at 2 p.m.?
c. On Wednesday at 9 a.m., Winston went diving. Near the beach, the ocean’s surface was at an elevation of -2.5 feet. During his deepest dive, Winston reached an elevation that was times the elevation of the ocean’s surface. What elevation did Winston reach during his deepest dive?
d. While diving, Winston stopped at a point located halfway between his deepest dive and the ocean’s surface. At what elevation was Winston when he stopped halfway?
1 When an aero plane took off, it was noted that for every 100 m rise in altitude, the temperature dropped by 1 1/2 C. The plane reached an altitude 25 times the distance of 100 m, by how much the temperature would have dropped if the Ground temperature was 27 1/2 C
Answer:
37 1/2 C
Step-by-step explanation:
25 × 1 1/2 C = 37 1/2 C
The temperature would have dropped 37 1/2 C.
_____
The ground temperature is irrelevant to the question.
Caleb will be going to college next year. He would like to save some money for living expenses. Select the goal that would be the most helpful for him.
I will earn a college degree in business from the University of Vermont by the time I am twenty-two years old.
I will save $2,600 in one year by depositing $50 dollars per week in a savings account.
I will save $100 per paycheck.
I will attend college.
Answer:
save 100$ each check.
Step-by-step explanation:
Answer:
I will save $2,600 in one year by depositing $50 dollars per week in a savings account.
Step-by-step explanation:
When you set a goal, it should clearly state what you want to accomplish, it has to be measurable and relevant according to what you want to do. Also, it has to establish a deadline and it should be something that you can achieve.
According to this and the options given, the goal that would be most helpful for Caleb is I will save $2,600 in one year by depositing $50 dollars per week in a savings account because it is well defined, it is measurable and establishes a deadline as he will save $50 dollars per week to get $2600 in a year. Additionally, the goal can be accomplished and it is relevant to what he wants to do that is to save money for living expenses because he is going to college next year.
A farmer produces both beans and corn on her farm. If she must give up 16 bushels of corn to be able to get 6 bushels of beans, then her opportunity cost of 1 bushel of beans is ______________.
Answer:
2.67 bushels of corn
Step-by-step explanation:
We can see it in the picture.
Dr. Cyril conducts a simple random sample of 500 men who became fathers for the first time in the past year. He finds that 23% of them report being unsure of their ability to be good fathers, plus or minus 4%. What is another term for the 4% value?
Answer:
The another term for the 4% value is : Margin of error
Step-by-step explanation:
Dr. Cyril conducts a simple random sample of 500 men.
He finds that 23% of them report being unsure of their ability to be good fathers, plus or minus 4%.
Now, the another term for the 4% value is : Margin of error
Means the estimate of father being unsure about his ability would be between 19% and 27%.
When sample size is increased, the margin of error becomes smaller.
What is the simplified form of StartRoot 64 x Superscript 16 Baseline EndRoot?
Answer:
[tex]8x^8[/tex] (Please see my interpretation of the problem.)
The problem:
Simplify [tex]\sqrt{64x^{16}}[/tex] (Please tell me if I did or didn't interpret your problem correctly. Thank you!)
Step-by-step explanation:
[tex]\sqrt{64x^{16}}[/tex] (Given)
[tex]\sqrt{64}\sqrt{x^{16}}[/tex] (if u and v are positive then [tex]\sqrt{uv}=\sqrt{u}\sqrt{v}[/tex])
[tex]8\sqrt[2]{x^{16}}[/tex] ([tex]\sqrt{ }=\sqrt[2]{}[/tex])
[tex]8x^{\frac{16}{2}}[/tex] ([tex]\sqrt[n]{x^m}=x^\frac{m}{n}[/tex])
[tex]8x^8[/tex] (simplified/reduced the fractional-exponent)
Answer:
8x8
Step-by-step explanation:
so B
Simplify. Write the answer in scientific notation. HELP ASAP!!
Answer:
The answer to your question is: the last option 3.0 x 10⁻¹⁰
Step-by-step explanation:
First divide 3.3 by 1.1
3.3 / 1.1 = 3
Then subtract -8 - (2) = -8 -2 = -10
Finally use scientific notation where the power will be -10
result : 3 x 10 ⁻¹⁰
x is -4
f(x)= 5x^8-3x
The ^8 is the exponent for 5x!!!
Answer:
327692
Step-by-step explanation:
[tex]65536 = (-4)^{8} \\ \\ 65536 \times 5 = 327680 \\ \\ 327680 - 3(-4) = 327680 + 12 = 327692[/tex]
According to the Order of Operations [GEMS(A)\BOMDAS\PEMDAS etc.], in this case, you evaluate the exponent BEFORE multiplying. This is a common mistake people make.
I am joyous to assist you anytime.
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Answer:
The answer is (C) 8
Step-by-step explanation:
First, let's calculate the length of the side of the square.
[tex]A_{square}=a^2[/tex], where [tex]a[/tex] is the length of the side. Now, let's try to build the square. First we need to find a point which distance from (0, 0) is 10. For this, we can use the distance formula in the plane:
[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex] which for [tex]x_1=0[/tex] and [tex]y_1 = 0[/tex] transforms as [tex]d=\sqrt{(x_2)^2 + (y_2)^2}[/tex]. The first point we are looking for is connected to the origin and therefore, its components will form a right triangle in which, the Pythagoras theorem holds, see the first attached figure. Then, [tex]x_2[/tex], [tex]y_2[/tex] and 10 are a Pythagorean triple. From this, [tex]x_2= 6[/tex] or [tex]x_2=8[/tex] while [tex]y_2= 6[/tex] or [tex]y_2=8[/tex]. This leads us with the set of coordinates:
[tex](\pm 6, \pm 8)[/tex] and [tex](\pm 8, \pm 6)[/tex]. (A)
The next step is to find the coordinates of points that lie on lines which are perpendicular to the lines that joins the origin of the coordinate system with the set of points given in (A):
Let's do this for the point (6, 8).
The equation of the line that join the point (6, 8) with the origin (0, 0) has the equation [tex]y = mx +n[/tex], however, we only need to find its slope in order to find a perpendicular line to it. Thus,
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{8-0}{6-0} \\m = 8/6[/tex]
Then, a perpendicular line has an slope [tex]m_{\bot} = -\frac{1}{m} = -\frac{6}{8}[/tex] (perpendicularity condition of two lines). With the equation of the slope of the perpendicular line and the given point (6, 8), together with the equation of the distance we can form a system of equations to find the coordinates of two points that lie on this perpendicular line.
[tex]m_{\bot}=\frac{6}{8} = \frac{8-y}{6-x}\\ 6(6-x)+8(8-y)=0[/tex] (1)
[tex]d^2 = \sqrt{(y_o-y)^2+(x_o-x)^2} \\(10)^2=\sqrt{(8-y)^2+(6-x)^2}\\100 = \sqrt{(8-y)^2+(6-x)^2}[/tex] (2)
This system has solutions in the coordinates (-2, 14) and (14, 2). Until here, we have three vertices of the square. Let's now find the fourth one in the same way we found the third one using the point (14,2). A line perpendicular to the line that joins the point (6, 8) and (14, 2) has an slope [tex]m = 8/6[/tex] based on the perpendicularity condition. Thus, we can form the system:
[tex]\frac{8}{6} =\frac{2-y}{14-x} \\8(14-x) - 6(2-y) = 0[/tex] (1)
[tex]100 = \sqrt{(14-x)^2+(2-y)^2}[/tex] (2)
with solution the coordinates (8, -6) and (20, 10). If you draw a line joining the coordinates (0, 0), (6, 8), (14, 2) and (8, -6) you will get one of the squares that fulfill the conditions of the problem. By repeating this process with the coordinates in (A), the following squares are found:
(0, 0), (6, 8), (14, 2), (8, -6)(0, 0), (8, 6), (14, -2), (6, -8)(0, 0), (-6, 8), (-14, 2), (-8, -6)(0, 0), (-8, 6), (-14, -2), (-6, -8)Now, notice that the equation of distance between the two points separated a distance of 10 has the trivial solution [tex](\pm10, 0)[/tex] and [tex](0, \pm10)[/tex]. By combining this points we get the following squares:
(0, 0), (10, 0), (10, 10), (0, 10)(0, 0), (0, 10), (-10, 10), (-10, 0)(0, 0), (-10, 0), (-10, -10), (0, -10)(0, 0), (0, -10), (-10, -10), (10, 0)See the attached second attached figure. Therefore, 8 squares can be drawn
Determine all the roots given function (solve for the unknown variable)?
Answer:
The roots are:
a) z1 = 0
b) z2 = -2
c) z3 = ∛2 or 1.26
Step-by-step explanation:
First we factor z from the original equation
z⁷ + 6z⁴ - 16 z = z ( z⁶ + 6z³ -16)
z ((z³)² + 6z³ -16) express z⁶ as a power
z (z³ + 8)(z³ -2) factor
Now, equal to zero each term
z1 = 0 first answer
z³ + 8 = 0 z³ = -8 z2 = -2 second answer
z³ -2 = 0 z³ = 2 z3 = ∛2 or 1.26 third answer
When determining the roots of a function, you set the function equal to zero and solve for the variable. For example, the roots of the function f(x) = x² - 5x + 6 would be x = 2 and x = 3.
Explanation:Though the specific function is not provided in the question, the general process to determine all the roots of a function lies in setting the function equal to zero and solving for the unknown variable. The roots of the function are the values of the unknown variable that make the equation true. For example, if you have a function f(x) = x² - 5x + 6, by setting it to zero and following the method you obtain the roots as x = 2 and x = 3.
Learn more about Finding roots of a function here:https://brainly.com/question/34196915
#SPJ2
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. In a poll conducted by a certain research center, 809 adults were called after their telephone numbers were randomly generated by a computer, and 20 % were able to correctly identify the secretary of state. Which type of sampling did the research center use?
Answer:
This is random sampling.
Step-by-step explanation:
Given condition is - In a poll, 809 adults were called after their telephone numbers were randomly generated by a computer, and 20 % were able to correctly identify the secretary of state.
This research center used random sampling.
Random because the telephone numbers were randomly generated by the computer. It could have been any number and any person.
---------------------------------------------------------------------------------------------
Other sampling methods either use groups to conduct survey or survey the easiest available sample as in convenience sampling. So, rest options are wrong.
Therefore, it is random sampling.
Planes X and Y and points J, K, L, M, and N are shown. Vertical plane X intersects horizontal plane Y. Point L is on the left half of plane Y. Point N is on the bottom half of plane X. Point M is on the right half of plane Y. Point K is on the top half of plane X. Point J is above and to the left of the planes. Exactly how many planes contain points J, K, and N? 0 1 2 3
Answer:
1
Step-by-step explanation:
Three points define 1 plane.
Answer:
The answer is plane 1
Step-by-step explanation:
Planes X and Y and points J, K, L, M, and N are shown.
Please check for me and if any are incorrect please explain!
Answer: (1) 14.4% (2) 3.78% (3) $222.48 (4) 21,176.47
(5) $425 (6) 14.3 cents per mile
Step-by-step explanation:
1) This is a calculator question. I = 0.144 --> 14.4%
[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\bullet \text{A = Accrued amount (total amount paid)}\\\bullet \text{P = Principal (initial cost of the car)}\\\bullet \text{r = rate (interest rate in decimal form)}\\\bullet \text{n = number of times in a year (number of months)}\\\bullet \text{t = number of years}\\\\A = m \times nt\\\bullet \text{m = monthly payment amount}\\\bullet \text{nt = number of payments made}\\\implies m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]
2) m = 93.33
nt = 36
P = 3000
n = 12
[tex]m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\\93.33\times 36=3000\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\3359.88=3000\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\1.11996=\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\1.00315198=1+\dfrac{r}{12}\\\\\\0.00315198=\dfrac{r}{12}\\\\\\0.0378=r\\\\\\\large\boxed{3.78\%}=r[/tex]
3) same equation as #2 but deduct the down payment from the Principal
nt = 42
P - d = 5,555 - 555 = 5,000
r = 18% --> 0.18
n = 12
[tex]m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\\m\times 42=(5,555-555)\bigg(1+\dfrac{.18}{12}\bigg)^{42}\\\\\\42m=5000(1.015)^{42}\\\\\\42m=5000(1.868847)\\\\\\42m=9344.23557\\\\\\m=\large\boxed{222.48}[/tex]
4) Gas + Oil = cost per mile × number of miles
1000 + 800 = 0.085x
1800 = 0.085x
[tex]\large\boxed{21,176.47}=x[/tex]
5) [tex]\text{Annual Depreciation}=\dfrac{\text{Cost of car - Trade-in value}}{\text{Years driven}}[/tex]
[tex].\qquad =\dfrac{3800-1250}{6}\\\\\\.\qquad =\dfrac{2550}{6}\\\\\\.\qquad = \large\boxed{425}[/tex]
6) [tex]\dfrac{\text{(Cost of car - Market value) + Gas & Oil + Parts, Maintenance + Insurance}}{\text{Miles driven}}[/tex]
[tex]=\dfrac{(5000-3800)+750+250+300}{17,500}\\\\\\=\dfrac{2500}{17,500}\\\\\\=0.142857\\\\=\large\boxed{14.3\ cents\ per\ mile}[/tex]
Enter your answer and show all the steps that you use to solve this problem in the space provided.
x y
7 11
8 13
9 15
10 17
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
Answer:
y DOES NOT vary directly with x
Step-by-step explanation:
If variation is direct, the ratio of y to x is a constant. Here, we have ...
11/7 ≠ 13/8
so variation is not direct.
___
It appears that y = 2x-3, rather than y = kx for some k. The added constant (-3) means variation is not direct.
To determine if y varies directly with x, we calculate the ratios between the corresponding values. The ratios are approximately constant, so y varies directly with x. The equation representing the direct variation is y = 1.57x.
Explanation:To determine whether y varies directly with x, we need to check if the ratio between the corresponding values of y and x is constant. Let's calculate the ratio for each pair of values:
For x = 7, y = 11, the ratio is 11/7 = 1.57For x = 8, y = 13, the ratio is 13/8 = 1.63For x = 9, y = 15, the ratio is 15/9 ≈ 1.67For x = 10, y = 17, the ratio is 17/10 = 1.7Since the ratios are approximately constant, we can conclude that y varies directly with x. To find the constant of variation (k), we can choose any of the ratios. Let's take the ratio from the first pair: 11/7 ≈ 1.57. Therefore, the equation that represents the direct variation is y = 1.57x.
Learn more about Direct variation here:
https://brainly.com/question/34355670
#SPJ2
A hackberry tree has roots that reach a depth of 6 adn 5/12 meters. The top of the tree is 18.28 meters above the ground. Find the total height from the bottom of the roots to the top of the tree.
Answer:
24 209/300 m ≈ 24.69667 m ≈ 24.70 m
Step-by-step explanation:
The total height is the sum of the above-ground height and the below-ground depth:
6 5/12 m + 18.28 m = (6 + 18) m + (5/12 + 7/25) m
= 24 m + (125+84)/300 m
= 24 209/300 m ≈ 24.6966666... m ≈ 24.70 m
_____
The problem statement does not say what rounding is required. The least-resolution number is 18.28, with resolution of 1 cm, so the answer might rightly be rounded to that resolution: 24.70 m. If we take the numbers to be exact, their sum can only be represented exactly as the ratio of integers or a mixed number or a repeating decimal.